Special Relativity and the nature of time

[Modax]

I have been grappling with the physics concepts brought up here over the past few months. I'm posting what I've learned, to share my thoughts and to find out if I've got any of it right.

My understanding so far: In special relativity, observers moving relative to one another will have different ideas about which events belong in the past present and future. This effect becomes more significant the farther two observers are separated by distance and relative velocity. So far so good. Now I want to understand the implications of this.

We say that when people die, information is destroyed and from the perspective of the people with whom they shared a planet, that information is gone forever.

But there are billions of galaxies, and most of them are moving at huge speeds relative to each other. So you should be able to find observers whose relative conception of the present is shared with Earth's Cambrian era, 2010 A.D, or the Sun's transition into a red giant. So in some cosmic sense, would it be correct to say that the past, present and future are artificial distinctions? For all intents and purposes, this doesn't really matter, because the speed of light limits communication and preserves causality; but in principle is it ever correct to say that information is really destroyed?

To me, it is a nice thought, that the history of the universe is in some sense conserved by relative space time. Does this idea have any truth to it? What implication does the acceleration of the universe have for this?

[adam_grif]

Even if the "information" is preserved in some portion of space, it doesn't do you any good because it has undergone entropy and is totally lost to you and yours.

Anticipating a detailed response from Surlethe.

[starslayer]

We say that when people die, information is destroyed and from the perspective of the people with whom they shared a planet, that information is gone forever.

Who is "we"? I've never heard of anyone in the physics community saying anything like this. If you mean their memories, that is a misunderstanding of what a physicist considers information. When someone dies, yes, their state changes, but that in no way implies a loss of information. Instead, it implies a change in their information content. Information is never destroyed, to my knowledge, except in the case of matter or energy falling into a black hole, and even then, that's up for debate (the current leading opinion, IIRC, is that the information is not destroyed).

It is also not true that the past, present, and future are artificial distinctions in a cosmic sense. Just because they are frame dependent does not mean they do not really exist. They are simply different for each frame. You also should not be able to find a frame in any way contemporaneous with ours that views the Sun as a red giant, or any point in its future beyond about 8 minutes from now. If something has not happened in the object's own frame, it has not happened in any frame, as long as we stick to sub-light speeds. However, it is easy to find a frame where Earth is still in the Pre-Cambrian era: just pick a random star at least about 600 million light years away.

Even if the "information" is preserved in some portion of space, it doesn't do you any good because it has undergone entropy and is totally lost to you and yours.

Sorry, no... just no. Entropy is a physical property of a system; something does not "undergo" entropy. Go pick up an elementary thermodynamics textbook, or hit up Wikipedia. I don't think I really understand it well enough myself to really explain it, beyond saying S = k*log(W), where S is the entropy, k is the Boltzmann constant, and log(W) is the natural log of the number of possible microstates of a system.

[adam_grif]

Worded poorly, but what I'm trying to get at is similar to information theoretic death, where past states and their associated information is lost to you, and entropy would have to be reversed in order to get it back. From there it's easy to see why I'd phrase that as "the information has undergone entropy", being both layman and moron.

[Modax]

Who is "we"? I've never heard of anyone in the physics community saying anything like this. If you mean their memories, that is a misunderstanding of what a physicist considers information. When someone dies, yes, their state changes, but that in no way implies a loss of information. Instead, it implies a change in their information content. Information is never destroyed, to my knowledge, except in the case of matter or energy falling into a black hole, and even then, that's up for debate (the current leading opinion, IIRC, is that the information is not destroyed).

Some information has meaning for humans and some simply does not, being merely noise. I suppose you could say that 'meaning' is destroyed when a person dies, if not information.

It is also not true that the past, present, and future are artificial distinctions in a cosmic sense. Just because they are frame dependent does not mean they do not really exist. They are simply different for each frame. You also should not be able to find a frame in any way contemporaneous with ours that views the Sun as a red giant, or any point in its future beyond about 8 minutes from now. If something has not happened in the object's own frame, it has not happened in any frame, as long as we stick to sub-light speeds.

If past present and future are different for each frame shouldn't we expect to find inertial frames with observers whose present is equivalent to our future? If not, that seems to imply that there is something special about our own inertial frame. And why 8 minutes? Why should there be anything special about the time it takes light to travel to earth from the Sun? That sounds very fishy, but I don't know enough to argue the point properly.

Edited for grammar

[Channel72]

Well, I suppose if you interpret the Universe as a closed, four-dimensional construct of space-time, it is essentially static and eternal.

[starslayer]

If past present and future are different for each frame shouldn't we expect to find inertial frames with observers whose present is equivalent to our future? If not, that seems to imply that there is something special about our own inertial frame. And why 8 minutes? Why should there be anything special about the time it takes light to travel to earth from the Sun? That sounds very fishy, but I don't know enough to argue the point properly.

Take the Sun and a far away observer, say 6 billion light years away. If he looks at the Sun, he doesn't anything, because the Sun hasn't formed yet from his perspective; therefore its formation is in his future. If he waits 1.5 billion years, so the Sun forms in his frame, the Sun's formation is now in his present, because the information of its formation has finally reached him, via photons. Everything else in the Sun's history up till now, which we regard as in our past, is in our observer's future, because it is restricted by light travel time. This sort of thing will be the case for any observer moving at any sublight speed. Because the speed of light is the same for all observers, you can't know about something before it has happened without invoking FTL somewhere.

Let's try this same thing with the observer now moving with respect to the Sun; now he perceives the Sun's clock as ticking slower than his, and vice versa. To the Sun, the observer's clock ticks slower, and everything is still preserved, as he still can't get any information before the Sun sends it out. With the observer, the Sun's timescale seems to dilate as well, and again everything's fine; he thinks the Sun takes even longer to do anything, so he still doesn't see the Sun's future before it does.

In fact, I challenge you to go through a good mathematical (don't worry; unless you stumble upon the original derivation of the Lorentz transformations or something, it's nothing too complicated) treatise on SR and see if you can construct a frame, without invoking FTL, where an observer can see an object's future before it does (that is, before the object's future becomes its present). I think you'll find that you can't.

[Steel]

The 'surface of simultaneity' and the fact it takes light to travel from far away places are totally different things.

Two observers with zero relative velocity have the same idea of 'now' no matter how far apart they are. It does not matter that separated by distance d they see each other as they were d/c ago.

If they have a relative velocity then they will not agree on when 'now' is at different points in space.

I can't detail the maths as I'm typing on a phone and extended writing is miserable. Main point: do not confuse when you see someone and when 'now' is where they are.

[starslayer]

Whoops. Guess I better go back and read over my SR again too; thought I was fucking something up. Even with that, however, I think the original point still stands, unless I'm missing something else.

[Steel]

My first sentence should be '...takes light TIME to travel...' obviously.

By your original point do you mean the sun not having formed in their frame bit? Thats not right.

The sun has formed in the far away person's frame. They just cant see it yet. This is an entirely different thing to the formation of the sun actually being in the future.

I only have my phone till I get my laptop back, so hopefully someone will detail the lorenz transformation momentarily. It'll be quicker than waiting for me to type it on this at least...

[Feil]

There are several concepts in your question. I will attempt briefly to address one:

There does exist definitive present and past for any event. Picture space as two-dimensional (the video game Asteroids suffices for an example). Now add a third dimension normal to the plane projection of 3-space. This dimension is time. The natural units for this coordinate system are (c*s)=1 unit distance in the space axes and s=1 unit time in the time axis. Now suppose an omnidirectional pulse of light emanating from the origin of this 3-space (an EVENT). It will form a three dimensional cone with a half-angle of 45 degrees, with circular cross-sections in the space plane. (These correspond to spheres in 3-space, which have been projected onto the plane. Imagine putting a baseball on a slide projector.) Anything inside this cone will always and forever measure the event as occurring in its past. Because velocity may not exceed c, anything which starts inside the cone can never get to a place where the event will not be in its past, and anything outside of the cone can never get to a place where the event will be in its definitive past.

The principle of reversibility gives us the past of the event: just invert the time axis of the cone. Now we have an hour-glass looking thing, the cone below the plane being the definitive past of the event and the cone above the plane being the definitive future of the event.

For a physical example, imagine a contrived futuristic scenario. Two spaceships, originally at the same point, turn and start flying away from one another at the same rate relative to an observer at the original point. Each ship counts off exactly ten hours and then fires off a radio message to the other ship, saying "I'm first." A few seconds later, each ship receives the message from the other ship. Who sent the message first?

The observer at the original point receives each message at the same time.

Each spaceship observes their own message being first.

Obviously, neither spaceship is in the past cone of the other ship when it sends its message. Which one is first depends on reference frame.

Now let us suppose that in stead of waiting ten hours and sending their message, the observer at the original point waits ten hours and sends a message: "Send your radio message now." Each space ship will still see themselves send their message first, but both will agree that the observer at the original point sent his message before they did. Indeed, every observer everywhere will agree to this fact, because by the time they observe any of the three messages, that message must be in its past cone, and because the message from the starting point is in the past cone of both of the other messages, it must also be in the past cone of the observer.

The light cone method provides a concrete physical definition for past and present. Any event not in the light cone of another event is neither in its past nor in its present.

[Kuroneko]

The mathematically clearest analogy to the Lorentz transformation is an ordinary Euclidean rotation. In Euclidean 2-space, distance formula is Δr² = Δx² + Δy², which is just the Pythagorean theorem in another guise. So, for example, the set of points a distance r from the origin, r² = x² + y², is a circle of radius r. The trigonometry of Euclidean space is defined through cos θ = x/r, sin θ = y/r, from which we have cos²θ + sin²θ = 1. Note in particular that tan θ = y/x.

Spacetime in STR is not like that. Rather, the way spacetime distance is computed is Δs² = c²Δt² - Δx² (physically, Δs is the duration of time measured by an inertial observer going between the two events (t0,x0) and (t1,x1)). So the "circle" of points a distance s from the origin, s² = c²t² - x², is actually a hyperbola, leading to hyperbolic trigonometry with cosh²α - sinh²α = 1. Here, tanh α = (sinh α)/(cosh α) = (x/s)/(ct/s) = (x/t)/c, which is the velocity as a fraction of c.

The usual Lorentz transformation is a rotation based on different trigonometry. In matrix form:

Code: Select all

    Euclidean rotation                 Lorentz transformation
[x'] = [ cos θ  -sin θ ][x]  |  [t'] = [  cosh α  -sinh α ][t]
[y'] = [ sin θ   cos θ ][y]  |  [x'] = [ -sinh α   cosh α ][x]

If this form is unfamilar, substitute v/c = tanh α, γ = 1/√1-(v/c)² = 1/√sech²α = cosh α, and γv/c = sinh α. Rotations around the origin preserve the distance, so that in Euclidean space, rotations happen along circles, which loop back on themselves for large enough angles θ... but in STR, this happens along hyperbolas, which do not.

Code: Select all

\future/    ^ time
.\abs./     |
  \  /      L----> space
___\/_________ present t = 0 (not absolute), aka the
   /\          "surface of simulateneity" through the origin
  /  \  <-- the edges of the light cone are t = ±x/c, the
./abs.\     asymptotes of the hyperbolas some constant
/ past \    distance from the origin

The top of the interior of the light cone is the absolute future of the event at the origin. In other words, all observers will agree that any event that region is in the origin's future, and similarly for the absolute past.

So in some cosmic sense, would it be correct to say that the past, present and future are artificial distinctions?

In a sense, the present is an 'artificial' construction, but not so for the absolute past the absolute future. In jargon, events outside the lightcone are "spacelike separated" from the origin, and strictly speaking are neither in the past nor future. There is, a natural surface of simultaneity that can be physically defined by reflected light signals, or mathematically by orthogonality with the time direction, but different inertial observes will not agree as to which surface that is because their time directions are different (each observer measures time along their trajectory in spacetime, including the non-inertial observers).

If past present and future are different for each frame shouldn't we expect to find inertial frames with observers whose present is equivalent to our future?

Well, yes, but that 'present' is conventional anyway, and has no physical relevance to either observer. Since one can't send signals outside one's lightcone, calling one special surface (or line, in the above diagram) the "present" is only useful for convenience.

The first two paragraphs might be more illuminating if they are not done in geometric units -- e.g., Δs² = c²Δt² - Δx² instead of what is posted.

Oh, fine.

[Surlethe]

The first two paragraphs might be more illuminating if they are not done in geometric units -- e.g., Δs² = c²Δt² - Δx² instead of what is posted.

[starslayer]

By your original point do you mean the sun not having formed in their frame bit? Thats not right.

No, you covered that; I was conflating a couple of things from SR, and ignored the niggling voice in the back of my head saying something wasn't right. Thanks for straightening me out. My original point was that Modax's thinking was wrong; specifically, his statement that there is a frame contemporaneous with ours in which the Sun is already a red giant. According to my understanding of SR, that is incorrect.