Time dilation problem question

In summary: Not if you use your own clock to measure their velocity. Which is really the only way to do it that makes sense.
  • #36
We can think this way. When Herb passed by John, their clocks showed the same readings. Then, if Herb has another synchronized clock (of his reference frame) adjacent to Bob's clock, that Herb's - 2 clock shows different time than Bob's. But this method is equivalent to introducing Herb's rest frame. Then Bob approaches Herb from distant location. When they meet, Herb will make a conclusion, that Bob's clock dilated. However, If Bob will compare his time with time in Herb's reference frame, he will make a conclusion that time in Herb's reference frame accelerates.
The thing is that we change reference frames. John introduces his frame first and Herb moves in it. Herb dilates. Then Herb introduces his rest frame. John dilates. Bob is at rest and John is at rest either. If we will stay in one chosen frame, observations will not be reciprocal.
Observer "at proper rest" measures dilation. Observer "in proper motion" measures acceleration, since his own clock dilates in certain reference frame. Depending on "proper state" observations will be different.
If you are "at rest", you introduce your own frame. If you are "in motion", you don't introduce your own frame but use that you are "in motion" in.
 
Last edited:
Physics news on Phys.org
  • #37
Bartolomeo said:
While moving clock makes 3 oscillations, any stationary makes 7. When Herb compares his own readings with John's readings, their clocks show 12 hours. When Herb compares his clock with Bob's, Herb's clock show 3 PM and Bob's 7 PM. And Bob's clock is perfectly synchronized with any other clock. What will be Herb's conclusion about stationary clocks? Simple comparison of clock readings show, that time in reference frame runs faster since his in motion in the reference frame John – Tony - Jack – Bob runs faster at gamma. So as to measure, that any single clock dilates, Herb has to change state of proper motion into proper rest (to change reference frame). Herb will introduce a new reference system then, in which he is at rest. Then every single clock, which moves in his reference frame will dilate.

I think you are missing the fact that in Herb's frame, Bob's clock is NOT synchronized with John's clock.

Here's a demo that I created that explains the time dilation from two different frames.

http://dee-mccullough.com/relativity/

It was created without reference to your exact problem, but you can make the connection by assuming that
  • Herb's light clock corresponds to the right red clock.
  • John's light clock corresponds to the left green clock.
  • Bob's light clock corresponds to the right green clock.
  • Tony and Jack were cut out of the demo, for budget reasons.
Click "Start" to see time dilation from the point of view of the John/Bob frame. In this frame:
  • John's clock and Bob's clock are synchronized.
  • John's clock and Herb's clock show the same time, initially: 12:00
  • Herb's clock is advancing at half the rate of John's clock or Bob's clock.
  • When Herb gets to Bob's clock, his clock only shows 12:30, while Bob's clock shows 1:00.
Click "Reset" and then "Red ship's frame" and then "Start" to see what things look like in Herb's frame. It's still true that
  • Initially, John's clock and Herb's clock show the same time, 12:00.
  • At the end, Bob's clock shows 1:00 while Herb's clock shows 12:30
But in Herb's frame:
  • Bob's clock is ahead of John's by 45 minutes. It starts off showing time 12:45
  • Bob's clock advances at half the rate of Herb's.
  • So when Bob reaches Herb, Bob's clock has advanced only 15 minutes, to 1:00, while Herb's clock has advanced 30 minutes, to 12:30.
 
  • #38
stevendaryl said:
I think you are missing the fact that in Herb's frame, Bob's clock is NOT synchronized with John's clocks

I understand that very well. But when you say "in Herbs frame" that means that Herb (in Herb's mind) changes state of proper motion into proper rest. Since he introduces his own rest frame and places Einstein - synchronized clocks in different spatial positions. In this case he compares readings of a SINGLE moving clock, which moves in his reference frame.
 
  • #39
Bartolomeo said:
I understand that very well. But when you say "in Herbs frame" that means that Herb (in Herb's mind) changes state of proper motion into proper rest. Since he introduces his own rest frame.

Well, as far as the demo is concerned, Herb is always at rest in his frame, and John/Bob are always at rest in their frame. What's changing is our choice of whether to look at things from Herb's point of view or the John/Bob point of view. Herb isn't changing. (Well, I guess he could transform to John's frame as well as we can, but for the sake of the demo, assume that he always uses his own rest frame.)
 
  • #40
Herb and John move relatively to each other at velocity v=0.9 c. There is a reference frame, in which Herb is at rest, and John moves with velocity 0.9 c. In this frame Herb sees dilation and John acceleration. There is a frame, in which John is at rest, and Herb is in motion at 0.9 c. In this frame John sees dilation and Herb acceleration. There is a frame, in which John and Herb move at velocity 0.45 and 0.45 respectively. They see the same clock rate. Is there a frame, in which John and Herb move with velocities 0 and 0 respectively?
Amount of time dilation depends on relative speed. But relative contributions of time dilation are frame dependant.
 
  • #41
Whether an observer will see dilation or acceleration or the same clock rate purely depends on arbitrary choice of the reference frame.
 
  • #42
Bartolomeo said:
Herb and John move relatively to each other at velocity v=0.9 c. There is a reference frame, in which Herb is at rest, and John moves with velocity 0.9 c. In this frame Herb sees dilation and John acceleration.

Why do you bring up acceleration? Can't we, for the sake of simplicity, just assume that Herb and John have always been at rest in their respective rest frames?

There is a frame, in which John is at rest, and Herb is in motion at 0.9 c. In this frame John sees dilation and Herb acceleration.

I don't know what you mean. Whether Herb or John accelerates is something that Herb and John can determine on their own. It's not frame-dependent (well, the magnitude might be, but the fact that the acceleration is nonzero is frame-independent).

There is a frame, in which John and Herb move at velocity 0.45 and 0.45 respectively.

No, there isn't. Using the velocity addition formula, if John is moving at speed 0.45 in one direction, and Herb is moving at speed 0.45 in the other direction, then the speed of John relative to Herb is:

[itex]v_{rel} = \frac{v_{john} + v_{herb}}{1 + \frac{v_{john} v_{herb}}{c^2}} = \frac{.9 c}{1.2025} = 0.75 c[/itex]

They see the same clock rate. Is there a frame, in which John and Herb move with velocities 0 and 0 respectively?
Amount of time dilation depends on relative speed. But relative contributions of time dilation are frame dependant.[/QUOTE]

To have a relative speed of 0.9 c, then in a frame where they are moving at the same speed, that speed would have to be around 0.63 c.

Is there a frame, in which John and Herb move with velocities 0 and 0 respectively?

No, that would mean that they would both be at rest in that frame, which would mean that they aren't moving, relative to one another.
 
  • #43
Bartolomeo said:
Whether an observer will see dilation or acceleration or the same clock rate purely depends on arbitrary choice of the reference frame.

I think you're using the word "acceleration" incorrectly here. But you're right--whether a clock is dilated depends on the choice of reference frame. On the other hand, the fact that (as shown in my demo http://dee-mccullough.com/relativity/) Herb's clock (the right red clock) is 30 minutes behind Bob's clock (the right green clock) is frame-independent.
 
  • #44
I think Bartolomeo is using "acceleration" to mean the opposite of time dilation. So he's either using frames in which the speed of light is not isotropic (so Herb's frame's synchronisation convention is equivalent to Einstein synchronisation performed by John) or a truly bizarre definition of "see". Or both.
 
  • #45
stevendaryl said:
I don't know what you mean. Whether Herb or John accelerates is something that Herb and John can determine on their own. It's not frame-dependent (well, the magnitude might be, but the fact that the acceleration is nonzero is frame-independent).

I mean acceleration of time in the reference frames he moves in. If all processes in Herb's body slow down, he will see that all processes around him run very fast.

stevendaryl said:
To have a relative speed of 0.9 c, then in a frame where they are moving at the same speed, that speed would have to be around 0.63 c.

I simplify. Sure, there is relativistic velocities addition. That doesn't matter. There is a frame, in which they move with equal velocities. Herb dilates at gamma, and John dilates at gamma.
 
  • #46
Ibix said:
I think Bartolomeo is using "acceleration" to mean the opposite of time dilation. So he's either using frames in which the speed of light is not isotropic (so Herb's frame's synchronisation convention is equivalent to Einstein synchronisation performed by John) or a truly bizarre definition of "see". Or both.

I didn't ever mention another way of synchronization for moving observer. You have come to this conclusion yourself taking into account all the evidence. I think that you understand everything very well. Yes, if he will synchronize clocks in his frame not by Einstein, but will take into account his own velocity and will conduct measurements, all pieces of puzzle will take proper places. Everything leads straight to that, including transverse doppler effect.
Then even observations (measurements) by means of synchronized clocks would lead straight to the same outcome, that transverse Doppler effect and rate of time "from the point of view" of a single moving clock,
 
Last edited:
  • #47
Bartolomeo said:
I mean acceleration of time in the reference frames he moves in. If all processes in Herb's body slow down, he will see that all processes around him run very fast.

No, he won't. Herb sees nothing at all changed by his state of motion. Everything around him works as normal. What his motion does is:
  • It makes it seem as if John's and Bob's clocks are running slow (in my demo, they advance at half the rate of Herb's clock)
  • It makes it seem as if John's and Bob's clocks are out of synch (in my demo, Bob's clock is 45 minutes ahead of John's clock)
  • It makes it seem as if the distance between John and Bob has shrunk (in my demo, it's half what it is in the John/Bob frame)
At no point does Herb see anything accelerated.
 
  • #48
stevendaryl said:
At no point does Herb see anything accelerated.

Sure as soon as he makes measurements by means of Einstein synchronized clocks. Because he arbitrarily synchronizes clock by Einstein. And everyone does the same.
 
  • #49
Ibix said:
I think Bartolomeo is using "acceleration" to mean the opposite of time dilation. So he's either using frames in which the speed of light is not isotropic (so Herb's frame's synchronisation convention is equivalent to Einstein synchronisation performed by John) or a truly bizarre definition of "see". Or both.

Bartolomeo said:
By the way. Imagine that red moving clock is the Aliens. Row of green synchronized clock are identical brothers Joes. Clockfaces of green clocks are higlighted in green monochromatic light. Aliens compare their own single clock rate with the time in the „Joes green“ reference frame. They see that the set of clocks runs faster at gamma. What color of clockfaces they will see? If they look straight down, it will be red. But since they move, they have to look into front. Due to aberration clockfaces will be blue. Frequency increases at gamma too. Now set of clock (time in reference frame) runs faster and every single clock too.

Please note that Einstein measuring technique is based on ASSUMPTION. It is not fact. You can make your own assumptions if you wish.
 
  • #50
@Ibix, think about photocamera. Contracted or stretched? Hint: does film in moving photocamera Lorentz - contracts? Does it contracts, if the camera is "at rest"? If the film Lorentz contracts, will the square appear contracted or stretched on the photo?
How to put it into accordance with clock synchronization in different frames?
 
  • #51
Depends on the details of the camera. Is it a normal lens-based camera (which can be treated as a pinhole camera offset in the y direction) or a shadow camera that we have to treat as a plane close to the square?
 
  • #52
Bartolomeo said:
Sure as soon as he makes measurements by means of Einstein synchronized clocks. Because he arbitrarily synchronizes clock by Einstein. And everyone does the same.

Then what are you claiming about "acceleration"? Nobody sees any acceleration.
 
  • #53
Ibix said:
Depends on the details of the camera. Is it a normal lens-based camera (which can be treated as a pinhole camera offset in the y direction) or a shadow camera that we have to treat as a plane close to the square?
Obsura. Long enouh so as light would reach film an not to hit walls
 
  • #54
stevendaryl said:
Then what are you claiming about "acceleration"? Nobody sees any acceleration.
Look at the diagram again. Observer slows down himself and everything around appears running faster. Dilates that observer who moves in certain frame. All amount of relative time dilation belongs to him. Amount of time dilation is mutual.
 
  • #55
Bartolomeo said:
Look at the diagram again. Observer slows down himself and everything around appears running faster.

No, it does not. You are misunderstanding it. Herb does NOT see any clocks running faster while he is traveling at a constant speed. He sees John's clock run SLOWER.
 
  • #56
stevendaryl said:
No, it does not. You are misunderstanding it. Herb does NOT see any clocks running faster while he is traveling at a constant speed. He sees John's clock run SLOWER.

In my humble opinion, it's clearer in my demo here: http://dee-mccullough.com/relativity/
  • From the frame of the red clocks (Herb's), it is the green clocks that are running slowly.
  • From the frame of the green clocks (John and Bob), it is the red clocks that are running slowly.
  • Nobody sees anybody's clocks running faster than their own.
The gif here https://en.wikipedia.org/wiki/Time_dilation#/media/File:Time_dilation02.gif shows the same thing: In the frame in which the red clocks are at rest, the green clock runs slower. In the frame in which the green clocks are at rest, the red clock runs slower. (The diagram only shows one moving clock, but 4 stationary clocks.)
 
  • #57
stevendaryl said:
In my humble opinion, it's clearer in my demo here: http://dee-mccullough.com/relativity/
  • From the frame of the red clocks (Herb's), it is the green clocks that are running slowly.
  • From the frame of the green clocks (John and Bob), it is the red clocks that are running slowly.
  • Nobody sees anybody's clocks running faster than their own.
The gif here https://en.wikipedia.org/wiki/Time_dilation#/media/File:Time_dilation02.gif shows the same thing: In the frame in which the red clocks are at rest, the green clock runs slower. In the frame in which the green clocks are at rest, the red clock runs slower. (The diagram only shows one moving clock, but 4 stationary clocks.)
I saw your diagram. Very nice! It shows what I have already told. Any chosen single clock dilates relatively to a set of synchronized cloks. Succesively looking at synchronized clocks single clock will see that they run faster. Why do you discriminate single moving clock and don't want to listen to it's opinion?
 
  • #58
Bartolomeo said:
I saw your diagram. Very nice! It shows what I have already told. Any chosen single clock dilates relatively to a set of synchronized cloks. Succesively looking at synchronized clocks single clock will see that they run faster. Why do you discriminate single moving clock and don't want to listen to it's opinion?

What are you talking about? There are two frames: the red frame, in which the red clocks are stationary, and the green frame, in which the green clocks are stationary. In the red frame, the green clocks are running slow. In the green frame, the red clocks are running slow. In no frame is any clock running faster than the clocks that are stationary in that frame.

More details:

According to the red frame:
  • the right green clock is 45 minutes ahead of the left green clock
  • Both green clocks advance at half the rate of the red clocks
According to the green frame:
  • the left red clock is 45 minutes ahead of the right red clock
  • Both red clocks advance at half the rate of the green clocks
Nobody sees anything running faster.
 
  • #59
stevendaryl said:
What are you talking about? There are two frames: the red frame, in which the red clocks are stationary, and the green frame, in which the green clocks are stationary. In the red frame, the green clocks are running slow. In the green frame, the red clocks are running slow. In no frame is any clock running faster than the clocks that are stationary in that frame.

More details:

According to the red frame:
  • the right green clock is 45 minutes ahead of the left green clock
  • Both green clocks advance at half the rate of the red clocks
According to the green frame:
  • the left red clock is 45 minutes ahead of the right red clock
  • Both red clocks advance at half the rate of the green clocks
Nobody sees anything running faster.
I am traveling in a train and have a clock on my wrist. I am traveling along a platfotm. There are posts with a clock on the platform every 100 yards. I see clocks succesively. First, second, third etc. I see that clock hands rotate much faster than my own. I have no more clock in posession. You insist that I would place another clock in next carriage or even in each carriage. But I have to have an assistant then in my train. Then we have to sinchronize our clocks by light. Then my assistant takes readings from any chosen clock on platform. If we sinchronize clocks by einstein, we will see that any chosen clock dilates. Bur neither my assistant nor I have never heared about Einstein. Even if we heared, we don't trust him. We are not sure that one way speed of light is c. Why do you insist so as I would hire an assistant? I have to make an assumption about synchronization, but I don't like to make assumptions.
Why do you insist so I have to introduce my own frame? Why platform's is not good?
Why should I employ the same synchronization procedure for my clocks as for those on platform?
 
  • #60
Bartolomeo said:
I am traveling in a train and have a clock on my wrist. I am traveling along a platfotm. There are posts with a clock on the platform every 100 yards. I see clocks succesively. First, second, third etc. I see that clock hands rotate much faster than my own.

No, you don't. You see the clocks on the platform running SLOWER than your clock.
 
  • #61
Bartolomeo said:
Why do you insist so I have to introduce my own frame? Why platform's is not good?
Why should I employ the same synchronization procedure for my clocks as for those on platform?
Because if you look at the clock 100m ahead and the one 100m behind you will see that they show different times. So they are either not synchronised, or the speed of light is anisotropic according to you. Which is just making your life difficult for the sake of it.
 
  • #62
Ibix said:
Because if you look at the clock 100m ahead and the one 100m behind you will see that they show different times. So they are either not synchronised, or the speed of light is anisotropic according to you. Which is just making your life difficult for the sake of it.
I look at a clock which is straight in the front. Straight in the front. just my nose separates us. In immediate vicinity as that should be done in Special Relativity and compare readings of my own clock and that clock. One after another. At each post in platform.
 
  • #63
stevendaryl said:
No, you don't. You see the clocks on the platform running SLOWER than your clock.
He's not looking at one clock. He's looking at the clock infront of him - so he's comparing ##t|_{x=0}## and ##t'|_{x=0}##. So he's using the Einstein synchronisation convention in someone else's frame, in short.
 
  • #64
Bartolomeo said:
Bur neither my assistant nor I have never heared about Einstein. Even if we heared, we don't trust him. We are not sure that one way speed of light is c. Why do you insist so as I would hire an assistant? I have to make an assumption about synchronization, but I don't like to make assumptions.
Why do you insist so I have to introduce my own frame? Why platform's is not good?
Why should I employ the same synchronization procedure for my clocks as for those on platform?

Without making any assumptions, you can't compare the rates of two clocks that are not side-by-side. What does it mean to say that one clock (Herb's) is running faster or slower than another clock (John's)? What you have is the following situation:
  • When Herb's clock passes John's clock, they both show time 12:00. (Call this event [itex]e_0[/itex])
  • At some time after [itex]e_0[/itex], Herb's clock shows time 12:30 (Call this event [itex]e_1[/itex])
  • At some time after [itex]e_0[/itex], John's clock shows time 12:30 (Call this event [itex]e_2[/itex])
So to determine whose clock is running slow or fast, you need to know this: Did [itex]e_1[/itex] take place before or after [itex]e_2[/itex]? How do you answer that question? You have to rely on a convention, or assumption.
 
  • #65
Suggestion: People should stop using the word "see" in this thread unless they mean visually. I think "measure" or "calculate" would be the better word for considering time dilation.
 
  • Like
Likes Ibix and stevendaryl
  • #66
Bartolomeo said:
I look at a clock which is straight in the front. Straight in the front. just my nose separates us. In immediate vicinity as that should be done in Special Relativity and compare readings of my own clock and that clock. One after another. At each post in platform.
And how were those clocks synchronised? The mechanism chosen contains the assumptions you are trying to hide by "not employing an assistant" and "not trusting Einstein".
 
  • #67
Ibix said:
And how were those clocks synchronised? The mechanism chosen contains the assumptions you are trying to hide by "not employing an assistant" and "not trusting Einstein".

In the rest frame of platform we synchronize clock by Einstein, admitting that velocity of light in all direction is the same. Space is isotropic, nothing surprising.
 
  • #68
Battlemage! said:
Suggestion: People should stop using the word "see" in this thread unless they mean visually. I think "measure" or "calculate" would be the better word for considering time dilation.
"Seeing" in special relativity means comparison of your clock with another clock in immediate vicinity, just in front of you, nothing else. Not turning you head up and down, left and right and observing distant material bodies.
Well, excuse me, we can also make pictures and measure frequency. But there are very important details in this case,
 
  • #69
Bartolomeo said:
In the rest frame of platform we synchronize clock by Einstein, admitting that velocity of light in all direction is the same. Space is isotropic, nothing surprising.

But not in the frame of the train?
 
  • #70
Bartolomeo said:
In the rest frame of platform we synchronize clock by Einstein, admitting that velocity of light in all direction is the same. Space is isotropic, nothing surprising.
Then a lightspeed measurement you make will not be isotropic. You can do that if you want, but you are just making life more difficult for yourself - throwing away symmetries that can simplify maths instead of using them.
Bartolomeo said:
"Seeing" in special relativity means comparison of your clock with another clock in immediate vicinity, just in front of you, nothing else. Not turning you head up and down, left and right and observing distant material bodies.
Well, excuse me, we can also make pictures and measure frequency. But there are very important details in this case,
That is not the common usage, at least not on this forum. It is used in the precise sense of the receipt of light signals by an observer, and sometimes in the sloppier sense of "what Minkowski diagram would someone draw".
 

Similar threads

Replies
14
Views
522
Replies
58
Views
3K
Replies
18
Views
170
Replies
46
Views
2K
Replies
16
Views
1K
Replies
17
Views
2K
Replies
4
Views
1K
Replies
1
Views
1K
Back
Top