joigus

Leonardo.

The concept of entropy I'm familiar with is itself an average on the particle or state index (sum to all microscopic entities), and does not depend on time or space (sum or integral to all positions). I've sometimes heard the words "local entropy production" but I've always found them confusing. It sounds to me like you're talking about fluctuations, but I don't see anything non-local in that either. Maybe I'm not understanding the problem either. I'm also aware that you know much more about kinetics than I do.

You're not. The nature of the problem is difficult. In order to show the effects of interference you need the wave to come together again so to speak. OTOH, the "electron in two different places" is a kind of language developed to try to express puzzling nature of the situation but it's not correct, actually, it's plain wrong, and it refers to the immediate past. While the wave was going through the slits, the wave must have split. But upon arrival and detection, the electron always appears as a particle. Here's the apparent paradox: Classical thinking makes you think "either the wave went through slit 1 or through slit 2". Not true! No matter how compelling it sounds. It's not "the electron went through slit 1 and 2 at the same time" either. This is nonsense. The conclusion is weaker (weaker assertions are safer): "Neither the electron went through slit 1, nor it went through slit 2 as long as no interaction was set to detect which slit the electron went through". It's about what you cannot say, not about what you can say. You must read Feynman chapters 1 and 2. Nobody has explained this as illuminatingly. Weaker assumptions are much more solid, much less likely to be incorrect.

The double slit experiment is about measuring the position of electrons one at a time. But all of the electrons respond to the same preparation (the same quantum state). So it's never two electrons at the same time. So the wave is the same, it represents a situation, reproduced exactly as before. But the electrons are one electron, and then another, and then another. Although in a way, you can think of it as the same electron doing different things under the same initial conditions. I hope that helps. It's the most common source of confusion in relation to this experiment. The first 2 chapters of Feynman's Lectures on Physics, Vol III are a classic.

No. Momentum and energy would make little jumps, but on the average they would be conserved. It's more involved with angular momentum. I see a problem with the conservation of angular momentum and the quantities related to the boosts, which have to do with the motion of the centre of energy of the system. But I see the problem if space-time were a regular lattice. The reason is that a regular lattice is very anisotropic, and angular momentum has to do with isotropy. Yes, you guys are right. At Planck scales some discretization must be introduced. I'm not sure it's just dividing space-time in little cells or a more sophisticated idea, like charts must be changed around cells the same way charts must be changed around a point in a sphere (for topological reasons, not because the sphere has any kind of discrete structure). Anyway... But last night when I wrote that comment, I started thinking about that too. Plus I tried to limit the sweeping character of my assertion when I said: What I meant is: I'm pretty sure that the discretization of space-time in a regular lattice does not sit well with rotational/boost symmetry, but if instead of a lattice, we had a random discrete structure, right now I see no reason why it wouldn't be possible. Yet, I've heard some physicists still use that argument (last time it was Nima Arkani-Hamed). I must come clean and say I strongly dislike the idea, but I have no robust argument against it, really.

Time is continuous in QM. It's the observables that are not continuous in general. There have been attempts to define a time operator, but they have been unsuccessful. The strongest argument I know against discrete space-time defined by elementary cells comes from reasoning in terms of continuous symmetry. You can define translation invariance as a discrete transformation, similar to what happens in a crystal lattice. If the points of the lattice were extremely close together, you wouldn't be able to tell the difference. But what's more difficult is to give consistency to rotation invariance and Lorentz transformation boosts (shifts from an inertial frame to another one moving at uniform speed with respect to the first, equivalent to a "hyperbolic shift") in a granular lattice. Lattice structures have nothing remotely similar mathematically to a group of such a high index of symmetry that can look like a continuous group at all scales. Keep in mind that rotations by a small angle shift far away points to arbitrarily large distances. And for all we know continuous rotations can't tell of any anisotropy of space-time at far-away distances. Edit: x-posted with @AbstractDreamer Edit 2: I'm having second thoughts about what I've just written. I'm sure this argument has been wielded by physicists, but... If the discrete time structure were not a regular lattice, but a random homogeneous and isotropic web of points, the symmetry argument would no longer be valid.

I went through an experience that reminds me of yours, so I understand. Some jobs seemed completely brain-dead to me. I would add selling insurance to your list, or selling anything, AAMOF. Well, don't do them, unless you absolutely need to. There must be a reason why you have that instinct. There might be other jobs. If you're good at teaching, try tutoring kids to keep science alive in your head while you make some extra money. Maybe jobs on offer are not in science, but there are other possibilities with more room for a certain creativity, using your analytic skills, etc., which is more science-like. And, as @Curious layman says, don't give up on studying and developing your intellect, it always pays off. Science is not just a way to make a living; it's an instrument to understand other people, your own life, the workings of absolutely everything. It transforms your life because it transforms the way you look at the world. That's my advice for what it's worth.

Good answer. +1 It must be some way in which your nervous system (autonomous or otherwise) cannot "not know" that you're about to get tickled.

I know. 🙄 But you only took up the questions having to do with death. Any insights into the question having to do with laughter? What makes you tick (or tickle)❓

1) Ants can’t die from falling Because of their body proportions and tough exoskeleton, an ant’s terminal velocity isn’t enough to kill or hurt it on impact. They can survive being dropped from the Empire State Building and walk away unharmed. 2) You can't kill yourself by holding your breath At the very worst, voluntary breath-holding will only lead to unconsciousness. 3) You can't tickle yourself ---------- 1) and 2) make a lot of sense. Why 3)?

Good point about the Higgs. +1 But in the case of the Higgs the "inflation" is making massless particles gain weight. Higgs is like free-delivery pizza for all citizens. The inflaton is rather like more elbow room for everybody. It affects the expansion parameter. Similar to free real estate for all citizens. And there's always the question of who put the ball at the top of the hill? The question of the initial conditions of the universe. But you make a very interesting point there. If the "ball" (the state of the Higgs phi) started on top of the hill, it must have liberated kinetic energy. I don't see it as inflation of space, but as liberation of kinetic energy, and thereby heating. Maybe that's already contemplated by cosmologists. But it's a very good argument. Maybe @Mordred has an interesting answer to it when he comes back. And radiation-dominated comes from the sequence of states after the big bang: 1) Universe opaque to radiation --> ending with decoupling of photons/charged particles 2) Energy density proportional to const./a (radiation dominated) 3) Energy density proportional to const./a3 (matter/dark matter dominated) 4) Energy density proportional to const. (vacuum dominated = the present epoch) where a is the expansion parameter and the Hubble parameter would be, \[H=\frac{\dot{a}}{a}\] I think you're using it right.

Everything we can detect is within the observable universe. Beyond the last scattering surface, the universe is opaque to radiation and we can't see anything, except maybe with gravitational waves; and beyond that, not even with gravitational waves. I agree that local objects bend space, but on average the universe looks very (spatially) flat. Around black holes and very massive objects you can detect local curvature, like e.g. Einstein rings, but the sphere of the sky looks pretty flat overall. What the paper that @iNow has linked to seems to imply is that within the observable universe the telescopes have detected large-scale lensing that must have to do with curvature within the horizon. That's what's very surprising to me. I'd like to follow up on that.

But inflation corresponds to slow-roll down the hill, so that's previous to reheating, and thereby previous to plasma epoch, baryogenesis, radiation-dominated epoch and everything else. The super-stretching is always previous to big-bang cosmology. And the inflaton looks nothing like a Higgs potential (Mexican hat). It's a completely different animal: Although there are other models. But the parts of the graph that has received good confirmation is the part with a gentle slope and the steep fall. The breaking of the symmetry that we commonly associate with the acquisition of mass came much later. After re-heating. V(phi) is the potential and phi is the inflaton. The V(phi) for the Higgs is very different: Online lectures that I found very useful to understand how the inflaton is very different from other scalar fields are (Lenny Susskind, Stanford): https://www.youtube.com/watch?v=gdFldkitkJA&list=PLvh0vlLitZ7c8Avsn6gUaWX05uD5cedO-&index=8 1h 15' 12'' to the end And then: https://www.youtube.com/watch?v=gdFldkitkJA&list=PLvh0vlLitZ7c8Avsn6gUaWX05uD5cedO-&index=8 The Higgs potential is a static situation. The inflaton dynamics, on the other hand, is analogous to the dynamics of a body falling under viscous drag. And the Hubble parameter plays the role of the friction.

Sure, but you have to provide the energy. That's what's happening when you hit a proton with an energetic particle. You put in the required energy for some of these virtual particles to persist. In the inflationary theory it's the inflaton field that provides that energy. But my next question would be: What's the status of the inflaton field? Is itself a quantized field, with quanta? Why wasn't it in a superposition of states when all that transition happened? I think there are possible answers to that. For example, superselection rules, which are strict prohibitions for superpositions of different quantum numbers to exist. But the whole thing becomes more and more contrived... The inflaton field is acting like the physical element that defines the fate of these fluctuations. It's kind of jerry-built. Successful, useful, very impressive to be sure, but it doesn't give you anything like this feeling of inevitability that you normally demand of fundamental theories. Like something remains to be understood.

This is actually, IMO, an outstanding question, because I haven't the faintest idea how you would apply the principles of the quantum theory of measurement to the vacuum. I don't suppose you can do that. Certainly, as there were no real particles, only those ephemeral virtual states, how did something actually happen? Nothing would qualify as an observer or as an apparatus. Decoherence is not it, IMO, because I don't know of any instance in which the vacuum can be argued to bring about decoherence and thereby qualifying as producing a measurement. This is a part of the quantum theory of measurement that's slipped into oblivion: the problem of the pointer positions. What physical tag says that something, and not something else, has actually happened? What tips the arrow? If anybody knows of any answer to that I would be the first to thank them, because I've longed to know for more than 20 years. It was very frequently referred to in the old papers and books about measurement, but no longer is. Old papers and books: https://press.princeton.edu/books/hardcover/9780691641027/quantum-theory-and-measurement

I no longer think a quantum theory of gravity is likely to happen. Not the canonical way, and not with Feynman diagrams and renormalization the traditional way. Maybe a more topological language for QFT/gravitation has to be developed. I do believe that the holographic principle partially grasps something very surprising about gravitation. My own intuition guided by comments, lectures, reflections and papers of other physicists is that something very fundamentally different happens at Planck's scales that must be interpreted in some new way, maybe that the interior of a very small region of space-time no longer makes sense. Or maybe the distinction interior/exterior becomes fuzzy at that scale... But I'm old enough and battered by experience enough to accept whatever proves to be a better solution. If it just so happened that discreteness for space-time works better, so be it. I hope it's within my lifetime.

I suppose I agree with this, in some way, and I also think it goes deep. +1 My phrasing of it would be, "there's always something."

Oh, the Greek humanity!!!

Ok, but suppose that the naive idea of this "nothing" approached by mentally picturing the removal of things that happen to be there into nonexistence does not ultimately make sense. It's not about getting hold of these things (a planet here, a giant star there) and taking them somewhere else; it's more like snapping your fingers and decreeing that they never were. That's not an operation that you can do, or even think of doing. I think you guys know me by now. I'm very mathematically minded. I always try to write the equations we know to work and have them tell me something, suggest something to me. Not because I think I'm good at maths, but because I trust the equation more than my words or concepts. At some time in the past I read a book by George Gamow that quoted Dirac as saying "the equation knows best". I think that's one of the most brilliant thoughts in physics that's ever been formulated. Whenever you find conflict, you must stick to the equation and try to make sense of it. Right now, what the equations seem to suggest is that there is no simple formulation of "nothing". So, "what's the next best thing?", my question would go. And the most plausible next thing is either the remote-past "nothing" (quantum vacuum confined to a Planckian-size bubble, rolling down a hill, with no real particles) or huge extensions of interstellar space, devoid of matter, in the remote future, if the picture of the accelerated expansion of the universe is correct. Right there you've got two different pictures of "nothing". How can that be? So my conclusion would be: I'm puzzled by the fact that we can so easily conceive this nothingness (or we think we can: close your eyes and think of nothing), and yet the universe doesn't let us even get closer to it, or make sense of it. Different versions of nothingness or incremental approaches to it just doesn't add up in my mind. I also like the idea of ridding ourselves of the background. I'm sorry I'm not all that familiar with LQG. Although some of the ideas are attractive to me. It's the discretization of ST that I don't like.

Sorry, 50 e-foldings, not e50, meaning the universe multiplied its size by e (=2.718...) 50 times (at least). https://arxiv.org/pdf/1405.5538.pdf

Yes, you're right. But I do have lots of problems with the concept of nothing, because whenever I try to think about it, it's from some kind of somethingness. Following the current cosmological models, this quantum vacuum had to go through the slope of the inflaton field, and it had to have cooled before re-heating for billions upon billions of "years" (e50 plus e-foldings) so... Is the inflaton nothing? And the quantum vacuum? I don't know. I wouldn't even know how to get started trying to answer that kind of question. None of that seems like nothing to me. It's so similar to something that only someone who's an real expert about the something/nothing characterisation would be able to tell the difference.

Good point. The best explanation I can think of comes from classical relativistic mechanics, and it foreshadows the need for a quantum field theory, including "messenger particles" and vacuum polarization. 1) Classically, you cannot have a massive particle emit a photon 2) Classically, you cannot have a pair of particles appear from the vacuum Proof: 1) Particle at rest goes to particle + photon From conservation of momentum: \[\left(m,0,0,0\right)=\left(E,p,0,0\right)+\left(p,-p,0,0\right)\] \[m=E+p\] From Einstein's energy-momentum relation: \[\Rightarrow E^{2}-p^{2}=E^{2}+p^{2}+2Ep\Rightarrow\] So that, \[p^{2}=-Ep\Rightarrow\] So either, \[p=0\] (the particle does not decay) or else, \[p=-E\] Impossible, as we've assumed p>0 2) Particle-antiparticle pairs (from the vacuum) \[\left(0,0,0,0\right)=\left(E,p,0,0\right)+\left(E,-p,0,0\right)\] \[2E=0\] So E is zero, which is again impossible. --------------- There are more examples, but they all go to prove that particles that are produced at one point and annihilated at another are a mathematical impossibility from the classical POV. In the case of the massive particle sending a photon out, you need another charged particle coming nearby and absorbing that photon so that the uncertainty principle allows the intermediate particle go unnoticed. The closer both charged particles are, the more efficient this exchanging mechanism is, so that the force must decrease with the distance. If you think about it, it makes sense that it be an inverse square law. In the case of vacuum polarization, it is required that the pair disappears soon enough that the UP allows you to, again, get away with it (UP). These particles that appear at one point and disappear at another are what in quantum field theory corresponds to so-called "internal legs" of the Feynman diagrams. You can and must use them, they appear in the space-time picture as intermediate steps in the evolution of the overall quantum states, but they are ephemeral presences, doomed to be turned back into the vacuum or absorbed by real particles sooner rather than later.

I wish to clarify first that the animation is not mine. Also correct my grammatical mistakes: The first occurrence that I know of in the history of physics that something like the concept of changing physical laws appeared in physics was due to Dirac. He made the observation that different ratios of the most natural physical parameters in the universe (number of protons, size of cosmic horizons, number of photons, leptons, fundamental constants, like Newton-Cavendish' famous G, etc.) were very simple powers of a number the order of 1040. So Dirac thought something like "maybe all these constants are not really constants, but are related to the age of the universe by some simple power law and they are changing with cosmic time". Then the idea fell out of favour and something like that kind of reasoning has seen a re-birth, mainly possibly spurred by Alan Guth and followers. The question of meta-laws (using words I've heard to Lee Smolin) I think is a very interesting one. It is not inconceivable that Planck's constant may have been nearly zero at the starting point, or GNewton had assumed a much bigger value in the past, etc. Who knows. Guth's inflationary idea, when you think about it, is a kind of revival of something very similar in a perhaps more tractable version. In that case it's the vacuum in quantum field theory that plays the role of changing parameter, monitoring most everything else, in particular the Hubble expansion parameter. My feeling is that Guth has captured something quite right about how it all must have started to give rise to the big bang of which we're seeing the remnants in the sky. In particular, quantum fluctuations must have played a very important role, being essential to the seeding of inhomogeneities that gave rise to cluster, supercluster, and galaxy formation. So I generally agree with what Eise has explained about uncertainty and I think it complements very well the points I have let loose. It's the uncertainty principle in combination with the choice of a convenient vacuum that gave rise to the structure. Until a better idea is found, it seems to work pretty well. The problem of the "when", that Studiot has brought up, is something that worries me particularly (the "where" worries me a little bit less), because you always seem to need a parameter to deploy all the physics as a sequence of events. When we're assuming Planckian scales in the spacial sections of space time, does it really make sense to talk about eternal inflation or slow roll? That's why the question of emerging time is so important. The only way I can think of that something like this could be achieved is by deriving time from a metric in field space, which is what I tried to suggest in the thread "What is time?" @Markus Hanke didn't seem to agree with me or see very clearly what I meant. And I tend to take Markus' disagreement very seriously. But that's another story and belongs in other thread. ------- PD.: I kind of have an idea of what this timeless scenario (from which a time can be derived that could make mathematical sense) may be derived from, but it's embryonic and very mathematical, and this is probably not the right medium for it. I will also have to pass on the fine philosophical/mathematical points that Studiot suggests, for the time being (and important though they may be) as I don't feel qualified to talk about them. The idea of constructing something from nothing still boggles my mind. I'll try and think more about it. I suppose everything depends on what is nothing and what is something.

Which actually goes to prove that you mustn't take anything literally.

As to what concerns the OP's question, I totally agree with this. +1 The question of planarity of the observable universe, for all I know, is about spatial flatness and has nothing to do with the rate of expansion. Preprint is here: https://arxiv.org/abs/1911.02087 I think a wildly-varying curvature would have noticeable effects in the aberration of light. I'm not sure I understand your onion picture but, wouldn't that have problems with isotropy/homogeneity at large scale? Although I agree that not even in a spherical universe would you necessarily move in periodic orbits. Only if you followed geodesics you would.