Length Contraction in the Muon Experiment

[funkstar]

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.

No, it isn't. The initial condition is that the muon is created at the edge of the atmosphere, and the atmosphere has some apparent length in the muon frame. Just because that in the muon frame at time t=0 there's 2,000 meters to the Earth, it doesn't hold that the Earth will agree that these two events are simultaneous:

1) As viewed from the Earth, the 2,000 long ruler the muon extends in front of it touches ground.
2) The muon is created.

These event are seperate in spacetime, and can therefore only be simultaneous in one frame, and one frame only! In this case it is the muon frame. But then the Earth frame disagrees.

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

Yes, but the next bit is the clincher:

Now just change the names:

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

These two experiment are in no way the same. There the muon and the Earth observer can never agree that there was 2,000m from the muon to the Earth when it was created. If they agree on a non-zero distance (relative to the direction of motion, of course), they must be in the same reference frame. They aren't.

The two situations are dependent on who accelerates. This is vital!

No. I assumed no acceleration at all in my quantitative treatment from the muon frame to 2inq above, and it was perfectly consistent.

Otherwise, the "twin paradox" has no resolution.

I have a link somewhere about that...

Hm. I'll see if I can find it later, but I'm not certain you're right.

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"?

You are treating two (far) seperated spacetime events as having occured simultaneously, but that can only be true for one frame. There's no universal "NOW" ticking away, remember?

[funkstar]

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.

Correct.

So the proper length of the atmosphere is 10,000m in the Earth frame, check.

Yes.

The muon measures the proper length of the atmosphere to be 2500m in the Earth frame, un-check.

No. The muon measured the apparent length of the atmosphere to be 5,000m. The atmosphere is moving in the muon frame. Apparent length of an moving object and it's proper length are related as

al = pl / gamma

So

pl = al * gamma

Hence, the muon finds a proper length of the atmosphere to be 10,000m.

Doesn't add up - sorry.

You're just doing it wrong. The apparent length of a moving object is shorter than it's proper length by a factor of gamma. That's all there is to it.

Whether you specifically said the Earth is not moving is not the point, sorry.

It is when you said I didn't. I don't like being misrepresented.

Have you done the full Lorentz transformation, yet? Whatever we may say, the Lorentz transforms have the final say on what str predicts, and I want to see if you get what I did.

[Aer]

No. The muon measured the apparent length of the atmosphere to be 5,000m. The atmosphere is moving in the muon frame.

We already went over this. The muon measures the proper length from it to the Earth as seen in the Earth frame to be 2500m when it is created. This is just as logical a conclusion to the length of the atmosphere in the Earth frame as the method you keep describing. You get two different results.

You're just doing it wrong. The apparent length of a moving object is shorter than it's proper length by a factor of gamma. That's all there is to it.

What is the distance between the muon and the Earth as the muon would say the Earth frame sees? I am sure you will say 10,000m, but that is not what the length contraction formula says - it says 2500m.

Otherwise, you have to change the time-dilation equation as well and say that more time goes by in the Earth frame according to the muon's frame. This is not reciprocity as the special theory of relativity advocates.

[superluminal]

funkstar,

I'm well aware of the simultaneity issues of relativity. I think we are getting our wires crossed here. Your first response to me above tells me you didn't understand what I was saying. No problem. I think we should back up and create a new, simpler experiment that we can all agree on. Yes? And then work our way up from there. ?

For the record, I completely agree with the 10000m / 5000m observations of the earth vs muon created in the atmosphere.

[superluminal]

Aer:

What is the distance between the muon and the Earth as the muon would say the Earth frame sees? I am sure you will say 10,000m, but that is not what the length contraction formula says - it says 2500m.

No. You MUST take into account the velocity history. Just back calculating using gamma from the muon frame is a naive application.

[Aer]

For the record, I completely agree with the 10000m / 5000m observations of the earth vs muon created in the atmosphere.

While I agree that this is what special relativity says if you assume the muon accelerates - I am not going to take the position that it is actually truely what happens until we get some experiments to confirm length contraction and simultaneity of relativity.

I have other reasons to question the validity of these two requirements in special relativity. Most notably to do with string theories and requirements by certain theories there. Now string theories aren't as experimentally sound as special relativity - not by a long shot. But the only experiement special relativity has going for it is time-dilation which can be explained in some string theories without length contraction or relativity of simultaneity. I hope you understand my perspective.

[Aer]

No. You MUST take into account the velocity history. Just back calculating using gamma from the muon frame is a naive application.

Yes, you are refering to acceleration, no?

[superluminal]

This entire scenario starts in the EARTH frame. The muon is created in the EARTH frame at 10000m. It accelerates to 0.866c and sees the distance to earth as 5000m. These are immutable numbers. The muon must divide by gamma toi get calculate the earths view of the distance because he knows he was created in the EARTH frame and accelerated. He should calculate 10000m for the earth view.

[Aer]

This entire scenario starts in the EARTH frame. The muon is created in the EARTH frame at 10000m. It accelerates to 0.866c and sees the distance to earth as 5000m. These are immutable numbers. The muon must divide by gamma toi get calculate the earths view of the distance because he knows he was created in the EARTH frame and accelerated. He should calculate 10000m for the earth view.

Only if he does the acceleration. Describe precisely what you mean by "created in the earth frame". Do you mean "created stationary for an infinitesimal amount of time in the earth frame"?

[superluminal]

Aer,
Yes I understand, but we are talking about what SR currently says, right or wrong. Right?

And while I refer to acceleration, it's the delta v that matters. The actual acceleration is unimportant. That's why I use instantaneous acceleration in my examples. It avoids confusion as otherwise you would have to include the integrated velocity over the period of acceleration.

[Aer]

Aer,
Yes I understand, but we are talking about what SR currently says, right or wrong. Right?

Correct.

And while I refer to acceleration, it's the delta v that matters. The actual acceleration is unimportant. That's why I use instantaneous acceleration in my examples. It avoids confusion as otherwise you would have to include the integrated velocity over the period of acceleration.

Nevertheless, you cannot ignore the instantaneous acceleration. One of the two objects has to do the acceleration if they are first in the same frame when the muon is first created, no?

[superluminal]

Only if he does the acceleration. Describe precisely what you mean by "created in the earth frame". Do you mean "created stationary for an infinitesimal amount of time in the earth frame"?

Yes! A gamma ray strike an atom in the atmosphere. This causes the STATIONARY atom to generate a muon (about 300 x the electron mass - still very light) accelerated to 0.866c.

[Aer]

Yes! A gamma ray strike an atom in the atmosphere. This causes the STATIONARY atom to generate a muon (about 300 x the electron mass - still very light) accelerated to 0.866c.

Like I said, we are in agreement on this issue

[superluminal]

Nevertheless, you cannot ignore the instantaneous acceleration. One of the two objects has to do the acceleration if they are first in the same frame when the muon is first created, no?

Correct. All that matters is that the muon zipped up to 0.866c (almost instantaneously - the acceleration is huge in reality).

[Aer]

I might add that I lean more to the string theory explaination of time-dilation than that advocated by special relativity. Specifically because (this is my personal opinion), if length contraction and relativity of simultaneity were truely real, we'd more than likely have had experiments to confirm them already given the 100 year history of the theory.

[superluminal]

Well, I can think of a very simple experiment to demonstrate length contraction that is enormously expensive. To verify these things you need to get spacecraft moving inertially at fairly high speeds.

Send a spacecraft with an atomic clock on a high speed trip to nowhere, oriented on the earth with transmitter beacons at each end of a 100m boom. The beacons will show doppler shift but the relative delay between the fore and aft beacons will shorten as the spacecraft velocity increases due to length contraction. If you encode the beacons with atomic time data you can also show simple time dilation.

To most physicists this would be a complete waste of money that could be used for important science. Since relativity has been verified in many other ways, it is certain that these effects are real, otherwise, all of relativity falls apart and the existing verifications could not have worked at all.

If you have even more money, you can make the spacecraft bigger, with more fuel, and have it return to earth and show less accumulated time, thus showing the "twin paradox".

[superluminal]

For the actual muon situation can we agree on the following statements:

1) In the earth frame the creation distance is 10000m.

2) In the muon frame the creation distance is 5000m.

3) The above numbers are fixed in the fabric of reality since the muon creation is an event.

4) The earths velocity history is static.

5) The muons velocity history is includes high acceleration at time of creation.

Do we all agree on this?

[Aer]

Well, I can think of a very simple experiment to demonstrate length contraction that is enormously expensive. To verify these things you need to get spacecraft moving inertially at fairly high speeds.

I do not think that you would have to build expensive spaceships to do any experiment on length contraction - that just shows little creativity as you are relying on "thought experiments" to translate to an actual experiment. You are probably right, most scientists more than likely consider it a waste of time. But like I've said - only time dilation has been experimentally proven and the bulk of all special relativity experiments are just another time-dilation experiment. To me - those extra time-dilation experiments would be the waste of money, but I digress...

I've tried as hard as I might, but I just cannot get a string theory to jive with special relativity. It always amounts to creating local ethers and assuming only time-dilation is real. Ahh well, I'll just have to try a new approach. Though it may all be in vain, as history may yet prove string theory to be a cute but useless theory.

[superluminal]

that just shows little creativity as you are relying on "thought experiments" to translate to an actual experiment.

I thought it was pretty creative. And BTW, I seem to be the only one here who's even attempted a description of an actual experiment to test an SRT prediction...

[Aer]

I thought it was pretty creative. And BTW, I seem to be the only one here who's even attempted a description of an actual experiment to test an SRT prediction...

I've come up with a few, all land based - so they shouldn't be too terribly expensive. But I've never posted them anywhere and don't have them written down. They'd probably require a little bit of t'inkering if I wanted to put them into words on this forum.