Muon experiment and SR (revisited)

[BurtJordaan]

Over the years, I have received a number of questions on whether the classical muon experiment in Earth's atmosphere, e.g. the the Frisch-Smith_experiment, demonstrate reciprocal time dilation or not. The problem seems to be that many books and articles state that "one observer sees time dilation, the other sees length contraction, but neither sees both".



This is just an artifact of the way that the atmospheric muon experiments have to be performed and then explained in the simplest possible way. Some explanations picture imaginary little clocks that are 'created' high in the atmosphere, and that move at relativistic speed down towards Earth. But this is not quite representative of the said muon experiment, which was a statistical count of the rate of muon detection (number per hour) at the altitude of Mount Washington and comparing them to the number detected at ground level in Cambridge. The figure above is about a slightly different scenario, but the principle is the same.

Since the average kinetic energy of the muons was also detected in the process, it was possible to calculate the speed of the muons relative to the detectors and hence deduce the relativistic time dilation that would account for the difference, as per the latter of the two reference given. There was no length contraction observable in the detector frame, simply because muons don't have a 'rest size'. If they were little clocks with physical rest-sizes, sure, the length contraction in the detector frame could have been observed.

In the incoming muon frame, nothing was actually observed, but the logical deduction is made that the altitude difference between the detector locations has been length contracted to allow the observed number of muons to survive until reaching the bottom detector, given their observed decay statistics when moving slowly. If there were hypothetical observers riding with the muons, they could have measured this length contraction directly. Likewise, they could have, through cunning experimental setups, observed that muons slow-moving in earth laboratories are actually time dilated in the hypothetical observer frame.

So, the confusing statement quoted above is an experimental limitation, not a physical one. Reciprocal time dilation and length contraction are both alive and well, unless you bring difference in spacetime profiles into the picture, like in the classical "twins-paradox". Actually, the muon experiments discussed here do have a degree of non-symmetry due to gravity and atmospheric resistance, but the influence is tiny and it is anyway compensated for in the actual experimental reports.

[ralfcis]

My confusion is about the definition of the start and end of a spacetime path which the muon example exacerbates for me.

1. Alice taking off from earth to deep space at .6c is an example of reciprocal time dilation wrt Bob on earth. Although there is acceleration from the start point, it is co-located with Bob so it is not the same thing as Alice decelerating to a stop wrt Bob at some distance away. Once news of the stop reaches Bob (either through a light signal or Alice's clock handoff to Charlie returning to earth, that would be a valid end of the spacetime path and permanent age difference between Bob and Alice could be established. This could not be established with Alice continuing into deep space.

2. If Alice was an alien that came from deep space and landed on earth, this would be the opposite of 1. No valid start but a valid end. If the alien sent out a signal indicating its age from a distance, would earth be able to establish the alien aged less from its signal start point or would it be simple reciprocal time dilation because there was no valid start to the spacetime path?

3. The constant relative velocity of the GPS example also has a valid start but no end to the spacetime path unless the GPS clock is brought down to earth or the earth clock brought into space. Without that, permanent age difference could not be established with the earth, it's only reciprocal time dilation.

4. The muon example has no valid start but since its tiny clock co-locates with the earth detector at the end, it has a valid end to the spacetime path. It differs from 2 because the space coordinate of its start is known whereas the alien's signal might not be a valid start. I don't know if that constitutes a valid start or if 2's signal to earth constitutes a valid start but isn't the co-location at the end validate permanent age difference. From both the muon's and earth perspective, the muon has aged farther than it should have if relativistic effects hadn't helped it. Both perspectives agree whereas there is no agreement in reciprocal time dilation.

So my question is, wouldn't the muon example be closer to the GPS clock being brought down to earth example? This would mean it's a twin paradox age difference scenario and not just reciprocal time dilation.

[ralfcis]

I think I now see where I've been making a grave mistake. I think a valid start and a valid end can both be characterized as co-location (0 distance) at any velocity or 0 velocity at any distance (minus the time delay for info to propagate between the participants that they are at 0 relative velocity.

So the twin paradox example of Alice making a round trip is actually 2 spacetime paths one right after the other. My grave mistake was that the signal sent by Alice if she stopped was the end of 1 spacetime path but if she turned around, that signal was also the start of the 2nd spacetime path which ended at co-location. I was looking for the final answer too early. Ok, problem solved, back to personal theories.

[BurtJordaan]

Ralf, I'm glad to see that the muon experiment somehow triggered the correct conclusion from your side.

Maybe, if you get bogged down again, return here and let the muons help you out. ;)

[ralfcis]

I still have some residual confusion:

1. If Alice leaves Bob and then stops momentarily and sends a signal then continues, that's a valid start and stop so age difference can be established until the stop? Or is the stop somehow too short to establish age difference and this is still an example of reciprocal time dilation?

2. If alien Alice comes from deep space, all she has to do is signal Bob from a known distance what her age is and that's a valid start? She doesn't have to stop to send the signal like she did in 1?

3. Is the muon example like a GPS clock coming back down to earth making it a twin paradox example or is it like Alice coming in from deep space without a start signal making it a reciprocal time dilation example?

4. When the muon is created at speed, is that considered a transition from 0 relative velocity with earth? Is the speed of no thing, nothing (0) even though the particle that created the muon had a speed?

[BurtJordaan]

I still have some residual confusion ...

Why am I not surprised? Ralfitivity seems to be based on something like "what are the valid rules for determining differential aging?" We have discussed it before: "rules" are not the way to go, because there are a zillion scenarios possible and each may need a different subset of the relativity principles to be applied.

Your question 1: The "stop" must be long enough for two-way signals to be exchanged before a theory independent assessment of who has aged less can be made. A momentary "stop" retains the reciprocal time dilation.

2: It is all reciprocal, for the same reason.

3. The muon experiment represents neither. It is a specific scenario observed in a specific way. I think the OP treats much of what there is to say.

4. AFAIK, the general view is that particles created in collisions are 'born' with a specific velocity, depending on the portion of the collision energy that goes into it. Velocity and energy are obviously reference frame dependent.

[ralfcis]

Yes that unmentionable theory is as you said but it can't have final answers that differ from relativity. If it does, then I have not understood relativity correctly and hence my questions. However, I'm not too keen on ad hoc scenario dependent rules because that would require a higher understanding on what rules to apply when.

1. This STD is of Alice's age difference stopping for a year and then continuing compared to no age difference if she just kept going. It takes 3 yrs after the jump back to .6c for this to be established but the STD does show the shorter the stop, the smaller the established age difference.

(STD would not download so I will add it in next post)

2. So this must be the same for alien Alice coming in. I was wrong in saying a signal from a distance would set a valid start to the age difference accumulation. The amount of time she stopped, not the amount of time she sped in after the stop is where the age difference happens, the rest is reciprocal time dilation.

3. The muon example can't be pigeon-holed because it compares Mt Washington to Cambridge and not the edge of space to Cambridge?

4. Since there's no 2-way communication possible with the muon to establish it was stopped for the required amount of time before creation, it can't be an example of age difference just like the alien Alice scenario where no stop time can be established.

Ok, it's all clear now. Thanks

[ralfcis]

Something must be temporarily wrong with the uploader.

[ralfcis]

I still can't upload my STD but here's an interesting example based on what I learned here:

Alice leaves earth at .6c, Charlie is coming in from deep space at .6c. Neither will have an age difference wrt earth or each other at any time. At the point they cross, 3ly from earth, and handoff clock info, there is a black hole that they can either use to slingshot around or just keep going. Earth doesn't know if Charlie or Alice will be landing on earth. If it's Charlie, his clock will have aged 2 yrs less than the earth clock while he would not have aged less at all. If it's Alice, her and her clock will both have aged 2 yrs less than the earth clock.

[ralfcis]

Now back again to my age old question:

If Charlie had a very fast ship capable of going close to c. The time Alice handed off to him when they passed was 4. When he lands on earth at 8, it would have taken him 3 yrs to get there but the time info that Alice was 4 had barely moved at all on his clock. Bob is 8 but he knows the delay of the info was 3 yrs so he can calculate he was 5 when Alice was 4.

This result is not age difference because Alice had never changed her relative velocity to Bob so she is 5 and Bob is 5. It wouldn't even be a 1 yr age difference if it had been Alice landing instead of Charlie. I believe, although I don't know how to prove it, that if it had been Alice landing after returning at c, she would have been 4 and Bob 8 which means the answer is she aged 4 yrs less than Bob. Jorrie keeps telling me the false result of Bob=5 and Alice=4 is coordinate time. I'm afraid i don't know what that means. What does coordinate time tell us if it has nothing to do with age difference? Is it just a manifestation of Einstein's clock sync method?

[BurtJordaan]

Alice leaves earth at .6c, Charlie is coming in from deep space at .6c. Neither will have an age difference wrt earth or each other at any time. At the point they cross, 3ly from earth, and handoff clock info, there is a black hole that they can either use to slingshot around or just keep going.

I guess that what you meant to say is that neither can observe any aging difference between themselves and earth. In your scenario, Alice and Bob can potentially observe an aging difference between them, if she returns to earth, but never if she just keeps going. Bob and Charlie can never observe any aging difference between them.

I think we have been through this dozens of times! And forget about the black hole - it complicates matters severely and will just increase your confusion.

PS: Your follow-on question illustrates gross misunderstanding of SR, something that I have failed to correct in more than a decade of trying...

Maybe some else might try?

[ralfcis]

Yes it does. Ok I'll fix it. 2 coordinate systems on 1 STD. The values at a point change depending on which coordinate system you use. If you travel through space like Alice's system you are travelling less through time. So Bob's time in his cartesian coordinates is 5 and Alice's is 4 because she is travelling through space and Bob is only travelling through time.

A constant relative velocity yields reciprocal time values when seen from each perspective. Either participant can be the cartesian coordinates so these time values must be reciprocal and independent on how you draw the relative velocity.

Age difference must be made with either no separation of clocks at any velocity or at 0 velocity at any separation taking into account the light delay to overcome the separation in order to arrive at a final value. These criteria are not met so long as Alice is engaged in relative velocity with Bob. She either has to return to Bob or stop relative to Bob and wait for the news of her stop reaches Bob.

Sorry, I'm going to paste this on my head so I don't forget.

[BurtJordaan]

Age difference must be made with either no separation of clocks at any velocity or at 0 velocity at any separation taking into account the light delay to overcome the separation in order to arrive at a final value.

More precisely: "Aging difference must be observed with either no separation of clocks at any velocity or at 0 velocity at any separation, taking into account the light delay to overcome the separation in order to arrive at a final value".

This essentially makes it a two-way observation, like the twin 'paradox' was intended to be.

But, the emphasized statement attempts to make a 'rule' again, which will work until someone comes up with a scenario where it does not. Then confusion reigns again! That's why I keep on saying: solve each scenario on its own merits, just using the fundamentals of the theory of relativity.

[ralfcis]

Ok thanks for allowing me to visit. I'll go back to personal theories and correct ralfativity.