# Relativity, spacetime, and determinism

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If relativity treats time more or less as a dimension, must it then also treat the world as deterministic?

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I also treat time as a dimension in classical physics. So I don't quite see the striking difference considering the question of determinism.

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Space and time are not currently defined as things, but are defined as reference variables. We can not weight out a pound of time and add it over there. So when something stretches the fabric of space-time (short for fabrication of space-time) nothing tangible is being stretched. Only the equations change in magnitude. We could just as well have called space-time, pixie dust and then stretch that. Just we don't have math formulas centered on pixie dust. That could be a reference variable.

I prefer to visualize space and time as tangible things, so when they do stretch, something innately tangible is changing properties. If space and time were tangible, this allows us to stretch space and time, together or independently.

This would be analogous to the EM force. It is made up of many tangible things and not just a bunch of reference variables. It has both electrostatic and magnetic components that we can store in a bottle. These can act as one integrated thing, or they can act separately. Being tangible allows more properties.

Say one could alter time (the thing) apart from space.We leave space just as it is but add an extra pinch of time (potential). This would create odd perturbations in what should be consistently timed events, using a consistent reference.

Let us do this the other way. We will alter space (distance potential) independently of time. This could satisfy the concept of determinism. As time flows at a given rate to lowest potential, perturbations in 3-D space funnel events to a given position in space-time. It is like the membrane of space is being poked and prodded to make the marble end at Z. Time is flowing along at a consistent pace as we poke and prod the marble in the membrane of space.

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I also treat time as a dimension in classical physics. So I don't quite see the striking difference considering the question of determinism.

Classical physics is also deterministic.

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Classical physics is also deterministic.

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If relativity treats time more or less as a dimension, must it then also treat the world as deterministic?

This depends on what you mean here.

To be a little more concrete lets think about special relativity for a moment. The only real requirement here is that the system be Poincare invariant. There is no constraint for the physics to be deterministic, i.e. not just deal with probabilities.

The dynamics of a classical relativistic particle is deterministic. But what about the quantum dynamics? Or what about quantum field theory? One can also think about relativistic stochastic processes.

General relativity is deterministic if you consider globally hyperbolic space-times and think about the evolution of the space slices. It is also deterministic if you think about the classical dynamics of particles and fields. But again, one can consider quantum field theory on such space-times.

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If relativity treats time more or less as a dimension, must it then also treat the world as deterministic?

That isn't a logical necessity. "Non-deterministic" would simply mean that the state of a future point cannot be fully extrapolated from the state of a past point. My street has the dimensions of length and width, but I couldn't fully extrapolate its width at every point based on its width at one point. (Length is time in that analogy.)

To say "but the future already exists" would not be meaningful, because "already" is a word denoting the present. The width of my street down the block is not "contained in" the width right in front of me, though its shape could be described as a 2D object. Just as you could describe a 4D object in a non-deterministic universe that did not have its 3D future cross-sections determined by its 3D past cross-sections.

Edited by Sisyphus
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General relativity is deterministic if you consider globally hyperbolic space-times and think about the evolution of the space slices. It is also deterministic if you think about the classical dynamics of particles and fields. But again, one can consider quantum field theory on such space-times.

How are clocks synchronized in GR? Or is that an invalid question?

Merged post follows:

Consecutive posts merged
To say "but the future already exists" would not be meaningful, because "already" is a word denoting the present. The width of my street down the block is not "contained in" the width right in front of me, though its shape could be described as a 2D object. Just as you could describe a 4D object in a non-deterministic universe that did not have its 3D future cross-sections determined by its 3D past cross-sections.

I understand that, but that is still deterministic, albeit unknowable determinism, no? Kind of like Fate -- it's predetermined but often unknown. The house down the street could be yellow, green, pink, blue, etc., but I can't say that it could be any of those until I observe it. It already has been that color, and that is simply information I do not have.

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How are clocks synchronized in GR? Or is that an invalid question?

The same way they are in SR, with the addition of non-inertial corrections, e.g. gravitational potential (gh/c^2) and Sagnac. I suspect the correction for the gravitational potential is applied to the clock's rate before synchronization; it is for GPS satellites.

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I understand that, but that is still deterministic, albeit unknowable determinism, no? Kind of like Fate -- it's predetermined but often unknown. The house down the street could be yellow, green, pink, blue, etc., but I can't say that it could be any of those until I observe it. It already has been that color, and that is simply information I do not have.

I don't see it that way. It wouldn't be simply unknown, because the information would not exist. There would be nothing about the present - not even unknowable hidden variables - that determine the future. Is that not the very definition of non-deterministic?

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The same way they are in SR, with the addition of non-inertial corrections, e.g. gravitational potential (gh/c^2) and Sagnac. I suspect the correction for the gravitational potential is applied to the clock's rate before synchronization; it is for GPS satellites.

OK, this is done using clocks synchronized by a light burst, right? So suppose we synchronize two clocks separated by a significant distance. Then, we observe a quantum effect at the location of clock 1. According to quantum mechanics, this effect is random, and there is no "hidden variable" that determines what the result would be, yes? But, clock 2 is far enough away that the event has not happened yet according to it. So observers near clock 1 already know the result. I guess they can't really tell the folks at clock 2 before they could observe it though.

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OK, this is done using clocks synchronized by a light burst, right? So suppose we synchronize two clocks separated by a significant distance. Then, we observe a quantum effect at the location of clock 1. According to quantum mechanics, this effect is random, and there is no "hidden variable" that determines what the result would be, yes? But, clock 2 is far enough away that the event has not happened yet according to it. So observers near clock 1 already know the result. I guess they can't really tell the folks at clock 2 before they could observe it though.

If they are not moving wrt each other then they would agree on simultaneity, regardless of the distance.

Of course they would not know immediately what had happened.

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• 2 months later...

I don't see it that way. It wouldn't be simply unknown, because the information would not exist. There would be nothing about the present - not even unknowable hidden variables - that determine the future. Is that not the very definition of non-deterministic?

He was probably thinking tenselessly about time, i.e. that all points of time exist on par. In that case, there must be either true or false whether a sea battle happens tomorrow, whether or not we have the ability to predict it using the information within the present point of time. I think the right term for this is logical determinism, and this should be compatible with causal indeterminism in the way you explain in your post above.

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Don't mind me, my post was based on a mistaken understanding of synchronization in relativity. I had thought it said that one observer could see an event when a second observer would say the event had not happened yet (with both observers in the light-cone of the event, of course).

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Does randomness exclude determinism ?

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Does randomness exclude determinism ?

Well, in the sense that "random" means "not determined," then yes.

However:

There is still statistical determinism. If you flip a coin 1 billion times, you can be very sure that you will get very close to 50% heads and 50% tails, even though every possibility - including 1 billion heads and zero tails - has a finite probability. In this way, the universe could behave "deterministically" most of the time on the macroscopic scale even while being random on the smallest scales.

Also, there's always the many worlds interpretation. Some say that whenever a particle could equally well zig or zag, it actually does both and the universe splits in two - one where it zigged and one where it zagged. Any observer would conclude that it is truly random, but it is also deterministic, because whatever can happen does happen.

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My question goes like this;

when you flip a coin, you get a coin, not a dice, nor a banana or a cow. There is a law, statistical, that rules the result. But there may be another law, more precise, that rules the result too. The statistical law embrace the restrictive law, it does not exclude the hypothetical deterministic one.

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Oh, I see. "More than one thing could happen" is not the same as "anything at all could happen." It is "determined" that the result be one of a limited set of possible outcomes. Right?

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Yes. But not only.

In the coin example, there are 2 possibilitie, say A & B.

There may be a fully deterministic law that will give the result AABABBBABBAAAAABBBBABABABBAABAABB which is also random-like and also statistically coherent. (Incidentally, I typed the sequence without counting, really).

As an example, the number Pi is random-like, but totally deterministic. A sequence as AAABAAAABAAAAABBBBBBBBBAABBBBBBAAAAABBBAAAAABBBBBBBBAAAAAAAAABBBBBBBAAAAAAAAA would be random-like, but is not.

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• 4 weeks later...

Hello,

the question is very difficult and in fact we don't know the answer.

On the one hand, the Einstein equations are deterministic from a mathematical point of view. On the other hand the theory of general relativity do not forbid time travel. This is a problem for example if you want to play a Novikov Billiard.

Gödel found interesting solutions which would deduce that the theory of general relativity is not deterministic but we don't know if this Gödel universes exist.

greetings

Edited by Jungspund
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Hello,

the question is very difficult and in fact we don't know the answer.

On the one hand, the Einstein equations are deterministic from a mathematical point of view. On the other hand the theory of general relativity do not forbid time travel. This is a problem for example if you want to play a Novikov Billiard.

Gödel found interesting solutions which would deduce that the theory of general relativity is not deterministic but we don't know if this Gödel universes exist.

greetings

Wow!

The Gödel metric admits the possibility of a violation of causality/time travel if Gödel is correct. If Gödel is correct, then it is possible GR is logically inconsistent.

Thanks for pointing this out.

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