# Thread: Length Contraction in the Muon Experiment

1. Originally Posted by Aer
I am well aware that the relativity of simultaneity offers a "way out" for special relativity regarding the length contraction issue - but even that shows to be faulty when you try to do the experiment in the Muon frame and ignore any measurements you have in the Earth frame.
Read the lower part of my post to 2inq, just a few posts above your own.

In it I do exactly what you suggest, and guess how it comes out.

2. Originally Posted by funkstar
Yes, there is. That's what length contraction is all about! Only moving objects length contract.
Either object can be considered moving according to the other - UH OH!

Originally Posted by funkstar
If something is moving in my frame it is length contracted by gamma. To get it's proper length I therefore have to multiply it's apparent length by gamma.
So the Muon is moving in my frame - I therefore have to multiply it's apparent length to get it's proper length - wait, that isn't what we did before!

Originally Posted by funkstar
Seeing as you post about the validity of the derivation of the Lorentz transformation equations I'm frankly surprised that I have to explain something like this to you...

Originally Posted by funkstar
Anyway, is the atmosphere moving in the muon frame? Yes, it is. Is the atmosphere moving in the Earth frame? No, it's not. Therefore, if the muon sees the moving atmosphere as having length l, then the length contraction formula predicts it as having length gamma*l in it's own frame, which is the same as the Earth frame.
The length contraction is one way according to your argument. Thus the time dilation should also be one way - that is, the Muon doesn't see less time on the Earth clock - how is that so.

3. Originally Posted by funkstar
Read the lower part of my post to 2inq, just a few posts above your own.

In it I do exactly what you suggest, and guess how it comes out.
You obviously miss the point - take my questions as asked to Janus58 and answer them without contradicting yourself or Janus-self.

4. Originally Posted by superluminal
Work with two objects with an obvious velocity history. This is still relative velocity, but the delta v affects the symmetry of the situation.
Are you reverting back to the original argument that the Muon neccessarily accelerates so we cannot consider the experiment from the muon frame? As I said then, this is the only acceptable answer although I don't know if it is correct or not.

5. Originally Posted by superluminal
I think you are all missing something important. In this "experiment" one of the objects changes velocity.
I don't agree. A constant relative velocity works just fine.
Velocity is important. Just as the change in velocity breaks the symmetry in the "twin paradox". If you start in the earth frame, the muon appears at 10000m. You calculate that the muon sees 2000m.
Agree.
An equally valid situation is that the muon is in existence and the earth is created 2000m above the muon moving at .98c. The earth will see 398m to the muon.
No, the Earth will not agree that this is the distance at the time the muon is created in the Earth frame!

Why? Because this distance is frame dependent. The muon will not agree that the muon was created at the time it's 398m from the Earth (in the Earth frame). It will claim that the muon was created long before, in fact, at the time it was 10,000 m from the Earth frame. Remember, just because these two events:

1. The muon is created.
2. The Earth is 2,000 m from the muon in the muon frame

are simultaneous in the muon frame, it doesn't mean that they are simultaneous in the Earth frame!

It would be so much easier if we all just used the Lorentz transforms to start with...

6. Originally Posted by Aer
Either object can be considered moving according to the other - UH OH!
"Uh oh!" What? There's no contradiction. Moving objects contract, stationary objects don't, and it's all frame dependent. I never claimed otherwise.
So the Muon is moving in my frame - I therefore have to multiply it's apparent length to get it's proper length - wait, that isn't what we did before!
*sigh*

No, because the atmosphere is an Earth frame object, not a muon frame object. Things have only one proper length, you know.

In your frame, the apparent length of a moving object, al, is related to it's proper length, pl, by the length contraction equation:

al = pl / gamma.

Is manipulating this equation really so difficult?
I used the Lorentz transforms explicitly, you used intuition. Which one of us do you think has the right str answer, based on that?
The length contraction is one way according to your argument.
Absolutely not. We are considering an object at rest in the Earth frame. Nothing about a relativistic muon will make this object contract in the Earth frame.
Thus the time dilation should also be one way - that is, the Muon doesn't see less time on the Earth clock - how is that so.
It isn't.

7. One more time, then.

Originally Posted by Aer
Quick sequential set of questions:
Is the Muon moving relative to the Earth?
Yes.

Does the atmosphere move with the Earth?
Yes. Hence the atmosphere is also moving relative to the muon.

How deep is the atmosphere as measured in the Muon frame?
Assume it's apparent length 5,000m.

What length does this transform to as measured in the Earth frame using the above formula for v=.866c?
Using the above formula yield that an object at rest in the muon frame, with proper length 5,000m will be 2,500m long when viewed from the Earth frame. There is no such object in the muon frame, however. What we do have is a moving object with apparent length 5,000m. That yields a proper length of 10,000m.

How deep is the Earth atmosphere then according to the Earth frame?
10,000m.

Where does the muon form?
Edge of the atmosphere.

How far is the muon from the Surface of the Earth when its forms as measured in its own frame?
Still 5,000m.

Consistent enough for you?
Then start with the muon frame - with the questions above, knowing no information from the Earth frame - that is, you are an observer in the Muon frame taking measurements - you have no prior knowledge of any measurements in the Earth frame.
I've already done this once in this thread. Look it up, you might learn something.

Better yet, do it yourself. Here's a guide:

1) Set up reference frames S and S' for the muon and Earth. Let them coincide on some spacetime event. I set it up so that in the Earth frame S', x'=0 described the surface of the Earth and that (x,t)=(0,0) and (x',t')=(0,0) described the same event.

2) Find a function f(t) to describe the position of the surface of the Earth in the coordinates of frame S.

3) Find a function g(t) to describe the position of the edge of the atmosphere in frame S.

4) Using the Lorentz transforms, find the position of g(t) in terms of the coordinates of S', compare with (x',t')=(0,t').

5a) Thank me the help in dispelling a longstanding confusion of yours or
5b) Deny that the Lorentz transforms work and become MacM.

8. Originally Posted by funkstar
"Uh oh!" What? There's no contradiction. Moving objects contract, stationary objects don't, and it's all frame dependent. I never claimed otherwise.
You are only taking the perspective that the muon is moving. I don't wish to look at it this way - I want to do the same experiment in the muon frame. The Earth is moving.

But your response to my position that the Earth is moving is:

Originally Posted by funkstar
*sigh*
And then your proceed to say:

Originally Posted by funkstar
No, because the atmosphere is an Earth frame object, not a muon frame object. Things have only one proper length, you know.
So, the Earth is not moving because it has an atmosphere! Oh geez... wow, I don't know where to start explaining anything to you here. Do I start with definitions for English words and go through an entire English course? Or should I be able to stick to just scientific definitions and scientific principles? I don't know!

Let's try this:
The Earth is a basketball, the muon is a pebble. Do the same experiment in the depths of space - there goes your atmosphere is moving with the Earth frame argument. In other words, I don't care how the atmosphere is moving, that is not important.

Originally Posted by funkstar
In your frame, the apparent length of a moving object, al, is related to it's proper length, pl, by the length contraction equation:

al = pl / gamma.
The muon is perfectly capable of measuring it's own proper length and judging the proper length in another frame - just as we have done in the Earth frame.

Originally Posted by funkstar
Is manipulating this equation really so difficult?
You are neglecting the definitions of L and L' when applying the equation to any other frame other than Earth's frame!

Originally Posted by funkstar
I used the Lorentz transforms explicitly, you used intuition. Which one of us do you think has the right str answer, based on that?
I did not use "intuition" - I just started the experiment in the muon frame.

Originally Posted by funkstar
Absolutely not. We are considering an object at rest in the Earth frame. Nothing about a relativistic muon will make this object contract in the Earth frame.
You seem to forget that I don't care what I measured the depth of the Earth atmosphere to be in the Earth frame, what part of "you are an observer in the Muon frame taking measurements - you have no prior knowledge of any measurements in the Earth frame" do you not understand?

9. funkstar,

SL:
“ An equally valid situation is that the muon is in existence and the earth is created 2000m above the muon moving at .98c. The earth will see 398m to the muon.
No, the Earth will not agree that this is the distance at the time the muon is created in the Earth frame!
Why not? The muon is not "created" in the earth frame. The earth is "created" in the muon frame. This is the exact opposite of the original situation. Redo the experiment with the muon being created at 2000m in the earth frame. The muon will see 398m to the earth surface.

Now just change the names:

...the earth being created at 2000m in the muon frame. The earth will see 398m to the muon surface.

The two situations are dependent on who accelerates. This is vital! Otherwise, the "twin paradox" has no resolution.

If I leave on a one way trip to alpha centauri at 0.98c I will arrive and report that I have aged only .79 years while you have aged 4.08 years. How do you explain this without symmetry breaking due to inherent change in velocity on the part of the "traveller"?

10. Originally Posted by funkstar
What length does this transform to as measured in the Earth frame using the above formula for v=.866c?
Using the above formula yield that an object at rest in the muon frame, with proper length 5,000m will be 2,500m long when viewed from the Earth frame. There is no such object in the muon frame, however. What we do have is a moving object with apparent length 5,000m. That yields a proper length of 10,000m.
So our muon rest frame is a moving reference frame. Great! The Earth is the absolute rest frame, this is a very important find by you!

11. Who does the delta v is vital. All along we assume the muon is created and accelerated to .98c in the earth frame. Assume the earth is created and accelerated to .98c in the muon frame.

This is why using muons which are "created" clouds the issue.

12. Originally Posted by superluminal
This is why using muons which are "created" clouds the issue.
I agree with you superluminal, acceleration can be the only explaination.

But even this explaination falls apart if you assume local ethers exist. However, I don't wish to go into this discussion since I cannot find any experiments to prove or disprove it - as such an experiment would essentially have to prove one way or the other whether length contraction and relativity of simultaneity exists.

13. Well, yes. There is no evidence for "ethers" local or otherwise.

14. Originally Posted by Aer
You are only taking the perspective that the muon is moving. I don't wish to look at it this way - I want to do the same experiment in the muon frame. The Earth is moving.
In the muon frame, yes. I never claimed otherwise.
So, the Earth is not moving because it has an atmosphere!
It's easy to reply to something I never said, isn't it.

Ok, find the specific post in which I claimed that from the muons point of view the Earth isn't moving.

"I dare you, I double-dare you, motherfucker, say 'What?!?' again!"
Let's try this:
The Earth is a basketball, the muon is a pebble. Do the same experiment in the depths of space - there goes your atmosphere is moving with the Earth frame argument. In other words, I don't care how the atmosphere is moving, that is not important.
The initial condition of the experiment is that the moun forms on the edge of the atmosphere. Take that away, and you are no longer describing the same experiment.
The muon is perfectly capable of measuring it's own proper length and judging the proper length in another frame - just as we have done in the Earth frame.
Of course, it is, because apparent length is related to proper length via the length contraction equation.
You are neglecting the definitions of L and L' when applying the equation to any other frame other than Earth's frame!
Absolutely not! Let L be proper length and L' be apparent length. The length contraction equation merely states that

L' = L / gamma.

Now, from the muon frame:

The atmosphere has an apparent length, does it not? What is it?

Is it moving in the muon frame? At what speed?

How does one calculate the proper length of the atmosphere given these to numbers from the length contraction equation?
I did not use "intuition" - I just started the experiment in the muon frame.
I didn't see any spacetime coordinates, equations or anything else.

No, you used intuition. Don't do that.
"you are an observer in the Muon frame taking measurements - you have no prior knowledge of any measurements in the Earth frame"
Again, I've already done so. It comes out as I say if you use the Lorentz transform.

15. Originally Posted by Aer
So our muon rest frame is a moving reference frame. Great! The Earth is the absolute rest frame, this is a very important find by you!
The moving object is the Earth atmosphere, as viewed from the muon's frame.

You're grasping at straws.

16. Originally Posted by funkstar
Ok, find the specific post in which I claimed that from the muons point of view the Earth isn't moving.
The muon is created at the edge of the atmosphere, check. The muon measures the atmosphere to be 5000m (your numbers), check. The atmohsphere is moving with respect to the muon, check. So the atmosphere has an apparent length of 5000m, check. So the proper length of the atmosphere is 10,000m in the Earth frame, check. The muon measures the proper length of the atmosphere to be 2500m in the Earth frame, un-check. Doesn't add up - sorry. Whether you specifically said the Earth is not moving is not the point, sorry.

17. I think we are fighting two distinct experiments against each other.

In one, the muon is created at 10000m in the earth frame and will see 2000m in it's own frame. These are immutable no matter how you do the calculation. The earth's velocity history is static, while the muons velocity history is not. As an observer on the muon, you know this and must take it into account. You will always calculate the earth frame distance as 10000m.

In the other, we say the earth is created in the muon frame at 2000m. I am now stating that the muons velocity history is static (this is why using muons is semantically confusing, call it planet number two?) and the earths velocity history is not (it was created and accelerated) and will see the earth-muon distance as 398m.

For real muons in the real world, the first case is always true. I think if we use two particles with known velocity histories this will all be much clearer.

18. Shit. why do we keep switching numbers?

19. Originally Posted by superluminal
Shit. why do we keep switching numbers?
Blame Janus - I've always used the 10,000m and 2000m myself. I guess his animations were just easier with the other numbers.

20. Ok, so we'll use his numbers...

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