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Physicists rewrite a quantum rule that clashes with our universe
- dls2016 4y agoDang, I did my phd in L2-based spaces... completely worthless now!
- trhway 4y agoC'mon. The L(2+eps) of expanding universe is approximated very well locally by L2.
- AnimalMuppet 4y agoOnce more, in English? (Or maybe in ELI5-speak?)
- sp332 4y agoIt may not describe the entire universe, but it's a useful approximation for short distances. Like pretending the earth is flat.
- Groxx 4y agoOr assuming spherical cows.
- quickthrower2 4y agoThe earth is flat for mapping say a small town?
- tgv 4y agoL2 is also known as Euclidean space. It says the length of a vector is the square root of the sum of the squares of its components. There are other ways of defining vector length (or distance). E.g., in L1 is the sum of the absolute value of the components. The way distance is measured changes the properties of a space. E.g., in L2, Pythagoras is trivially true, but in L1 the hypotenuse would be as long as the sum of both other sides. That has far reaching consequences. E.g., in L1, you can't take a shortcut. Wikipedia is not your friend, it seems. It's just terse definitions. Perhaps other math sites are more helpful.
- dls2016 4y agoAnd my original "joke" is that the Schrodinger operator is unitary on L2 spaces (which is like a mathematical statement of conservation of "energy"), so if we're throwing out unitarity then I may as well throw out my phd. I actually studied dispersive pdes (Schodinger, KdV, etc.), though not with a computer. In that study, the properties of the Fourier transform on L2-based spaces are very important. The other joke is a that I do software now, so of course the phd was useless, haha!
- AnimalMuppet 4y agoAh, that. OK. I know it under a different name (2-norm or 2-metric).
- gus_massa 4y agoDon't burn your phd yet. They are embedding the Hilbert space that represents (is?) the current universe in a larger Hilbert space that represents (is?) the universe in the future. They change the "size"[1], but they don't change the L2 norm. [1] The dimension of both is probably infinite, but one is a proper subspace the other.
- Bolkan 4y agohttps://youtu.be/TG15s3Brbrw https://youtu.be/TG15s3Brbrw
- martin1975 4y agoSo is the rule or the universe off? Or is there something else missing to a more complete description of the quantum universe?
- AnimalMuppet 4y agoThe fine article argues that it's the rule that's off - that the universe that exists doesn't actually do unitarity, because of the expanding universe. Well, you know, given that the problem is reconciling QM with general relativity, this seems like a very interesting direction to pursue.
- db48x 4y agoNo, it’s clearly the universe that is wrong. :P
- quickthrower2 4y agoWorks on my universe!
- danwills 4y agoI found this fascinating! Unitarity does seem to suggest that the future somehow equals the past, which does seem to leave a bit of explaining to do (why would time exist/happen at all?) I also like the way that the new 'isometry' method resolves this by extending into a new dimension. It reminds me of the idea of the self-organisation of space (from previously dimensionless information) proposed by process-physics back in the 90s.
- tandr 4y agoWhat is "process-physics", what does it deal with, sorry?
- toombowoombo 4y agoRecently stumbled on the "process philosophy" concept and it means something in the lines of: the world is not made up by entities, but it's made up from dynamic transformations. Basically the world doesn't have matter at its base, but processes. It's still an idea in progress of being understood for me, but seems quite cool stuff. I heard it being mentioned that it might be linked with quantum field theory and somehow with string theory also, but I didn't yet understand how. Maybe process physics is different tho.
- AlessandroF6587 4y agoMaybe process informatic is functional programming
- danwills 4y agoProcess Physics does include some initial ideas/structures that do feel a bit like functional programming I agree but I think that actually it swings far away from that once the rubber of the idea (speculatively, of course) hits the road. Specifically the way that it explicitly avoids using syntactic information (ie anything symbolic (like how space is symbolic in the standard model)) and instead models the universe with only semantic (indeed ultimately self-referential) information instead. This is curiously similar to Neural-networks where the details of how it arrives at a result may be very well hidden in the details of the entire behavior of the network. A framework to think about bootstrapping the universe when there was no universe before is kinda a major component of the whole PP thing in my opinion. This does seem to move the idea to a quite different realm than FP in my opinion. (maybe just a point of view thing?), but I imagine it more like some incredibly-infinitely parallel process like GOL/reaction-diffusion (without the virtual aspect we usually have with our normal computers) or even something more turing-machine-like (anything with turing-universal compute-capability can follow rules, right?) I'm not trying to sound authoritative about this at all! I am certainly not a physicist (Visual Effects Artist/Pipeline/Teacher!), this is just something I took an interest in and I don't think it got anything approaching the reception that it perhaps could've had if there were a little more open-minded-ness and willingness to take conceptual leaps, in the surrounding academic community.
- plaguepilled 4y agoPossibly a dumb question, but why does that article state a photon's wavelength increases with time? I am paraphrasing the line where they explain how expanding universes suggest black holes cause photons in the thought experiment. Also, if we do chuck out unitarity, does that mean we can "break" experiments like stern Gerlach by just making them take a really long time?
- dtx1 4y agoThe Expansion oft the universe would cause a slow increase in wavelengh over time
- dvsfish 4y agoDoes this mean that the notion of conservation of energy is actually preserved? Everywhere says its not except on local scales but this almost sounds like dark energy/the creation of more space is fuelled by light.
- andrewflnr 4y agoEnergy conservation is... tricky. Under Noether's Theorem it's guaranteed by time translation symmetry, which is kind of sketchy at cosmological scale. My understanding is that it can be violated under conditions of changing gravitational fields or somesuch, but don't really understand what specific circumstances do the trick. Ed: don't get hung up on "expansion of space is fuelled by light" or whatever, they only picked a photon for their thought experiment because it was easy to reason about.
- 9991 4y agoThe total “energy” of all photons in the universe is declining, but the acceleration is increasing. Hard to believe the first is causing the second.
- absolutelynobo 4y agoYou can easily break Stern-Gerlach by spreading the “measurements” super far apart, so far that interactions with other matter destroys the effects of the first measurements. It’s incredibly easy to lose coherence in other quantum experiments as well.
- deleted 4y ago[deleted]
- cycomanic 4y agoI'm not a quantum physicist, but it seems like theoreticians always resolve to adding more dimensions when they can't solve a problem. In a way this sounds like string theory 2.0. Also it might not be clear to every one, but unitary also implies energy conservation, I assume isometry also conserves it otherwise it would be a pretty big ask to adopt it.
- the_cramer 4y agoI have a very similar feeling, when i read about quantum superposition. It feels like a super theoretical theory. If you don't measure something it can be either state, but if you measure something it has a state, just like a entangled other piece you did not measure before. Knowing nothing in-depth about this topic, it seems like a philosophical problem. The cat is dead and alive because you just don't know it. But it surely is one or the other, isn't it? edit: maybe I'm confusing superposition and entanglement. I thought of these to be a similar problem in physics.
- bowsamic 4y agoThe principle of superposition is that any addition of quantum states is also a valid quantum state. For example, you can have a system that has a state which is both "the particle is at x = 1m" and "the particle is at x = 2m". What really happens physically when you measure the position of the particle is not specified by the theory, but the Copenhagen interpretation says that one of those positions will be chosen depending on the coefficient in front of each state, e.g. if we have a state |psi> = 1/sqrt(2) |x = 1m> + 1/sqrt(2) |x = 2m> then we get either 1m or 2m with 50/50 probability. Then if we measure 1m we will find that afterwards the state will be |psi> = |x = 1m>. Again, what actually happens during this process is not well understood by physics yet, and also is one of the things that differentiates different interpretations of quantum mechanics, so yes that is "philosophy". > The cat is dead and alive because you just don't know it. But it surely is one or the other, isn't it? The Copenhagen interpretation says it is both dead or alive, or that the above particle really was in two places at once. Other interpretations, such as the Many World Interpretation (MWI), say different things. For example, MWI says that upon measurement the universe actually branches into many universes, one for each possible outcome, and that we live in one such universe (the universe with a living cat, for example), but that the state itself is not ontologically a mixture of those two orthogonal possibilities. Entanglement is a very different beast. Basically it means that two systems interact such that measurements on them are highly correlated, i.e. by measuring something on system A you immediately know something about system B, even if they are very far apart. Again, how you interpret entanglement (i.e. whether or not "spooky action at a distance" actually happens) depends on your interpretation of quantum mechanics.
- kleiba 4y agoWhen particles interact, the probability of all possible outcomes must sum to 100%. Unitarity severely limits how atoms and subatomic particles might evolve from moment to moment. It also ensures that change is a two-way street: Any imaginable event at the quantum scale can be undone, at least on paper. I know, I'm just a mesely computer scientist and not an honorable physicist, but these two sentences from the third paragraph don't make sense to me. Why does the fact that the you cannot exceed a probability of 1.0 when considering all possible outcomes (which is typically one of the foundational axioms that build the basis of the definition of probability) be limiting? How does the bit about "can be undone" (at least at quantum scale!) follow? What is meant by "at least on paper"?
- whimsicalism 4y agoI'll try my best but it has been a few years since quantum for me. Basically, over time a quantum system can be transformed by applying an operator to the original state to yield the new state. These operators can be represented as a "transformation" between one quantum space to another (the one at the future time). Because these transformations preserve probability (which is like a norm of the system), they must have a property known as being unitary. Unitary matrices are invertible, so this is what they mean by "can be undone."
- currenciessfe 4y agoSomething related. In classical computers you can do: X = 4 X = 5 In quantum computers this sequence of operations is impossible, because the program needs to respect unitarity and need to be able to be undone/run backwards. But you can't run this program backwards because the second operation (=5) completely erases the information from the first step (=4)
- Maro 4y agoClassically, isn't the reverse program just (?): X = 5 X = 4 I feel like 2 things are being mixed. In QM/QC, the operators must be unitary, which roughly means they "rotate" states and their inverse "rotation" exists, so (in principle) the reverse operation can be performed; so (in principle), we can construct the reverse operations, execute them, and kinda reverse the time evolution. But it doesn't mean that the quantum state (at time t) of the system encodes the time history (t'<t) of the state.
- hinkley 4y ago> But the extra photon wasn’t created by that special process, so instead of disappearing when you turn back time, its wavelength will eventually get impossibly small, concentrating its energy so greatly that the photon collapses into a black hole. This creates a paradox, absurdly implying that — in this fictional, expanding universe — microscopic black holes convert into photons. The thought experiment suggests that a naïve mashup of unitarity and cosmic expansion doesn’t work. The Laws of Thermodynamics state that you can’t create a photon from nothing, so isn’t introducing an “extra photon” into the universe already a paradox? Who would be the least bit surprised that paradoxes create paradoxes?
- lapsis_beeftech 4y agoIf the supposed experimental conditions cannot plausibly occur in nature I don't think it's a valid thought experiment.
- prox 4y agoAfaik particles can seem to appear “out of nothing”, random in nature. They are called virtual particles. I believe the effect is very pronounced in the Casimir Effect https://en.wikipedia.org/wiki/Casimir_effect https://en.wikipedia.org/wiki/Casimir_effect The analogy is imprecise though, according to people know the maths/physics behind it, maybe someone can answer it better than me.
- bowsamic 4y agoThe Casimir effect is better explained by the zero point energy of the quantum vacuum, rather than "virtual particles". The latter is not necessary to explain it
- cwillu 4y agoVirtual particles are not particles. https://profmattstrassler.com/2011/10/10/virtual-particles-not-particles-at-all/ https://profmattstrassler.com/2011/10/10/virtual-particles-n...
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- michaelwww 4y agoI'm not a physicist but how much of modern physics is real and not just math?
- bowsamic 4y agoI'm a postdoc in theoretical quantum optics. The answer is: both all of it and a none of it. All of it is real in the sense that Quantum Mechanics has been aggressively and extensively tested against measured observations of reality and has not yet found a discrepancy with it. None of it is real in the sense that it is all a mathematical model that is supposed to make predictions about reality.
- michaelwww 4y agoInteresting. So there are mathematical systems that describe reality extremely well and this is testable. There's beauty in that, like the sun flower and Fibonacci. I was looking for something to rekindle my interest in math and this might be it.
- orlp 4y ago> Quantum Mechanics has been aggressively and extensively tested against measured observations of reality and has not yet found a discrepancy with it That isn't true. Here's a discrepancy: the universe appears to be following the laws of general relativity, but quantum mechanics does not account for this and returns wrong answers. Here's another discrepancy: quantum field theory predicts an energy density of the vacuum off by 120 orders of magnitude of the observed value. "All models are wrong, but some are useful." But it's disingenuous to claim we haven't even found any discrepancies and that it appears to be a perfect model.
- bowsamic 4y agoSorry, I meant only non-relativistic quantum mechanics and quantum optics. I don't know anything about QFT or GR
- solarist 4y ago
- renox 4y agoI wonder if there is an experiment which could test this "rule"?
- _cs2017_ 4y agoThe article didn't really explain why expanding universe is in any kind of a conflict with unitary. The fact that a randomly added photon would become a black hole in the past isn't convincing since one can't just add a particle out of nowhere.
- currenciessfe 4y agoSurely the physicists are aware of such a trivial fact. So the photon example is probably a simplification of the real example which does sort of work.
- codeflo 4y agoYes, but we’re discussing the article, not the mind of the physicist. Stating “Surely they have an answer” doesn’t give the answer.
- alecst 4y agoI think that’s the gist actually. Unitarity does seem to raise problems in the cosmos (information loss) but naively violating it by adding a photon gets you this ridiculous paradox of black holes turning into photons. So if you’re going to relax the unitarity assumption, you have to do it carefully. I guess this is their program with isometry.
- raattgift 4y agoIt probes the question, "is the theory stable under small perturbation?", which is almost always a good question. Stability here means that the effects of introducing a small perturbation are proportional to the perturbation itself. Unitarity implies this kind of stability. Perturbation theory has been an important tool in physics for hundreds of years <https://en.wikipedia.org/wiki/Perturbation_theory#History https://en.wikipedia.org/wiki/Perturbation_theory#History>, and randomly adding a photon to a known universe and tracing out its effects is a perfectly reasonable application of it. It amounts to a "What if?" story but with mathematics and ideally some rigour. "What if we had a universe described by the Standard Model of Particle Physics, and the Standard Model of Cosmology, and introduced a single photon at various energies and at various times? How does that change the universe? Can we do better than just 'materialize' it out of thin air, by giving it some consistent back-story/history, no matter where we 'materialize' it and no matter what energy it has at that materialization point? Can we do all of the above within the constraints imposed by the two standard theories?" In an expanding universe, the broad family of theories discussed in the article seem to be only semi-stable, breaking the world in one direction even given only a tiny perturbation. Small perturbations practically anywhere in the expanding universe all lead to small future effects, but under time reversal may lead to large past effects (or equivalently, our small perturbation can only have a consistent history if produced by an extreme event). In the direction where the universe's matter gets ever thinner and colder, the small-perturturbation-photon ("spp") gets redder and redder, and might travel eternally without interacting without interacting with anything else. We can effectively guarantee that by introducing our spp in the extremely distant future, when there is less than one galaxy cluster per Hubble volume. Coupled to the expansion, the spp's wavelength grows to cosmological lengths and it traverses increasingly empty space, and for all we know it could continue to evolve that way eternally, growing ever redder (wavelength increasing) and with ever decreasing probability of interaction. Even if it were to interact with some other matter, the effect would be diminishingly tiny over time. But in the opposite timelike direction, over time the probability of interacting with something else grows. It can't fly to the eternal past because there is dense structure in the past, so the probability of interaction increases. That interaction will be with the ever hotter gamma ray the backwards-in-time spp evolves into. Moreover that hot gamma ray can't grow ever bluer if there is a minimum wavelength. So we've already revealed some shortcomings in the "ultraviolet completion" of the Standard Model as long as the spp is introduced far enough into the big bang's future and allowed to travel back in time with the contraction (time-reversed expansion) of the universe. We can also ask about whether an spp's earliest state and latest state are physically plausible. The far future of our universe will have lots of very low frequency photons zipping through practically empty space; the spp is not physically different from them, and if we looked we could probably find a photon with a "natural" origin in the system that we perturbed with the spp such that the spp and the "natural" photon are indistinguishable. We can even start with a super-hot gamma ray photon as our spp and have a very good chance that it will simply cool down (gravitationally redden) in the future direction, eventually becoming just like other low-frequency photons. It barely matters where or when we "initially" introduce a forward-in-time-travelling gamma ray spp, so long as it has an unobstructed path to deepest space. So the spp's late times are perfectly plausible. The early times however require us to take care in where we introduce the spp and how long its wavelength is "initially" (at the point where we introduce it). If it's very short wavelength then very soon before the "initial" introduction, the backwards-in-time travelling spp hits the wall in our understanding of the extremely-high-energy behaviour of the Standard Model. If the "initial" introduction is too far in the future then even a radio-frequency spp will blueshift so much that it will hit the wall. We don't see arbitrarily high-energy gamma rays in our sky, so our spp might be pretty easy to distinguish from any "mere" <https://en.wikipedia.org/wiki/Ultra-high-energy_gamma_ray https://en.wikipedia.org/wiki/Ultra-high-energy_gamma_ray> with produced naturally in the universe we are trying to negligibly perturb. The article's line trying to summarize Giddings, "... its wavelength will eventually get impossibly small, concentrating its energy so greatly that the photon collapses into a black hole" captures the idea above, making an educated guess about the possibility of a minimum wavelength for a photon. But the point that wasn't captured is that a small perturbation doesn't raise any theoretical questions in one timelike direction, but very likely does in the other timelike direction. The feature associated with this "hey, did we break the entire theory by adding just a single low-energy particle?" is the expansion of space in one timelike direction / the contraction of space in the opposite timelike direction. If we have a non-expanding space, then there will be no cosmological redshift, so our "initial" photon's wavelength is the same as its final wavelength, in both directions of time and out to eternity. The small perturbation photon's effects remain proportionately small everywhere and everywhen (rather than that being only the case practically everywhere in the future, and only in some places in the past).
- denton-scratch 4y agoIANAP. The article says that as the Universe expands, "new space" gets created. is that correct? I thought it was space itself that expanded. I didn't get the reasoning, but the Paradox of the Irreversible Photon seems to be an implication of this creation of new space. I find the article frustrating, because I can't follow the reasoning, because they've left out critical steps. I wonder where I can find an explanation of this stuff that I can understand.
- pfortuny 4y agoIt is indeed frustratingly oversimplified and abstruse, in my view. Space “expanding”: imagine a 10cm ruler (with markings) such that the markings “compress”. Now you have the same ruler but “longer”. That is what is meant by space “expanding “. (in some sense, obviously).
- pmontra 4y agoOK, the expansion of universe creates new space but why should it create photons to fill that space? Or why isn't the total energy still a constant (a new photon there one less photon here)?
- raattgift 4y agoThe total energy of what? In general it is hard to assign a total energy to a universe in General Relativity. This is a FAQ <https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_...>. To that we can add that we just don't know enough about our universe -- how big is it? how much matter is in it? -- because we can only see a fraction of the total universe both because a lot of it has expanded away from our view and because our instruments are not yet good enough to pick out features obscured by dust and gas and/or by very low interaction with electromagnetism (doesn't create strong spectral emission or absorption lines). What we can do is consider the energy-density at a point in a general curved spacetime. That quantity can be subdivided into roughly the part that moves ultra-relativistically (including radiation like photons), that which moves slowly compared to that (including the overwhelming majority of protons and neutrons). From there we can justify a universal average because the universe is (at large scales) homogenous and isotropic: with a wide enough view everything looks the same, and in every direction. Once we have the average energy-density we can think of how it evolves in an expanding universe. Non-relativistic matter stays mostly clumped in galaxies and those separate, but because we take an average this means that non-relativistic matter's contribution to the energy-density at any point drops with expansion. Ultra-relativistic matter spreads everywhere, so it too dilutes, and additionally it gets colder (seen as e.g. a drop in the energy-density of photons at a point, which corresponds with a drop in a the average photon's frequency or equivalently a stretching of the average photon's wavelength; the latter might lead to an intuitive understanding that an average photon gets smeared over increasing numbers of points, so there is less photon or less photon-energy at any point). So far this is treating photons like classical particles, or even like discrete quantum particles. In physical cosmology, one would want to consider them as the field content of the electromagnetic field of the Standard Model, which is a relativistic quantum field theory (QFT). Often wanting to do it "properly" runs into tractability problems in calculations, but there are some important features of a QFT compared to a non-relativistic theory where there is some constant number of photons. The most important part is that last: in a QFT, the count of photons depends on the observer's acceleration. An accelerated observer sees more particles than a freely-falling, zero-angular-momentum, zero-force observer who cannot measure any acceleration. This is the Unruh effect. Both the accelerated observer and the unaccelerated one count correctly, and can calculate what the other observer counts, although each may have different explanations about why its count differs from the other's. The equivalence principle tells us that an observer standing on a gravitating object (like the surface of the Earth) sees most of the effects an observer in deep space accelerated by some propulsive mechanism. The energy-density at a point, in a QFT on curved spacetime, is an observer-dependent quantity. An accelerating expanding universe has tremendous spacetime curvature, and one result is that the particle-counts obtained by an observer depends on when the particles are counted, all other things being equal. A future observer will count more particles than a past one. (This is also how Hawking radiation works: an observer in the past of an evaporating black hole sees fewer particles than a later observer; those particles are mostly in the region near the black hole; by contrast a late-time cosmological observer will see "extra" or "new" particles at great distances). So, what can we say about the total photon content? Firstly, it's time-dependent. Secondly, it depends on how the observer is moving against the electromagnetic field in the appropriate QFT. Thirdly, it depends on detailed knowledge of the distribution of photons (practically impossible, so we average). Fourthly it depends on detailed knowledge of the expansion, curvature, and acceleration parameters of the expanding spacetime (in practice that's also hard to measure). Fifthly, it would depend on recovering details of the universe that are most likely inaccessible to us because of the expansion carrying that out of view, but also because the hot dense early days of our universe are electromagnetically opaque, and the hotter denser earlier moments of our universe probably have no photons at all (the start of the "electro-weak epoch"). Consequently, our best modelling is only approximations based on the information we have at any given moment. However, such modelling is amenable to perturbative methods, where we add a small difference "by hand" and trace out the consequences to the modelled universe. Adding a photon here does not require removal of a photon there, and in any rate the model should not keep the total photon count constant for general observers (if you hold it constant for a particular chosen observer or family of observers, it won't be constant for other, different observers). So for "Eulerian" observers freely floating and looking at the expansion flow, adding a small perturbation like an "extra" photon should not make much difference. So instead we might want to treat the new photon as a "Lagrangian" observer, tracing out its peculiar experience of the expanding universe in which it exists. Taking that latter approach, we find that we can readily introduce a photon such that at its distant past it must have had a truly microscopic wavelength, and thus at the point it occupies it vastly exceeds the average photon-energy density of the universe. When we make a small perturbation we expect only small effects. But in this case, by adding a pretty vanilla photon at a point in the universe's distant future and tracing out the consequence, we find we require a big change -- the energy-density "bump" at the points in our test photon's past gets higher and higher, and it ultimately becomes a significant anisotropy and inhomogeneity that disrupts the justification of our averaging. In extremis, the result would be a part of the universe that stands out as obviously very different from what we see in the sky. Indeed, we can set things up so that we can't even make a prediction from Standard Model physics about the behaviour of the ultra-high-energy early photon that we expect to redshift into our test photon we added in as a small perturbation. In essence, this is just another example of the difficulties one might encounter when mixing quantum field theory with general relativity. General relativity does not in itself forbid even infinite energy at a point, but the behaviour of the Standard Model (a quantum field theory) is not well understood above about 10^14 GeV/c^2 energies. General relativity requires a constraint imposed upon choices of initial values, which in the case of our test photon it might get from an extension to the Standard Model, or which might be put in "by hand"; the Standard Model needs an ultraviolet completion for it to provide or at least justify the constraint.
- amluto 4y agoThis is an interesting theory for an expanding universe, but it seems to imply that the universe cannot contract: in a contracting universe, the time evolution operator would have to be a dimension-reducing isometry, which doesn’t exist. It would certainly be interesting if the true laws of quantum gravity don’t allow contraction regardless of initial conditions.
- deleted 4y ago[deleted]