Andromeda paradox and determinism?

[WannabeNewton]

Seems to me like te simultaneity concept in physics was made because the mathematics of it worked well, but the consequences may be contradictory and everybody's making thousand premises just to save relative simultaneity, while in fact, it's not only counter-intuitive, it leads to bizarre scenarios that are beyond common sense, but logic also.

Welcome to physics, where nature doesn't have to obey your elementary classical conceptions of "common sense" and "logic"

 

[pervect]

So, putting it simply, you're basically saying that somebody with a great velocitiy towards you can have your future as its present in its own referential frame.

That doesn't sound very logical to me.

I couldn't quite follow that. But I think what you mean is:

Somebody with a great velocitiy towards you has in your reference frame, some particular event that is in your present in your frame. An observer at that event can have your future as its present in its own reference frame.


Likewise, somebody with a great velocity away from you has some partciular event that is in your present in your frame. An observer at that event can have your past is its present in its own reference frame.

That's a simple example of the relativity of simultaneity. Which a while ago you were saying you didn't have problems with.

Now you are saying that you do have some problem, but you don't seem to be able to state what it is. I could see where you might say "it's not what you're used to", but when you say "it's not logical", it sounds like there must be some sort of paradox. However, you don't seem to be able to actually point out anything that i logically inconsistent with this state of affairs - it's just that you don't like it, as near as I can tell.

 

[AnTiFreeze3]

Welcome to physics, where nature doesn't have to obey your elementary classical conceptions of "common sense" and "logic"

Welcome to high school physics, where everything is in a vacuum, and air resistance is negligible.

 

[WannabeNewton]

Welcome to high school physics, where everything is in a vacuum, and air resistance is negligible.

Not at my high school

 

[AnTiFreeze3]

Not at my high school

My high school: Everything is in a vacuum, air resistance is negligible, and calculus is nonexistent

 

[ghwellsjr]

As promised, here are some more IRF diagrams showing a black spacecraft leaving Earth at 0.725c traveling toward the Andromeda galaxy. Once again, we start with the mutual rest frame for the Earth and Andromeda:

The Andromedians can detect the launch of the spacecraft 2.5 million years after the supernova explodes as depicted by the thin blue line. After one million years of Proper Time for the spacecraft , it intercepts the image of the supernova depicted by the thin red line and about 0.4 million years after the Andromedians see the launch of the spacecraft , they can detect that the spacecraft has intercepted the image of the supernova as depicted by the thin black line. However, we earthlings still have to wait 2.5 million years after time zero before we can see the supernova as depicted by the thin red line. The spacecraft arrives at Andromeda after about 2.35 million years of travel according to its own Proper Time. (I have shown its worldline continuing after arrival to make it easier to determine its arrival time.) As far as the Andromedians are concerned, the spaceship arrives about 3.5 million years of their own Proper Time after the supernova explodes.

Now we'll see how this all looks in the IRF moving at 0.4c towards the galaxy with respect to the original IRF:

Even though all the time and location coordinates for all the events are different (except the one at the origin), all the events follow exactly the same pattern as they did originally and all parties see, measure and observe exactly the same things as they did in the original IRF according to the Proper Times on their own clocks.

And here is the IRF traveling in the opposite direction at 0.4c:

Same story--different coordinates, same Proper Times and same observations for all parties.

The next post will have one more IRF in which the spacecraft is at rest.

 

[ghwellsjr]

And one last IRF transformed from the original one in my previous post moving at 0.725c so that the spacecraft is at rest:

Please refer to my previous post for an explanation of the different events and the different light signals. I hope you can see that any IRF is just as good as any other IRF for showing everything that is happening in any scenario and that no IRF is preferred, not even one in which an observer is at rest. Even though the spacecraft is at rest in this IRF, it does not provide the spacecraft with any additional information than any other IRF. The same thing can be said for the IRF in which Earth and Andromeda are at rest.

The only thing different in these IRF's is the values of the coordinates for the different events and it's these coordinate values that determine simultaneity issues in an IRF. That's why simultaneity is relative. It's relative to the IRF that you are looking at the scenario in. Transform to a different IRF and you get different time coordinates and therefore different simultaneity. But no paradoxes, agreed?

Any questions?

 

[durant]

Now you are saying that you do have some problem, but you don't seem to be able to state what it is. I could see where you might say "it's not what you're used to", but when you say "it's not logical", it sounds like there must be some sort of paradox. However, you don't seem to be able to actually point out anything that i logically inconsistent with this state of affairs - it's just that you don't like it, as near as I can tell.

Nah, it's not the case that I don't like it. In fact, I find it very interesting. But the case is that it's confusing stuff for somebody who isn't familiar with relativistic physics, that's why I read every post carefully and point out, what are, in my opinion debatable parts of the theory. I know much less than you about it, but we are all on the approximately same level as far as logic comes. Except the fact that it takes time for me to develop the concepts that you're already familiar with.

 

[durant]

@Ghwellsjr, thanks for the diagrams, I'll explore them later today because I'm in a kind of rush right now but anayway I appreciate your work.

 

[Dale]

So, putting it simply, you're basically saying that somebody with a great velocitiy towards you can have your future as its present in its own referential frame.

That doesn't sound very logical to me.

It doesn't sound very logical because you are using terribly sloppy language to describe it. Here is a more rigorous way to say it which hopefully makes it clear:

Due to the relativity of simultaneity, if we have two spacelike separated events, A and B, then there exists an inertial frame, F, such that $t_A=t_B$ and there exists another inertial frame, F', such that $t'_A<t'_B$ and there exists a third inertial frame, F'', such that $t''_A>t''_B$.

Clearly there is nothing illogical here if you state things clearly.

 

[durant]

It doesn't sound very logical because you are using terribly sloppy language to describe it. Here is a more rigorous way to say it which hopefully makes it clear:

Due to the relativity of simultaneity, if we have two spacelike separated events, A and B, then there exists an inertial frame, F, such that $t_A=t_B$ and there exists another inertial frame, F', such that $t'_A<t'_B$ and there exists a third inertial frame, F'', such that $t''_A>t''_B$.

Clearly there is nothing illogical here if you state things clearly.

Stated like that, there clearly are no contradictions.

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.

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).

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.

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 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.

If we were co-located with the object we would see what is really happening to it now, that's why it confuses me how can an observer that is moving towards the object see even later stages of the object (or will he see the latest state also). I hope you understand my example and question.

 

[ghwellsjr]

Stated like that, there clearly are no contradictions.

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.

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).

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.

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 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.

If we were co-located with the object we would see what is really happening to it now, that's why it confuses me how can an observer that is moving towards the object see even later stages of the object (or will he see the latest state also). I hope you understand my example and question.

It doesn't matter what example you want to dream up. Define it clearly in one IRF. Draw a diagram with light signals at 45 degree angles from different events to different observers. That is all there is to it.

But if you want, you can transform to another IRF, such as one in which a different observer is at rest and you will see that the coordinate values for time and locations all change but it has no bearing on what any observer sees with respect to the Proper Times on their own clocks.

EDIT: Your description is not clear. It's probably clear in your mind but you haven't communicated what you are thinking. Are you asking about a bunch of different observers in different states of motion but all colocated some distance away from the exploding car at the time that they all simultaneously see the explosion? You have to state all the details or no one will have any idea what you are talking about.

 

[durant]

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?

 

[Nugatory]

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?

Right. Now what is the physical significance of saying that an event does or does not lie in the same plane of simultaneity as some other event?

 

[durant]

Right. Now what is the physical significance of saying that an event does or does not lie in the same plane of simultaneity as some other event?

Well, two space-like events should be simultaneous for the observer in that reference frame. That's the signifance. My point is, does there exist a state of the object which will be the present for every observer that is moving towards the object.

 

[ghwellsjr]

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?

I understand your issue, I don't understand your new scenario. And I don't understand why you introduced a new scenario when you haven't processed the diagrams for your previous scenario(s). Why do you think a new scenario will provide any more insights or issues or concerns or problems or paradoxes than your previous one(s)?

 

[ghwellsjr]

Well, two space-like events should be simultaneous for the observer in that reference frame. That's the signifance. My point is, does there exist a state of the object which will be the present for every observer that is moving towards the object.

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. If you would study the drawings I made, it would be abundantly clear. Please use your time to study those diagrams instead of launching into new directions.

 

[Nugatory]

Well, two space-like events should be simultaneous for the observer in that reference frame. That's the significance.

That's no answer, because "simultaneous for the observer" is just another way of saying "lies in the same simultaneity plane" - indeed, "simultaneous for an observer" is a definition of a simultaneity plane.

You will not be able to move past this unhelpful circularity until you describe the situation in terms of physical phenomena (at this point in spacetime the fleet took off; at that point in spacetime a light signal might have been emitted; at some other point in spacetime that light signal is received) that could in principle be observed and measured, and "simultaneous" is not such a thing.

My point is, does there exist a state of the object which will be the present for every observer that is moving towards the object.

There does not. Ghwellsjr's spacetime diagrams will help you see this.

 

[durant]

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. If you would study the drawings I made, it would be abundantly clear. Please use your time to study those diagrams instead of launching into new directions.

Could you be more concrete, at least for this example?

If I currently have some state of the Andromeda galaxy as present in my reference frame, what would somebody who is traveling 0.9c towards the Andromeda galaxy have as its present in their own reference frame. A distant future event relative to the event that I have in my presen reference frame?

Or there exists a limit by which some observer cannot have 'the distant future' of the object in its own reference frame, no matter how fast he is traveling towards to it.

 

[PeterDonis]

there exists a limit by which some observer cannot have 'the distant future' of the object in its own reference frame, no matter how fast he is traveling towards to it.

Yes, there is such a limit. It's called the future light cone. Pick any event in spacetime; call it event E. The portion of spacetime bounded by the set of all possible light rays that can be emitted from event E is the event's future light cone. No event within the future light cone of event E can be in the "present" for *any* observer passing through event E, regardless of the observer's velocity. So for any object that is spatially separated from any observer passing through event E, the portion of that object's worldline that is within the future light cone of event E must be "in the future" for that observer, regardless of the observer's velocity.

 

[durant]

That's no answer, because "simultaneous for the observer" is just another way of saying "lies in the same simultaneity plane" - indeed, "simultaneous for an observer" is a definition of a simultaneity plane.

You will not be able to move past this unhelpful circularity until you describe the situation in terms of physical phenomena (at this point in spacetime the fleet took off; at that point in spacetime a light signal might have been emitted; at some other point in spacetime that light signal is received) that could in principle be observed and measured, and "simultaneous" is not such a thing.



There does not. Ghwellsjr's spacetime diagrams will help you see this.

So if one passenger walks towards the Andromeda he will have a present in its own frame where the crew already take off to Earth, and if another one is moving with a much greater velocity towards the Andromeda he will have a state that is days, weeks or even months after the state in which the crew took off..

So, basically the question is, where's the borderline? The faster we travel towards the object, the later state of it will become our present. Is this proposition true? And if not, what would happen in the previously mentioned scenario.

 

[PeterDonis]

where's the borderline?

See my post #55; it looks like it and your #56 "crossed in the mail", so to speak.

 

[durant]

See my post #55; it looks like it and your #56 "crossed in the mail", so to speak.

:)

I've just red it, it appeared as soon as I posted the previous one. So the future light cone is the boundary we're speaking of?

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.. That would seem to be reasonable.

 

[Nugatory]

Or there exists a limit by which some observer cannot have 'the distant future' of the object in its own reference frame, no matter how fast he is traveling towards to it.

Whether you are traveling towards or away is irrelevant to the definition of "present", although it does affect how long it will take for the light from events that are happening "right now" in the distant location to reach me. If light from an event X light-years away hits my eyes at time T, I'll say that the event happened at time X-T years ago and in the meantime the light has been in flight; and in that sense the event was in my "present" at time "X-T". Traveling away just means that both the X and T values can be larger, but doesn't have to change the value of X-T (nor affect the fundamental lack of physical significance in that definition of "present").

Or there exists a limit by which some observer cannot have 'the distant future' of the object in its own reference frame, no matter how fast he is traveling towards to it.

There does exist such a limit.

Consider an observer traveling towards an object. Imagine that the object is emitting periodic flashes of light (arbitrarily close to one another, so we don't have to worry about what's going on in the interval between flashes). No matter how fast the observer is approaching the object, [strike]the observer's "present" will never include any event at the object that occurs after the most recently received flash was emitted from the object[/strike]. (Note that if the observer remains on course and eventually reaches the object, the travel time of the last flash will be zero - the observer cannot ever see beyond his arrival, and the faster he travels the sooner he arrives).

again... Ghwellsjr's space-time diagrams will help a lot.

[edit - the overstruck part is not correct. The approaching obsever's "present" during the approach will never include anything that happens at thebobjeft after a light signal from the observer would have made it to the object]

 

[ghwellsjr]

Could you be more concrete, at least for this example?

If I currently have some state of the Andromeda galaxy as present in my reference frame, what would somebody who is traveling 0.9c towards the Andromeda galaxy have as its present in their own reference frame. A distant future event relative to the event that I have in my presen reference frame?

Or there exists a limit by which some observer cannot have 'the distant future' of the object in its own reference frame, no matter how fast he is traveling towards to it.

Why do you want me to be more concrete? What's wrong with the four diagrams I made for you with a spacecraft traveling at 0.725c from Earth to Andromeda? They are concrete. Your new example is fuzzy. I have no idea what you are asking. Instead of bringing up a new traveler going at 0.9c, please copy one of my diagrams with the spacecraft and draw in whatever you are asking and then upload it so that I can understand what your concern is.

 

[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?