Yet another Twin Paradox thread

[sylas]

Huh? Two clocks "remain synchronized" but one of them is slower? How does that work?

Thanks for picking that up. Bad phrasing on my part, sorry!

What I mean is that the two clocks remain at a fixed distance from each other, so that observers at the clocks can agree without ambiguity as to which clock is running slower, and by how much.

This principle is used in the GPS system, for example, to run the clocks on the satellite slightly slower, so that they match clocks on Earth.

You can't do this with two inertial clocks with some velocity relative to each other. The distance is constantly changing. Each observer receives signals from a receding clock at a slower rate, and from an approaching clock at a faster rate; so you can't slow down or speed up either clock to get a match in the rate for each observer.

There's probably a different word to use for this; but what I mean is that by slowing down one of the clocks you can get a match in the ticking rate as observed by either observer.

Cheers -- sylas

 

[phyti]

refer to drawing:
For simplicity the times are referenced as A or B followed by the year.
Twin B leaves twin A moving at .8c, reverses direction at B12, and returns.
Fig. 1 shows A's view of B's trip. The axis of simultaneity (gray) for B is (A7.2, B12) outbound, and (B12, A32.8) inbound. The instantaneous jump from A7.2 to A32.8 is due to excluding any period of acceleration for B to transfer from the outbound to the inbound frame of reference. The ratio of B-time to A-time is 24/40 = .60.

Fig. 2 is B's view using the Einstein simultaneity convention. The discontinuous motion of A at A4 reflects the switching of frames without acceleration. The extreme distortion of times and locations, using this convention, is noted with A4 simultaneous with B-36, 36 years before they parted! The ratio of A-time to B-time is 4/6.7 = 36/60 = .60 for both path segments.

At this point the slow clock rate is reciprocal.

Fig. 3 is B's view using a horizontal axis of simultaneity, i.e. a translation of positions, and A moving at .8c. The initial conditions place A in the 'chosen' static frame and B moving therefore light speed relative to B is c-v and c+v (magenta). The ratio of A-time to B-time is 4/2.4 = 36/21.6 = 1.67, in agreement with the result for the closed path in fig. 1. The time dilation is now asymmetrical as calculated by both A and B. The extreme space and time shifts are also removed.

Fig. 4 shows a more realistic case with a short period of acceleration for B transitioning between frames. B would explain the curved portion of A's motion as resulting from an equivalent g-field during his acceleration. This also provides an asymmetrical view with 40 A events to 24 B events.

The axis of simultaneity for B determines where B locates the A events, and that axis is determined by the clock synchronization. The simultaneity definition is the source of the distorted coordinates, where unequal path lengths are defined as equal, for the purpose of preserving constant light speed.

Absolute vs. relative speeds.
The question: How much time is required for a car moving at 60 mph, to overtake a car moving at 50 mph with a 1 mile lead?
The answer: distance/(v1-v2) = 1/(60-50) = 1/10 = .1 hr = 6 min.
It's the relative or closing speed that determines the answer. Neither car would expect the other to approach at 60 mph. If the lead car used 60 for the chase car rate, the initial separation would have been 60*.1 hr = 6 miles, not 1 mile. The absolute car speed is relative to the ground. The relative car speed is relative to the other car. They are two different types of relations. If light replaces the chase car, its speed c is relative to space, defined as an invisible but fixed frame of reference, and its relative speed as c-v, with v the speed of the object being chased. The fact that relative light speed is different from c, doesn't contradict its absolute speed, no more than the 10 mph closing speed alters the 60 mph chase car speed.

This quote clarifies the nature of the clock synch method and its purpose.
(M is the midpoint of the distance AB)

Relativity - The Special and the General Theory, Albert Einstein 1961, page 27:
"That light requires the same time to traverse the path AM as for the path BM is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity."

https://www.physicsforums.com/attachments/30035

 

[phyti]

A good example of this is a spaceship under a continuous constant acceleration (measuring acceleration at a given point on board gives a fixed acceleration) and which remains a fixed length (as measured by the people on board).

Using special relativity, you can calculate some consequences that may seem surprising at first glance.

Clocks at the front and the back of the spaceship are running at different rates. The clock at the front runs faster than the one at the rear. Also, the acceleration experienced at the front and back is different. There is a greater acceleration experienced at the rear than at the front. Any given point on the ship will have a fixed acceleration; but different points on board will show different fixed values, if the length remains constant for those on board.

If the acceleration decreases from back to front, i.e., the direction of motion, then the ship contracts. If the direction is reversed using a propulsion unit on the front end, the ship will contract more. By reversing directions enough times, the ship could be reduced to any desired length, and effectively disappear to outside observers. This would be a great contribution to stealth technology.
What do you think?

 

[sylas]

If the acceleration decreases from back to front, i.e., the direction of motion, then the ship contracts. If the direction is reversed using a propulsion unit on the front end, the ship will contract more. By reversing directions enough times, the ship could be reduced to any desired length, and effectively disappear to outside observers. This would be a great contribution to stealth technology.
What do you think?

Length contraction, like time dilation, depends on velocity, not acceleration.

The differing proper acceleration of the front and back of a spaceship is a normal consequence of the fact that the length as measured on board remains constant. During the acceleration phase of the ship this may be an added wrinkle for describing the matter from the perspective of an inertial observer.

Any paradox (nearly always) arises by failing to consider the relativity of simultaneity. Length contraction goes hand in glove with differing perspectives of what is simultaneous for the front and rear.

If the ship stops accelerating at some point, then from the perspective of those on board, the front and the rear stop accelerating at the same time. For an external observer, the rear (which had a greater acceleration) will stop accelerating before the front, and all parts of the ship end up at the same velocity, and with the corresponding length contraction.

When it comes to applications of stealth technology, you can, of course, get length contraction by virtue of high velocity. The issue of length is confounded by that of energy; people will notice side effects from something passing through the air above at velocities approaching that of the speed of light. Also, if you play tricks with simultaneity to achieve a lasting length contraction somehow, you are actually squashing your stealth vehicle. You can achieve the same contractions more easily with a large pile driver; though there may be negative consequences for the pilot and instrumentation on board.

Cheers -- sylas

 

[Buckethead]

I'm slowly (painfully slowly) seeing the light here I think. BTW, thanks to everyone for taking the time to help me get through this. I'm a logic junkie and getting this right helps me to sleep at night.

One thing I'm glad to weed out is that acceleration has absolutely nothing to do with the twin paradox. I wish that I hadn't read so many other twin paradox threads in this forum that insisted that it did and that everything works out if you just remember one is accelerating and the other one is not. ACCELERATION HAS NOTHING TO DO WITH IT. Don't anyone try and change my mind on this or I will surely go out of my mind.

OK, now that I have that straight I would like to ask if the following conclusions are correct. These assume the scenario of 2 ships passing each other as in my opening post.

1. As ship 1 passes Earth on the way out, it sees the clock on Earth moving slower and the Earth sees the clock on the ship moving slower and each will continue to measure the others clock moving slower by the available Earth-ship communications as the two separate.

2. The observations made in the above conclusions are not "real" events since the idea of "simultaneity" has no real meaning at this time. In other words we are truly only talking about "observations". Another way to say this might be, that both clocks really are moving more slowly with respect to the other, but it's irrelevant since no real syncing can be done until the test is over at which time only one will have aged more slowly (the ship in this case).

3. At the point in time when the two ships pass each other to sync clocks, the encoded time of the Earth clock from ship 1 and ship 2 is the same (since they are getting the same time code message) but because ship 2 is going in the opposite direction Earth appears to be much further away, so ship 2 calculates that the actual time of Earth is much later than the calculated time of ship 1.

4. Ship 2 will continue to notice the Earth clock is moving slower but because of the calculated later time in step 3, when the ship arrives at Earth the Earth time will actually be later.

Did I get all that right so far?

One additional question. I had learned that if you travel to a star 10 l.y. away near the speed of light that you will observe that you arrive in less than 10 years. Is that true or not? I thought it was, but if the observed distance to a star you are traveling to seems to move further away the faster you go, it appears to all cancel out and you can never really get very far no matter how fast you go.

 

[yuiop]

2. The observations made in the above conclusions are not "real" events since the idea of "simultaneity" has no real meaning at this time. In other words we are truly only talking about "observations". Another way to say this might be, that both clocks really are moving more slowly with respect to the other, but it's irrelevant since no real syncing can be done until the test is over at which time only one will have aged more slowly (the ship in this case).

In Einstein's SR, both clocks are "really" running slower than each other. In Lorentz Ether Theory, one observer's clock is "really" running slower than the other. The slow clock (and length contracted rulers) of this observer causes this observer to incorrectly measure the clock of the other observer to be running slower than his own. The end result is that it is impossible to determine which observer has absolute motion and which observer really has the slower running clock. The mathematical predictions of SR and LET are identical and the differences are purely philosophical. There is no way in either theory to determine which inertial clock is really slower and there is also no way to determine if the philosophy of SR or LET is the correct philosophy. Nature has the last laugh because some things about how nature works are truly un-knowable to the human mind.

One additional question. I had learned that if you travel to a star 10 l.y. away near the speed of light that you will observe that you arrive in less than 10 years. Is that true or not?

It's true. If you travel at 0.8c it will take you 7.5 years by your own clock.

I thought it was, but if the observed distance to a star you are traveling to seems to move further away the faster you go, it appears to all cancel out and you can never really get very far no matter how fast you go.

You have this the wrong way round. The observed distance to the star according to the traveller is 6 lightyears (when traveling a 0.8c). The traveller concludes he has traveled 6 lightyears in 7.5 years which equate to a velocity of 6/7.5= 0.8c. The Eath to star distance is length contracted from the travellers point of view. Taking both length contraction and time dilation into account, you can in principle travel a distance of a million light years in a year of your own biological time or more extremely, anywhere in the universe in a second of your own time (without exceeding the speed of light).

 

[sylas]

ACCELERATION HAS NOTHING TO DO WITH IT. Don't anyone try and change my mind on this or I will surely go out of my mind.

Shrug. We all lose our minds and some point on the way to understanding relativity, or it feels like it. It doesn't last.

Acceleration does have something to do with it, because acceleration is what causes the change in frame. Acceleration is not directly a cause of time dilation, but in so far as accelerating is how you change frames, you can't say it has NOTHING to do with it. You just have to follow the nature of the association -- which means focusing on relative velocities and how they change.

1. As ship 1 passes Earth on the way out, it sees the clock on Earth moving slower and the Earth sees the clock on the ship moving slower and each will continue to measure the others clock moving slower by the available Earth-ship communications as the two separate.

Keep in mind the difference between "seeing" the clock, where you have to consider the change in how long it takes for light to reach you as well as dilation effects. The dilation effect refers not to what you SEE the other clock doing, but to what you infer the other clock is doing "at the same time" as your clock.

Hence, a clock moving at 60% light speed relative to you is running 1.25 times more slowly, no matter its direction. But what you SEE of the other clock is something else again.

If the other clock is moving tangentially to you, then the distance to the clock remains unchanged, and you see the ticking proceeding 1.25 times more slowly.

If the other clock is moving away from you, you see the ticking twice as slowly, because the signals are taking longer and longer to reach you.

If the other clock is moving towards you, you see it ticking twice as fast! It is still running more slowly by the same dilation factor of 1.25, but because the signals take less and less time to reach you, you actually see them speeded up by a factor of two, rather than slowed down.

In each case, the dilation factor remains the same, and depends only on velocity.

2. The observations made in the above conclusions are not "real" events since the idea of "simultaneity" has no real meaning at this time. In other words we are truly only talking about "observations". Another way to say this might be, that both clocks really are moving more slowly with respect to the other, but it's irrelevant since no real syncing can be done until the test is over at which time only one will have aged more slowly (the ship in this case).

No. Simultaneous DOES have a meaning. The point to grasp is that the meaning is relative. That is, events that are simultaneous in one frame may not be simultaneous in another.

You CAN draw conclusions about simultaneity, and they are meaningful.

3. At the point in time when the two ships pass each other to sync clocks, the encoded time of the Earth clock from ship 1 and ship 2 is the same (since they are getting the same time code message) but because ship 2 is going in the opposite direction Earth appears to be much further away, so ship 2 calculates that the actual time of Earth is much later than the calculated time of ship 1.

Yes.

4. Ship 2 will continue to notice the Earth clock is moving slower but because of the calculated later time in step 3, when the ship arrives at Earth the Earth time will actually be later.

Both ships with infer that the clock on Earth is moving more slowly. But the one approaching will SEE it sped up. Both ships will agree on what time Earth clocks will show when the approaching ship gets to Earth. Of course, the (x,t) location of this arrival event will differ for the inertial frame of the different ships.

Did I get all that right so far?

Point 3 was the important one, I think.

One additional question. I had learned that if you travel to a star 10 l.y. away near the speed of light that you will observe that you arrive in less than 10 years. Is that true or not? I thought it was, but if the observed distance to a star you are traveling to seems to move further away the faster you go, it appears to all cancel out and you can never really get very far no matter how fast you go.

Got that one backwards. As you move faster, the distance between Earth and the star CONTRACTS, not lengthens.

Eg. If a ship approaches a star 10ly away (from Earth's perspective) at 60% light speed, then it will take about 16 years and eight months (16.666 years) for the ship to get there (though of course it takes 10 years more to see the arrival).

From the point of view of the ship, the distance is contracted to 8 light years, and at 60% light speed (the speed the star is approaching) it will take 13 years and 4 months. (13.3333 years.)

The effects of relativity, if you could travel at sufficiently high relative velocities, allow you to travel all over the galaxy in as little experienced time as you like. From your own perspective as the traveler, all the distances between stars would be reduced.

Cheers -- sylas

 

[ghwellsjr]

You are still mixed up on several points but you are making progress. Let me comment:

1) The easiest way for each ship and Earth to communicate their time to the others is through a clock that emits a bright flash periodically, say once an hour. Each observer has two counters, one to count its own outgoing flashes and one to count the other observer's incoming flashes. When they are at their closest approach, they each reset all their counters to zero. Then as they move apart, they will each observe that the incoming flashes are coming in at a slower rate than their outgoing flashes. They can each calculate the ratio of the rate of incoming flashes to outgoing flashes and it will be a number less than one and they both will get the same ratio. From this ratio, they each can determine the relative speed between them and from that, they can each determine the time dilation factor. Look up relativistic doppler for more information.

2) You should not consider the measurements to be not real, even though you are right that simultaneity is not an issue here but that's because simultaneity is only a concern when you are comparing results between two different frames of reference and we are not defining any frame of reference in this explanation. Later on, if you want to, you can revisit this scenario from different frames of reference and you will discover that what I am describing here is the same no matter which frame of reference you use. Just remember, what each observer measures and observes will be the same however you analyze the situation.

3) Ship 1 communicates the value on its counters to ship 2 which then sets its counters accordingly. The ships at this point cannot tell by observing the flashes how far away the Earth is. Ship 1 can calculate how far it has traveled by simply multiplying the number of outgoing flashes by the distance traveled per flash which is .866 light hours. Ship 2 can do the same calculation (because the value in the outgoing counter from ship 1 has been communicated to it) and will arrive at the same distance. There is no meaning to your statement that the Earth appears further away or "the actual time of Earth is much later than the calculated time of ship 1". These kinds of conclusions would be frame dependent and not invariant. We aren't concerned about a frame in this analysis.

4) As ship 2 takes over the role of counting incoming flashes to outgoing flashes and calculating the ratio of their rates, it immediately sees the ratio as much larger, in fact, it is the reciprocal of what ship 1 saw. But using the Relativistic Doppler formula, it calculates exactly the same relative speed between itself and Earth and therefore, exactly the same time dilation as ship 1 saw. We should mention that at the point of switch over, ship 1 shuts off its flashes and ship 2 turns on its flashes, we don't want the Earth observer to later on get confused seeing flashes from two different ships at the same time. And be aware that the observer on Earth is completely unaware of this "turn-around" event happening and keeps measuring the same low Relativistic Doppler rate as before for a very long time, but they both continue to observe the same time dilation throughout this entire scenario.

Now here is the key to the different aging: from the moment of "turn-around" to the end of the scenario, the ships have spent an equal amount of time counting incoming flashes from Earth, half of them at a low rate (ship 1) and half of them at a high rate (ship 2). But the Earth doesn't see the transition from low rate to high rate until much, much later because it has to wait for all those flashes that were in transit from the ships' "turn-around" event to Earth to finally get back to Earth. When they do see the "turn-around" event, long after it happened, they will start counting the high rate for a relatively short period of time and this results in a much lower count on Earth's incoming counter than on the ship's incoming counter. Remember, counters on clocks keep track of accumulated time.

I explained all this, by the way, in post #2. Also, this is a description of what actually happens and has nothing to do with the Theory of Special Relativity or any other theory. As I said earlier, once you understand what is actually happening, you can go ahead, pick a frame of reference and "explain" it again using Special Relativity. A good frame of reference to start with would be the one in which Earth is at rest. Then you can do it again with the frame of rest for ship 1 and again for the rest frame of ship 2 and then a fourth frame could be the "average" between ship 1 and Earth where they are each traveling at the same speed in the opposite direction. Doing this explanation in many different frames will give you great insight into how Special Relativity works but it is never necessary to "solve" any problem in more than one frame because they all give the same result.

 

[D H]

You should not consider the measurements to be not real

Your use of a double negative threw me for a loop. I initially read that statement as "You should not consider the measurements to be real", a statement with which I was about to take exception until I re-read it.

Those measurements, IMO, are very real. Measurements are what distinguish philosophical ramblings from physics.

 

[Buckethead]

Got that one backwards. As you move faster, the distance between Earth and the star CONTRACTS, not lengthens.

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

 

[Mike_Fontenot]

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

It's the usual problem of what is meant by "sees" ... that term gets used with different meanings, by different people, in special relativity.

The image currently being SEEN by an approaching ship IS smaller than the image currently being SEEN by a stationary ship at that same location. But the approaching ship is seeing the Earth NOT as it currently IS, but as it WAS at an earlier time, when it was farther away. When those on the approaching ship correct for that delay in the propagation of light, they will conclude that the Earth is closer than what those on the stationary ship conclude.

Mike Fontenot

 

[Buckethead]

It's the usual problem of what is meant by "sees" ... that term gets used with different meanings, by different people, in special relativity.

The image currently being SEEN by an approaching ship IS smaller than the image currently being SEEN by a stationary ship at that same location. But the approaching ship is seeing the Earth NOT as it currently IS, but as it WAS at an earlier time, when it was farther away. When those on the approaching ship correct for that delay in the propagation of light, they will conclude that the Earth is closer than what those on the stationary ship conclude.

Mike Fontenot

But there is only one true way to determine the DIFFERENCE in distance between what a stationary ship and the approaching ship measures as the distance to Earth and that is to listen to an encoded time message from Earth. If it says "good morning travelers, the time now is 7:00AM" , then they can both conclude that they are the same distance from Earth. And this of course will be what they both hear since they are in the same location. So it may appear smaller (as I said earlier, because its an illusion) and it can also appear to be closer because their time has slowed down and they will reach Earth in less time than they thought, but both of these are an illusion because in fact the moving ship and the stationary ship and the departing ship are all the same distance from the Earth as indicated from the encoded message from Earth. So it appears I am still missing something.

 

[michelcolman]

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

When you are traveling towards or away from the earth, the Earth will "be" closer to you than if you would be standing still at exactly the same location. You could measure this distance by multiplying your travel time with your speed, so it's a "real" distance. Also, experiments sending a laser beam back and forth would be perfectly consistent with this distance. Of course people on Earth would not agree, and neither would people at the same location as you but that are not moving relative to earth. For you, however, this shorter distance will be perfectly real.

The visual effect, however, is a bit different.

If you are moving towards the earth, its physical size will appear smaller because your field of view widens. Basically, you are receiving the same light as a stationary observer, but the rays seem to come from smaller angles. In fact, if you go fast enough, you will even see objects that are at an angle behind you but that appear to be in front of you! So, when accellerating to really high speeds, you will get the visual impression that you are going backwards. Everything in front of you will also become brighter and blueshifted.

When moving in the opposite direction, away from Earth and looking backwards, the Earth will look bigger but fainter and redshifted. While accellerating, the objects behind you (that you are accellerating away from) will actually appear to be coming closer to you. So in this case too, the accelleration will create the illusion of going backwards.

You can see these effects in action on:
http://www.anu.edu.au/Physics/Searle/

 

[michelcolman]

But there is only one true way to determine the DIFFERENCE in distance between what a stationary ship and the approaching ship measures as the distance to Earth and that is to listen to an encoded time message from Earth. If it says "good morning travelers, the time now is 7:00AM" , then they can both conclude that they are the same distance from Earth. And this of course will be what they both hear since they are in the same location. So it may appear smaller (as I said earlier, because its an illusion) and it can also appear to be closer because their time has slowed down and they will reach Earth in less time than they thought, but both of these are an illusion because in fact the moving ship and the stationary ship and the departing ship are all the same distance from the Earth as indicated from the encoded message from Earth. So it appears I am still missing something.

What's missing is how long it took for the message to reach you. One person may say that Earth's message was sent an hour ago, while the other will say that the same message was sent two hours ago. That means they will disagree on the current time on earth, and the current distance from earth.

If you are moving away from earth, you will say that the Earth is moving away from you and therefore it is now further away from you than it was when the message was sent. Somebody receiving the same message but going towards earth, will say that the Earth is coming towards him and therefore it is now closer than it was when the message was sent. That also means current time at Earth is now later, since the message had to travel a longer distance so it must have been sent longer ago. Both will be right, from their point of view! The speed of light relative to themselves is indisputably c, and therefore their conclusions are the only possible explanation.

 

[Buckethead]

When you are traveling towards or away from the earth, the Earth will "be" closer to you than if you would be standing still at exactly the same location. You could measure this distance by multiplying your travel time with your speed, so it's a "real" distance. Also, experiments sending a laser beam back and forth would be perfectly consistent with this distance. Of course people on Earth would not agree, and neither would people at the same location as you but that are not moving relative to earth. For you, however, this shorter distance will be perfectly real.

The visual effect, however, is a bit different.

If you are moving towards the earth, its physical size will appear smaller because your field of view widens. Basically, you are receiving the same light as a stationary observer, but the rays seem to come from smaller angles. In fact, if you go fast enough, you will even see objects that are at an angle behind you but that appear to be in front of you! So, when accellerating to really high speeds, you will get the visual impression that you are going backwards. Everything in front of you will also become brighter and blueshifted.

When moving in the opposite direction, away from Earth and looking backwards, the Earth will look bigger but fainter and redshifted. While accellerating, the objects behind you (that you are accellerating away from) will actually appear to be coming closer to you. So in this case too, the accelleration will create the illusion of going backwards.

You can see these effects in action on:
http://www.anu.edu.au/Physics/Searle/

Thank you, this is what I thought which is why in a much earlier post I said that the Earth only looks further away, an illusion. And yes I can see how it will "actually" be closer because of the slowing of time for the returning traveller. These are all consistant with my understanding.

Somehow though, this still feels circular to me because you are saying the Earth is closer upon returning because all measurements indicate that it is closer (which is fine). But of course it is not closer than the departing ship when they are in the same location because of the encoded time message which is the same for both.

So far I am just seeing that everything is just an illusion except for the slowed time when the ship returns to Earth. The departing ship sees the Earth aging more slowly , but this is an illusion, the two ships see different distances to Earth and this is also an illusion, and the returning ship sees the Earth clock moving more slowly which is also an illusion, so the only thing that is not an illusion is the clock on the two ships is going slower than the clock on Earth. I don't think I'll ever understand this.

 

[Mike_Fontenot]

[...]
But there is only one true way to determine the DIFFERENCE in distance between what a stationary ship and the approaching ship measures as the distance to Earth and that is to listen to an encoded time message from Earth. If it says "good morning travelers, the time now is 7:00AM" , then they can both conclude that they are the same distance from Earth.
[...]

No, that's not correct. They DO each hear EXACTLY the same message, but when they each CORRECTLY allow for the transit time of that message, they get DIFFERENT answers. They are BOTH correct.

And there are easier ways for them to determine their current distance from the earth.

They can use the Lorentz equations.

They can use the length-contraction result.

They can use the time-dilation result, combined with their known velocity with respect to the earth.

All four methods yield exactly the same result.

Mike Fontenot

 

[Buckethead]

What's missing is how long it took for the message to reach you. One person may say that Earth's message was sent an hour ago, while the other will say that the same message was sent two hours ago. That means they will disagree on the current time on earth, and the current distance from earth.

If you are moving away from earth, you will say that the Earth is moving away from you and therefore it is now further away from you than it was when the message was sent. Somebody receiving the same message but going towards earth, will say that the Earth is coming towards him and therefore it is now closer than it was when the message was sent. That also means current time at Earth is now later, since the message had to travel a longer distance so it must have been sent longer ago. Both will be right, from their point of view! The speed of light relative to themselves is indisputably c, and therefore their conclusions are the only possible explanation.

OK, yes I can see this, but I think it's fair to say that when one ship says it was sent a different time than the other, they are simply using their instruments and calculators to say that and that in fact the message had to have been sent at the same time (it's only one message) and had to have been received at the same time (they are both there to receive it), and the message says the same time to both of them, so the only conclusion to be made from this is that THIS is the actual distance from Earth and it's one and the same distance for both ships. What I understand can't be determined is the actual distance in units as both ships will come up with a different number. So both numbers must be wrong since the two numbers MUST agree with each other since they are in the same location.

 

[Buckethead]

No, that's not correct. They DO each hear EXACTLY the same message, but when they each CORRECTLY allow for the transit time of that message, they get DIFFERENT answers. They are BOTH correct.

And there are easier ways for them to determine their current distance from the earth.

They can use the Lorentz equations.

They can use the length-contraction result.

They can use the time-dilation result, combined with their known velocity with respect to the earth.

All four methods yield exactly the same result.

Mike Fontenot

Agreed. But see post #67. You can't both be at different distances and at the same distance at the same time, this is a paradox

 

[Mike_Fontenot]

[...]
But see post #67. You can't both be at different distances and at the same distance at the same time, this is a paradox
[...]

They each agree how old the home twin was when she SENT the message ... her message tells them that.

And they each agree about how old THEY each were when they simultaneously RECEIVED her message.

But they disagree about how much the home twin aged during the message transit, and therefore they disagree about how old the home twin was when they RECEIVED her message.

There are no true paradoxes and/or inconsistencies in special relativity. But it is very easy to THINK you see an inconsistency, whenever you allow yourself to be even the slightest bit imprecise in your statements, or when you allow a subconsciousassumption to creep in, that is obviously true in Newtonian physics, but which is NOT true in special relativity. Everyone who has ever carried out any calculations in special relativity has been burned before (usually multiple times) because they haven't been sufficiently precise in their statements.

Mike Fontenot

 

[phyti]

They each agree how old the home twin was when she SENT the message ... her message tells them that.

And they each agree about how old THEY each were when they simultaneously RECEIVED her message.

But they disagree about how much the home twin aged during the message transit, and therefore they disagree about how old the home twin was when they RECEIVED her message.

There are no true paradoxes and/or inconsistencies in special relativity. But it is very easy to THINK you see an inconsistency, whenever you allow yourself to be even the slightest bit imprecise in your statements, or when you allow a subconsciousassumption to creep in, that is obviously true in Newtonian physics, but which is NOT true in special relativity. Everyone who has ever carried out any calculations in special relativity has been burned before (usually multiple times) because they haven't been sufficiently precise in their statements.

Mike Fontenot

But what if ships 1 and 2 do not synchronize their clocks upon leaving earth?
What would they conclude about the message?

 

[Mike_Fontenot]

But what if ships 1 and 2 do not synchronize their clocks upon leaving earth?
What would they conclude about the message?

Irrelevant to the above discussion.

 

[sylas]

But in an earlier post you said the returning ship would see the Earth as being 4 times as far away as the leaving ship. Doesn't this mean the returning ship would see the Earth as being twice as far as a ship in the same location that is not moving relative to the Earth?

Yes, it does.

Specifically, consider a star that is six light years from Earth, as measured in a frame where the star and Earth are at rest. Consider Earth sending a radio message to the star. I'll locate events using (x,t) co-ordinates (distance and time) in different frames, but I will keep the event (0,0) to be the event of receiving the message at the distant star, with positive x in the direction of Earth. Units are years and lightyears, and so Earth is at rest at location x=6 in the star rest frame.

In the star rest frame, the event of Earth sending the message is (6,-6). It was six years ago.

In the rest frame of a ship moving past the star at 60% light speed, towards the Earth, the event of Earth sending the message is (12,-12). In the rest frame of a ship moving past the star away from the Earth at 60% light speed, the event is (3,-3).

These are not illusions. They are co-ordinates in different frames, with no frame standing out as correct. All distance and time measurements between events are always relative to some frame. There is no one correct value.

Cheers -- sylas

PS. Note that this is the distance between events; NOT the distance between Earth and the star. In the rest frame of the ship, Earth and the star are both moving at 60% light speed, and they are 4.8 light years apart from each other.

A radio message between Earth and the star takes 12 years one way and 3 years the other way because the speed of light is totally unaffected by the motions, and the light signal is chasing a moving receiver. In 3 years the receiver moving at 60% light speed moves 1.8 light years, and if this is reducing the distance light must travel from emission, then the distance to cover is 4.8 - 1.8 = 3 light years.

In 12 years the receiver moving at 60% light speed moves 7.2 light years. If this is increasing the distance light must travel from emission, then the distance to cover is 4.8 + 7.2 = 12 light years.

In the star rest frame, the receiver is not moving, and the distance from Earth to star is 6 light years.

 

[phyti]

Irrelevant to the above discussion.

Is that your final answer?

 

[phyti]

Yes, it does.
These are not illusions. .

Yes they are because of the simultaneity and synchronization definitions.
The absolute propagation speed c is sustituted for the relative (closing) speed of light.
1905 paper, par 1 & 2.

 

[sylas]

Yes they are because of the simultaneity and synchronization definitions.
The absolute propagation speed c is sustituted for the relative (closing) speed of light.
1905 paper, par 1 & 2.

You are being cryptic -- and not only in response to me. I'm not bothering with this unless YOU make the effort to give a clear exposition of what you mean.

A suitable translation into English of Einstein's famous paper On the Electrodynamics of Moving Bodies is available at the link. It does not have the word "illusion" in any paragraph; and the paragraphs you might be referring to do not back up your denial of what I posted and explained previously.

In the meantime, what I said is entirely correct. I am not speaking of illusions, but of genuine distance and time measures.

While we are at it. I agree entirely with Mike Fontenot that your post about not synchronizing clocks was irrelevant to the discussion; but whether a reply is "final" or not actually depends on YOU describing what you mean much better. If your "final" input on synchronization is given, then Mike's response is apt as a "final" response. If you want to keep talking, then the ball is in your court; not Mike's.

Sylas

 

[John232]

Say, two ships start raceing toward each other at a speed close to the speed of light. Each ship looks at the other ship and they both measure each others clocks going slower then their own. Then Earth looks at both ships, they both took off from an Earth station, and Earth measures both of their clocks to measure the same time that is slower than Earths clock. They both accelerated at the same rate to reach the same speed close to the speed of light.

What does each ship and Earth clock say to agree that they both read each others clock as being slower while Earth reads both their clocks as being the same slower speed?

The problem is that the 3 observers wouldn't be able to agree on anything the other clocks should read. They couldn't read a slower time and the same time at the same time. Each observer would have to see a different reading on the clock than the person traveling along with the clock. It would seem almost like there would have to be a separate reality for each observer to achieve what SR would say about the situtation.

 

[ghwellsjr]

The only problem is you have the two ships racing toward each other when I think you want them racing away from each other (and from the earth) but otherwise this is no different than the first half of the Twin Paradox.

Any two observers in relative motion will see the other one's clock as running slower than their own and by the same amount. You have three such pairs of observers. The two ships will measure more time dilation between them than either of them with the earth. Each earth-ship measurement will be the same assuming that both ships are traveling at the same speed but in opposite directions.

If you had both ships turn around at the same time and head back to earth, their times would end up identical but smaller than the time on the Earth clock.

 

[John232]

The only problem is you have the two ships racing toward each other when I think you want them racing away from each other (and from the earth) but otherwise this is no different than the first half of the Twin Paradox.

I don't see how direction of motion is a issue. But, yes it is just the first half of the Twin Paradox. Say, the ships went close enough to the speed of light they aged 3 times slower.

Three Earth secounds goes by, Earth reads each clock on each ship to only have read 1 secound. Each ship reads his clock to have read 3 secounds, and Earth and the other ship 1 secound. They all try to sync their clocks to read the same time. How is this possible if they all read different times on each others clocks?

 

[michelcolman]

I don't see how direction of motion is a issue. But, yes it is just the first half of the Twin Paradox. Say, the ships went close enough to the speed of light they aged 3 times slower.

Three Earth secounds goes by, Earth reads each clock on each ship to only have read 1 secound. Each ship reads his clock to have read 3 secounds, and Earth and the other ship 1 secound. They all try to sync their clocks to read the same time. How is this possible if they all read different times on each others clocks?

The answer to your problem is that it is impossible to sync their clocks unambiguously if they are not in the same location. Earth and the ships will not agree on the exact time at which the others "synced" their clocks, they will all say that the others pushed their triggers too early or too late. If Earth observes the two ships pressing their sync triggers simultaneously, each ship will say the other pressed it a lot earlier (if moving towards each other) or later (if moving away from each other).

For example:

Two ships are approaching Earth from opposite directions. As seen from earth, they are at exactly the same distance, each traveling at 0.5c, and will of course arrive simultaneously. One minute before their arrival, Earth sends out a signal to sync the clocks of the ships. The ships are at that moment 30 light seconds away, and light travels towards them at a relative speed (seen by earth) of 1.5c (light going one way at c, ship going the other way at 0.5c), so it will take 20 seconds for the signal to arrive at both ships, which are at that time 20 light seconds away. Both start their timers, and on arrival both clocks show 34.64 seconds have passed (instead of 40 as measured by earth). This is of course because both clocks are only running at 87% of their normal speed.

Now, imagine we are on board of one of the ships.

We can consider ourselves to be stationary, while the Earth is moving towards us with a speed of 0.5c, and the other ship is approaching us with 0.8c (relativistic addition of 0.5+0.5). This means that the other ship has a speed relative to Earth of only 0.3c. Since we arrived at the same time, this means the distance between Earth and the other ship must have been 60% of the distance between us and the Earth at any given "simultaneous" time before arrival.

We received the signal 34.64 seconds before arrival, when Earth was 17.32 light seconds away. Earth would measure that as 20 light seconds because of length contraction (87%). Since Earth is moving towards us at 0.5c, the message must have been sent when Earth was twice as far away, at 34.64 light seconds from us. So the message was sent 69.28 seconds before our arrival (but Earth will have measured that as only one minute because their clocks are slower at a rate of 87%).

When Earth sent the message, the other ship was 20.78 light seconds away from Earth (69.28 times 0.3). Since the message travels at a speed of 1.8c relative to the other ship (light going one way at c, ship going the other way at 0.8c), it was received after 11.55 seconds, which is 57.73 seconds before arrival, when they were... 17.32 light seconds from Earth (57.63*0.3). At least we agree we received the signal at the same distance from earth! They just got to that distance a lot earlier than us, and took longer to reach Earth from there, but of course they would measure those 57.73 seconds as only 34.64 seconds because their clock is ticking at 60% of normal speed. That explains why their clock is indicating exactly the same elapsed time as ours.

Getting dizzy yet? ;-)