Perspective on Relativity and Length Contraction

[universal_101]

Are you saying that an object that has accelerated in the past is physically(geometrically) different from an object that has not?

No, I'm not saying anything fancy like that, instead my point is local measurements does not give you the speed independently from other frames, since the speed must be relative to some frame, what I'm implying is that the speed is w.r.t the frame of beacons which is stationary and never accelerated.

 

[universal_101]

Ah I see, thought you gave preference there. Seems you mean just from an interpretation perspective. George's graphs (spacetime diagrams) show that stuff very clearly, and the acceleration is made irrelevant via duration, and that specifically really clears up the hard to recognize part. In other words considering the acceleration in this kinda of scenario trying to determine "which frame experienced less/more/equal time compared to the other frame." adds no value to the results.

duration in which reference frame, and how does it work(maybe an example).

 

[universal_101]

The bolded text above represents a confusion about what a frame is. There's no such thing as accelerating a frame; when you hear people talking about an "accelerating frame" they really mean "a frame in which an accelerating observer is at rest".

Thus, the frame in which the ship is at rest when it passes the beacon at constant relative speed is not the frame in which the ship was at rest while it was accelerating through the takeoff.

OK, I should have replied to this first, I think that is exactly the source of confusion. Then again I thought it was lucid enough, that a frame which never got accelerated is different from the frame of an object which was accelerated and then put in inertial motion.

Nonetheless there is no real meaning to the phrase accelerating a frame in SR, it is always the object accelerating and then analyzing the infinitely many instantaneous frames in between the acceleration or the frame of the object after the acceleration ceases.

 

[universal_101]

I don't suppose you can produce a reference illuminating this supposed contradiction either?

Note, "physical effect" is your term, and is not in PAllen's comments.

OK let me put it another way,

TD and LC are frame dependent, both effects are present in muon's as well as Earth's frame. [Keeping in mind that the only physical effect that we have is number of muons reaching Earth measurement, at two different heights.]

From muon's frame, the Earth is time dilated and the space is length contracted. From Earth's frame muon is time dilated and the space is length contracted.

So, instead of choosing muon to be time dilated in Earth's reference, we can choose the space to be length contracted in both frames(E's and M's), and we would easily be able to explain how muons got to earth.

Next, we can choose both of them to be time dilated w.r.t each other and explain the results from their respective frames, it is easy to see how time dilated muons would make it to the surface of Earth in more numbers than expected, but the same follow if we analyse the situation from muon's frame and consider Earth to be time dilated, since in muon's frame Earth is slow in time whereas muons are perfectly fine and not time dilated, the particular number 'n' muons would reach the surface of the Earth in less time because clocks at Earth are Time Dilated. That is the Earth's clock would register 'n' muons reaching in less time due to Time Dilation which is same as more muons reaching Earth than expected.

This means we can explain the results by using any of the above combination, but this does not validate that the co-ordinates(time and space) we used to explain the invariant effect(number of muons reaching earth) are somehow related to the reality. They are just co-ordinates of a transform!

 

[PAllen]

Never implied that measurements are not local, instead the resultant speed that you get with this measurement is w.r.t the beacons, because those lasers you are using, which the rocket needs to interrupt(pass through) are stationary in beacon's frame. So laser's frame is none other but the beacon's frame, and the speed you get is also w.r.t the beacons.

Edit: And ofcourse speed of passing beacon is same as the speed of rocket w.r.t beacons. Its the relative velocity between the two, which is invariant..

This is pure and simply a lie. The lasers are attached to the rocket, moving with it, and the rocket does not cross them. No measurement is made in the beacon frame.

Since this has been explained multiple times, and is a simple fact of the set up, there is no longer a discussion going on.

 

[PAllen]

OK, I should have replied to this first, I think that is exactly the source of confusion. Then again I thought it was lucid enough, that a frame which never got accelerated is different from the frame of an object which was accelerated and then put in inertial motion.

This is nonsense for local measurements. There is a sense in which for events distant in time and/or space, such that the difference in the past between the motion of two observers affects later observations, that you cannot ignore the difference. However, none of this is matters to local measurements.

Again, we are at the point of ludicrous, unsupportable, and unsupported claims being made.

 

[PAllen]

OK let me put it another way,

TD and LC are frame dependent, both effects are present in muon's as well as Earth's frame. [Keeping in mind that the only physical effect that we have is number of muons reaching Earth measurement, at two different heights.]

From muon's frame, the Earth is time dilated and the space is length contracted. From Earth's frame muon is time dilated and the space is length contracted.

So, instead of choosing muon to be time dilated in Earth's reference, we can choose the space to be length contracted in both frames(E's and M's), and we would easily be able to explain how muons got to earth.

Next, we can choose both of them to be time dilated w.r.t each other and explain the results from their respective frames, it is easy to see how time dilated muons would make it to the surface of Earth in more numbers than expected, but the same follow if we analyse the situation from muon's frame and consider Earth to be time dilated, since in muon's frame Earth is slow in time whereas muons are perfectly fine and not time dilated, the particular number 'n' muons would reach the surface of the Earth in less time because clocks at Earth are Time Dilated. That is the Earth's clock would register 'n' muons reaching in less time due to Time Dilation which is same as more muons reaching Earth than expected.

This means we can explain the results by using any of the above combination, but this does not validate that the co-ordinates(time and space) we used to explain the invariant effect(number of muons reaching earth) are somehow related to the reality. They are just co-ordinates of a transform!

This is total nonsense. The rate of Earth clocks is completely irrelevant in the muon frame. A bunch of muons are sitting at rest. The Earth is approaching at a given speed. The muon's have certain half life T. In time T, the Earth moves by vT. This is 600 meters. None of this can be impacted in any way by what clocks on Earth are doing compared to muon clocks. The only thing that can cause the Earth to reach the muons before T when the muon rest frame measures the Earth's speed as v (no Earth clocks can affect this speed measurement) is for the Earth to be closer than vT.

 

[nitsuj]

No, I'm not saying anything fancy like that, instead my point is local measurements does not give you the speed independently from other frames, since the speed must be relative to some frame, what I'm implying is that the speed is w.r.t the frame of beacons which is stationary and never accelerated.

Ah okay, then I'm not sure what you are suggesting. Reading through the thread it seems you are looking for "hard evidence" of length contraction. Dalespam listed a number of solid popular examples.
imo the postulate and support for c being invariant is proof enough.

 

[TheBC]

Length Contraction is observer dependent(i.e. it is not Lorentz invariant), same as Time Dilation is observer dependent. But because, Time Dilation exhibits measurable physical effects(differential aging-Twin Paradox-fast moving muons) which are ofcourse Lorentz invariant, whereas unlike Time Dilation, Length Contraction has no measurable physical effect, it is safe to say it is an apparent effect(or observer dependent).

In other words you do not consider the physical experience of the other train car ends at stretched arms length a valid measurement to find out what is really in front of their body?
Do you consider the whole proces of 'experiencing' only apparent and/or illusionary?
Do you mean there is in fact ('actually') no short train between stretched armes?
If not, then what is there between or at stretched arms of Green and Red passenger?

 

[dvf]

In other words you do not consider the physical experience of the other train car ends at stretched arms length a valid measurement to find out what is really in front of their body?

Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the back too soon, so no wonder that Red thinks that the green car is shorter than the red car.
(*2) in the bottom figure, where Green touches the red car simultaneously with both hands, Red protests and says that Green is cheating because he does not touch his red car simultaneously. According to Red, Green touches the red car's front too late and the back too soon, so no wonder that Green thinks that the red car is shorter than the green car.

 

[TheBC]

Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the back too soon, so no wonder that Red thinks that the green car is shorter than the red car.
(*2) in the bottom figure, where Green touches the red car simultaneously with both hands, Red protests and says that Green is cheating because he does not touch his red car simultaneously. According to Red, Green touches the red car's front too late and the back too soon, so no wonder that Green thinks that the red car is shorter than the green car.

Fwiw? I think it's worth nothing at all. I do not like the way you formlate it. Sounds as if experiencing the shorter train is 'cheating' or 'incorrect thinking' of the observer train passenger. You get nowhere with this approach. No train passenger is cheating or thinking in a wrong way...

 

[Nugatory]

Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the back too soon, so no wonder that Red thinks that the green car is shorter than the red car.
(*2) in the bottom figure, where Green touches the red car simultaneously with both hands, Red protests and says that Green is cheating because he does not touch his red car simultaneously. According to Red, Green touches the red car's front too late and the back too soon, so no wonder that Green thinks that the red car is shorter than the green car.

Of course these protests are misguided, as they are both overlooking the relativity of simultaneity. Understanding how that can be is the key to resolving this and many related paradoxes.

 

[dvf]

Fwiw? I think it's worth nothing at all. I do not like the way you formlate it. Sounds as if experiencing the shorter train is 'cheating' or 'incorrect thinking' of the observer train passenger. You get nowhere with this approach. No train passenger is cheating or thinking in a wrong way...

Fwiw--not much apparently--I think you missed the point, but feel free not to lose any sleep over it

 

[Simon Bridge]

Of course these protests are misguided, as they are both overlooking the relativity of simultaneity.

It's a bit like two observers disagreeing about the height of a a building (say) without taking into account the (Galilean) laws of perspective.

It's just that we would intuitively expect the train observers to get the same measurement. It's natural, in that situation, think we've already corrected for perspective.

The diagrams in post #59 are, in fact, demonstrating the error in that intuition.

This is why the disagreement between the observers is fairly described as "apparent".

It is also fair to point out that the different measurements are quite real just like the different measurements of the heights of the buildings are real. The mistake, then, is equally described as lack of care in defining the "real" length being measured. In the latter case, it is the length measured by an rulers right next to the building.

I gave a link right at the start of this thread which explains this.
There's four chapters and an introduction.

 

[Dale]

I don't know why there is any need to add poorly-defined descriptors like "real" or "apparent" or "illusion" or "physical" or whatever else. Why not just stick to the well-defined and accurate terms like "frame variant".

Length is frame variant. Scientifically that is complete. Any additional non-scientific terminology you might choose to use is either wrong or must be defined so that it means "frame variant".

I wish people wouldn't make a clear concept fuzzy and confusing this way.

 

[Simon Bridge]

I don't know why there is any need to add poorly-defined descriptors like "real" or "apparent" or whatever else.

Well that's easy:
1. the above debate demonstrates the need for specific, specialized, descriptors;
2. the terms are in common use and so need to be addressed. At the very least, we have to demonstrate the need for a specialized term or people will wonder why they have to say "frame dependent" when they have "perfectly good" words like "real" and "apparent".

I think "apparent length" as distinguished from "true length" is reasonable.
People using the terms do need to make sure the listener is using the same definition though.[*]
In this sense, "apparent" just means "measure in a frame that is not at rest with respect to the thing".

It is too easy to confuse that meaning with the use that describes an optical illusion, or something that is not real for the person doing the measuring. The apparent length of the rail car (for example) is what you'd use to make sure you cross the rails just behind it as it passes you. If the length reduction were not real, you'd bang into car.

--------------------

[*] there's nothing new about this - we have the same problems when introducing newcomers to "force", "work" "color" "strangeness" etc.

 

[PAllen]

But why pick on length for apparent? Kinetic energy is frame variant in both Galilean relativity and SR. Do we say that the only 'non apparent' KE is zero (that measured in the rest frame), and all other KE's are apparent?

Neutral, objective terms like rest length, and length avoid such judgments. These can be considered to correspond to rest mass and total energy (no one calls this 'apparent' because it is frame variant). (length=rest length in rest frame; total energy = rest energy = mc^2 in rest frame).

 

[Dale]

2. the terms are in common use and so need to be addressed.

The way to address them is simply to point out that they are not scientifically well defined. Then you can proceed to explain the scientific terms, which you cannot avoid anyway.

I don't remember any of my professors using terms like "apparent" or "physical" when teaching me about momentum or forces or velocity, despite the fact that they are common terms. And when they did use words like "real" and "fictitious" in teaching me about forces they were careful to point out that the scientific meaning is different from the common meaning.

 

[Simon Bridge]

You'll find the FAQ I link to earlier is also careful in the same way.
And for much those reasons.

I believe we are in agreement here.

I agree with PAllen: Nobody calls frame variant things "apparent" - but they do refer to a measurement that is not made in the rest frame "apparent". A quick trawl through the net yields about 20,900,000 results (0.44 seconds) where a length is described as "apparent" in the context of special relativity.

If you want to know why they are inconsistent in their labelling, you'd have to ask them. Probably things like kinetic energy do not get called "apparent kinetic energy" for the same reason nobody says "rest kinetic energy": the former is a tautology and the latter an oxymoron ... the nature is already included in the usual definition in a way that it is not included in the usual definitions for length and time.

i.e. Famously: Vladimir Varićak (1911) asserted that length contraction is "real" according to Lorentz, while it is "apparent or subjective" according to Einstein.[1] Einstein replied:

[Vladimir] unjustifiably stated a difference of Lorentz's view and that of mine concerning the physical facts. The question as to whether length contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer.[2]​

Which, I think, sums up the POVs and puts them into perspective.

The use of the word "apparent" to refer to observation by a non-comoving observer is all through the literature and through undergraduate textbooks teaching relativity. However, I don't think very many people familiar with relativity use the word "real" very much - though I see the word "true" used a lot for the rest-values.

I agree with DaleSpam about the way to address the use of these terms.
The confusing and argument we have seen in this thread is due to this approach simply not being followed.
Which is pretty much what I hoped people would take away from my last two posts.
Maybe I should have spelled it out more - but I wanted to hear from OP before launching into a lecture.

-------------------------------------

[1] Miller, A.I. (1981), "Varičak and Einstein", Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911), Reading: Addison–Wesley, pp. 249–253, ISBN 0-201-04679-2

[2] Einstein, Albert (1911). "Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variĉaks Aufsatz". Physikalische Zeitschrift 12: 509–510.

 

[ghwellsjr]

I read a quite a few 'appears'/'appearance' vocabulary in this thread. Why should a moving train car 'appear' contracted (as if an optical illusion is involved), and not simply 'be' contracted? It does not make sense.
In the sketch I show how relative moving travellers experience reciprocally a moving contracted train car.

Unfortunately, a static sketch of a dynamic situation can lead to some false conclusions. Spacetime diagrams can clear up these false conclusions. Here is a spacetime diagram depicting the scenario you describe. The vertical red lines depict the red train car and its passenger. The endpoints of the train car are shown as the dark red lines on the left and on the right with another dark red line in the center showing the brain of the red passenger. The light red lines in between the dark red lines show the fingertips of the red passenger. Similarly, the long diagonal green lines depict the moving green train car and its passenger. The shorter darker red and green lines depict the signals traveling from the fingertips of each passenger to their brains. Note that each signal starts at the coincidence of a dark line of one color and a light line of the other color. I have chosen to make these signals travel at a little less than one-half the speed of light (44.7%c) just to keep the diagrams small enough to fit on a page although the same correct conclusions can be drawn no matter what their speeds are or even if they are different for each passenger (but the same for each arm of each passenger):

The moving train car does not 'appear' to fit between the passenger's fingertips (and does not 'appear' contracted to be able to fit between his fingertips). The train car simply does fit between his fingertips. The signals (information of the events) of the front and rear of the moving train at his fingertips are traveling simultaneously, from his fingertips through his arms and reaching his brain simultaneously. That's no illusion or arbitrarily chosen frame calculation.

I agree it's no illusion but the statement that the two signals for each passenger are traveling simultaneously from their fingertips to their brain is based on an arbitrarily chosen frame calculation. In this case, it is true for the red passenger but not for the green passenger. And that is the point of length contraction. 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.

There is a shorter train between the fingertips at the end of the passenger's arms. One may call this 'measuring from the passenger's frame'; it simply means what the passenger's 3D space of simultaneous events (his 3D reality at one moment in time) is made of.

If you consider a train car at rest in front of you, you do not say the train car at rest 'appears' x meters long. You don't do this because you do not refer to any 'optical illusion'.
Stating that a moving train car 'appears' contracted insinuates there is some optical illusion involved. But there is no optical illusion invoved. Therefore there is also no reason to state that a moving train car 'appears' contracted. If the moving train car 'appears' contracted, then a train car at rest also only 'appears' measuring a certain length.

The reason why people often think the contraction only 'appears' as such is because the contraction is reciprocal. How can relative moving train cars be contracted reciprocally if its not an optical illusion effect?
Because the 3D worlds of simultaneous events of both passengers are different. Consider the train cars as 4D spacetime structures instead of evolving 3D objects. The different contracted train cars are different objects of simultanous events, cuts with different 'direction' through the 4D spacetime train car structures (like cutting a loaf of bread in different directions results in different 'objects'/slices of bread). Minkowski or Loedel diagrams visualize this very well.

Now I want to show the above spacetime diagram transformed to the rest frame of the green train car and its passenger to show the reciprocal effects that you are talking about but first, I have to correct the bottom image of your sketch to show that the train tracks are also length contracted:

And here is the corresponding spacetime diagram. All of my comments regarding the rest frame of the red train car apply in a reciprocal nature in the rest frame of the green car:

And since you mentioned a Loedel diagram, I show another spacetime diagram transformed such that both trains are moving at the same speed in opposite directions:

The point of all these diagrams is that they are all equally valid and all depict exactly the same observations that each passenger and each object makes in the different frames. None of the frames are preferred, not even the rest frame of each passenger. 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.

And as I said earlier, a static sketch of a dynamic situation can lead to false conclusions. If you had made animations showing the sensing by the fingertips of the opposing train cars and the propagation of each signal along each arm and the simultaneous arrival of each pair of signals in the brains of the two passengers, then the false conclusions could have been avoided. Your sketch depicts just one snapshot of such an animation.

 

[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.