Time dilation of Muons and a Paradox

[universal_101]

Unless the Earth frame sees a time dilation, and the muon frame sees length contraction there will be a paradox. So if time dilation is 'real', so is length contraction.

Agreed, But it is the very use of Lorentz transformation, which is supposed to only transform the co-ordinates around a event, that makes the Length contraction a necessity, to which we don't have any experimental Evidence even after more than 100 years of it's introduction.

But since we, in our frame, use the Lorentz transformation to explain the Time dilation of unstable particles, which it was not supposed to be used because it is just a co-ordinate effect.

And It makes me think that, can the decay of these Time Dilating unstable particles be dependent on the Sun, since I already encountered several papers confirming the same.

It's a coordinate effect. I don't know if that makes it real.

I don't think a co-ordinate effect can be real, it cannot be by it's mere definition.

 

[Mentz114]

The physical situation in the muon scenario is simple - a muon is created at a certain place and time, travels to another point in space and time and decays. Special relativity predicts correctly what happens, which is support for the idea of time dilation/length contraction, but I don't believe those phenomena can be directly observed. I think you made this point earlier. They must belong to that class of things which are part of successful theories but cannot be directly observed. Like the wave function, or the vector potential.

Whether something which cannot be directly observed is 'real' may just be an argument over words.

 

[Dale]

But if Lorentz transformation is just a co-ordinate transform, then how can it support/explain/justify the real events like Time Dilation of Muons and a real Length contraction in order to justify the Time Dilation of Muons themselves.

The Lorentz transform can be used to explain experimental observations because the laws of physics are invariant under Lorentz transforms.

Besides, I included every thing you asked me to include in my calculations, but in the end what you are suggesting is, just do a co-ordinate transform for the reference frame of Muons.

You can do a coordinate transform to any frame you like. It doesn't have to be the rest frame of the muons. I just picked that frame because it made the mistake very obvious.

 

[universal_101]

This expression is incorrect because the time that it takes for the muons to reach the detector is not equal to L_r/v_r in any frame except the accelerator frame. For example consider v=-v0, i.e. v_r=0 or the muon's rest frame. In this frame, since the muons are at rest, the formula L_r/v_r predicts that the time to reach the detector is infinite. However, the detector is moving towards the muons and therefore the muons reach the detector in a finite amount of time (specifically L_r/v0).

I would recommend using the invariant form of the equation. It solves all of the hassles immediately.

I think you are right, that the expression for the v_r is incorrect, since I did not include the relative speed of the accelerator in this new frame, when I calculated v_r,

But soon after, I realized that v_r, is the relative velocity of the Muons w.r.t the accelerator, and therefore a invariant, which implies, v_r = v_0 simply.

But even then I can't seem to get any closer to the understanding or the correct result.

 

[universal_101]

...Special relativity predicts correctly what happens, which is support for the idea of time dilation/length contraction, but I don't believe those phenomena can be directly observed. I think you made this point earlier.

First of all, Thanks for the insight on your part.

But what do you mean by, we cannot observe Time Dilation directly, since Experimentally we do observe the Time Dilation.

The problematic part is Length Contraction which we cannot observe because Everything else changes relativistic-ally.

Remembering that, it is the Explanation/support of Time Dilation of Muons(which is real/observable) from Special Relativity, that necessitated the introduction of real/observable Length contraction, to which we don't have any experimental Evidence,

And NOR do we Expect it in near Future, because according to some people here and me, any object does not change it's state just because a observer is moving relative to it. Even though, some how the strings breaking in Bell's spaceship paradox does exactly the same(Until and unless it is the acceleration which make the string to break, but then again, how?).

They must belong to that class of things which are part of successful theories but cannot be directly observed. Like the wave function, or the vector potential.

But Time Dilation of Muons is observable, unlike the wave function(which is extended interpretation concept).

Whether something which cannot be directly observed is 'real' may just be an argument over words.

Agreed, but Time Dilation of Muons can be directly observed.

 

[universal_101]

The Lorentz transform can be used to explain experimental observations because the laws of physics are invariant under Lorentz transforms.

If the Lorentz transformation keeps the laws of Physics invariant, then how were we able to comprehend the Time Dilation of Muons themselves, when we do a Lorentz transform to some observer who is moving w.r.t them.

But if we look at all this in the following way, Everything then makes sense,

That is if, Time Dilation of Muons, itself is a law of physics, which is invariant under Lorentz transform, we can make every other consequences like, real Length contraction etc. Go away. They can then just be only tools to transform from one frame to the other, around an event or state of an object.

You can do a coordinate transform to any frame you like. It doesn't have to be the rest frame of the muons. I just picked that frame because it made the mistake very obvious.

I corrected my equations, for the new frame,

Thanks.

 

[Mentz114]

Agreed, but Time Dilation of Muons can be directly observed.

I must have missed this. How ?

 

[universal_101]

Whether something which cannot be directly observed is 'real' may just be an argument over words.

Agreed, but Time Dilation of Muons can be directly observed.

I must have missed this. How ?

I am not sure how to respond to this. But I'm guessing you don't want to discuss Logic anymore.

 

[Dale]

But soon after, I realized that v_r, is the relative velocity of the Muons w.r.t the accelerator, and therefore a invariant, which implies, v_r = v_0 simply.

Actually, it is the approaching speed which is important.

 

[Samshorn]

It is the Explanation of time dilation of muons ... that necessitated the introduction of ... length contraction, to which we don't have any experimental evidence...

I assume you've been told many times that that's completely false, both historically and conceptually. Historically, length contraction was introduced by Fitzgerald and Lorentz in order to account for the results of the Michelson-Morley experiment, long before anyone ever dreamed of muons or even special relativity. And of course the MM experiment along with all other failed attempts to measure absolute velocity and all the experimental demonstrations of the invariance of light speed, and indeed the Lorentz invariance of all physical phenomena in terms of standard inertial coordinates, collectively are irrefutable experimental evidence of both length contraction and time dilation. Also, length contraction emerges from Lorentz's theorem of corresponding states based on the already-known laws of electrodynamics, and of course Lorentz always stressed the physical reality of (and necessity of) this contraction for active transformations.

An object does not change it's state just because a observer is moving relative to it.

You need to distinguish between intrinsic and extrinsic state variables, and between passive and active transformations.

 

[universal_101]

Actually, it is the approaching speed which is important.

Are you talking about the approaching speed of Muons w.r.t the other End ?

Is it different from the relative velocity of Muons w.r.t the the other End ?

And how important exactly !

 

[universal_101]

I assume you've been told many times that that's completely false,

Since you are assuming what have happened so far, can I safely assume that you did not read the previous discussions.

...Historically, length contraction was introduced by Fitzgerald and Lorentz in order to account for the results of the Michelson-Morley experiment, long before anyone ever dreamed of muons or even special relativity.

I agree, that Fitzgerald introduced/coined the term Length contraction to explain the results of MMX. But again, we are not discussing when was it first proposed.

And of course the MM experiment along with all other failed attempts to measure absolute velocity and all the experimental demonstrations of the invariance of light speed, and indeed the Lorentz invariance of all physical phenomena in terms of standard inertial coordinates, collectively are irrefutable experimental evidence of both length contraction and time dilation.

MMX was about the light and its properties, whereas, Time Dilation of Muons has nothing to do with Light and it's properties because if it does, there are contradictions of Logic. Again for the later part you need to read the previous posts.

Also, length contraction emerges from Lorentz's theorem of corresponding states based on the already-known laws of electrodynamics, and of course Lorentz always stressed the physical reality of (and necessity of) this contraction for active transformations.

Why don't then you just give me a real example of this physical reality, it will end all the conflicts.

You need to distinguish between intrinsic and extrinsic state variables, and between passive and active transformations.

Unfortunately, I don't know what all this mean. I suggest you read the previous discussions, if you think, there is an obvious mistake somewhere.

 

[Vanadium 50]

This thread is going around in circles. Enough.