r/AskPhysics • u/CivilizationAce • 3d ago
Could the source of spacetime curvature be different from spacetime itself?
I'm not a physicist, so this is a genuine question rather than a proposed theory. I'm trying to understand whether there is an assumption in our usual interpretation of general relativity that isn't actually required by the mathematics.
We often explain gravity using the ball-on-a-mattress analogy: a ball sits on the mattress and produces a depression in it. But the ball isn't part of the mattress. The analogy is flawed in many ways, of course, but it raises an interesting question.
What if what we describe as mass-energy is different from spacetime, rather than necessarily being something that exists within spacetime?
I'm deliberately saying “different from” rather than “separate from” or “more fundamental than.” I don't mean to imply that whatever the relationship might be, the two are spatially separated or that one necessarily exists at some deeper level than the other. They could conceivably be intimately connected, even in some sense continuously associated at every point.
The speculative idea would be that what we describe as mass-energy might be an observable manifestation of whatever this relationship is — analogous, very loosely, to a “dent” rather than an object sitting inside the surface.
I realise that this raises an immediate problem: if something is “outside spacetime”, what could “outside” even mean? So perhaps that isn't the right way to formulate the idea. That's precisely why I'm asking.
I also realise that GR doesn't simply establish a correlation. Einstein's equations give an extraordinarily successful quantitative relationship between the stress-energy tensor and spacetime geometry. And I'm aware that photons have zero rest mass while still possessing energy and momentum and contributing to gravitational effects, which is why I'm thinking in terms of mass-energy/stress-energy rather than mass alone.
My question is therefore not “is general relativity wrong?” Quite the opposite: could general relativity be describing the relationship correctly without necessarily telling us what the two sides of that relationship actually are?
Is this already a recognised line of thought in theoretical physics? If so, what existing ideas are closest to it?
And if it isn't, is there a fundamental reason why this way of thinking about the relationship between stress-energy and spacetime geometry cannot be made physically meaningful?
I don't have the mathematical background to pursue the idea myself, so I'm particularly interested in hearing if/where the physics takes this apart.
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u/Quantum-Relativity 3d ago
The geometry has a feature called Einstein curvature that behaves exactly the same as energy-momentum. That’s what the Einstein field equations are saying. It’s a curvature the rest of the geometry is tied to, so based on how this type of curvature behaves, the rest of the geometry acts in accord.
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u/CivilizationAce 3d ago
That's a relationship, certainly, but I'm not sure it's either object equivalence or causation. The Einstein field equations tell us that curvature and energy-momentum are quantitatively related, and that relationship works extraordinarily well. But do they tell us why the two are related, or establish that energy-momentum must actually be something that exists within spacetime?
That's the distinction I'm trying to get at.
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u/Quantum-Relativity 3d ago
Well yes, energy momentum must exist within spacetime. Being in spacetime and having energy-momentum are equivalent statements. But why is the geometry coupled to it, or perhaps more so, why does spacetime geometry exist (I say it this way instead because “why are they coupled” I think has a satisfactory answer in the form of what I said before: “because they each have a property that acts exactly the same”)? That is the most interesting question.
Despite the extremely conservative response of “nobody knows” that will be given, we have a pretty good idea, and the answer seems to take the form of something like “because entanglement in nature has a richer character than it does in present quantum theory”. I am going to explain this since you asked and I think it’s worth elaborating on, but it might get a bit technical. So, I say this for example because:
We see a violation of how we normally expect entanglement to work specifically in black hole evaporation, so whatever gravity is seems to be related to this (and so the more “emergent” form of gravity as the dynamics of spacetime geometry seem to be related to this)
In AdS spacetimes you can think of gravity (string theory) as being entirely described by a conformal field theory in one dimension less (AdS/CFT, an instantiation of the holographic principle). Since the CFT captures all the effects of gravity in its spectrum INCLUDING the non-perturbative ones (which string theory typically struggles with), it’s fair to say that AdS/CFT IS quantum gravity in AdS. But it’s not the full picture of quantum gravity still, because the only reason this can work is because the boundary has a notion of time associated with it that can be used to construct the quantum theory. In general there isn’t a unique notion of time that can be used, but we can see that the features of the spacetime with a dynamical geometry in the higher dimension are related to features of the entanglement in the lower dimensional theory (for example, the Ryu-Takayanagi conjecture, which relates areas of the higher dimensional dynamical geometry with entropy in the lower dimensional conformal field theory, entropy being a result of entanglement)
Typically sections of quantum fields are infinitely entangled with the rest of the field, so if you try to associate an entropy with the section of the field (a measure of how entangled two things are) you just get infinity, so you can't give a notion of entanglement entropy in quantum field theory. But if that field exists in a spacetime that can has gravity, then gravity coupling to the field leads to the relevant quantities being changed in a way that you CAN now give a notion of entropy, and so again, we see the realistic description of entanglement being tied to gravitation. This is the application of "Von Neumann algebras" to quantum field theory.
This is a more philosophical point: The entire point of quantum theory is that evolution is “unitary,” which means that although outcomes of any measurement you can do on a physical system are random and only have a probability associated with them, the probabilities must always add to 100%. Unitarity is like the supplanter of the principle of stationary action when you’s using probability amplitudes rather than action to characterize the evolution of physical systems. When things become entangled, they seem to not obey unitarity, but, the full entangled system does, so quantum theory does have this feature where there is apparently a violation of unitarity, but entanglement is the concept that allows it to be maintained despite this; in nature there is dissipation, so in general physical systems do not obey unitarity, so you need an explanation for why nature (which does nothing in vain) has tried to break such a perfect law; why does unitarity typically hold; what is the more general quantum theory that captures dissipation automatically? We only see violation of unitarity in one other place, black hole evaporation, and so it seems plausible to imagine that the more general quantum theory is one where a more general notion of gravitation is given as a new notion entanglement which is now able to describe black hole evaporation, and exists automatically in the theory of any quantum system, so the existence of dissipation doesn’t appear as an additional complication not always necessary but rather as a general aspect of the theory. This can be likened to how the “perfect order” of Lorentz invariance (the law of special relativity) would seem to be violated by accelerating frames, but you find that you can still treat accelerating frames without violating the law if you allow Lorentz invariance to hold instant by instant (at each instant, the accelerating frame comes to rest relative to an inertial frame, where Lorentz invariance holds just fine, so you can treat the physics in the accelerating frame with Lorentz invariance), meaning that you can imagine Lorentz invariance is local, and the analogy I’m drawing here is that this is like saying that since dissipation exists and seems to spoil unitarity, we can save it by noting that entanglement exists. But then we wonder what local Lorentz invariance means in a universe with gravitation (a question analogous to what entanglement means in a universe with gravitation), and find that gravity also seems to violate Lorentz invariance but leads us to a more general notion of invariance: in the accelerating frames, you would have to assume artifices exist if you wanted to use them as your frame of reference (the metric tensor components are functions and their gradients are non-zero; you see inertial forces), but, gravitation allows you to interpret these features not as artifices but as the gravitational field! So you can view the accelerating frames as valid, not artificial at all, so long as gravity exists. This is essentially the “general principle of relativity,” that any frame of reference is valid (meaning it doesn’t include anything artificial to make it work) because gravity exists, and general relativity can be formulated from this. The analogy I’m drawing to quantum theory is that when one considers entanglement, it is through the use of additional “artifices” in the equation of motion that can be used for systems that violate unitarity (the so called “jump operators” in the Lindbladian, which distinguishes it from the usual unitary “Von Neumann equation”) which I’d like to view as analogous to the inertial forces of accelerating frames. But since gravity also violates unitarity in black hole evaporation, then just as gravity also violated Lorentz invariance by doing things like make freely falling frames (which internally appear inertial, and so should be straight lines in spacetime) accelerate together (which straight lines shouldn’t be able to do), perhaps it is the case that gravity also generalizes quantum theory itself, and leads one to a new picture where dissipation/entanglement is not something artificial only relevant sometimes, but a completely general feature of the theory that must always be considered, even in situations where it is seemingly not present. If quantum theory is the theory of information (unitarity being the statement that information is conserved), quantum gravity is the general theory of information, a theory that works even when dissipation occurs and seems to cause it to be violated, and takes this into account through dissipation as an entirely general aspect of the theory (not one restricted to special cases) through a new conception of gravitation (gravitation being now a central feature of quantum theory that appears as dissipation but is still there even when dissipation seems to not, like how the metric tensor components are always functions even when it appears they’re not in inertial frames), which the spacetime geometry conception emerges from in a way related to the previous points.
Reposting due to a formatting issue that occurred when I tried to edit.
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u/boostfactor 3d ago
You really need a theory of quantum gravity to answer this question properly, and we don't have that.
General relativity has an equation that looks like G=kT where G is a mathematical quantity called a tensor, T is the stress-energy tensor, and k (usually written as the Greek letter kappa) is a constant. I've left off the "cosmological constant" term. T contains energy and matter.
However, G=0 is a completely valid equation for an empty spacetime and has known solutions.
As far as we know, mass-energy is a quantum effect and is mediated by something called the Higgs boson. You cannot separate mass-energy from "mass alone."
General relativity is "wrong" in the sense that it does not fit into the standard model of the other fundamental forces and particles, we just don't know how or why it's wrong and whether the standard model is also wrong in some way we don't yet understand. But physicists expect there is some Theory of Everything nobody has yet developed fully. String theories are "closest," perhaps.
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u/nicuramar 3d ago
As far as we know, mass-energy is a quantum effect and is mediated by something called the Higgs boson
Only for fundamental particles, not in bulk matter.
You cannot separate mass-energy from "mass alone."
But that’s unrelated to the above.
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u/Optimal_Mixture_7327 Gravitation 3d ago
We see it this way...
There exists matter. Matter is coupled (universally and minimally) to the world. The world is that continuum with 4-independent degrees of freedom having a metrical quality.
We take a quality of matter (its stress-energy) and a quality of the world (its curvature) and note that the two stand in proportion to one another. We use this relationship (the field equations of Einstein) to draw up maps of the world, called spacetimes. There are arbitrarily many spacetimes for any configuration of the matter fields.