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This is an interdisciplinary (philosophical physics) question.

In Newton's absolute spacetime model, spacetime is described as a physical entity. However, in the relational spacetime model (supported by many including Plato, Aristotle, Descartes, Leibniz and even Einstein), spacetime is not a physical entity. It is just a mathematical tool.

Later, black holes were discovered. Black hole singularity is a hole in the fabric of spacetime. If there is no fabric, there can be no holes. This means that spacetime is a fabric - a real entity.

Moreover, space is expanding. If it is just a mathematical construct, how can space expand (there is evidence of expansion)? This also implies that spacetime must be a real entity.

If I remove all matter and energy in this universe and also the quantum fields, will there be a fabric/fluid of spacetime still left in the universe?

If so, what can be this fabric made of?

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    Calling space a fabric and calling black holes holes in space are just metaphors, not to be taken literally. Also, I don't think anyone says that space is "just a mathematical tool". The principle debates are whether space is an object or a relationship between objects and whether real or ideal. Commented Apr 8, 2023 at 16:37
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    Be careful of use-mention errors and map-territory errors. If I have a ladder that is five feet long, and lean it against a wall so that it only reaches up the wall by four feet, is the ladder really only four feet tall?
    – BillOnne
    Commented Apr 8, 2023 at 16:56
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    Indeed there's been long debate in philosophy of physics between spacetime substantivalism vs relationalism. Shape dynamics as a possible contemporary alternative to GR was initiated by physicist Barbour based upon quotient spaces of rigid translations, rotations and dilatations of the configuration space with the symmetries of dynamical theories explain the seemingly real and substantive spacetime (conformal) geometry aka gravitational ether. For similar effort also see Pooley 2013, Substantivalist and Relationalist Approaches to Spacetime... Commented Apr 9, 2023 at 4:45
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    Why are you asking a physics question on philosophy.SE?
    – RonJohn
    Commented Apr 11, 2023 at 13:38
  • @RonJohn Physics SE is concerned with questions regarding mainstream physics. One cannot ask questions regarding topics which are still debated.
    – user65403
    Commented Apr 12, 2023 at 12:34

5 Answers 5

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You are wrong to state that Einstein considered spacetime to be just a mathematical tool. For a good perspective on this, have a look at Minkowski's writings on the nature of spacetime, and Einstein's subsequent responses to him.

Spacetime is a physical entity with physical properties which may not make intuitive sense to us (and are intangible to our human senses) but which are real nonetheless. We can actually measure those properties (its capacity for conveying electric and magnetic fields, for example) and directly calculate from them the speed with which local changes in those fields will propagate through space and time (yielding the speed of light).

Spacetime is usually referred to by physicists as the vacuum and it has been known for decades that the vacuum is not empty of everything. It contains quantum fields whose values in "empty space" are not zero even at zero temperature, and if their presence is not taken into account then the predictions furnished by classical physics will be in error. Much has been written about the quantum vacuum and anyone desiring to explore what philosophical consequences its properties might have should read up on this topic.

A handy place to start is with Timothy Boyer's paper, The Classical Vacuum. From there, you'd move into a treatment of the quantum vacuum. The people on the Physics Stack Exchange can recommend to you some of the standard works on it.

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  • Of course, "real" is a contentious word in the philosophy of science. But it's fair to say that it's as real as anything else we deal with, like subatomic particles.
    – Barmar
    Commented Apr 10, 2023 at 14:12
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    This answer is somewhat misleading, because the quantum fields that we know of (like e.g. the electromagnetic field) aren't themselves spacetime (absent any quantum gravity theory). Yes, "empty space" isn't actually empty, but the question is about spacetime absent any electromag, weak or strong force related fields.
    – ajd138
    Commented Apr 10, 2023 at 22:12
  • @ajd138, spacetime is never absent of those fields and even if it were, gravity would still propagate in it. Commented Apr 10, 2023 at 22:18
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Although Einstein entertained relational ideas in the early years under Mach's influence, he did not support a relational spacetime after developing general relativity. He believed that it requires spacetime to be a physical entity, albeit different from Newton's, and was even willing to call it "gravitational ether", see his address Ether and Relativity (1920). It was delivered well after his hole argument of 1916, which is considered a strong argument for relational spacetime, meaning that Einstein was not impressed by it.

Einstein identifies the physical nature of spacetime with the measurement relations expressed by the metric tensor and the ubiquitous gravitational field. However, it is a peculiar entity that lacks its own mechanical properties, and only manifests physically by setting up measurement standards and affecting ponderable bodies and other fields. So it is, perhaps, unsuitable to think of it as a "fabric" made of something, which we'd expect to have such properties of its own.

Considering that the invariant essence of a metric is its curvature, one can also say that Einstein's spacetime rather manifests by "curving" other fabrics, like mechanical and electromagnetic processes. Some authors even go as far as to say that it is "made of geometry", being an evolving Riemannian manifold. Here is Einstein in his own words:

"This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials g_mn), has, I think, finally disposed of the view that space is physically empty. But therewith the conception of the ether has again acquired an intelligible content although this content differs widely from that of the ether of the mechanical undulatory theory of light. The ether of the general theory of relativity is a medium which is itself devoid of all mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events.

[...] As to the part which the new ether is to play in the physics of the future we are not yet clear. We know that it determines the metrical relations in the space-time continuum, e.g. the configurative possibilities of solid bodies as well as the gravitational fields... There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space. On the other hand a part of space may very well be imagined without an electromagnetic field...

[...] Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."

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  • Shall I satisfy myself by saying that even when all matter and energy and also the quantum fields are removed from the universe, there is a field of spacetime left in the universe.
    – user65403
    Commented Apr 9, 2023 at 5:27
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    @AgnibhoDutta Perhaps. And it is a curious one. Unlike other fields that have their own intrinsic qualities and state of motion, this one subsists by making their motion meaningful, and affecting it. A peculiar "fabric made of geometry" in the almost literal sense of "geometry" — land measurement. It lacks mechanical properties because it makes mechanical properties possible in the first place. Reminds me how some theologians say that God does not have existence because he is the source of existence.
    – Conifold
    Commented Apr 9, 2023 at 6:29
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If so, what can be this fabric made of?

Science today does not know. All we know is, even in its emptiest state, as an absolute vacuum, containing absolutely no physical particles, the vacuum seems to be filled with something that fluctuates constantly and creates stuff that pops into and out of existence.

What is behind this phenomenon? It's all speculation.

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Re: Newton's absolute spacetime model and the fabric of spacetime

If you can join separate relativistic frames by knowledge or calculation, such as how GPS satellites can be synchronised, then in the larger scale you may have an absolute manifold of simultaneity which can progess temporally as Newtonian spacetime. The fault-lines happen at gravitational singularities where synchronisation would then seem to be impossible. Up to those asymptotic limits the fabric is fairly tangible — everyone being-in-their-worlds, now. But it must remain theoretical, since the principle of unobservability prevents confirmation beyond causal limits, i.e. connected by speed of light.

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The fabric is made up of observations.

Now it may seem impossible for space to be observed everywhere, but you (like many in science) forget one important detail: GOD.

If YHVH/GOD is real, then everything is related to an observation ("and it was good"). This create a quantum entanglement you may call a fabric of spacetime, because it is remembered.

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    What is the meaning of "YHVH/GOD"?
    – user65403
    Commented Apr 14, 2023 at 4:19
  • It is defined roughly as "all that is", which would include space and time, but notably does not include Man's mind nor the disharmonious movements of "satan".
    – Marxos
    Commented Apr 14, 2023 at 22:39

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