# Thread: Logical testing of Einstein's Relativity

1. The purpose of this thread is to discuss different logical tests (problems) of the Theory of Relativity. If you have any new thought experiments that you think either reveal some strengths or weaknesses of the relativistic model then you can post them here.

I will start off with an adaptation of the well known twin paradox (Twin paradox - Wikipedia, the free encyclopedia), where relativity dictates that because of close to the speed of light relative movement of the twins there must be a difference in the observed rates of time. Within the model the twin in the non-inertial reference frame is selected to experience the actual slower rate of time.

The logical problem
Instead of twins there are now three brothers and two space ships for two different voyages. Two of the brothers embark to travel towards perfectly opposite directions from Earth, the travel speed is 0.9 * c for both ships. They have synchronized clocks and the travel paths of the ships have been chosen so that the gravitational environments the ships will be traveling through are equal. The ships begin their voyage at the same time, travel along the direct path for one year and then at the same Earth time they turn back in perfectly identical fashion and travel back home along the same direct path at the same 0.9*c speed. The ships arrive back to Earth at the same time.

Relativistic comparison of the reference frames and rates of time:
1. the reference frames of the travelling brothers are the non-inertial reference frames, therefore the brother who stayed on Earth has aged more than them
2. logically according to Einstein's relativity both travelling brothers must have aged equally relative to the brother who stayed back

Conclusion
The two brothers experience extremely fast motion relative to each other, in their own rest frames they both observe the other move away at very close to the speed of light. Einstein's model necessitates the following logical conclusions
1. the relativistic model dictates that all relative motion must result in different rates of time observed in the reference frames
2. the relativistic model dictates that relative motion without different rates of time is possible

The model contradicts itself. Currently I do not know of any logical deduction chain that allows Einstein's relativity to survive this problem. If you are able to come up with a sound logical deduction chain that saves the model, please do explain it.

2.

3. Dear Grandi,

Your next post in the physics sub-forum will need to be your calculation of the deflection of light by the sun. Should you continue posting nonsense there, you will be banned.

4. Originally Posted by Harold14370
Dear Grandi,

Your next post in the physics sub-forum will need to be your calculation of the deflection of light by the sun. Should you continue posting nonsense there, you will be banned.
There is a thread of experimental testing of GR in the physics sub-forum. You baffle me, why is not a thread of logical testing of GR allowed there?

Are you referring to this thread as nonsense? If so, why is that?

Do you have a logical answer to the proposed logical problem of GR?
If you do, please enlighten me, because I would like to understand if there is a solution to this problem. I have tried to find a solution but wasn't able to. I accept that there may be some particular view point that I may have missed. If you find a logical view point that solves this problem for GR I will gladly accept it.

5. Ok, to start with, here is a formal mathematical proof that SR is internally self-consistent, i.e. that it is impossible to derive any contradiction from its axioms :

General Proof that Special Relativity is Self-Consistent

As for this specific scenario :

1. Both moving twins are in locally non-inertial frames because they experience acceleration
2. Because they both move non-intertially even relative to each other, the full treatment under GR is necessary. Each of the twins will measure a proper time of

Since you said that

the travel paths of the ships have been chosen so that the gravitational environments the ships will be traveling through are equal
we know that the metric tensor g must be equal for both of them - therefore the above proper time is also equal for both of them. In other words, once they arrive back at the stay-at-home observer, both travellers will have recorded the same time on their clocks. There is no contradiction anywhere here. During their travel the clocks are not necessarily synchronized due to the acceleration and relativity of simultaneity, but once they arrive back at rest in the same frame both clocks show the same outcome.

The important point to understand here is : there is no requirement for both clocks to remain synchronised in any particular way while the non-inertial motions are in progress. The only physically meaningful comparison between the two clocks which the travellers can perform in this case is when they are both at rest in the same frame of reference. At that time it is trivially easy to show that both travellers' clocks will show the same readings after their non-inertial motion, as demonstrated mathematically above.

Based on the level of understanding you have demonstrated over in the other two threads I would not expect you to comprehend the fact that there is no contradiction of any kind in this scenario.

6. Have a read through there. Have fun. http://www.thescienceforum.com/physi...ty-primer.html

7. I have tried to find a solution but wasn't able to.
I am not surprised - there is no solution, because no problem exists in the first place.

I accept that there may be some particular view point that I may have missed.
Indeed. See post 4.

If you find a logical view point that solves this problem for GR I will gladly accept it.
See post 4. There is no problem for GR in this, you just need to realize that you are trying to compare two non-inertial frames during accelerated motion. The whole point of the twin paradox is to compare the clocks when they meet again after the accelerated motion.

8. Since this is about non-inertial frames, the special relativity primer thread is not the appropriate answer to this question. Sorry about that.

9. Originally Posted by grandi
Einstein's model necessitates the following logical conclusions
1. the relativistic model dictates that all relative motion must result in different rates of time observed in the reference frames
2. the relativistic model dictates that relative motion without different rates of time is possible

The model contradicts itself. Currently I do not know of any logical deduction chain that allows Einstein's relativity to survive this problem. If you are able to come up with a sound logical deduction chain that saves the model, please do explain it.
If the twins feel the same forces and cover the same proper distance, they experience the same proper time.

Simple as that. The only people who claim the model contradicts itself are people who do not understand it properly. There are no contradictions in Special Relativity.

10. Originally Posted by Markus Hanke
Ok, to start with, here is a formal mathematical proof that SR is internally self-consistent, i.e. that it is impossible to derive any contradiction from its axioms :

General Proof that Special Relativity is Self-Consistent

As for this specific scenario :

1. Both moving twins are in locally non-inertial frames because they experience acceleration
2. Because they both move non-intertially even relative to each other, the full treatment under GR is necessary. Each of the twins will measure a proper time of

Since you said that

the travel paths of the ships have been chosen so that the gravitational environments the ships will be traveling through are equal
we know that the metric tensor g must be equal for both of them - therefore the above proper time is also equal for both of them. In other words, once they arrive back at the stay-at-home observer, both travellers will have recorded the same time on their clocks. There is no contradiction anywhere here. During their travel the clocks are not necessarily synchronized due to the acceleration and relativity of simultaneity, but once they arrive back at rest in the same frame both clocks show the same outcome.

The important point to understand here is : there is no requirement for both clocks to remain synchronised in any particular way while the non-inertial motions are in progress. The only physically meaningful comparison between the two clocks which the travellers can perform in this case is when they are both at rest in the same frame of reference. At that time it is trivially easy to show that both travellers' clocks will show the same readings after their non-inertial motion, as demonstrated mathematically above.

Based on the level of understanding you have demonstrated over in the other two threads I would not expect you to comprehend the fact that there is no contradiction of any kind in this scenario.
Thank you for the thorough answer. I understand exactly what you mean. However, there is one more factor here about which I feel I need to ask you in order to perceive your understanding of this scenario better.

Lets further clarify this experiment, making the following premises:
1. they have clocks that tick perfectly at the same rate in the same environment
2. they are able to perfectly synchronize the accelerations/decelerations and the velocities of the ships
3. the velocity vectors of the ships are constantly perfectly opposite and equal in magnitude at all times (relative to Earth)

The ships keep frequent logs marking their position relative to Earth at 1 second intervals, the log entry is [observed ship time - distance to Earth]. These logs now contain very accurate data from these voyages including the initial acceleration and the midpoint decelation and acceleration.

When the ships return and compare their recorded logs, do you expect these logs to be identical, or differ in some specific way?

11. Originally Posted by grandi
The purpose of this thread is to discuss different logical tests (problems) of the Theory of Relativity. If you have any new thought experiments that you think either reveal some strengths or weaknesses of the relativistic model then you can post them here.

I will start off with an adaptation of the well known twin paradox (Twin paradox - Wikipedia, the free encyclopedia), where relativity dictates that because of close to the speed of light relative movement of the twins there must be a difference in the observed rates of time. Within the model the twin in the non-inertial reference frame is selected to experience the actual slower rate of time.

The logical problem
Instead of twins there are now three brothers and two space ships for two different voyages. Two of the brothers embark to travel towards perfectly opposite directions from Earth, the travel speed is 0.9 * c for both ships. They have synchronized clocks and the travel paths of the ships have been chosen so that the gravitational environments the ships will be traveling through are equal. The ships begin their voyage at the same time, travel along the direct path for one year and then at the same Earth time they turn back in perfectly identical fashion and travel back home along the same direct path at the same 0.9*c speed. The ships arrive back to Earth at the same time.

Relativistic comparison of the reference frames and rates of time:
1. the reference frames of the travelling brothers are the non-inertial reference frames, therefore the brother who stayed on Earth has aged more than them
2. logically according to Einstein's relativity both travelling brothers must have aged equally relative to the brother who stayed back

Conclusion
The two brothers experience extremely fast motion relative to each other, in their own rest frames they both observe the other move away at very close to the speed of light. Einstein's model necessitates the following logical conclusions
1. the relativistic model dictates that all relative motion must result in different rates of time observed in the reference frames
2. the relativistic model dictates that relative motion without different rates of time is possible

The model contradicts itself. Currently I do not know of any logical deduction chain that allows Einstein's relativity to survive this problem. If you are able to come up with a sound logical deduction chain that saves the model, please do explain it.
You are neglecting both the effects of length contraction and the relativity of simultaneity. A simple way of dealing with this is to avoid switching frames halfway through and stick with one frame throughout.

Thus if we stick with the "outbound" frame of Brother 1, we see this: Brother 1 remains at rest while the Earth travels away at 0.9c and brother 2 travels away at ~0.99c (addition of velocities). We'll assume that, in the Earth frame, the brother's travel 10 ly before turning around. The length contraction factor at .9c is ~0.436, meaning that according to the outbound frame of Brother 1, the 10 ly contracts to 4.36 ly, and the 20 ly between the turn around points of the Brothers is 8.72 ly. This also means that when Brother 1's clock reads 4.84 yrs, the turn around point has reached him. At this point, twin 1 accelerates to .99c towards the Earth ( again according to the outbound frame). However, at this point, brother 2 is only 4.8 lys away and almost 4 ly short of reaching his turnaround point.

So at this point, according to the frame we are dealing with, we have the Earth traveling away at 0.9c and undergoing the time dilation due to this speed, and both brothers traveling away at ~.99c both undergoing the same time dilation which is greater than that of the Earth's. When Brother 2 finally catches up with his turn around point, he comes to a stop, and waits for the Earth and Brother 1 to come to him.

Now if you add up all the elapsed times for the Earth, Brother 1, and Brother 2 as measured from this frame, you find that upon their reuniting you will get the same answer as you do if you calculate things from the Earth frame.

The same is true no matter which frame you work from.

Where people get confused is when they try and jump from one frame to another without taking into account all the consequences of doing so.

The upshot is that your proposed scenario causes no contradictions or problems for Relativity. It only causes an apparent contradiction when you piecemeal it and try to deal with just one aspect (time dilation) and neglect the rest of the theory.

12. Originally Posted by Janus
Where people get confused is when they try and jump from one frame to another without taking into account all the consequences of doing so.

The upshot is that your proposed scenario causes no contradictions or problems for Relativity. It only causes an apparent contradiction when you piecemeal it and try to deal with just one aspect (time dilation) and neglect the rest of the theory.
Can you give your view and response to post #9 which focuses on the actual recorded observations the relativistic model predicts for the two travelling brothers?

13. Originally Posted by grandi
When the ships return and compare their recorded logs, do you expect these logs to be identical, or differ in some specific way?
They will be exactly the same, because their proper times are the exact same. Like I stated in my reply, the outcome of the experiment will be the same for both twins, which is why there is no contradiction at all. That does not mean however that the twins will agree on what is happening while they are moving non-inertially, because the notion of "simultaneity" is no longer well defined in this scenario. They will however agree as to the outcome once they are back together at rest. And because the outcome is the same for all observers, there is of course no paradox.

Do you see the difference ?

14. Originally Posted by grandi
Can you give your view and response to post #9 which focuses on the actual recorded observations the relativistic model predicts for the two travelling brothers?
He has already answered that in his post, just from a different perspective.
I prefer to always just calculate the proper times & distances, and then compare them. If you do that it is immediately obvious that there is no paradox here, because the proper times agree perfectly.

15. Just in case it isn't obvious, mathematics is an exercise in logic, so if the maths work, relativity passes the logic test. That alone doesn't mean it is automatically true, but that falls outside of the apparent premise of this thread. For that the tests of relativity sticky is a good source.

16. Originally Posted by Markus Hanke
Originally Posted by grandi
When the ships return and compare their recorded logs, do you expect these logs to be identical, or differ in some specific way?
They will be exactly the same, because their proper times are the exact same. Like I stated in my reply, the outcome of the experiment will be the same for both twins, which is why there is no contradiction at all. That does not mean however that the twins will agree on what is happening while they are moving non-inertially, because the notion of "simultaneity" is no longer well defined in this scenario. They will however agree as to the outcome once they are back together at rest. And because the outcome is the same for all observers, there is of course no paradox.

Do you see the difference ?
Ok. You refer to the actual observed rate of time as proper time. So the real actual observations and predicted observations are what matter here. The model predicts that according to the recorded observations on the ships they will indeed be observing the same rate of time.

Why would anyone then say that the two ships in relative movement would be observing different rates of time?

17. Originally Posted by grandi
Ok. You refer to the actual observed rate of time as proper time.
Proper time is what a clock measures that travels together with the twins in their frame of reference. Since both twins go through the same accelerations and gravitational potentials, their proper times will of course be the same.

Why would anyone then say that the two ships in relative movement would be observing different rates of time?
Because proper time is not the only way to measure time - one could also measure time from the standpoint of a stationary observer at infinity who is looking back at the moving spaceships. Such an observer could potentially ( but not necessarily ) see different rates of time for the two ships, depending on their state and direction of motion and acceleration in relation to that observer. This is called coordinate time. However, just like before, once the two ships come back together at rest even their coordinate times at infinity will once again agree, because they both must have done a 180 degree turnaround somewhere along their trajectory , cancelling out all acceleration and motion effects. Refer here :

Coordinate time - Wikipedia, the free encyclopedia

18. Originally Posted by Markus Hanke
Because proper time is not the only way to measure time - one could also measure time from the standpoint of a stationary observer at infinity who is looking back at the moving spaceships. Such an observer could potentially ( but not necessarily ) see different rates of time for the two ships, depending on their state and direction of motion and acceleration in relation to that observer. This is called coordinate time. However, just like before, once the two ships come back together at rest even their coordinate times at infinity will once again agree, because they both must have done a 180 degree turnaround somewhere along their trajectory , cancelling out all acceleration and motion effects. Refer here :

Coordinate time - Wikipedia, the free encyclopedia
Yes there's the notion that depending on how a third observer is situated in relation to the two travelling ships light from the ships may take different amounts of time to reach the observer and the doppler effect may cause compression or expansion of the visual information carried by light leading into appearance of different rate of time.

From the strict scientific perspective where the observers are the ones with the actual clocks the factual notion is that the prediction and the true recorded observation is that the ships in relative movement are in this case observing the exact same rate of time. Do you agree with this?

19. Originally Posted by grandi
Yes there's the notion that depending on how a third observer is situated in relation to the two travelling ships light from the ships may take different amounts of time to reach the observer and the doppler effect may cause compression or expansion of the visual information carried by light leading into appearance of different rate of time.
No, different rates of time are found after accounting of light-travel time and Doppler effect.

20. Originally Posted by SpeedFreek
Originally Posted by grandi
Yes there's the notion that depending on how a third observer is situated in relation to the two travelling ships light from the ships may take different amounts of time to reach the observer and the doppler effect may cause compression or expansion of the visual information carried by light leading into appearance of different rate of time.
No, different rates of time are found after accounting of light-travel time and Doppler effect.
Just the opposite. To the third observer it might seem that the rates of time on the ships are different due to the natural effects of propagation of light. When the effects of light are accounted for the calculations of the third observer must indicate that the rates of time on the ships are the same. That is a necessity because it is the prediction of the model, otherwise the model would be falsified.

21. Not unless you are trying to use some sort of absolute frame, one that has been shown not to exist.

22. Let's call the original two frames of reference A and B, both moving away from the starting point, at the same speed, in opposite directions.

Now let's have observer C following A, but at half the speed of A.

Observer C will correctly calculate that, relative to his frame of reference, time is passing differently in frame A than it is in frame B.

And this is not just an apparent effect due to light travel time or Doppler.

23. Originally Posted by SpeedFreek
Not unless you are trying to use some sort of absolute frame, one that has been shown not to exist.
What are you talking about? This is about the observer's perception of the rates of time on the ships. There is no absolute frame, the observer will use his own frame as an "anchor" for the calculations of the time rates.

24. Originally Posted by grandi
What are you talking about? This is about the observer's perception of the rates of time on the ships. There is no absolute frame, the observer will use his own frame as an "anchor" for the calculations of the time rates.
See my follow on post, above.

Relative to C, B is moving faster than A, and hence C will find B time-dilated by a larger amount than A. After subtracting for time of light effects like Doppler.

25. Originally Posted by SpeedFreek
Originally Posted by grandi
What are you talking about? This is about the observer's perception of the rates of time on the ships. There is no absolute frame, the observer will use his own frame as an "anchor" for the calculations of the time rates.
See my follow on post, above.

Relative to C, B is moving faster than A, and hence C will find B time-dilated by a larger amount than A. After subtracting for time of light effects like Doppler.
You started changing the experiment. The additional observer Markus brought up is stationary. So the separate observer is in the same rest frame with Earth. The relative spatial location of this observer will dictate the relative projection of the velocity vectors of the two ships and thus also the speed at which the ships will be moving closer to or away from the additional observer. It is this projected speed that dictates the nature of the natural effects causing distortion in the visual information carried by light from the ships.

26. Grandi,

Is this going to turn into another one of those endless threads where someone who doesn't believe in relativity keeps asking the same question over and over? I'm tired of those.

27. Okay...

28. Originally Posted by Harold14370
Grandi,

Is this going to turn into another one of those endless threads where someone who doesn't believe in relativity keeps asking the same question over and over? I'm tired of those.
This has nothing to do with anyone believing in anything. This is simply logical arguments sorting each other out. The result of the order of the logical arguments is to be seen.

You have not presented any logical arguments here. Do you understand the logical argumentation that is going on here?

29. So, I am still unsure as to why you think there is any contradiction here:

Originally Posted by grandi
Conclusion
The two brothers experience extremely fast motion relative to each other, in their own rest frames they both observe the other move away at very close to the speed of light. Einstein's model necessitates the following logical conclusions
1. the relativistic model dictates that all relative motion must result in different rates of time observed in the reference frames
2. the relativistic model dictates that relative motion without different rates of time is possible

The model contradicts itself. Currently I do not know of any logical deduction chain that allows Einstein's relativity to survive this problem. If you are able to come up with a sound logical deduction chain that saves the model, please do explain it.
1. There needs to be an asymmetry in the scenario to find different proper times at the end of the experiment.

2. If the relative motions are symmetrical, then so is the time-dilation.

These are both predictions of Special Relativity. What exactly is it you that you think is a contradiction?

30. Originally Posted by grandi
Just the opposite. To the third observer it might seem that the rates of time on the ships are different due to the natural effects of propagation of light. When the effects of light are accounted for the calculations of the third observer must indicate that the rates of time on the ships are the same. That is a necessity because it is the prediction of the model, otherwise the model would be falsified.
Are you saying that there is no time dilation; it is just an result of the doppler effect?

31. Originally Posted by grandi
Originally Posted by Harold14370
Grandi,

Is this going to turn into another one of those endless threads where someone who doesn't believe in relativity keeps asking the same question over and over? I'm tired of those.
This has nothing to do with anyone believing in anything. This is simply logical arguments sorting each other out. The result of the order of the logical arguments is to be seen.

You have not presented any logical arguments here. Do you understand the logical argumentation that is going on here?
Yes, I do. The arguments about time dilation, simultaneity of relativity, etc. have been rehashed here ad nauseum with others like yourself, who cannot fathom that there is not an absolute frame of reference or an absolute time scale.

32. Originally Posted by SpeedFreek
1. There needs to be an asymmetry in the scenario to find different proper times at the end of the experiment.
2. If the relative motions are symmetrical, then so is the time-dilation.

These are both predictions of Special Relativity. What exactly is it you that you think is a contradiction?
It is possible that there is no contradiction. I'm also looking for a correct interpretation of the predictions of the relativistic model because I am not sure I have the correct interpretations.

Science is about predictions of actual observations and then testing to make those actual observations.

It is this comment from my above message that I am at this moment seeking an answer to:
From the strict scientific perspective where the observers are the ones with the actual clocks the factual notion is that the prediction and the true recorded observation is that the ships in relative movement are in this case observing the exact same rate of time. Do you agree with this?

The mathematical model of time dilation is for all relative movement. So how does the result of the modeled time dilation relate to the above actual predicted observations?

33. Originally Posted by Strange
Originally Posted by grandi
Just the opposite. To the third observer it might seem that the rates of time on the ships are different due to the natural effects of propagation of light. When the effects of light are accounted for the calculations of the third observer must indicate that the rates of time on the ships are the same. That is a necessity because it is the prediction of the model, otherwise the model would be falsified.
Are you saying that there is no time dilation; it is just an result of the doppler effect?
I am not saying that. Time dilation is real and observed from GPS satellites and experiments done on airplanes.

34. Originally Posted by Harold14370
Yes, I do. The arguments about time dilation, simultaneity of relativity, etc. have been rehashed here ad nauseum with others like yourself, who cannot fathom that there is not an absolute frame of reference or an absolute time scale.
I have already stated above that there is no absolute frame, so why do you say this then?

35. Originally Posted by grandi
It is this comment from my above message that I am at this moment seeking an answer to:
From the strict scientific perspective where the observers are the ones with the actual clocks the factual notion is that the prediction and the true recorded observation is that the ships in relative movement are in this case observing the exact same rate of time. Do you agree with this?
That question is a bit confusing. Can we break it down a bit?

Does the "observers with the clocks" refers to the two brothers who leave the earth and later come back?

And when you say "observing the exact same rate of time", do you mean how they measure their own local time? Or how they measure the time of the other brother?

Each observer will always measure their own local (proper) time running as "normal". After all, how could they not: their clocks tick at their proper time.

If each observer could somehow see their brother's clock (obviously not practical) then they would both see the other's clock running slow relative to their own.

I'm not sure if that is what you are asking though...

36. Originally Posted by grandi
It is this comment from my above message that I am at this moment seeking an answer to:
From the strict scientific perspective where the observers are the ones with the actual clocks the factual notion is that the prediction and the true recorded observation is that the ships in relative movement are in this case observing the exact same rate of time. Do you agree with this?
(My bold). Yes I agree with this.

Originally Posted by grandi
The mathematical model of time dilation is for all relative movement. So how does the result of the modeled time dilation relate to the above actual predicted observations?
The model says that, as all motions are symmetrical between the two ships relative to the rest frame of the Earth, they will both be time-dilated by the same amount in relation to the rest frame of the Earth.

The model says that it would be an error on the part of one of the brothers in a spaceship to think his brother on the other spaceship would experience a proper time any different to his own, as that brother would not be taking into account the fact that there was no asymmetry between their changing frames of reference.

If all three brothers started out in the same frame, then the brothers on the ships have changed frames in exactly the same way as each other, but the brother on Earth did not change frames at all.

37. Originally Posted by Strange
1. Does the "observers with the clocks" refers to the two brothers who leave the earth and later come back?

2. And when you say "observing the exact same rate of time", do you mean how they measure their own local time? Or how they measure the time of the other brother?

3. Each observer will always measure their own local (proper) time running as "normal". After all, how could they not: their clocks tick at their proper time.

4. If each observer could somehow see their brother's clock (obviously not practical) then they would both see the other's clock running slow relative to their own.
I'll try numbering so perhaps the response will be a bit cleaner...

1. Yes, the clocks on the ships.
2. They record logs of ship time and distance from Earth, these logs contain the observed proper times and the two logs match.
3. Yes, and according to the predicted recorded observations the rates of times in the ships should match.
4. This is contradicted by the comment by Markus in post #12.

edit:
4. Or did you mean that see over the distance, so propagation of light causes delay in the receiving of the visual information?

... This should result in observation of slower rate time when moving away and faster rate of time when moving closer.

38. Originally Posted by grandi
I'll try numbering so perhaps the response will be a bit cleaner...
Good idea.

1. Yes, the clocks on the ships.
2. They record logs of ship time and distance from Earth, these logs contain the observed proper times and the two logs match.
3. Yes, and according to the predicted recorded observations the rates of times in the ships should match.
OK. I think we all agree about that.

4. This is contradicted by the comment by Markus in post #12.
I don't see the contradiction, I'm afraid. What exactly seems to be a contradiction?

edit:
4. Or did you mean that see over the distance?
I'm not sure what "see over the distance" means.

Note that once they both return to Earth they will have no relative velocity and will see each other's clocks ticking at the same speed (and will agree on the total elapsed time).

39. Originally Posted by grandi
... This should result in observation of slower time when moving away and faster rate of time when moving closer.
If both ships flash a beacon at regular intervals, the observed period of the flashes is longer when the observers are separating and shorter when they are converging, yes.

But that is not an observation of either proper or coordinate time.

40. Strange, I think for point 4 grandi first took your comment to mean if one observer could somehow magically see what was going on in the other ship, instantaneously as it were, which might find a conflict with the relativity of simultaneity. Hence the question as to whether you meant they were just observing at a distance (with a very good telescope!).

41. Originally Posted by SpeedFreek
Originally Posted by grandi
... This should result in observation of slower time when moving away and faster rate of time when moving closer.
If both ships flash a beacon at regular intervals, the observed period of the flashes is longer when the observers are separating and shorter when they are converging, yes.

But that is not an observation of either proper or coordinate time.
Let's say that they flash the beacon 1.0 second intervals. While they are not accelerating they will get a good sense of the other ship's observed proper time if they know their relative speed (and this had been agreed on in the supposed experiment).

Originally Posted by SpeedFreek
Strange, I think for point 4 grandi first took your comment to mean if one observer could somehow magically see what was going on in the other ship, instantaneously as it were, which might find a conflict with the relativity of simultaneity. Hence the question as to whether you meant they were just observing at a distance (with a very good telescope!).
Correct, I wasn't sure which case was indicated.

Getting pretty late over here so need to hit the sack. Back on the horse in the morning

42. ... This should result in observation of slower rate time when moving away and faster rate of time when moving closer.
No, the direction of movement has no effect. It's the difference in relative velocity which causes time dilation. g

43. Originally Posted by AlexG
... This should result in observation of slower rate time when moving away and faster rate of time when moving closer.
No, the direction of movement has no effect. It's the difference in relative velocity which causes time dilation. g
I was referring to the natural effects to propagation of light and the way doppler effect for example distors the the 1.0 second falshes made by the ship. Light is the one constant for the observers, so light can be used to relay information of proper times.

44. Originally Posted by SpeedFreek
The model says that it would be an error on the part of one of the brothers in a spaceship to think his brother on the other spaceship would experience a proper time any different to his own, as that brother would not be taking into account the fact that there was no asymmetry between their changing frames of reference.
The ships are moving at very close to the speed of light with respect to each other, in both rest frames the other is observed to move very fast. Your comment above leads to the conclusion that extremely fast relative movement without any actual time dilation is possible.

Is my interpretation of the mathematical relativistic time dilation model wrong? So relativistic time dilation does not always apply? In this case there is no contradiction in the model, but how could we ever find the actual time dilation between two moving frames if they have no common rest frame?

45. In this case there is no contradiction in the model, but how could we ever find the actual time dilation between two moving frames if they have no common rest frame?
You find the dilation of time from whichever frame you choose to work it out from. There is no preferred frame and no "actual time dilation". It is all relative.

46. Originally Posted by KALSTER
In this case there is no contradiction in the model, but how could we ever find the actual time dilation between two moving frames if they have no common rest frame?
You find the dilation of time from whichever frame you choose to work it out from. There is no preferred frame and no "actual time dilation". It is all relative.
Then there's a problem with SpeedFreek's comment. How is it possible that the model dictates close to the speed of light relative movement without any actual time dilation?

edit:
Sorry, for some reason I missed the notion of "no actual time dilation" first.

What do you mean by that? Science can only deal with the actual observed proper times. Those are the only times that can be tested.

47. What I mean is that you can work out the dilation of time of other frames using relativity. In the case of the two brothers departing from earth, they will agree on their observations when they return, but during the trip each will calculate a divergence of each other's clocks. After they turn around though and arrive back at the earth, their clocks will be in synch due to the symmetry of their trips, BUT both of them will have aged differently to the third brother. So while each brother kept time and each clock measured their proper time, you find that the third brother's clock does not match that of the first two. That in itself is a prediction of GR that can be verified by observation and indicates that the different rates of time each travelling brother calculates for the other are accurate while they are travelling.

But, all of this was explained in greater detail in Markus' first post in this thread, so I don't quite understand what you are still having problems with?

When you apply these calculations to muon decay in our atmosphere for instance, you also calculate different proper times for both the muon and the observer on the earth and it gets confirmed when you observe the muon actually making it to the surface, while without taking diverging proper times into account, the muon should have decayed on average long before reaching the surface. That is why I referred you to the Tests of Relativity sticky in the physics section to go over.

*By "actual time dilation" I thought you meant from an absolute frame of reference. I see you have already acknowledged that such a thing doesn't exist.

Edit: Here is a nice explanation of the Muon experiment: http://hyperphysics.phy-astr.gsu.edu...ativ/muon.html

48. Originally Posted by KALSTER
What I mean is that you can work out the dilation of time of other frames using relativity. In the case of the two brothers departing from earth, they will agree on their observations when they return, but during the trip each will calculate a divergence of each other's clocks. After they turn around though and arrive back at the earth, their clocks will be in synch due to the symmetry of their trips, BUT both of them will have aged differently to the third brother. So while each brother kept time and each clock measured their proper time, you find that the third brother's clock does not match that of the first two. That in itself is a prediction of GR that can be verified by observation and indicates that the different rates of time each travelling brother calculates for the other are accurate while they are travelling.

But, all of this was explained in greater detail in Markus' first post in this thread, so I don't quite understand what you are still having problems with?

When you apply these calculations to muon decay in our atmosphere for instance, you also calculate different proper times for both the muon and the observer on the earth and it gets confirmed when you observe the muon actually making it to the surface, while without taking diverging proper times into account, the muon should have decayed on average long before reaching the surface. That is why I referred you to the Tests of Relativity sticky in the physics section to go over.

*By "actual time dilation" I thought you meant from an absolute frame of reference. I see you have already acknowledged that such a thing doesn't exist.
Well there seems to be calculable time dilation that does not match reality, which then needs to be compensated with this "divergence" of the clocks.

Lets say that two spaceships unknown to each other from different galaxies travel towards each other with a relative speed of 0.9 * c and then stop to investigate each other at a distance of 10 kilometers in a single rest frame. They don't share a common rest frame where they had originated from for those travels so there is no way for them to know the actual time dilation that occurred between them while they were travelling. Would you agree?

49. Originally Posted by grandi

Well there seems to be calculable time dilation that does not match reality, which then needs to be compensated with this "divergence" of the clocks.
Well, what do you define as "reality"? Proper time? The whole premise of relativity is that "reality" is relative and experiments like the muon decay experiment confirms just this. The calculated time dilation from each ship reflects reality from their perspective.

Lets say that two spaceships unknown to each other from different galaxies travel towards each other with a relative speed of 0.9 * c and then stop to investigate each other at a distance of 10 kilometers in a single rest frame. They don't share a common rest frame where they had originated from for those travels so there is no way for them to know the actual time dilation that occurred between them while they were travelling. Would you agree?
Yes, but time dilation and length contraction happens whether it is calculated and measured or not. They could make comparisons between their origins and then work out the amount of time dilation and such though. For instance, if their origins are comoving and, say, 1 light year apart, they would take a lot less than a year to reach each other as measured by both.

50. Sorry, I meant they would take less than 6 months to reach each other. And the comoving thing is not a prerequisite, it would just be easier to calculate that way.

51. Originally Posted by grandi
Lets say that two spaceships unknown to each other from different galaxies travel towards each other with a relative speed of 0.9 * c and then stop to investigate each other at a distance of 10 kilometers in a single rest frame. They don't share a common rest frame where they had originated from for those travels so there is no way for them to know the actual time dilation that occurred between them while they were travelling. Would you agree?
There might be some confusion (in my mind at least) as to what you are referring to as "time dilation". I was thinking of it as the difference in the "rate" at which time passes for each person, as perceived by the other (the difference between proper and coordinate time).

But you seem to mean something like the total elapsed time since some event. In which case, I don't think any such comparison is possible in the example you give. Firstly, there would be the problem of defining some common starting point - if they have never been in the same frame of reference then all the problems of simultaneity and synchronization arise. Then, in order to calculate the elapsed time experienced by the spaceship, the first would have to know the complete history of accelerations etc that the other had experienced.

But I may be wrong and I may have misunderstood the question ...

52. Originally Posted by KALSTER
Well, what do you define as "reality"? Proper time? The whole premise of relativity is that "reality" is relative and experiments like the muon decay experiment confirms just this.
Reality is that which is observed and produces the results of the experiments. So yes, the actual observed proper time and how that can be relativisticly modeled. Reality can not be relative, observations of reality by different observers can be relatively distorted. Compensation of the distorted observation through the model must agree with the actual reality observation made on the other ship.

Originally Posted by KALSTER
The calculated time dilation from each ship reflects reality from their perspective.
By that do you mean that the calculation represents the observable reality on the other ship?

Originally Posted by KALSTER
Lets say that two spaceships unknown to each other from different galaxies travel towards each other with a relative speed of 0.9 * c and then stop to investigate each other at a distance of 10 kilometers in a single rest frame. They don't share a common rest frame where they had originated from for those travels so there is no way for them to know the actual time dilation that occurred between them while they were travelling. Would you agree?
Yes, but time dilation and length contraction happens whether it is calculated and measured or not. They could make comparisons between their origins and then work out the amount of time dilation and such though. For instance, if their origins are comoving and, say, 1 light year apart, they would take a lot less than a year to reach each other as measured by both.
Indeed. So basically if the two common rest frames can not be found then no calculation can be done. The initial common rest frame in this case would be the result of the calculation of the origins of the two ships.

This is actually nicely reflected by the Halefe-Keating experiment where eastward movement on Earth caused -184 ns kinematic effect of time dilation and westward +96 ns. From here we see that the relativity between the two airplanes alone does not dictate time dilation but the relativity of these planes in regards to Earth affects it also. Arguably if these planes had traveled north and south then there would have been no kinematic time dilation measured.

53. Originally Posted by KALSTER
Sorry, I meant they would take less than 6 months to reach each other. And the comoving thing is not a prerequisite, it would just be easier to calculate that way.
No problem, we're dealing with the overall concepts here so that's what matters. I wasn't checking

54. Originally Posted by Strange
Originally Posted by grandi
Lets say that two spaceships unknown to each other from different galaxies travel towards each other with a relative speed of 0.9 * c and then stop to investigate each other at a distance of 10 kilometers in a single rest frame. They don't share a common rest frame where they had originated from for those travels so there is no way for them to know the actual time dilation that occurred between them while they were travelling. Would you agree?
There might be some confusion (in my mind at least) as to what you are referring to as "time dilation". I was thinking of it as the difference in the "rate" at which time passes for each person, as perceived by the other (the difference between proper and coordinate time).

But you seem to mean something like the total elapsed time since some event. In which case, I don't think any such comparison is possible in the example you give. Firstly, there would be the problem of defining some common starting point - if they have never been in the same frame of reference then all the problems of simultaneity and synchronization arise. Then, in order to calculate the elapsed time experienced by the spaceship, the first would have to know the complete history of accelerations etc that the other had experienced.

But I may be wrong and I may have misunderstood the question ...
This is a good point actually. I was referring to time dilation as the real actual scientifically testable difference in observed rates of time between the two frames.

Perception is something virtual, perception can be considered to be the prediction which then needs to match the actual observed reality when tested.

55. Originally Posted by grandi
. Reality can not be relative, observations of reality by different observers can be relatively distorted. Compensation of the distorted observation through the model must agree with the actual reality observation made on the other ship.
Despite your repeated denials this suggests you think that there is an absolute reality.

56. Originally Posted by John Galt
Originally Posted by grandi
. Reality can not be relative, observations of reality by different observers can be relatively distorted. Compensation of the distorted observation through the model must agree with the actual reality observation made on the other ship.
Despite your repeated denials this suggests you think that there is an absolute reality.
Well there is no single observable absolute reality. Everyone's absolute reality is different. So why call it "absolute"?

What is absolute for you are your own observations (the observable facts). Some other observer moving relative to you will have slightly different observations of the same observed thing.

57. Originally Posted by grandi
This is a good point actually. I was referring to time dilation as the real actual scientifically testable difference in observed rates of time between the two frames.
Then all that is required is the relative velocity. A sees B travelling at 09.c and calculate the the relative time dilation (and, if he had a way of measuring it, he could measure it). He will determine that time is passing roughly half as fast on the other ship. B can do the same regarding A and will come to the same conclusion.

When they stop to talk to each other, they will be in the same frame of reference and their clocks/time will be ticking at the same rate.

Where they came from and what their past histories are and whether they have ever previously shared a common frame of reference would seem to be irrelevant.

I'm not sure whey you see a problem with that scenario.

Perception is something virtual, perception can be considered to be the prediction which then needs to match the actual observed reality when tested.
Perception was not a good word: I meant measured and/or calculated (these will be the same).

58. Originally Posted by grandi
Reality is that which is observed and produces the results of the experiments. So yes, the actual observed proper time and how that can be relativisticly modeled. Reality can not be relative, observations of reality by different observers can be relatively distorted. Compensation of the distorted observation through the model must agree with the actual reality observation made on the other ship.
Like John says, it still looks like you are getting confused by this. Look again at the muon experiment. Muon Experiment in Relativity

Which measurement of elapsed travel time would you say reflect "reality"? The answer is both measurements are equally real.

You can easily substitute a space ship travelling towards a planet.

59. Originally Posted by Strange
Originally Posted by grandi
This is a good point actually. I was referring to time dilation as the real actual scientifically testable difference in observed rates of time between the two frames.
Then all that is required is the relative velocity. A sees B travelling at 09.c and calculate the the relative time dilation (and, if he had a way of measuring it, he could measure it). He will determine that time is passing roughly half as fast on the other ship. B can do the same regarding A and will come to the same conclusion.

When they stop to talk to each other, they will be in the same frame of reference and their clocks/time will be ticking at the same rate.

Where they came from and what their past histories are and whether they have ever previously shared a common frame of reference would seem to be irrelevant.

I'm not sure whey you see a problem with that scenario.
How do you fit that to the Halefe-Keating experiment where the rotation of Earth must be taken into account in addition to the relative movement between the planes?

Originally Posted by Strange
Perception is something virtual, perception can be considered to be the prediction which then needs to match the actual observed reality when tested.
Perception was not a good word: I meant measured and/or calculated (these will be the same).
Sure. "Calculated" then means what ship A calculates for the ship B and "measured" relates to the measurements made on ship B.

60. Originally Posted by KALSTER
Originally Posted by grandi
Reality is that which is observed and produces the results of the experiments. So yes, the actual observed proper time and how that can be relativisticly modeled. Reality can not be relative, observations of reality by different observers can be relatively distorted. Compensation of the distorted observation through the model must agree with the actual reality observation made on the other ship.
Like John says, it still looks like you are getting confused by this. Look again at the muon experiment. Muon Experiment in Relativity

Which measurement of elapsed travel time would you say reflect "reality"? The answer is both measurements are equally real.

You can easily substitute a space ship travelling towards a planet.
Yes, I understand your point. In that particular case we have a significant change in the gravitational environment of the muon frame so that investigation becomes more complex.

If you look at a situation of no change in gravitational environment of the frames but only relative velocity between two frames. Observers in these frames will calculate the same value of time dilation for each other simply from the relative velocity and by default already one of them must be wrong.

61. Originally Posted by grandi
How do you fit that to the Halefe-Keating experiment where the rotation of Earth must be taken into account in addition to the relative movement between the planes?
I'm not sure why that is relevant. You had two spaceships, in space, with a relative speed of of 0.9c. If you introduce rotation, acceleration, gravity, etc then it is a different situation and it may no longer be symmetrical. But that doesn't seem to be the case in this example.

62. Originally Posted by grandi
If you look at a situation of no change in gravitational environment of the frames but only relative velocity between two frames. Observers in these frames will calculate the same value of time dilation for each other simply from the relative velocity and by default already one of them must be wrong.
Why must one of them be wrong? This is a fundamental part of the theory (and it seems one that many people struggle with).

They will both perceive the other to be time dilated (and length contracted) by the same amount.

63. Originally Posted by Strange
Originally Posted by grandi
How do you fit that to the Halefe-Keating experiment where the rotation of Earth must be taken into account in addition to the relative movement between the planes?
I'm not sure why that is relevant. You had two spaceships, in space, with a relative speed of of 0.9c. If you introduce rotation, acceleration, gravity, etc then it is a different situation and it may no longer be symmetrical. But that doesn't seem to be the case in this example.
In the Halefe-Keating experiment the gravitational environment of the two planes is equal. So you're saying that due to rotation the case in that experiment is no longer symmetrical? You may be right on that one.

Originally Posted by Strange
Originally Posted by grandi
If you look at a situation of no change in gravitational environment of the frames but only relative velocity between two frames. Observers in these frames will calculate the same value of time dilation for each other simply from the relative velocity and by default already one of them must be wrong.
Why must one of them be wrong? This is a fundamental part of the theory (and it seems one that many people struggle with).

They will both perceive the other to be time dilated (and length contracted) by the same amount.
Well I'm referring to the scientific testing part in this case. They both will calculate dilation values and when they stop to compare ship logs they find out that at least one of them has calculations that do not agree with the recorded observations made on the other ship.

64. Originally Posted by grandi
Well I'm referring to the scientific testing part in this case. They both will calculate dilation values and when they stop to compare ship logs they find out that at least one of them has calculations that do not agree with the recorded observations made on the other ship.
That is a bit vague. What specific recorded observations would not agree?

If they could observer/measure the other persons clock as well as calculate the time dilation then those observations would match the calculation.

When they stopped and met up they would both say, "Hey, your clock was running slower than mine." and "Yeah, ain't relativity cool."

65. Originally Posted by Strange
Originally Posted by grandi
Well I'm referring to the scientific testing part in this case. They both will calculate dilation values and when they stop to compare ship logs they find out that at least one of them has calculations that do not agree with the recorded observations made on the other ship.
That is a bit vague. What specific recorded observations would not agree?

If they could observer/measure the other persons clock as well as calculate the time dilation then those observations would match the calculation.

When they stopped and met up they would both say, "Hey, your clock was running slower than mine." and "Yeah, ain't relativity cool."
Lets look at the two travelling brothers case discussed in this thread. We already established the fact that their recorded observations will show that they observed the exact same rates of proper time during the whole experiment. If they during their trips were predicting the rate of time of the other ship using the time dilation model and their relative velocity they ended up with wrong calculated values.

66. Originally Posted by grandi
In the Halefe-Keating experiment the gravitational environment of the two planes is equal. So you're saying that due to rotation the case in that experiment is no longer symmetrical? You may be right on that one.
Yes, he is right. None of the frames in the Hafele-Keating experiment were inertial frames, and due to the rotation of the Earth the two planes motions were not symmetrical.

Relative to an inertial frame at rest in relation to the axis about which the Earth rotates, the plane flying eastwards is moving the fastest, the clock in the U.S. Naval observatory is moving slower and the plane flying westwards was moving the slowest of all - hence the results.

Originally Posted by grandi
Well I'm referring to the scientific testing part in this case. They both will calculate dilation values and when they stop to compare ship logs they find out that at least one of them has calculations that do not agree with the recorded observations made on the other ship.
It is time to start considering the relativity of simultaneity here. Coordinate time isnt required to match proper time.

67. Originally Posted by grandi
Lets look at the two travelling brothers case discussed in this thread. We already established the fact that their recorded observations will show that they observed the exact same rates of proper time during the whole experiment. If they during their trips were predicting the rate of time of the other ship using the time dilation model and their relative velocity they ended up with wrong calculated values.
This is a more complicated case and the simple answer I gave (they both see the other running slow) only applies in the case of two inertial frames. In this case there are periods of acceleration and changing frames of reference during the entire trip. If you do the math for both of them (including what they calculate/observe happening to the other) then it all works out. I am not confident of doing that correctly, so I will leave it up to Markus or someone. (Oh, he has already done it in post #4; but do you need a more detailed step by step breakdown?)

68. Originally Posted by SpeedFreek
Originally Posted by grandi
In the Halefe-Keating experiment the gravitational environment of the two planes is equal. So you're saying that due to rotation the case in that experiment is no longer symmetrical? You may be right on that one.
Yes, he is right. None of the frames in the Hafele-Keating experiment were inertial frames, and due to the rotation of the Earth the two planes motions were not symmetrical.

Relative to an inertial frame at rest in relation to the axis about which the Earth rotates, the plane flying eastwards is moving the fastest, the clock in the U.S. Naval observatory is moving slower and the plane flying westwards was moving the slowest of all - hence the results.
Agreed.

Originally Posted by SpeedFreek
Originally Posted by grandi
Well I'm referring to the scientific testing part in this case. They both will calculate dilation values and when they stop to compare ship logs they find out that at least one of them has calculations that do not agree with the recorded observations made on the other ship.
It is time to start considering the relativity of simultaneity here. Coordinate time isnt required to match proper time.
I'm not sure that I follow you. Your view is that the time dilation model does not model observable reality?

69. Originally Posted by grandi
Lets look at the two travelling brothers case discussed in this thread. We already established the fact that their recorded observations will show that they observed the exact same rates of proper time during the whole experiment. If they during their trips were predicting the rate of time of the other ship using the time dilation model and their relative velocity they ended up with wrong calculated values.
Only if they fail to take into account their own accelerations versus the accelerations of their brother. If they know they themselves accerated in exactly the same way as their brother, then they know that they cannot consider themselves to be at rest.

The solution is the same as in the classic twins paradox - it is only a paradox if you consider a frame to be rest frame when it isn't.

70. You cannot observe proper time at distance for a frame in motion relative to you, you HAVE to calculate it by tranforming to the other frame. You can calculate coordinate time for the other frame based on your own frame, but coordinate time and proper time do not have to match up, due to the relativity of simultaneity.

71. Originally Posted by Strange
Originally Posted by grandi
Lets look at the two travelling brothers case discussed in this thread. We already established the fact that their recorded observations will show that they observed the exact same rates of proper time during the whole experiment. If they during their trips were predicting the rate of time of the other ship using the time dilation model and their relative velocity they ended up with wrong calculated values.
This is a more complicated case and the simple answer I gave (they both see the other running slow) only applies in the case of two inertial frames. In this case there are periods of acceleration and changing frames of reference during the entire trip. If you do the math for both of them (including what they calculate/observe happening to the other) then it all works out. I am not confident of doing that correctly, so I will leave it up to Markus or someone. (Oh, he has already done it in post #4; but do you need a more detailed step by step breakdown?)
I don't see how that logically follows. The premise was that there is the extreme symmetry of the velocity vectors of the ships always being opposite and equal in magnitude.

72. Originally Posted by SpeedFreek
You cannot observe proper time at distance for a frame in motion relative to you, you HAVE to calculate it by tranforming to the other frame. You can calculate coordinate time for the other frame based on your own frame, but coordinate time and proper time do not have to match up, due to the relativity of simultaneity.
The observation of the proper times is the reviewing of the recorded proper times from the ship logs. And these logs match perfectly. We are not dealing with specific time co-ordinates here, that is dealt with simultaneity and we know that observers do not agree on the times different events occur.

This matter is simply about the rates of time observed and modeled through the time dilation model. Simultaneity problems do not affect the modeled rates of time.

73. Originally Posted by grandi
I don't see how that logically follows. The premise was that there is the extreme symmetry of the velocity vectors of the ships always being opposite and equal in magnitude.
But there are changes in their velocities. The time at which A starts slowing down is different from the time that he considers B to start slowing down (according to A's clock). This is not something you can reason about in a "handwavy" way; you need to work through the math.

74. Originally Posted by Strange
Originally Posted by grandi
I don't see how that logically follows. The premise was that there is the extreme symmetry of the velocity vectors of the ships always being opposite and equal in magnitude.
But there are changes in their velocities. The time at which A starts slowing down is different from the time that he considers B to start slowing down (according to A's clock). This is not something you can reason about in a "handwavy" way; you need to work through the math.
Yes. I understand that. But the distortion of the observational visual information is significant. We know that when the ships reach the turning point they have both traveled almost one light year of distance away from Earth. So their distance is almost two light years. This is an awful distortion to the observations the ships are getting of each other, assuming they can somehow see each other over the distance. Do you agree with this?

From the recorded ship logs they will then notice that the acceleration and deceleration times were the exact same for both ships.

75. Originally Posted by grandi
Yes. I understand that. But the distortion of the observational visual information is significant.
I am not talking about "visual distortion" (I assume you mean doppler effeects) but rather relativity of simultaneity.

From the recorded ship logs they will then notice that the acceleration and deceleration times were the exact same for both ships.
Yes, in their proper times. But in A's proper time they do not change acceleration at the same time. That is why you need to work through the math; it isn't obvious.

By the way, I'm not sure if your insistence on having them travel near c in the example makes it more or less confusing.... On the one hand it make things like time dilation (43%?) really obvious but on the other, it introduces unimaginable scales like 1 light year! The same effects occur at more mundane velocities as Hafele-Keating and GPS show.

76. Originally Posted by Strange
Originally Posted by grandi
Yes. I understand that. But the distortion of the observational visual information is significant.
I am not talking about "visual distortion" (I assume you mean doppler effeects) but rather relativity of simultaneity.
These are actually the very same thing. Doppler effects cause distortion in the observed rates of time and different distances causes distortion in simultaneity.

Originally Posted by Strange
From the recorded ship logs they will then notice that the acceleration and deceleration times were the exact same for both ships.
Yes, in their proper times. But in A's proper time they do not change acceleration at the same time. That is why you need to work through the math; it isn't obvious.
The ship logs show that their proper times of acceleration match. Essentially this seems to be an observational issue dealing with propagation of light. When B reaches the midpoint A will observe it only much later when light reflected at that instant from ship B reaches the other ship A.

Originally Posted by Strange
By the way, I'm not sure if your insistence on having them travel near c in the example makes it more or less confusing.... On the one hand it make things like time dilation (43%?) really obvious but on the other, it introduces unimaginable scales like 1 light year! The same effects occur at more mundane velocities as Hafele-Keating and GPS show.
I just picked the values randomly from the top of my head . If other values seem better suited for the discussion we can of course adapt the examples.

So is your view that the time dilation equation does not model proper time but something else?

77. Originally Posted by grandi
Originally Posted by Strange
Originally Posted by grandi
Yes. I understand that. But the distortion of the observational visual information is significant.
I am not talking about "visual distortion" (I assume you mean doppler effeects) but rather relativity of simultaneity.
These are actually the very same thing. Doppler effects cause distortion in the observed rates of time and different distances causes distortion in simultaneity.
The speed of light is the same from any reference frame. Doppler effects only red- or blue shift the light that is received. It doesn't do anything to the time.

78. Originally Posted by KALSTER
The speed of light is the same from any reference frame. Doppler effects only red- or blue shift the light that is received. It doesn't do anything to the time.
The effects do cause distortion in how the observers observe the rate of time of other observers. Consider two ships stationary in one rest frame 1.0 light minutes apart in distance. One ship blinks a beacon with 1.0 second intervals. This will tell the other ship what is the observed rate of time on that ship. When they are stationary they both observe beacon blinks with 1.0 second intervals.

Now lets say that the ship with the beacon begins to travel towards the other ship which stays stationary while maintaining the 1.0 second blinking in its own rest frame. Doppler effect now causes the stationary ship to observe the blinking as compressed so the frequency is higher. They will conclude that their rate of time relative to the other ship must have increased.

79. Originally Posted by grandi
These are actually the very same thing. Doppler effects cause distortion in the observed rates of time and different distances causes distortion in simultaneity.
The relativity of simultaneity has nothing to do with doppler shift or distance.

So is your view that the time dilation equation does not model proper time but something else?
It models the relationship between the proper times of different frames of reference.

80. Originally Posted by Strange
Originally Posted by grandi
These are actually the very same thing. Doppler effects cause distortion in the observed rates of time and different distances causes distortion in simultaneity.
The relativity of simultaneity has nothing to do with doppler shift or distance.
Distance dictates how long it takes for light to travel to observers from some event and therefore observers at different distances do not agree on when an event took place. These observers may also be observing different rates of time which further complicates the scenario.

Originally Posted by Strange
So is your view that the time dilation equation does not model proper time but something else?
It models the relationship between the proper times of different frames of reference.
So how can you mathematically model the proper times of the two ships to make the correct numeric predictions of exact same proper times?

81. Originally Posted by grandi
Distance dictates how long it takes for light to travel to observers from some event and therefore observers at different distances do not agree on when an event took place.
That has nothing to do with relativity of simultaneity.

So how can you mathematically model the proper times of the two ships to make the correct numeric predictions of exact same proper times?
Using the equations of relativity.

82. Originally Posted by Strange
Originally Posted by grandi
Distance dictates how long it takes for light to travel to observers from some event and therefore observers at different distances do not agree on when an event took place.
That has nothing to do with relativity of simultaneity.
From the observational stand point it deals with the same thing. Relativity of simultaneity is a bit more complex story of course.

Originally Posted by Strange
So how can you mathematically model the proper times of the two ships to make the correct numeric predictions of exact same proper times?
Using the equations of relativity.
You are referring to the mathematical model of time dilation (time dilation - Wolfram|Alpha)?

83. Originally Posted by grandi
Originally Posted by KALSTER
The speed of light is the same from any reference frame. Doppler effects only red- or blue shift the light that is received. It doesn't do anything to the time.
The effects do cause distortion in how the observers observe the rate of time of other observers. Consider two ships stationary in one rest frame 1.0 light minutes apart in distance. One ship blinks a beacon with 1.0 second intervals. This will tell the other ship what is the observed rate of time on that ship. When they are stationary they both observe beacon blinks with 1.0 second intervals.

Now lets say that the ship with the beacon begins to travel towards the other ship which stays stationary while maintaining the 1.0 second blinking in its own rest frame. Doppler effect now causes the stationary ship to observe the blinking as compressed so the frequency is higher.
Not immediately. There would be a delay due to propagation delay. Thus if the Ships start off 1 light hour apart. It won't be until 1 hr after the one ship starts moving before the second ship will start seeing the increased blink rate. On the other hand, if both ships have blinking lights, the ship that starts accelerating towards the other will see an immediate change in the flash rate.

They will conclude that their rate of time relative to the other ship must have increased.
Only if they include relativistic effects into their conclusion. The increased blink rate by itself is not enough to conclude this. Non-relativistic Doppler shift would have them seeing an increased blink rate without the conclusion that time rates have changed between the ships.

84. Originally Posted by Janus
Not immediately. There would be a delay due to propagation delay. Thus if the Ships start off 1 light hour apart. It won't be until 1 hr after the one ship starts moving before the second ship will start seeing the increased blink rate. On the other hand, if both ships have blinking lights, the ship that starts accelerating towards the other will see an immediate change in the flash rate.
True.

Originally Posted by Janus
They will conclude that their rate of time relative to the other ship must have increased.
Only if they include relativistic effects into their conclusion. The increased blink rate by itself is not enough to conclude this. Non-relativistic Doppler shift would have them seeing an increased blink rate without the conclusion that time rates have changed between the ships.
If the relativistic model is used and the blinking rate changes then only one of two conclusions can be made:
1. the other ship changed the blinking mode of their beacon
2. the other ship started relative movement

Well there is the third option of combination of these two but that leads into a huge mess

The premise here would be that the ships have agreed on the other ship starting to move and not change the blinking mode. Given this premise the other ship must make the above conclusion of relative rates of time.

85. Originally Posted by grandi
You are referring to the mathematical model of time dilation (time dilation - Wolfram|Alpha)?
I thought that was the subject of this thread, yes. Note that the simple equation there (the Lorentz transform) is only valid for special relativity, where you are dealing with inertial frames of reference. You can use it in your "two brothers" example although it is is tricky: you need to integrate over the periods of acceleration and keep track of the different frames of reference involved. For anything more complex (gravitational fields, rotation, etc) you would need the full GR treatment.

86. Originally Posted by grandi
Originally Posted by Strange
Originally Posted by grandi
Distance dictates how long it takes for light to travel to observers from some event and therefore observers at different distances do not agree on when an event took place.
That has nothing to do with relativity of simultaneity.
From the observational stand point it deals with the same thing. Relativity of simultaneity is a bit more complex story of course.

Originally Posted by Strange
So how can you mathematically model the proper times of the two ships to make the correct numeric predictions of exact same proper times?
Using the equations of relativity.
You are referring to the mathematical model of time dilation (time dilation - Wolfram|Alpha)?
You seem to be confusing time dilation with "difference in accumulated time". They are not one and the same. Time dilation is the measured time rate difference between two frames with relative motion; It is merely one relativistic effect which, with others, can lead to a difference in accumulated time.

For example, in the twin paradox, In the for the Earth twin, the difference in ages between himself and his twin is attributed to time dilation ( his brother ages more slowly on the outbound and inbound legs of the trip.

However, for the traveling brother, the difference in ages are a result of the combination of time dilation, length contraction and the relativity of simultaneity. From his position, the total distance traveled is shorter than that as measured by his brother (length contraction), his brother aged more slowly than he does on the outbound and inbound legs, and his brother aged [b]faster[/i] than he did when he reversed direction and went form the outbound to inbound leg. (relativity of simultaneity). The combination of these effects give the end result that, upon the return to Earth, he comes up with the same age difference between himself and his brother as his Earth twin does.

And both brothers are equal correct as to how the age difference came about.

Adding another traveler heading in the opposite direction from the Earth does not change anything fundamentally about this situation, it just makes things a bit more complex for the travelers to calculate the age of the other. (More complex, but not impossible and in the end they both agree on the final result. )

87. Originally Posted by Janus
You seem to be confusing time dilation with "difference in accumulated time". They are not one and the same. Time dilation is the measured time rate difference between two frames with relative motion; It is merely one relativistic effect which, with others, can lead to a difference in accumulated time.

For example, in the twin paradox, In the for the Earth twin, the difference in ages between himself and his twin is attributed to time dilation ( his brother ages more slowly on the outbound and inbound legs of the trip.
I am not talking about difference in accumulated times, but just simply difference in the rates of time which is what the time dilation model is for.

Originally Posted by Janus
However, for the traveling brother, the difference in ages are a result of the combination of time dilation, length contraction and the relativity of simultaneity. From his position, the total distance traveled is shorter than that as measured by his brother (length contraction), his brother aged more slowly than he does on the outbound and inbound legs, and his brother aged [b]faster[/i] than he did when he reversed direction and went form the outbound to inbound leg. (relativity of simultaneity). The combination of these effects give the end result that, upon the return to Earth, he comes up with the same age difference between himself and his brother as his Earth twin does.

And both brothers are equal correct as to how the age difference came about.

Adding another traveler heading in the opposite direction from the Earth does not change anything fundamentally about this situation, it just makes things a bit more complex for the travelers to calculate the age of the other. (More complex, but not impossible and in the end they both agree on the final result. )
The established fact of the identical ship logs indicates that the proper times of both of the ships match at all equal distances from Earth.

How can you fit different rates of aging on outbound and inbound trips with the recorded data of the ship logs which is identical for both ships?

88. Originally Posted by grandi

How can you fit different rates of aging on outbound and inbound trips with the recorded data of the ship logs which is identical for both ships?
To use you blinking lights, each space ship will see their own blinking lights remain constant, while seeing the other ship's blinking rate change as relative motion changes, yet at the end both their logs of proper time will be identical, as well as the calculated particulars of the other's journey. If each had a dial showing a continuous calculation of the other's proper time, they would each get the same results all the way through, including when they meet up again at the start when their own proper time dials will agree with the dials showing the proper times of the other ship.

89. Originally Posted by KALSTER
Originally Posted by grandi
How can you fit different rates of aging on outbound and inbound trips with the recorded data of the ship logs which is identical for both ships?
To use you blinking lights, each space ship will see their own blinking lights remain constant, while seeing the other ship's blinking rate change as relative motion changes, yet at the end both their logs of proper time will be identical, as well as the calculated particulars of the other's journey. If each had a dial showing a continuous calculation of the other's proper time, they would each get the same results all the way through, including when they meet up again at the start when their own proper time dials will agree with the dials showing the proper times of the other ship.
Yes. This blinking light is a good analogy here. But because the blinking rates do not match with the logged proper times, doesn't that mean that the observed rates of blinking from the other ship is an "illusion" that does not correspond with the observations that the other ship is actually making?

90. No. That is why I talked about the muon decay experiment, where there is no symmetry so you can see that measurements from both frames are equally real. The muon experiment is dominated by special relatavistic effects, not GR effects. The differences in proper times for the earth and the muon is due to the relative movement.

Again, even though the two dials in the ship (one showing it's own proper time and the other showing the time of the other ship) differ throughout the trip, neither is more real than the other. Both are correct from the frame it is measured from. The blinking light will do exactly what they are expected to do and nothing of it has to do with Doppler shift, i.e. The observed change in blinking rates has nothing to do with Doppler shift. The other ship actually is running on a different time than its own. Otherwise the muon experiment would not have given the results it did.

91. Originally Posted by grandi
Originally Posted by Janus
You seem to be confusing time dilation with "difference in accumulated time". They are not one and the same. Time dilation is the measured time rate difference between two frames with relative motion; It is merely one relativistic effect which, with others, can lead to a difference in accumulated time.

For example, in the twin paradox, In the for the Earth twin, the difference in ages between himself and his twin is attributed to time dilation ( his brother ages more slowly on the outbound and inbound legs of the trip.
I am not talking about difference in accumulated times, but just simply difference in the rates of time which is what the time dilation model is for.

Originally Posted by Janus
However, for the traveling brother, the difference in ages are a result of the combination of time dilation, length contraction and the relativity of simultaneity. From his position, the total distance traveled is shorter than that as measured by his brother (length contraction), his brother aged more slowly than he does on the outbound and inbound legs, and his brother aged [b]faster[/i] than he did when he reversed direction and went form the outbound to inbound leg. (relativity of simultaneity). The combination of these effects give the end result that, upon the return to Earth, he comes up with the same age difference between himself and his brother as his Earth twin does.

And both brothers are equal correct as to how the age difference came about.

Adding another traveler heading in the opposite direction from the Earth does not change anything fundamentally about this situation, it just makes things a bit more complex for the travelers to calculate the age of the other. (More complex, but not impossible and in the end they both agree on the final result. )
The established fact of the identical ship logs indicates that the proper times of both of the ships match at all equal distances from Earth.

How can you fit different rates of aging on outbound and inbound trips with the recorded data of the ship logs which is identical for both ships?
Assume that you have a line marked out at even intervals in the Earth frame. Each brother notes the time on his clock as he passes each mark. He also notes the time on his brother's clock when he passes each of his marks. This happens on both the inward and outward legs. Each will agree with each other's readings. If brother 1's clock reads 1 yr when he passes marker 500, Both brother's agree to this and both brother's agree that Brother 2's clock reads 1 yr when he passes his marker 500.

However, neither brother will agree that at the instant he passes marker 500 and his clock read 1 yr, that his brother's clock reads 1 yr or that he is passing his marker 500. According to each twin, His brother will both age slow and age fast during different different points of the trip, but in the end, both brothers will be the same age. Just because the Brother's agree that they are the same age at the end of the trip does not mean that they agree that they are the same age at every moment of the trip.

92. Originally Posted by grandi
Originally Posted by Janus
Not immediately. There would be a delay due to propagation delay. Thus if the Ships start off 1 light hour apart. It won't be until 1 hr after the one ship starts moving before the second ship will start seeing the increased blink rate. On the other hand, if both ships have blinking lights, the ship that starts accelerating towards the other will see an immediate change in the flash rate.
True.

Originally Posted by Janus
They will conclude that their rate of time relative to the other ship must have increased.
Only if they include relativistic effects into their conclusion. The increased blink rate by itself is not enough to conclude this. Non-relativistic Doppler shift would have them seeing an increased blink rate without the conclusion that time rates have changed between the ships.
If the relativistic model is used and the blinking rate changes then only one of two conclusions can be made:
1. the other ship changed the blinking mode of their beacon
2. the other ship started relative movement

Well there is the third option of combination of these two but that leads into a huge mess

The premise here would be that the ships have agreed on the other ship starting to move and not change the blinking mode. Given this premise the other ship must make the above conclusion of relative rates of time.

Let's set up the following example and see what happens.

Start with two ships, 1 light hr apart from each other. Each has a light that blinks at a rate of 1 blink per sec. Let's further stipulate that each blink carries a time stamp that gives the time at the emitting ship at the time of the emission. The clocks on both ships start out synchronized.

Thus when it 1 pm on ship 1, it is 1 pm on ship 2. However, since each ship is 1 light hr from the other when each ship's own clock reads 1 pm, it is receiving a blink with a 12 pm time stamp from the other ship. Each ship. as long as both remain stationary see 1 blink/sec from the other ship.

At 1 pm by its own clock, ship 2 instantly starts moving towards ship 1 at 0.866c

What ship 1 sees:

At 2:00 pm it starts to see ship 2 move towards it. At this time, it sees the blink rate of ship 2 increase to 3.732... blinks/sec. the time stamp reads 1 pm at the start of the increase. 558 sec ( at 2:09:18) later, ship 2 arrives. ( It take 1 hr for the light to travel 1 light hr, and 1.155 hrs for Ship 2 to cross the same distance, so the ship arrives 0.155 hrs after the light signaling the start of its journey does.) Thus ship 1 records ~2079 blinks between the time it sees ship 2 leave until it arrives. This means that the time stamp it receives upon arrival of ship 2 should be ~1:34:39 PM. In other words, it sees ship 2 advance ~ 0.5775 hr from start to finish of the trip.

What Ship 1 concludes:

What does ship 1 then conclude about the time rate on ship 2? Does he conclude that since he saw ship 2's time advance 00:34:19 in 00:9:17 of it own time, that ship 2 clock ran 3.732 times faster than his own?. No. Because he knows that the 1 pm time stamp that he received at the start of the rate increase was one hr out of date, and the that ship 2 had actually started out when ship 1's clock read 1 pm. Thus ship 2's clock advanced ~00:34:39 during the time ship 1's clock advanced ~1:09:17. This is half as fast, and exactly as predicted for time dilation at 0.866c.

What Ship 2 sees:

Immediately After instantly achieving 0.866c at 1pm by its clock, Ship 2 sees the blink rate from ship 1 increase to 3.732... blinks/sec. The time stamp from ship 1 will read 12:00:00.

We know from above that Ship 2's light will blink 2079 times between then and when it reaches ship 1. This means that it will see ship 1's light blink ~7758 times during the trip. Therefore, the last time stamp received from Ship1 will be ~02:09:18 pm. This agrees with what Ship 1 records on its clock when Ship 2 arrives.

What does ship 2 conclude?

Ship 2 sees ship 1's clock advance 02:09:18 while it own clock advances by 00:34:39. But he cannot conclude that Ship 1's clock ran 3.732 times faster than his own (anymore than ship 1 could conclude from what he saw that Ship 2's clock ran that much faster than his.)

We have to delve a little deeper into SR to determine what he can conclude.

Point one is that he measures 00:34:39 from the time he starts until he meets Ship 1. If ship 1 is 1 light hr away, this would require him to have a speed greater than c relative to Ship 1. This turns out to be not the case due to length contraction. Upon reaching 0.866 c, the distance to ship 1 length contracts to 0.5 light hr. This allows the distance between them to close at 0.866c and still complete the trip in 00:34:39 by Ship 2's clock.

The second factor involves determining what time it is at Ship1 when Ship 2 begins its journey, according to Ship 2. Unfortunately, this is not quite as straight forward as it was for Ship 1 when it determined the time for Ship 2 when it started the trip. Ship 1 could directly record the time on ship 2's clock, Ship 2 has to determine the time at ship 1. Nor is it just a simple matter of just taking the distance between the two ships and accounting for propagation delay. (IOW, you can't just say that since the two Ship's are 0.5 light hrs apart according to ship 2 and ship 1 see's a time stamp of 12:00:00, that it is actually 12:30:00 at ship 1.)

Instead, you have to take the relativity of simultaneity into account. In effect, events that are simultaneous in one frame will not be simultaneous for a frame with a relative velocity to the first frame. Imagine that we have a clock, at rest with respect to ship1 and synced to Ship 1's clock (in both it's and ship 1's frame). This clock is right next to ship 2 when it makes its velocity change. It reads 01:00:00 at the instant of velocity change. After the velocity change, it still reads 01:00:00 according to ship2. However, since Ship 2 is now in motion with respect to it and Ship 1, it is no longer in sync with Ship 1's clock. Because of the relative speed of Ship 2 and the distance between the two clocks, this time difference works out to be 00:51:59.

So, not only does ship 1 go from being 1 light hr away to 0.5 light hr away, the time on its clock goes from reading 01:00:00 pm (before ship 2 changing velocity) to reading 01:51:59. It is important to note, that Ship 2 does not see a change in ship 1's clock when its goes from at rest to respect to ship 1 to moving at 0.886c with respect to it, instead, what changes is the determination as to what Ship 1 clock reads at the moment. Before the change in velocity it is 1 pm, afterwards 01:51:59.

Ergo, according to Ship 2: The clock at Ship 1 goes 01:51:59 to 02:09:18 from the start of Ship 2's trip to when it arrives at Ship1, for a total elapsed time of 00:17:19.5 passing on ship 1's clock. In other words, The clock on Ship 1 runs half as fast as the Clock on Ship 2. According to ship 2, Ship 1's clock undergoes time dilation during the trip. So the change of reference frame by ship 2 causes Ship 1's clock to "jump forward" by ~51 min and 59 sec and then ship 1's clock undergoes time dilation accumulating an additional ~17min 19 sec for a total time change of 2 hrs 9 min and 19 sec. (As measured from before the velocity change to arrival at ship 1.)

93. Originally Posted by grandi
The established fact of the identical ship logs indicates that the proper times of both of the ships match at all equal distances from Earth.
Only according to their own proper times. If they both kept these logs according to A's proper time, for example, then they wouldn't match at every stage (but they would agree on the total elapsed time).

How can you fit different rates of aging on outbound and inbound trips with the recorded data of the ship logs which is identical for both ships?
Relativity of simultaneity.

Because you are unwilling to do the math, your instinct is based on a non-relativistic mindset and is giving you the wrong answer.

It is a bit like discussing the Voyager missions with Aristotle; he would insist that they should have slowed down an stopped unless they were continually firing their engines. In a post-Newtonian world we no longer make those assumptions.

94. Originally Posted by KALSTER
No. That is why I talked about the muon decay experiment, where there is no symmetry so you can see that measurements from both frames are equally real. The muon experiment is dominated by special relatavistic effects, not GR effects. The differences in proper times for the earth and the muon is due to the relative movement.

Again, even though the two dials in the ship (one showing it's own proper time and the other showing the time of the other ship) differ throughout the trip, neither is more real than the other. Both are correct from the frame it is measured from. The blinking light will do exactly what they are expected to do and nothing of it has to do with Doppler shift, i.e. The observed change in blinking rates has nothing to do with Doppler shift. The other ship actually is running on a different time than its own. Otherwise the muon experiment would not have given the results it did.
The muons are not in a uniform gravitational environment but in a constantly changing gravitational environment. So there is changing gravitational dilation and also the velocity based dilation. For the two ships there is the premise of perfect symmetry, the velocity vectors being perfectly opposite and equal in magnitude at all proper times of the ships.

It was mentioned here that time dilation is supposed to model the proper times. The calculation of time dilation is the prediction, the recorded logs of proper times on both ships are the observation and when they compare the ship logs they are found identical. Are you indicating that the prediction does not match observation?

95. Originally Posted by Janus
Assume that you have a line marked out at even intervals in the Earth frame. Each brother notes the time on his clock as he passes each mark. He also notes the time on his brother's clock when he passes each of his marks. This happens on both the inward and outward legs. Each will agree with each other's readings. If brother 1's clock reads 1 yr when he passes marker 500, Both brother's agree to this and both brother's agree that Brother 2's clock reads 1 yr when he passes his marker 500.

However, neither brother will agree that at the instant he passes marker 500 and his clock read 1 yr, that his brother's clock reads 1 yr or that he is passing his marker 500. According to each twin, His brother will both age slow and age fast during different different points of the trip, but in the end, both brothers will be the same age. Just because the Brother's agree that they are the same age at the end of the trip does not mean that they agree that they are the same age at every moment of the trip.
The line marks produce the same verification as the ship logs which are more accurate and contain data for each second of proper times. The ship logs are identical, and they know that ships are at every point in proper time the same distance away from Earth.

The notion of each brother aging slower and faster as if there were two separate realities during the trip is not testable and is not falsifiable.

96. Originally Posted by grandi
The notion of each brother aging slower and faster as if there were two separate realities during the trip is not testable and is not falsifiable.
I'm sure you have already been given links to the thousands of experimental and observational confirmation of relativity. So, yes, the theory is testable and falsifiable. Whether this specific case could be tested? I'm sure it could in principle.

97. Originally Posted by Strange
Originally Posted by grandi
The established fact of the identical ship logs indicates that the proper times of both of the ships match at all equal distances from Earth.
Only according to their own proper times. If they both kept these logs according to A's proper time, for example, then they wouldn't match at every stage (but they would agree on the total elapsed time).

How can you fit different rates of aging on outbound and inbound trips with the recorded data of the ship logs which is identical for both ships?
Relativity of simultaneity.

Because you are unwilling to do the math, your instinct is based on a non-relativistic mindset and is giving you the wrong answer.

It is a bit like discussing the Voyager missions with Aristotle; he would insist that they should have slowed down an stopped unless they were continually firing their engines. In a post-Newtonian world we no longer make those assumptions.
Ok. Lets do some simple math here. Let us investigate what the true effect of the propagation of light is to the observation of the brother going to the other direction. I'll simplify the experiment so that for this purpose each brother will travel one year to the midpoint and wait there until he sees the other brother in his midpoint.

So. Each brother reaches the midpoint at 0.9 light years distance from Earth at the same Earth time. The distance between these two points is 1.8 light years, so each brother has to wait for an additional 1.8 years at the midpoint for the other brother seemingly reach his midpoint.

Would you conclude that each brother must think that the rate of their proper time during the trip was higher and thus the other brother seemed to travel slower?
Or would you conclude that due to the "slow" propagation of light the brothers get delayed visual information of their brother's location?

98. Originally Posted by grandi
Ok. Lets do some simple math here. Let us investigate what the true effect of the propagation of light is to the observation of the brother going to the other direction
That is the wrong math. It is nothing to do with the "true effect of the propagation of light".

99. Originally Posted by Strange
Originally Posted by grandi
Ok. Lets do some simple math here. Let us investigate what the true effect of the propagation of light is to the observation of the brother going to the other direction
That is the wrong math. It is nothing to do with the "true effect of the propagation of light".
How is that the "wrong math"? That is simply investigating the propagation of light and how it affects observations. Could you at least answer the question?

100. Originally Posted by grandi
Originally Posted by KALSTER
No. That is why I talked about the muon decay experiment, where there is no symmetry so you can see that measurements from both frames are equally real. The muon experiment is dominated by special relatavistic effects, not GR effects. The differences in proper times for the earth and the muon is due to the relative movement.

Again, even though the two dials in the ship (one showing it's own proper time and the other showing the time of the other ship) differ throughout the trip, neither is more real than the other. Both are correct from the frame it is measured from. The blinking light will do exactly what they are expected to do and nothing of it has to do with Doppler shift, i.e. The observed change in blinking rates has nothing to do with Doppler shift. The other ship actually is running on a different time than its own. Otherwise the muon experiment would not have given the results it did.
The muons are not in a uniform gravitational environment but in a constantly changing gravitational environment. So there is changing gravitational dilation and also the velocity based dilation. For the two ships there is the premise of perfect symmetry, the velocity vectors being perfectly opposite and equal in magnitude at all proper times of the ships.
Yes, I am well aware of the fact that there are gravitational differences, but, like I said, the vast majority of time dilation and length contraction effects in the muon experiment is due to special relativistic effects. Can you acknowledge that fact?

It was mentioned here that time dilation is supposed to model the proper times. The calculation of time dilation is the prediction, the recorded logs of proper times on both ships are the observation and when they compare the ship logs they are found identical. Are you indicating that the prediction does not match observation?
Let's run through it again. In each ship there are two dials: One shows the time running on the ship and the other shows the continuously calculated time of the other ship relative to the first one. When the ships start off, all the dials on both ships agree and when they return, all of them agree again. BUT, during the trip, each ship will notice that their dial for the time of the other ship will start to diverge in both directions, depending on the relative motion between the two.

The notion of each brother aging slower and faster as if there were two separate realities during the trip is not testable and is not falsifiable.
Once again, that is why I keep bringing up the muon experiment. It effectively an unambiguously demonstrates the very real divergence between two reference frames. The muon measures a different amount of time for the trip than an earth-bound observer does, as well as a different distance covered. With your ship experiment you just do the dilation in both directions so it matches up again at the end, while during the trip the divergence is just as real as that between the muon and earth. Why wouldn't it be? Each of the brothers will have aged differently to the one that stayed on the earth, don't you agree? If the brother that stayed behind then left the other two and made the same trip, he would come back the same age as his other brothers, completing his own symmetry. Would you deny that he was ever of a different age than his brothers?

101. Originally Posted by KALSTER
Yes, I am well aware of the fact that there are gravitational differences, but, like I said, the vast majority of time dilation and length contraction effects in the muon experiment is due to special relativistic effects. Can you acknowledge that fact?
Just to make sure I understand exactly what you are asking.. You propose that vast majority of time dilation and length contraction in the muon experiments can be accounted with natural effects modeled by SR. Did I get that exactly right? To the question of do I agree with that I can not give a clear answer because the situation is extremely complicated.

Let me show you mathematically that the separation between SR and GR time dilation is quite vague:
For time dilation we have
velocity: 1/γ = √(1-vē/cē)
gravity: 1/γ = √(1-2GM/(rcē))

Gravitational acceleration due to M at distance r is derived from the field strength as g = GM/rē and this is backed by observations.
From centripetal acceleration we know that a = vē/r.
Considering the centripetal acceleration while travelling along geodesics we get:
a = GM/rē
vē/r = GM/rē
vēr = GM

Substitute that in to gravitational time dilation you get:
1/γ = √(1-2vēr/(rcē)) = √(1-2vē/cē)

So in the end we have:
velocity: 1/γ = √(1-vē/cē)
gravity: 1/γ = √(1-2vē/cē)

I just love the irony in that.

Originally Posted by KALSTER
Let's run through it again. In each ship there are two dials: One shows the time running on the ship and the other shows the continuously calculated time of the other ship relative to the first one. When the ships start off, all the dials on both ships agree and when they return, all of them agree again. BUT, during the trip, each ship will notice that their dial for the time of the other ship will start to diverge in both directions, depending on the relative motion between the two.
Are the dials supposed to represent the proper time of the other ship? Because the dials are now in disagreement with the ships logs of recorded proper times (time/distance recorded every second during the trip).

Originally Posted by KALSTER
Once again, that is why I keep bringing up the muon experiment. It effectively an unambiguously demonstrates the very real divergence between two reference frames. The muon measures a different amount of time for the trip than an earth-bound observer does, as well as a different distance covered. With your ship experiment you just do the dilation in both directions so it matches up again at the end, while during the trip the divergence is just as real as that between the muon and earth. Why wouldn't it be? Each of the brothers will have aged differently to the one that stayed on the earth, don't you agree? If the brother that stayed behind then left the other two and made the same trip, he would come back the same age as his other brothers, completing his own symmetry. Would you deny that he was ever of a different age than his brothers?
I understand what you mean by doing the dilation in both directions, but that will be in disagreement with the recorded ship logs of proper times and distances.

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