joigus

Yes, I think we are, to the extent that I can follow all the arguments. It's a recurring theme in Nature, I think. Simple principles, very complicated consequences.

You may be interested to know that Lee Smolin changed his mind about this question relatively recently. If you do a search of "time as fundamental" you're likely to find as many entries as for "time as emergent," which goes to prove that the question is far from settled. If you propose time as fundamental, your first order of business should be answering why it is that it appears to be a dimension, and has infinitely many versions corresponding to infinitely many observers. I'm not sure that Smolin and collaborators have got around to this question as yet. It would be nice to know if they have. I don't.

I do not expect it to be different.

That's what I like to dream. But one look at the standard model is enough to realise that the dream seems to vanish in one fell swoop. It's like the basic idea is extremely simple, but Nature uses it to make crossroads and turnarounds in any possible way: Arbitrary mixings, symmetry "offsets," apparently idle copies of the same thing with arbitrary displacements. It's as if a master engineer had made a thing of beauty, and a naughty kid had been playing with it. I agree, but I would like to add a note of optimism to it. Gravitational waves are something no ordinary primate would have dreamt of "seeing." We have this capacity to build an extraordinary prosthetics to extend the reach of our senses by cleverly arranging pieces of material.

Something we should never overlook as a possibility. We might have blind spots that are impossible to overcome. Why should the rules of the universe be written in a language that primates can understand?

To me it's not. I also think for @TheVat it isn't either --from a previous post. But QM goes further than probability. It speaks of amplitudes, which seem to be on a sub-level with respect to probabilities. What is this sub-level about? Why do we need a choice of global and local phase, but the gauge principle makes it completely irrelevant? Those are questions that keep me awake. I'm wary of interpretations that summon the brain into the big picture. I don't think it's a matter of brains. I also abhor of interpretations based on gravity, but I find a bit more difficult to explain why. I think it's more a question of classical mechanics appearing as a fully-fledged assymptotic approximation from within quantum mechanics, rather than by analogy or correspondence, plus a series of artificial assumptions.

This seems to suggest that the very process of observation involves some kind of "translation"... But the original "language" is not available to us. Pardon my quotation marks.

Razor-sharp.

How do you know?

Good point. Maybe observation carries with it this illusion of entities. It doesn't look like QM with its linear+unitary description alone can do that. The reason is that quantum superpositions evolve forever in every subspace allowable. In simple words: The "quantum curse" that everything that can happen, does happen, propagates to every degree of freedom available. Even to the degrees of freedom of the interacting system. It contaminates everything, there's no way around it. So, if you take QM to the ultimate consequences, not only both the dead cat and the living cat keep going, but also the observer that sees a dead cat, and the observer that sees a living cat, in a quantum superposition of observers in different states of observation. We still need Copenhagen to make sense of the ordinary, even though it's so ugly and we don't know how to interpret it in a cosmological context. As to cosmology, where we really need to make sense of this, and need it badly, we can't afford to have 7-odd interpretations to choose from.

Translate to scientific language: Is the world a simulation? Or could it be in any sense? Could something like reincarnation be programmed in such a simulation? Then proceed to, How could we prove that is the case? What is the substrate on which such simulation is running? etc.

Perhaps ontology in a weaker sense inspired by the oft-newfangled concept of "emergent"? In fact, it is incumbent upon us to explain why the world looks like entities moving around, or standing still. It does look like that. We must admit the world resembles exactly that: Numbers of entities having lifetimes, births and extinctions, checkpoints and rendezvous. You're welcome. There is a very interesting series of lectures by Lee Smolin on Time in Quantum Gravity (Perimeter Institute) in which he gets hands dirty with topological theories as theories with #(DoF)=#(constraints) until you totally remove all local degrees of freedom. It's as if the field variables get as close as it gets to doing nothing. I'm struggling with intuitive ways to put it in words...

This is not exactly what I meant, although it does partially overlap with what I meant. The adjective "topological" I didn't mean as applied to the background manifold, but to certain classes of solutions of differential equations on those manifolds. Thus, you can have many field theories defined on a topological manifold. Among all these theories, only a very restricted class of theories are topological, and most other theories are not. Topological theories have a Lagrangian not involving the metric. One interesting feature of these theories is that they are useful tools to study topological invariants of the manifold, like Wilson loops, probably Betti numbers too, and the like. They are invariant under diffeomorphisms, and once you incorporate the constraints --se below-- with the method of Lagrange multipliers, the constrained Hamiltonian becomes identically zero on the constraint surface. I say all this just to guarantee that we're talking about the same thing. But from the strictly dynamical point of view, topological fields are very constrained in the way the can evolve. In fact, they are maximally constrained. They --the fields-- have no local degrees of freedom, which means they do not propagate. The number of constraints exactly equals the number of degrees of freedom. Let me be as clear as humanly possible. As a warm-up, taking a 1st-order in time point-particle theory as a particularly simple example, what I mean by having #(DoF) = #(constraints) is the following: \[ q_{1}\left(t\right),\cdots,q_{n}\left(t\right) \] So a set of initial conditions \( q_{1}\left(0\right),\cdots,q_{n}\left(0\right)=q_{10},\cdots,q_{n0} \) completely determines the trajectory in the configuration space. Equivalently, if we're extremely lucky --the system is integrable--, we may manage to find a set of n integrals of motion: \[ \mathcal{J}_{1}\left(q_{1}\left(t\right),\cdots q_{n}\left(t\right)\right)=0 \] \[ \vdots \] \[ \mathcal{J}_{n}\left(q_{1}\left(t\right),\cdots q_{n}\left(t\right)\right)=0 \] This is (modulo condition of non-vanishing Jacobian) equivalent to fixing the previous n initial conditions. Integrals of motion for integrable systems depend on 1to1 on initial conditions. Now, what are constraints? Constraints are both mathematically and physically very similar, but with a very important nuance. Assume n constraints: \[ F_{1}\left(q_{1}\left(t\right),\cdots q_{n}\left(t\right)\right)=0 \] \[ \vdots \] \[ F_{n}\left(q_{1}\left(t\right),\cdots q_{n}\left(t\right)\right)=0 \] But these relations being in place for every set of initial conditions. What does this imply mathematically? It implies nothing other than that the system cannot move at all. Cannot evolve in any meaningful way at all. It's frozen dynamically. How much? It's just a point in configuration space. Now, what happens to a field theory under analogous strictures? We must now promote the \( q_{i}\left(t\right) \) to some \( \varphi_{a}\left(\boldsymbol{x},t\right) \), where \( a \) goes from 1 to n. If we impose n initial conditions, that means specifying the value of the \( \varphi \)'s, \[ \left.\varphi_{1}\left(\boldsymbol{x},\tau\right)\right|_{\varSigma^{d-1}}=f_{1}\left(\boldsymbol{x}\right),\cdots,\left.\varphi_{n}\left(\boldsymbol{x},\tau\right)\right|_{\varSigma^{d-1}}=f_{n}\left(\boldsymbol{x}\right) \] where \( \tau \) is some curvilinear coordinate that specifies the sub-manifold \( \varSigma^{d-1} \) the space-like foliations that define the Cauchy problem. If, instead, we have a set of n constraints, and as any constraints worth their salt, they do not depend on initial conditions, but are the same for all posible initial conditions, we will have the system extremely limited in its evolution. But it is no longer true that the set of states compatible with this situation "shrinks" to a point in configuration space. It does freeze, but due to the presence of the space variables \( \boldsymbol{x} \) it does so --it must-- to a fixed function sitting on the topological space. Or perhaps to a finite or countable set of such "frozen" functions. It is in that sense that I was talking about a quasi-rigidity. Known examples of constraints in field theory (valid for all sets of initial conditions) are transversalities and Gauss or Lorentz gauge-fixing constraints. Photons are known to "inhabit" a space of configurations with 4 degrees of freedom when you give them mass by assumption. If you impose masslessness, gauge fixing, they become more and more restricted in their evolution. If you imposed further constraints, there would be no dynamical situation that implies propagation. They would be "frozen." But not to a point. Instead they would be frozen to a pretty restrictive class of what I've tried to refer to by this term "quasi-rigidity." The previous discussion generalises trivially to a 2nd-order-in-time system by substituting 1,...,n with 1,...,n,...2n, and the \( \varphi \)'s to those plus their canonical momenta. Now, I know these musings not to be totally out of whack, because I've posed the question (the one about quasi-rigidity) elsewhere appropriate and I know for a fact that knowledgeable people consider it a totally-non-silly conjecture at least. Or, if you want, a question worth answering. But what would come next --the relation to the interpretation of QM-- does have speculative elements on my part, and would probably require a thread of its own.

Obviously, I meant consciousness. I'm not implying anything about the cat's morality.

It's a question having to do with quantum mechanics of open systems interacting dissipatively with billions of atomic degrees of freedom. The environment "learns" pretty fast whether the cat is dead or alive, because the environment makes the alternatives (corresponding to quantum numbers that gave rise to the fateful event) decohere with each other --in modern parlance. So it's nothing to do with conscience. It's about the system interacting in a complex way with its environment. Conscious beings are but a particular example of this occurrence. The cat is no exception, I'm sure, as it's also made up of billions of subatomic degrees of freedom, so the cat learns pretty fast too about his own health state just before he dies. There's a question pending about the so-called pointer states that's still not solved. But it has no consequences from the practical point of view. Different people embrace different interpretations of quantum mechanics in order to make a mental picture of what happens to the previous quantum states.

How do you reconcile this with charge conservation? The initial electron has charge -e. The e+ e- pair, on the other hand, has charge 0. --As pointed out by @swansont and @Mordred.

I'm aware of it. That's part of the reason why I said that DBB theory cannot be the whole story. Silicone droplets are indeed not particles, when you think about it. They are, in a manner of speaking, non-linear "excitations carried on top of the linear, or quasi-linear modes" of the field --or perhaps analogues of those. In the last decades there has been extensive study of topological field theories. Topological field theories have no propagating degrees of freedom, even though quite a number of people who are allegedly "in the know" are not totally clear about this, or chose not to answer to that particular point: https://physics.stackexchange.com/questions/550561/on-tqft-and-theories-without-propagating-degrees-of-freedom https://math.stackexchange.com/questions/701100/topological-quantum-field-theories Also, my own question @ physics.stackexchange which received no answer about the particular point I was asking (topological field theories do not propagate, therefore their degrees of freedom must be "quasi-rigidities")... https://physics.stackexchange.com/questions/614516/criteria-to-define-a-classical-topological-field-lagrangian-conjecture?noredirect=1&lq=1 I know for sure that a number of people consider this particular aspect at the very least intriguing. But not many people, AFAIK, have thought at much depth, if any, about it. I find that especially revealing. Revealing of what? Well, revealing, if nothing else, of the fact that almost no one is interested, not of whether or not it can be done, or of whether or not it's a dead end, or irrelevant, etc.

Yes. Part of the difficulty is that experiments are getting really costly. I also think that people who conceive them should spend more effort in trying to disprove quantum mechanics, or find where different interpretations could produce different predictions. Also interesting are experiments that build particle-like analogues of quantum particles. More should be done in this direction, I think. So far it's been a bunch of mavericks. Look at what Yves Couder did: This goes to prove that what I said --that particle-like self-sustaining bundles of the field carried along with the quantum state is not that outlandish an idea. Bohm's theory could the precursor of a much deeper, much more complex underlying level, I suspect. One not involving point particles, of course, but dynamics of non-linear phenomena. You must ponder the fact that what this man has done in a laboratory was once declared even impossible to conceive by great physicists. We should be ready for surprises. But effort must be spent in looking for them.

DBB is a theory of point particles. It fails at several levels. But IMO we should not disregard the fact that it really offers a natural explanation of why objective collapse works so well for all practical purposes. As to @Mordred's statement that he's happy with particles corresponding to just excitations in quantum fields, I agree that it's good enough for all practical purposes, including relativistic contexts in which the Born interpretation is not so easy to invoke unambiguously. I would just keep a bunch of people examining this reasonable possibility, the very same way that people keep working on string theory, supersymmetry, etc, which are very reasonable possibility, although they probably don't work in the way they were formulated. The thing about physical hypotheses is one never knows what hidden assumption could be dropped and give way to a real breakthrough. It's very difficult to be precise about when it's worth spending the effort. I tend to see these ideas that seem to be characterised by a spectacular --although very partial-- success as definitely worth keeping under scrutiny, and tinkering with a panoply of possibilities to modify them. x-posted with @Markus Hanke

You actually don't need movement. The depletion of material being a well-known example of clock particularly suitable to measure the age of rocks or stuff of biological origin --using the exponential function-- or a linear function --rate of mutations. Curiously enough, it's always one kind or another of exponential --periodic phenomena are ruled by a complex exponential... Coincidence?

Because a few decades is a long time for experiments not to end up catching up dramatically with our frontiers of knowledge, and because it's never been the case that a breakthrough in our basic understanding of scientific issues has left the technological landscape untouched. It's bound to happen sooner rather than later. Seemingly unsolvable problems in basic science seem to be piling up, and something's got to give.

I think we're living in an age of confusion and that this confusion must have been pretty much unavoidable all along. Copenhagen's interpretation works like a dream for anything that doesn't deeply involve questions of very early cosmology, quantum gravity, or vacuum energy. Little surprise there: Where does the universe come from? Why is there something rather than nothing? What is time? You can't get more essential than that. I also think there's the social factor that not many high-profile theorists since the likes of Einstein and Schrödinger have been attracted to this problem nearly compellingly enough. That's probably because so far there hasn't been much at stake from the point of view of solving fundamental problems --or getting a university tenure. This particular factor, I feel, could be about to change in the decades to come. As to interpretations, one possibility is that, wherever the description of physical systems & processes hinges on QM, we've finally hit a fundamental logical obstacle which could have to do with the completeness vs consistency of mathematics itself, which we know by now to be an actual issue. The reason being: Why not? If that's the case, we will have to give up on matters of interpretation. My personal feeling is that we haven't taken the question seriously enough. And my battlecry --or baby cry, who knows--, is that we must change the attitude to that of the cartographer: Our quantum-state variables, and space-time and internal-gauge, spin variables, etc. would be but a parametrisation of physics that simply cannot do the job of explaining everything at every level. At some point we have to drop them, propose new variables, and explicitly build formulae connecting the different domains. This is very similar to what a cartographer who wants to faithfully describe Antarctica must do if she's been working only with the Mercator projection previously. In a way that's what we do all the time. As to my own interpretation, I think there must be some kind of a non-linear dynamics of solitons, kinks and domain walls, etc, going on in the gauge degrees of freedom, that's not completely inconsequencial, complex enough that it's gone unnoticed for all these years as a possibility, and can perhaps under suitable ancillary hypothesis be statistically related with a De Broglie-Bohm model as an approximation. So in that sense I think the De Broglie Bohm interpretation, although it cannot be the whole story, does capture something important as a crude approximation. Sorry for the split infinitive, and for so many words for what basically is my two cents.

Fascinating story. Their brethren, the Onge people and the Jarawa, weren't that lucky. The Onge were the first to fall, and were relocated. The Jarawa resisted a bit longer. They complain bitterly of contact with the world now. The North Sentinelese still stand. There was only one sucessful contact from what I know, by a delegation from India. But they remain isolated. Apparently the Indian government has given up on all attempts to contact them.

The term "beables" is not mine. It's due to John Bell. The question about beables wasn't meant to address quantum correlations. Quantum correlations are sufficiently explained by wave functions once we accept Born's rule. John Bell conjectured this notion of beables in order to give total mathematical consistency to quantum mechanics, and thus escape the insatisfaction associated to the standard projection postulate. But of course no concrete formulation of beables will ever be able to circunvent the fact that quantum mechanics establishes very clear limits to what is given to us to know about "physical reality" (what we see and measure.) In that sense, and as far as I understand them, those would-be beables should not be observables. The mapping to what we perceive as reality should be expressed in such a way that their mathematical formulation made clear what is "lost in translation" so to speak, so that we perceive this projected or apparent reality that cannot be determined, even though these objects are perfectly defined at this internal, and fundamentally unobservable, level.

Ok. I totally understand what you mean. I've been trying to sketch the proof that you suggest and, yes, that would be the way to go. Even with the simplification of radial fall, the equation is not the simplest to solve, but it can be solved. In particular, it can be integrated to the expression that @Genady proposed --which is shown in many documents online-- with just one additional qualification about signs: \[ \frac{\dot{r}}{c}=\pm\left(1-\frac{r_{S}}{r}\right)\sqrt{\frac{r_{S}}{r}} \] This comes from integrating the geodesic equation, so it corresponds to bodies falling radially in Schwarzschild's metric, either approaching or escaping from the source. That it corresponds to very special initial conditions can be seen --by first picking out the minus sign--, and by analysing these limiting cases: Radial velocity at spatial infinity --dotted expressions meaning "derivative with respect to coordinate time," not with respect to proper time: \[ \dot{r}_{\infty}=\lim_{r\rightarrow\infty}-\left(1-\frac{r_{S}}{r}\right)\sqrt{\frac{r_{S}}{r}}c=0 \] Radial velocity at Earth's Schwarzschild radius: \[ \dot{r}_{r_{S}}=\lim_{r\rightarrow r_{S}}-\left(1-\frac{r_{S}}{r}\right)\sqrt{\frac{r_{S}}{r}}c=-c \] Radial velocity at Earth's radius: \[ \dot{r}_{r_{\oplus}}=-\left(1-\frac{r_{S}}{r_{\oplus}}\right)\sqrt{\frac{r_{S}}{r_{\oplus}}}c\simeq-11.144\times10^{3}\textrm{m}\textrm{s}^{-1} \] which approximately matches Earth's radial escape velocity with a minus sign corresponding to the motion being an approach. Now, one thing that I think should not be overlooked is the fact that such a trajectory --interpreted as "letting go" of an object with initial zero radial velocity--, is only consistent with doing so from spatial infinity, not from a finite distance. The observation might seem trivial, as far enough away we can disregard the difference to the effect of estimating velocities, but not so clearly --at least not to me-- to the effect of inferring relations between times. There is the possibility that it isn't, as a particle freely falling from infinity would make so with an infinite total proper time, as well as infinite total coordinate time. In any case, if we use the last relation \( \dot{r}\left(r\right) \) for the trajectory, and directly substitute in the expression for the proper time, we get, \[ d\tau\simeq\left[\left(1-\frac{r_{S}}{r}\right)-\left(1+\frac{r_{S}}{r}\right)\left(1-\frac{r_{S}}{r}\right)^{2}\frac{r_{S}}{r}\right]^{1/2}dt= \] \[ =\left(1-\frac{r_{S}}{r}\right)^{1/2}\left[1-\frac{r_{S}}{r}+\left(\frac{r_{S}}{r}\right)^{3}\right]^{1/2}dt\simeq\left(1-\frac{r_{S}}{r}\right)dt \] If, on the other hand, we go directly to the expression of a body falling freely from a radius --no matter how big but finite-- with initial zero velocity, we can go directly to the expression for the proper time in terms of a general radial trajectory \( r\left(t\right)=r_{C}\left(t\right) \), and substitute, \[ d\tau^{2}\simeq\left[\left(1-\frac{r_{\textrm{s}}}{r}\right)-\left(1+\frac{r_{\textrm{s}}}{r}\right)\left(\frac{\dot{r}}{c}\right)^{2}\right]dt^{2} \] and already disregard the term in \( \dot{r}/c \) from the start, because it's never going to reach a significant value in comparison with \( r_{S}/r \). But this produces half the value that's inferred from using the Schwarzschild escape velocity functional relation. I think my argument that the Shapiro delay between the orbiting object and the object on the Earth surface would be intermediate between both still holds. We want the initial velocity to be zero at a finite distance, not coming from spatial infinity. The difference might look like small potatoes, but it could be non-trivial to the effect of inferring relations between proper times.