Perspective on Relativity and Length Contraction

[universal_101]

The reason I think, that K.E despite being frame variant is not referred as apparent is because it has physical consequences, like more energy would do more work.

Another reason would be the way LT is used to explain the physical results, for-example Earth-Muon system, that is one can get curious, that why is that in Earth frame the space is not contracted(instead it is usually explained as the muon being time dilated).

I think everyone here agrees that the two frames(Earth and muon) are just as the picture in post #59, so why do we even bother about muons being time dilated, instead one can simply understand that in both frames it was the space that contracted. Just like the red train(let's say muon) and blue train(Earth) sees each other contracted.

 

[ghwellsjr]

The reason I think, that K.E despite being frame variant is not referred as apparent is because it has physical consequences, like more energy would do more work.

Another reason would be the way LT is used to explain the physical results, for-example Earth-Muon system, that is one can get curious, that why is that in Earth frame the space is not contracted(instead it is usually explained as the muon being time dilated).

I think everyone here agrees that the two frames(Earth and muon) are just as the picture in post #59, so why do we even bother about muons being time dilated, instead one can simply understand that in both frames it was the space that contracted. Just like the red train(let's say muon) and blue train(Earth) sees each other contracted.

I don't agree. You just said that in the Earth frame the space is not contracted (which is correct) and then you say that in both frames the space is contracted (which is not correct).

In the Earth frame, the muons are the only things that are moving and the only things that are length contracted (but it doesn't matter) and the only things that are time dilated (which does matter). In the muons' frames, the Earth (which doesn't matter) and the space (which does matter) are length contracted and are time dilated (which doesn't matter).

Maybe the picture in post #59 gave you the wrong impression because it incorrectly shows the tracks not length contracted in both frames. I corrected that picture in post #70.

 

[universal_101]

I don't agree. You just said that in the Earth frame the space is not contracted (which is correct) and then you say that in both frames the space is contracted (which is not correct).

It was inquisitive, why is the space in Earth's frame not contracted ?

Since, there is NO difference between the two frames, one sees the other moving i.e. the situation is exactly symmetrical, there is nothing to choose between the two

In the Earth frame, the muons are the only things that are moving and the only things that are length contracted (but it doesn't matter) and the only things that are time dilated (which does matter). In the muons' frames, the Earth (which doesn't matter) and the space (which does matter) are length contracted and are time dilated (which doesn't matter).

How do you get to choose ? which frame sees space contracted, there is not a single difference between the Earth frame seeing muon moving and Muon frame seeing Earth moving. So again, how did you get to choose which frame experience what ?

 

[TheBC]

It is frame dependent. In the rest frame of the red train car, the green train car and its passenger are length contracted and his signals are not simultaneous except at the point where they become coincident at his brain. The fact that each passenger senses in his brain the two signals simultaneously (true for any frame) does not mean that the signals started out simultaneously at their two widely separated fingertips. The top image in your sketch shows only the instant that the two signals started out simultaneously in the rest frame of the stationary red car on the railroad tracks, in other words, at the Coordinate Time of zero in the above spacetime diagram. That image does not show how the signals propagate along the arms of either passenger on their way to their brains. In fact, it does not show where the signal is in the left arm of the green passenger nor where the green car is when the red passenger senses the two signals in his brain.

I do not understand the point you want to make. Obviously I do know how to draw diagrams and what happens as far as relativity of simultaneity is concerned.
Actually for Red the two events (rear and front of car) DO happen simultaneously, BECAUSE the signals (let's consider speed of light) travel equal lengths in equal time. Period. What Green thinks about it doesn't matter. You make kind of the same 'mistake' as dvf in one of the previous posts.

For Green the front and rear events are for him simultaneous simply because for him light signals travel equal path lengths in equal time. What Red thinks about those signals doesn't matter.
A real Loedel diagram shows this immediately. (I hesitate to put time in drawing one because Ifeel my loedel diagrams are not appreciated on this forum).

... to show that the train tracks are also length contracted:

I don't care about the train tracks. It's about the two cars. I didn't even mention whether one of the cars is at rest on the tracks or not, because that's irrelevant in this exercise.

 

[ghwellsjr]

It was inquisitive, why is the space in Earth's frame not contracted ?

Because it's not moving.

Since, there is NO difference between the two frames, one sees the other moving i.e. the situation is exactly symmetrical, there is nothing to choose between the two

How do you get to choose ? which frame sees space contracted, there is not a single difference between the Earth frame seeing muon moving and Muon frame seeing Earth moving. So again, how did you get to choose which frame sees what ?

You start by describing the situation according to one frame and you transform to the other frame. We start by defining what happens in the Earth frame and transform to the muon's frame (or any other frame we chose). You can't just describe it in one frame and then without doing the calculations decide what you think it looks like in another frame.

Instead of using The BC's picture, you should go back to the diagrams I made in post #3 which are more analogous to the muon situation.

 

[TheBC]

I think "apparent length" as distinguished from "true length" is reasonable.

Why not simply calling the moving (contracted) train length the 'moving length'?
Rest length vs moving length makes a lot more sense than rest length vs 'apparent' length.

Is there a full train between the passengers hands or not?
Let's be more specific: Will the passenger himself confirm his physical experience of feeling the full train between his hands -i.o.w. Feeling the ends of the cars simultaneously? Yes. Is the length he measured (twice his arm length...) an 'apparent' length? Of course not.

Simon Bridge, the fact there are on the internet search '20,900,000 results (0.44 seconds) where a length is described as "apparent" in the context of special relativity' does not impress me at all. They all copy from each other, because they all think the reciprocal length contraction can not make sense if no form of optical illusion is involved.
'Apparent' does make sense if it's interpreted as 'as it shows', or 'as it is'. But in that sense it would be logical to call the rest length also 'apparent'. Nobody does this.
Why? I do not agree that 'apparent' is only used to make a distinction with 'rest'. Proof: why is it that in so many -probably another 20,900,000 results on the net- the moving train SEEMS contracted/shorter? Does -for the train passenger- the other train SEEM to fit between his hands? Obviously not. The train simply does fit between his hands.
I bet the use of 'apparent/appears' is used in the same semantic meaning as 'seems'. In other words: erroneously.

(Note . Actually the 'appear' vocabluary originates in the translation of the german 'erscheinen'. In his 1905 paper Einsteins used two different verbs: 'scheinen' and 'erscheinen'. He doesn't mix these at random. They have specific different meanings:
'Sheinen' means: illusion - an appearance that does not correspond to reality - it appears so, but it may not be true - what you see is mere appearance - only outward show, things are not what they seem to be, etc.
'Erscheinen' is: as it shows, come to light, as it is, etc.
In the english version 'sheinen' and 'erscheinen' are translated by one verb only: 'appear'. Strictly speaking the translation is not wrong (ask google to translate and somehow you will find 'appear'), but the very important difference in meaning in german disappears in the english word for word translation. Prove is that in thousands of texts dealing with Special Relativity the english 'appears' is often replaced by 'seems', which is a synonym of 'appears', but not the correct one to match the german significance of 'erscheinen'.)

 

[Mentz114]

In the case of the muon trajectory, the observed facts that everyone can agree on are the

1. decay time measured by on the muons clock (t)
2. the same interval measured on the Earth clock (T)
3. the relative velocity between muon and Earth (β=v/c)
4. the distance traveled in the Earth frame (X)

The first three are frame invariant.

In the Earth coordinates X=vT and in the muon coordinates x=vt, where x is the length the muon 'observer' would measure for the distance.

Where's the problem ?

 

[nitsuj]

Another reason would be the way LT is used to explain the physical results, for-example Earth-Muon system, that is one can get curious, that is why in the Earth frame the space is not contracted(instead it is usually explained as the muon being time dilated).

There is no physical difference between the two, it's postulated that c is invariant so we know(believe) the muon measures c to the same value the Earth observers do.

So it's not much of a leap to think; if that muon is "ticking" more slowly, yet measures the same value of c, it must also measure a shorter distance. and everything less the geometry stays neat and orderly.

 

[ghwellsjr]

I do not understand the point you want to make. Obviously I do know how to draw diagrams and what happens as far as relativity of simultaneity is concerned.
Actually for Red the two events (rear and front of car) DO happen simultaneously, BECAUSE the signals (let's consider speed of light) travel equal lengths in equal time. Period.

The two events happen simultaneously in the frame in which red is at rest. Red has no awareness of what is happening remotely until the signals reach him and even then, he cannot construct the coordinates of his rest frame unless he has also sent out radar signals and waited for their return as I mentioned in post #11. After all the signal reach him, after the scenario is ended, then he can construct his rest frame and figure out what was simultaneous. But, he can then also transform to any other frame and see what it looks like in green's rest frame or any other frame.

The point I'm making is that no frame is preferred, not even an observer's own rest frame, and all frames show the same observations that all observers and objects experience, witness, observe, measure, see, etc. No observer can tell anything different just because we use his rest frame to describe the scenario. Period.

What Green things about it doesn't matter. You make kind of the same 'mistake' as dvf in one of the previous posts.

Green can also send radar signals and log their returns along with the Doppler images and construct his own rest frame and from that transform to red's rest frame or construct the frame for a Loedel diagram, he just can do it in real time, he has to wait for all the information to reach him.

For Green the front and rear events are for him simultaneous simply because for him light signals travel equal path lengths in equal time. What Red thinks about those signales doesn't matter.
A real Loedel diagram shows this immediately. (I hesitate to put time in drawing one because Ifeel my loedel diagrams are not appreciated on this forum).

No one is going to object to a loedel diagram. Just take my last frame diagram and add whatever you want to make it a real loedel diagram. Just don't think that it is any more preferred or contains any more information than any other diagram for any other frame.

I don't care about the train tracks. It's about the two cars. I didn't even mention whether one of the cars is at rest on the tracks or not, because that's irrelevant in this exercise.

Maybe you don't care about the train tracks but they apparently led someone else astray. You did show in one case that only one car was moving and in the other case that only the other car was moving and the tracks remained the same in both cases. As such, your pictures indicate two different scenarios that don't show the reciprocity of a single scenario viewed from two different frames.

 

[WannabeNewton]

There seems to be a lot of semantics being thrown back and forth here. George has been trying judiciously to explain things using his diagrams but people are ignoring his efforts and just arguing semantics.

Let's get one thing straight: physical observables need not be frame invariants. Whoever originally said that (and I believe it was universal_101) is completely incorrect. If this were true then even things like the electric and magnetic fields would be discounted as physical observables. A physical observable/physically measurable quantity can certainly be frame dependent and mathematically corresponds to contracting tensor components with the basis vectors of the frame; physically this corresponds to the observer at rest in the frame making measurements of tensor components using his/her apparatus (mutually orthogonal meter sticks and a clock); Time dilation and length contraction are certainly accounted for in this prescription.

Secondly, length contraction has dynamical consequences. People have already mentioned various examples of this and I mention again the Ehrenfest paradox; if you're going to object to this by claiming that Lorentz-Fitzgerald contraction is to be distinguished from Lorentz contraction then this is a matter for another thread and something that can be argued against your favor.

 

[PeterDonis]

physical observables need not be frame invariants.

I would put this somewhat differently; in fact, as it stands, I think it invites misinterpretation when combined with what you say later on about tensor components. See below.

A physical observable/physically measurable quantity can certainly be frame dependent and mathematically corresponds to contracting tensor components with the basis vectors of the frame; physically this corresponds to the observer at rest in the frame making measurements of tensor components using his/her apparatus (mutually orthogonal meter sticks and a clock)

If we take this as it stands, it is, as I noted above, inconsistent with the claim that physical observables need not be frame invariant, because tensor contractions in which there are no free indexes, which is what you have to have in order to obtain the number that is actually observed, *are* frame invariant! They have to be, because they're Lorentz scalars.

For example, if I measure the energy of an object with 4-momentum $p_{\mu}$, the result I will get is the contraction of that 4-momentum with my 4-velocity $u^{\mu}$, i.e., the measured energy is $E = u^{\mu} p_{\mu}$. This number is a Lorentz scalar; it is the same no matter what frame I compute it in. However, if you, who are moving relative to me, measure the energy of the same object, you will obtain (if your 4-velocity is $w^{\mu}$) the result $E' = w^{\mu} p_{\mu}$.

We often describe this by saying that "energy is frame-dependent", but both numbers, $E$ and $E'$, are Lorentz scalars. What changes when you change frames is the 4-velocity; $E'$ is different from $E$ because $w^{\mu}$ is different from $u^{\mu}$, i.e., because they are contractions containing *different* 4-vectors.

The term "physical observable" is, unfortunately, ambiguous: it can refer both to the general rule that tells you, once you've picked a frame, which 4-vectors (or, more generally, which tensors) to contract; or it can refer to the specific contraction you obtain when you apply the general rule in a specific case. The general rule is obviously frame-dependent, but the specific results for each individual case are not. It would be better if there were two different simple English expressions to describe these two different concepts, but AFAIK there aren't.

 

[universal_101]

Because it's not moving.

What do you mean it(space) is not moving ? Since when space belongs to the Earth frame and not to the Muon frame. The situation is as symmetric as the example of trains , that is each frame sees the space contracted, but you are choosing not to address the fact that space belongs to both the frame equally !

You start by describing the situation according to one frame and you transform to the other frame. We start by defining what happens in the Earth frame and transform to the muon's frame (or any other frame we chose). You can't just describe it in one frame and then without doing the calculations decide what you think it looks like in another frame.

My simple question is, do the frame of Earth and muon have any difference which may tell us why the space is only contracted in muon's frame and not in Earth's frame ?

And ofcourse as long as one is not allowed to question, a set of rules can give you almost any result you like!

 

[ghwellsjr]

What do you mean it(space) is not moving ? Since when space belongs to the Earth frame and not to the Muon frame. The situation is as symmetric as the example of trains , that is each frame sees the space contracted, but you are choosing not to address the fact that space belongs to both the frame equally !

My simple question is, do the frame of Earth and muon have any difference which may tell us why the space is only contracted in muon's frame and not in Earth's frame ?

And ofcourse as long as one is not allowed to question, a set of rules can give you almost any result you like!

The muons are created in the upper atmosphere which is not moving with respect to the earth.

 

[universal_101]

Proof: why is it that in so many -probably another 20,900,000 results on the net- the moving train SEEMS contracted/shorter? Does -for the train passenger- the other train SEEM to fit between his hands? Obviously not. The train simply does fit between his hands.
I bet the use of 'apparent/appears' is used in the same semantic meaning as 'seems'. In other words: erroneously.

If only that experiment(or similar) could have been performed, Nobody would in his right mind would label Length contraction apparent. That is holding(even for the tiniest time interval) a train which is longer than your two arms length, in your stretched arms simultaneously !

This implies we don't have any proof to support that the train do contract to fit in the other person's stretched arms. Whereas, it is perfectly understandable, that one measure the two end of the train to be closer than what they are in their proper frame using light as the mean to do the measurements.

In other words, measuring(light) the increase or decrease in frequency due to relative motion w.r.t a source, does not mean that the source is actually/really/in it's proper frame/ also emitting the same frequency as measured, this is why we call it apparent frequency, but we all know it and understand without any toil. The exact same scenario happens for the length contraction, every moving observer measures the two end to be length contracted, but in it's proper frame it is just as we left it.

 

[universal_101]

In the case of the muon trajectory, the observed facts that everyone can agree on are the

1. decay time measured by on the muons clock (t)
2. the same interval measured on the Earth clock (T)
3. the relative velocity between muon and Earth (β=v/c)
4. the distance traveled in the Earth frame (X)

The first three are frame invariant.

In the Earth coordinates X=vT and in the muon coordinates x=vt, where x is the length the muon 'observer' would measure for the distance.

Where's the problem ?

The reason that, we have to apply Lorentz Transformation to the observed facts in-order to get the explanation of how muon reaches Earth in it's frame, does not justify in anyway, why there is contraction only in the muon's frame. And if one claims it is a fair justification, then it is rather a justification of the applicability of LT to situations like this.

 

[Dale]

It was inquisitive, why is the space in Earth's frame not contracted ?

Since, there is NO difference between the two frames, one sees the other moving i.e. the situation is exactly symmetrical, there is nothing to choose between the two


How do you get to choose ? which frame sees space contracted, there is not a single difference between the Earth frame seeing muon moving and Muon frame seeing Earth moving. So again, how did you get to choose which frame experience what ?

In the muon's frame the Earth is time dilated and length contracted. The fact that the Earth is time dilated is irrelevant. The fact that the Earth is length contracted explains how the muon reaches the ground.

In the Earth's frame the muon is time dilated and length contracted. The fact that the muon is length contracted is irrelevant. The fact that the muon is time dilated explains how the muon reaches the ground.

It isn't a matter of choosing between the two, nor a matter of some supposed difference between the frames. It is simply a matter of identifying which effects are relevant to explaining the outcome in each frame. All the relativistic effects apply equally, but they are not equally relevant to the explanation.

 

[universal_101]

In the muon's frame the Earth is time dilated and length contracted. The fact that the Earth is time dilated is irrelevant. The fact that the Earth is length contracted explains how the muon reaches the ground.

If I may, let me correct you, the fact that Earth is Length contracted in Muon's frame explains nothing, it is always the distance between the two which must contract in-order to explain how muon's reached Earth in muon's frame.

 

[universal_101]

The muons are created in the upper atmosphere which is not moving with respect to the earth.

What does atmosphere got to do with anything ? It does not matter a bit if the upper atmosphere is moving or not. The space between the two objects(Earth and muon) is not made up of atmosphere(In a sense atmosphere is not space).

 

[Dale]

If I may, let me correct you, the fact that Earth is Length contracted in Muon's frame explains nothing, it is always the distance between the two which must contract in-order to explain how muon's reached Earth in muon's frame.

I was considering the atmosphere to be part of the earth. The "distance between the two" as you call it is the same as the length of the atmosphere.

 

[universal_101]

I was considering the atmosphere to be part of the earth. The "distance between the two" as you call it is the same as the length of the atmosphere.

Let me put a counter argument, Are you suggesting that since Earth is a planet which has atmosphere, somehow make the Length contraction valid only in muon's frame.

Because one can always think of planets which do not have atmosphere, then what would be your reasoning ?

 

[TheBC]

Maybe you don't care about the train tracks but they apparently led someone else astray. You did show in one case that only one car was moving and in the other case that only the other car was moving and the tracks remained the same in both cases. As such, your pictures indicate two different scenarios that don't show the reciprocity of a single scenario viewed from two different frames.

Sorry about that. I was really dealing with relative moving trains.

I owed you the loedel diagram. I did change the contraction length to correspond with one of my standaard loedels. I was too lazy to draw loedel specific for the sketches I posted.
For the uninitiated the diagram might be too difficult to read. I find Minkowski diagram too difficult to read ... Contrary to Minkowski diagram, on the loedel diagram the length units on all axis have same length.

 

[jartsa]

A rule: "when you see an object coming towards you, then the distance between you and the object is contracted"

If you are a myon, that rule makes sense, I quess.

If you are a planet, then the rule does not make so much sense.

 

[Nugatory]

A rule: "when you see an object coming towards you, then the distance between you and the object is contracted"

That's just plain not true (unless by "contracting" you mean "diminishing over time" in which case it's true until the object passes you, and which has nothing to do with length contraction or any other relativistic effect).

If you are a muon, that rule makes sense, I quess.
If you are a planet, then the rule does not make so much sense.

It doesn't make any more sense if you're a muon.

 

[jartsa]

That's just plain not true (unless by "contracting" you mean "diminishing over time" in which case it's true until the object passes you, and which has nothing to do with length contraction or any other relativistic effect).

But the distance to the approaching object's rear is contracted, because the approaching object is contracted?

But the distance to the approaching object's front is not contracted?

Very strange.

 

[PAllen]

But the distance to the approaching object's rear is contracted, because the approaching object is contracted?

But the distance to the approaching object's front is not contracted?

Very strange.

A distance that is contracted is the distance between two objects at rest relative to each other, moving toward you (or away from you, doesn't matter). Then, you can say that the distance you measure between them is smaller than the distance they measure between each other. But there is no sense in which you can talk about distance to a single object being contracted. Contracted relative to what? For contraction, you must have a distance or length measured in two different frames.

 

[Dale]

Are you suggesting that since Earth is a planet which has atmosphere, somehow make the Length contraction valid only in muon's frame.

Yes. Muons are created at the top of the atmosphere and detected at the bottom. Thus the length of the atmosphere is a critical part of the problem.

Btw, I didn't say "valid", I said "relevant". Length contraction is valid (i.e. it happens) in both frames, but the length of the muon is irrelevant to the problem and the length of the atmosphere is relevant to the problem.

Because one can always think of planets which do not have atmosphere, then what would be your reasoning ?

Such planets do not have the effect at all.

 

[Mentz114]

The reason that, we have to apply Lorentz Transformation to the observed facts in-order to get the explanation of how muon reaches Earth in it's frame, does not justify in anyway, why there is contraction only in the muon's frame. And if one claims it is a fair justification, then it is rather a justification of the applicability of LT to situations like this.

(my emphasis)

I don't understand what you mean by this. The distance contraction in the muon coordinates is mentioned because we have chosen to work in the Earth coords. If the muon were considered stationary, then the reciprocal state would pertain, viz the Earth would 'see' a contracted distance.

 

[jartsa]

A distance that is contracted is the distance between two objects at rest relative to each other, moving toward you (or away from you, doesn't matter). Then, you can say that the distance you measure between them is smaller than the distance they measure between each other. But there is no sense in which you can talk about distance to a single object being contracted. Contracted relative to what? For contraction, you must have a distance or length measured in two different frames.

Yes, but I haven't said anything, I just transformed a sentence.

This kind of sentence has been said many times:

A short lived myon can reach the surface of the earth, because the distance is short, and the distance is short because of lorentz contraction. All this in myon's frame.

In short: Distances to approaching objects are shortened. (In the frame of the thing that is being approached)

And yes that is wrong.

 

[WannabeNewton]

If we take this as it stands, it is, as I noted above, inconsistent with the claim that physical observables need not be frame invariant, because tensor contractions in which there are no free indexes, which is what you have to have in order to obtain the number that is actually observed, *are* frame invariant! They have to be, because they're Lorentz scalars.

...

The term "physical observable" is, unfortunately, ambiguous: it can refer both to the general rule that tells you, once you've picked a frame, which 4-vectors (or, more generally, which tensors) to contract; or it can refer to the specific contraction you obtain when you apply the general rule in a specific case. The general rule is obviously frame-dependent, but the specific results for each individual case are not. It would be better if there were two different simple English expressions to describe these two different concepts, but AFAIK there aren't.

Thanks for pointing out the ambiguity. It hadn't crossed my mind when I posted it, I apologize for that. When I was referring to frame-dependence of the contractions what I was intending to convey was that different choices of frame $\{e_{\alpha}\}$ result in different values for the components of some tensor $T$, the physical correspondence being that different observers making measurements of tensor components using their meter sticks and clocks get different values for said components.

 

[PeterDonis]

different choices of frame $\{e_{\alpha}\}$ result in different values for the components of some tensor $T$

Yes. But IMO this is more of a definition of what tensor components are than a statement about physics. The physics is that different choices of frame mean different choices of what basis vectors you contract the tensor with, and therefore different numbers obtained when you evaluate the contractions (corresponding to different predictions for actual physical measurements). The fact that we happen to call the contractions of a tensor with the basis vectors of some frame the "components" of the tensor in that frame doesn't add anything to the physics; it's just a convenient shorthand terminology.

 

[universal_101]

(my emphasis)

I don't understand what you mean by this. The distance contraction in the muon coordinates is mentioned because we have chosen to work in the Earth coords. If the muon were considered stationary, then the reciprocal state would pertain, viz the Earth would 'see' a contracted distance.

Exactly, this is how Lorentz transform work, that is, it is arbitrary to say which frame is stationary and therefore in which frame one calculates the coords.

In other words, applicability of LT suggests both frame sees the space contracted and the other object Time Dilated, which further extends to the apparent nature of Length contraction and Time Dilation.

 

[universal_101]

Yes. Muons are created at the top of the atmosphere and detected at the bottom. Thus the length of the atmosphere is a critical part of the problem.

Btw, I didn't say "valid", I said "relevant". Length contraction is valid (i.e. it happens) in both frames, but the length of the muon is irrelevant to the problem and the length of the atmosphere is relevant to the problem.

Such planets do not have the effect at all.

I think you don't understand how the experiment takes place, let me show you why I say so.

It doesn't matter a bit when and where muon's were created, because experiment measures the number of muons passing at two different heights(in Earth's frame), now comparing the number of muons registered in a particular given time(in Earth's frame) knowing the relative velocity(frame invariant) of muons, one can deduce that more number of muons have reached the lower height, than that a non time dilated muon scenario allows.

So it is very unscientific to say that Earth's atmosphere allows one to choose what is relevant or irrelevant.

 

[Mentz114]

In other words, applicability of LT suggests both frame sees the space contracted and the other object Time Dilated, which further extends to the apparent nature of Length contraction and Time Dilation.

So you're actually arguing about what term to use for a coordinate dependent quantity ? That is a waste of time.

 

[universal_101]

So you're actually arguing about what term to use for a coordinate dependent quantity ? That is a waste of time.

No, rather what is the physical nature of the terms used for a coordinate dependent quantity. Even though it is easy to see their apparent nature, everybody seems to ignore it, and some are even defending by introducing atmosphere as a way to make preferred coordinates relevant or irrelevant for that matter.

 

[Doc Al]

I think you don't understand how the experiment takes place, let me show you why I say so.

It doesn't matter a bit when and where muon's were created, because experiment measures the number of muons passing at two different heights(in Earth's frame), now comparing the number of muons registered in a particular given time(in Earth's frame) knowing the relative velocity(frame invariant) of muons, one can deduce that more number of muons have reached the lower height, than that a non time dilated muon scenario allows.

So it is very unscientific to say that Earth's atmosphere allows one to choose what is relevant or irrelevant.

Realize that the muons, which have a finite lifetime, are created at the top of the atmosphere. So the distance they must travel through the atmosphere to reach the surface is clearly relevant. (And is frame-dependent.)