Yet another Twin Paradox thread

[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? ;-)