# B Time Dilation Derivation

#### jbriggs444

Homework Helper
This is your version of the "third postulate" of special relativity I was talking about. I agree that this postulate implies the kinematical character of boosts and ultimately the 4D geometry of space-time. However, my point is that one can imagine a world where this "consistency requirement" does not hold, but all other laws of physics are still valid.
The requirement that a single event map to a single coordinate and vice versa is a rule for constructing a valid manifold. As such, it is not a property of the model, not of the laws of physics.

There is no problem imagining coordinate systems which are not one to one and onto (just look at any road map with an inset). But I have great difficulty seeing how such could be a property of a hypothetical universe.

#### meopemuk

This raises no consistency issues of the kind raised by clocks ticking both at the same rate and different rates does. Sure you can change "now" from being t=0 to t=1 to t=-1, but if you work out any direct observable consequences to that switch you will find there are none. There is no way to set up an experiment such that a person can say "a bomb has gone off, now it hasn't, now it has again". If clocks tick at different rates then there can be direct observable consequences that vary when you switch frames - and you allow this kind of exploded-not-exploded-exploded-again behaviour.
There is a slight difference between dynamical time translations and dynamical boosts. In the case of time translations, you cannot change the time parameter of your frame at will: you are stuck with the flow of time. So you see the bomb only in one sequence; not-exploded -> exploded. In the case of boosts, you can jump between frames with different velocities and see the bomb as exploded in one frame and not exploded in the other one.

Eugene.

#### PeroK

Homework Helper
Gold Member
2018 Award
There is a slight difference between dynamical time translations and dynamical boosts. In the case of time translations, you cannot change the time parameter of your frame at will: you are stuck with the flow of time. So you see the bomb only in one sequence; not-exploded -> exploded. In the case of boosts, you can jump between frames with different velocities and see the bomb as exploded in one frame and not exploded in the other one.

Eugene.
I'm not going to argue whether it's possible to do physics this way, but we have a "B" level thread here on time dilation. Discussion on the nature of physical consistency is off topic for this thread.

#### Ibix

However, my point is that one can imagine a world where this "consistency requirement" does not hold, but all other laws of physics are still valid.
In that case I'd be very interested in your view on #23. Does the bomb explode (leaving one frame with no explanation for why), not explode (leaving the other frame with no explanation for why), or both (leaving it possible to change a bomb you have observed to explode into an unexploded one at will).
There is a slight difference between dynamical time translations and dynamical boosts. In the case of time translations, you cannot change the time parameter of your frame at will: you are stuck with the flow of time. So you see the bomb only in one sequence; not-exploded -> exploded. In the case of boosts, you can jump between frames with different velocities and see the bomb as exploded in one frame and not exploded in the other one.
You miss the point. The problem with your idea is that a bomb that you have observed to have exploded can be turned into a bomb that you can observe to have not exploded just by changing frames - a mere choice. No amount of time translation (just resetting your watch) nor boosting (just resetting and rate-adjusting all your clocks [edit: and mucking around with your rulers]) can do this. The fact that I cannot rewrite history just by wishing it isn't anything to do with kinematical character or not. It's a fundamental requirement for scientific method to work at all. Which is why I keep challenging you when you say you can imagine a world where this does not hold but there are physical laws.

I mean - just imagine that my analysis shows that the bomb did not go off, but your analysis shows that it went off and was powerful enough to kill me. Can I phone you up and gloat about my survival? Or not?

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#### stevendaryl

Staff Emeritus
This is your version of the "third postulate" of special relativity I was talking about. I agree that this postulate implies the kinematical character of boosts and ultimately the 4D geometry of space-time. However, my point is that one can imagine a world where this "consistency requirement" does not hold, but all other laws of physics are still valid.

Eugene.
It's hard for me to imagine how the laws of physics could be the same in all other respects. According to one observer, Alice is at a particular table at the same time that a chocolate doughnut is there, and she eats it. According to a different observer, she was not there at the same time the doughnut was, so she had no opportunity to eat it. That sounds like an out-and-out contradiction. Maybe you can resolve it by proposing multiple alternative realities as in a science fiction story, but it certainly is not physics as we know it.

#### Mister T

Gold Member
If you insist that clocks of different design are always in sync for all observers, you'll have to introduce this statement as a separate (third) postulate of special relativity
The same can be said of a large number of pieces of information, whether you call them assumptions or postulates. It is not true, however, that history needs to be rewritten to accommodate them. When the consequences of a theory don't match observation the theory gets modified or replaced. Does the modification you suggest have any consequences that can be measured experimentally, even in principle?

Einstein's theory assumes far more than just the two postulates he used in 1905. Everybody knew that then as well as now. Because it's true of all theories. One hundred fourteen years later we are not going to add a third postulate to the theory.

Clocks measure time and events are invariant. That is part of the physics of special relativity.

#### A.T.

you can jump between frames with different velocities and see the bomb as exploded in one frame and not exploded in the other one.
It's not about whether the bomb has already exploded at some time. It's about whether it will ever explode at all.

For example, If the trigger is deactivated after one of the two clocks reaches a certain timeout, the bomb can never explode according to it's rest frame. But it must explode before the timeout, according to any inertial frame where the clocks were ticking at different rates. This is the contradiction, which means there are such inertial frames.

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#### meopemuk

Does the modification you suggest have any consequences that can be measured experimentally, even in principle?
Yes.

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Measuring propagation speed of Coulomb fields", Eur. Phys. J. C 75 (2015), 137.
arXiv:gr-qc/1211.2913v2

Eugene.

#### pervect

Staff Emeritus
Yes.

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Measuring propagation speed of Coulomb fields", Eur. Phys. J. C 75 (2015), 137.
arXiv:gr-qc/1211.2913v2

Eugene.
The note by Gitman, Shabad, and Shishemarey, published in response to this paper, i.e. https://link.springer.com/article/10.1140/epjc/s10052-016-4108-7 , suggests that Feynman's formulation (which I'm not familiar with), doesn't give any different result that the than using the Lienard-Wiechart potentials. Which is what I'd expect, otherwise Feynamn's formulation would not be classical electromagnetism, but a new theory.

Gitman et al said:
In connection with the discussion and the measurements fulfilled in Ref. (Eur Phys J C 75:137, 2015), the full identity is demonstrated between the Feynman formula for the field of a moving charge and the Liénard-Wiechert potentials.

#### meopemuk

The note by Gitman, Shabad, and Shishemarey, published in response to this paper, i.e. https://link.springer.com/article/10.1140/epjc/s10052-016-4108-7
To be fair to the authors I should mention that they have published a response to their critics:

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Why the interpretation of Measuring propagation speed of Coulomb fields'' stands",
Eur. Phys. J. C, 77 (2017), 75. arXiv:gr-qc/1611.06935v1

Eugene.

#### PeroK

Homework Helper
Gold Member
2018 Award
To be fair to the authors I should mention that they have published a response to their critics:

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Why the interpretation of Measuring propagation speed of Coulomb fields'' stands",
Eur. Phys. J. C, 77 (2017), 75. arXiv:gr-qc/1611.06935v1

Eugene.
In any case, I would say that a "B" level thread has been well and truly hi-jacked!

#### benorin

Homework Helper
So then the clocks are separated along an axis perpendicular to the motion, right? Boom! Now what?

#### Ibix

So then the clocks are separated along an axis perpendicular to the motion, right? Boom! Now what?
You need to include the effects of the boost on the communication between clocks. Since the clocks are moving, whatever signal says "tick completed" has a different distance to travel and possibly a different velocity compared to measurements when the clocks are at rest. These differences will always result in the "tick completed" signal arriving at a given location simultaneously in all frames, or non-simultaneously in all frames. And since the bomb can only be in one position, whether the "tick completed" signals are received at its position at the same time is the only thing that matters.

Avoiding this unnecessary complication was why I proposed a thought experiment with colocated clocks.

#### PeroK

Homework Helper
Gold Member
2018 Award
So then the clocks are separated along an axis perpendicular to the motion, right? Boom! Now what?
In that case, the clocks are equidistant from the bomb in both frames. I.e. equidistant in the rest frame; and equidistant in the moving frame.

It doesn't need to be a bomb, it just needs to be a device that confirms that communications (ticks) from each clock arrive at the same time.

If the clocks were running at different rates in the moving frame, then the communication with the central device would get out of synch, which would be a physical fact at that central location. This is then the element of "reality". Because the central device is a single device at a single location, you can't have two realities: two communications arrive at the same time or they do not and this cannot be dependent on whether the device is seen to be moving or not.

Dramatically, you could use the device to trigger a bomb and then the reality becomes whether the bomb goes off or not.

"Time Dilation Derivation"

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