Twin Paradox - Question on Space Time Diagram Analysis Resolution

[ghwellsjr]

That is exactly the place where I needed to rethink my though process wrt distances and that is the key. I see what you are saying. At time zero, from Stella's perspective , when Earth is at the same place as she is, the distance between the space station and Earth is 4.8 light years as Station and Earth are moving at 0.6c and hence distances between them should be contracted through Lorentz contraction to 4.8 light years. That means at time zero there are two people (Stella at rest and Earth guy moving at 0.6 c wrt Stella) side by side. And at time zero, Stella and Earth guy both see the same person on the space station and they both come to different conclusions that he is 4.8 Light years away and 6 Light years away from them respectively.

At time zero, they do both see the same image of the space station person but not in a way that they could come to any conclusion about his distance.

Suppose the Earth guy has a measuring scale on Earth which is 6 Light years long - he uses that scale and touches the space station guy and gets convinced that he is 6 Light years away. But Stella will look at this and say the measuring scale is just 4.8 light years long. This is all happening at time zero. Suppose there are other observers at varied velocities (wrt Stella) side by side to Stella at time zero, they will all measure different values for the distance between them and the space station. Let us say all stand in a line hold a large rod which touches the space station - each observer will look at rods of all the other observes and say all rods are equal in length meaning the start and end points of all the rods coincide. But when asked for a number for the length each will say different numbers - one will say 4.8 and the other will say 6. This is because their measuring systems are out of sync and not the reality they see.

Aside from the impracticality of using such large rods to measure distances and the impossibility of the observers seeing both ends of their rods at the same time, rods are no longer the standard for measuring distances. Instead we use the defined constant for the speed of light, the defined distance for how far light travels in a given time interval and a laser range finder or radar techniques.

This brings us to the fundamental question as to what is distance in space or what is meant by size/length of an object or any measurement in space. All these space measurements are only relative to the reference measuring system of the measurer. The size of the universe or galaxies or planets are all different from the perspective of the guy who measures depending on how he moves relative to others. Distances, lengths and sizes are relative and lies in the eyes of the beholder!

I wouldn't say it's in the eyes of the beholder because it isn't something that can be seen. Rather, it's a matter of meticulous data collection, analyzation, and the application of Einstein's second postulate--that laser or radar signals take just as long to reach their target as the echoes take to get back. Then it's a simple matter, in principle, to show how each observer can get a different answer to the question of how far away is the space station.

To illustrate this, we need a spacetime diagram that starts earlier and where all participants are inertial:

First, I want you to note the thin black line coming up from the bottom of the thick black line. This represents what both observers see of the space station person at time zero.

Next, note the blue observer sent a radar signal to the space station at his Proper Time of -6 years and received its echo at +6 years. When he receives the echo, he concludes that the space station was 6 light-years away, 6 years earlier at his time zero.

Similarly, the red observer sent a radar signal at his Proper Time of -4.8 years and received the echo at +4.8 years so he concludes that the space station was 4.8 light-years away at his time zero.

Now if we transform to the rest frame of the red observer, we see that all the signals start and arrive at the same Proper Times as in the original diagram:

I don't want you to think that it is only rest frames that are important so here's one where all participants are traveling at 1/3 of c:

With this understanding and acceptance of this idea, I can now see how the paradox is solved. I have to now convince myself further whether this understanding is truly sound by understanding experimental data which attests to this understanding.

Thank you for that right push. I suppose I am right in the way I have formulated my understanding of how things are wrt distances.

Have my comments and diagrams helped your understanding?

 

[ghwellsjr]

Thank you for the response.

Let me understand this.

For the below diagram to plot the red and blue line wrt a rest frame moving at a speed 0.6 c right wrt Earth

Are these the inputs you provided?

The velocities :
Red line velocity -> Zero velocity for first part of the journey and (-1.2/1.36 c) for the second part of the journey
Blue line velocity -> (- 0.6 c)

No, I used the parameters for the first diagram and then transformed to a speed of 0.6c.
Red: 0.6c for 8 ticks then -0.6c for 8 ticks.
Blue: 0c for 20 tick

The proper time ticks :
Red line - 8 ticks for the first half and 8 ticks for the second half
Blue line - 20 ticks for the entire journey

 

[ghwellsjr]

Also I suppose your provide initial coordinates as in some cases the line won't start at (0,0) - say in the case of the black line for the space station in a later diagram you created.

Yes.

 

[Mentz114]

Please also let me know what is the tool you use to draw these diagrams. Thank you.

There is a space-time diagram tool linked to in this thread https://www.physicsforums.com/threads/interactive-minkowski-diagrams-tool.813899/

 

[controlfreak]

No, I used the parameters for the first diagram and then transformed to a speed of 0.6c.

When you mean transform I suppose at a high level you are using one transformation subroutine and one drawing subroutine in your code.

To draw the first diagram, it doesn't need transformation and is given directly to the drawing subroutine:

Red: 0.6c for 8 ticks then -0.6c for 8 ticks.
Blue: 0c for 20 tick

I suppose to draw your second diagram you call your transformation sub-routine/function passing the above inputs, whose output will be as below:

Red line velocity -> Zero velocity for first part of the journey (8 ticks) and (-1.2/1.36 c) for the second part of the journey (8 ticks)
Blue line velocity -> (- 0.6 c) - 20 ticks

and I suppose this output you the feed it to the same drawing subroutine used above to draw the second diagram.

Aside from the impracticality of using such large rods to measure distances and the impossibility of the observers seeing both ends of their rods at the same time, rods are no longer the standard for measuring distances. Instead we use the defined constant for the speed of light, the defined distance for how far light travels in a given time interval and a laser range finder or radar techniques.

I wouldn't say it's in the eyes of the beholder because it isn't something that can be seen.

I exaggerated the imagery to highlight the relativity of SR using a common phrase used in context of beauty and here we are talking abt distance. It also helps in my mind to recognize that how measuring systems measure apparently same length rods (all rods end points "apparently" meet) and come up with different lengths because they use measuring scales which are different. But this result does make me question are they of the same length in the first place or do their ends meet in the first place. Radar is a complex and more practical measuring scale which can be used to measure with high precision unlike measuring rods. But the concept is the same.

The problem with my imagery is how do we state that the ends points of two rods meet? To say I will ascertain that by seeing both rods is misguiding and that is the origin of the supposed paradox in my mind's eye as we truly cannot see that well and so we can only assert by measuring through using measuring sticks or radars like you mentioned. But infact if we really had the ability to see long distance and measure them precisely with an enhanced eye machinery, we will come to the conclusion that end points don't meet as how can end points of rods of varying lengths meet. In fact we cannot make an apriori assertion about whether the rods are same length or ends meet before we measure. Only measurement by precise means will give us the info to make assertions. In this case, we get the answer the rods are of different length and the distances are of different length and the right course of action is that we should go with it as there is nothing called absolute length anyway and all lengths are measured lengths, measured in the context of a particular reference frame.

It was helpful to see the light paths in the diagram and it really elucidated very well your point. Overall all the diagrams you had shared took me in the right direction and this last post I feel helped me refine my understanding further. Thank you.

 

[ghwellsjr]

When you mean transform I suppose at a high level you are using one transformation subroutine and one drawing subroutine in your code.

Yes.

To draw the first diagram, it doesn't need transformation and is given directly to the drawing subroutine:

Red: 0.6c for 8 ticks then -0.6c for 8 ticks.
Blue: 0c for 20 tick

Not exactly, even for the first diagram I pass the setup data through the transformation routine which doesn't do anything when the speed is zero.

I suppose to draw your second diagram you call your transformation sub-routine/function passing the above inputs, whose output will be as below:

Red line velocity -> Zero velocity for first part of the journey (8 ticks) and (-1.2/1.36 c) for the second part of the journey (8 ticks)
Blue line velocity -> (- 0.6 c) - 20 ticks

and I suppose this output you the feed it to the same drawing subroutine used above to draw the second diagram.

Yes, as long as you realize that the program does the same thing for all speeds.

I exaggerated the imagery to highlight the relativity of SR using a common phrase used in context of beauty and here we are talking abt distance. It also helps in my mind to recognize that how measuring systems measure apparently same length rods (all rods end points "apparently" meet) and come up with different lengths because they use measuring scales which are different. But this result does make me question are they of the same length in the first place or do their ends meet in the first place. Radar is a complex and more practical measuring scale which can be used to measure with high precision unlike measuring rods. But the concept is the same.

The problem with my imagery is how do we state that the ends points of two rods meet? To say I will ascertain that by seeing both rods is misguiding and that is the origin of the supposed paradox in my mind's eye as we truly cannot see that well and so we can only assert by measuring through using measuring sticks or radars like you mentioned. But infact if we really had the ability to see long distance and measure them precisely with an enhanced eye machinery, we will come to the conclusion that end points don't meet as how can end points of rods of varying lengths meet. In fact we cannot make an apriori assertion about whether the rods are same length or ends meet before we measure. Only measurement by precise means will give us the info to make assertions. In this case, we get the answer the rods are of different length and the distances are of different length and the right course of action is that we should go with it as there is nothing called absolute length anyway and all lengths are measured lengths, measured in the context of a particular reference frame.

It was helpful to see the light paths in the diagram and it really elucidated very well your point. Overall all the diagrams you had shared took me in the right direction and this last post I feel helped me refine my understanding further. Thank you.

You're welcome.

 

[lucaex baronium]

I started a thread previously (https://www.physicsforums.com/threads/time-dilation-happens-on-moving-frame-but-which-one.814622/) around this concept but it got closed by one of the staff after helpfully pointing me to http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_spacetime.html.

I read that link and it does nicely explain how Stella's elapsed "proper" time is lesser when analysed using the lens of Minkowski spacetime, from the frame of reference of Terrence (assuming Terrence is at rest). But suppose if we do the same calculation from the frame of reference of Stella (assuming Stella is at rest), wouldn't we get different worldlines? In fact the worldlines will switch between them. So from Stella's frame of reference, she will calculate that the elapsed "proper time" of Terrence is less than Stella and he would have aged less. So as I see it the paradox isn't avoided and infact reinforced by this elaborate calculation.

What am i missing?

I am basically a novice in the field of physics, but I had this odd realization not too long ago.
I'll begin simply...

Isn't there a way to work backwards, canceling out ALL influential velocities that we experience with the use of a formula, to test the accuracy of the time dilation theory?
Asumming this is possible, could we also find out if TIME really is just an illusion created by MOTION? Can you make sense of this?

 

[PAllen]

I am basically a novice in the field of physics, but I had this odd realization not too long ago.
I'll begin simply...

Isn't there a way to work backwards, canceling out ALL influential velocities that we experience with the use of a formula, to test the accuracy of the time dilation theory?
Asumming this is possible, could we also find out if TIME really is just an illusion created by MOTION? Can you make sense of this?

Velocities relative to what? You don't 'experience velocity', you have velocity relative to something, different for various somethings.

 

[lucaex baronium]

I think in this diagram, I feel there should be a correction made. The red line should go from (0,0) to (0,10) and not to (0,8) and the bend for the red line happens at (0,10) and then the line goes to (-15,25). At coordinate time 10 yrs, Terrence location will be -6 in x-axis which is correct as at the turn around point Terrence and Stella are separated by 6 light years. And also Terrence would have also spent proper time of 8 years (check graph) and so 2 years slower than Stella as we expected. So it is not 8/6.5 but 10/8 between Stella and Terrence at the turn around point as suggested by the above figure, an exact reverse of the world lines as seen from Terrance side (atleast for the first part of the journey) like I initially pointed out in my first post. But after that for the second part of the journey lines slope in such a manner we get back to original answer of 16 years for Stella and 20 years for Terrence at (-15,25) which tallies well with the answer we expected at the end of the journey. No confusion there if we don't change frames midway following Stella.

Considering this to be the case, then I can go back to my original thought experiment which I believe is now valid if the above reasoning is valid.

Here is a thought experiment.

Restating the problem which we have been discussing - Assume relative velocity between the two frames (Terrence & Stella) is 0.6 c. Stella travels from Earth to a space station which is 6 Light years away and then turns around and comes back. In the first part of the journey symmetry is not broken and so both Stella and Terrence's frames are equivalent. Both think the other person's time is slower. As per Stella she reaches the space station in 10 years, Terrence thinks she reaches the space station in 8 years.

Say Stella is a cancer patient and will die around 9 years if left untreated. Suppose the medicine for treatment is present in the space station at the end of the first part of the journey and suppose they get the medicine when they pass that station during the turn around and give it to Stella after that, Stella will be cured. Now the question if Stella is alive when she returns, then she reached the space station before 9 years which means the time was running slow in the spaceship which is what Terrence will argue if the journey is viewed from his reference, otherwise if she is dead when she returns then the time was running faster in spaceship which is what Stella herself will argue if she viewed the whole journey from her reference.

What is the truth? She can't be both dead and alive?

Answer is simple...
FAST and SLOW are synonymous terms in this instance, due to relativity. Stella (aboard the ship) appears to be slowed down to Terrance, but ONLY because the rate at which SHE is experiencing time has been sped up compared to him (think about it, high speed camera captures slowed down footage, right? Right.)
So,
With her temporal perception opperating at a higher rate than Terrances, the progression of her disease would cause her to reach death even quicker... I think... Hmm, maybe not so simple then, haha.
I think an important factor to scrutinize here would be how stellas body reacts to the velocity on the molecular level.
Intuitively, it makes sense to say it follows the same logic, but what about extremes?
What repercussions could come about from atomic vibrations slowing their rate too much?

I conclude with this, she would be dead... Not alive.

 

[lucaex baronium]

Velocities relative to what? You don't 'experience velocity', you have velocity relative to something, different for various somethings.

Velocity relative to ALL the velocities that are influencing our temporal perception, of course.
You may not be able to discern velocities, but you definitely experience them in one way or another.

Imagine if physicists used atomic clocks to measure precise variations in time passage (with our perception of time as the neutral) at different velocities?? One on a bullet train, one in a shuttle (a shuttle which has left the Earth -- no longer affected by its rotational and orbital velocity -- and has countered its directional velocity with thrusters (or what have you), and one that is simply sitting in a living room within a house on earth.
Now, after about 24hrs (im guessing) there should be noticable difference in the chrono synchronization of the clocks.

Using this data, the differences in time passage could be plotted on a graph and (with calculations and possibly more data) a precise numerical relation could be discovered between the passage of time over velocity.
From here a formula could be created.
Then, using this formula, it would be possible to CANCEL OUT each layer of universal velocity -- in the form of planetary rotation, solar orbit, galaxy distribution/MOTION, etc... all the way up to universal expansion -- by calculating these velocities into the formula and setting to zero.
So,
After all has been accounted for, what would the passage of time itself equate to?

That is to say, once MOTION is set to zero -- no movement in galaxy, solar system, planet -- what happens to the rate of time passage relative to our perspective?
Hmm?
Without motion aiding our experience, does time itself just appear to be standing still?

I hope all of what I just typed was even mildly ccomprehensive. If not, then please correct me, haha

 

[Ibix]

That is to say, once MOTION is set to zero -- no movement in galaxy, solar system, planet -- what happens to the rate of time passage relative to our perspective?
Hmm?
Without motion aiding our experience, does time itself just appear to be standing still?

I hope all of what I just typed was even mildly ccomprehensive. If not, then please correct me, haha

You appear to believe that there is some absolute definition of motion - that we can find some state that is "truly" at rest, and any other state is moving. This is not correct.

The whole point of relativity is that, as long as the accelerometer in your pocket measures zero, you are at rest. Whether you are in a spaceship traveling to another star (or waiting for the star to come to you, you could say) or in a space station waiting for the rocket to return, you can consider yourself to be at rest and everyone else to be moving. There is no experiment that will tell you otherwise.

In the case of the twin paradox, one of the twins (Stella) used her rockets to turn around and come back. The differences in experience for the twins means that there is an absolute sense in which one twin traveled out and back, and this leads to a difference in aging between the two. It does not mean that there is an absolute sense of motion.

The maths of this is well understood, and has been tested experimentally. There is no absolute "MOTION" to find.

 

[PAllen]

Velocity relative to ALL the velocities that are influencing our temporal perception, of course.
You may not be able to discern velocities, but you definitely experience them in one way or another.

No you don't, not at all. There is only velocity relative to other things.

Imagine if physicists used atomic clocks to measure precise variations in time passage (with our perception of time as the neutral) at different velocities?? One on a bullet train, one in a shuttle (a shuttle which has left the Earth -- no longer affected by its rotational and orbital velocity -- and has countered its directional velocity with thrusters (or what have you), and one that is simply sitting in a living room within a house on earth.
Now, after about 24hrs (im guessing) there should be noticable difference in the chrono synchronization of the clocks.

Using this data, the differences in time passage could be plotted on a graph and (with calculations and possibly more data) a precise numerical relation could be discovered between the passage of time over velocity.
From here a formula could be created.
Then, using this formula, it would be possible to CANCEL OUT each layer of universal velocity -- in the form of planetary rotation, solar orbit, galaxy distribution/MOTION, etc... all the way up to universal expansion -- by calculating these velocities into the formula and setting to zero.
So,
After all has been accounted for, what would the passage of time itself equate to?

That is to say, once MOTION is set to zero -- no movement in galaxy, solar system, planet -- what happens to the rate of time passage relative to our perspective?
Hmm?
Without motion aiding our experience, does time itself just appear to be standing still?

I hope all of what I just typed was even mildly ccomprehensive. If not, then please correct me, haha

The rest of this basically nonsense contradicted by experiment. There is no universal velocity. If two clocks move by each other rapidly, an observer associated with each would determine that the other is slow, and both are right.

 

[lucaex baronium]

You appear to believe that there is some absolute definition of motion - that we can find some state that is "truly" at rest, and any other state is moving. This is not correct.

The whole point of relativity is that, as long as the accelerometer in your pocket measures zero, you are at rest. Whether you are in a spaceship traveling to another star (or waiting for the star to come to you, you could say) or in a space station waiting for the rocket to return, you can consider yourself to be at rest and everyone else to be moving. There is no experiment that will tell you otherwise.

In the case of the twin paradox, one of the twins (Stella) used her rockets to turn around and come back. The differences in experience for the twins means that there is an absolute sense in which one twin traveled out and back, and this leads to a difference in aging between the two. It does not mean that there is an absolute sense of motion.

The maths of this is well understood, and has been tested experimentally. There is no absolute "MOTION" to find.

So what you're saying is without something to be compared side to side with said velocity, it might as well be zero because there is NOTHING to inform of otherwise. Acceleration and directional variance is all that matters?
Doesn't that seem to be lacking somewhat?
I mean, isn't there a reason things can't move faster than c?
If independent velocity didn't matter by itself, then why is light speed (non-varying) such an exception? Things going that fast aren't the same as zero, are they?

 

[lucaex baronium]

No you don't, not at all. There is only velocity relative to other things.

The rest of this basically nonsense contradicted by experiment. There is no universal velocity. If two clocks move by each other rapidly, an observer associated with each would determine that the other is slow, and both are right.

No universal velocity? Then what about relative to us?
We know how fast the Earth rotates and have measured how fast we orbit the sun (deciphered through earthly units of measure)
Are you saying that adding these two sums together is not rational because they do not affect each other in the least?

 

[PAllen]

No universal velocity? Then what about relative to us?
We know how fast the Earth rotates and have measured how fast we orbit the sun (deciphered through earthly units of measure)
Are you saying that adding these two sums together is not rational because they do not affect each other in the least?

How could you possibly believe that speed relative to 'us' is universal??!

Of course, speed relative to 'us' well defined (assuming you define 'us'). But how does it have more relevance than speed relative to the 3d moon of a planet orbiting some nearby star?

 

[PAllen]

So what you're saying is without something to be compared side to side with said velocity, it might as well be zero because there is NOTHING to inform of otherwise. Acceleration and directional variance is all that matters?

Exactly ! ..

Doesn't that seem to be lacking somewhat?

only lacking a superfluous, obsolete, concept.

I mean, isn't there a reason things can't move faster than c?
If independent velocity didn't matter by itself, then why is light speed (non-varying) such an exception? Things going that fast aren't the same as zero, are they?

The invariance of light speed disproves any notion of absolute speed. You turn on a laser pulse moving away from you at c. I move in the same direction past you at .99999c. With a sense of absolute velocity, you might expect the light is moving only .00001 c relative to me. Instead, it is moving c relative to me, and you are moving at .99999c away from me. Each of thinks we are at rest. There is no way to choose. That is the essence of relativity. If there were any way to choose based on experiment 'who is really moving' all of relativity would be disproven.

 

[Ibix]

So what you're saying is without something to be compared side to side with said velocity, it might as well be zero because there is NOTHING to inform of otherwise. Acceleration and directional variance is all that matters?

Not quite. As long as I am not accelerating there is no way to say if I am moving or not. The presence or absence of other objects is not relevant to that. If there are other objects around it may sometimes be convenient to consider them to be moving, to consider myself to be moving, or both, but there's no obligation to use one of them.

Doesn't that seem to be lacking somewhat?

The Principle of Relativity, which is the formal name for the notion, underpins pretty much every physical theory we have. In other words, it underpins pretty much everything we do or have done, from pouring a drink on a train to traveling to the moon and everything in between. I'm not sure in what sense that is "lacking".

I mean, isn't there a reason things can't move faster than c?

There is - the principle of relativity. Google for "Nothing but Relativity" by Pal. It's only six pages long and requires only high school maths.

If independent velocity didn't matter by itself, then why is light speed (non-varying) such an exception? Things going that fast aren't the same as zero, are they?

The concept of an invariant speed, one that is the same in all frames of reference, follows from the principle of relativity. Things traveling at that speed cannot be considered to be at rest, true, so it is indeed an exception. This does not alter the fact that any other speed can always be treated as at rest - and you were talking about massive objects like space shuttles which cannot travel at light speed.