Perspective on Relativity and Length Contraction

[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.)

 

[Mentz114]

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,

In this case, the coordinate dependent quantities are measurements made (by observers or machines) using those coordinates for their local frame. So their physical meaning is clear.

and some are even defending by introducing atmosphere as a way to make preferred coordinates relevant or irrelevant for that matter.

I think you might have misunderstood someting.

 

[universal_101]

Once they are created, there is no use of atmosphere, we don't need atmosphere to conduct the experiment. Because the experiment takes place after the creation of muon, so it does not matter where and when the muon's were created.

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.)

That being said, the distance they must travel in between them is length contracted in both frames, by the application of Lorentz transform to the situation. And it is just as much relevant in Earth's frame as in the muon's frame.

And what would happen if one fires muon from a muon gun at the surface of a planet without atmosphere?

 

[Dale]

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.

No, you apparently don't understand. Without an atmosphere the cosmic ray collisions that produce muons would occur randomly everywhere. There would be no significant difference in the number of muons at different heights.

It is precisely because muons are systematically produced at the top of the atmosphere that leads to the observed phenomenon of altitude dependence. You simply cannot do away with the atmosphere. Wherever you position your detector, the relevant length is from the top of the atmosphere to the detector.

 

[universal_101]

In this case, the coordinate dependent quantities are measurements made (by observers or machines) using those coordinates for their local frame. So their physical meaning is clear.

I think you are overstating your position on measurements, the only measurements available are that you posted in your post #77.

 

[TheBC]

In all of them, they each detect in their brains the signals from their fingertips simultaneously even though they may or may not start out simultaneously and may or may not travel along their arms simultaneously.

My bold.

This seems wrong. Correct me if I do not read you correctly.
Let's consider red observer feeling a shorter green car.
What you say is: Red feels simultaneity, but the signals from the events he feels may not start out simultanously?
This does not make sense.
Red's arms have equal length. Period.
The signals (let's take light speed) travel for him at same speed. Period.
Hence both signals left simultaneously. Period.

I think you made the following error.
The contracted green train is not the green rest train 'but measured differently'.
The contracted green train (simultaneous events for red) is made of completely different events (different content) than the events of that train for a co-moving observer/passenger.
That's the reason for reciprocal length contraction (*). Not because of signals not traveling at same speed, or signals of events that did not start simultaneously but arrived simultaneously.

For Red the green REST car is made of non-simultaneous events. But Red does not measure that car (those events) contracted. He measures simultaneous events, i.e. OTHER events from the green 4D spacetime train. (No wonder for so many people not grasping the essence of realtivity the moving train only 'appears' shorter... )

Your IRF charts are O.K., but -tell me I'm wrong- it appears (sic) that you hesitate to read a full 4D spacetime diagram correctly. Different relative moving train passengers cut through/refer to completely different (content of) events of the 4D train! The simultaneous green car events are 'really' 'physically' out there between the red passenger's hands. Similar reasoning for the green observer/passenger feeling the red car.

What the red observer thinks about light signals from the green rest train is irrelevant. Do me a favor. Draw on the diagram the light paths from the rear and front of the green rest train and see where they end at red's head. That's a complete different story, irrelevant for red's measurement of a shorter green train.

Because the contracted train has in fact nothing to do with the events of the train at rest of the co-moving observer, strictly speaking the train does not really get contracted. Unfortunately when one says or reads that the train at rest in fact does not contracts, then everybody will interpret this erroneously as: the contracted moving train is only an illusion, or only mathematical frame feature, or only 'appears' as such, etc.

Ghwellsjr, I really do appreciate the time and effort you put into drawing your IRF charts, you are one of the few visualizing data, but it might be interesting as well to scrutinize a full 4D spacetime diagram as well. Especially Loedel diagram because of equal time and space lengths on all axes (making it eassier to keep track of proper time and length in both frames of simultaneous events).

(*) ... and time dilation, but I'm afraid that will take another thread to explain...

 

[TrickyDicky]

Universal, if your main point here is to highlight that a preferred frame is being chosen and therefore SR's Lorentz symmetry is apparently broken unless one speaks in terms of appearances or illusions , that was I'd say settled in the "Explanation of EM-fields using SR" thread (#132).

Read about "spontaneous symmetry breaking" and "hidden" symmetries in physics. Even for theories that are formally symmetric, when the system is interacted with that creates an asymmetry and therefore a frame measures are made against.

It is true most people is not aware of this and therefore it is an issue prone to attract debates.

 

[Mentz114]

I think you are overstating your position on measurements, the only measurements available are that you posted in your post #77.

I mention two coordinate dependent quantities, the distances X and x. They are measurements in principle.

Neither of them is 'apparent' or 'illusory'.

 

[universal_101]

No, you apparently don't understand. Without an atmosphere the cosmic ray collisions that produce muons would occur randomly everywhere. There would be no significant difference in the number of muons at different heights.

It is precisely because muons are systematically produced at the top of the atmosphere that leads to the observed phenomenon of altitude dependence. You simply cannot do away with the atmosphere. Wherever you position your detector, the relevant length is from the top of the atmosphere to the detector.

I think as an Experimental physicist ZapperZ can clear it up easily, but let me also put it across how the Experiment is conducted.

---------------------------------------
----------muons created---------------
---------------------------------------

|||||||||||||||||||||||||||||||||||||||
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv muon's coming down(and decaying).


__________________________________detector 1, mesaures the number of muons passed in a
--------------------------------------- particular given time.


| | | | | | | | | | | | | | | | | | | | | | |
v v v v v v v v v v v v v v v v v v v v v fewer muons coming down(and decaying)


__________________________________detector 2, mesaures the number of muons passed in the
---------------------------------------same particular given time.

The only distance that matters here is the distance between the detectors, the only number that matters here is the number of muons registered by the two detectors(in same time), the only speed matters here is ofcourse the relative velocity.

So, when we are talking about the length contraction we are always referring to the distance between the two detectors, and this distance has nothing to do with, where and when the muons were created.

 

[Histspec]

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 ?

You seem to have problems understanding the operational foundations of "proper length" and "contracted length". Of course, the measured space is mutually contracted, but this has nothing to do with the actual measurement situation in this specific muon experiment. Look, it's simple:

In Earth's frame, we measure one muon at distance L from Earth's surface. What does this statement mean? It means, for instance: In Earth's frame, there is a measuring rod of 10km length, which defines the space-length of 10km between the two detectors. Since this "rod" is at rest in the Earth frame, its length is by definition the rest length of the rods and thus of the distance of 10km between those two places.

Of course, you principally can do the same in the muon frame. That is, you can measure a rest length of 10km with their own measuring rods. Since it is at rest in the Muon's frame, this length is by definition the rest length of the rods and thus of the distance of 10km between those two places.

This symmetrical situation can be seen in the following image:
One blue rod of proper length L resting in the Earth frame - if the muon hits the other end we call it event Y.
One red rod of same proper length L resting in the muon frame – if Earth hits the other end we call it event X.
As we can see, the rods are mutually length contracted.

However: Which length is relevant for our specific muon experiment? Of course, it's the blue length since we are asking for the appearence of the muon at one end of length L in the Earth frame, i.e. we are asking for event Y.

Do you now understand why this specific length is shorter in the muon frame?

 

[universal_101]

I mention two coordinate dependent quantities, the distances X and x. They are measurements in principle.

Neither of them is 'apparent' or 'illusory'.

What principle, please elaborate.

the distance X is a physical measurement, agreed. The distance x is not a physical measurement, it is calculated/deduced by using LT on this particular scenario.

 

[Mentz114]

What principle, please elaborate.

the distance X is a physical measurement, agreed. The distance x is not a physical measurement, it is calculated/deduced by using LT on this particular scenario.

What 'in principle' means in this context, is that x could be a physical measurement if we used a machine that mimic'd the muon and had apparatus to do the measurement. It is a measureable quantity. There is no physical reason to prevent it being measured.

 

[Dale]

And what would happen if one fires muon from a muon gun at the surface of a planet without atmosphere?

Then the relevant length is the distance from the muon gun to the detector. That length is contracted in the frame where the gun and detector is moving. It is not contracted in the frame where the gun and detector are at rest. Thus length contraction is not relevant in their rest frame.

The length of the atmosphere is relevant in the standard scenario because the length of the atmosphere is the distance between the "gun" and detector. I.e. the top of the atmosphere is the "gun".

 

[Dale]

The only distance that matters here is the distance between the detectors, the only number that matters here is the number of muons registered by the two detectors(in same time), the only speed matters here is ofcourse the relative velocity.

So, when we are talking about the length contraction we are always referring to the distance between the two detectors, and this distance has nothing to do with, where and when the muons were created.

First, without the atmosphere (or a gun) the muons are moving randomly and isotropically, so your little arrows would not be correct, they would not all be moving down but rather moving isotropically in random directions.

Second, you are correct that you can place multiple detectors. The problem is usually stated in terms of a source (the top of the atmosphere) and a single detector (at the bottom of the atmosphere). You could do it in terms of a source and two detectors different distances from the source, but you still need a source. Without a source you would not get the muons moving in the same direction and decaying systematically. The distance between the source and each detector will determine what fraction gets to the detector. That is the relevant length (and in the standard scenario is equal to the length of the atmosphere).

In a frame where that length is not contracted then length contraction is irrelevant. How can you not get that? How can you possibly think that length contraction is relevant in the Earth's frame? The only thing that is length contracted in that frame is the muon itself. In what way is the length of the muon relevant for the problem?

 

[universal_101]

What 'in principle' means in this context, is that x could be a physical measurement if we used a machine that mimic'd the muon and had apparatus to do the measurement. It is a measurable quantity. There is no physical reason to prevent it being measured.

Yeah, but your assertion is rather philosophical than scientific. The matter of fact is there are so many properties that are apparent under relative motion, like Doppler effect/aberration/etc. which are measured physically, but are never considered as actual.

And these effects are not even mutual, like the coordinates of LT, namely LC and TD.

 

[ghwellsjr]

Yeah, but your assertion is rather philosophical than scientific. The matter of fact is there are so many properties that are apparent under relative motion, like Doppler effect/aberration/etc. which are measured physically, but are never considered as actual.

And these effects are not even mutual, like the coordinates of LT, namely LC and TD.

Huh? Who ever said that physically measured properties are not actual?

And who said that Doppler effect/aberration are not mutual (if by that you mean reciprocal), at least for inertial objects?

That is one application of the Principle of Relativity, Einstein's first postulate, having nothing to do with his second postulate from which the effects of LT, LC and TD are derived.