Some questions about time dilation (muon etc.)

Main Question or Discussion Point

I have some questions about time dilation I not really understand to come further (and I find it all very interesting).

1) I understand that the situation between A (standing still) and (moving) B is SRT symmetric, so if they compare clocks they both see the same time. In fact there is no time dilation in this situation to messure (you can not suppose if you are standing still, that your clock is going slower because somebody else is going to move compared with you, let's say an astronaut in space) ? Does this mean that a time is measured in this case included a time dilation (and same of course) ?

2) Only if forces are used, a time dilation is to measure ?

3) But why is a Muon lifetime to measure ? (let's say his time is always 4 seconds if standing still (A), if moving (B) his 4 seconds takes 6 seconds for (A), so we see on our clock 6 seconds, if the Muon could show a clock it should show 4 seconds, where is now the symmetry)

4) Some professor in the SRT says, the most time dilation (A or B) is for whom travels the longest worldline (path in a time space diagram). But it is always symmetric ?

5) Can you express time with light waves between two points in space e.g. point 1 is our reference point Earth and point 2 has a constant speed going into space ?

Related Special and General Relativity News on Phys.org
Simon Bridge
Homework Helper
1. moving clocks run slow - you always see yourself as stationary, so everyone elses clock runs slow. So if we are moving at c/2 with respect to each other, and I look at your clock, I see it tick off one second each time mine ticks off 1.15 seconds. So your clock is going slow. However - when you look at my clock, you see the same thing.

2. Nope.

3. The "muons" (per your example) clock ticks off 4 seconds in the time it takes our clock to tick off 6 seconds. The muon sees the same thing back.

5. You can use light waves as a clock ... but there is no way to make a clock that is the same for all observers.

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1. moving clocks run slow - you always see yourself as stationary, so everyone elses clock runs slow. So if we are moving at c/2 with respect to each other, and I look at your clock, I see it tick off one second each time mine ticks off 1.15 seconds. So your clock is going slow. However - when you look at my clock, you see the same thing.

2. Nope.

3. The "muons" (per your example) clock ticks off 4 seconds in the time it takes our clock to tick off 6 seconds. The muon sees the same thing back.

5. You can use light waves as a clock ... but there is no way to make a clock that is the same for all observers.
Thanks Simon for the answers (also for the mass question, I want to be sure, some books are not always clear). You will see that I still don't understand the symmetry.

1) I hope I understand this once, not yet So you say person (A) standing still see 1.15 seconds on his clock and moving person (B) 1.00 seconds, ok time dilation (.15 seconds). They are moving and can't see the other clock ? When they come together, the clocks are the same, what is proofed now for (A) and (B) ?

2) Nope = no I guess, but the Twin's Paradox is based on forces, the traveller come's back and is younger because forces are used (acceleration), otherwise the clocks were the same again ?

3) Still difficult (you should expect that things would be clear in books and internet, not for me in this case). So it's a fact that we see when standing still 4 seconds on our clock for the muon (not moving and until it disappears ), and when the muon is moving we see 6 seconds on our clock (until it disappears), so now we measure a real time dilation of 2 seconds for the muon ? His clock shows 4 seconds (his lifetime of always 4 seconds, by example) .. I still don't understand the symmetry .. what exactly should see the muon ?

4) See 2) ?

5) But you can say (by agreement), all light clocks made in (A)), the time is here (A) x and (B) x+y on the other place with a calculation when you know speed V and the one-time meassured distance to (B) and seen in 1 direction (off A), based on the light speed (distance / time)?

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Simon Bridge
Homework Helper
OK: back to 1.
We imagine that each observer can see each other's clocks at all times during the motion - and they compensate appropriately for the time-lag it takes light to reach them from wherever the other person is at that time.

This is just an engineering problem in the design of the experiment and does not contribute to the time dilation measured.

In the video I gave you (do watch it) the example setup has three clocks: one moving with respect to the other two which are stationary with respect to each other, and show the same time. The moving clock starts next to the first stationary clock and their times are compared. When it reaches the second stationary clock the times are compared again.

2 (and 4) Nearly right - in the twin's paradox, the accelerating reference frame breaks the symmetry between the twins. You do not need an acceleration to get a time dilation.

Consider: the twin's Alice and Beth are identical. Alice goes on a long near-light-speed journey and returns younger than Beth. Beth feels this is fine because of time-dilation. But Alice will have a problem with this: from her point of view, she saw Beth go off on a near-light-speed journey so by the same math it is Beth who should be younger. So what happened? How did the physics come to favor Alice over Beth?

3. I don't understand what you expect to be different. The symmetry is that nobody can tell who is doing the moving.

5. Fine - but whose clock to we choose to be the reference clock? How do you choose it? There's no advantage to doing it this way.

Perhaps you'd benefit from a more exacting treatment:
http://www.physicsguy.com/ftl/html/FTL_part1.html
... this is quite accessible and explains the whole symmetry thing using geometry rather than algebra. There are four parts - read all of them. When you get back to me you should be able to draw space-time diagrams.

This is just an engineering problem in the design of the experiment and does not contribute to the time dilation measured.
Thanks Simon for your answers, I go to watch the video's but I understand already the time dilation and I know it must be symmetric, but I can't see that clearly in one simple example (it's always the one way time dilation in all examples on the internet, even on universities).

Can you give 1 simple example (with words only and a speed and some times) for persons with clocks, where the clocks are, and both persons thinks in this scenario included time being used for light waves to see their clocktimes (and what the times are what they see), that both see a same time dilation, because it's symmetric. I tried and tried, but I can't. Of course I can do it twice in one way (seen from one).

... but maybe you have to see it only from their rest frames, ok symmetric and that's enough already (both thinks they are moving with their own tests, so you can't say who is moving) ... but if you can give such example would be nice for perfect understanding ... or somebody else of course ...

Simon Bridge
Homework Helper
you have to see it only from their rest frames, ok symmetric and that's enough already (both thinks they are moving with their own tests, so you can't say who is moving)
That's correct.

The symmetry is that each observer sees themselves as stationary. They see everyone else as time dilated and length contracted.

The FTL articles - part 3 I think, covers several paradoxes and describes what each observer sees. Generally, people agree on the broad strokes of what happens but disagree about how it happened.

The muon experiment does consider the situation from the POV of the muons (which they call "mu mesons") as well - that's the bit where they point out that Mt Washington is much shorter as far as the muon in concerned.

I'm tired of spaceships - how about DC Comics: Justice League
The Flash zzzzipps past you and you time him over 100m.
You both have ultra-super clocks, capable of measuring very small times.

By your clock, it took the flash 1 microsecond to do 100m, so he was doing about a third lightspeed. Gamma is 1.06.

Your clock has a huge big dial that the Flash can see, and running in one direction while looking in another is something Superman is meaning to talk to him about. Meanwhile, you have a second clock which is updated from his wristwatch by wifi. A computer receives the wifi updates, factors out the time-delay by the distance to the Flash.

So he can watch your clock and you can watch his.

When he passes the 100m mark, his clock shows1/1.06=0.94mcs
Thing is, this is what he sees on your clock - so who is "right"? Mind you, by his reckoning, the 100m mark is wrong - he's only run 94.3m.

Puzzled, he slows down to talk to you about it ... what happens when he slows down?
What he sees is your clock suddenly starts speeding up - the microseconds just wizz by - by the time he's stopped, your clock has overtaken his.

And that's how you get a one-way time dilation from the symmetric case.

They have a better description.

It's weird and counter-intuitive and it takes a while to get used to it. If you don't get it right away, don't worry ... it takes everyone a long time. I didn't really get it till post-grad and I had to teach it :) I can still mess this up so I have to double-check everything even now. There are people on these forums who are better at this that I am so don't be surprised if one of them starts telling me off.

At that level there is a sadistic collection of mind-warping puzzles for the student that all the professors seem to know. At your level you get things like:

Booster Gold was tasked with getting a new quivver with a lid for the Green Arrow. But he didn't pay attention and got one that was slightly too short - so the arrows wouldn't fit. Superman and the Flash come to his aid: Superman thrown the arrows at the quivver so fast they are length-contracted, so they fit. The Flash closes the lid at the exact moment the arrows are in the quivver. Problem solved?

Lets say the quivver is 1% too short - so for 400mm arrows, the quivver is 396mm long.
How fast do the arrows go when they enter the quivver?
What is the energy the quivver has to absorb when the arrows hit?
But - what about the symetrical case: as far as the arrows are concerned, the quivver is the one that is moving - so it's length is contracted. The misfit will actually get bigger! So how do the arrows fit?

It helps if we imagine the quivver is the kind with a lid on both ends. The Flash holds both ends open. When he sees the arrows completely inside the tube, he closes both ends at the same time, then opens them (quick as a um flash), allowing the arrows through.

Captain Atom makes himself really small and rides along on the arrows. What does he see happen?

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The Flash zzzzipps past you and you time him over 100m.
You both have ultra-super clocks, capable of measuring very small times.

By your clock, it took the flash 1 microsecond to do 100m, so he was doing about a third lightspeed. Gamma is 1.06.

Your clock has a huge big dial that the Flash can see, and running in one direction while looking in another is something Superman is meaning to talk to him about. Meanwhile, you have a second clock which is updated from his wristwatch by wifi. A computer receives the wifi updates, factors out the time-delay by the distance to the Flash.

So he can watch your clock and you can watch his.

When he passes the 100m mark, his clock shows1/1.06=0.94mcs
Thing is, this is what he sees on your clock - so who is "right"? Mind you, by his reckoning, the 100m mark is wrong - he's only run 94.3m.

Puzzled, he slows down to talk to you about it ... what happens when he slows down?
What he sees is your clock suddenly starts speeding up - the microseconds just wizz by - by the time he's stopped, your clock has overtaken his.

And that's how you get a one-way time dilation from the symmetric case.

I understand the time of The Flash, but can you explain (and what time) The Flash sees on my clock ?

In real life for eg. satellites calculations (GPS etc.) both time dilations are used in calculations (for us and for the satellite itselves) ?

Simon Bridge
Homework Helper
From the flash's POV:
He is running at a pole in the ground that you have written "100m" on.
But, to him, the sign lies - the pole is only 94.3m away.
He runs watching your clock, since it is moving, he sees your seconds tick by slowly.
When he hits the pole, his watch says 0.94mcs - which is correct, he reasons, because he has not run 100m yet. He looks at your clock, it says 0.94/1.06=0.89mcs!
When he has run for 1mcs by his watch, he reckons he has done the 100m, and he looks at your clock and sees a time of 0.94mcs.
This is where he has his WTF moment and slows down to talk to you ... as he slows down, he sees you clock start to speed up. The exact effect depends on the acceleration in question ... but we've left special relativity behind here.

To understand it you need to go draw the space-time diagrams.

Basically - events that are simultaneous for one observer are not simultaneous for another. Your clock reading 1mcs is simultaneous with the flash passing your 100m marker only in your reference frame. In the Flash's reference frame, it comes later.

IRL relativity we calculate the time dilation that the observer of interest sees. So for GPS we want to know the dilation for satellite clock because we treat ourselves as at rest (we are the observer).

However - for very fine calculations, the surface of the Earth is an accelerating reference frame, which goes faster at the equator than at the poles. So we need General Relativity.

From the flash's POV:
Thanks Simon, I understand now, I go to read my books and if I have some questions after a while you see me again.