# Thread: Length Contraction in the Muon Experiment

1. Hi pete,

Pete:

In Earth's frame, this stick will have a length of 2500m - But in Earth's frame, at the instant the muon is created the stick is not touching Earth - it's 7500m away. So, the 2500m is not a measure of the distance from Earth to the Muon at the instant of its creation.
This is the problem with using earth and muons. We are fixing the real creation height of the muon at 10000m in the earth frame. That's wonderful and all our assesments agree. 5000m above the surface in the muon frame, and 10000m to the muon in the earth frame. Excellent.

And it's why I think we are having semantic difficulties. The tacit assumption (actually the blatant assumption) has been that the muon is created, in reality, at 10000m in the earths frame. Toss that. We all agree on the analysis of this event, given that we KNOW the real creation altitude in the earths frame.

I want to say Ok, Forget the atmosphere. Forget the earth. A "particle" pops into existence above a planet moving at 0.866c. This particle measures the distance to the planet as 5000m. What does the particle calculate the planet must see for the distance to the particle? 2500m.

My argument is that the only way to know the true situation is to know the velocity histories of the two objects. If the "particle has always been in existence, and a planet pops into existence in the particles frame and accelerates instantly to 0.866c at 10000m, the particle will measure 10000m to the planet while the planet will see 5000m to the particle.

2. Originally Posted by Aer
This is why the atmosphere was ignored. However, if you wish to take the position that you cannot ignore the atmosphere, well - shit.
OK, let's ignore the atmosphere.

In the muon's frame, at the instant of its creation, the Earth is 5000m away.

Sticking out from Earth past the muon is a calibrated rod, marked with altitude in metres. It's moving with Earth, naturally enough.

At the instant the muon is created, what number is it passing on the Earth's rod?

Since the rod is length contracted by 2 in the muon's frame, and the other end of the rod is 5000m away, it must read 10000m.

3. We're really on different wavelength's here. And somebody's tuning knob is busted.

4. It's a good thing you are forcing the issue superluminal, because I gave up a long time ago and wished everyone all the best in what I percieved as blind explainations to this experiment.

5. Originally Posted by Aer
Nice of you to explain everything. It is all clear now.
I'm assuming you're capable of applying a Lorentz transform to (0,0) and (0,0.0000192s)???

6. Originally Posted by Aer
Sorry to barge in unannounced. Why isn't this analysis given for the 10,000m to 5000m calculation?
What do you mean?

7. Originally Posted by Pete
I'm assuming you're capable of applying a Lorentz transform to (0,0) and (0,0.0000192s)???
Don't assume too much, it is getting late and I am tired.

8. Originally Posted by Pete
What do you mean?
You gave special analysis to the 5000m to 2500m calculations. I merely pointed out that the 10,000m to 5000m calculation felt left out. (In my head that is... This probably is really driving me crazy)

9. OK, let's ignore the atmosphere.

In the muon's frame, at the instant of its creation, the Earth is 5000m away.

Sticking out from Earth past the muon is a calibrated rod, marked with altitude in metres. It's moving with Earth, naturally enough.

At the instant the muon is created, what number is it passing on the Earth's rod?
2500m or 10000m.

Since the rod is length contracted by 2 in the muon's frame, and the other end of the rod is 5000m away, it must read 10000m.
How do you know that??? We're in the muon frame only!

if the muon is created at 10000m in the earth frame, then the muon will see the earth 5000m away.

If the earth is created in the muons frame (use your imagination - POP! Earth, created and accelerated to 0.866c toward the muon) at 5000m then the earth will see the muon at 2500m.

10. This is why I want to stop using muons. The actual muon situation is well understood and accepted by all.

11. Originally Posted by superluminal
(use your imagination - POP! Earth, created and accelerated to 0.866c toward the muon)
While I am all for creating Earths, would this approach be acceptable: An observer is already in the muon frame. Observses the muon created. Takes measurements in the muon frame?

12. The question that started this whole thing was, "why dosen't the earth see the distance to the muon contracted?"

Answer: because the muon accelerated toward the earth.

If the earth had accelerated toward a preexisting muon, the opposite would be true.

Done.

13. Man, im getting tired.

14. Then other people said no no no and threw these curve balls at us. They hurt OUCH.

15. Aer:

While I am all for creating Earths, would this approach be acceptable: An observer is already in the muon frame. Observses the muon created. Takes measurements in the muon frame?
Thats the same as just being created at the same time as the muon. Get's you nopthing.

16. Maybe we need a new thread without the word "muon" in the title?

17. Won't help. Besides, it'll just be yet another relativity thread.

18. I think it all boils down to what I initially said. Length contraction can only exist with the relativity of simultaneity. Not only am I saying this, but I have linked to a paper on arxiv.org that says this. I claim that neither has been experimentally proven. Basically you have one bad idea cancelling out another bad idea. I haven't read the paper yet, but I think that is the conclusion they draw in a more rigorous way. Time will tell - whenever I get around to reading it.

19. Aer and Superluminal,

You both have the same problem with the calculation, which was nicely expressed by superluminal:

From the beginning I stated that the muon must see the distance to earth as 5000m and the earth must see the muon distance as 10000m. When I placed myself in the muons rest frame, I knew to use the reverse transform because I knew the the constraing FACT that the earth really saw the muon created at 10000m, because that's how we set up the scenario (in our godlike way).

If, however, you are not god, and are just a freshly created muon, how do you know whether to do the natural thing and use the forward transform based on your 5000m measurement of the oncoming earth (yielding 2500m for the distance to earth), or the reverse transform?

I claim that the determining factor is the velocity history within the bounds of the experiment (this in no way implies any MacM-like absolute references or even a third frame. It's just knowing who accelerated).
You have hit on the major stumbling block which every undergraduate eventually hits at some point in their studies of relativity (if they go far enough to recognise the apparent problem).

What you've done, in effect, is to analyse only half of the problem. You've thought about the length aspect of the problem, but almost completely ignored the time aspect. Both are important.

In my example, we had a muon, at some particular time, level with the top of a nearby mountain. The spacetime event "muon is level with top of mountain" happens whichever frame you're in - muon frame or earth frame. When that event happens, the distance from the muon to the ground is 10000 m in Earth frame and 5000 m in the muon frame, unambiguously. There is no way to argue in either frame that when the muon is level with the top of the mountain, the mountain is only 2500 high. From the Earth's point of view, the mountain has its usual rest height, which cannot change just because a muon happens to be flying past it. And from the muon's perspective, the mountain is definitely moving, so the muon MUST be seeing a contracted mountain.

The muon and the Earth observer can both unambigously deduce that when the event "muon is level with top of the mountain" occurs, the muon will measure the distance from the top of the mountain to the ground to be shorter than the Earth observer will measure. There's no way to "choose the reverse transformation". The muon sees the mountain move. Therefore, it must be length contracted. The earth observer does not see the mountain move, therefore it has its rest height.

If you want to abstract this by one step, replace the mountain with an imaginary ruler. This makes no essential difference to the problem. The ruler is fixed to the Earth at one end and the muon at the other end, at the particular time when "muon is level with top of ruler and bottom of ruler rests of the ground".

Suppose now that we start from the muon's point of view, with no information, as Aer wants.

The muon measures the mountain coming at it at 0.866c. At some time, the muon sees the top of the mountain as being level with it. Suppose at that time the muon measures the height of the mountain to be 5000 m.

What is the correct height of the mountain in the Earth frame? Is it 2500 m, or 10000 m?

The muon sees the mountain moving, so it knows the mountain is length contracted. It therefore deduces that the rest height of the mountain must be greater than 5000 m. It can measure the gamma factor (2), and therefore can calculate the rest length of the mountain to be 10000 m. There is no way that it could do otherwise, since to get 2500 m it would need to assume that the mountain is at rest in the muon frame, which is obviously not true.

In the quote above, superluminal says that ultimately, to make a choice of rest frame vs. moving frame, we need to know velocity histories, or "who accelerated". Hopefully it is clear that is wrong. All we need are two spacetime events, occurring at the two ends of whatever "ruler" we are using. In this situation, it is quite ok to use:

Event 1: Muon is level with top of mountain.
Event 2: Ground clock at bottom of mountain registers time "zero".

At the risk of opening a can of worms, I note that, if these two particular events are used, then events 1 and 2 are simultaneous in the ground frame (by definition, and my original description of the problem, above), but not simultaneous in the muon's frame, as can be seen by applying the Lorentz transformations.

20. You had to include a mountain as a reference and say it was moving for your analysis to conclude anything. In all reality, we have no such mountain. All we have is empty space (let's ignore the atmosphere as well). Is our empty space moving? I don't like where this is going... If that was your best effort, then we are just going to have to agree to disagree.

I'll leave it at what I said before: Length contraction can only exist with the relativity of simultaneity and neither has been proven.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•