High School Time dilation problem question

[Herman Trivilino]

And the Earth would also see the muon flattened, if that means anything, its horizontal cross section is much smaller.

Right. But the length contraction of the muon is not relevant, only the length contraction of the height of Earth's atmosphere.

Likewise, the dilation of any elapsed proper time measurements taken with an Earth clock is not relevant, only dilation of elapsed proper time measurements taken with the muon's "clock".

Perhaps the author's statement could have been better written as "One observer uses time dilation, the other uses length contraction, but neither uses both (to calculate the relative velocity of the other)."

 

[IvicaPhysics]

I found a solution by looking at the formula for time dialation. And the I realized that they are experiencing less time tham me, not more. That pretty much solves the problem

 

[Bartolomeo]

John, Tony, Jack and Bob are allocated at certain distance from each other. Let's say 1000 miles. Each of them possesses a light clock. They synchronize clocks by Einstein technique. Now these clocks oscillate synchronously in John – Tony - Jack – Bob reference frame.

Herb possesses a light clock too. He moves in John – Tony - Jack – Bob reference frame. His clock oscillates slower in the John – Tony - Jack – Bob reference frame because "in his clock light moves by hypotenuse". Everything is all right.

Herb passes by John, then Tony, then Jack and finally Bob. He compares clock readings i.e. how many oscillations his own clock has already done and any clock in reference frame John – Tony - Jack – Bob.

Look at this diagram. https://en.wikipedia.org/wiki/Time_dilation#/media/File:Time_dilation02.gif

How many oscillations Herbs clock did during time of travel? How many any synchronized one?

Does Herb see dilation or acceleration of time in the reference frame John – Tony - Jack – Bob?

What he has to do, so as to see that any clock (for example John's) dilates? What clock rate will measure John in Herb's reference frame then?

 

[stevendaryl]

John, Tony, Jack and Bob are allocated at certain distance from each other. Let's say 1000 miles. Each of them possesses a light clock. They synchronize clocks by Einstein technique. Now these clocks oscillate synchronously in John – Tony - Jack – Bob reference frame.

Herb possesses a light clock too. He moves in John – Tony - Jack – Bob reference frame. His clock oscillates slower in the John – Tony - Jack – Bob reference frame because "in his clock light moves by hypotenuse". Everything is all right.

Herb passes by John, then Tony, then Jack and finally Bob. He compares clock readings i.e. how many oscillations his own clock has already done and any clock in reference frame John – Tony - Jack – Bob.

Look at this diagram. https://en.wikipedia.org/wiki/Time_dilation#/media/File:Time_dilation02.gif

How many oscillations Herbs clock did during time of travel? How many any synchronized one?

Does Herb see dilation or acceleration of time in the reference frame John – Tony - Jack – Bob?

I can't tell from your post whether you are asking questions because you want to know the answers, or whether you are using the "Socratic method" of teaching others by asking them questions. That's why I never really liked Socrates. He was always asking questions that he perfectly well knew the answers to, like a manipulative lawyer.

In this scenario, there are certain things that everyone agrees on, in both reference frames. Let t_{1,john} be the time on John's clock when Herb passes him. Let t_{1, herb} be the time on Herb's clock when he passes John. Let t_{2,bob} be the time on Bob's clock when Herb passes him. Let t_{2, herb} be the time on Herb's clock when he passes Bob. Then both frames agree on the following values:

1. The elapsed proper time, \delta \tau_{herb} = t_{2,herb} - t_{1,herb} on Herb's clock between the time he passes John's clock and the time he passes Bob's clock.
2. The elapsed coordinate time, \delta t = t_{2,bob} - t_{1,john} in the John, Tony, Jack, Bob coordinate system.

They all agree that \delta \tau_{herb} < \delta t. But the two frames differ in how they explain this discrepancy:

• In Bob's frame, it is explained by the fact that Bob's clock is not synchronized with John's clock; it's ahead by a certain amount. So the time difference \delta t is comparing apples to oranges: times on two different unsynchronized clocks.
• In the John/Tony/Jack/Bob frame, it is explained by the fact that Bob's clock is running slower.

 

[Bartolomeo]

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.

 

[Bartolomeo]

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.

 

[stevendaryl]

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.

 

[Bartolomeo]

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.

 

[stevendaryl]

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.)

 

[Bartolomeo]

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.

 

[Bartolomeo]

Whether an observer will see dilation or acceleration or the same clock rate purely depends on arbitrary choice of the reference frame.

 

[stevendaryl]

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:

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

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.

 

[stevendaryl]

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.

 

[Ibix]

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]

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.

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.

 

[Bartolomeo]

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,

 

[stevendaryl]

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.

 

[Bartolomeo]

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.

 

[Bartolomeo]

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.

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.

 

[Bartolomeo]

@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?

 

[Ibix]

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?

 

[stevendaryl]

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.

 

[Bartolomeo]

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

 

[Bartolomeo]

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.

 

[stevendaryl]

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.

 

[stevendaryl]

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.)

 

[Bartolomeo]

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?

 

[stevendaryl]

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.

 

[Bartolomeo]

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?

 

[stevendaryl]

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.