Relativity and the arrow of time

[josephwouk]

Relativity and the arrow of time...

It seems to me that the arrow of time is a direct consequence of the Theory of Relativity.

Relativity says that everything in the universe is traveling though space-time at the speed of light. Motion through space diminishes motion through time. However, the sum of motion through time and motion though space must always equal the speed of light. The photon gets all that speed though space , hence a photon exists without time passing.

The arrow comes from the simple fact that if motion through time were anything less than zero, motion through space would have to be greater than the speed of light in order for the sum to equal the speed of light.

According to relativity, this is impossible. Thus the arrow of time comes from the speed limit set by electromagnetic waves though empty space.

Comments?

 

[JesseM]

Relativity says that everything in the universe is traveling though space-time at the speed of light.

Some authors like Brian Greene explain relativity in this way, but very few textbooks talk about any notion of "speed through spacetime", and I think there are some good reasons to see this terminology as confusing to newcomers (see my comments in post #3 of this thread for example).

The arrow comes from the simple fact that if motion through time were anything less than zero, motion through space would have to be greater than the speed of light in order for the sum to equal the speed of light.

The notion of the arrow of time has nothing to do with not allowing "motion through time" to be "less than zero", which doesn't even have any clear physical meaning in terms of Greene's explanation as far as I can see (the direction of increasing proper time along a worldline is basically a matter of arbitrary convention, so it's equally a matter of arbitrary convention whether the 'speed through time' $$d\tau /dt$$ is positive or negative, and it won't make any difference to Greene's equation since this term is squared anyway, it certainly won't mean that the 'speed through space' must be faster than light). The question of the "arrow of time" has to do with the fact that there is no arrow of time at the level of the basic equations of physics, because these laws are "time-symmetric" (technically some laws of particle physics are actually invariant under CPT reversal but this doesn't explain the mystery of why many phenomenon on a human scale do not seem to work symmetrically forward and backwards). I gave a quick rundown on what "time-symmetry" of the fundamental laws means in [post=2888539]this post[/post] if you want to know more.

 

[josephwouk]

You are correct that Greene mentions travel through space-time always being C, though he is hardly the only one who draws this conclusion from Einstein's equations.

The fact that equations are "time symmetric" seems to me somewhat irrelevant to the question of the "arrow".

The arrow refers only to our experience of time "flowing" in one direction only. Why should time "flow" at all instead of remaining static like the other 3 dimensions?

It seems to me that the reason it "flows" and the reason it's unidirectional can best be explained by this aspect of relativity. For photons which travel at C, time in fact doesn't flow and is static.

In 4 dimensional space-time there is no meaning at all to time "flowing" which is why Einstein called it a "persistent illusion."

We live in a subset of space-time created by the electromagnetic force, the three spatial dimensions and the "flowing" dimension of time which directly results from the speed of light.

 

[Dale]

The fact that equations are "time symmetric" seems to me somewhat irrelevant to the question of the "arrow".

Huh?!? That is the key fact to the question. The question about the arrow of time is essentially the following: given that the fundamental laws of physics are time symmetric what distinguishes the "tail" from the "head" in the "arrow of time".

It certainly is not the fact that the square of the Minkowski norm of the four-velocity is c² (i.e. the length of a unit vector is unity), since that fact would not change if the tail and the head were reversed.

 

[josephwouk]

Fair enough on the question of the physical equations.

I am looking at the "flowing" quality of time as experienced by us. The symmetry you refer to is not the issue I am trying to address.

I believe our experience of the "flow" is a result of our motion through the time dimension of space-time that taken together with our motion through space equals C.

 

[Dale]

I am looking at the "flowing" quality of time as experienced by us. The symmetry you refer to is not the issue I am trying to address.

I believe our experience of the "flow" is a result of our motion through the time dimension of space-time that taken together with our motion through space equals C.

How do you make that connection? It sounds like you are trying to relate a very complicated psychological experience to something as simple and tautological as the length of a unit vector being unity. I really don't see the connection at all.

 

[josephwouk]

I disagree with you on that. It's not "psychological." For us, time does flow. We all get older. Nobody gets younger. There is an arrow, despite what the equations say.

This is what I'm attempting to explain using simple relativity theory.

 

[Dale]

I disagree with you on that. It's not "psychological." For us, time does flow. We all get older. Nobody gets younger.

You are really confused. This is exactly what JesseM was talking about in post 2 and what I was talking about in post 4 and which you rejected in posts 3 and 5. Please make up your mind. Are you talking about:

1) physics - in which case the question is how to physically distinguish the future from the past given the time symmetry of the laws of physics
2) psychology - in which case the question is how are you attempting to relate relativity to a psychological phenomenon

I believe that you think you are interested in the physics question but apparently don't realize that the physics question is all about time reversal symmetry.

 

[josephwouk]

Dale...

Forgive me if I've been unclear. I'm not talking about the time reversal symmetry of the equations or the psychological issue of our experience of time.

I'm talking about the actual arrow of time that exists despite the reversal symmetries. Greene devotes an entire chapter to the issue in Cosmos focusing in particular on the 2nd law of thermodynamics.

His explanation that the 2nd law can explain the arrow because of the super low entropy after the big bang left me cold.

Say what you will about the potential effects of gravity, to claim low entropy for the pure plasma of electrons that existed at the beginning is absurd on its face.

This is one of my motivations for looking to relativity to explain the arrow that is there, even though it doesn't show up in other equations.

 

[Dale]

I'm talking about the actual arrow of time that exists despite the reversal symmetries.

Exactly. The physics question is how can the observed arrow of time exist given the symmetry of the equations that describe the laws of physics. If the equations were not time symmetric then there would be no physical conundrum, the cause of the arrow of time would be clear. So the discussion about the symmetry of the equations is absolutely central to the topic you wish to address.

This is one of my motivations for looking to relativity to explain the arrow that is there, even though it doesn't show up in other equations.

It won't help you at all. The equations for relativity are time-symmetric also, so you wind up in the same situation as with all of the other laws of physics.

 

[bcrowell]

You are correct that Greene mentions travel through space-time always being C, though he is hardly the only one who draws this conclusion from Einstein's equations.

Greene is the only person I've ever heard of who described it this way.

 

[bcrowell]

Say what you will about the potential effects of gravity, to claim low entropy for the pure plasma of electrons that existed at the beginning is absurd on its face.

The low entropy of the early universe is not scientifically controversial. If it's counterintuitive to you, then you just have to work on understanding it better.

 

[josephwouk]

"is not scientifically controversial"

Means to me only that people aren't thinking about it. Accepting concepts like that as "true" is not the way forward, anymore than accepting the "luminiferous ether" was.

 

[Vanadium 50]

Means to me only that people aren't thinking about it.

Let me get this straight - you don't want to work on understanding it better, but other people have to?


It is entirely possible that you are right and that everyone else is wrong, but I can guarantee you that your opinion is scientifically worthless until you understand why everyone else believes it. If you're not willing to put that effort in, well...

 

[josephwouk]

Dale...

The equations are not central to the issue of where the arrow comes from. They indicate that there should be no arrow. That's why it's important to search for the source of the arrow elsewhere.

My belief is that relativity provides a much better explanation for it than does the 2nd law which requires increased entropy in both directions from the present.

 

[JesseM]

"is not scientifically controversial"

Means to me only that people aren't thinking about it. Accepting concepts like that as "true" is not the way forward, anymore than accepting the "luminiferous ether" was.

So what's your position here? Are you arguing that the fact that certain processes are only observed to happen in one direction but not the other--say, ink dropped in a glass of water becoming more evenly distributed over time, not spontaneously becoming more concentrated in one part of the glass--has nothing to do with the 2nd law of thermodynamics (the fact that the entropy of an isolated system naturally tends to increase over time)? Or are you somehow arguing that even if these asymmetric processes are a matter of entropy increase, we don't need a low-entropy initial state to explain them?

Also, you said earlier:

The arrow refers only to our experience of time "flowing" in one direction only. Why should time "flow" at all instead of remaining static like the other 3 dimensions?

In relativity spacetime is modeled as a "static" 4-dimensional structure with various frozen worldlines in it. This type of model works just fine for making predictions about what events will occur at what positions and times--if you're not talking about our psychological feeling of time moving forward (which can be explained in terms of the fact that our brains can contain records of past events but not future events, and that fact can itself be explained in thermodynamic terms), what specific quantitative physical measurements do you think contradict this model? Or are you objecting to this picture on more of a philosophical level, favoring the presentist philosophy of time to the eternalist philosophy? Of course physics cannot settle such philosophical questions, but if there is such a thing as an objective "present", relativity says there can never be any physical way to determine which set of events happen at the same "present moment" due to the relativity of simultaneity (which Brian Greene explains in that section on Itchy and Scratchy and how you can slice a 'block' of spacetime at different angles to produce different definitions of which events happened at the 'same time', see pages 54-58 of Fabric of the Cosmos)

 

[josephwouk]

Jesse...

It is precisely Greene's explanation of the relativity of simultaneity and his discussion of there being different equally valid "nows" with different "now lists" which coexist that inspired me to come up with a new approach to explaining inertial and gravitational mass.

I'm writing a book at the moment entitled The Mass of Nows where I detail the new theory.

I'm asking these questions on the forum to firm up in my mind some of the aspects of the theory. There are a number of other issues I'll be asking for input beyond the difference in information content between 3 and 4 dimensions and the arrow of time.

I want to thank everyone here for their input, even if it's to disagree strongly with me...

Cheers!

Joe

 

[Dale]

The equations are not central to the issue of where the arrow comes from. They indicate that there should be no arrow. That's why it's important to search for the source of the arrow elsewhere.

You don't even understand the question. Good luck on finding an answer.

My belief is that relativity provides a much better explanation for it than does the 2nd law which requires increased entropy in both directions from the present.

Your belief is wrong for the reason pointed out above.

 

[josephwouk]

Thanks for your input, Dale.

I apologize if my questions irritated you.

Joe

 

[Dale]

It is not your questions that are irritating. It is the fact that you ignore the answers and simply re-assert your original statement that is irritating. When one side does that then it is impossible for the dialogue to progress and all that is left is a pair of monologues.

Real questions are fine, but if you are not interested in the answers then why waste everyone's time asking?

 

[JesseM]

Jesse...

It is precisely Greene's explanation of the relativity of simultaneity and his discussion of there being different equally valid "nows" with different "now lists" which coexist that inspired me to come up with a new approach to explaining inertial and gravitational mass.

I'm writing a book at the moment entitled The Mass of Nows where I detail the new theory.

I'm asking these questions on the forum to firm up in my mind some of the aspects of the theory. There are a number of other issues I'll be asking for input beyond the difference in information content between 3 and 4 dimensions and the arrow of time.

If you're interested in input on the arrow of time, could you answer the questions I asked in my previous post about whether you think the 2nd law of thermodynamics plays any role in the fact that we see certain processes only in the "forward" direction of time but not in reverse, and also my questions about whether you think there are any empirical observations that contradict the "eternalist" view of spacetime as a static 4D entity, or whether you are criticizing eternalism in a more philosophical way?

Also, you never really addressed my point that when Greene talks about everything having a speed through spacetime of c, he is basing this on the equation $$\sqrt{c^2(d\tau/dt)^2 + (d\vec{x}/dt)^2 } = c$$, so since the "speed through time" component $$d\tau/dt$$ is squared, it makes no difference whether we define the proper time $$\tau$$ to be increasing relative to coordinate time t (so $$d\tau/dt$$ is positive) or whether we define it to be decreasing relative to coordinate time (so $$d\tau/dt$$ is negative), it won't change what value of $$d\vec{x}/dt$$ (speed through space) is needed to make the whole thing equal to c (in contradiction to your claim that negative speed through time would imply speed through space must be faster than light)

 

[josephwouk]

Jesse...

Thank you for your continued input on this issue.

You are asking my opinions on matters that are not directly related to what I'm interested in, but I'll be happy to answer them as best I can.

The 2nd law of thermodynamics is as you know a statistical prediction based on the behavior of massive numbers of events. As such, it is very reliable as a predictor but is not a "law of nature" per se. In other words, while a decrease in entropy is extremely unlikely, it is nevertheless possible. For this reason alone, I believe it is a mistake to rely on the 2nd law as the basis of the absolute arrow of time.

Empirical observations made from the limited 3 dimensional subset of the 4 dimensional universe we inhabit are incapable of determining the precise nature of the 4 dimensional universe. The loss of information in the step-down is too great. (See my other inquiry about information theory.)

Thus the question of whether the "eternalist" view of the 4 dimensional space-time is correct or not would appear to be a metaphysical question, not subject to empirical review.

In terms of the formula used to determine the motion off all things through space-time at C, the mathematical formalism used to calculate should not be overly interpreted as reflecting reality.

We know from relativity that speed through space diminishes relative speed through time. We also know that photons exist without time passing at all, and that C is the speed limit in our 3 dimensional subset of the universe. It therefore stands to reason that if it were possible to exceed the speed of light, one would go backward in time. The reverse therefore would also be true.

A good way to consider the importance of the reality behind the formula is to compare it to imaginary numbers.

Imaginary numbers tell us nothing about reality, and yet they are used all the time in calculating concrete applications in a variety of scientific and related areas such as signal processing, control theory, electromagnetism, fluid dynamics, quantum mechanics, cartography, and vibration analysis.

 

[JesseM]

The 2nd law of thermodynamics is as you know a statistical prediction based on the behavior of massive numbers of events. As such, it is very reliable as a predictor but is not a "law of nature" per se. In other words, while a decrease in entropy is extremely unlikely, it is nevertheless possible. For this reason alone, I believe it is a mistake to rely on the 2nd law as the basis of the absolute arrow of time.

Why do you think there is an absolute arrow of time? If you agree that spontaneous reversals of entropy are possible even if they are very unlikely for large systems, then you should agree it's possible that somewhere in the universe there is a time-reversed planet with time-reversed people who "remember" what we would call the future rather than the past (though they of course would use opposite terminology), where they rise from graves and get younger until returning to the womb, where broken glasses always spontaneously recombine into into intact ones but the reverse never happens, etc. etc.

In terms of the formula used to determine the motion off all things through space-time at C, the mathematical formalism used to calculate should not be overly interpreted as reflecting reality.

We know from relativity that speed through space diminishes relative speed through time.

We only "know" that based on the fact that the formula $$\sqrt{c^2(d\tau/dt)^2 + (d\vec{x}/dt)^2 } = c$$ can be derived from the basic equations of relativity, and if we choose to define the term $$d\tau/dt$$ as "speed through time" along with the standard definition of $$d\vec{x}/dt$$ as "speed through space". Do you disagree, and think there is some indpendent basis for believing that "speed through space diminishes relative speed through time"?

We also know that photons exist without time passing at all, and that C is the speed limit in our 3 dimensional subset of the universe. It therefore stands to reason that if it were possible to exceed the speed of light, one would go backward in time. The reverse therefore would also be true.

Why does that "stand to reason"? In fact, the rate that a clock is ticking relative to coordinate time is given by the formula $$d\tau/dt = \sqrt{1 - v^2/c^2}$$, you can see that this becomes smaller and smaller as v gets larger until it reaches 0 at v=c, but if you plug in a v > c it doesn't become negative, instead it becomes imaginary.

 

[josephwouk]

Jesse...

I'm unwilling to entertain the notion of a universe where different laws apply in different locations. While that may in fact be true, it would imply the uselessness of science as we know it.

Actually, we "Know" that speed through space diminishes speed through time by numerous experimental results. The latest are even capable of measuring the time dilation resulting from the motion of my walking away from you.

Years ago atomic clocks measured the difference on a jet flying around the world.

Relativistic time dilation is constantly experienced in particle accelerators and must be included in all calculations regarding them.

That the numbers become imaginary rather than negative implies that speed greater than C is impossible and that reversing the arrow of time is also impossible.

 

[JesseM]

Jesse...

I'm unwilling to entertain the notion of a universe where different laws apply in different locations. While that may in fact be true, it would imply the uselessness of science as we know it.

Are you talking about the reverse-Earth idea? I never said anything about "different laws", you yourself said the 2nd law is statistical prediction rather than a "a law of nature", and that "while a decrease in entropy is extremely unlikely, it is nevertheless possible". Do you deny that all the asymmetric phenomena I mentioned, like the fact that glasses are observed to spontaneously go from intact to broken but never the reverse, are consequences of the 2nd law, and thus that reversals--like shards of broken glass spontaneously reassembling into an intact glass--are extremely unlikely, but nevertheless possible? Obviously the possibility of such macroscopic reversals is astronomically unlikely, but even if the probability is something ridiculously small like 1 in 10^1000000, it isn't zero. Similarly there is no basis in any known laws of physics to believe an entire thermodynamically reversed Earth has zero probability ('thermodynamically' because you are free to believe there is some thermodynamics-independent 'arrow of time' that still runs forward even as all these physical processes seem to run backward), though the actual probability is certain to be astronomically small. Do you disagree?

Actually, we "Know" that speed through space diminishes speed through time by numerous experimental results.

That's not what I was asking about--I wasn't just asking about time dilation, I was asking if you think there is any basis for saying that the combination of speed through space and speed through time is equal to c other than the equation $$\sqrt{c^2(d\tau/dt)^2 + (d\vec{x}/dt)^2 } = c$$. Do you think there is any way to show this besides multiplying the square of $$d\tau/dt$$ times c^2 and then adding the square of the speed through space, and verifying that the sum is c?

Also, while there is of course plenty of evidence for time dilation, the statement "speed through space diminishes speed through time" is only true relative to a given inertial coordinate system, it isn't true in any coordinate-independent way. If you have two clocks A and B, and in A's rest frame B has a large speed through space and thus a slower speed through time (i.e. a slower rate of ticking relative to that frame's time-coordinate t), then in B's rest frame the reverse is true, with A having a large speed through space and a slower speed through time.

That the numbers become imaginary rather than negative implies that speed greater than C is impossible and that reversing the arrow of time is also impossible.

You still haven't explained what you think the "arrow of time" even means, if it is supposed to be something separate from the observation that certain phenomena like breaking glasses are only observed to happen in the forward direction but never in reverse. Certainly there is nothing stopping us from defining proper time to increase in the opposite direction as coordinate time, so that $$d\tau/dt$$ is negative; this is merely an arbitrary labeling convention with no physical significance, like the choice of which type of electric charge to label as positive and which to label as negative.

 

[Phrak]

Certainly there is nothing stopping us from defining proper time to increase in the opposite direction as coordinate time, so that $$d\tau/dt$$ is negative; this is merely an arbitrary labeling convention with no physical significance, like the choice of which type of electric charge to label as positive and which to label as negative.

I'm glad you brought up labels.

Einstein: "Time is what we measure with a clock." It makes the discussion a little more concrete to replace the label convension with hardware--clocks distributed throughout a region of space, each counting upward in agreement with each other.

As far as I know, it's possible in principle to construct a clock that is isentropic. See for example http://arxiv.org/abs/physics/0401077" , so that it is in no way tied to the thermodynamic arrow of time.

I might add to Einstein's statement, that local clocks agree in progression. This is a a local invariance. It seems a fairly reasonable to extend this local invariance of progression to global status; that two clocks at the same place will still progress in the same sense after each has moved over some arbitrary path and returned to the same neighbourhood. The alternative is that matter could be translated through space and return as antimatter.

All this has been the long way of saying, there are two contenders for temporal labeling: local and global.