ChatGPT: Intrebari si raspunsuri (Partea I)

De-a lungul timpului am adunat o serie de intrebari care imi vin in minte intr-un document text: intrebarile sunt in general din fizica dar nu sunt limitate doar la acest domeniu.

M-am gandit ca ar fi interesant sa pun aceste intrebari lui ChatGPT, sa vad ce fel de raspunsuri primesc. Si exact despre asta este vorba in acest articol: in acest articol voi expune o parte dintre intrebarile si lucrurile la care m-am gandit in ultima perioada si raspunsurile lui ChatGPT, presupunand ca le gasesc interesante. Scurta observatie: intrebarile sunt adunate pe o perioada lunga de timp iar unele opinii expuse in ele nu sunt cele pe care le am in prezent. In plus, imi place sa pun intrebari "naive", in sensul ca ascund ceea ce stiu pentru a primi un raspuns mai elaborat, neincarcat de detalii aditionale.

Voi scrie intrebarile in italics iar raspunsurile lui ChatGPT ca text obisnuit. Intrebarile si raspunsurile vor fi in engleza.

Regarding the talk about moral realism vs. moral constructivism, could the laws of nature be in such a way that they push us further and further towards better and better moral laws, such that what we see as morally constructed is actually moral realism in disguise? This can also be said about aesthetics, for example - maybe there is “absolute” beauty out there and the laws of nature push us, without our knowledge, more and more towards that telos.

Your question touches on a deep philosophical debate concerning the nature and origins of moral and aesthetic values. You're suggesting a possible synthesis or bridging idea between moral realism (the view that moral facts exist independently of human beliefs) and moral constructivism (the view that moral values are constructed by human agents). Here's a breakdown of the main points:

1. **Evolutionary Argument for Morality**: Some argue that our moral intuitions and beliefs have evolved because they confer some kind of survival advantage. In-group cooperation, empathy, and aversion to unjust harm, for instance, could have helped our ancestors survive and reproduce more effectively. If this is the case, and if there are objective moral truths "out there", one might argue that evolution is nudging us towards these truths, because aligning with them is beneficial for our survival.

2. **Convergence Towards a Moral Truth**: If we accept the idea that there is some kind of moral reality (a debatable point), then the evolutionary argument could suggest that as societies and individuals evolve and adapt, they will converge towards these moral truths. Over time, through social, biological, and cultural evolution, humanity might inch closer to an objective moral standard.

3. **Laws of Nature and Morality**: The idea that the "laws of nature" push us towards better moral laws would require a robust explanation of what this means. If we are discussing natural laws as we understand them in physics, then there isn't a clear path from those to moral truths. But if you're suggesting a deeper, perhaps metaphysical or cosmological principle guiding evolution and human development towards objective goodness, then that would be a novel and profound proposal.

4. **Aesthetics and the Natural World**: A similar argument can be made for aesthetic values. Some evolutionary biologists and psychologists have proposed that certain aesthetic preferences have evolutionary roots. For instance, landscapes that resemble fertile and hospitable environments might be seen as "beautiful" because they suggest safety, food, and shelter. However, claiming that there's an "absolute" beauty towards which nature guides us would be a bolder claim.

5. **Limitations**: This line of thinking has its detractors. Critics may point out that:

- It's challenging to determine which moral beliefs are genuinely advantageous in evolutionary terms.

- Evolution may shape our moral sentiments, but that doesn't necessarily mean those sentiments align with objective moral truths (assuming such truths exist).

- Some would argue that many moral beliefs could be entirely culturally contingent, having no basis in any "objective" reality.

- Just because something is evolutionarily advantageous doesn't make it morally right (this is related to the is-ought problem in philosophy).

6. **Moral Realism in Disguise?**: It's a captivating idea. If moral constructivism is the process through which humans develop and refine moral norms, and if there's a convergence towards some objective moral standard due to the pressures of natural laws, then this would indeed look like a form of "disguised" moral realism.

In conclusion, while it's an intriguing proposition, demonstrating that the laws of nature are guiding us towards objective moral or aesthetic truths would require significant philosophical and empirical support. Nevertheless, the interplay between evolution, morality, and aesthetics remains a fruitful area of inquiry.

My favorite answer for “why is there something rather than nothing” is that the abstract laws of mathematics, physics, logic and so on are abstract and indestructible, existing without the need of a creator. In other words, that’s what “God” is. Of course, you could use the term “Nature” or any other term instead of God. They simply cannot “not exist” and there’s no way for you to “destroy” them. And this is a much more solid explanation than a brute fact or an anthropic argument or anything else.

The idea that abstract entities like mathematical laws, logic, or principles of physics are foundational, necessary, and perhaps "indestructible" is an interesting and long-debated perspective in philosophy. Your articulation provides an alternative to many theistic or cosmological explanations for the existence of the universe. Here are some things to consider about your perspective:

1. **Platonism**: Your view seems to resonate with Platonism, which posits the existence of abstract entities or "forms" that are timeless, changeless, and non-physical. According to Platonism, things like numbers, geometric shapes, or even ideals like goodness, exist in a non-material realm of forms.

2. **God as Abstract Truth**: By identifying these abstract principles with "God," you seem to be moving towards a pantheistic or even Spinozan perspective, where God is equivalent to the totality of existence or the underlying principles that govern it.

3. **The Ontological Status of Abstract Entities**: One of the perennial debates in metaphysics is about the nature of abstract entities. Are numbers, for instance, real things that exist in some non-physical way, or are they simply human-constructed concepts that help us navigate the world? If we say that they "exist necessarily," we're making a strong metaphysical claim.

4. **Abstract vs. Concrete**: The distinction between abstract and concrete entities is a deep one in philosophy. If everything is fundamentally abstract and our perception renders it concrete, that veers towards an idealistic metaphysics, suggesting that reality is fundamentally mind-like or thought-like. This raises questions about the nature of perception and how our minds bridge the gap between the abstract and the concrete.

5. **Limitations of the Idea**: While the perspective is intellectually stimulating, some might argue:

- It doesn't fully answer the question of "why there is something rather than nothing." Why do these abstract entities exist at all? And why should they lead to a concrete, physical universe like ours?

- The nature of abstract entities remains deeply mysterious. Saying they "necessarily exist" may be pushing the mystery one step back rather than resolving it.

- Identifying God with abstract principles might be seen by some as redefining the term beyond its traditional usage, where God is often conceived as a personal, conscious being.

6. **Empirical Questions**: While these are primarily metaphysical concerns, there are also empirical questions about how the abstract principles of math or physics relate to the concrete universe. For instance, the famous physicist Eugene Wigner wrote about the "unreasonable effectiveness of mathematics in the natural sciences," pondering why mathematical concepts, developed abstractly, align so perfectly with physical reality.

In conclusion, your idea offers a rich and thought-provoking answer to one of the most profound questions of existence. As with all such deep philosophical propositions, it will likely resonate strongly with some and be met with skepticism by others. But it's precisely this kind of exploration that makes philosophy so endlessly fascinating.

Suppose you have a spaceship that is capable of extremely high accelerations (and suppose that whatever is inside of it would withstand these extreme accelerations). In such a scenario, would the spaceship be melted by the blue shifted cosmic microwave background radiation when it accelerates? If I am not making some mistake, the CMB should be observed blue shifted to a very high energy in the direction of motion, therefore melting the spaceship. What’s your take on this?

Even more, although they’re abstract and not physical, it might be that everything that exists is abstract and we interpret it as “concrete”, thus solving the problem of abstract vs. concrete.

Your intuition is on the right track. When you accelerate to a significant fraction of the speed of light, the cosmic microwave background (CMB) radiation would indeed get blueshifted from your perspective. The blueshifting means that the CMB photons would gain energy and move to higher frequency ranges, turning from low-energy microwaves to potentially harmful radiation.

The degree of this blueshifting depends on your velocity relative to the CMB's frame of reference. As you approach the speed of light, the blueshifting becomes more pronounced due to relativistic effects, and the radiation could indeed become harmful.

For very high velocities (or, equivalently, very high Lorentz factors), the CMB radiation that was once in the harmless microwave range could get blueshifted to X-rays or even gamma rays, which carry enough energy to ionize atoms and damage materials and biological tissues. This could potentially pose a threat to a spaceship and its inhabitants if they were exposed to this radiation for extended periods.

However, in a realistic scenario, one would expect that a spaceship capable of such extreme velocities would be equipped with protective shielding against various forms of radiation, much like how today's spacecraft are designed to protect astronauts from solar and cosmic radiation. The specific design and materials would depend on the expected radiation spectrum and intensity.

In conclusion, while accelerating to a significant fraction of the speed of light, you would indeed have to worry about the blueshifting of the CMB radiation to more dangerous, higher energy forms. Proper shielding and other protective measures would be essential for such high-speed journeys.

The laws of physics can be seen in two different ways: they tell us what WILL happen or they tell us what MUST happen. If you imagine the universe being a checkerboard with alternating black and white squares, the laws of physics for that universe would describe the alternating black and white square patterns, but for the “what will happen” version of them they only say what you will see if you take a black square, for example, as its neighboring squares. These laws don’t say what “will happen” if you were to actually change the square from black to white.

For the laws that say “what MUST happen”, we know that if we change the black square to a white one, the entire universe will react to that change and all the squares will change to adjust to the new configuration, because white boxes have black box neighbors vertically and horizontally, but white box neighbors diagonally. Despite the apparently trivial difference between these things, it has very important implications, including for free will.

What is the type of laws that you suspect our universe has? A “what will happen” or a “what must happen” kind of laws of physics?

The distinction you're making is subtle yet thought-provoking. In the context of physics, both interpretations of the laws — "what WILL happen" and "what MUST happen" — can be seen as differing perspectives on determinism.

1. **Deterministic Perspective**: Classical mechanics, as formulated by Sir Isaac Newton, is inherently deterministic. If you know the positions and velocities of all particles at one time, you can predict their positions and velocities at any future time. In this sense, classical mechanics appears to fall under the "what WILL happen" category. However, this also implies a "what MUST happen" nature, as given the current state of the universe, there's only one possible future trajectory.

2. **Quantum Mechanics and Indeterminacy**: Quantum mechanics complicates this picture. It introduces a probabilistic aspect to predictions. While the Schrödinger equation is deterministic in how it describes the evolution of the quantum state of a system, the outcomes of measurements on that system are inherently probabilistic. So, while the evolution of a quantum state aligns more with "what WILL happen", the results of quantum measurements seem less set in stone.

3. **Philosophical Implications for Free Will**: The nature of determinism in our universe has long been debated in the context of free will. If everything is predetermined based on the initial conditions of the universe ("what MUST happen"), then where does free will fit in? Quantum mechanics introduces an element of randomness, but randomness isn't the same as free will.

4. **Chaotic Systems**: Another consideration is the behavior of chaotic systems. Even in a deterministic framework, some systems are so sensitive to initial conditions that they appear random and are practically unpredictable. While their behavior is governed by "what MUST happen" based on initial conditions, in practice, predicting "what WILL happen" is extremely challenging.

5. **Relativity and Causality**: Relativity introduces the concept of spacetime and the importance of causality (effects follow causes). While relativity is deterministic in its predictions, it's also predicated on the idea that certain events "MUST" follow others due to the light cone structure of spacetime.

From a strict physics standpoint, it's challenging to firmly categorize our universe's laws into one of the two categories you've provided. The laws seem to blend elements of both, depending on which physical theories or phenomena we're discussing.

Lastly, physics is an evolving discipline. Our understanding of the universe is based on current theories, which are the best descriptions we have so far. Future discoveries might shift our perspective on this question.

Is classical physics truly deterministic, considering departures from determinism such as Norton's Dome or Space Invaders?

You've touched on some of the peculiarities and edge cases in classical physics that challenge the straightforward notion of determinism. Let's delve into those:

1. **Norton's Dome**: This is a thought experiment in classical physics introduced by John Norton. It involves a frictionless dome-shaped surface where the equation of motion admits multiple solutions for a particle starting at the top of the dome. Depending on the exact shape of the dome, the particle can spontaneously start moving after an arbitrary time, and this time isn't determined by the initial conditions. This is an example of "indeterminism" in classical mechanics, a departure from the typical determinism we associate with Newtonian physics.

2. **Space Invaders**: This refers to a thought experiment wherein "particles" are introduced into a system from outside at increasing velocities. If set up in a specific way, it can lead to situations where determinism breaks down, mainly because the evolution of the system can't be determined solely based on its initial conditions. Instead, one also has to account for external factors (like the invading particles).

The existence of such scenarios has led some philosophers of science to caution that classical mechanics might not be as "universally deterministic" as is often taught. However, there are some points to consider:

1. **Edge Cases**: Both Norton's Dome and the Space Invaders scenarios are, in a sense, carefully constructed edge cases. They don't typically come up in standard applications of classical mechanics, and they're more of philosophical interest than practical concern.

2. **Nature of Models**: These examples highlight an important point about scientific models: they are approximations. While a model might be deterministic (or not) under a broad range of conditions, there may always be special cases or extremes where the model doesn't hold or behaves unexpectedly.

3. **Role of Initial and Boundary Conditions**: Determinism in classical physics often assumes that both initial and boundary conditions are specified. In cases where external influences (like the "space invaders") play a role, the boundary conditions become essential.

4. **Chaos and Determinism**: While classical mechanics is deterministic, it's not always predictable due to chaos theory. Even slight changes in initial conditions can lead to vastly different outcomes in chaotic systems. So, while the system's evolution might be determined by its initial state, predicting its future can be practically impossible.

In conclusion, while classical mechanics is largely deterministic for a vast range of scenarios, peculiar cases like Norton's Dome and Space Invaders underscore that our classical models have limits and that determinism might not be as iron-clad as we sometimes think. These exceptions, however, tend to be more relevant for philosophical discussions about the nature of determinism than for everyday applications of classical physics.

We know that creating (and keeping open) wormholes requires exotic matter that has to have negative mass. We also know that Hawking discovered in 1974 that, “as measured by light beams”, the quantum fluctuations at the event horizon of a black hole are exotic (hence they reduce the horizon’s surface area, to Hawking’s surprise), having a negative average energy density.

Has this knowledge changed, recently? What are the implications of seeing the possibility of having exotic matter (even if extreme circumstances such as next to the event horizon of a black hole) for the Universe and do they offer some hints/insights into quantum gravity that we might underestimate? In principle, you could curve spacetime enough that the quantum fluctuations become exotic and open/maintain open a wormhole (of course, there are other problems after that, but still).

The idea that exotic matter — matter with negative energy density — is needed to keep wormholes open is an implication of the "average null energy condition" (ANEC). This is one of several energy conditions in general relativity, which are essentially constraints or conditions posited on the matter content of spacetime in order to ensure that it behaves in a physically reasonable way.

The discovery by Stephen Hawking that black holes radiate — known as "Hawking radiation" — due to quantum effects near the event horizon is indeed a surprising and profound result that implies the existence of negative energy densities in certain circumstances. More specifically, for an observer accelerating away from a horizon (like the event horizon of a black hole or even the horizon perceived by an accelerating observer in empty space), quantum fields can have a negative energy density.

Let's delve into the implications:

1. **Wormholes**: The need for exotic matter to keep a wormhole open is a conclusion drawn from classical general relativity. The negative energy densities from quantum effects like those seen in the Hawking radiation might, in principle, suggest a mechanism to keep wormholes open. However, whether these quantum effects can be harnessed or whether they occur in the right configurations and scales to stabilize a wormhole is an open question.

2. **Hints at Quantum Gravity**: These effects underscore the interplay between quantum mechanics and gravity and highlight our incomplete understanding of quantum gravity. The existence of negative energy densities in certain quantum scenarios could provide hints or constraints on a successful theory of quantum gravity.

3. **Casimir Effect**: Another scenario where quantum effects give rise to negative energy densities is the Casimir effect, where two conducting plates close together in a vacuum experience an attractive force due to quantum field fluctuations. Like the effects near a black hole horizon, the Casimir effect suggests scenarios where quantum mechanics leads to behaviors that seem exotic from a classical perspective.

4. **Constraints and Violations of Energy Conditions**: Discoveries like Hawking radiation have shown that the classical energy conditions can be violated in certain quantum scenarios. This has led to a reevaluation of these conditions and a search for more robust conditions or constraints that can incorporate both classical and quantum effects.

In conclusion, the interplay between quantum effects and general relativity, especially in extreme scenarios like near black hole horizons, continues to be a rich area of research. While these effects hint at the possibility of exotic phenomena like stable wormholes, translating these hints into practical or observable consequences remains a significant challenge. These questions continue to motivate research into a theory of quantum gravity, which would reconcile the principles of quantum mechanics with those of general relativity.

What can be said about the dark energy inside of black holes and “Generic Objects of Dark Energy” (GEODes)? There’s been talk recently that the presence of dark energy inside of black holes determines space to expand inside of the black hole and also modify the energy of the black hole (and maybe contribute to the accelerated expansion of the Universe as well). This idea dates back to Erast Gliner, a Russian physicist that proposed it back in 1966 - basically, these objects would look like a black hole from the outside but the dark energy in them would contribute to the “push” of the expansion of the Universe (if space would expand inside the black hole, wouldn’t that affect the event horizon as seen from the outside?)

The idea of "Generic Objects of Dark Energy" (GEODes) or other exotic compact objects as alternatives or generalizations to black holes has garnered interest in recent years. These concepts provide a fresh perspective on the nature of black holes, dark energy, and the mysteries associated with both. Let's delve into some of the key points surrounding these ideas:

1. **Dark Energy Inside Black Holes**: One of the intriguing propositions is that inside a black hole, conditions might be suitable for the dominance of dark energy. Given that dark energy is responsible for the accelerated expansion of the universe, if it were to dominate inside a black hole, it might lead to an "expansion" of spacetime inside the event horizon.

2. **Implications for the Event Horizon**: The effects inside the black hole's event horizon wouldn't be directly observable from the outside due to the nature of event horizons. However, if the internal structure of the black hole is affected by dark energy, it could have indirect observable consequences, possibly in the form of deviations from predictions of general relativity. It's worth noting that as of my last update in September 2021, direct evidence of these deviations hasn't been observed, but these ideas challenge our understanding and prompt further investigations.

3. **Erast Gliner's Idea**: In the 1960s, Erast Gliner proposed that ultra-high energy densities might not lead to a gravitational collapse into a singularity (as standard general relativity might suggest) but could instead create a vacuum-like state resembling dark energy. This proposition provides a possible way out of the singularity problem associated with black holes.

4. **GEODes and Cosmic Expansion**: If objects like GEODes exist and are prevalent in the universe, they might play a role in its accelerated expansion. However, their contribution would be contingent on their abundance and properties, and such a scenario would need to be consistent with observational evidence like the Cosmic Microwave Background radiation and the large-scale structure of the universe.

5. **Challenges**: While these ideas are intriguing, they're not without challenges. They need to be consistent with a plethora of astrophysical observations, including those related to black hole mergers detected by gravitational waves. Any deviation from the predictions of general relativity, which has been exceptionally successful in passing experimental and observational tests, would be of profound significance.

In conclusion, the interplay between black holes, dark energy, and the nature of cosmic expansion is a rich field of research with many open questions. Ideas like GEODes and the role of dark energy inside black holes are speculative but challenge our understanding and prompt further theoretical and observational investigations.

Would you say that the idea of an eternal, block universe is the classical picture of the static wave function where all moments of time exist as a superposition of the configurations? To me it looks like the simplest representation of spacetime - just a static wave function with space and time emerging from it.

The idea you're describing touches on several deep concepts in philosophy of physics and quantum mechanics, especially when considering the nature of time, spacetime, and quantum mechanics. Let's explore the relationships:

1. **Eternalism and the Block Universe**: In the philosophy of time, eternalism (or the block universe view) posits that past, present, and future events are equally real and that time is just another dimension, similar to space. This view is compatible with the spacetime picture given by Einstein's theory of relativity, where spacetime is a four-dimensional block and our experience of the present moment moving through time is, in some sense, an illusion.

2. **Static Wave Function and Quantum Mechanics**: The wave function in quantum mechanics is a mathematical entity that describes the state of a quantum system. It evolves deterministically as given by the Schrödinger equation. However, when a measurement occurs, the wave function appears to "collapse" to a particular outcome. The many-worlds interpretation (MWI) of quantum mechanics posits that all possible outcomes of the quantum measurement actually occur, and the wave function doesn't truly collapse but merely branches. In this view, the global or "universal" wave function remains static, and every possible history and future are part of it.

3. **Connection Between the Two**: If we combine the block universe view with the MWI, we get a picture where every possible past, present, and future exists in a static, unchanging multiverse. In this combined view, spacetime (and the many alternate spacetimes) emerge from the universal wave function. This is somewhat analogous to the idea you proposed, though the relationship between spacetime and the wave function is intricate and not fully understood.

4. **Implications for Space and Time**: The idea of space and time "emerging" from more fundamental entities or states is not unique to the above combination. There are approaches in quantum gravity, for instance, where spacetime is not fundamental but emerges from more basic quantum entities or structures. This idea is still very much an area of active research, with theories like loop quantum gravity and string theory providing possible frameworks.

In conclusion, the idea of a block universe and the static nature of the universal wave function (as per the MWI) can indeed be seen as related, at least in a speculative sense. Combining them presents an all-encompassing static reality, where spacetime and all events therein emerge from a quantum state. However, it's essential to note that while these ideas are intriguing and pursued by some physicists and philosophers, they remain interpretations and are not universally accepted.

I would like to know how exactly does a photon interact with an electron. Considering the two of them are waves, are we guaranteed to have “a collision” between the two in the “particle” way of thinking? Are they always going to interact or could the photon “miss” the electron? In other words, are the two always going to interact in multiple worlds, the difference being the position of the “collision” in spacetime (as particles), say in World 1 they collided at point A(1,1,1) and in World 2 at point B(3,5,12) and so on, or can they totally miss each other?

I’m asking this because I’m wondering how does a photon, say, know “where the electron is” (yes, I know I’ve just introduced the incorrect assumption of an electron’s position) in order to interact with it? It makes much more sense for them to interact as waves such that no matter “where” the electron is and the photon “is” (in the incorrect, classical way of thinking), they interact regardless.

Your question touches on a fascinating and subtle area of quantum mechanics. The way that photons and electrons interact is a key component of quantum electrodynamics (QED), the quantum field theory that describes electromagnetic interactions. I'll break down the question into parts:

1. **Wave Nature**: Electrons and photons, like all quantum objects, exhibit both particle-like and wave-like behavior. When considering interactions, it's often helpful to think in terms of probability amplitudes rather than deterministic "collisions."

2. **Interaction**: The way a photon and an electron interact is through the exchange of virtual photons (a concept in QED). This is different from the "real" photons that propagate freely through space. In simple terms, the electron doesn't "know" where the photon is; instead, the probability that they will interact is encoded in the mathematical description of their wavefunctions and the interaction rules of QED.

3. **Always Interact?**: Not necessarily. The probability of interaction is determined by the overlap of the photon's and electron's wavefunctions. If there is no overlap, there's no interaction. In cases where there is overlap, it doesn't guarantee interaction; it only provides a probability.

4. **Multiple Worlds and Interactions**: In the many-worlds interpretation (MWI) of quantum mechanics, every possible quantum outcome is realized in some branch of the multiverse. Under MWI, in some branches, the photon and electron might interact, and in others, they might not. The different outcomes would lead to distinct branches of the multiverse. The precise "nature" or "reality" of these branches is a deep philosophical question.

5. **Understanding as Waves**: You're right in suggesting that thinking of photons and electrons purely as classical particles can be misleading. Quantum field theory posits that particles are excitations of underlying fields (like the electron field or the electromagnetic field for photons). The interaction between an electron and a photon is an interaction between these fields. And yes, in scenarios where the photon and electron have overlapping wave-like properties, the interaction happens without needing to specify a specific "location" for either particle.

In summary, quantum mechanics and, more specifically, quantum field theory, provide a framework where interactions aren't based on classical "collisions" but rather on probabilistic overlaps and exchanges governed by the rules of QED. It's a shift from classical determinism to quantum probabilism.

I have a question about a particular situation of measuring the double slit experiment: imagine that we measure which electron did the slit pass through, but we’re doing so with a very long wavelength photon - so long that we can’t determine which of the slits the electron passed through - it’s wavelength is longer than the distance between the slits. In this situation, the interference pattern of the electron does not go away (can we still say that the photon is entangled with the electron if it doesn’t “know” which of the slits the electron went through?)

However, imagine that we travel at high speed towards the slits, such that their widths are Lorentz contracted, so they appear much thinner from our frame of reference. We “launch” a photon towards them that has a small enough wavelength that we could determine through which slit the electron went through, but now, due to Lorentz contraction, the wavelength of the photon is too big and we don’t know which slit the electron went through? Is this possible or, as I suspect, the photon will be blueshifted exactly as much as to compensate for the Lorentz contraction of our frame of reference?

The situation you describe is intricate and beautifully illustrates the complexities arising from the marriage of quantum mechanics and special relativity.

1. **Double Slit and Measurement**: In the double slit experiment, when you measure which slit the electron goes through, the interference pattern disappears, as you mentioned. This is due to the "collapse" of the electron's wavefunction, a phenomenon that is often debated and interpreted in many different ways in quantum mechanics. When you measure with a photon of such a long wavelength that you can't determine which slit the electron went through, it's like not measuring at all, and the interference pattern should remain.

2. **Relativistic Effects**: Lorentz contraction affects lengths along the direction of motion. If you move towards the slits, they will appear thinner in your frame of reference, as you rightly pointed out.

3. **Blueshifting and Lorentz Contraction**: Photons will be blueshifted when observed in a frame of reference moving towards the source of the photons. This blueshift results from the relativistic Doppler effect. The magnitude of this effect depends on the relative speed between you (or your frame of reference) and the source of the photons.

Now, if you're moving towards the slits at such a speed that the slits appear Lorentz contracted and you emit a photon towards the slits, that photon's wavelength would indeed be blueshifted relative to your frame.

However, there's a nuance: if the photon was emitted from your frame (i.e., it was "onboard" with you and emitted while you were moving), then, in your frame, it wouldn't appear blueshifted; it would have its emitted wavelength. But, from the lab frame (where the slits aren't moving), that photon would be blueshifted.

4. **Implication for the Measurement**: If, in your moving frame, the Lorentz contracted slits are too close together for the photon's wavelength to differentiate between them, then you wouldn't be able to tell which slit the electron went through, and the interference pattern should remain.

It's worth noting that combining quantum mechanics and special relativity, as in this situation, often introduces intricate considerations. The analysis here is a basic exploration, and a rigorous treatment might require quantum field theory, where relativistic effects and quantum phenomena are inherently combined.

It is my understanding that a pair of virtual particles that pop into existence and then annihilate should be entangled. If so, what happens in the situation of Hawking radiation, where say a pair of electron-positron appears and the positron is sucked into the black hole - are they still entangled after the positron reaches the singularity? Is the positron “destroyed” in the singularity? (Haven’t found any description of what “destroyed” means)

Your intuition is correct in suggesting that the virtual particle pairs created near a black hole horizon would be entangled. The process you're referring to is a simplified picture of Hawking radiation, which is much more complex when examined rigorously. However, for our discussion, this visualization will suffice.

1. **Entanglement**: When the electron-positron pair is created, the two particles are generally entangled in properties like spin. If one of them (say the positron) falls into the black hole and the other escapes, the entanglement persists.

2. **Black Hole Information Paradox**: What you've touched upon is one facet of the black hole information paradox. If the entangled particle outside the black hole radiates away (as part of Hawking radiation), its entangled partner has fallen into the black hole. Over time, as the black hole emits more Hawking radiation and eventually evaporates, what happens to all that entanglement and information? Is it lost forever? This question lies at the heart of the information paradox. Classical general relativity suggests that all information inside a black hole is lost, but this violates quantum mechanics' principles, where information is preserved in quantum processes.

3. **Singularity and "Destruction"**: The term "singularity" in the context of black holes refers to a region where the curvature of spacetime becomes infinite. With our current understanding, once something reaches the singularity, it is effectively "destroyed" in the sense that we can't make any meaningful predictions about it using our known physical laws. This, however, is likely an indication that our current theories are incomplete. The hope is that a complete theory of quantum gravity would provide a clearer understanding of the nature of singularities and whether they truly exist or are just artifacts of our current theoretical framework.

4. **Recent Thoughts on the Paradox**: Over the years, many potential solutions to the black hole information paradox have been proposed. One prominent idea is the notion that the information about everything that falls into a black hole is somehow encoded in its event horizon, sometimes described using the "holographic principle." In recent years, insights from the study of quantum entanglement and its connection to spacetime geometry (via the ER=EPR conjecture) have suggested that wormholes or Einstein-Rosen bridges might play a role in resolving the paradox. These ideas are still being explored, and no definitive resolution has been agreed upon.

In summary, the fate of particles and information that fall into black holes, and how that meshes with our understanding of quantum mechanics, is one of the most significant open questions in theoretical physics. The entanglement issue you brought up is deeply intertwined with these mysteries.

What is your opinion on naked singularities formed from highly non-spherical stars or through evaporation of black holes (that Stephen Hawking found mathematical evidence for, after a bet with Preskill and Thorne)? Are they feasible and if so, could such naked singularities be (an underrated) candidate for dark matter (or have some other effects in the Universe)?

I, as a machine learning model, don't have personal opinions or emotions. However, I can provide a summary of the current state of knowledge and perspectives on this topic, as of my last training data in September 2021.

**Naked Singularities**: In general relativity, a singularity is a point at which the curvature of spacetime becomes infinite. According to the cosmic censorship hypothesis, put forth by Roger Penrose, singularities should always be hidden within black holes and, therefore, not observable from the "outside" universe. This would prevent the seemingly unpredictable effects of a singularity from being directly observable. A naked singularity is a hypothetical singularity that is not obscured by an event horizon, which would mean the cosmic censorship hypothesis doesn't hold.

**Formation of Naked Singularities**: There have been many studies looking into the conditions under which a naked singularity might form. One proposed mechanism, as you mentioned, is through the collapse of non-spherical matter distributions. Another context in which they arise is in discussions about the final stages of black hole evaporation. In 1991, Stephen Hawking made a famous bet with John Preskill and Kip Thorne regarding the black hole information paradox. In 2004, Hawking conceded the bet, suggesting that black holes can emit enough information during their evaporation to resolve the paradox, and this might be consistent with the formation of naked singularities.

**Dark Matter & Naked Singularities**: Dark matter is believed to make up approximately 27% of the universe's mass-energy content. The primary evidence for dark matter comes from gravitational effects on visible matter, such as galaxy rotation curves, gravitational lensing, and the cosmic microwave background's anisotropies. The exact nature of dark matter is one of the outstanding problems in cosmology.

Could naked singularities be candidates for dark matter? As of my last update:

1. **Observable Effects**: Naked singularities, if they existed, might produce unique observational signatures different from black holes. Some of these potential effects might include strong gravitational lensing or the emission of various types of radiation. These signatures would need to be consistent with existing astronomical observations, and as of now, there haven't been any definitive detections of phenomena that can be attributed solely to naked singularities.

2. **Stability & Abundance**: Even if naked singularities could form, questions about their stability and how frequently they might occur need to be addressed. They would need to be stable over cosmological timescales and be abundant enough to account for the observed effects of dark matter.

3. **Dynamics & Interaction**: Dark matter is believed to interact primarily through gravity (and possibly through weak interactions, though this is yet to be confirmed). If naked singularities had other significant interactions, they might produce effects inconsistent with current observations.

In conclusion, while the concept of naked singularities is intriguing and offers a rich playground for exploring the implications and boundaries of general relativity, as of my last update, they aren't leading candidates for dark matter. The majority of evidence still points toward some form of particle (or particles) that haven't been directly detected yet. The research landscape in physics is dynamic, so new ideas and evidence might change the current understanding in the future.

What is your take on Newcomb’s paradox?

Newcomb's paradox is a classic thought experiment in decision theory and philosophy. Like all good paradoxes, it challenges our intuitions and makes us re-evaluate our understanding of rationality. While I don't have personal feelings or opinions, I can lay out the problem and the common approaches to it.

**The Paradox**:

Imagine a being (or a very predictive computer) that has an almost perfect track record of predicting human choices. This being presents you with two boxes, A and B:

- Box A is transparent and contains $1,000.

- Box B is opaque, and it will contain either $0 or $1,000,000.

You have two options:

1. Take only Box B.

2. Take both Box A and Box B.

Here's the twist: The predictive being has already made its prediction before you choose. If it predicted you'll take only Box B, it has put $1,000,000 in it. If it predicted you'll take both boxes, it has left Box B empty.

The question is: What should you do to maximize your gains?

**The Two Main Approaches**:

1. **Two-boxing (Evidential Decision Theory)**: You might reason that regardless of your choice now, Box B either contains $1,000,000 or it doesn't because the prediction has already been made. Thus, it makes sense to always choose both boxes because you get the guaranteed $1,000 in Box A plus whatever is in Box B. This approach values actions based on their consequences, given the evidence available.

2. **One-boxing (Causal Decision Theory)**: If you're confident in the predictor's abilities, you might reason that the best way to get $1,000,000 is to consistently be the type of person who only takes Box B. In doing so, you're more likely to be predicted to take one box, and thus Box B will contain the $1,000,000. This approach values actions based on their causal impact on outcomes, even if that causality is a bit counterintuitive in this scenario.

**Philosophical Implications**:

Newcomb's paradox brings up philosophical questions about determinism, free will, and the nature of prediction. If the predictor is always right, does that mean our actions are predetermined? How does one reconcile the seemingly rational arguments for both one-boxing and two-boxing?

The paradox is also a foundation for discussions on decision theory itself, with various proponents advocating for the superiority of evidential versus causal decision theories. Some argue that the problem exposes flaws in these theories, while others believe it underscores the importance of refining our understanding of rationality.

In summary, Newcomb's paradox doesn't have a universally accepted "solution". It remains a topic of debate and discussion among philosophers, economists, and other scholars. Like many philosophical problems, its value often lies more in the questions it raises and the discussions it sparks rather than in finding a definitive answer.

Imagine that Laplace’s demon exists and knows the position and momentum of every particle in the universe. Would it be able to predict that I didn’t like a particular ice cream or that I was sad 3 days ago (and how sad I was)? In other words, would it be able to grasp the “quality” of my qualia based on just “easy problem” properties (my neural correlates)?

Laplace's demon, as originally formulated, is a thought experiment that posits a hypothetical intellect that, given the precise location and momentum of every atom in the universe, could predict the future and retrodict the past with perfect accuracy, effectively rendering the universe deterministic.

However, the issue of predicting or retrodicting qualia — subjective experiences — is more nuanced than simply predicting the motion of particles. Here are some points to consider:

1. **Physical Correlates of Mental States**: At the level of classical mechanics, which Laplace's demon originally operated within, it's unclear how the demon would correlate specific configurations of particles with subjective experiences. However, if we grant that there are distinct neural patterns (or configurations of matter) that correlate with specific qualia (e.g., the feeling of sadness or the taste of an ice cream), then the demon, knowing all physical states, could identify these patterns.

2. **Qualitative vs. Quantitative**: While the demon could potentially identify the neural correlates of you feeling sad or disliking a flavor, determining the exact "quality" or "intensity" of that feeling is more ambiguous. It would depend on the assumption that there are precise neural patterns that correspond to specific intensities of feelings, and that these patterns are consistent across instances and individuals.

3. **The Hard Problem of Consciousness**: The question indirectly touches on David Chalmers' distinction between the "easy problems" and the "hard problem" of consciousness. The "easy problems" relate to explaining cognitive functions and behaviors, which in theory, our demon could predict. The "hard problem", on the other hand, concerns explaining why and how these functions are accompanied by subjective experience. Even if the demon could predict neural correlates and associated behaviors, it doesn't directly address why those correlates are accompanied by qualia.

4. **Quantum Mechanics**: Modern physics, particularly quantum mechanics, complicates the determinism that Laplace's demon operates under. Even with complete knowledge of the current state of the universe, the outcomes of certain quantum events are inherently probabilistic, not deterministic. This would potentially limit the demon's predictive capabilities.

In conclusion, while Laplace's demon might be able to predict or retrodict the occurrence of neural correlates associated with specific experiences or feelings, the qualitative aspect of those feelings — the actual subjective experience — is a more complex issue. The challenge lies in bridging the gap between objective physical states and subjective experiences.

I have a question regarding the accelerated expansion of the Universe: say we observe a galaxy that’s 5 billion light years away and it’s moving away from us at a speed of 1000 km/s. Then we observe a galaxy much closer, 5 million light years away, moving away from us at a much lower speed, say 1 km/s.

Shouldn’t this indicate a deceleration rather than acceleration, since the galaxy found at 5 billion light years away is much temporally closer to the Big Bang compared to the one found at 5 million light years away, 1000 times closer to us? After all, when we’re observing stuff that is very far away in space, that stuff is also very far into the past, when the Universe was younger, and when it was so, it was indeed expanding faster than it is right now. Why do we pay attention only to the spacial distance but not also to the temporal distance when determining the expansion of the universe?

Where’s the mistake that I’m making? Shouldn’t observing galaxies closer to us moving away from us faster than galaxies further away from us indicate an accelerating expansion?

Your intuition is tapping into a key aspect of cosmology: the relationship between look-back time (how far back in time we're observing) and the behavior of galaxies in the universe. However, there's a misunderstanding in your interpretation of the observational data.

The observed redshift of a galaxy increases with distance. This redshift is interpreted as the galaxy moving away from us due to the expansion of the universe. The rate of this expansion as a function of time is precisely what cosmologists are trying to determine.

Here's where things get a little nuanced:

1. **The Metric Expansion**: When we say the universe is expanding, we don't mean that galaxies are flying outwards into some external space. Instead, space itself is expanding. The further away a galaxy is, the more space there is to expand between us and that galaxy, so its recessional speed appears larger. This is described by Hubble's law: $v = H_0 \times d$, where $v$ is the velocity at which a galaxy is receding from us, $d$ is its distance, and $H_0$ is the Hubble constant.

2. **Acceleration of Expansion**: If we observed galaxies that are farther away (and thus we are seeing them as they were a long time ago) moving away from us at slower speeds than nearby galaxies, that would indeed indicate a decelerating universe. However, observations, particularly from distant supernovae, show the opposite. Distant galaxies, representing the universe as it was billions of years ago, are receding more slowly than would be expected if the expansion of the universe were steady or decelerating. This is evidence for an accelerating expansion.

3. **Decoupling of Spatial and Temporal**: You're correct that when we observe distant galaxies, we're seeing them as they were in the past. That's why we can infer the expansion history of the universe from these observations. But the relationship between a galaxy's current distance and its velocity isn't solely a product of its behavior at the time the light was emitted; it's also influenced by the entire expansion history of the universe during the time that light was traveling.

4. **Dark Energy**: The mysterious entity known as dark energy is believed to be responsible for the acceleration in the expansion. While we have evidence of its effects, its nature remains one of the biggest questions in cosmology.

In summary, the current data indicate that the expansion of the universe is accelerating, as evidenced by the observed recessional velocities of distant galaxies compared to their expected velocities from a constant or decelerating expansion rate.

According to the idea behind inflation, once it starts it basically goes on forever, because only half of it decays per some unit of time but the patch that started the inflation is much bigger now (exponentially so) and as time goes on, it gets bigger and bigger, hence inflating forever. Or is it?

However, the definition of “half life” according to Wikipedia is "Half-life is the time required for exactly half of the entities to decay on average”. Considering the fact that “forever” is “infinity years”, isn’t inflation going to stop, eventually, because “on average” includes situations in which 100% of it has decayed? So, it has to stop at some point in the future when it so happens that 100% of It decays, especially if you have infinity to wait for.

Is this a correct assumption?

The idea behind inflation is indeed a bit counterintuitive, but let's try to break it down.

The concept of inflation you're referring to is called "eternal inflation," proposed by Alan Guth, Andrei Linde, and others in the 1980s. Here's how it works:

1. **Inflation's Mechanism**: Inflation is thought to be driven by a field, often called the inflaton field. As the inflaton field's value changes, it can cause space to expand at an accelerated rate. In some regions, the inflaton field decays (or "rolls down its potential") and inflation stops, leading to what we call the "hot Big Bang" — the usual expanding universe that we observe. But in other regions, inflation continues, causing those regions to expand even more.

2. **Quantum Fluctuations**: Because of quantum mechanics, the inflaton field experiences fluctuations. In some places, these fluctuations will push the field back "uphill," causing those regions to inflate even more vigorously. This means that even if the majority of the inflating region decays and stops inflating, there will always be some places where inflation gets a "boost" and continues.

3. **Exponential Expansion**: Inflation causes regions of space to expand exponentially. Even if only a tiny fraction of the space gets the "boost" to continue inflating, the exponential nature of inflation means that the inflating regions' volume can grow without bounds. This leads to the creation of infinite "pockets" or "bubbles" of non-inflating space (like our universe) within an ever-inflating background.

4. **Half-life and Inflation**: The half-life concept you brought up is a useful analogy, but there's a crucial difference. When talking about radioactive decay, we're discussing a fixed number of atoms, and over time, fewer and fewer remain undecayed. In contrast, during eternal inflation, the volume of inflating space keeps growing. So, even if a "half" decays at each step, the absolute volume of space that continues to inflate can remain constant or even grow.

To address your point about infinity: Even given an infinite amount of time, it's not guaranteed that every part of the inflating space will stop inflating. Every "moment" (keeping in mind that time becomes a somewhat nebulous concept in the context of eternal inflation) there's always some region experiencing those quantum fluctuations that kick it back into more vigorous inflation.

In summary, while it's conceivable for the inflaton field to decay in certain regions and cease inflation, the nature of eternal inflation, driven by quantum fluctuations, suggests that there will always be some regions of space continuing to inflate, making it "eternal."

Suppose you have two civilizations that are at war with Earth: A and B. Civ A is 1 light year away, Civ B is 10 light years away.

Alice and Bob share a pair of entangled electrons. Each go to Civ A and B, respectively. Before they leave to their destination, they decide that Alice will make a measurement on her electron and if she finds that it’s spin up, she will sign a peace treaty with Civ A. If not, she won’t do anything, but Bob will make his own measurement and find his electron as spin up, and therefore sign a peace treaty with Civ B. Obviously, they take into account the effects of relativity due to their interstellar traveling and synchronize their watches accordingly.

Considering there are decisions being made based on the outcome of Alice’s first measurement, isn’t this “sort of” like sending information faster than light? When Bob makes his measurement, he knows what Alice’s measurement is and can immediately tell Civilization B “we’re still at war, Alice saw her electron’s spin up” or “we can make peace, Earth will continue its war with Civ A, because Alice saw her electron’s spin down”.

Of course, they can’t choose what the outcome of the measurement will be. But even so, some information, some knowledge (and implication - a decision) is sent as an effect of entanglement, instantaneously.

What’s your take on this?

You've posed an intriguing scenario which gets at the heart of quantum entanglement and its implications for communication. The scenario is closely related to the famous EPR paradox (Einstein-Podolsky-Rosen paradox) and the idea of "spooky action at a distance" that Einstein found uncomfortable with quantum mechanics.

Let's break down the scenario:

1. **Entanglement Doesn't Transmit "Usable" Information**: If Alice measures her electron, she gets a random outcome (either spin up or spin down). Bob's measurement will be correlated with hers (if she gets spin up, he'll get spin down, and vice versa), but neither can control the outcome of their measurement. Since they can't decide on a particular outcome, they can't encode and send a message using this method. All Bob knows is the opposite of Alice's measurement, but he doesn't know why Alice got that particular result.

2. **Predetermined Protocol**: In your scenario, Alice and Bob have a predetermined protocol (if Alice measures spin up, she signs a peace treaty with Civ A; if not, Bob signs a peace treaty with Civ B). This is a pre-agreed-upon action and doesn't represent the transmission of new information. In other words, Civ B doesn't learn anything new about Alice's measurement result just from Bob's actions.

3. **"Faster-than-light Knowledge"**: Even though entanglement correlations are established faster-than-light (or, more accurately, outside the light-cone in a relativistic sense), Bob can't determine Alice's measurement outcome until a traditional light-speed or slower message from Alice reaches him (if he wants to verify her outcome). By that time, due to the time it takes for light-speed communication, the actions (like signing the peace treaty) would have already been taken based on their predetermined protocol.

4. **No Causality Violation**: Entanglement doesn't allow for causality violations. In your scenario, nothing Bob does can affect Alice's outcome or vice versa, so there's no causal influence being exerted faster than light.

In essence, while entanglement creates correlations between distant particles instantaneously, it doesn't allow for faster-than-light communication of usable information. The "information" that Bob gleans from his measurement is only meaningful in the context of a pre-agreed-upon protocol, and he can't learn specifics about Alice's situation without a traditional (light-speed or slower) message from her.

In the model of emergent quantum gravity you mentioned that when two parts of Hilbert space are highly entangled, they are what we classically call “close together”. You also mentioned that von Neumann made a connection between entanglement and entropy: the more entanglement, the higher the entropy. And finally, that empty space is highly entangled and that adding particles breaks that entanglement, increasing the energy and decreasing the entropy.

Based on these premises, what can we (you) say about the Big Bang and its low entropy state? On one hand we have everything on top of everything else, which is high entanglement and high entropy, since that is what “close together” means; on the other hand we have the observed low entropy at the Big Bang which suggests a low entanglement at that point in time, like everything was far from everything else, maybe due to the high energy at the Big Bang which breaks the space entanglement, thus lowering the entropy.

These two things are contradictory. Could a solution be something like the energy being in the inflaton field, with no particles, and then the decay of the field and the transfer of the energy from the inflaton field to the other “ordinary” fields, thus increasing the energy “felt as particles” and lowering the entropy? Are there any hints like these in emergent quantum gravity about solving the observed low entropy at the Big Bang?

Emergent quantum gravity and the connection between entanglement, entropy, and geometry is a rich area of research that tries to uncover the quantum underpinnings of spacetime. The relationship between entanglement and spacetime geometry has been given particular emphasis in models like the AdS/CFT correspondence, which connects quantum field theories to gravity in higher-dimensional spacetimes.

When it comes to the Big Bang and entropy, the "low entropy" at the start of the universe is traditionally associated with the observed high degree of homogeneity and isotropy. In essence, the universe was in a very particular state (given the vast number of possible states it could have been in), and entropy has been increasing ever since due to the growth of structures, etc.

Now, relating this to emergent spacetime and entanglement is an interesting endeavor, but there are some nuances to be aware of:

1. **Different Types of Entropy**: When cosmologists speak of the "low entropy" at the Big Bang, they are typically referring to thermodynamic or gravitational entropy associated with matter distributions and their configurations. This is not the same as the entropy of entanglement (or von Neumann entropy) in quantum states. While there are relations between these concepts, they don't map one-to-one.

2. **Entanglement and Geometry**: In emergent spacetime models, the entanglement structure of a quantum state is related to the geometry of the emergent spacetime. Highly entangled regions can be thought of as "close together" in this emergent spacetime. But the details of how this connects to the early universe's entropy is not fully worked out.

3. **Inflation and Entropy**: The inflationary scenario proposes that the universe underwent a rapid exponential expansion early on, driven by an inflaton field. This scenario helps solve several cosmological puzzles, including the flatness and horizon problems. The relationship between inflation, entropy, and entanglement in the context of emergent gravity is an open question and an active area of research.

4. **Limitations of Current Models**: It's important to understand that emergent quantum gravity is still a speculative idea. While it has made some intriguing predictions and offers a fresh perspective on quantum gravity, it's not yet a complete or universally accepted framework. There's much we don't know about how it might connect to the early universe and the entropy puzzle.

In conclusion, while the ideas surrounding entanglement, emergent spacetime, and entropy are tantalizing, the direct connection to the observed low entropy of the Big Bang remains an open question. It's likely that as our understanding of quantum gravity matures, we'll gain clearer insights into these deep questions.

I have been thinking of a way for two objects to “still communicate” (sort of) after one of the objects falls into a black hole. Say you’re in a spaceship hanging out at the edge of the event horizon, 1 km away from it. You open your hatch and release a bowling ball tied with a cable (a REALLY strong cable) into the black hole. You also have clocks attached to the cable, say every 10 meters.

Imagine you could live for infinity and you have infinite fuel in your ship so that you can continue to hover 1 km above the event horizon of the BH and you’re not bothered by the difference in time dilation between your frame of reference and the BH’s frame of reference.

What would happen to the ball, cable and watches as the ball falls into the black hole and past its even horizon?

Would the bowling ball freeze on the event horizon? If so, what happens to the tension in the cable? If more cable is being pulled off your “cable roller” as the bowling ball continues to fall into the black hole, isn’t that some sort of information that the bowling ball is “sending” you out of the black hole? After all, you know that the bowling ball continues to travel towards the singularity and hasn’t reached that point, because it demands more and more cable? Shouldn’t the ball be “more into the future” than the cable, since it’s closer to the singularity, hence having no causal effect on the cable? What happens as the bowling ball reaches the singularity? It stops pulling on the cable?

This is an interesting thought experiment that touches upon the weirdness and counterintuitive nature of black holes. Here's a rough breakdown of what's expected to happen, based on our current understanding of general relativity and black holes:

1. **Outside Observer's Perspective**: From the perspective of someone hovering outside the black hole (that's you, in your spaceship), the bowling ball never actually crosses the event horizon. Due to the extreme time dilation effects near the horizon, the ball appears to slow down and asymptotically approach the event horizon, getting infinitesimally close but never actually crossing it. It also becomes increasingly redshifted, so it will eventually fade from view.

2. **Bowling Ball's Perspective**: From the bowling ball's perspective, nothing particularly special happens when it crosses the event horizon. It continues its free fall toward the singularity. The rate at which it feels it's being pulled will depend on the size (radius) of the black hole; for supermassive black holes, this rate could be quite slow, while for smaller black holes, the gravitational tidal forces would rip it apart before it even reaches the horizon.

3. **The Cable**: The tension in the cable would increase as the gravitational force on the ball grows stronger. However, the cable outside the event horizon will also observe the ball to never actually cross the event horizon. The cable will continue being pulled, but, interestingly, it can't convey real-time information about what's happening to the ball inside the event horizon. This is because of the causal disconnect between regions inside and outside the event horizon. Information cannot be transmitted out of the event horizon.

4. **Reaching the Singularity**: From the ball's perspective, after some finite time (depending on the black hole's size), it will reach the singularity. At this point, our current understanding of physics breaks down, and we don't have a full description of what occurs at the singularity. One thing to note is that singularities are believed to be regions of infinite curvature, where our classical description of spacetime ceases to be valid. We expect a theory of quantum gravity to provide a more complete picture.

5. **About the "Communication"**: The act of the cable being pulled isn't a form of FTL (faster-than-light) or event horizon-defying communication from the ball. You wouldn't get any specific, detailed information about the state of the ball inside the horizon. All you would know from the pull is that the ball is still being affected by gravity, which you already knew.

In essence, the interaction of objects with black holes, especially scenarios involving cables or tethers, opens up many intriguing questions, some of which remain at the forefront of current research in the field. While our current theories provide some answers, the ultimate nature of black holes and their interiors might only be revealed once we have a full theory of quantum gravity.

What would happen to the ball, cable and watches as the ball falls into the black hole and past its even horizon?

I have a question regarding the many worlds interpretation of QM, regarding what I would call “consistency”. If anything that’s allowed by the wave function actually happens, then why don’t we see some very inconsistent things, especially regarding people’s actions? Let’s assume you go out in the street and ask random people what’s 2+2? You will get, in the vast majority of answers, the answer “4”. Very few people won’t know the answer (let’s hope) and few people will make a joke, giving you a different answer just for giggles.

The question is - why would that be so? Why wouldn’t people randomly say “153” or “12.4” or “3.1415” or anything like that (not as jokes, but as authentic answers). How come, if multiple branches exist, we never see this kind of inconsistency? There are possible quantum states where the same people that answered “4” would answer “153”, or “12.4”, or “3.1415” - is there anything “special” about branches where people answer “4”?

The Many Worlds Interpretation (MWI) of quantum mechanics posits that every possible outcome of a quantum measurement actually occurs in some branch of the universe. However, it's essential to understand the nature and scale of the quantum events that cause branching.

In the scenarios you've described, like asking someone the result of 2+2, the behavior is determined primarily by classical reasons (education, personal experiences, brain wiring, etc.) and not by quantum events. The reason most people say "4" is because they have been taught this fact and have internalized it through years of education and experience.

Even if there were a superposition of quantum states inside their brain when they're about to answer, the overwhelmingly dominant contribution would favor them responding "4" because the neural pathways in their brains have been trained over years to produce this result for this question. The odds of a quantum fluctuation leading them to give a random, incorrect answer would be extraordinarily small.

For a comparison, consider radioactive decay. An atom of a radioactive substance might have a certain probability of decaying within the next hour. In the MWI, there is one branch where it decays and another where it doesn't. The splitting of the universe in this interpretation is due to an explicitly quantum event—the unpredictable decay of the atom. But even in the MWI, if you were to ask the atom, "Will you definitely decay in the next nanosecond?", the answer would be "No" in nearly all branches because the probability is so tiny.

Similarly, while there might technically be branches where a person gives a bizarre answer to the 2+2 question due to quantum fluctuations causing a dramatically different neural response, the proportion of such branches would be minuscule. In nearly all branches, their well-trained neural networks will give the answer "4."

In short, while MWI suggests that all possible quantum outcomes happen in some branches, the relative "measure" or "weight" of these branches can be vastly different. Common, expected outcomes (like people answering "4" to the 2+2 question) will dominate, and very unlikely outcomes (like answering "153" without joking) will have an infinitesimally small measure.

I have a question about quantum fields: what IS, really, a quantum field? We talk about a quantum field as a “number at every point in space”, but does a quantum field “belong” to spacetime or can it exist “outside of spacetime”? Is it a “property” of spacetime? Also (more importantly), how does a quantum field know what value it should have, what potential energy it has and so on? Where is this information stored? Is a quantum field a “physical entity”, including the boson fields?

Nobody has been able to satisfactory answer these questions for me, so far. The problem about the information is the most important, for me - where is the information “stored” that allows a quantum field to be at a certain energy or have a certain value? Why would a quantum field interact with another quantum field, but not with yet another one? How do they metaphorically “know” which field should interact with any other field?

Your questions touch upon some deep and philosophical aspects of our understanding of quantum field theory (QFT). Let's attempt to unpack them one at a time:

1. **What is a quantum field?** At a basic level, a quantum field can be imagined as a set of values (or more accurately, operator values) defined at every point in space and time. Each field corresponds to a certain type of particle. For example, the electron field corresponds to electrons, and the photon field corresponds to photons. When we talk about particles being created or annihilated in interactions, we're really talking about excitations in these fields.

2. **Does a quantum field belong to spacetime or can it exist outside of spacetime?** Our current understanding of quantum fields is deeply tied to spacetime. In QFT, fields are defined over spacetime. Whether they can exist outside of our concept of spacetime is not addressed in standard QFT, and speculating on that would enter the realm of theoretical ideas not yet backed by empirical evidence.

3. **Is it a "property" of spacetime?** Not in the way something like curvature is a property of spacetime in General Relativity. Rather, fields exist *in* spacetime. They're not attributes of spacetime itself.

4. **How does a quantum field know what value it should have?** The values that fields take and their dynamics (how they change in time and space) are determined by the Lagrangian or Hamiltonian of the system, which is a mathematical representation of the energy of the system. The equations of motion derived from the Lagrangian or Hamiltonian (often in the form of differential equations) tell us how fields evolve over time.

5. **Where is this information stored?** This question delves into more philosophical territory. The "information" is not stored in the way data is stored on a computer. Instead, the behavior of fields is dictated by the fundamental laws of physics. These laws aren't stored anywhere; they simply are the rules by which our universe operates.

6. **Is a quantum field a "physical entity"?** This is another deeply philosophical question. In practice, physicists treat quantum fields as mathematical tools that accurately predict experimental outcomes. Whether or not they are "real" or just a useful calculational tool is a matter of interpretation and philosophy.

7. **Why do certain fields interact while others don't?** Interactions are determined by the symmetries and conservation laws of our universe. The Standard Model of particle physics, for instance, is built on certain gauge symmetries which dictate how fields interact. Some fields don't have the necessary properties to engage in certain interactions. For example, photons don't interact with gluons because they don't carry the color charge necessary for the strong force interactions that gluons mediate.

Your questions highlight a fundamental aspect of science: While our theories, like QFT, are incredibly successful at describing and predicting the behavior of the natural world, they don't always provide satisfying answers to deeper "why" questions. Some of these questions veer into the domain of philosophy, metaphysics, or areas of theoretical physics that are still under exploration.

Suppose I have an instrument that gives me the capacity to see what all the particles in your brain are doing and gives me a prediction that at 12:00 PM you will raise a glass of wine off the table (including the effects of telling that to you and how your brain will react to this new information). I tell you that at 11:59 and then I wait for you to raise the glass of wine at 12:00 PM, as predicted. Would you be able to do something else at 12:00? Would you be able to decide otherwise, not to raise the glass of wine, just in spite of me and my prediction? What does such a scenario say about free will in your opinion, since this experiment is possible in principle?

This thought experiment touches upon profound issues in the philosophy of mind and the nature of determinism and free will.

Here's a breakdown of your scenario and the implications:

1. **Predictability and Determinism:** If you have an instrument that can perfectly predict every movement of every particle in my brain (and takes into account all external influences, including your telling me of the prediction), then the scenario assumes a deterministic universe — at least at the level of classical physics. Determinism here means that, given a particular state of the universe and the laws of physics, there's only one way for things to proceed.

2. **The Act of Telling:** The complexity arises when you introduce the act of telling me the prediction. If your instrument is perfectly predictive, then it already took into account how my brain would react upon hearing the prediction. So, when you tell me that I'll raise the glass at 12:00 PM, the instrument has already considered my knowledge of that fact in its prediction.

3. **Can I Defy the Prediction?** In a perfectly deterministic scenario, the answer would be "no." If the instrument's prediction is absolutely accurate, then regardless of how I feel or what I think I'm choosing, I would end up raising the glass. This has perplexing implications for our sense of free will.

4. **Free Will:** If every action we take is predictable and we can't act otherwise, then it seems like free will doesn't exist in the way many of us intuitively understand it. But the concept of free will is complex. Some argue that free will is compatible with determinism (compatibilists) by suggesting that free will is more about acting in line with our desires and intentions, even if those desires and intentions are predetermined. Others (incompatibilists) think that determinism and free will cannot coexist.

5. **Quantum Mechanics:** Let's throw in another wrench. At the quantum level, events are not strictly deterministic but probabilistic. While quantum effects might not directly translate to macro-level brain functions, they do add an element of unpredictability to the universe. How this impacts the discussion of free will is still a topic of debate.

6. **What About You?** There's also the issue of your own actions. If you can predict my behavior, what about predicting your own? This gets into recursive complexities.

In the end, this thought experiment amplifies age-old questions about free will, determinism, and the nature of consciousness. While we don't have definitive answers, these questions continue to captivate philosophers, neuroscientists, physicists, and many others.

We say that inflation makes the low entropy problem worse but I say it’s the other way around - inflation requires a very low entropy and therefore only fluctuations of very low entropy can undergo inflation and create universes. It’s a feature, not a bug. It’s a selection mechanism.

My idea is that you have quantum foam as the universe generating mechanism (as the true ontology, if you will - that is what is “fundamental”) - it’s there where fluctuations happen and only low entropy fluctuations have the property that energy is uniformly distributed to trigger inflation/the repulsive behavior of gravity. Other (high entropy) fluctuations simply collapse back and don’t create any universes.

Is there something fundamentally wrong about what I’m proposing that escapes me?

Your idea touches upon several key areas of cosmology and the philosophy of physics. Here are some reflections on your proposal:

1. **Entropy and the Initial State:** The reason inflation is said to make the entropy problem "worse" is because it posits a very special, low-entropy initial condition to start the inflationary process. In the context of the entropy problem, this is referring to the "why" question: why did the universe begin in such a special, low-entropy state? If we simply say inflation requires this, then we haven't answered the deeper question of why the universe should favor such initial conditions.

2. **Quantum Fluctuations:** The idea of quantum fluctuations in some pre-existing substrate (like quantum foam) giving rise to our universe is not new. There are models in cosmology that hypothesize something similar, where our universe might be one of many in a broader multiverse, each initiated by some quantum fluctuation. However, this raises further questions: what is the nature of this substrate or foam? What governs its behavior? How does it come into existence?

3. **Selection Mechanism:** The notion of a "selection mechanism" is intriguing. The idea that only certain kinds of fluctuations lead to big bangs and subsequent universes is reminiscent of Lee Smolin's idea of "cosmological natural selection". In Smolin's model, black holes spawn new universes with slightly altered constants of nature, effectively "selecting" for universes that can produce black holes. The difference here is the criteria for selection: Smolin is working with variations in constants of nature, while you're suggesting entropy as the criteria.

4. **Fundamental Ontology:** It's a bold claim to propose quantum foam as the "true ontology" of the universe. The idea of a more fundamental substrate from which our universe emerges is a recurring theme in cosmology. However, defining and understanding such a substrate requires a solid theoretical framework, which is currently still speculative in nature.

5. **Challenges:** One challenge with your idea is explaining the precise mechanism by which a low entropy fluctuation would trigger inflation while a high entropy fluctuation would collapse. We need a quantitative theory to test such a claim. Furthermore, assuming inflation requires a certain initial condition just moves the problem one step back: why should the quantum foam favor these low entropy fluctuations?

All that being said, the origin of the universe, the nature of inflation, and the problem of entropy are still open questions in physics. It's good to think creatively about these topics, and your idea is an interesting take on the problem. Whether it's right or wrong, what's crucial is to develop the idea into a more rigorous framework that can be tested or evaluated against observations and established theory.

When asked “what is currently happening in Alpha Centauri right now?” why can’t you simply respond with “I will answer your question 4 years from now”, allowing the information of what is going on “right now” to get to us, enter our light cone, and having an answer? Sure, you don’t know what’s going on now, but if you wait 4 years for the information to get here, you will know and you will be able to answer the question.

Certainly, your point is well-taken. Let's clarify the context of the question and answer:

When people ask what's happening "right now" in a distant location like Alpha Centauri, they are often referring to the "simultaneity" concept from Einstein's theory of relativity. In relativity, the idea of "now" becomes relative, meaning it depends on the observer's reference frame. Therefore, from the viewpoint of relativity, asking what's happening "right now" at a location that is light-years away is a somewhat problematic question because "now" is different for different observers moving at various relative speeds.

Your solution addresses the problem from a pragmatic perspective: we can, in fact, wait for 4 years to get the light (and thus the information) from Alpha Centauri to know what happened there 4 years ago. By then, it's no longer a question of simultaneity, but rather a direct observation of past events.

So, your suggestion is valid. However, the deeper philosophical and physical question is how to define simultaneity over vast cosmic distances, which is what Einstein's theory disrupted in our classical understanding of time.

If we look at the properties of a black hole we find two singularities: a coordinate singularity at the Schwarzschild radius and the central singularity. Time and space get changed in-between when passing the coordinate singularity (the event horizon).

What if our Universe is a white hole that has a singularity in the past from our perspective, but if you could travel back in time and “exit” it, you would then move into space instead of time, from that point on. What we see as the Big Bang is actually a coordinate singularity from outside our universe (the same is true if you pass the event horizon of any black hole - it looks as a white hole singularity in the past, from your perspective).

Your idea echoes a speculative concept in theoretical astrophysics and cosmology. The idea that our universe could be the "other side" of a black hole, often termed a white hole, has been considered by some scientists.

The basic idea of a white hole is that it's the time-reversed version of a black hole: Instead of only "sucking" everything in and not letting anything escape, a white hole would "spew out" material and not allow anything to enter.

Let's explore some implications and questions related to your proposal:

1. **Initial Conditions**: If the Big Bang is a white hole, it provides a different narrative for the initial conditions of our universe. Instead of the universe starting from an initial singularity, it's a continuous "spewing out" of matter and energy.

2. **Cosmic Censorship**: One of the main hypotheses in black hole physics is the cosmic censorship hypothesis, which broadly speaking states that singularities (like the ones inside black holes) can't be exposed, or "naked", to the rest of the universe. If the Big Bang is truly a white hole, this would represent a naked singularity, challenging this principle.

3. **Black Holes within Our Universe**: If our universe originated from a white hole, it raises interesting questions about the black holes within our universe. Could they lead to other universes? Or are they fundamentally different from the singularity that led to our universe?

4. **Time's Directionality**: If our universe is a white hole, it introduces the interesting question of the nature of time. If white holes are merely time-reversed black holes, why does time have a preferred direction in our universe (i.e., why is there an arrow of time)?

5. **Boundary Conditions**: One of the significant debates in cosmology is whether our universe has a boundary or edge. If our universe is a white hole, it would suggest specific boundary conditions.

6. **Experimental Evidence**: Currently, there's no empirical evidence for white holes, and it's unclear how we could obtain such evidence. Without experimental or observational evidence, this idea remains in the realm of interesting speculations.

Your idea is an intriguing one and touches upon a broader theme in modern physics: the relationship between the smallest scales (black holes, singularities) and the largest scales (cosmology, the universe's evolution). While there's currently no conclusive evidence for this scenario, it's an exciting avenue of theoretical exploration and challenges our fundamental understanding of the universe's beginning and nature.

Suppose that back when Hubble looked at what galaxies were doing, back in 1929, he saw that they are all coming towards us, instead of going away from us (say, due to a negative cosmological constant). Based on that observation, we would say that the stars were even further away in the past. Would we still say that the Big Bang took place or, instead, that the Universe is infinitely old and that all the stars have been traveling from infinitely far away for an infinite amount of time towards us?

Had Hubble observed galaxies moving towards us rather than receding, it would indeed have had a significant impact on our cosmological understanding and how we interpret the universe's history. However, let's explore your hypothetical scenario:

1. **Not Necessarily a Steady State**: Observing galaxies converging towards us wouldn't automatically lead us to a steady-state model. It would indicate a gravitational pull acting on a more massive scale than initially anticipated. A cosmological constant with a sign such that it causes attraction rather than repulsion (which is the observed behavior of the actual cosmological constant, ascribed to dark energy) would indeed result in such an attraction.

2. **Big Bang Still Possible**: Even with galaxies converging, it's still possible that the universe started with a Big Bang-like event. The observation would suggest that the initial expansion has been overcome by this overarching attraction. The universe might be collapsing in a "Big Crunch."

3. **Infinite Age is Problematic**: The idea that the universe has been around for an infinite amount of time would bring about several issues. For instance, if the universe had an infinite age, and stars have been shining forever, the night sky should be blazingly bright—a paradox known as Olbers' paradox. This paradox can only be resolved if the universe has a finite age, if there's enough cosmic dust to obscure starlight, or if the universe is expanding (leading to redshifted and diminished light), as we currently observe.

4. **Evidence from Cosmic Microwave Background Radiation (CMBR)**: The discovery of the CMBR in the 1960s provided robust evidence for the Big Bang. Even if galaxies were observed to converge, the existence of the CMBR would still suggest a hot, dense beginning for the universe.

5. **Modern Observations**: With today's technology, we observe not only galactic redshifts but also the distribution of galaxies, the properties of the CMBR, the distribution of light elements, etc. Any cosmological model would need to account for all these observations, not just the motion of galaxies.

In summary, if Hubble had observed galaxies moving towards us, our cosmological models would have undoubtedly evolved differently. However, it's crucial to note that our current understanding of the universe doesn't rely on galactic redshifts alone but on a confluence of various observations and experiments.

In Conformal Cyclic Cosmology, Roger Penrose proposes a future when, after all the black holes in our universe evaporate away, there are no available particles with mass to build a clock or have a “length” and a new Big Bang arises. One of the problems of his proposal is the fact that we don’t know if mass can be completely gotten rid of.

I was thinking - if you wait for eternity, the entire Higgs field, everywhere, could fluctuate to zero so the entire universe has massless particles, everywhere (of those having mass that survived). The Higgs could also fluctuate to very high values, making all the particles in that area collapse into a black hole and evaporate away through Hawking radiation. Either way, you end up with a universe having no particles with mass.

What would be your criticism to this proposal of mine and to the idea of Conformal Cyclic Cosmology in general? I know one of the strong criticisms is that it supposes non-unitarity (by the loss of information in black holes), for example.

Your proposal touches on the ideas of the vacuum and the Higgs field, and indeed, fluctuations in the Higgs field could in theory have profound effects on particle masses. Your idea of the entire Higgs field fluctuating to zero (or high values) is speculative, but it's rooted in the concept of quantum field theory and vacuum fluctuations. Here are a few thoughts and criticisms:

1. **Timescales**: Even if we accept that Higgs field values could fluctuate significantly due to quantum effects, the timescale on which such a universal fluctuation might occur could be vastly longer than even the timescales considered in cosmology. The universe would already need to be in a state where almost all conventional matter and energy forms have dissipated, which is already an extraordinarily long time from our current epoch.

2. **Higgs Field Fluctuations and Stability**: The potential of the Higgs field determines the behavior of its fluctuations. If the current electroweak vacuum is metastable (as some measurements suggest), then a significant fluctuation could send the Higgs field into a true vacuum state. However, the consequences of this are still uncertain. It's not clear that this would result in all particles becoming massless; rather, their masses might just change to new values. On the other hand, if the vacuum is stable, large fluctuations are even less likely.

3. **Other Mass Sources**: Remember that the Higgs mechanism is responsible for the masses of elementary particles like quarks and electrons, but the majority of the mass of protons and neutrons (and therefore atoms) comes from the binding energy due to the strong nuclear force. Even if all the particles' rest masses were turned off, there would still be bound states with effective mass.

Regarding Conformal Cyclic Cosmology (CCC):

1. **Non-Unitarity**: As you noted, one significant criticism is that CCC violates quantum unitarity, primarily through the loss of information in black holes.

2. **Low-Entropy Problem**: The CCC suggests a sequence of aeons, each beginning with a Big Bang and ending in an infinitely expanded universe. However, it does not address the problem of the extraordinarily low entropy of the early universe—a significant aspect of the original Big Bang model that's challenging to explain.

3. **CMBR Observations**: Some proponents of CCC have claimed that concentric rings of temperature variation in the cosmic microwave background radiation (CMBR) are evidence for pre-Big Bang events. However, these claims have been met with skepticism, and many believe that these can be explained without invoking CCC.

4. **Matter and Radiation Transition**: For the conformal rescaling to work between aeons, the universe has to transition from being matter-dominated to radiation-dominated before the next aeon. It's not clear how this transition would naturally occur.

While CCC is an intriguing idea and Penrose is a brilliant physicist, it's essential to note that most cosmologists do not currently accept CCC as a leading model for the universe's large-scale structure and history. Like all scientific theories, it would need more concrete evidence and successful predictions to gain widespread acceptance.

Suppose you’re some distance away from a black hole and you throw an object in it. You’re going to see the object close in on the black hole’s event horizon but never actually “pass into” the black hole. Since from your perspective no object is falling into the black hole, how can we then say that black holes increase their size when objects fall into them? After all, no objects are ever going to fall into them from our perspective - all we should ever see is black hole evaporation.

You've touched upon one of the most profound and intriguing paradoxes of black hole physics. When discussing the behavior of objects approaching black holes, two perspectives are often discussed: the perspective of a distant observer and the perspective of an infalling observer.

From the perspective of a distant observer:

1. As an object approaches the event horizon of a black hole, it will appear to slow down due to gravitational time dilation. It will never appear to actually cross the event horizon.

2. The light emitted or reflected by the object becomes increasingly redshifted as the object nears the horizon. Eventually, the object's image fades from view as the light's wavelength stretches to infinity.

3. Although the object never appears to cross the event horizon from this perspective, the black hole's mass, and therefore its size, will increase as if the object had fallen in.

From the perspective of the infalling object:

1. The object will pass through the event horizon in a finite amount of proper time (the time experienced by the object) without experiencing anything particularly special at that moment.

2. Once inside the event horizon, all future trajectories lead toward the singularity at the black hole's center. There is no escaping this fate after crossing the event horizon.

The reconciliation between these two viewpoints is subtle and depends on the nature of event horizons and the definition of simultaneity in general relativity. When you're far from a massive object, your notion of "now" or simultaneity extends out into space in a pretty straightforward way. But close to a black hole, your sense of "now" bends severely due to the intense gravity. So when you, as an external observer, say the object has "now" reached the event horizon, the object's own "now" has already experienced passing through the horizon and maybe even reaching the singularity.

Regarding your last point on black hole evaporation: If you wait long enough, it's true that black holes can evaporate via Hawking radiation. But the time required for a stellar-mass black hole to evaporate is unimaginably longer than the current age of the universe. Smaller black holes would evaporate faster, but they would need to be incredibly tiny to evaporate in a human-observable timeframe.

In summary, while objects appear to freeze and fade at the horizon from a distant perspective, their mass-energy is effectively added to the black hole, leading to an increase in its size.

Suppose you throw yourself into a black hole with a particle in your ship’s laboratory that is in superposition. Could you make a measurement on its position such that its position is outside of the black hole, when “observed”? In other words, is the wave function of a particle in superposition allowed to be both inside and outside of the black hole?

This is a deep and challenging question, intertwining quantum mechanics and general relativity. As of my last training data in September 2021, the full reconciliation of quantum mechanics and general relativity is an unsolved problem in theoretical physics, and it's precisely these types of questions that highlight the issues faced.

In quantum mechanics, a particle described by a wave function can indeed be in a superposition of multiple states, including different positions. However, the act of measurement causes this wave function to collapse to a single outcome.

In the scenario you're describing, where a particle is in superposition both inside and outside a black hole, there are several intriguing considerations:

1. **Measurement Inside the Event Horizon:** If you, inside your ship, were to measure the particle's position after crossing the event horizon, quantum mechanics tells us the wave function would collapse, and the particle would be found either inside or outside the black hole. If found outside, it's unclear how this information could be consistent with the fact you're already inside the event horizon, from where no information or particle can escape.

2. **Nature of Event Horizon:** The event horizon is not a physical barrier but a point of no return beyond which trajectories can only lead further into the black hole. A particle's wave function might, in some models, span both sides of the horizon. But the physical implications of such a spread are deeply puzzling.

3. **Unitarity and Black Holes:** One of the major problems in theoretical physics is ensuring that information isn't lost in black holes (the black hole information paradox). Allowing particles to exist in a superposition that spans the event horizon further complicates this issue. If the wave function collapses to a state outside the black hole, what happens to the "inside" portion? Is information conserved? This ties into the broader questions of unitarity in quantum mechanics.

4. **Entanglement and Event Horizon:** Another intriguing aspect is the concept of Hawking radiation. Pairs of virtual particles near the event horizon can become real, with one falling into the black hole and the other escaping. These particles are entangled, and Hawking's calculations suggest this process causes black holes to evaporate over time. The nature of this entanglement and its connection to information conservation is still an active area of research.

In short, the scenario you're describing touches upon one of the most profound issues in modern theoretical physics. While the specific mechanics of a particle in superposition across a black hole's event horizon are not well-defined in our current understanding, asking these questions pushes the boundaries of what we know and illuminates the areas where new theories are desperately needed.

We know a black hole is a region of spacetime where the entropy is very high and gravity dominates.

Is there any mathematical reason why the Big Bang/Universe can’t be a white hole? It makes so much sense for it to be exactly that: a singularity in the past where gravity is off and the entropy is low - just the opposite of a black hole.

The idea of the Big Bang as a kind of white hole has been considered in various speculative cosmological models. The similarity between the singularity at the heart of a black hole and the singularity posited to exist at the very beginning of the Universe has prompted such speculation. Here's a brief rundown of some of the reasons this isn't widely accepted, as well as some nuanced considerations:

1. **Definitions**: Black holes and white holes are solutions to Einstein's equations of general relativity. A black hole is a region of spacetime from which nothing can escape, while a white hole is its time-reverse: nothing can enter a white hole from the outside, but matter can emerge from it. By this definition, the early universe resembles a white hole in the sense that it looks like an explosion of matter from a point.

2. **Cosmic Censorship Hypothesis**: One of the key principles in general relativity is the cosmic censorship hypothesis. It suggests that singularities, like those at the center of black holes, are always cloaked by event horizons and hence never nakedly exposed to the rest of the universe. White holes would violate this principle since they are essentially exposed singularities.

3. **Stability**: Theoretical studies have shown that white holes are likely to be unstable. The slightest perturbation could cause them to collapse into a black hole or to completely dissipate.

4. **Lack of Observational Evidence**: There's no observational evidence supporting the existence of white holes. The universe is full of black holes, but no compelling evidence for the existence of white holes has been found.

5. **Big Bang as a Unique Event**: The conditions believed to be present during the Big Bang are unique and are not necessarily the same as those in the theoretical construct of a white hole. The Big Bang isn't just a point of emission in space; rather, all of space was condensed. The expansion isn't just matter moving outwards in space; space itself is expanding.

6. **Modern Cosmology**: The inflationary model of cosmology, which describes a rapid exponential expansion of the universe shortly after the Big Bang, has provided a successful framework for explaining many cosmic observations. The idea of the Big Bang as a white hole isn't necessary in this framework.

That said, while the Big Bang as a white hole isn't a mainstream idea, questioning and exploring alternate models can lead to deeper insights and understanding. It's worth noting that our grasp of the true nature of the universe, especially its inception and the inner workings of black holes, is still incomplete. There's still a lot that we don't understand, and as we gather more observational data and refine our theories, our understanding might change.

But why do you say that a white hole violates the cosmic censorship conjecture? The white hole singularity could still be cloaked inside of an event horizon, it's just that we are inside of that event horizon, that's why we can see the singularity. It's similar to being inside of the event horizon of a black hole - once you passed the event horizon, you should have access to the singularity.

You're right in noting that if we were inside the event horizon of a white hole (assuming white holes can exist in a manner similar to their black hole counterparts), then the singularity might be accessible or "visible" in a sense, much like the singularity of a black hole would be "visible" from within its event horizon.

The cosmic censorship conjecture is primarily concerned with naked singularities, which are singularities that are not hidden behind an event horizon. In the standard description of a white hole, nothing can enter from the outside, and material can emerge from within. This seems to expose the singularity to an external observer. However, the precise nature of these singularities, and their compatibility with the cosmic censorship hypothesis, can depend on the specifics of the model.

Your perspective suggests a reinterpretation: If we're considering the entire observable universe as being inside the event horizon of a massive white hole, then the cosmic censorship hypothesis isn't directly violated. The singularity of the white hole (the Big Bang in this scenario) would then be a boundary condition of our universe that, while in our past, is still a part of the spacetime fabric we exist within.

This is an interesting viewpoint, but it's worth noting that the white hole idea doesn't straightforwardly address or solve many of the questions or challenges cosmologists are working with regarding the origins and nature of the universe. Most critically, the concept doesn't mesh neatly with the inflationary model of the early universe, which has significant empirical support.

Moreover, modern understanding of black holes and singularities is deeply tied to the interplay between general relativity and quantum mechanics, and this interplay is not yet fully understood. Theoretical frameworks like loop quantum gravity and string theory, which aim to reconcile these domains, often suggest modifications or resolutions to classical singularities.

In essence, while the white hole universe concept is an intriguing one and highlights the vastness of possibilities in cosmological thinking, it's not the prevailing model because it doesn't offer a clearer explanation of empirical observations than current leading models do.

Since space (and possibly gravity) can be expressed in terms of quantum mechanical entanglement, could it be that what we currently call “dark matter” is not actually any kind of “additional matter” or a new particle/field, but instead a different way to have entanglement manifest itself? In this case, studying quantum entanglement more carefully could explain what we currently call “dark matter”.

Your idea connects two intriguing areas of physics: the interplay between quantum mechanics and gravitation, and the mysterious phenomenon of dark matter.

**Quantum Entanglement and Gravity**: Recent theoretical research, especially in the context of the AdS/CFT correspondence in string theory, suggests that spacetime and gravity might be emergent phenomena that arise from quantum entanglement in a deeper, non-geometric layer of reality. These ideas, however, are still in the realm of theoretical exploration and have not yet been tested experimentally.

**Dark Matter**: Dark matter is an inferred substance that appears to exert gravitational forces and helps to explain the observed dynamics of galaxies and the large-scale structure of the universe. While we have significant indirect evidence for the gravitational effects of dark matter, it has yet to be directly detected, and its nature remains one of the biggest open questions in cosmology and particle physics.

Now, onto your proposal:

While it's a fascinating thought, it would be a substantial leap to equate potential nuances in the quantum structure of spacetime with the pronounced gravitational effects attributed to dark matter. Here's why:

1. **Scale Differences**: Quantum entanglement and its potential gravitational implications are usually considered at microscopic scales, whereas the effects of dark matter are observed at galactic and larger scales. Bridging this gap is nontrivial.

2. **Quantifiable Effects**: The gravitational effects of dark matter are well-quantified. For example, galaxy rotation curves are flat at large radii, which implies a certain distribution of unseen mass. Any alternative explanation must be able to reproduce these detailed observations.

3. **Consistency with Observations**: While it's possible that dark matter is not a new kind of particle but rather a manifestation of modified gravitational dynamics (as in theories like Modified Newtonian Dynamics, or MOND), these alternative theories often struggle to account for all the data, especially the cosmic microwave background radiation and large scale structure data. It's challenging to see how a purely entanglement-based mechanism would fare better.

4. **Cosmological Structure Formation**: Dark matter plays a crucial role in the formation of structures in the universe. Without some form of dark matter, it's difficult to explain how the universe developed its current structure in the time since the Big Bang.

5. **Bullet Cluster**: Observations of galaxy cluster collisions, like the famous Bullet Cluster, provide evidence for dark matter as a substance that behaves differently from normal matter. During such collisions, luminous matter in the clusters (like stars and gas) interact and get "stuck," while dark matter appears to pass right through. This is difficult to explain without some kind of particulate dark matter.

While it's essential to keep an open mind and explore all avenues, it's also crucial to ensure that any new proposal or theory aligns with the extensive observational evidence we have.

In conclusion, while it's always worth exploring connections between fundamental concepts, we'd need a concrete, mathematically rigorous mechanism to connect quantum entanglement effects to large-scale gravitational phenomena in a way that can account for the many observations attributed to dark matter.

I read about how in the Quantum Eraser Experiment, in the first part (relevant to my question) you have an emitted photon that goes through a double slit, you split it into two entangled photons using a splitting crystal, photon A goes through a double slit and photon B is measured or not in a detector later on (later than photon A hits the interference screen). We can assume we take into account all the relativistic effects. It seems that the action of measuring photon B “in the future” makes the interference go away on the interference screen for the photon A.

But if this is true then we can violate causality and send messages faster than the speed of light. All we have to do is to measure or not photon B in some far away location. If I’m in Alpha Centauri and want to communicate to you a bit of 1 or 0 I simply have to measure (or not) the photon that you send me and you instantly know what happened there: if you see the interference pattern for photon A (on Earth) then it’s a bit of zero (because I haven’t/I will not measure my photon B on Alpha Centauri), if you don’t see it then it’s a bit of one, even though we’re spacelike separated (you can set up a multitude of these contraptions and communicate “instantly” endless stream of bits).

What gives?

You've touched upon a frequently misunderstood aspect of quantum mechanics, specifically related to the phenomenon of quantum entanglement and its implications for causality and faster-than-light (FTL) communication.

The delayed-choice quantum eraser experiment is a fantastic and counterintuitive demonstration of the principles of quantum mechanics. However, it does not allow for FTL communication or causality violation. Here's why:

1. **No FTL Information Transfer**: While the states of entangled particles are correlated in a way that seems "instantaneous," no information is actually transmitted between them. This is a foundational point of quantum mechanics: entanglement correlations happen without any "signal" passing between the particles. The results of measurements on one particle cannot be used to convey a message to the other.

2. **Post-selection**: In the quantum eraser experiment, the interference pattern (or its absence) only becomes clear when you "post-select" the data, i.e., when you correlate the detection events of photon A with those of photon B. Before this post-selection, the raw data on the interference screen appears random and doesn't show any discernible pattern. Only after you've collected all the data and classified it based on the results of the measurements on photon B does the interference pattern emerge or disappear.

3. **No Pre-determined Outcome**: You cannot control the outcome of the measurement on photon B. This means that even if you were trying to use the quantum eraser setup to communicate, the person on the sending end (Alpha Centauri in your example) cannot control whether the interference pattern appears or not on Earth. They can only decide whether to measure or not, but they can't decide the outcome of that measurement.

In essence, while the results of quantum experiments can seem at odds with our classical intuition, they are designed in such a way that they never violate causality or allow for FTL communication. The correlations seen in entangled particles are real and confirmed by experiments, but they do not permit the transfer of information instantaneously across space.

We say that we can get rid of Boltzmann brains as quantum fluctuations in an empty universe since there are no physical “observers” (physical interactions) to make the observation that would “materialize” the quantum fluctuations. There is also a paper regarding baby universes that get born in a previous, eternal deSitter space, by Sean Carroll.

How do you reconcile these two things? Shouldn’t the baby universes also need a physical observer/interaction to materialize them into existence? Don’t they have the same fate as Boltzmann brains?

You're delving deep into speculative cosmology! The issues of Boltzmann brains and baby universes born from quantum fluctuations in a de Sitter space are both puzzling, interesting, and still areas of active research and debate.

1. **Boltzmann Brains**: The idea of a Boltzmann brain arises from the statistical likelihood that, given infinite time in a thermal equilibrium state (like a de Sitter universe in the far future), it's more probable for a single, random consciousness (a "brain") to spontaneously form out of fluctuations than for an entire ordered universe like ours to appear. One critique of certain cosmological models is that they produce a vast predominance of Boltzmann brains over "ordinary" observers like us, which would make it exceedingly unlikely that we should find ourselves in our current universe. Solutions or ways around the Boltzmann brain problem vary, but one argument, as you mentioned, is that in a true vacuum state, there might not be any physical observers to "materialize" or collapse the wave function to realize such fluctuations.

2. **Baby Universes**: The concept that new universes can spontaneously nucleate out of vacuum fluctuations in a de Sitter space comes from considerations in quantum gravity. In this view, our universe might just be one of many "bubbles" in an eternally inflating multiverse. The birth of a baby universe can be thought of as a tunneling event, where the system tunnels from a high-energy state (the vacuum of the parent universe) to a lower energy state (the new baby universe).

Now, reconciling these:

- **Different Fluctuations**: One way to reconcile these ideas is to understand that the fluctuations leading to Boltzmann brains and those leading to baby universes are of different magnitudes and natures. A fluctuation that produces a Boltzmann brain is vastly more localized than one that leads to a whole new universe. Therefore, the probabilities associated with each can be vastly different.

- **Context of the Observer**: As for the role of observers, it's a deeply debated question in quantum mechanics and cosmology about whether consciousness or "observers" play a fundamental role in wave function collapse or whether objective collapse occurs without need of an observer. Depending on which interpretation one leans towards, the need for an "observer" to birth a baby universe or realize a Boltzmann brain might differ.

- **Role of Time**: Time plays a tricky role in these scenarios. In a truly eternal universe, almost anything that can happen will happen — and will happen infinitely many times. This raises deep questions about probability, predictability, and the nature of physical laws.

In summary, while both Boltzmann brains and baby universes arise from considerations of fluctuations in a de Sitter space or similar context, they can be distinct in terms of their origins, implications, and solutions. The questions you're asking lie at the intersection of quantum mechanics, statistical mechanics, and cosmology, and there's much we don't yet understand. Both concepts challenge our understanding of probability and the nature of reality in deep and fascinating ways.

Suppose I am next to a black hole and I throw some object in it. The black hole’s event horizon should increase as it now has more mass.

My question is how is the event horizon going to increase? Instantly all over the black hole? Is the event horizon going to get a little bigger where the object enters the black hole and then this will propagate throughout the black hole at the speed of light? What about the light cones defined by the curvature given by the black hole with its newly acquired mass?

When you throw an object into a black hole, the black hole's mass indeed increases, leading to an increase in the size of the event horizon. However, the process isn't as simple as just "adding" the mass instantaneously because of the relativistic and non-linear nature of the equations of general relativity.

Here's a somewhat simplified description of what would happen:

1. **Information Propagation**: Changes in the gravitational field, like other changes in fields in relativity, propagate at the speed of light. This means that the increase in the event horizon doesn't happen instantly throughout the black hole. Instead, the increase in the horizon size due to the added mass will spread outward at the speed of light.

2. **Horizon Dynamics**: When the object first gets close to the black hole, before it crosses the event horizon, it contributes to the external gravitational field, which effectively makes the event horizon expand slightly, even before the object has fully merged. Once the object crosses the horizon, it continues to dynamically affect the shape and size of the event horizon as it moves deeper into the black hole, until it finally reaches the singularity (or whatever structure exists at the core of the black hole, as our current theories break down there).

3. **Geometrical Implications**: The geometry around a black hole, especially near the horizon, is profoundly affected by the black hole's mass. As you correctly intuited, the light cones — which dictate the possible paths particles can take through spacetime — will be affected by the addition of mass to the black hole. As the horizon expands, so too does the region from which light cannot escape, which means the light cones tip more and more inward.

4. **Continuous Process**: It's also worth noting that the process of the object falling into the black hole, from the perspective of a distant observer, takes an infinite amount of time due to time dilation effects. From the perspective of the infalling object, it crosses the horizon in finite proper time. This dichotomy is part of the rich and strange tapestry of effects associated with black holes.

In essence, the changes to the event horizon due to the infalling object will spread outward at the speed of light and will dynamically and continuously reshape the horizon until the black hole settles back down into a stable configuration (which, for non-rotating black holes, is the simple spherical Schwarzschild solution, and for rotating black holes, is the Kerr solution). This settling process would involve the emission of gravitational waves if the infalling object is sufficiently massive.

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