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> quantum tunneling seemed to allow faster-than-light travel, a supposed physical impossibility It's only an impossibility in space-time. But the quantum worl

> quantum tunneling seemed to allow faster-than-light travel, a supposed physical impossibility It's only an impossibility in space-time. But the quantum world, until the wave function collapses, exists outside of space-time. Entanglement is under the same effect -- space-time simply isn't involved. It's the collapsing of the wave function that brings it into space-time. At least that's how I understood it.

drdeca 6y ago
That doesn't seem to fit with my understanding all that well? Alternatively, I'm just not sure what you mean by saying that it ( wait, what is the "it"? "the quantum world"? But the world is the quantum world?) "exists outside of space time" . If one said "the number 3 exists outside of spacetime", that would make sense to me, as saying that it isn't a thing with a location in spacetime, but just a thing. But I don't think I know what you mean.
- vez- 6y ago
  The thing I think the original commenter was trying to get at is that spacetime (the mathematical model) and quantum mechanics (the mathematical model) for the most part are in no way unified. Things that happen in quantum mechanics are not necessarily explainable using spacetime. Although in general physicists believe a lot of things from spacetime for QM, like that information can't travel faster than light, it isn't actually baked into QM. That's my understanding at least.
  - drdeca 6y ago
    By spacetime do you mean like, in a general relativity sense? Because aiui quantum field theory is quite consistent with special relativity.
  - raattgift 6y ago
    The https://en.wikipedia.org/wiki/Dirac_equation https://en.wikipedia.org/wiki/Dirac_equation is now more than ninety years old and put quantum mechanics into the Minkowski spacetime of special relativity. There are several textbooks[1] covering extensions of this approach to curved spacetimes generally, and one will encounter the https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation#Gravitational_interaction https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation#... in graduate school settings. Quantum mechanics on some specific curved spacetimes are exactly Klein-Gordon solvable. The Standard Model of Particle Physics incorporates the Poincaré Group, which is the group of Minkowski spacetime ("flat spacetime") isometries. This means that the Standard Model particles are the same independent of where and when they are in empty flat spacetime (3 spacelike and 1 timelike translation invariances), their orientation (rotational invariance about the three spacelike axes), and they transform reliably under boosts (differences in constant velocity along the spacelike axes). So the Standard Model is defined by flat spacetime: and the causal structure of flat spacetime (in which the constant c plays a key role) is very much baked in. Studying modern quantum mechanics mostly means looking at patches of effectively flat spacetime in which there are particles of the Standard Model occupying different locations in the patch, boosted relative to each other, and interacting via the other mechanisms captured in the Standard Model's formulation. We inhabit a type of curved spacetime in which General Relativity guarantees at least an infinitesimal patch of exactly flat spacetime around every point in the universe. In regions with only gentle curvature -- like laboratories on the surface of the Earth, or in space probes in the solar system -- any curvature corrections to the assumed exactly flat spacetime of the Standard Model are tiny, because the region of effective (rather than exact) flatness is very large compared systems of particles under experimental study of their quantum behaviour. "Pretend it's flat" works exceedingly well in practice. When a researcher has to consider curvature (e.g. in relativistic massive objects like neutron stars) she or he can continue to work perturbatively against a flat-by-definition spacetime. The problems arise in the difference between a guarantee of a microscopic region of flat spacetime and an infinitesimal region of flat spacetime: if the radius of curvature is small compared to the spatial extent of a particle, things get ugly quickly, especially as we take the wavelength of the particle smaller (which means the energy of the particle climbs, and that is the sort of energy which creates spacetime curvature, so we get a nonlinear feedback, and classical General Relativity and Quantum Field Theory in Curved Spacetime make annoyingly different and incompatible predictions about what happens as one takes the limits of high particle energy and high curvature. Fortunately this incompatibility seems likely to occur only hidden inside event horizons, so it is a problem for the theories rather than a practical problem for all of us who are not actually rapidly approaching death within a black hole -- there also may be consequences for as-yet-undiscovered ancient tiny black holes, or stellar black holes many trillions of trillions of years in our future, so again we can take our time to understand the theoretical conflict). A bit more technically, the problem arises in perturbative approaches to QFT on curved spacetime: at low energies and low curvatures we have a fairly small number of correction terms which can be written out as a https://en.wikipedia.org/wiki/Taylor_series https://en.wikipedia.org/wiki/Taylor_series which we can truncate because the higher-order terms are demonstrably irrelevant. As we increase energies and curvature, irrelevant terms become marginal, then relevant; additionally, we start having to add more non-irrelevant terms. https://en.wikipedia.org/wiki/Renormalization https://en.wikipedia.org/wiki/Renormalization allows us to squash some of these terms together, but eventually we get an overwhelming growth of non-ignorable corrective terms and lose the ability to make predictions using this approach. This breakdown in perturbative renormalization ("perturbative quantum gravity" [2][3]) gives a useful qualitative definition of "strong gravity": it's where the perturbative approach breaks down. In terms of Feynman diagrams, it's where loops of gravitons enter into the picture; a bit more colloquially, it's where "gravitation's self-gravitation starts becoming non-ignorable". Although not a dead area of research, looking for ways to make renormalization work for strong gravity is less fashionable than looking for non-perturbative quantum gravity that (a) matches perturbative quantum gravity right up to the weak-side boundary of strong gravity, including classical General Relativity in weak gravity, (b) is calculable in practice, and (c) solves other non-gravitational problems that plague high energy particle physics that are amenable to testing, since we probably can't extract observational or experimental data from regions of strong gravity. Additionally, classical General Relativity fairly generically predicts the presence of gravitational singularities in spacetimes with significant amounts of matter[4]. Such singularities destroy the total predictability of the entire spacetime from a total sample of all the variables on an arbitrary slice across the whole space at a given time coordinate. In other words, there's an incompatibility between classical General Relativity and traditional initial values surfaces approaches to solving physics problems. This problem worsens in the presence of Quantum Fields because of Hawking Radiation: instead of a literal singularity there is instead a trapping structure that evaporates (or mostly evaporates, in "remnant" proposals) in the far future of most black hole systems. But the matter that is released in the evaporation cannot be predicted from the matter that was thrown into the black hole before evaporation, and at late times we lose the ability to account for quantum entanglements that existed when the black hole was growing. Unfortunately there are numerous black hole candidates in our universe, which we also know is filled by matter representable by quantum fields. Although this is not strictly an incompatibility of General Relativity and Quantum Field Theory, quantum physicists are very keen on preserving https://en.wikipedia.org/wiki/Unitarity_(physics) https://en.wikipedia.org/wiki/Unitarity_(physics) which is lost in black hole evaporation as is understood today. Preserving unitarity in the presence of strong gravity is a fourth goal of modern research into quantum gravity. - -- [1] e.g. Parker & Toms, QFT in Curved Spacetime (2009), https://books.google.co.uk/books?id=5nNuGMBBTjMC&dq=L.+Parker,+D.+Toms+(2009).+Quantum+Field+Theory+in+Curved+Spacetime:+Quantized+Fields+and+Gravity https://books.google.co.uk/books?id=5nNuGMBBTjMC&dq=L.+Parke... [2] http://www.staff.science.uu.nl/~hooft101/lectures/erice02.pdf http://www.staff.science.uu.nl/~hooft101/lectures/erice02.pd... [3] https://en.wikipedia.org/wiki/Canonical_quantum_gravity https://en.wikipedia.org/wiki/Canonical_quantum_gravity [4] https://en.wikipedia.org/wiki/Raychaudhuri_equation https://en.wikipedia.org/wiki/Raychaudhuri_equation is a good place to start
gizmo686 6y ago
Quatom mechanics doesn't really have a concept of space-time. The notion of space-time is entirely a construction of relativity; and the two theories have yet to be unified. Collapsing the wave function doesn't bring a system into the domain of relativity. That happens at a fuzzy point where a system become massive enough for relativistic effects to become significant. In thoery, we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity. There is semiclassical gravity; which essentially says that the quantum fields described quantum mechanics occurs in the curved spacetime of relativity. This is (by design) just an approximation of the still unknown theory of quantum gravity; and we don't have good experimental evidence telling us how accurate of an approximation it is.
- c1ccccc1 6y ago
  Quantum mechanics doesn't work well with general relativity (gravity), but it works just fine with special relativity. Special relativity still has a concept of spacetime, it's just that the spacetime is flat, not curved like in general relativity. (In fact, you can even do quantum mechanics in curved spacetime, as long as the spacetime has a predefined fixed curvature. But in GR, the curvature depends on how the matter and energy inhabiting the spacetime are distributed. That is what gives quantum gravity theorists trouble.)
- tsimionescu 6y ago
  Quantum mechanics is fully unified with special relativity, and has a clear concept of spacetime. The Dirac equation was discovered in 1928 and was the key to solving this problem. This means that quantum mechanics is fully compatible with time dilation at large speeds, that it respects the limits of the speed of light (current article notwithstanding) etc. The only incompatibility is between quantum mechanics and general relativity - quantum mechanics can't work with the general relativityequations for a curved spacetime or for the gravitational effects of particles being in multiple places at once. These are the things that a theory of quantum gravity must solve.
- raattgift 6y ago
  > Quatom mechanics doesn't really have a concept of space-time The Standard Model of Particle Physics incorporates the Poincaré group, which is the isometry group of the flat spacetime of Special Relativity, so it has an exact concept of spacetime built right into the formulation. Quantum mechanics and Special Relativity were unified in the 1920s by Dirac. Solutions for some curved spacetimes came not much later, and are now taught in several textbooks. The problem is that we don't have a general solution for quantum mechanics on arbitrary curved spacetimes (and some curved spacetimes are known to make quantum field theories insoluble with current methods). I refer you to my sibling comment https://news.ycombinator.com/item?id=24877746 https://news.ycombinator.com/item?id=24877746 for more details. > (by design) just an approximation of the still unknown theory of quantum gravity Kind-of. It is manifestly an approximative approach because the equation includes "mean" angle-brackets around the stress-energy tensor, which, speaking roughly, indicate that the curvature is generated by the averaged value of the stress-energy generated by the quantum field(s) are used, rather than an exact value at each and every infinitesimal point in the solution. This "classicalizes" the source term of the classical curvature, erasing quantum effects. It is not really in the strictest sense an approximation to a theory of quantum gravity, however any candidate quantum gravity theory had better explain results from semiclassical gravity that find some support in astronomical observations. Contrasting approaches -- like canonical quantum gravity -- "quantumize" the metric, leaving the source term fully quantum mechanical and non-averaged, and results from such approaches also find some support in astronomical observations. These are arguably approximations to a full theory of quantum gravity since one can cast them as a series of terms similar to a Taylor series; the problem is that the set of such terms appears to grow without bounds as one takes energy-momentum into the "ultraviolet" regime (UV ~ extreeeeeemely high energy-momentum densities). Worse, the relative weight of the contribution of some of the far-from-leading-order terms grow stronger in the UV limit, so not only can't we just ignore them, we also can't apply perturbative renormalization. Fortunately this probably only happens inside black hole event horizons and near the big bang, one of which is probably not observable, and the other of which is at high enough individual energies that the Standard Model doesn't predict results even if their collective mutual gravitation (and the contribution of dark matter and other energy-densities) could be factored out. > we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity We can calculate the effects of a boost, even an ultraboost, on particles with mutually-entangled properties just fine thanks to the Poincaré invariance baked into post-Dirac relativistic quantum mechanics. If you were flying past from an entanglement experiment in deep space at ultrarelativistic speeds, one could predict your observed redshift (etc) of the entangled properties exactly with no worries. (If you were flying radially to or from an Earthbound experiment at ultrarelativistic speeds you might want to incorporate some corrections from the https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultraboost https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultrab... for greater accuracy. The post-Newtonian expansion leading-order corrections attributable to Earth's gravity will not be large; linearized gravity is enough. Errors from the next-to-leading-order corrections will not be measurable with current technology, and we can brute force calculate at least next-to-next-to-leading order corrections, which is good enough for accelerating down towards the surface of a neutron star, like the material that is blown onto the Hulse-Taylor binary members.
tsimionescu 6y ago
Relativistic quantum mechanics exists and is a complete theory - the Dirac equation shows how particles move taking into account the speed of light limit, and in the limit of small speeds reduces to the Schrodinger equation. Moreover, one of the most important results that confirmed entanglement is possible was the no-communication theorem, that proved that it is impossible to use entanglement to communicate faster than light. This is also suggests that wave-function collapse of an entangled system can't really be a physical phenomenon.
- tashi 6y ago
  > can't really be a physical phenomenon Can you say more about that? What are the alternatives to being a physical phenomenon?
  - sdenton4 6y ago
    Being a mathematical formalism which happens to nicely describe the reality, perhaps?
  - tsimionescu 6y ago
    If you want to learn more about this, it is usually referred to as "measurement problem". Basically, quantum mechanics is extremely accurate at predicting experimental results by using 2 completely separate rules: the Schrodinger equation on one hand, and the Born rule on the other. The Born rule is what is also referred to as wave function collapse: if you want to accurately predict what happens to a particle after it interacts with a detector (but NOT after an interaction with another particle), then you have to use the Schrodinger equation as a probability. Now the physical meaning of these 2 different rules are debated. In the standard (Copenhagen) interpretation of QM, it doesn't make sense to talk about the properties of particles until you measure them, so neither the wave function nor the Born rule can be given a physical meaning. In the MWI interpretation, all results of the Schrodinger equation exist in different worlds, so there is no collapse, the detector just finds out "in which world you live". In superdeterministic theories, the Schrodinger equation is just an approximation of a currently unkown fully deterministic theory of motion. In pilot-wave theory, the Schrodinger equation describes an actual wave that particles generate themselves (the motion of the wave and the motion of the particle influence each other); entangled particles are just particles that live on the same wave. There is no collapse here, but the wave from each particle exists in the whole universe and can change non-locally.

drdeca 6y ago

That doesn't seem to fit with my understanding all that well? Alternatively, I'm just not sure what you mean by saying that it ( wait, what is the "it"? "the quantum world"? But the world is the quantum world?) "exists outside of space time" . If one said "the number 3 exists outside of spacetime", that would make sense to me, as saying that it isn't a thing with a location in spacetime, but just a thing. But I don't think I know what you mean.

vez- 6y ago
The thing I think the original commenter was trying to get at is that spacetime (the mathematical model) and quantum mechanics (the mathematical model) for the most part are in no way unified. Things that happen in quantum mechanics are not necessarily explainable using spacetime. Although in general physicists believe a lot of things from spacetime for QM, like that information can't travel faster than light, it isn't actually baked into QM. That's my understanding at least.
- drdeca 6y ago
  By spacetime do you mean like, in a general relativity sense? Because aiui quantum field theory is quite consistent with special relativity.
- raattgift 6y ago
  The https://en.wikipedia.org/wiki/Dirac_equation https://en.wikipedia.org/wiki/Dirac_equation is now more than ninety years old and put quantum mechanics into the Minkowski spacetime of special relativity. There are several textbooks[1] covering extensions of this approach to curved spacetimes generally, and one will encounter the https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation#Gravitational_interaction https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation#... in graduate school settings. Quantum mechanics on some specific curved spacetimes are exactly Klein-Gordon solvable. The Standard Model of Particle Physics incorporates the Poincaré Group, which is the group of Minkowski spacetime ("flat spacetime") isometries. This means that the Standard Model particles are the same independent of where and when they are in empty flat spacetime (3 spacelike and 1 timelike translation invariances), their orientation (rotational invariance about the three spacelike axes), and they transform reliably under boosts (differences in constant velocity along the spacelike axes). So the Standard Model is defined by flat spacetime: and the causal structure of flat spacetime (in which the constant c plays a key role) is very much baked in. Studying modern quantum mechanics mostly means looking at patches of effectively flat spacetime in which there are particles of the Standard Model occupying different locations in the patch, boosted relative to each other, and interacting via the other mechanisms captured in the Standard Model's formulation. We inhabit a type of curved spacetime in which General Relativity guarantees at least an infinitesimal patch of exactly flat spacetime around every point in the universe. In regions with only gentle curvature -- like laboratories on the surface of the Earth, or in space probes in the solar system -- any curvature corrections to the assumed exactly flat spacetime of the Standard Model are tiny, because the region of effective (rather than exact) flatness is very large compared systems of particles under experimental study of their quantum behaviour. "Pretend it's flat" works exceedingly well in practice. When a researcher has to consider curvature (e.g. in relativistic massive objects like neutron stars) she or he can continue to work perturbatively against a flat-by-definition spacetime. The problems arise in the difference between a guarantee of a microscopic region of flat spacetime and an infinitesimal region of flat spacetime: if the radius of curvature is small compared to the spatial extent of a particle, things get ugly quickly, especially as we take the wavelength of the particle smaller (which means the energy of the particle climbs, and that is the sort of energy which creates spacetime curvature, so we get a nonlinear feedback, and classical General Relativity and Quantum Field Theory in Curved Spacetime make annoyingly different and incompatible predictions about what happens as one takes the limits of high particle energy and high curvature. Fortunately this incompatibility seems likely to occur only hidden inside event horizons, so it is a problem for the theories rather than a practical problem for all of us who are not actually rapidly approaching death within a black hole -- there also may be consequences for as-yet-undiscovered ancient tiny black holes, or stellar black holes many trillions of trillions of years in our future, so again we can take our time to understand the theoretical conflict). A bit more technically, the problem arises in perturbative approaches to QFT on curved spacetime: at low energies and low curvatures we have a fairly small number of correction terms which can be written out as a https://en.wikipedia.org/wiki/Taylor_series https://en.wikipedia.org/wiki/Taylor_series which we can truncate because the higher-order terms are demonstrably irrelevant. As we increase energies and curvature, irrelevant terms become marginal, then relevant; additionally, we start having to add more non-irrelevant terms. https://en.wikipedia.org/wiki/Renormalization https://en.wikipedia.org/wiki/Renormalization allows us to squash some of these terms together, but eventually we get an overwhelming growth of non-ignorable corrective terms and lose the ability to make predictions using this approach. This breakdown in perturbative renormalization ("perturbative quantum gravity" [2][3]) gives a useful qualitative definition of "strong gravity": it's where the perturbative approach breaks down. In terms of Feynman diagrams, it's where loops of gravitons enter into the picture; a bit more colloquially, it's where "gravitation's self-gravitation starts becoming non-ignorable". Although not a dead area of research, looking for ways to make renormalization work for strong gravity is less fashionable than looking for non-perturbative quantum gravity that (a) matches perturbative quantum gravity right up to the weak-side boundary of strong gravity, including classical General Relativity in weak gravity, (b) is calculable in practice, and (c) solves other non-gravitational problems that plague high energy particle physics that are amenable to testing, since we probably can't extract observational or experimental data from regions of strong gravity. Additionally, classical General Relativity fairly generically predicts the presence of gravitational singularities in spacetimes with significant amounts of matter[4]. Such singularities destroy the total predictability of the entire spacetime from a total sample of all the variables on an arbitrary slice across the whole space at a given time coordinate. In other words, there's an incompatibility between classical General Relativity and traditional initial values surfaces approaches to solving physics problems. This problem worsens in the presence of Quantum Fields because of Hawking Radiation: instead of a literal singularity there is instead a trapping structure that evaporates (or mostly evaporates, in "remnant" proposals) in the far future of most black hole systems. But the matter that is released in the evaporation cannot be predicted from the matter that was thrown into the black hole before evaporation, and at late times we lose the ability to account for quantum entanglements that existed when the black hole was growing. Unfortunately there are numerous black hole candidates in our universe, which we also know is filled by matter representable by quantum fields. Although this is not strictly an incompatibility of General Relativity and Quantum Field Theory, quantum physicists are very keen on preserving https://en.wikipedia.org/wiki/Unitarity_(physics) https://en.wikipedia.org/wiki/Unitarity_(physics) which is lost in black hole evaporation as is understood today. Preserving unitarity in the presence of strong gravity is a fourth goal of modern research into quantum gravity. - -- [1] e.g. Parker & Toms, QFT in Curved Spacetime (2009), https://books.google.co.uk/books?id=5nNuGMBBTjMC&dq=L.+Parker,+D.+Toms+(2009).+Quantum+Field+Theory+in+Curved+Spacetime:+Quantized+Fields+and+Gravity https://books.google.co.uk/books?id=5nNuGMBBTjMC&dq=L.+Parke... [2] http://www.staff.science.uu.nl/~hooft101/lectures/erice02.pdf http://www.staff.science.uu.nl/~hooft101/lectures/erice02.pd... [3] https://en.wikipedia.org/wiki/Canonical_quantum_gravity https://en.wikipedia.org/wiki/Canonical_quantum_gravity [4] https://en.wikipedia.org/wiki/Raychaudhuri_equation https://en.wikipedia.org/wiki/Raychaudhuri_equation is a good place to start

gizmo686 6y ago

Quatom mechanics doesn't really have a concept of space-time. The notion of space-time is entirely a construction of relativity; and the two theories have yet to be unified. Collapsing the wave function doesn't bring a system into the domain of relativity. That happens at a fuzzy point where a system become massive enough for relativistic effects to become significant. In thoery, we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity. There is semiclassical gravity; which essentially says that the quantum fields described quantum mechanics occurs in the curved spacetime of relativity. This is (by design) just an approximation of the still unknown theory of quantum gravity; and we don't have good experimental evidence telling us how accurate of an approximation it is.

c1ccccc1 6y ago
Quantum mechanics doesn't work well with general relativity (gravity), but it works just fine with special relativity. Special relativity still has a concept of spacetime, it's just that the spacetime is flat, not curved like in general relativity. (In fact, you can even do quantum mechanics in curved spacetime, as long as the spacetime has a predefined fixed curvature. But in GR, the curvature depends on how the matter and energy inhabiting the spacetime are distributed. That is what gives quantum gravity theorists trouble.)
tsimionescu 6y ago
Quantum mechanics is fully unified with special relativity, and has a clear concept of spacetime. The Dirac equation was discovered in 1928 and was the key to solving this problem. This means that quantum mechanics is fully compatible with time dilation at large speeds, that it respects the limits of the speed of light (current article notwithstanding) etc. The only incompatibility is between quantum mechanics and general relativity - quantum mechanics can't work with the general relativityequations for a curved spacetime or for the gravitational effects of particles being in multiple places at once. These are the things that a theory of quantum gravity must solve.
raattgift 6y ago
> Quatom mechanics doesn't really have a concept of space-time The Standard Model of Particle Physics incorporates the Poincaré group, which is the isometry group of the flat spacetime of Special Relativity, so it has an exact concept of spacetime built right into the formulation. Quantum mechanics and Special Relativity were unified in the 1920s by Dirac. Solutions for some curved spacetimes came not much later, and are now taught in several textbooks. The problem is that we don't have a general solution for quantum mechanics on arbitrary curved spacetimes (and some curved spacetimes are known to make quantum field theories insoluble with current methods). I refer you to my sibling comment https://news.ycombinator.com/item?id=24877746 https://news.ycombinator.com/item?id=24877746 for more details. > (by design) just an approximation of the still unknown theory of quantum gravity Kind-of. It is manifestly an approximative approach because the equation includes "mean" angle-brackets around the stress-energy tensor, which, speaking roughly, indicate that the curvature is generated by the averaged value of the stress-energy generated by the quantum field(s) are used, rather than an exact value at each and every infinitesimal point in the solution. This "classicalizes" the source term of the classical curvature, erasing quantum effects. It is not really in the strictest sense an approximation to a theory of quantum gravity, however any candidate quantum gravity theory had better explain results from semiclassical gravity that find some support in astronomical observations. Contrasting approaches -- like canonical quantum gravity -- "quantumize" the metric, leaving the source term fully quantum mechanical and non-averaged, and results from such approaches also find some support in astronomical observations. These are arguably approximations to a full theory of quantum gravity since one can cast them as a series of terms similar to a Taylor series; the problem is that the set of such terms appears to grow without bounds as one takes energy-momentum into the "ultraviolet" regime (UV ~ extreeeeeemely high energy-momentum densities). Worse, the relative weight of the contribution of some of the far-from-leading-order terms grow stronger in the UV limit, so not only can't we just ignore them, we also can't apply perturbative renormalization. Fortunately this probably only happens inside black hole event horizons and near the big bang, one of which is probably not observable, and the other of which is at high enough individual energies that the Standard Model doesn't predict results even if their collective mutual gravitation (and the contribution of dark matter and other energy-densities) could be factored out. > we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity We can calculate the effects of a boost, even an ultraboost, on particles with mutually-entangled properties just fine thanks to the Poincaré invariance baked into post-Dirac relativistic quantum mechanics. If you were flying past from an entanglement experiment in deep space at ultrarelativistic speeds, one could predict your observed redshift (etc) of the entangled properties exactly with no worries. (If you were flying radially to or from an Earthbound experiment at ultrarelativistic speeds you might want to incorporate some corrections from the https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultraboost https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultrab... for greater accuracy. The post-Newtonian expansion leading-order corrections attributable to Earth's gravity will not be large; linearized gravity is enough. Errors from the next-to-leading-order corrections will not be measurable with current technology, and we can brute force calculate at least next-to-next-to-leading order corrections, which is good enough for accelerating down towards the surface of a neutron star, like the material that is blown onto the Hulse-Taylor binary members.

tsimionescu 6y ago

Relativistic quantum mechanics exists and is a complete theory - the Dirac equation shows how particles move taking into account the speed of light limit, and in the limit of small speeds reduces to the Schrodinger equation. Moreover, one of the most important results that confirmed entanglement is possible was the no-communication theorem, that proved that it is impossible to use entanglement to communicate faster than light. This is also suggests that wave-function collapse of an entangled system can't really be a physical phenomenon.

tashi 6y ago
> can't really be a physical phenomenon Can you say more about that? What are the alternatives to being a physical phenomenon?
- sdenton4 6y ago
  Being a mathematical formalism which happens to nicely describe the reality, perhaps?
- tsimionescu 6y ago
  If you want to learn more about this, it is usually referred to as "measurement problem". Basically, quantum mechanics is extremely accurate at predicting experimental results by using 2 completely separate rules: the Schrodinger equation on one hand, and the Born rule on the other. The Born rule is what is also referred to as wave function collapse: if you want to accurately predict what happens to a particle after it interacts with a detector (but NOT after an interaction with another particle), then you have to use the Schrodinger equation as a probability. Now the physical meaning of these 2 different rules are debated. In the standard (Copenhagen) interpretation of QM, it doesn't make sense to talk about the properties of particles until you measure them, so neither the wave function nor the Born rule can be given a physical meaning. In the MWI interpretation, all results of the Schrodinger equation exist in different worlds, so there is no collapse, the detector just finds out "in which world you live". In superdeterministic theories, the Schrodinger equation is just an approximation of a currently unkown fully deterministic theory of motion. In pilot-wave theory, the Schrodinger equation describes an actual wave that particles generate themselves (the motion of the wave and the motion of the particle influence each other); entangled particles are just particles that live on the same wave. There is no collapse here, but the wave from each particle exists in the whole universe and can change non-locally.