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Old 2007-11-07, 13:27   #1
Zeta-Flux
 
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Default Simultaneity- a physics question

I'm trying to understand some philosophical implications of relativity, and I was hoping some of you physics gurus could help me out. As I understand it, the following can happen.

A rocket can be shooting towards a barn door at nearly the speed of light. From one frame of reference A, the rocket hits the barn door at time t_0, and a person in frame A pushes a button to signify this act. From another frame of reference B, it appears that the person in frame A pushed the button too soon.

Would this imply the following?: From my point of view, there is a frame of reference occuring *now*, from which it appears I am not born yet? [What I mean is that there is some alien named Charles who, it looks to me, exists right now. However, from his point of view, even taking into account the speed of light, I will only be born years from now.] I'm really trying to get a grasp on what "now" means, and it seems to depend on the frame of reference. Further, it doesn't seem to be a symmetric or transitive relation.

Am I understanding this correctly?

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Old 2007-11-07, 16:05   #2
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Originally Posted by Zeta-Flux View Post
I'm trying to understand some philosophical implications of relativity, and I was hoping some of you physics gurus could help me out. As I understand it, the following can happen.

A rocket can be shooting towards a barn door at nearly the speed of light. From one frame of reference A, the rocket hits the barn door at time t_0, and a person in frame A pushes a button to signify this act. From another frame of reference B, it appears that the person in frame A pushed the button too soon.

Would this imply the following?: From my point of view, there is a frame of reference occuring *now*, from which it appears I am not born yet? [What I mean is that there is some alien named Charles who, it looks to me, exists right now. However, from his point of view, even taking into account the speed of light, I will only be born years from now.] I'm really trying to get a grasp on what "now" means, and it seems to depend on the frame of reference. Further, it doesn't seem to be a symmetric or transitive relation.

Am I understanding this correctly?

Thanks,
Zeta-Flux
"Before", "after" and "simultaneous" are not particularly useful concepts in relativity. As you state, everything depends on the reference frame.

The concepts that make more sense are "causally connected", "not causally connected" and "on the same light cone".

If two events are "on the same light cone", they are separated in spacetime such that a photon can travel (in either direction) between the events and so that either event could have caused the other. This is probably the closest to a true notion of simultaneity that exists in relativity.

If two events x and y are causally connected (and not on the same ligh ctone) every observer can agree on exactly the same ordering of the two events. Either x could have caused y (and therefore the x could be interpretated as happening "before" y), or the reverse situation holds (and x occurs "after" y); no-one observes the events occurring simultaneously.

In the acausally connected situation, some observers will claim that the event occur in one order, other observers that they occurred in the reverse order and still others that they occurred simultaneously.

I don't know how much this helps, if any.


Paul
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Old 2007-11-07, 16:20   #3
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Originally Posted by Zeta-Flux View Post
Would this imply the following?: From my point of view, there is a frame of reference occuring *now*, from which it appears I am not born yet? [What I mean is that there is some alien named Charles who, it looks to me, exists right now. However, from his point of view, even taking into account the speed of light, I will only be born years from now.] I'm really trying to get a grasp on what "now" means, and it seems to depend on the frame of reference. Further, it doesn't seem to be a symmetric or transitive relation.

Am I understanding this correctly?
I 'm not sure whether you are understanding it correctly or not.

Consider this model. Charles lives a hundred light years away from you. On your tenth birthday you saw Charles being born. Ten years later into your life (as you measure time), Charles appears to be ten years old. OK? However, the information that you have been born has reached only 20 light years into space and so Charles can not know of your existence. Your birth and Charles' birth are acausally connected events.

To some observers you were born before Charles. An examples is given by someone who left Charles' home less than ten years before his birth and travelled at very high speed towards you, passing you before photons signalling Charles' birth had caught up with the traveller.

Another observer, on the same trajectory as the first but moving a little bit slower, would see Charles' birth at exactly the same time as he sees your birth.

Others, such as a still slower traveller, sees Charles' birth before yours.

Again, I don't know whether this helps.

Paul
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Old 2007-11-07, 16:21   #4
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xilman,

Quote:
If two events are "on the same light cone", they are separated in spacetime such that a photon can travel (in either direction) between the events and so that either event could have caused the other. This is probably the closest to a true notion of simultaneity that exists in relativity.
What do you mean by "on the same light cone"? The sun emits a photon, and about 5 minutes later (from my frame of reference) it hits my eye. Is my eye on the "same" light cone as the sun was when it emitted the photon. Or are you speaking of "same" in some other sense (e.g. the identical light cone, from both frames of reference??). I'm simply not following you here. Could you take the time to clarify?

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Old 2007-11-07, 16:23   #5
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Paul,

I'm not speaking of what they *see* happening first (which clearly depends on when the photons reach them). As I understand it, EVEN accounting for the speed of light, events can happen in different orders, from different frames of reference.
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Old 2007-11-07, 17:05   #6
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xilman,

What do you mean by "on the same light cone"? The sun emits a photon, and about 5 minutes later (from my frame of reference) it hits my eye. Is my eye on the "same" light cone as the sun was when it emitted the photon.
Yes. At the instant that photon hit your eye your eye and the point of origin of the photon lay on the same light cone. Before the photon hit your eye, your eye was outside the light cone and afterwards it is inside the light cone.
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Or are you speaking of "same" in some other sense (e.g. the identical light cone, from both frames of reference??). I'm simply not following you here. Could you take the time to clarify?

Thanks,
Zeta-Flux
Also yes. Everyone, no matter where they are or how they are moving with respect to each other, agree that the two events are on the same light cone.

Not sure whether you understand the origin of the phrase "light cone". Forgive me if you don't need the explanation that follows.

In two dimensions, one of which is space and the other time, the path of a photon looks like a straight line and no matter who draws the diagram the line has exactly the same slope. The line is straight because everyone measures that travels at a constant velocity (we're talking about light in vacuo here). The line has the same slope because everyone measures light travelling at exactly the same velocity c. Conventionally in relativity we set the measurement scales such that c = 1, so the line is at an angle of 45 degrees to the axes.

Bringing in two spatial dimensions, the path of a photon now lies on the surface of a cone which has a vertex angle of 45 degrees. This is the "light cone".

In four-dimensional spacetime (such as we apparently live in), the path of a photon is on the surface of a hypercone with vertex angle 45 degrees.

Try to keep in mind that relativity describes events in spacetime and that it's impossible, in general, to separate space from time such that every observer agrees on which is which. Situations arise (called acausally connected events) such that some observers measure events to occur at the same place but at different times, or at the same time but at different places, or at different times and different places.


Paul

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Old 2007-11-07, 17:20   #7
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Paul,

I'm not speaking of what they *see* happening first (which clearly depends on when the photons reach them). As I understand it, EVEN accounting for the speed of light, events can happen in different orders, from different frames of reference.
"See" in this model (and most explanations of the equations of relativity) is shorthand for something like "measure experimentally" and "light" is shorthand for "information carrier". A postulate of relativity is that no information can be transmitted from one place to another faster than a certain speed c no matter what method is used. It so happens that light travels at c and, at the time Einstein developed the theory, it was the only phenomenon determined experimentally to do so.

Another postulate of relativity is that every observer always measures the speed of light to have exactly the same value of c no matter how they are moving with respect to othe observers.

It's unfortunate, perhaps, that "see" is ambiguous in this context. Try translating "see" and "light" (or "photon" as appropriate) in my models of you, Charles and the travellers into "measures by experiment" and "information" respectively to see (there's that word again) whether that helps.


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Old 2007-11-07, 17:54   #8
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xilman,

I'm following you now. It seems highly counter-intuitive to me to call two events on the same light-cone "simultaneous". Do many people follow this convention? Is this because from some frames of reference, two events on a light cone can "trade-places" so to speak?

At any rate, I think I can now frame the precise question which has puzzled me. I fire a gun and the bullet shatters a vase. From my point of view, there is a flash of light in-between the gun firing and the vase shattering. There is a frame of reference in which the vase shattering is outside the light cone formed by the flash of light, correct? However, in all frames of reference, *after the fact*, they can tell/measure that from my frame of reference, the gun fired first.

How do physicists talk about causality? Clearly the bullet's firing caused the vase to shatter. But, apparently, the *order* of occurances doesn't matter, except in certain frames of reference. What is the method of determining which frame of reference is the 'right' one in which to view causality of events? Or is it possible that there are events which happen, which seem to have no *cause* in any frames we can come up with?
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Old 2007-11-07, 19:13   #9
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xilman,

I'm following you now. It seems highly counter-intuitive to me to call two events on the same light-cone "simultaneous". Do many people follow this convention?
They are not really "simultaneous" in the conventional sense, because the conventional interpretation of that word is nonsensical in relativity. Perhaps I shouldn't have used the sentence "This is probably the closest to a true notion of simultaneity that exists in relativity." earlier because it can be too easily misinterpreted. The sentence must be read in the context of those immediately preceding it.

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Is this because from some frames of reference, two events on a light cone can "trade-places" so to speak?
Yes, and not only in some frames of reference but in all frames. That's how I'd intended it to be interpreted.
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At any rate, I think I can now frame the precise question which has puzzled me. I fire a gun and the bullet shatters a vase. From my point of view, there is a flash of light in-between the gun firing and the vase shattering. There is a frame of reference in which the vase shattering is outside the light cone formed by the flash of light, correct?
First off, every observer everywhere in spacetime agrees on whether a point in space time (an "event") is inside, outside or on any particular light cone and, specifically, that defined by your flash of light.

Let's assume that the bullet is an object with mass, as I think you intended. I.e. the bullet travels slower than light in all frames of reference and your gun is not (for example) a laser. Let's assume the vase is a light year away and your bullet, as you measure it, is travelling at half the speed of light. (You have a very powerful gun and a very good aim.) Of course, as the bullet measures things, it is stationary, you and the gun are receding at c/2 and the vase is approaching at c/2. A light year behind you, a flash of light occurs such that it arrives where you are when the bullet is (as you measure things) 90% of the way to the target. As far as you are concerned, the flash happens before the bullet hits the vase. From the point of a view of an observer sitting in the vase, the flash occurs well after the bullet arrives (assuming the observer survives the collision with the bullet!).

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However, in all frames of reference, *after the fact*, they can tell/measure that from my frame of reference, the gun fired first.
ow do physicists talk about causality? Clearly the bullet's firing caused the vase to shatter. But, apparently, the *order* of occurances doesn't matter, except in certain frames of reference. What is the method of determining which frame of reference is the 'right' one in which to view causality of events? Or is it possible that there are events which happen, which seem to have no *cause* in any frames we can come up with?
In all frames of reference, the gun fired before the vase was smashed by the bullet. That's what is meant by "causally connected". Because it is possible for information ("light") to be transferred between the point in spacetime where the gun fires and the point where the vase breaks, it is possible for the firing to break the vase. All observers agree on that.

Acausal pairs of events ("event" is a code word for "point in spacetime") are those which, because of their separation in spacetime, information can not be transferred between them. They are, in a real sense, too far apart for light (i.e. information) to travel between them. Depending on who is doing the measurements, either or neither of the pair could occur first.

In the gun and vase model, the emission of the flash of light and the smashing of the vase are acausally connected events.

Paul

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Old 2007-11-07, 20:04   #10
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xilman,

Thank you for taking the time to explain this. One more question. What makes it so that the light flash and the vase shattering are acausally connected events?

In other words, what if the light flash is caused by the bullet passing a light emittor sitting out in space? The light emittor senses the bullet passing, and sends out a flash of light. Isn't it clear that the flash happens *before* the vase is shattered, in all frames of reference? Or is it that one cannot tell whether the light emittor performed its specified task?

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Old 2007-11-07, 20:29   #11
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xilman,

Thank you for taking the time to explain this. One more question. What makes it so that the light flash and the vase shattering are acausally connected events?

In other words, what if the light flash is caused by the bullet passing a light emittor sitting out in space? The light emittor senses the bullet passing, and sends out a flash of light. Isn't it clear that the flash happens *before* the vase is shattered, in all frames of reference? Or is it that one cannot tell whether the light emittor performed its specified task?
You've just described a situation in which the creation of the flash of light and the shattering of the vase are causally connected and, indeed, all observers agree that the flash occurs before the vase is shattered.

A difference between your scenario and my earlier one is that the creation of the flash of light could (respectively could not) have caused the vase to smash before (whether observed by you, the bullet or the vase) the bullet arrived at the vase. That's what is meant by two events being causally connected --- one event could possibly have caused the other. Two events which are acausally connected are located at points in space time such that neither could have caused the other because they are too far apart (in spacetime remember, not just in space or time separately) for a light signal (meaning information) to travel between them. In this latter case, different observers will observe the two events to occur in either order or at the same time, depending on where they are in space and time.

Paul

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