The title is expanded below, for discussion, results are valid for both SR and GR.

Opinions on if spacetime is real, as a "physical thing", are not metaphysics-- and this is evidenced just by asking the very question and even doubting it. For example, asking about virtual particles or hidden states is not metaphysics, as most physicists would agree (as seen in citation references).

Some may think it is not real, but evidence points -- for more than 100 years -- that it is as real as movement. We do not wage to think we are immobile, and that movement is a mathematical concept. The consequences of spacetime, and further dimensions yet unexplored in physics, are part of a 4D+ reality where they show new aspects. One of these aspects is a fusion of space and time that we cannot uniquely separate.

Of course, by asking for opinions, we are positively using RG, far away from a supposed confidence on any person, no matter how famous or capable.

Rather, we are not positioned as ad hominem targets, but as partners in a dialogue. Opinions are fallible, including mine. My opinion is in this discussion head, and below. The theme is gathering importance, the decision time is closer, and there are optons. We want to hear.

PROLOGUE -- Welcome to the party!

The discussion is not about contesting SR. We just do not believe in it, it has been observed too many times to not be real, and calculated, coherently.

We also see, everyday, relativistic accelerators of neutral particles -- a frequent philosophical objection to SR, that one would not see time dilation or length contraction with neutral particles, but here they are, provided by nature [1]. There is no ontological question anymore, as we shall see, no question about SR to accelerate neutral particles. We refer the reader to [1], to further explanations on why this point might be important. See also [2,3].

The current 4D spacetime formulations, in SR and GR, see [4,5], are confirmed, when space transforms into time, and vice-versa, plus the other arguments below. Rather than "fighting" the other formulations, such as the original formulation by Einstein, and others, they are included, also Clifford(3,1), where nature is 3D +1D, as right. Some even say 3D, such as Newton, which is also considered right.

How? Any of these 3D and 3D+1D theories are right, because 4D ⊃ 3D +1D ⊃ 3D, in set theory, a fundamental theory in maths. In other words, the other theories with less dimensions are grandfathered in 4D spacetime, with nothing left to discuss about this.

Their region of validity, though, is less. Someday, if the universe is revealed to be 5D, the same will happen with the current 4D theory -- it will continue to be right, in its region of validity. And the same is true even for the 3D Newtonian theory today, where time is absolute -- useful, as comoving observers feel no effect in SR, and no effect in GR if in free fall in a gravitational field.

The working assumption of this discussion is that at least 4D spacetime exists, while 3D +1D, 3D, and even 2D (as the rock example can show, in [1]) exist too. Welcome to the party!

IF SR EXISTS... THEN GR...

This discussion -- IF one will "believe" in SR -- is about how to measure time and space in SR and GR. Since both SR and GR depend on spacetime, as we are using the Minkowski formulation for SR, we can treat them together, even though the metric differs.

This a standard technique in the scientific method, to take the IF YES branch and investigate what would happen, used also in maths with the yet unproven Riemann Hypothesis, no one is blocking. Let us take the IF YES, as one may say, in spite of the facts already showing SR.

A rock thrown on Earth, with a clock attached to it, will follow an accelerated motion, then decelerate to a stop. After the apex, the rock is in free fall in the gravitational field, including the Earth, the Moon, the Sun and other influences, here assumed as all just gravitational.

The trajectory can be calculated using SR in the 4D spacetime formulation, which works with accelerated motion, but not using the original SR formulation by Einstein, that works only with inertial motion.

The original formulation, however, is still taught today in US colleges and Ivy League universities in undergraduate studies, for example using the physics textbook by Serway.

The clock, comoving with the rock, will measure what is called the proper time, an invariant in 4D spacetime, calculated by the inverse function of the arc-length function, and the space coordinates will be zero, it does not travel in space. To an observer at rest in the ground frame, the rock does travel in space coordinates, and the time coordinate measured is dilated.

Time and space do not exist without the other. We see in our measurements in nature, such as the rock above, that the existence of 4D spacetime, is not just mathematical but experiential (see below). Thus, the 4D spacetime SR is also the law in the universe, even far away from the Earth and the rock [1, 2].

There is no valid ontological question anymore, as we show below, space and time can transform into each other, in nature that we can experience. One can still, of course, discuss the acceptance of this fact, here on Earth, consciously, freely, openly, but without ontological questions left on the nature of the universe, as far as, literally, anyone can see, billions of years in the past.

ONTOLOGICAL QUESTION

Turning to the ontological question, what is place in the scheme of things in nature, of SR 4D spacetime: maths or physics?

Is 4D spacetime just a use of mathematics, or does it represent nature in ways that using lesser dimensions just can not do?

Is 4D spacetime like a spreadsheet of calculations, not really necessary, for a reality that is entirely experienced as 3D +1D, or even 3D with time as a parameter?

Names seem to not matter, as expected, in physics. it would seem that it does not matter, then, if someone, for example, chooses a geodesic to extend Newton's First Law, overcome beautifully our limitation then (to define "straight line"), and designates it as an extended "inertial motion" -- the geometric basis is the same, the physics did not change. Or, like Mashhon, describe an infinte family of comoving observers, 3D, each one as a flash in time. One would seem to need less mathematics, it can all be solved in 3D +1D, even 3D, not needing 4D. But the context is just more limited, the region of validity is less, as we show next.

It is physically limiting to use names that do not distinguish curvature as stretching (as done in 4D spacetime), only considering curvature as bending. The spacetime that was being considered is flat, it can be seen in 3D like a stretched, flat pizza dough. The spacetime is flat but if the world trajectory is curved, it still fits with curvature as intrinsic, as stretching, so not just world straight lines "fit" in flat spacetime!

The 4D spacetime, in SR or GR, therefore, works for world-curves, as they may curve, in the world we see as flat spacetime, locally, as SR, or curved spacetime, as we see in GR. Only the 4D spacetime formulation of SR and GR can do that, we cannot use lesser dimensions, may be more.

The visible world, however, as viewed, is NOT 4D spacetime, it seems at first sight. The world is apppearing to us as 3D +1D, or 3D plus time as parameter. But, the world is governed in 4D spacetime, which manifests itself through laws that 3D or 3D+1D cannot represent, but we can see in everyday experience -- just like we do not see the Earth going around the Sun, we see the Sun going around the Earth, apparently, but we do have seasons, and the ancient Greeks measured the circumference of the Earth, with no rockets, quite correctly, through mathematics.

Therefore, the relatity, the world we live in, the truth-conditions, is at least 4D. Some just experience life less, as 3D+1D, or 3D, or even 2D. But the mechanism works in at least 4D, and 3D cannot represent it, as shown in SR and GR experiments. For example, with length contraction or time dilation for non-comoving observers, only.

This is, perhaps, new to philosophers only.

GAUSS AND DIFFERENTIAL GEOMETRY

In 4D spacetime, the worldline curvature is measurable without any external reference frame. Following Gauss, this does not imply that an absolute reference frame exists, nor that an extrinsic reference frame is even need.

This cannot be done with space as 3D and time separare as a passing parameter. This falsifies ANY SR and GR theories, such in SR the original Einstein formulation, Clifford(3,1), Lorentz ether, and by Mashoon, that do NOT consider a "fusion" of at least a 4D spacetime. In those theories, at least one external, inertial reference frame must also be used, which is limiting. Also, as shown elsewhere, they cannot fully represent non-eucliden geometry.

Higher dimensions than 4D are possible, not less. Also, 4D spacetime is not equal to geometric 4D, as the interval can be zero or negative, but a geometric metric has to be positive definite. Thus, 4D spacetime coordinates are not somehow geometric dimensions that we see, but that we experience through a particular 3D space plus a particular time. This difference, between seeing and experimenting, has been a stumbling block for many.

CURVATURE IN GR, MEASURING TIME

If there is no curvature of the worldline, or if there is cartesian translational symmetry, it is inertial motion. This is possible when sufficiently away from any mass.

On the other hand, worldline curvature no cartesian translational symmetry no inertial motion. Free fall is not inertial motion, and always follows a geodesic, a path defined by the external gravitational field. The center of mass (CM) of a body in free fall obeys SR. For a man in a box, the box can be not locally relevant, insofar it does not shield, increase, or decrease, the external gravity. The CM of the man is in free fall, obeys SR.

Any point non-comoving with the CM should be affected locally, including centripetal and coriolis forces, which are locally representable, therefore locally exist in the GR formalism.

The experimental difficulty to measure time at all, or to be be comoving, can be removed under the criteria that small defects are acceptable, vanishingly small to some, but still the main objection remains, as shown elsewhere.

The lack of cartesian translational symmetry (as Stefano Quattrini pointed out, when it crashes...) or when it curves, in both cases with a curvature of the worldline, shows that the motion is not inertial.

MINKOWSKI: FUSION IN SPACETIME

More than 100 years ago, Minkowski and Einstein, by way of Gauss, made new mathematics. They fit all the known experimental facts, uniquely, without exception, creating a "fusion" that we can distinguish only globally -- here one sees time, there one sees space -- but they must stay together locally, as one and single expression of spacetime -- there are no two spacetimes.

Opinions may seem to totally diverge from each other, in that for one, time is all that exists, for other only space exists, for another time is not even seen. But, actually, such divergent views are a proof of the "fusion" of space and time. How? This "fusion" happens so that there is no unique way to split spacetime into space and time, all observers explained by the same theory, of "fusion". One can separate differently than another, all thereby valid, intersubjectively.

This universe is, in all aspects we can see now, including Hubble flow and quantum mechanics, at least 4D. Note that comoving and non-comoving, as well as length contraction and time dilation, are not just words or optical illusions -- what they denote can cross a barrier, can produce thermodynamic work. They define different physics, different truth-conditions, not just different truth values.

Note also that length contraction and time dilation manifest, or not, always in the same conditions. They only exist for non-comoving observers, and do not exist for comoving observers. In cosmology, there is the non-conflicting addition of the Hubble Flow, which allows comoving observers to separate.

In all cases, there is only some sort of union we cannot separate -- or "fusion" -- between space and time. In other words, this "fusion" happens so that there is no unique way to split spacetime into space and time. But, we can have slices of 3D here and 2D there, or even 1D behavior. Likely we can have more, in dimensions to infinity, and even beyond.

The spacetime is exactly the same, 4D as it should be, in special relativity and general relativity, as (t,x,y,z). The metric is different, because the former is certainly flat and the later can be curved as well, with gravity modelled as curvature, but that "fusion" concept in 4D spacetime stays exactly the same, it just "fuses" differently (with a different metric). In cosmology, the metric also gets to be different, but spacetime remains as a kind of "fusion" in the same 4D.

NOTES:

A. In SR and GR spacetime, accelerated motion is defined absolutely, for example, with no absolute reference system or geodesics, of course, by extrinsic and intrisic geometric properties of the curvature.

Names seem to not matter, as expected, in physics. it would seem that it does not matter, then, if someone, for example, chooses a geodesic to extend Newton's First Law, overcome beautifully our limitation then (to define "straight line"), and designates it as an extended "inertial motion" -- the geometric basis is the same, the physics did not change. Or, like Mashhon, describe an infinte family of comoving observers, 3D, each one as a flash in time. One would seem to need less mathematics, it can all be solved in 3D +1D, even 3D, not needing 4D. But the context is just more limited, the region of validity is less, as we show next.

It is physically limiting to use names that do not distinguish curvature as stretching (as done in 4D spacetime), only considering curvature as bending. The spacetime that was being considered is flat, it can be seen in 3D like a stretched, flat pizza dough. The spacetime is flat but if the world trajectory is curved, it still fits with curvature as intrinsic, as stretching, so not just world straight lines "fit" in flat spacetime.

The 4D spacetime, in SR or GR, therefore, works for world-curves, as they may curve, in the world we see as flat spacetime, locally, as SR, or curved spacetime, as we see in GR. Only the 4D spacetime formulation of SR and GR can do that, we cannot use lesser dimensions, may be more.

The visible world, however, as viewed, is NOT 4D spacetime, it seems at first sight. The world is appearing to us as 3D +1D, or 3D plus time as parameter. But, the world is governed in 4D spacetime, which manifests itself through laws that 3D or 3D+1D cannot represent, but we can see in everyday experience -- just like we do not see the Earth going around the Sun, we see the Sun going around the Earth, apparently, but we do have seasons, and the ancient Greeks measured the circumference of the Earth, with no rockets, quite correctly, through physics and mathematics.

It all works for geodesics, world-curved as they may in the world we see as flat spacetime, locally, which is NOT spacetime but governed by a flat spacetime, there is no ontological status anymore, and this is beautiful, not just right. This is also, perhaps, new to philosophers.

B. In summary:

The usual 4D spacetime, such as in the Minkowskian signature, and similar in GR, are non-Euclidean.

We sit, at least, in a 4D spacetime reality. This can be locally Euclidean and globally non-Euclidean, and defines what and how we live, even though we daily experience 3D and passing time.

The acts that shape 4D spacetime, also shape existence in models below, in 3D+1D, 3D + time, 2D, and even in 1D plus time.

When something is correct, this is a sign that it can be be proved in more than one way. In support of this question, we found evidence of the same answers, in additional diverse ways. References are provided, see [1-11], and in self search.

There is no ontological question anymore, on the nature of 4D spacetime reality as we do see it. We just see through a "filter" that we do not identify commonly, reality looking to an observer at rest like if it exists (i.e., as a persistent illusion) in 3D and time is just passing.

Spacetime "fusion" of space and time, Euclidean and non-Euclidean, here discussed in depth, is critical to the effects we observe in 3D, not just to the understanding of the maths.

REFERENCES

[1] Ed Gerck, Preprint On Four Relativistic Neutral Particle Accelerators

[2] Cosmology, SR, and GR, at http://www.astro.ucla.edu/~wright/cosmo_02.htm

[3] H. Minkowski. ​ Space and Time: Minkowski's Papers on Relativity​. 2012. Online at: http://rgs.vniims.ru/books/spacetime.pdf

[4] C. P. Burgess. ​ General Relativity: the Notes​. 2009. Online at: http://www.physics.mcmaster.ca/~cburgess/Notes/GRnotes.pdf

[5] While the original but limited formulation of special relativity is still taught at various college-level textbooks, such as Article Physics: For Scientists and Engineers J. .W. Jewett and R.A. Serway. Physics for Scientists and Engineers with Modern Physics. Thomson Brooks/Cole. 2012

[6] In another version of the SR, by Mashhoon, an accelerated observer is in effect replaced — on the basis of the hypothesis of locality — by a continuous infinity of hypothetical momentarily comoving inertial observers. Here, the accelerated observer and the otherwise identical instantaneously comoving inertial observer have the same velocity and position. In SR, two observers comoving are defined as having the same velocity and position. Cited by 36 references, with 14 occurrences of "comoving", Mashhoon paper at arXIv may further his treatment of accelerated motion in SR, and illuminate the use of "comoving" in SR and Newtonian mechanics,, where it is described as a "material point": at https://arxiv.org/pdf/0805.2926

[7] For the spacetime formulation, also this book: Taylor and Wheeler. Spacetime Physics. . W. H. Freeman and Company. 1966.

[8] https://www.researchgate.net/post/What_are_the_worse_yet_enduring_misconceptions_about_mass_and_energy_in_special_relativity

[9] This question, and links as well as comments, even apparently dissonant comments, may help provide a solution to craft more free time in undergraduate courses, and today: https://www.researchgate.net/post/Should_college_students_learn_about_electromagnetism_before_mechanics

[10] https://www.researchgate.net/post/Is_only_one_or_even_infinite_inertial_reference_frame_enough_in_physics2

[11] https://www.researchgate.net/post/Different_formulations_of_special_relativity_and_4D_spacetime_as_its_corpus Version: 1.40