Space and Time
Introduction
Notes on space and time and the theory of relativity.
Introduction

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.
Thesis and Antithesis
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 Space-Time as Physics Thesis

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,

The Antithesis

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 acknowledging that gravitational influence is propagated at the speed of light.

Doubts and Questions
The antithesis is not watertight, synthesis uncertain, questions remain.
Doubts

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.

Questions

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?

Usenet Formulation

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.

The Symmetric Twins Conundrum
This is the content of a message I posted to sci.physics.relativity. http://groups.google.com/group/sci.physics.relativity/msg/3135a122e8455d27. The upshot of the ensuing discussion was that I ended up understanding how this situation works out in special relativity. The enlightenment came primarily from reading the FAQ.
Introduction

This is a variant on the "twins paradox". It is a situation which I don't understand, which seems on the face of it to involve strange consequences of the special and general theories of relativity, and I would appreciate it if anyone can enlighten me on what the theories really say happens in these circumstances.

Scenario

The traditional "twins paradox" is asymmetric. One of the twins travels on a geodesic and the other does not, and the other therefore ages less in the process. In this case, we arrange for the two twins to undertake symmetrically opposite journey's which are therefore identical in relation to time dilation from the point of view of an inertial third person observing their journeys.

We start with the two twins and an independent observer all at rest together relative to some inertial frame. All three have clocks which they synchronise together. The two twins accelerate rapidly to near the speed of light in opposite directions. They then travel at uniform velocity for a good long time before turning round, coming back together at the same speed and decelerating to a stop as they once again meet.

Analysis

This is my half-baked misunderstanding of what goes on, I'm inviting people to come up with the correct analysis.

The main part of these journeys is covered by the special theory, the brief periods of acceleration are covered by the general theory. From the predictions of special relativity together with considerations of symmetry we come to some strange ideas about what the general theory must say about the behaviour of clocks during periods of acceleration.

Considerations of symmetry tell us that the clocks of the two twins will agree when they meet after their journeys. Special relativity tells us that each twin observes the other's clock running slowly during the periods of uniform motion. Ergo, during the periods of acceleration they must observe the other's clock as running fast.

The periods of uniform motion can be changed arbitrarily without making any change to the periods of acceleration. If this is done the time lost during these period will vary, and the time gained during the periods of acceleration must increase correspondingly for the clocks to match when they meet up.

Hence the general theory must predict a speed up during acceleration which is not determined by the amount of acceleration and its duration.

What else could it depend upon? What else does it depend on? What's wrong with this partial analysis?

Resolution

There are two misconceptions which lead to my puzzlement.

The first is that the special theory of relativity is applicable only to inertial frames and non-accelerating bodies. This misunderstanding is understandable, because this is said often in the literature, and was said even by Einstein himself. However, the Minkowski conception of relativistic space-time improves upon Einstein's original account in such a way as to obviate the need for these restrictions.

The second is that special relativity tells us that various aspects of phenomena depend upon the frame of reference of the observer. In fact, any phenomenon can be described relative to any inertial frame of reference, it is the frame of reference relative to which the phenomenon is described which affects the details of the description, not any aspect of the observer, who must take into account his circumstances in drawing conclusions about reality from his observations.

Now the conundrum was that strange things would appear to happen when the two participants in this experiment accelerated, and that the extent of these strangenesses seemed to depend upon considerations (such as the amount of time they had moved apart or the distance they were separated), which one would not have expected to have the relevant significance. However, because I was thinking relative to the twins, I was thinking of how things would look from an accelerating frame of reference. This is a bizzarre thing to do. Naturally if we are continually changing the frame of reference relative to which we are describing the phenomena, then we will get a descriprion whose characteristics may be dominated not by what is happening but by the change in perspective, and particularly, are influenced by the rate at which we are changing the frame of reference.


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