Having studied GR as far as Einstein's tensor equation and a bit beyond, I'm just doing a bit of a double-take wondering what we mean when we talk about spacetime. Frequently it is referred to as if it is a thing that exists, like mass and energy. For example, we say that spacetime is curved as if it is a thing in the universe that is curved. If hypothesising about multiverses we might talk about there being numerous distinct spacetimes as if they were all different things. On reflection though, I have gravitated towards the following view: 1.- spacetime is just a mathematical model that's useful for predicting the interaction of mass-energy 2.- it has no independent existence of its own and without mass or energy there would be no meaningful concept of spacetime 3.- when we talk about spacetime being curved we are just talking about properties of the theoretical 4-dimensional manifold we use to determine what path light rays will follow, particles will fall etc. Does this view make any sense?
It does to me. Surely all mathematics is abstraction ? What is amazing that nature can be so well described by it. Maybe mathematics contains all possible physical laws and it's just a matter of finding those that explain the data best. Pretty soon I expect someone will point out that space exists ( we can measure it with rulers), and so does time because clocks measure it. But spacetime is a weird mixture of these with possible curvature or translational defects which look like abstractions to me.
Spacetime can't not exist. Why. Just imagine the Big Bang. Spacetime grows from near planck size to the entire universe with billions and billions of galaxies. How can something not real grow. Hence spacetime as manifold should be something that exist and can grow and morph. How can mere math models produce the Big Bang. Space actually expand. How can space expand if space (or spacetime) is not some kind of fabric like thing.
I think it makes sense and it has a nontrivial content. Points in space or spacetime have no independent existence. There is something called "the hole argument" that makes this clear. A geometry is an equivalence class of manifolds and metrics. It is not the unique correct metric that expresses the world's geometry. A geometry is more abstract, more like a web of relationships between events. There is no objectively real rubber sheet. I find it hard to say. We talked about this here: https://www.physicsforums.com/showthread.php?t=166997 Einstein said something about this when talking about the principle of General Covariance (diffeomorphism invariance): “Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität. ..." “Thereby time and space lose the last vestige of physical reality”. for an online source see page 43 of www.tc.umn.edu/~janss011/pdf files/Besso-memo.pdf In another context ( In the introduction of the paper on the perihelion motion presented on 18 November 1915), Einstein wrote “durch welche Zeit und Raum der letzten Spur objektiver Realität beraubt werden,” “... time and space are robbed of the last trace of objective reality” To summarize, both quotes are from Nov-Dec 1915, one is from a paper on perihelion motion and the other is from a letter to Moritz Schlick a few weeks later. ================================== There is something meaningful here. It's not just empty words. I find it hard to pinpoint exactly. Maybe he is saying that locations have no objective reality. the story is told in terms of relationships. Events are located in relation to other events. Bohr said something like this: Physics is not about how nature is. It is about what we can say of it. All we have are the measurments we can make, and the predictions and the observations. We cannot make absolute statements about what nature is. We can only say how it responds to measurements. This also is a kind of relational point of view---coming from the other direction, from QM rather than from GR. Ultimately a physical theory boils down to the finite information we have, and how these finite pieces of information are related. There is no spacetime continuum, and no wave function either. they are mathematical conveniences. It's past my bedtime, Mr.Kirk. I've tried to respond to what you said, but may not have managed to be very coherent.
At the end of the above thread you shared. There was this statement by a poster called Mejennifer and she said (no follow up to it): "At any rate, I am not aware of any experiment that proofs or even suggests that reality is diffeomorphism invariant (whatever that might mean). And I think it is even doubtful if an experiment could ever determine that." Is that true. No experiments can determine General Covariance (diffeomorphism invariance)? If not and experiments have proven it, is this proven categorically already? If so, and spacetime points dont' have solidity and it is just the relationship of the geometry, then it's very highly likely that this universe is just a simulation in a computer or occuring in some distance horizon in the holographic principle and our universe some kind of projection. This makes sense in light of the fact that spacetime and the wavefunction don't really exist but just equations.
This statement will prove that spacetime does have an independent existence of its own ONCE gravitational waves have been detected. As their detection has been sought so far for about forty years without success I would say it is still an open question..... Garth
Another thing. I was re listening to Brian Greene The Hidden Reality audio and he said something like this: "If instead of zero, he entered a positive number on the third line, endowing the spatial fabric with a uniform positive energy, he found every region of space would push away from each other producing what most physicists thought impossible, repulsive gravity... " Brian was describing the cosmological constant. If space was not an entity, where is the cosmological constant repulsive gravity contained, if not in the "fabric" of space? Einstein proposed this after 1920's so didn't it conflict his Hole Argument?
If you frame it like this, then yes: It "exists", in the same sense in which "mass and energy" exist The concepts called "mass" and "energy" are just parts of models as well.
Due to the size of the material, it's difficult. I'd like to find a quote from Maxwell's treatise I remember where he points out that all mathematical models are ultimately suspect in representing all facets of reality. They sooner or later break down and misrepresent some aspect of reality (whatever that is, apart from what we can measure and sense)
They haven't been detected directly, but we can be absolutely certain that they exist and carry energy, since we see energy disappearing from the Hulse-Taylor binary pulsar at exactly the rate predicted by GR.
I am a relativist and 'believe' that spacetime together with gravitational waves 'really exist'; however I concede that, unless detected in controlled laboratory experiments such as LIGO, alternative theories, which explain gravitational wave energy loss (and spacetime cuvature effects) by other means, cannot be excluded. We see energy disappearing from binary pulsars as predicted by GR, but that might be because GR emulates a deeper theory, which 'we' will call 'quantum gravity' for the sake of argument, that might explain gravitational forces, and the slowing down of the binary pulsar system, not as the effect of spacetime curvature but by the exchange of graviton virtual particles. Garth
That's really well said. Also, I think there are very well defined physical limitations for spacetime. That makes it seem really real to me. That comment also makes it seem really real.
I would consider this a valid reason for skepticism if there was an alternative to GR that was (a) well-motivated, (b) consistent with current observations, and (c) described energy loss from the Hulse-Taylor system as being due to something other than gravitational radiation, and (d) made predictions that differed from GR's in some way that was testable. Quantum gravity fails to satisfy c (and possibly d as well). Everybody doing current work on quantum gravity wants very much to make sure that whatever theory they manage to come up with reduces to GR in the classical limit. That means that if their theories were known not to have gravitational waves in them, they would already have been discarded as candidates for a theory of quantum gravity. In any case, quantum effects are irrelevant here, because the Hulse-taylor system doesn't have any structure on the Planck scale, so it is purely classical, to an incredibly high degree of precision -- more classical than a basketball sailing through the air.
1: Nearly so. Space-time has been a graphical representation of the mathematical description of positions and motions for centuries. Obviously that makes sense. And you might consider such concepts as "space" and "time" more abstract than "energy" and "mass" - but that is probably a matter of opinion. 2. Indeed, without our material world we would not have the means (or at least, not the same means) to define those concepts. 3. It is a fact that "curved spacetime" refers to the graphical (geometrical) description of the mathematical relationship - at least, that is the way people like Einstein used that kind of expressions. See for example http://www.bartleby.com/173/17.html : "space-time" describes the world of physical phenomena.
Don't forget about the Inflaton field. It is said to inflate spacetime after the Big Bang. So if spacetime is not real but just pure aid for calculation, how does inflaton interact with something non-existent. Pls. address this Marcus because I still think it's possible spacetime is not real because if space points are real.. General Covariance is not possible like you said.
That's an interesting perspective on it. Do you think they are different from electromagnetic waves in this regard, given that an EM wave consists of an E and a B field, each of which varies over time and space in accordance with the solution of a wave equation, whereas a grav wave is a gravitational field that varies over time and space in accordance with the solution of a different wave equation. When you say the waves have energy I interpret this to mean that: 1. The system that emits the waves loses energy by emitting them; and 2. The wave can perform work on another body/system Is there more to it than that?
Well, I wouldn't really describe it as an oscillating gravitational field, since it's a phenomenon described by GR, and GR doesn't really describe gravity in terms of a field. GR deals with tensors, and the gravitational field is not a tensor. GR describes a gravitational wave as an oscillating curvature of spacetime. Sure, I think that's fine. GR doesn't have a general principle of conservation of energy that applies to all spacetimes, but it does have one in special cases such as asymptotically flat spacetimes. That means that it covers the radiation from the Hulse-Taylor system, for example.
Einstein seems to have drifted to a different perspective as he aged - some of the quotes from his later years conform with the notion of a substantive spatial reality