High School Time dilation problem question

[Ibix]

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.

 

[Bartolomeo]

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.

 

[Ibix]

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.

 

[stevendaryl]

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 e_0)
  
• At some time after e_0, Herb's clock shows time 12:30 (Call this event e_1)
• At some time after e_0, John's clock shows time 12:30 (Call this event e_2)

So to determine whose clock is running slow or fast, you need to know this: Did e_1 take place before or after e_2? How do you answer that question? You have to rely on a convention, or assumption.

 

[Battlemage!]

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.

 

[Ibix]

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".

 

[Bartolomeo]

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.

 

[Bartolomeo]

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,

 

[stevendaryl]

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?

 

[Ibix]

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.

"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".

 

[stevendaryl]

"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,

You cannot determine whether Herb's clock is running faster or slower than John's clock by only looking at nearby clocks.

 

[Battlemage!]

"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,

Two clocks separated by large distances cannot be compared in the way you describe, but you can certainly look at a clock far away. What will your eyes tell you? Is this the same as what the equations tell you?

If you don't calculate for the finite speed of light then what you see with your eyes will be incorrect, or at least ambiguous.

 

[Bartolomeo]

Two clocks separated by large distances cannot be compared in the way you describe, but you can certainly look at a clock far away. What will your eyes tell you? Is this the same as what the equations tell you?

If you don't calculate for the finite speed of light then what you see with your eyes will be incorrect, or at least ambiguous.

Yes! That's why observer takes readings in immediate vicinity. Observer in SR is not a "physical person". It is the whole reference frame, which is filled with many people and each of them has a clock. They synchronize clocks by light signals and make judgement then. John is certain point of reference frame K. John has a clock. Bill is far away. Bill has a clock too. John and Bill are the relativistic observer together. They synchronize clocks by light. Jim passes by John first and compares his clock with Johns at this moment in immediate vicinity. Then Jim passes by Bill. They again compare clocks in immediate vicinity. John and Bill together make conclusion, that Jim's clock runs slower.

https://en.wikipedia.org/wiki/Observer_(special_relativity)
https://arxiv.org/abs/physics/0512013

 

[Bartolomeo]

You cannot determine whether Herb's clock is running faster or slower than John's clock by only looking at nearby clocks.

It is the core of special relativity. Einstein's work of 1905. Observer introduces a reference frame and allocates AT LEAST two clocks in different spatial positions. AT LEAST two clocks.
Observer in SR is not a "physical person". It is the whole reference frame, which is filled with many people and each of them has a clock. They synchronize clocks by light signals and make judgement then. John is certain point of reference frame K. John has a clock. Bill is far away. Bill has a clock too. John and Bill are the relativistic observer together. They synchronize clocks by light. Jim passes by John first and compares his clock with Johns at this moment in immediate vicinity. Then Jim passes by Bill. They again compare clocks in immediate vicinity. John and Bill together make conclusion, that Jim's clock runs slower.

https://en.wikipedia.org/wiki/Observer_(special_relativity)
https://arxiv.org/abs/physics/0512013

 

[Battlemage!]

Yes! That's why observer takes readings in immediate vicinity. Observer in SR is not a "physical person". It is the whole reference frame, which is filled with many people and each of them has a clock. They synchronize clocks by light signals and make judgement then. John is certain point of reference frame K. John has a clock. Bill is far away. Bill has a clock too. John and Bill are the relativistic observer together. They synchronize clocks by light. Jim passes by John first and compares his clock with Johns at this moment in immediate vicinity. Then Jim passes by Bill. They again compare clocks in immediate vicinity. John and Bill together make conclusion, that Jim's clock runs slower.

https://en.wikipedia.org/wiki/Observer_(special_relativity)
https://arxiv.org/abs/physics/0512013

This doesn't really address the point that what you see with your eyes isn't necessarily the same thing as what is going on locally at what you are looking at, due to the finite speed of light. The Doppler effect needs to be taken into account if you're going by what you see.

 

[Battlemage!]

It is the core of special relativity. Einstein's work of 1905. Observer introduces a reference frame and allocates AT LEAST two clocks in different spatial positions. AT LEAST two clocks.
Observer in SR is not a "physical person". It is the whole reference frame, which is filled with many people and each of them has a clock. They synchronize clocks by light signals and make judgement then. John is certain point of reference frame K. John has a clock. Bill is far away. Bill has a clock too. John and Bill are the relativistic observer together. They synchronize clocks by light. Jim passes by John first and compares his clock with Johns at this moment in immediate vicinity. Then Jim passes by Bill. They again compare clocks in immediate vicinity. John and Bill together make conclusion, that Jim's clock runs slower.

https://en.wikipedia.org/wiki/Observer_(special_relativity)
https://arxiv.org/abs/physics/0512013

What does Jim conclude as he passes both? (or rather, as they pass him, given that he is justified in claiming he is at rest)

 

[Bartolomeo]

This doesn't really address the point that what you see with your eyes isn't necessarily the same thing as what is going on locally at what you are looking at, due to the finite speed of light. The Doppler effect needs to be taken into account if you're going by what you see.

"To see by eyes" can be interpreted in various ways. A scientist has tools. Rods, clocks, spectrometers, photo cameras. You can do no measurements without introducing a reference frame. Reference frame is synchronized clocks in different spatial positions.

 

[Bartolomeo]

What does Jim conclude as he passes both? (or rather, as they pass him, given that he is justified in claiming he is at rest)

That depends on how Jim will measure. He can introduce his own reference frame. He hires Jack and gives him a clock. Jack goes into another spatial position. He sends a beam of light to Jack. They adjust clocks , taking into account that speed of light was c. Now their clocks show the same time.
Tony and Bill fly towards them from the deep space. They chase each other. They have clocks too. Tony and Bill synchronize their clocks too with the same assumption.
Tony passes by Jack first and compare clocks. Let's their clocks show 12 o'clock each. Then Tony passes by Jim. Tony's clock show 3 PM and Jack's 7 PM o' clock.
Jim and Jack think, that Tony's clock runs slower. Tony thinks, that Jim's and Jack's clocks run faster.

Now upside down.

Jim passes by Tony. They compare clocks. For example, their clocks shows 12 each. Then Jim passes by Bill. Jim's clock shows 3 PM and Bill's 7 PM.
Tony and Bill together think, that Jim's clock runs slower. Jim thinks, that Tony's and Bill's clocks run faster.
https://en.wikipedia.org/wiki/Time_dilation#/media/File:Time_dilation02.gif

 

[Ibix]

Jim thinks, that Tony's and Bill's clocks run faster.

Only if Jim assumes Bill and Tony's clocks are synchronised. He has no reason to believe they are, though, since you seem to regard looking at anything not right in front of you as forbidden.

If he doesn't look, he's guessing. If he does look he's assuming. But what I do not understand is why you would choose to make anything other than an assumption of isotropy. You seem to pick one frame and let them assume isotropy, then force every other frame (edit: or rather, everyone not at rest in your chosen frame) to make a more complicated assumption. Why? Just to make things more complex?

 

[Bartolomeo]

Only if Jim assumes Bill and Tony's clocks are synchronised. He has no reason to believe they are, though, since you seem to regard looking at anything not right in front of you as forbidden.

If he doesn't look, he's guessing. If he does look he's assuming. But what I do not understand is why you would choose to make anything other than an assumption of isotropy. You seem to pick one frame and let them assume isotropy, then force every other frame to make a more complicated assumption. Why? Just to make things more complex?

Well, Jim is too stupid to assume something. He is very plain guy. He compares clocks and makes his own conclusions. I do not like or dislike certain synchronization procedures. I am a bit suspicious. Just in case. But I know, that another measuring technique of time dilation (transverse Doppler Shift) does not make any assumptions. And observations are not reciprocal. And that makes me even more suspicious.
Either Doppler effect and photo camera is rubbish or Einstein clock synchronization for every observer.

 

[Ibix]

Well, Jim is too stupid to assume something. He is very plain guy. He compares clocks and makes his own conclusions.

...thereby assuming that Bill and Tony's clocks are synchronised.

I do not like or dislike certain synchronization procedures. I am a bit suspicious. Just in case. But I know, that another measuring technique of time dilation (transverse Doppler Shift) does not make any assumptions. And observations are not reciprocal. And that makes me even more suspicious.

They aren't expected to be reciprocal in the Joe/alien example we discussed in the other thread because the situation you are examining is not symmetric betwen Joe and the aliens. As you yourself pointed out. If you reverse the experiment completely the results are reciprocal, as noted in the Wikipedia page you linked to in that thread.

 

[Bartolomeo]

...thereby assuming that Bill and Tony's clocks are synchronised.

They aren't expected to be reciprocal in the Joe/alien example we discussed in the other thread because the situation you are examining is not symmetric betwen Joe and the aliens.

Exactly. In no way they can be symmetrical. In no way. Green photon turns blue at the moving mirror. Not red. In no way red, whatever you do. Mirror dilates itself and concludes that source oscillates faster. Joe sees redshift (dilation), Aliens see blueshift (acceleration of time). Aliens see redshift (dilation), Joe sees redshift (acceleration of time). Joe makes picture of moving Aliens and see contraction. Aliens make picture of Joe and see stretching, since their photo - film contracts.

 

[Ibix]

Aliens see redshift (dilation), Joe sees redshift (acceleration of time). Joe makes picture of moving Aliens and see contraction. Aliens make picture of Joe and see stretching, since their photo - film contracts.

Not if they use the same experimental procedure. If they use different procedures it's hardly surprising that the results are different.

 

[Bartolomeo]

Not if they use the same experimental procedure. If they use different procedures it's hardly surprising that the results are different.

There are no procedures. What kind of procedures? Joe releases green photon straight up. The aliens have a mirror. Photon reflects and goes back to Joe "from the top". It comes back green again. What color was at mirror? Red? Blue! Only blue, newer red. For Joe the mirror is moving source, and photon which comes back to Joe from moving source redshifts, since moving source dilates. Blue and only blue! It is so simple. Never red!

 

[Ibix]

There are no procedures. What kind of procedures? Joe releases green photon straight up. The aliens have a mirror. Photon reflects and goes back to Joe "from the top". It comes back green again. What color was at mirror? Red? Blue! Only blue, newer red. For Joe the mirror is moving source, and photon which comes back to Joe from moving source redshifts, since moving source dilates. Blue and only blue! It is so simple. Never red!

If the aliens fire a green photon straight down so that it strikes Joe then bounces back you will find the exact same result with the roles reversed. They can't do it at the same time as Joe is doing his experiment because Joe is not in position to do so in their frame at that time - so they would be following a different experimental procedure if they try.

 

[Bartolomeo]

If the aliens fire a green photon straight down so that it strikes Joe then bounces back you will find the exact same result with the roles reversed. They can't do it at the same time as Joe is doing his experiment because Joe is not in position to do so in their frame at that time - so they would be following a different experimental procedure if they try.

Yes, but they have to take physical action and change direction of their tube. They can't look with one eye in two different direction at the same moment. But, so what? Yes, the Aliens will release green photon and it will be blue for Joe, Joe reflects it back and the Aliens see it red again. Now the photon is blue at Joe. Now Joe is in motion and his clock dilates. That what I told all this time. Who ascribes himself state of rest, sees dilation. Who ascribes himself state of motion, sees acceleration since he dilates himself.
But they can't ascribe themselves equal states of proper rest or motion.

 

[jbriggs444]

But they can't ascribe themselves equal states of proper rest or motion

This is unclear. What cannot be equal to what? And what is "proper rest".

Certainly two observers can each maintain that they are at rest and that their peer is not.

 

[Bartolomeo]

This is unclear. What cannot be equal to what? And what is "proper rest".

Certainly two observers can each maintain that they are at rest and that their peer is not.

Proper rest is a state, when you consider yourself as being at rest and interpret observations from the point of view observer at rest. Imagine that you stay at certain point at axis y, at point Y. You posses a long thin tube. You ascribe yourself a state of proper rest. You want to measure frequency of moving source - green monochromatic lamp. You turn the tube into the origin. You stay and wait. The lamp moves along x in negative direction. At certain moment you see a short flash, when the lamp passes the origin and a photon goes through you tube. The flash will be red in color due to Transverse Doppler Effect.
Then you ascribe yourself small velocity. You repeat the experiment but do nothing special in this case - just turn the tube a bit into front. Why? Because if photon flies along y-axis up, you approach the point of "intersection from the left" and you have to take aberration into account. You tilt tube so as the photon would be able to pass through it. You see a flash again. The photon will be a bit less red, than it was in the first experiment.
Then you repeat the experiment again, but ascribe yourself even larger proper velocity. You think that since your velocity increased, you tilt you tube even further an see that color of photon moved into blue range of spectrum.
In fact you do nothing, just turn you tube further an further into front and interpret every observation as transverse doppler effect, since photon according to you comes to you along y-axis and due aberration becomes more and more blue with each experiment.
So, ascribing yourself state of proper motion means that you simply turn your tube or gaze further and further into front.

If lamp emits dispersed light, you will always see it. But if the source emits narrow beam, the source will always have to adjust angle of emission at corresponding angle, so as the photon will go through your tube,
These angles are always tied with relativistic aberration formula. The more you tilt you tube into front, the less the source has to tilt his laser pointer back. At the moment, when these angles are the same, you will see no shift, neither dilation nor acceleration, because the source and you ascribe themselves equal velocities.
So, state of proper motion means, that you look into front but not straight down

 

[Ibix]

Yes, but they have to take physical action and change direction of their tube. They can't look with one eye in two different direction at the same moment. But, so what? Yes, the Aliens will release green photon and it will be blue for Joe, Joe reflects it back and the Aliens see it red again. Now the photon is blue at Joe. Now Joe is in motion and his clock dilates. That what I told all this time. Who ascribes himself state of rest, sees dilation. Who ascribes himself state of motion, sees acceleration since he dilates himself.
But they can't ascribe themselves equal states of proper rest or motion.

No. The result of Joe and the aliens isn't symmetrical because the circumstances aren't symmetrical. Joe fires the laser; the aliens do not. This is not the same as two people watching each other's clocks, which is a symmetrical situation and the results must be symmetrical, barring an absolute rest frame of some kind.

 

[jbriggs444]

Proper rest is a state, when you consider yourself as being at rest

So it's not a state at all. It's a decision about what reference frame to use.