Markus Hanke

You were originally referring to “19th century principles of science” - which were based on a Newtonian world view. And even back then, people were already aware of numerous problems and issues that didn’t fit that world view. No, it is an honest appraisal by someone who reads a lot of papers on these subjects. So are all the other theories, so you’ll have to give them the benefit of the doubt too. Yes, GTG is a specific example of a gauge theory of gravity, as opposed to a metric theory such as GR. It can be shown that there are, in fact, infinitely many such theories, all of which describe propagating 2-polarisation states of gravitational radiation, and which resemble GR (no spin) or Einstein-Cartan gravity (spin) under the appropriate circumstances. Within the domain that we can experimentally test and observe, these models are generally distinguishable from GR only insofar as they don’t contain any equivalence principle - therefore testing the equivalence principle is a good first step in testing for gauge theories of gravity. At present, no violations of the equivalence principle have been observed, not even in the strong field domain (BH mergers etc). This doesn’t invalidate all gauge theories, but it does constrain the form they can realistically take. There is another critical issue with this, however - because gravity now also couples directly to spin (unlike in pure GR), these theories introduce extra terms into the Dirac equation. These extra terms are too small for us to be able to experimentally detect them right now, but they would become important in the strong field regime. Again, I am not aware of any indications that such phenomena have been observed anywhere. As for exotic phenomena - these gauge theories exclude the possibility of singularities, even in the classical domain, which is definitely good. Wormholes are not categorically excluded though as far as I know, where did you read this? Note sure about CTCs, but it’s possible that these don’t occur, since no ring singularity forms. I personally like gauge theories of gravity, since the basic approach is very elegant, and there are no immediate conflicts with available data. I’d say that out of all the various alternatives (or rather: extensions) to GR, these are probably the most promising. I would say, though, that what we need isn’t an alternative to GR (unless some data becomes available that is in direct conflict with it), but rather a generalisation of it. But that’s only (sort of) true for ordinary non-relativistic QM, which is just a simplified approximation. Full quantum field theory is based on fields and their interactions, not particles. I have no idea what you mean by “unscientific” - both SR and GR are fully amenable to the scientific method, irrespective of the precise mathematical details of these models.

They remain valid - within their respective domains of applicability (which is why we all learn Newtonian physics in high school). The issue was that these domains turned out to be limited, and if you go beyond them, you need different physics. This is why relativity, QM, and (later) QFT came about. Alternative theories of gravity are legion, and the author(s) of each and every one of them generally insist that theirs is the only correct one, and solves all of GR’s problems. You need to take such claims with a huge grain of salt. What often happens is that these theories might match the data for one particular phenomenon very well, but then fail to do so for other aspects of gravity; or, which is worse, they flat out contradict some other aspect of known physics or observational data. For example, the model in the link you provided does not seem to be locally Lorentz invariant (AFAICS) in small regions if the extra parameters are anything other than identically zero - which is a huge problem, since local Lorentz invariance has been tested for to extremely high precision, and no preferred coordinate frames have ever been found. If you compare all the currently known models for gravity against one another, then GR still remains both the simplest model, as well as the only one that matches all available experimental and observational data very well, so far as classical gravity is concerned. Have a look here for quick introduction: https://en.wikipedia.org/wiki/Alternatives_to_general_relativity This being said, it is, I think, safe to assume that the domain of applicability of GR is itself also limited. I just think that whatever more general model underlies GR (to which GR will be the classical limit) will involve a paradigm shift far more radical than just adding a couple of extra terms to the gravity Lagrangian; my guess is we’ll be in for a complete overhaul of our understanding of what “space” and “time” mean on a fundamental level. If you feel the shift from Newtonian to relativistic and quantum physics was too radical, then I don’t think you’ll like what I think is coming

The wording is somewhat misleading. What happens is that, once the horizon is crossed, ageing into the future always corresponds to falling down radially - in other words, you cannot maintain a constant radial position, nor can you go radially upwards, irrespective of how much downward thrust you try to exert. Even photons must always fall down. Hence, space and time enter into a relationship whereby any ageing into the future must necessarily and always lead to a decay in radial position - and since ageing into the future is inevitable, so is falling further down into the BH. Because this is a relationship between space and time, you cannot cheat your way out of this situation by trying fancy tricks of motion (like slingshotting around the singularity etc) - it doesn’t matter at all how you move, you will, on average, always fall radially downward as your clock ticks into the future. If you were the free-fall body, you wouldn’t notice anything special as you fell. It’s only once you try to arrest your fall or get back out by firing thrusters, that you would notice that you are in fact unable to do so.

Well, that happened because those 19th century principles turned out to not work so well - or rather, they only work well under a very specific and limiting set of circumstances. Thus it was necessary to find better descriptions of the world around us.

You really don’t need to bang your shinbone on a stool that’s not in the way. The answer is simply that it measures the fact that a period of time has passed. This is in no way philosophically problematic, precisely because we don’t equate “time” with any specific clock mechanism. It’s only if you try to redefine physical time as “movement”, as you suggest, that you end up with all sorts of philosophical, mathematical, and physical issues and tautologies, because that’s simply not a good model of the world around us - there are plenty of specific examples of systems evolving without any “movement”. The crucial point here is that this is true for all clocks, entirely irrespective of what their internal mechanisms actually are. A digital wrist watch, an atomic clock, a decaying elementary particle, or the flipping of spins all show the same fact that time passes (ie that systems evolve and age into the future), and that this is entirely separate from any specific mechanism used to measure it. It’s as true for periodic motion as it is for motionless systems. You can see this even more clearly when you compare clocks by placing them at different points within a gravitational field - gravitational time dilation affects all clocks equally, irrespective of their internal mechanisms (or lack thereof). A vastly more interesting and pertinent question is whether - and in what sense - time (and also space, for that matter) is fundamental to the universe, or whether it is emergent from something more fundamental that is not in itself spatio-temporal in nature. This is still an open question, and very much subject to debate within the physics (and philosophy) community.

Because the human condition doesn’t magically end with the surface of our skin. We are a part of the universe, and thus ultimately a product of its origin and all the various processes that have been going on since then. It is delusion to think that we are somehow separate from everything else, so that these questions have no relevance to us. Understanding the universe means understanding ourselves and our human condition better. Also, the question carries connotations that the value of something is defined solely by the financial benefits it yields. This is another common delusion. Too many people these days confuse the price of things with their actual value, which isn’t always readily quantifiable, nor even commonly recognised. But I think it’s also important to realise that not everyone will “get” this, no matter how well you try to explain it, and how good your arguments are. Sometimes you just have to leave them to it, and move on.

The one that comes to mind is “Helgoland” by Carlo Rovelli; I found it to be a very good read. Do bear in mind though the final conclusion of the book does promote his own interpretation of QM, which is Relational Quantum Mechanics. But the historical overview is quite good.

Yes, but if one starts from the geodesic equations, then this can be fixed by supplying different initial/boundary conditions when solving them. I don’t know off hand what expression that would yield, but I do seem to remember that such a frame (free fall from finite distance) is called a ‘drip frame’ (as opposed to rain frame for free fall from rest at infinity, and hail frame for from finite distance with initial velocity v>0). In general though, the separation between events along a purely radial time-like in-fall geodesic from rest should simply be \[\displaystyle{\tau =\int _{r_{1}}^{r_{2}}\left(\frac{d\tau }{dr}\right) dr}\] The devil in the details of how to find that expression under the integral.

Yes, I definitely agree with this. This is why (as I have mentioned before) the physics community is very actively researching both quantum gravity, and alternative models of classic gravity - because eventually we would like to gain better insight into not just how gravity works, but also why it works in the specific way it does. Yes, you’re right. As mentioned above, this is something that is being worked on, and has been for some time. The only thing is that there is no guarantee that the why necessarily always falls into the domain of physics. We can never know for sure, we can just keep going forward.

Well, I profess myself agnostic so far as ontology is concerned. Just think about this for a minute - in physics we are trying to make models of “the world”. But what is this world we are referring to? It is what our brains present to us as “reality”, but this reality is itself already a model; it’s a construct built up from sense impressions, as well as specific modes of representing, structuring and integrating information, such as for example concepts of “space” and “time”. It stands to reason that, if our brains and minds were substantially different, then so would be our reality, and thus the models we make of it. It is not easy to tell just which elements of reality would differ, and which ones would remain the same. I am not saying that there’s nothing “out there”, I just think it might not actually be so easy to disentangle what belongs to the external world, and what really belongs to our own reality-model of it, which is a construct generated by our brain. Therefore, so far as physics is concerned, I am very careful to distinguish the map from the territory. They are not the same things at all. A map is “true” only insofar as it accurately reflects those features of the terrain which it was intended to reflect - and each and every map has limitations and things that it cannot reflect. So usefulness is a much better criterion than ontological truth, when it comes to models and theories in physics. My pleasure

This is pretty much what happens in what is called the “transactional interpretation” of QM. Needless to say that, just as the case with all interpretations, there are problems and issues with this, but truth be told I’m not familiar enough with this particular interpretation to offer more meaningful details. I think we have somewhat different ideas about what it actually is that physics as a discipline does. To me, physics makes descriptive models of certain aspects of the world around us; it is not in the business of putting forth ontological claims about “what things really are”. That job description belongs more to philosophy, though clearly there is a large amount of overlap too. Thus, to me, the standard QM formalism for entanglement is a pretty thorough description of what goes on here. I see no a priori reason why any other kind of causal mechanism must necessarily be involved in this. The initial interaction, to me, provides enough of a causal mechanism. You’re probably familiar with the old classical analogy of a pair of gloves being put into separate boxes (so that the handlers don’t know which glove is in which box), and those boxes then mailed to distant locations. Upon opening, and subsequent comparison of their handedness, a perfect anti-correlation will always be found. What is the causative mechanism of that anti-correlation? It’s because the statistical correlation was set up this way from the beginning, when the pair of gloves was first distributed into the boxes - there is no additional mechanism or interaction that is triggered by opening the boxes, somehow acting non-locally. We simply set up a correlation, which is then maintained through time. Thus, the statistical (anti-)correlation is a complete description of what goes on here; no further causative mechanisms are required, and you would probably agree with me that there is no mystery at all involved in any aspect of the glove scenario. You get either |LR> or |RL>, but never |LL> or |RR>. Quantum entanglement is really not much different - the only difference is that, unlike in the classical case involving gloves, there is no local realism, so there is no meaningful way to speak of the “state” of the system, unless a measurement is performed. That makes it all seem much more mysterious than it actually is; but ultimately the principle is the same one - a correlation is prepared by letting the particles interact in a certain way, and this correlation then persists up until an observation takes place. Note also that the act of measurement is itself a form of entanglement - when you measure one particle, it ceases to be entangled with the other particle, and instead becomes entangled with the measurement apparatus. How’s that for a head-wrecker

I never ever said or implied anything about there not being a causal explanation or physical basis. The causal link between a pair of entangled particles is their past interaction, which is when the entanglement relationship becomes first established. That’s the causal explanation. This is not in contention, and it’s not a mystery. You don’t get entangled pairs unless they first interact in certain ways to set up this relationship, and no one here has claimed otherwise. But the meaning of “entanglement” is nevertheless a statistical correlation of measurement outcomes, as I have attempted to explain. The thing is that, if you look at just one of these particles and perform a local (!) measurement there, then each outcome (‘0’ or ‘1’) will appear with equal probability of 0.5. The same is true for local measurements on the other particle - each outcome will appear with equal probability of 0.5 to that local observer. Neither observer can predict the outcome of his own local measurements, he can only define probabilities for them, and these probabilities are identical whether or not the particles are entangled. To put this differently - there is no local experiment you can perform that will tell you whether the single particle you have in front of you is entangled or not. Entanglement is meaningless when only a single particle is considered. It is only when you compare the outcomes of the two measurements on the two constituents of the system that you will find the overall two-particle state to be either |01> or |10> (with equal probability!), but never |11> or |00>. This is in contrast to unentangled particle pairs, which can yield any of the four possible states. So entanglement means you reduce the pool of possible global states by introducing a statistical correlation. So yes, entanglement is defined to be a statistical correlation between measurement outcomes. There’s nothing unphysical about statistics at all, it’s a straightforward description of what we actually see when we perform these experiments in the real world. Yes, of course - they’re caused by the initial interaction that sets up the correlation. This then persists until the entanglement is broken again, which happens if and when any of these two particles is interacted with in any way. There are plenty of concepts in physics that are statistical in nature, and don’t make sense for systems that have only one state, or only one constituent. Obvious examples that come to mind are things like temperature, and entropy. You cannot meaningfully apply these to a single particle - and the same is true for entanglement.

You are correct, in that all observers agree on physical events. In this case, this “event” is the intersection of the world line of the in-falling particle with the event horizon. While observers disagree on the where and when of this, they all agree that the two do in fact intersect - including the distant Schwarzschild observer. The reason why he can’t correlate that intersection with a reading on his own clock is that he shares no concept of simultaneity with a clock that’s actually at the horizon. The issue is simultaneity. He does, however, fully agree on the length and geometry of the in-fall world line, since these are all geometric quantities that are independent of specific coordinate choices. So, the fundamental difference between these two observers is that the in-falling one physically measures the length of this world line (since his clock falls along it), whereas the distant Schwarzschild observer does not. Thus it really isn’t a surprise that their clocks disagree. As I have said on many occasions, time becomes a purely local concept once gravity is involved. Exactly +1 Very nice analogy, I like it +1

I feel I need to quickly summarise here what my viewpoint actually is, because I think my main thoughts have somehow gotten lost amongst extraneous detail. What I am basically saying is that, if you take the “time” out of “spacetime”, you reduce the overall dimensionality of the universe to 3D+0 (all spatial dimensions). While this leaves the form of the Einstein equations unchanged, it nonetheless has important ramifications, because as we know from differential geometry, the Weyl tensor identically vanishes in anything less than 4D. This immediately precludes the existence of gravitational radiation. Furthermore, since the Einstein equations tell us that R=0 in vacuum, this implies that both the trace and the traceless part of the Riemann tensor vanish here, meaning you have no gravity whatsoever in vacuum. In the interior of mass-energy distributions, then, only the trace of the Riemann tensor is non-zero, so you have pure Ricci curvature here, which is quite different from the 4D case. So what I am saying is that taking time out of the equation absolutely does have ramifications for gravity. Furthermore, without time, I do not see how one could recover local Lorentz invariance, which is crucial for quantum field theory. Also, in a purely 3D universe, particles would not posses the property of spin. And so on. I haven’t really mentioned change in all this, my thoughts are mostly of a geometric nature here.

To be honest, I’ve been struggling a little to follow the approach you took in your initial post here - I’m not saying anything is wrong there, it’s just that I don’t fully get it. The way I would work out radial free-fall times is by starting at the geodesic equation, in order to obtain an expression for \(\frac{dr}{d\tau}\), and then either integrate this up over an appropriate path, or solve directly for \(\tau\) - this is doable so long as one assumes a purely radial in-fall, so that the pesky angular momentum terms all vanish. Already the geodesic expression automatically leaves me with an additional factor of 2, as compared to your approach here (unless I’m missing something in your formalism, which is possible). Curious to see how you resolved this

Just want to throw in here (as an uninvolved reader) that you all seem to be tacitly equating religion with theism. But these are not the same things at all - not all religions are theistic in nature. I think it is important to distinguish these concepts more carefully.

You cannot ‘separate’ nearby gravitational wells neatly, because gravity is non-linear - spacetime in the Earth-Moon system is not simply the sum of ‘Earth gravity well’ + ‘Moon gravity well’, but something more complicated (though GR effects are quite small here). The same is true for all other planets in our solar system, since they are all subject to the gravity of the Sun. Of course, that goes without saying - the entirety of physics is about making models that describe aspects of the world around us. We don’t do philosophy or metaphysics or religion here, so everything that is being talked about in the physics section of this forum has to do with models. And whatever idea you have in mind about gravity is also a hypothesis about gravity, and not gravity itself. But here’s the point - GR has been extensively tested, and found to be in excellent agreement with experiment and observation. So we can regard the model as valid within its domain of applicability, and thus extract predictions from it. Now, if you take the ‘time’ out of spacetime, thus reducing the universe to three dimensions, then GR tells us very clearly what would happen so far as gravity is concerned. As such, if you claim that gravity still works in 3D in the exact manner as we can observe around us, then the onus will be on you to present a mathematically self-consistent model that shows this, and we shall be happy to take a look at it. Of course it isn’t. That’s been known for at least the past 50+ years! I don’t know why you use the word ‘admitting’, as if this is something that secretive and kept hidden. It isn’t. Alternative theories of classical gravity, as well as theories of quantum gravity, are probably the two most active areas of research in modern theoretical physics. Just search for some related terms of arXiv, and see yourself the amount of hits you get. So yes - the idea that the domain of applicability of GR might be limited even within the classical regime, and thus that it might only be a special case of something more general, is most definitely conceivable, and is being actively researched; there is a very large number of alternative models in existence. Do note though that when doing a direct comparison, none of these models - with the possible exceptions of relativistic MOND and Einstein-Cartan gravity - come even close to the versatility and success of GR. Also do note - and this is important - that the domain of applicability of a model being limited is not the same as that model being wrong. We still use Newtonian gravity extensively to model scenarios where relativistic effects can be neglected, so the model continues to be right within its domain of applicability, even though we have had GR for over a century. It’s just that this domain is limited, and we have a pretty good idea exactly where those limits are. The same will eventually also be true for GR, though at the moment we have only a very rough idea where the limits might be, and only some educated guesswork about what lies beyond these. Within the classical domain, it is very unlikely that any successful model of gravity will have a notion of time that is substantially different from that of Einsteinian spacetime, because any such theory will need to preserve local Lorentz invariance (and thus CPT invariance), which puts stringent bounds on what such models can look like. There are also more fundamental reasons based in topology that dictate why GR looks the way it does, so the notion of spacetime isn’t just a wild guess. The domain of quantum gravity is another matter entirely though - it is not just possible, but nearly certain, that we will have to fundamentally rethink our notions of both time and space to make quantised gravity work. Note that GR would be the classical limit of any such model. So then, why is the GR definition a problem for you? It works really well.

Yes I can. As I have already pointed out, the kind of gravity we observe around us requires a very specific concept of time, which is the Einsteinian one. You can’t do away with it, or else the whole thing will no longer work. No, I’m not attached to anything (in fact, modified and alternative theories of gravity are a special interest of mine). I’m simply considering what works within a given domain of applicability, and what doesn’t. If you look at the classical low-energy regime, then clearly GR works very well in that it provides an excellent description of the phenomenology of gravity as we see and measure it, within its domain of applicability. The experimental evidence for this from the past 100+ years is incontrovertible and overwhelming. As I have said multiple times, this requires a specific notion of time - if you do away with that notion, or replace it with something different, then the model can no longer function. That’s all there is to it. Of course not. How could you think that? We already know that GR has a limited domain of applicability - at a minimum it cannot incorporate any quantum effects, and it is possible that even within the classical regime some phenomena might require modifications to ordinary GR. The jury is still out on that one. But that’s not the point here at all. This thread deals with your claim that time is not required for classical gravity to exist in the way we see it around us, and that’s manifestly false. MOND is only one example - there is in a fact a large number of alternative theories of gravity out there (none of which does away with time, btw!). The problem is that once you consider all available data (not just some isolated phenomenon), then none of the other models provide nearly as good a fit as GR does. We already know that it won’t be the final theory of gravity, but it really is the best one we have at present. It’s not - no one said such a thing. There are many different ways to define a concept of “time”, both in physics and in philosophy. The point we are making here is that classical gravity as we observe it around us requires a specific concept of time, being the Einsteinian one. Quantum field theory - which is the most fundamental theory we currently have - requires a Minkowski space-time background in order to work; the entirety of the Standard Model is formulated against this background, so Einsteinian time is as fundamental to QFT as it is to GR. To be precise, the Lorentz symmetry we find in local patches of Minkowski spacetime implies the CPT invariance of the Standard Model Lagrangian, and vice versa. One example of a model where a different notion of time is used is ordinary quantum mechanics - which is a low-energy, low-velocity, non-relativistic approximation to QFT that works only for systems where particle numbers are conserved. Here, time is simply a free parameter that is used to describe the evolution of a given system, it is not an observable of the theory, ie it can’t be consistently written as a Hermitian operator. GR and SR are models that describe aspects of the universe - as such they answer mostly only the how questions, but not the why ones, in the same manner as a map describes the topography of some territory without providing an explanation of the geological processes that gave rise to that territory. That doesn’t make the map any less useful, if you’re trying to find your way from A to B. The invariance of the speed of light is equivalent to saying that all inertial observers experience the same laws of physics; that’s an empirical finding about the world we find ourselves in. We don’t know yet why this is so, but if you really think about it, you’ll realise very quickly that the absence of this symmetry would immediately lead to physical and logical paradoxes that cannot be resolved, so at a minimum it is a matter of logical consistency. As for the gravity wells, the answer is in my signature. There is a well defined relationship between local sources of energy-momentum, and certain aspects of local spacetime geometry, as described by the Einstein equations. Thus, the relevant aspects of gravity in the interior of things like planets, stars etc are directly given by the distribution of energy-momentum there. But because spacetime as a manifold is everywhere smooth and continuous, the exterior vacuum geometry must match up with the interior geometry in a way that guarantees smoothness and continuity at the boundary. This provides a boundary condition that - along with the asymptotic behaviour far away from the central body - determines the exterior geometry. In most ordinary cases the embedding diagram belonging to this exterior geometry will look roughly like the “gravity well” you are referring to. This wasn’t the point. The issue is whether - given a geometric theory of gravity, be that GR or some of its viable alternatives - you can have gravitational radiation without there being time. The answer is clearly no. Thus, the presence of gravitational radiation implies some level of physical reality for time. Spacetime is not a physical medium, so there is nothing there that “vibrates” - that’s the kind of unfortunate misconception that is spread in pop-sci media. In reality, local geometry within some region of spacetime is determined not just by local energy-momentum, but also by distant sources. These do not appear explicitly in the field equations, but have to be provided in the form of initial and boundary conditions when solving them (they are differential equations after all). If it so happens that there is a distant source that has some form of non-vanishing quadrupole or higher multipole moment, then the local geometry will not be invariant under time translations, meaning you get tidal components that are explicitly time-dependent, even though all your local sources are stationary. This is how you get the characteristic effects of gravitational radiation.

The entire life cycle (from creation to decay) of elementary particles such as the muon can be visually observed in cloud chambers. You could also do something similar with flipping of spin directions, if one was to combine a cloud chamber with some suitable version of a Stern-Gerlach setup. The very existence of gravitational radiation depends on the reality of time (in the GR sense), so any type of gravitational wave detector is in effect an instrument that demonstrates the existence of “time” in a rather direct way. If you want to make things absolutely airtight you can combine gravitational radiation with movement-less clocks - so you could for example have a spatially extended sample of many decaying elementary particles, and observe the local variations in mean lifetimes of these as they are exposed to a gravitational radiation field. The effect would be exceedingly small, and way outside of what we can detect with current technology, but you get the general idea - not only will the mean lifetimes be effected even though these particles lack internal mechanisms, but all kinds of particles/clocks will be effected exactly equally, irrespective of their kind and internal make-up (if any). This demonstrates rather neatly that time exists independent of specific mechanisms.

I tend to agree. The “tick rate” of a clock is an observer-dependent quantity, so this type of question really does very little to demonstrate the underlying physics. A more illuminating kind of scenario would consider the total elapsed time on clocks, which is equal to the geometric lengths of their world lines, and thus a quantity that all observers agree on. Of course, one would have to connect the same set of events to make a meaningful comparison between world lines, which we don’t have in the OP’s scenario. As for the problem at hand, clock A on Earth is not inertial, but under constant acceleration; the same goes for distant B, unless it is far enough away that we can roughly consider it inertial. So you have two distant non-inertial frames, and one inertial frame in radial free fall. All of this is embedded in a curved spacetime, so one must also consider how to actually define simultaneity here, otherwise comparing distant clocks is meaningless.

The concept of Riemann curvature as it is used in ordinary GR applies in any dimension equal to or greater than 2. That means that yes, you can have “curved” 2D and 3D spacetimes as well. The big difference is the level of complexity - in 2D, the Riemann tensor has exactly one independent component, so it is simply a scalar; in 3D, it has 6 components, and can be shown to equal the tank-2 Ricci tensor. Hence these situation have a lot fewer degrees of freedom than we see in our 4D world. Geometrically speaking, in 2D you have only scalar curvature, so the only thing that can happen is that the area of a 2D surface differs as compared to the same situation in a flat spacetime. It is very simple. In 3D, you get a new kind of curvature which is Ricci curvature, which means that volumes may differ as compared to the same situation in flat spacetime. In 4D and above then you have, in addition to scalar and Ricci curvature, also Weyl curvature, which introduces (relative) tidal forces and shear between neighbouring geodesics, meaning it (roughly speaking) distorts shapes as compared to the flat spacetime situation. So yes, it is in fact possible and meaningful to talk about GR in three dimensions. However, since such as theory contains only scalar and Ricci curvature, but no Weyl curvature, the resulting phenomenology is very different from what we actually see in the real world - at a minimum there would be no gravitational radiation, no gravity at all in vacuum, and gravity in the interior of bodies would behave quite differently.

My post referred to gravity as we experience it (in the real world around us). Yes, you would also have some version of gravity in a universe without the GR concept of time (see my last post), but it would be very different from what we actually see in our universe.

The point wasn’t the decay process itself - rather, my point was that a well-defined period of time elapses between the creation of the muon and its decay, and that there is no “movement” of any constituent mechanism happening during that time, since it is an elementary particle. In the case of muons - nothing, because they are elementary particles without any “internal” mechanisms. Do you mean in the path integral formulation? If so, then no, the trajectories involved here are not in physical spacetime, but in the quantum system’s phase space; the path integral is a functional that returns a probability amplitude.

To sum up, “true reality” is clearly subjective, and meaningful only relative to a given observer: I’ll get my coat.

It is easy to find examples of processes that involve evolution of states, but no “movement” of any kind. Consider muons - they are elementary particles with a mean lifetime on the order of \(10^{-6}s\). As being elementary, they have no internal structure or “moving parts” of any kind; there’s nothing there that “moves” or even “changes” at all during their lifetime. And yet, they decay after a statistically well defined amount of time. So here you have got an example of an interval of time without “movement”; it’s an evolution of states without motion of constituent parts.