Muon travel distance vs Atmosphere Thickness?

[DrGreg]

The Lorentz transformation is$$\begin{align}
x' &= \gamma (x - vt) \\
t' &= \gamma ( t - vx/c^2),
\end{align}$$ and the inverse transformation is$$\begin{align}
x &= \gamma (x' + vt') \\
t &= \gamma ( t' + vx'/c^2).
\end{align}$$So, from (1), $x' = \gamma x$ is true only when $t = 0$, and, from (3), $x' = x / \gamma$ is true only when $t' = 0$.

So you need to look through the argument to see whether there is an implicit or explicit assumption that either $t = 0$ or $t' = 0$.

 

[ersmith]

I have no doubt that we can solve for $L' = \frac{L}{\gamma}$. The question is: what is the mistake in his manipulation of the same equation such that he obtains $L' = \gamma L$ ?

What it amounts to is that he identified the events $(0, L)$ in the Earth frame with $(0, L')$ in the muon frame. These are not the same spacetime events. This is obscured by his poor choice of coordinate systems and muddled notation.

 

[TSny]

Here's where I would pinpoint the main mistake in the paper.

From the paper we have:

The first relation $(x_{1-\mu}' = 0, t’ = t_1') \equiv (x_{1-\mu} = L, t = t_1)$ gives the primed and unprimed coordinates for the event of the muon creation at the top of the atmosphere. This looks correct if $t’_1$ and $t_1$ are defined to be the time of this event in the muon frame and earth frame, respectively.

The second relation $(x_{1-E}' = -L’, t’ = t_1') \equiv (x_{1-E} = L, t = t_1)$ is obscure and appears to refer to some event different from the event of the muon creation and different from the event of the muon arriving at the earth’s surface. If we accept the left side of this relation, this event takes place on the earth's surface at a time $t_1’$ according to the muon frame that is simultaneous with the muon creation event at the top of the atmosphere. Apparently, the author doesn't realize that this event is distinct from the event of the creation of the muons. He takes both relations given in the quote above as "for the event of the muons creation".

We could imagine a firecracker exploding at the earth’s surface at a time in the muon frame that is simultaneous with the muon creation. Then $(x_{1-E}' = -L’, t’ =t_1')$ would be the correct primed-coordinates for this event. But, then, we see that the right side of the relation cannot be correct. The right side says that the unprimed coordinates of the firecracker event are $(x_{1-E} = 0, t = t_1)$. The author has assumed that the unprimed time coordinate for the firecracker event is the same as the unprimed time coordinate of the muon creation ($t_1$). That is, the author has assumed that the muon creation event and the firecracker event are simultaneous events in both frames. However, this assumption contradicts the relativity of simultaneity incorporated in the LT equations between the primed and unprimed frames.

[In the paper the primed (muon) frame moves in the negative $x$-direction relative to the unprimed (earth) frame. So, if $v$ denotes the relative speed of the two frames (a positive number), the signs in front of $v$ in the paper’s LT equations are wrong.]

 

[Dale]

Oh, wow, @TSny you definitely put some effort into wading through a mess!

The first relation $(x_{1-\mu}' = 0, t’ = t_1') \equiv (x_{1-\mu} = L, t = t_1)$ gives the primed and unprimed coordinates for the event of the muon creation at the top of the atmosphere. This looks correct if $t’_1$ and $t_1$ are defined to be the time of this event in the muon frame and earth frame, respectively.

Did the author actually define $t’_1$ and $t_1$ that way in the paper? From the confusion of @curiousburke I suspect that the reader is just left to guess.

The second relation $(x_{1-E}' = -L’, t’ = t_1') \equiv (x_{1-E} = L, t = t_1)$ is obscure and appears to refer to some event different from the event of the muon creation and different from the event of the muon arriving at the earth’s surface.

That is a mess. In the picture you took the author states that they are talking about one event and then writes coordinates for two events.

If we accept the left side of this relation, this event takes place on the earth's surface at a time $t_1’$ according to the muon frame that is simultaneous with the muon creation event at the top of the atmosphere. Apparently, the author doesn't realize that this event is distinct from the event of the creation of the muons. He takes both relations given in the quote above as "for the event of the muons creation".

This leads me to believe that the author does not understand the most basic aspect of the mathematical framework of relativity: an event. An event is a single place at a single moment in time. Not two places at the same moment in time.

We could imagine a firecracker exploding at the earth’s surface at a time in the muon frame that is simultaneous with the muon creation. Then $(x_{1-E}' = -L’, t’ =t_1')$ would be the correct primed-coordinates for this event. But, then, we see that the right side of the relation cannot be correct. The right side says that the unprimed coordinates of the firecracker event are $(x_{1-E} = 0, t = t_1)$. The author has assumed that the unprimed time coordinate for the firecracker event is the same as the unprimed time coordinate of the muon creation ($t_1$). That is, the author has assumed that the muon creation event and the firecracker event are simultaneous events in both frames. However, this assumption contradicts the relativity of simultaneity incorporated in the LT equations between the primed and unprimed frames.

It appears that the author does not recognize that the coordinates of a given event in one frame are obtained by Lorentz transforming from the coordinates of that event in the other frame. You cannot freely specify both, once you specify the coordinates for some event in one frame you have to use the LT to calculate the coordinates in another frame.

I note that this is indeed an error of the type mentioned by @Ibix The author accidentally (?) uses the simultaneity in the primed frame for events in the unprimed frame. It is a very clear and unambiguous mistake.

 

[curiousburke]

We could imagine a firecracker exploding at the earth’s surface at a time in the muon frame that is simultaneous with the muon creation. Then $(x_{1-E}' = -L’, t’ =t_1')$ would be the correct primed-coordinates for this event. But, then, we see that the right side of the relation cannot be correct. The right side says that the unprimed coordinates of the firecracker event are $(x_{1-E} = 0, t = t_1)$. The author has assumed that the unprimed time coordinate for the firecracker event is the same as the unprimed time coordinate of the muon creation ($t_1$). That is, the author has assumed that the muon creation event and the firecracker event are simultaneous events in both frames. However, this assumption contradicts the relativity of simultaneity incorporated in the LT equations between the primed and unprimed frames.

Ahhh, yes! I see it now. Thank you! I'll be charitable and assume the author is making a mistake, but i assume his whole platform is based on similar errors. From a novice perspective, it seems rational to assume that whatever is happening on Earth when the muon is created is simultaneous between frames if the muon creation is simultaneous between frames, but of course it wouldn't be. My guess is that someone that does not agree with SR may simply say do not agree with the loss of simultaneity.

[In the paper the primed (muon) frame moves in the negative $x$-direction relative to the unprimed (earth) frame. So, if $v$ denotes the relative speed of the two frames (a positive number), the signs in front of $v$ in the paper’s LT equations are wrong.]

Nice, at least I had the sign right when it didn't match the paper.

 

[curiousburke]

Thank you Dale for continuing with this thread. Clearly, part of the problem was my attempt to sum up the paper without going into enough detail. The author does not do a great job of defining terms to begin with, but my telephone game describing his work just added to the mess.

 

[Dale]

i assume his whole platform is based on similar errors

I didn’t know he has a whole platform.

Anyone arguing that special relativity is not self consistent is simply wrong. All of special relativity comes from the invariance of $$ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2$$ That is just geometry, similar to Euclidean geometry. There is basically nowhere for it to be inconsistent. It is a single formula.

 

[Ibix]

There is basically nowhere for it to be inconsistent.

...but many, many ways for a person to apply it inconsistently. They are particularly vulnerable to doing this if they are invested in believing that relativity is wrong and hence predisposed to interpret errors as problems with the theory rather than problems with their understanding.

 

[hutchphd]

Generally, if you've got $\gamma L$ instead of $L/\gamma$ then you've used the simultaneity convention of the wrong frame. For example, if you use two events that are simultaneous in the unprimed frame and distance $L$ apart and measure their separation in the primed frame you'll get $\gamma L$, but the events aren't simultaneous.

I can't be bothered to check his maths, but that's the standard "I think I understand relativity better than I actually do" mistake.

I should not be surprised I suppose, but I find it breathtaking that someone should suppose to find such simple errors in a foundational theory more than a century old. It makes the hubris of many politicians seem quaint by comparison. Pride goes before the fall I fear.

 

[curiousburke]

I should not be surprised I suppose, but I find it breathtaking that someone should suppose to find such simple errors in a foundational theory more than a century old. It makes the hubris of many politicians seem quaint by comparison. Pride goes before the fall I fear.

I agree with you; however, I find it difficult to reconcile two related ideas. The first is that appeal to authority is not proof. The second is what you said. While a single authority isn't proof, the lifetimes works of a century of authorities should be weighed heavily.

 

[PeterDonis]

I agree with you; however, I find it difficult to reconcile two related ideas. The first is that appeal to authority is not proof. The second is what you said. While a single authority isn't proof, the lifetimes works of a century of authorities should be weighed heavily.

It's not a matter of "authority". As I pointed out in post #3 of this thread, relativity has extensive experimental confirmation. So anyone who claims they've found a proof that it's wrong is not going against the "authority" of other physicists, they're going against decades' worth of experimental results.

 

[Dale]

I agree with you; however, I find it difficult to reconcile two related ideas. The first is that appeal to authority is not proof. The second is what you said. While a single authority isn't proof, the lifetimes works of a century of authorities should be weighed heavily.

When people reference a scientific paper or a scientific body of research they are not appealing to authority. They are pointing you to the proofs and evidence that are found therein. Crackpots make that “appeal to authority” claim incorrectly.

 

[hutchphd]

I didn't bother to delve into the math details when I noted the following

1. "Debunked" in the title
2. "relativists" used as an accusation in the abstract
3. previous work :How the Special Relativity equations are fudged
   Preprint
   Full-text available
   • Jan 2019
   • 
     Radwan M. Kassir
   
   This work presents an indisputable mathematical demonstration revealing that the Special Relativity equations are fudged. It also shows that the actual equations resulting from Einstein’s assumptions are inconsistent, and lead to mathematical inconsistency, falsifying the special relativity predictions.

No further reesearch required for me......... saved me the agita

 

[Vanadium 50]

Appeal to authority is not a good argument, but it is better than an appeal to idiocy.

 

[berkeman]

Thread is paused for Moderation...

 

[Dale]

The thread has been well answered, so we will leave it closed at this point.