It is often claimed that modern physics has delivered radical changes to our conception of space and time through the special and general theories of relativity. However, for the philosophically minded lay person wishing to understand this better, difficulties arise. It is my purpose here simply to note the difficulties which seem to me to arise. To articulate certain questions to which I have not yet been able to discover an answer.

Since the formulation of Einstein's theories of relativity the nature of space-time has been firmly within the scope of science. Or has it?

The antithesis is not watertight, synthesis uncertain, questions remain.

The standard picture is as follows. The nature of space and time, which might at one time have been regarded as the province of metaphysicians, has been drawn in the twentieth century firmly into the scope of science by Einstein's theories of relativity.

The special and general theories of relativity, which have both been experimentally confirmed and are well established theories, give us a very definite picture of space and time which differs radically from what had hitherto been supposed.

The most radical and difficult to understand transformation in our conception of space and time comes with the special theory of relativity, which tells us that space and time are no longer independent and tells us that some very surprising facts about lengths, about the mass of objects, about velocities and how they add up follow from the nature of space and time which we infer from certain observable facts about the propagation of light. Special relativity tells us that rather the familiar distinct Euclidean spaces of space and time reality consorts of a space-time in which space and time are tangled up.

The general theory of relativity takes this radical reformation in our conception of space-time one step further by enhancing space-time to take over the role of gravity. Space-time ceases to be "flat", becomes non-Euclidean, and the effect previously attributed to gravitational attraction is incorporated into the geodesics in this space,

As soon as you dig just a little below the surface on this you find contrary views.

First, in relation to special relativity, it appears that the observable consequences of the theory are anticipated in the Lorentz contraction. The special theory results from an application of Occam's razor. "The Ether" proves to be undetectable. This fact can be accounted for by the idea that physical objects undergo a contraction when they are in motion relative to the ether, which is informally intelligible when it is understood that the electromagnetic forces determine the physical size of objects, and are themselves transmitted via the ether. Einstein's theory results when the undetectability of the ether is taken as demonstrating that the existence of the ether is a superfluous hypothesis with which we should dispense.

It seems to have been acknowledged by Einstein that the empirical content of his special theory is anticipated in the Lorentz theory.

In relation to the general theory of relativity, Henri Poincare argued at length against the use of curved space time in favour of retaining the flat Euclidean predecessor. The consensus solidified in favour of curved space-time. In more recent times however, the formulation of general relativity in a flat space-time has been accomplished using geometric calculus by Lazenby, Doran and Gull at the University of Cambridge.

General relativity is not entirely about space-time, if recast in a flat space-time it does not revert to Newtonian mechanics. As far as I know at present the only additional element is the replacement of "action at a distance" which is instantaneous with a gravitational influence which propagates with the speed of light.

It appears then, that the entire content of Einstein's theories of relativity in relation to the nature of space-time is properly metaphysical in the sense that it lacks any empirically observable consequences. We suspect this because it looks as if it might be possible to formulate a theory of gravitation which is observationally equivalent to the theories of relativity without any changes to our traditional conception of space-time. Relative to the Newtonian mechanics this would involve introducing the lorentz contraction as an effect of absolute motion, and aknowledging that gravitational influence is propagated at the speed of light.

Though there seem to be good sources for the observations which cast doubt on the definiteness of the space-time consequences of relativity, in the case of the special theory, Einstein's own observations, in the general case, reputable scientists such as Poincare, Lanzenby, Doran and Gull, these remarks seem all to be of an informal character. I am not aware of their having been made into precise statements suitable for rigorous demonstration. Informally, there seem grounds for doubt about how strong these claims would then be.

The relationship between the Lorentz contraction and the special theory of relativity is for me rendered doubtful by the following consideration. Special Relativity makes predictions for time dilation, and length contraction for inertial frames, and says nothing about what happens in accelerating frames. The Lorentz contraction is not specific to inertial frames, it forecasts length contraction and slowing of clocks (not actually of time) for objects which are in motion relative to the ether. If this is correct, then presumably the combination of Newtonian mechanics with the Lorentz contraction would yield predictions in circumstances in which special relativity would remain mute.

In the case of the recent flat-space formulations of General Relativity it is acknowledged that this is not a theory with empirical consequences identical with those of the original formulation, though they are thought to be equivalent in relation to known experimental or observational results. Some possibilities which are admitted by the curved space-time formulations seem unlikely to be consistent with the flat formulations. The possibility of "worm holes" is one such. The general theory of relativity has a more liberal conception of the possible structure of space-time, a demonstration of equivalence of a flat-space time model would depend on demonstrating a notion of equivalence which ignored possibilities which we have as yet had no way of testing.

I would like to know the answers to the following questions.

• Does the empirical content of the theories of relativity have any definite consequences for the nature of space-time?
• In what precise sense (if any) is the Lorentz contraction equivalent to the theory of special relativity? Has this been demonstrated?
• In what precise sense if any is the general theory as formulated with curved space-time equivalent to a theory formulated in a flat space time?
• Would it be possible to formulate a gravitational theory in Newtonian space-time in which the innovations relative to Newton were just the Lorentz contraction and the finite propagation speed for gravitational attraction?
• In what precise sense would such a theory be equivalent to General Relativity?

This is an aborted attempt to draft a question suitable for posting on sci.physics.relativity, held for future reference in case I have a resurgence of optimism about the possibility of getting useful responses.

I am interested in the question what, if anything, the special and general theories of relativity tell us about the structure of space and time. This is a philosophical interest. My level of knowledge of the relevant physics is not sufficient to resolve the issues and I am posting this question for clarification on what is known.

It appears in relation to special relativity that Einstein believed when this theory was put forward that it was in some sense equivalent in its predictions to the theory of Lorentz contractions.

In relation to the general theory, Henri Poincaré for decades argued that the theory should be formulated in flat rather than curved space-time. More recently general relativity has been reformulated using geometric calculus as a gauge theory in a flat space-time.

Though there is some suggestion here that the experimental confirmation of the theories of relativity fails to have definite (rather than perhaps pragmatic) implications for the nature of space-time, the relationship between the theories and the mooted alternatives seems complex.

In the case of the special theory, this restricts its predictions to inertial frames, which constraint is not present in relation to the Lorentz contraction. In what sense then could these theories be equivalent? My own understanding of special relativity is very limited, an example of how the theory remains puzzling to me is given below as the "symmetric twins conundrum". This seems to tell us some strange things about what happens under special relativity, but it seems doubtful that the same consequences could flow from the hypothesis of the Lorentz contraction.