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When a stone is thrown in water, water waves are created. The stone imparts its kinetic energy to water. Likewise a sound speaker imparts its kinetic energy to air molecules. When an electron falls down to a lower orbital, it releases a photon; photons constitute electromagnetic waves. It is said that when two black holes merge, they produce gravitational waves which travel through spacetime at speed of light.

I understand that mass could affect spacetime. A mass could distort spacetime, a rotating mass body could drag the spacetime along with it, etc. Coming back to the merger of two black holes. Informally speaking, when the black holes merge, there must be a kind of unfathomably rapid and huge blast and this blast creates a kind of sonic boom, and this is a crude description of generation of gravitational waves. It'd mean that spacetime is as real as it could be. If it was just a math object and not a real or physical the gravitational waves won't be able to propagate. The spacetime is the medium for gravitational waves.

I was reading this answer by @JohnRennie https://physics.stackexchange.com/a/156327/84624 where he says that spacetime is just a mathematical construct in general relativity and therefore when the space expands nothing new is created and nothing is stretched. Is spacetime just a math construct or what? Where am I going wrong? Could you please guide me?

Edit:

Replying to this comment, Gravitational waves manifestation of 'physical' spacetime? I didn't intend to pose a question in disguise. The reason being that one of my questions was closed as being a duplicate (though, in my humble opinion, it was not) and I was directed to a question where JohnRennie had answered. As a layman, I would say, JohnRennie's answer is too rigid, especially in the context of my closed question. Not sure if my question is waiting deletion but it's still accessible: Relationship between expanding space and dark energy

I don't think Einstein, 'founder' of spacetime, himself really thought of spacetime just as a math construct. He was convinced that there is more to the spacetime. Even some notable physicists went on to say that Einstein got rid of one aether for his one theory and went to embrace another form of aether for his other theory.

The following quote is first paragraph from Einstein's essay.

If we are here going to talk about the ether, we are not, of course, talking about the physical or material ether of the mechanical theory of undulations, which is subject to the laws of Newtonian mechanics, to the points of which are attributed a certain velocity .This theoretical edifice has, I am convinced, finally played out its role since the setting up of the special theory of relativity. It is rather more generally a question of those kinds of things that are considered as physically real, which play a role in the causal nexus of physics, apart from the ponderable matter that consists of electrical elementary particles. Therefore, instead of speaking of an ether, one could equally well speak of physical qualities of space. Now one could take the position that all physical objects fall under this category, because in the final analysis in a theory of fields the ponderable matter, or the elementary particles that constitute this matter, also have to be considered as ‘fields’ of a particular kind, or as particular ‘states' of the space. But one would have to agree that, at the present state of physics, such a point of view would be premature, because up to now all efforts directed to this aim in theoretical physics have led to failure. In the present situation we are de facto forced to make a distinction between matter and fields, while we hope that later generations will be able to overcome this dualistic concept, and replace it with a unitary one, such as the field theory of today has sought in vain.

On the Ether, Albert Einstein, 1924

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    $\begingroup$ This is a philosophical question in disguise, not really a physics-related one. It could be reformulated as "are things we observe faithfully reflecting reality?". Also, what do you mean by "physical space-time"? Is it different from space-time in general relativity? What do you mean by "real"? $\endgroup$ Mar 1, 2022 at 10:17

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This issue has had a long debate. One might say it is not strictly a physics issue, being on the border between physics and meta-physics. Meta-physics is concerned with such philosophical issues as how knowledge relates to the things known about, how physical models relate to the phenomena they describe, and what does the word "real" mean. However a good understanding of any area of physics is aided by good intuition about the nature of the things under discussion, so I think the question as asked is also a physics question. It can be interpreted as, 'what ways of thinking about spacetime and general relativity prove to be helpful in gaining understanding'. However there is not a complete consensus on the answer. It seems that some people are drawn to a more mathematical point of view where spacetime is not accorded the status of being 'real' (whatever that means). My own view is that spacetime is as real as can be, but its reality is of a highly subtle kind, because you cannot directly detect spacetime. For example, there is no sense in which a physical thing such as a planet can have a velocity or an acceleration relative to spacetime: the concept of motion is not like that. Motion is a way of referring to worldlines not being parallel. Spacetime is sort of hiding in the background here.

And yet.

And yet, energy and momentum can move around the universe via gravitational waves. So this lends some sense to the idea that spacetime is 'something' after all. It is just that it is not 'some thing'. But it is physical, and real (or so I would assert).

One can lend a bit more weight to the notion that spacetime is physical by reminding ourselves that it is not just an arbitrary manifold. At any given event it has one and only one Riemann curvature tensor. And that curvature tensor can be measured in complete detail (by using such observations as adding the internal angles of triangles oriented in various ways). So the curvature tensor has the status of 'just as physically observable and objective as anything else in physics'. So I think that tensor earns the right to be called 'real' (or 'an element of reality') as much as anything else in physics. And then one may reasonably ask, 'ok, so what is it the curvature of'? The answer is 'spacetime'.

Finally, among the ways of handling the mathematical treatment of general relativity there are the more 'field-theory-like' approaches. In this kind of approach we don't have to adopt the geometric interpretation, where spacetime is a manifold. Instead we forget about spacetime and just say that there is a collection of fields, one of which is the gravitational field, and all these fields couple together etc. etc. We don't have to specify a further structure called spacetime in this approach. But in these ways of describing the mathematics, the field called 'gravitational field' plays a role very much like the role played by spacetime in the geometric interpretation, so then it looks like this 'spacetime' is objective and physically influential after all.

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    $\begingroup$ Note that it is possible to formulate General Relativity with zero curvature, which could be seen as a counter-argument to it being "real". See arxiv.org/abs/1903.06830 $\endgroup$
    – scaphys
    Mar 1, 2022 at 18:17
  • $\begingroup$ @scaphys Yes that's a helpful comment! These alternatives are examples of what I had in mind with the final paragraph. But it still remains that the components of what is called Riemann curvature tensor are objectively measurable things, giving things like sums of interior angles of triangles. $\endgroup$ Mar 1, 2022 at 21:39
  • $\begingroup$ @AndrewSteane Thank you for the help. Your answer was really helpful along with some others. I have always thought of spacetime as something real but something very, very different from other 'real' or physical entities! $\endgroup$
    – PG1995
    Mar 2, 2022 at 2:01
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When a stone is thrown in water, water waves are created. The stone imparts its kinetic energy to water.

This is an observation with our eyes . Then we found that mathematical solutions of differential equations (called wave differential equations) not only allowed to fit with functions the observation, but also to be able to predict future set ups. The same hold true for sound, first comes observation, then the model.

Modeling mathematically light observations led to the Maxwell wave equations, that could fit observed light behavior and predict new set ups with great accuracy. For your photon observation you are mixing up the need for a new mathematical model to fit atoms and molecules, with the classical electromagnetic waves.Photons are quantum mechanical entities and fulfill quantum mechanical equations where the waves are probability waves. Fortunately the mathematical models for the quantum behavior of the photon can be shown ( see my answer here for links)to contribute to the emergence of the Maxwellian equations' light, by the confluence of zillions of photons.

General Relativity is necessary to model mathematically the observations of gravity, to fit existing data and be predictive of new situations, and is very successful in this. The fact that it does this with the complicated mathematical form of space time variations does not lead to suppose that space time is like the water the water waves need. Different mathematical functions, as with quantum mechanical waves, make up the theoretical model.

There is no independent existence of the wave function in quantum mechanics, it is just a mathematical tool that gives functions that fit the data.

In the link of @JohnRennie "Specifically, if we use the metric to calculate the distance between two comoving points we find that the distance we calculate increases with time. "

It is because we found experimentally that the distance increases with time, that we use the theory/model of GR that is able to fit this observation.

Lets take the simple example of the need of spherical geometry to describe large distances on earth, because euclidian geometry was violated. Would you say that "space is curved"?

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  • $\begingroup$ " first comes observation, then the model" Gravitational waves are actually a great example of the opposite occurring! $\endgroup$
    – TimRias
    Mar 1, 2022 at 10:32
  • $\begingroup$ Are you trying to claim that the pond is somehow more "real" than the electromagnetic field or spacetime? $\endgroup$
    – TimRias
    Mar 1, 2022 at 10:33
  • $\begingroup$ @mmeent I am saying that it is observations to start with that are fitted with the model, and then the model is validated by its predictions for new observations. The observation of gravitational waves is one more validation of the theory of GR $\endgroup$
    – anna v
    Mar 1, 2022 at 10:54
  • $\begingroup$ Thanks for the answer! $\endgroup$
    – PG1995
    Mar 2, 2022 at 2:02
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Spacetime is surely as real a physical object as any other object in physics. You directly experience here and now, not there and then. Gravitational waves are ripples in spacetime that carry energy. If you fall through the event horizon of a black hole you will surely experience real, physical consequences.

But, the rules governing how spacetime behaves are not the same rules that govern rubber sheets. It is often a mistake made by novices (and some who should know better) to apply intuition from our experience with terrestrial objects to spacetime itself. This intuition can get you in trouble: for example, it is incorrect to think that expanding spacetime requires the creation of "stuff" from nothing, as John Rennie correctly notes in the answer you linked to. To really understand what rules spacetime obeys, you need to understand an abstract, mathematical description in terms of Riemannian manifolds.

There are speculations that spacetime may not be a fundamental part of a theory of everything, but should emerge from some deeper structure. However, much like most people would agree a chair is a real object even if fundamentally it is "just" a particular arrangement of atoms, even if spacetime is an emergent phenomena, I think it is useful to think of it as real for describing our experience.

Therefore, I both think that it is useful to think of spacetime as a real, physical object, but also be aware there are caveats: be careful applying intuition based on more familiar objects, since it may not apply; and be aware that (like any object in physics) one day we may discover that spacetime is not a fundamental object but rather something that emerges from a deeper theory.

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  • $\begingroup$ I don't think you see an horizon if you fall to a black hole. The horizon exists for stationary faraway observers only. $\endgroup$ Mar 1, 2022 at 17:46
  • $\begingroup$ @Felicia If you fall past the horizon you will hit the singularity (or whatever the singularity is resolved to in quantum gravity). Before you hit that you will experience some pretty strong tidal forces. $\endgroup$
    – Andrew
    Mar 1, 2022 at 17:49
  • $\begingroup$ Yes, will experience pretty strong tidal effects, but not necessarily on the the horizon. If the hole is big enough, you dont experience much and can see light coming from a torch in front of you. Or not? Up to a certain point maybe. $\endgroup$ Mar 1, 2022 at 17:59
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    $\begingroup$ @Felicia I'm not saying that you experience tidal effects at the horizon. I'm saying if you cross the horizon, you will inevitably hit the singularity. On the way, the tidal forces become arbitrarily large. So you will inevitably hit a region of spacetime with strong enough tidal forces to spaghettify you if you cross the horizon. $\endgroup$
    – Andrew
    Mar 1, 2022 at 18:06
  • $\begingroup$ Thanks for the answer! $\endgroup$
    – PG1995
    Mar 2, 2022 at 2:02
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I think that GR spacetime is more than a construct because some results of the theory (as gravitational waves), were not known when it was developed.

On the other hand, a good example of a construct is the approach to Newtonian gravity by Cartan, using differential geometry. Without using SR and its Lorentzian metric, it explains the force of gravity as a connection $\Gamma^j_{00}$ in a (not GR) spacetime. And calculates the Riemann tensor, showing that the spacetime is curved. All the Newtonian gravity can be explained that way, and we could imagine that Riemann himself could have developed it, if lived longer.

But it is only a different (while very interesting) interpretation of Newtonian gravity, saying nothing about light deflection, mercury precession, and gravitational waves. All the known results are confirmed, but nothing new is predicted.

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  • $\begingroup$ Thanks for the answer! $\endgroup$
    – PG1995
    Mar 2, 2022 at 2:02
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The question reduces to: What is space? In the theory of hidden variables, in relation to quantum mechanics, every particle is submerged by hidden variables, directing the position and velocity of a particle. These can be considered constituting space. Then what about empty space? As you probably know, according to quantum mechanics, space is not empty, even when there are no particles in it. It could be the hidden variables accompanying this vacuum state making up the vacuum itself.

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Spacetime is a mathematical construct that we use to explain our sensory perception of the world. Imagine you send a light signal from sender to receiver. If they are literally not at the same place (thus identical), the transmission process would take some time because of the finiteness of light speed $c$. Now, let us assume the light propagates instantly, i.e. $c~\rightarrow~\infty$. Then, between sending and receiving of the signal no time passes. In such a world the notion of space (distance) would be not necessary. All would happen at the same 'point' - mathematically a zero dimensional space.

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  • $\begingroup$ Since classical, pre-relativity physics corresponds to the $c \rightarrow \infty$ limit, this would seem to imply that space is meaningless in Newtonian physics. $\endgroup$
    – Andrew
    Mar 1, 2022 at 19:46
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    $\begingroup$ @Andrew, you are right, what I have said would be probably true in the world without inertia $m~\rightarrow~0$. Obviously, it is not the case in Newtonian physics. $\endgroup$
    – JanG
    Mar 1, 2022 at 20:23

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