Andromeda paradox and determinism?

[Dale]

Stated like that, there clearly are no contradictions.

Any example in relativity, stated clearly, has no contradictions. Any contradictions you find are always in the statement, not relativity.

But now consider the situation :
A car on Earth is at rest with respect to the Earth. Suddenly the car explodes and creates smoke around it.

Now for observer who is in rest with respect to the car these events compose its present. One observer who is moving away from the car will have the car's state before the explosion as its present in his own plane of simultaneity.

Yes, in this case you are talking about spacelike separated events, so my above comments cover this case exactly.

I understand these two parts, and I also understand that it might be the case that an observer who is moving faster than the second one (who is moving away from the car) may have the state of the car that existed before the state where nothing happened to it (it may be also the same state where nothing happened, but an earlier one).

Also, spacelike separated, so my the above clear description applies.

Now, the trickiest question for me is this one: Will the third observer (or fourth, if we take it that way) who is moving in the direction of the car see 'the future' of the car, relative to the state of the car which is in the present of the stationary observer.

Here, by using the word "see", you are talking about lightlike (or null) separated events, not spacelike separated events. The statement is different, but can be made just as clear:

If we have two lightlike separated events, A and B, such that there exists an inertial frame, F, where t_A<t_B then \mathbf{x}_A \ne \mathbf{x}_B and in any other inertial frame, F', t'_A<t'_B and \mathbf{x'}_A \ne \mathbf{x'}_B. There does not exist any inertial frame, F'', such that t''_A>t''_B nor \mathbf{x''}_A = \mathbf{x''}_B.

And finally, if he was speeding with a greater speed, would he see the later temporal parts of the car (for instance, the ashes being removed), and so on, so if he would travel with a really great speed he would see all of its future

Again, this is still null separated events so my above comments apply.

in the sense that he would have (in the present of his reference frame) a state of the object which is, for instance, days after the state of the car that the stationary observer had in its present frame.

I don't know why you would ever use the word "see" to describe this since the present state of a distant object is never seen. You can only see the past. What you see now is always lightlike separated from now.

Furthermore, even if this is what you intended with the word see, then you should have used the same wording for all parts of your question and not switched wording from things like "present state" and "plane of simultaneity" to wording like "see". Notice, that the resulting contradictions stem from the confusing wording, not from relativity.

 

[Dale]

I was referring to the fact when they have a particular event in their present plane of simultaneity, not what they see. That's what relative simultaneity states anyway, right?

Yes, but you never see the present.

What you see at any moment is measurable and devices can be constructed which will react to what you see. Therefore, what you see must be frame invariant.

In contrast the present at any moment is a mere matter of convention. It is not measurable and no device can be constructed which will react to what is present. Therefore, what is present may be frame variant.

You should not use the word "see" to refer to the "present", they have very different physical characteristics. If you do so, then the inevitable contradictions are a result of the contradictory language, not relativity.

 

[Dale]

Simultaneity is not an issue for observers. It's an issue for reference frames. Nothing changes for any observer just because you use a different IRF.

Well said. This is an under-appreciated point. Any observer can use any reference frame in their analysis, they do not need to use a reference frame where they are at rest.

 

[PeterDonis]

So the future light cone is the boundary we're speaking of?

Yes.

That means that while some authors state that the observer who's moving towards the object can have 'the future' of the object in its present p.o.s., it's really the case that the future he sees is really the sequence of events that follow other events in the frame with a different velocity and direction..

I'm not sure exactly what you mean by this; perhaps it will help if I restate what I think you're saying.

Suppose we have three observers all passing each other at some event E. One observer is at rest with respect to some distant object; another is moving away from the object; the third is moving towards it. Then each observer will, using his natural notion of simultaneity, say that a different event on the distant object's worldline is in his "present" at event E (i.e., is simultaneous with event E):

* The event that is "present" for the observer moving away from the object will be to the past of the event that is "present" for the observer at rest with respect to the object.

* The event that is "present" for the observer moving towards the object will be to the future of the event that is "present" for the observer at rest with respect to the object.

But all three "present" events will be outside the future light cone of event E, and that will be true regardless of the relative velocities of the observers. (All three events will also be outside the *past* light cone of event E, again regardless of the relative velocities of the observers.)

 

[TheBC]

The basic issue Durant wants to highlight is whether or not to accept a simultaneous space-like event being as real as your own present event.
On this physics forum this discussion is considered a philosophical problem, because it transcends mathematics.
Therefore, Durant, you will not find answers here whether you should prefer/accept solipsism or 3D or 4D spacetime realism...

 

[Naty1]

Some great explanatory points from all you experts...Thanks for all the details...

I've always had trouble trying to figure out what the 'Andromeda paradox' was all about because with a finite speed of light, what I observe of a distant event always seemed in their past by time light borne information reaches me, what I call my present.

reading all the posts gave me some further insights I had not considered...especially the light cone descriptions. Finally a use for those thingys!

 

[pervect]

The basic issue Durant wants to highlight is whether or not to accept a simultaneous space-like event being as real as your own present event.
On this physics forum this discussion is considered a philosophical problem, because it transcends mathematics.
Therefore, Durant, you will not find answers here whether you should prefer/accept solipsism or 3D or 4D spacetime realism...

It is clearer to say that problems that transcend (i.e. are beyond the reach of) experiment are philosophical. Mathematics doesn't really have anything in particular to do with the problem.

It does appear that the OP is interested in metaphysics.

In any event metaphysical discussion is generally off limits. There might be a small amount of wiggle room here and there, but if the primary interest is metaphysical, it belongs on some other forum.

 

[Dale]

On this physics forum this discussion is considered a philosophical problem, because it transcends mathematics.

No, it is considered philosophical because there is no experiment which can determine it, as you well know.

And nobody besides you is talking about solipsism.

 

[TheBC]

No, it is considered philosophical because there is no experiment which can determine it, as you well know.

And nobody besides you is talking about solipsism.

If there is no experiment to prove the existence of space-like events (observer independent reality), then solipsism rules.

But then you have to explain me where the images of observations come from. Out of nothing popping up into your mind?
The light of Andromea reaching your eye is possible because the event of the light leaving Andromeda existed -observer independent as a spacelike event- before you actually see it. Refuting this means denying observer independent events and sliding into solipsism. Einstein hated it.

But again, I repeat, because all this is considered philosophy, member Durant will not find any answers here. Here he can only find answers about abstract coordinate and reference systems without considering what 'reality' -if any!- they are applied to. I thought it was interesting to highlight this to member Durant.

 

[WannabeNewton]

Why do people always have a need to bring philosophical garbage into physics?

 

[Dale]

If there is no experiment to prove the existence of space-like events (observer independent reality), then solipsism rules.

Irrelevant. Nobody is disputing the existence of space-like separated events. Only that there is any experimental method to choose between the block universe and LET. Neither LET nor the block universe implies solipsism.

Even a more extreme stance where you only assert the observer independent existence of events within your past light cone (and remain agnostic about any other events), still would assert the existence of space-like separated events since the past light cone contains many pairs of space-like separated events.

Your comments about solipsism are irrelevant and off topic for the forum. Nobody is promoting solipsism.

 

[15characters]

Thanks for the reply Naty. So in the particular case of the Andromeda paradox, the sequence of events on the Andromeda galaxy will be present in every distant reference frame, regardless of its motion. It's just the case that some observers will some events from the past of the Galaxy before another observer does (because of their relative distance). So it's something like the case that if we were really close to the sun we would see its specific past state before another observer on the Earth will, right?

I previously got confused by paradoxes until I understood how the plane of simultaneity works last week. In my opinion for beginners it is more important to understand

length X velocity = fixed time gap between observers

This phased time difference is key. It is calculated as relative velocity x distance. So for example at 0.5 c every light second of distance will produce 0.5 light seconds of time gap between observers. (0.5 x 1 = 0.5).

At 0.8c an event 10 light seconds away in distance will have a time phase gap of 8 seconds between observers ( 0.8 x 10)

The gap works both ways so if you are moving at 90% C then events 10 light years behind in distance will shift 9 years into the past while those 10 light years in front of you would shift 9 years into the future.

Example

We all see the photons arriving from the sun at the same time. Those stationary on Earth assume the photons were sent 8 minutes ago when the sun was 8 light minutes away. A passing spaceship at 50% of the speed of light, traveling past Earth towards the sun on seeing the same photons would see this a phase difference of 500 x 0.5 = 250 seconds.

What this means is they will assume events that we say happened on the sun NOW actually happen 250 seconds into the future or past - depending which way they are moving

For example moving towards the sun will move their sun 250 seconds into our future. They see

1) Earth and Sun rushing towards them at 0.5C.
2) Photons from the sun moving at C.

They would conclude that the photons just now arriving from the sun took some time to arrive and must therefore have been sent when the sun was further away from their current position than it is now (remember the Sun is rushing towards them). They will say this time was 250 seconds before what we think it is (8 minutes).

Therefore they will conclude the photons are from about 12 minutes ago not 8 minutes ago.

The formula for time phase gaps is simple = distance x velocity. Talk of moving clocks etc only confuses people.

Another example

Every passenger on the train has a clock. They all show the same time for people on the train.

From the outside to observers the train moves at 0.5C. For every light second of distance along the train the passenger's clocks appear 0.5 time seconds out of phase. Its a fixed phased gap related to distance.