Markus Hanke

The notion of a singularity is based on General Relativity, which is a purely classical model of gravity. Unfortunately, what happened at and immediately after the BB wasn’t classical - you need a model of quantum gravity for it, which we don’t yet have. However, even if there is a singularity, no physical infinities would occur, because none of the quantities you mention is meaningfully defined there; T=0 isn’t even part of the spacetime manifold. This is why it is defined as a region of geodesic incompleteness. You wouldn’t see anything at all; it would be completely dark. I’m sorry, but I fail to see any of this. What “theory” are you talking about, exactly? What alleged mystery does it address? What evidence are you referring to?

This is a meaningless concept - the BB represents a singularity in (classical) spacetime, so it is a region that is geodesically incomplete. If you were able to “stand” at the BB, all spatial distances would be zero, and no matter what kind of manoeuvre you performed, it would always take you only to the future. Asking what is before the BB is like asking what is north of the North Pole - it’s simply meaningless, because there are no past-oriented world lines there, just as there is no ‘north’ in any direction when standing directly on the pole. Also, once you account for quantum effects, a strong case can be made that smooth and classical spacetime breaks down long before you even reach the BB, so here too the concept of ‘before the BB’ is meaningless.

When you say ‘actually is’ you are assuming the existence of some absolute reference frame - but no such thing exists. Shape is based on measurements of space, which are relational quantities, and thus require an observer to make sense. The best you can do is define ‘actually is’ as being the rest frame of the Earth, but that’s an arbitrary choice; there’s nothing special about that particular frame. By using the appropriate formalism. In relativistic quantum mechanics, the wave function is always a representation of the Lorentz group - for bosons it will be a tensor of a rank equal to their spin; for spin-½ fermions, it will (in general) be a Dirac (bi)spinor. Both tensors and bispinors are covariant objects, meaning everyone agrees on them, and whether or not they describe a superposition of states is an invariant property. Thus, if there is no superposition in the rest frame, there is no superposition in any other frame too. The only thing observers disagree on is how far apart the particles are, but not whether there is a superposition; they’re just looking at the same system from a different angle in spacetime. You continue to be stuck on the idea that there must be some absolute notion of space and time, some way things ‘really are’ in 3D. The highlighted part is the issue, because spacetime isn’t 3D, and it’s not Euclidean. If you use the appropriate 4D description instead, then there is no issue and no contradictions. Until you can mentally perform the 3D->4D paradigm shift, you will remain stuck on this.

It is true that there are quantities in GR that do not depend on choice of reference frame, ie everyone agrees on them. These are tensors and their invariants. However, there are also coordinate quantities, which are those that are based on measurements of space, time or energy in isolation. These depend on the observer, as they are by nature relational quantities. So, whether or not the choice of frame is important will depend on which quantities you want to discuss. Saying that reference frames ‘don’t change anything’ is a bit too simplistic.

True enough. Just to make this extra clear though, what I wrote is simply an idea - not even a hypothesis, and certainly not a claim. I’m just curious if a large system, the parts of which only interact gravitationally (GR), could - at least in principle - exhibit unexpected dynamics akin to DM observations. This requires no new physics at all, it’s GR - a generally relativistic n-body problem with large n. Or to put it differently - what is the error introduced if one treats such an n-body system as continuous to make the computation possible, as compared to keeping is discrete? Are there global dynamics inherent in a discrete n-body system (again, based on GR) that aren’t found if the system is treated as a continuum? If so, DM would simply be due to our not using GR correctly, rather than any new physics. Again, just an idea. Due to the non-linearity of GR I think it is very difficult to estimate the error introduced by simplifying assumptions. Let us leave dark energy aside for now, since I think that is a different issue.

A quick Gedankenexperiment. Consider H2O molecules. The interactions between such molecules are of the electromagnetic and quantum mechanics kind, and are thus well enough described by Maxwell and/or Schrödinger equations. A very large ensemble of such molecules on the other hand becomes a fluid, which is described by the Navier-Stokes equations and exhibits dynamics and properties that aren’t present (or meaningful) on the scale of individual molecules. That’s an example of emergence. So far so good. Now instead of molecules imagine very massive objects, like stars eg, which interact approximately via gravity only, instead of EM and QM. The interactions are now well described by standard GR, there’s little mystery (but considerable computational effort) involved. So what happens if you have a very large ensemble of such objects, such as the stars in a galaxy, or the galaxies in the universe? It’s a lot like an ordinary fluid, except that the constituents now interact via gravity instead of EM - I propose the term gravitational fluid here. The big question then is - are there emergent dynamics in a gravitational fluid, just as there are emergent dynamics in an ordinary molecular fluid, given a sufficient number of constituents per volume? Could that be a potential model for dark matter? That way, DM wouldn’t require neither new particles nor modified gravity, but simply emergence. The caveat I see here is that the ~100 billion stars of our galaxy are a very small number of constituent elements, when compared to fluids like water; so perhaps no emergence can happen here, because there aren’t enough parts. On the other hand though the interactions between constituents in a gravitational fluid are non-linear and much more complex, due to being governed by GR. What are people’s thoughts on this?

To be honest, the entire concept of the Alcubierre bubble is interesting from a theoretical point of view - but as a propulsion technology it is completely useless. For one thing, the region of the bubble’s walls would harbour extreme tidal forces that would make it impossible for anything to enter or exit and still remain in one piece. The other big issue is that, once in motion, I see no physical way to steer/manoeuvre the bubble into a different direction, or even bring it to a halt. And there are several other problems as well, never even mind the need for exotic matter to create it in the first place. My concern here would also be of an ethical nature - if you were to create one of these bubbles with the right properties and direct it against a target, it would make for a very destructive weapon (tidal forces in its walls).

This person has somewhat of a reputation I’m afraid, so what he says is to be taken with a huge grain of salt.

And herein lies the problem - the energy density of a Casimir region is negative only relative to its non-confined surroundings; it isn’t negative in an absolute sense, it’s just lower than ordinary vacuum. That means the gravitational effect of such a region is the same as that of ordinary matter, and not related to what you’d get from exotic matter. You can’t build an Alcubierre bubble via the Casimir effect.

Obviously I don’t have definite answers on offer, since no one knows if macroscopic spacetime really is emergent, and if so, emergent from what. The only more ‘fundamental’ concept I can think of, which is in accord with known physics, and which might be able to give rise to spacetime somehow, are correlations. So we are talking information theory. And alas, a quick search on arXiv reveals that there is indeed work going on in that direction: https://arxiv.org/abs/2110.08278 Sounds good to me!

Indeed. I think it’s important to make this really clear - it’s based on a semiclassical approach, meaning it’s standard GR with standard quantum field theory thrown in, but accounting for more quantum effects than Hawking did. It’s not about full quantum gravity, and only seeks to address the specific issue of the information paradox. I’m personally excited that it appears to further hint at the idea of spacetime not being fundamental, but an emergent phenomenon.

For those of you who are interested in this. There’s been a flurry of papers on the subject over the past three years in particular, but it was very difficult to get the big picture. This is a nice, plain language summary. https://www.quantamagazine.org/the-most-famous-paradox-in-physics-nears-its-end-20201029/

That’s because the geometry of spacetime around a spinning mass is very different from that around one without angular momentum. In the former case, you need to perform more work to escape to infinity if you choose a path that runs counter to the direction of rotation, due to frame-dragging; in other words, there is no path-independence here. In GR this is true only in some highly symmetric special cases, but not in general. In Newtonian gravity it is always true, of course.

This is true only if you choose to parametrise the path using proper time - which physically just means that photons don’t have a rest frame. However, you can choose a different affine parameter, which will yield a non-zero result. Also, the world lines of the train’s constituent particles are time-like, so there shouldn’t be an issue.

I’m afraid I don’t follow you on this (maybe my fault). In this spacetime all the relevant components of the metric are explicitly time-dependent, so if the histories of these clocks differ, then they aren’t guaranteed to remain synchronised. Also, the dilation factor relative to the distant clock will be time and coordinate dependent. But maybe I misunderstood your thoughts.

Nice summary +1

Yes, exactly right. Note that the metric determines all relevant gravitational phenomena, so there’s really no need at all to try and carry over gravitational potential from Newtonian physics. How so? Time dilation between two points would be a time-dependent function rather than a single value, since all of spacetime here is filled with gravitational radiation.

Are we not overthinking this a bit? An object such as the train mentioned in this thread is just a collection of (many) individual world lines. The geometric length of each individual world line between given events is something all observers agree on; thus, the volume implied by an entire bundle (congruence?) of such world lines should also be something everyone agrees on. Or am I seeing this wrong?

Basically, the concept is meaningful only if it is independent of the specific path taken between the two events. This requires the presence of certain symmetries - which not all spacetimes have. For example, consider what happens if the spacetime is not stationary, such as in a binary star system. The work required to escape to infinity from any point within this system depends not only on where that point is, but also on when the escape happens, and what specific trajectory is taken. In other words, it depends on the path taken through spacetime, the metric of which now explicitly depends on both time and space coordinates. As such it isn’t possible to assign a single unique value that signifies gravitational potential to any point in that spacetime.

I didn’t mean to suggest that. Of course this needs to be done according to the proper rules and procedures of differential geometry in spacetime - the language of exterior calculus naturally lends itself to this. I remember MTW has a section that shows the proper procedure to construct volume integrals on semi-Riemannian manifolds; it’s that I was thinking of.

In 4D, you account for both space and time. If a boundary is contracted in space, it is expanded in time by the same factor, leaving the overall volume in spacetime unchanged. Or to put it more technically - the volume element in 4D is an antisymmetric tensor, so any volume constructed from it by integration will be a covariant quantity.

Well, the universe is a 4D structure, yes. But my main point was that in order to find quantities that all observers can agree on (ie that are independent of reference frame), you need to always go into 4D. So, length (3D) and time (1D) depends on observer, but hypervolume (4D) does not, for example. So the ontology of objects in spacetime is 4D.

Perhaps I should have been a bit more precise - it’s measurements of length that are relational, and the relationship depends on angles and orientation in spacetime. In practice that means that length contraction is observed along the direction of motion, but not perpendicular to it. Thus, for example, the initially spherical gold ions in the RHIC become flattened disks in the lab frame - and physically behave like flattened disks at the point of collision. So no, shape also depends on the observer. If you want to know about properties that do not depend on the observer, you need to consider all four dimensions of spacetime, and not just 3D measurements. For example, the train you previously mentioned would trace out a (4D) hypervolume in spacetime between two given events; this would be a quantity all observers agree upon, even if they don’t agree on isolated measurements of space and time. Thus, ontologically there are covariant and invariant quantities - but only in 4D. You always need to consider both space and time. It’s only our cognitive habit of separating these that creates confusion and misconceptions.

It is meaningless to ask about “size” separate from a specific observer, since this measurement designates a relationship between two frames in spacetime. It’s not an intrinsic property. Thus there’s no contradiction, because we are dealing with relational properties, so the ontology of this is also strictly relational. In other words - all observers are right, but only in their own local frames.

This is just getting bizarre now.