Perspective on Relativity and Length Contraction

[WannabeNewton]

You seem to conflate many things (illusory, observer dependent, falsifiable). Consider:

1) Einstein rings from gravitational lensing is illusory in the sense that the distant galaxy is not predicted to become a ring, only produce a ring in an image. This illusion is a falsifiable prediction that has been confirmed.

2) Penrose-Terrell rotation is illusory in the same sense as an Einstein ring (there is no prediction that the object rotates, only that its image does). It is a falsifiable prediction which has not been confirmed only due to extreme engineering challenges.

3) Length contraction is not an illusion in the sense of (1) and (2); it is not only a spatial prediction of 'geometric' SR, but also a prediction from the application of Lorentz invariant dynamical laws (e.g. Maxwell's equations) to an object moving in a frame. It is a falsifiable prediction. It is also frame dependent. It has not been confirmed in the most direct way due only to engineering difficulties.

Note that per (3), a falsification of length contractions would also be a falsification of the application of all of our fundamental physical laws to moving objects.

Authors who call it illusory typically try to say that any concept of spatial dimension of a moving object is dependent on definition of measuring approach. However, the only alternative that avoids contraction is the directive that it is invalid to measure length of a moving object. This is a weak argument, and a minority opinion.

I couldn't agree more with this post.

 

[universal_101]

You seem to conflate many things (illusory, observer dependent, falsifiable). Consider:

3) Length contraction is not an illusion in the sense of (1) and (2); it is not only a spatial prediction of 'geometric' SR, but also a prediction from the application of Lorentz invariant dynamical laws (e.g. Maxwell's equations) to an object moving in a frame. It is a falsifiable prediction. It is also frame dependent. It has not been confirmed in the most direct way due only to engineering difficulties.

Agreed, but there is inherent contradiction between the three underlined, "A frame dependent falsifiable prediction which is not illusory(i.e. a physical effect)". Since, a physical effect must be frame invariant. Just like differential aging is frame invariant, but the problem is Time Dilation and Length contraction are nothing alike. That is, we don't have net length contraction similar to the net Time Dilation effect(differential aging).

 

[PAllen]

and as always as per SR, the only way one would know if there is LC involved is by measuring the TD which can be measured physically.

There are no time dilation measurements anywhere in my proposal. Are you suggesting: If I accelerated in the past, but am now inertial, it is not valid to make direct local measurements? Instead I must ask someone who never accelerated?

 

[PAllen]

Agreed, but there is inherent contradiction between the three underlined, "A frame dependent falsifiable prediction which is not illusory(i.e. a physical effect)". Since, a physical effect must be frame invariant. Just like differential aging is frame invariant, but the problem is Time Dilation and Length contraction are nothing alike. That is, we don't have net length contraction similar to the net Time Dilation effect(differential aging).

There is no contradiction at all. Note that there is an invariant measurement (muon reaches the ground; rocket can complete journey without astronaut dying). The measurement just has a frame variant manifestation (time dilation, length contraction, or mixture, depending on frame). Measuring time in one frame, or distance in another, are both equally valid measurements.

 

[universal_101]

There are no time dilation measurements anywhere in my proposal. Are you suggesting: If I accelerated in the past, but am now inertial, it is not valid to make direct local measurements? Instead I must ask someone who never accelerated?

I think I don't understand what direct local measurement stand for, and if this measurement involves only the frame of rocket then how are we going to measure speed of rocket. Since speed must be w.r.t some other frame if it has to be non-zero and the only other frame here is of beacons, so the measured speed must be w.r.t beacons frame.

Exactly, you must ask who never accelerated.

 

[universal_101]

There is no contradiction at all. Note that there is an invariant measurement (muon reaches the ground; rocket can complete journey without astronaut dying). The measurement just has a frame variant manifestation (time dilation, length contraction, or mixture, depending on frame). Measuring time in one frame, or distance in another, are both equally valid measurements.

I think we can agree to disagree, as long as there is no observed length contraction effect(direct).

 

[PAllen]

I think I don't understand what direct local measurement stand for, and if this measurement involves only the frame of rocket then how are we going to measure speed of rocket. Since speed must be w.r.t some other frame if it has to be non-zero and the only other frame here is of beacons, so the measured speed must be w.r.t beacons frame.

Exactly, you must ask who never accelerated.

I can measure the speed of beacon going by: I just have it interrupt two laser beams 5 meters apart (for example), and time the interval between the interruptions. Rocket can 'easily' do this with some apparatus mounted outside the rocket. So, all within rocket frame (only one time rate involved, no comparisons), I measure beacon speed, and time interval between beacon's passing. Distance is v*passing_interval. During the whole time of these measurements, all in the vicinity of the rocket, the rocket is inertial. I find that on each passing, the beacons are getting closer together.

[edit: to be even clearer: the rocket uses only clocks on the rocket and one ruler for all its measurements. Thus no time dilation involved. ]

You really want to argue that if you've ever accelerated, you can no longer make valid local measurements?

 

[universal_101]

I can measure the speed of beacon going by: I just have it interrupt two laser beams 5 meters apart (for example), and time the interval between the interruptions. Rocket can 'easily' do this with some apparatus mounted outside the rocket. So, all within rocket frame (only one time rate involved, no comparisons), I measure beacon speed, and time interval between beacon's passing. Distance is v*passing_interval. During the whole time of these measurements, all in the vicinity of the rocket, the rocket is inertial. I find that on each passing, the beacons are getting closer together.

I think the laser beams that the rocket interrupts are lying across the path of the rocket.

Now, I think you would consider the beams to be stationary in the beacons frame.

This implies, the frame of lasers is none other than that of beacons.

Therefore, your speed is w.r.t the non-accelerated frame, and it is exactly what we need.

 

[PAllen]

I think the laser beams that the rocket interrupts are lying across the path of the rocket.

Now, I think you would consider the beams to be stationary in the beacons frame.

This implies, the frame of lasers is none other than that of beacons.

Therefore, your speed is w.r.t the non-accelerated frame, and it is exactly what we need.

Wrong. There is no measurement of rocket speed. The rocket is measuring speed of passing beacon. There is no acceleration in the rocket during a whole cycle of measurement. The lasers are mounted on the rocket outside the rocket. The clocks are mounted on the rocket. The sensors to detect lasers are mounted on the rocket.

<Rocket---->
R1-------- R2
|----------|
L1---------L2

R1 and R2 are receivers and associate clocks on the rocket. L1 and L2 are lasers. Their mounting is simply offset or angled so the beacon can go by without hitting the mounting.

 

[universal_101]

Wrong. There is no measurement of rocket speed. The rocket is measuring speed of passing beacon. There is no acceleration in the rocket during a whole cycle of measurement.

What is so special about it, its a simple setup you are describing.

Now, the rocket measuring the speed of passing beacon is same as the measurement of rocket speed w.r.t beacons. Since relative velocity is frame invariant. It does not matter how you measure it, it is same for all the inertial frames.

Ofcourse we don't need any acceleration in the rocket during measurement, I never implied anything like that

 

[universal_101]

You really want to argue that if you've ever accelerated, you can no longer make valid local measurements?

Never implied anything like that, what I said instead that your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

 

[PAllen]

Never implied anything like that, what I said instead that your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

Nonsense. All measurements are local measurements in a rocket inertial frame. We measure speed of a passing beacon, and time between one passing and then the other. One pair of local clocks, one ruler, all on/in rocket are all that are used.

 

[nitsuj]

The same applies to the later part, they both are time dilating w.r.t each other as long as they are in motion w.r.t each other, but it is hard to recognize which frame experienced less/more/equal time compared to the other frame.

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.

 

[nitsuj]

Never implied anything like that, what I said instead that your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

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

 

[Nugatory]

your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

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.

 

[nitsuj]

your measurement are w.r.t a frame which has never accelerated, and I think it is fairly easy to see through it.

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.

im sure universal_101 knows a frame actually isn't an object, so doesn't care if a frame cannot technically be said to be accelerating; due to the definition of a frame.

 

[Dale]

So it is hard to find any mainstream reference for the criterion.

Then it doesn't belong here.

 

[Dale]

Agreed, but there is inherent contradiction between the three underlined, "A frame dependent falsifiable prediction which is not illusory(i.e. a physical effect)".

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.

 

[Dale]

I think we can agree to disagree, as long as there is no observed length contraction effect(direct).

There is plenty of evidence for length contraction. Whether or not you choose to call it "direct" depends primarily on your definition of "direct" and not primarily on the quality of the evidence. The MMX, muons, and bunch length are all good solid evidence for length contraction. The bunch length, in particular, is in my mind what I would call "direct" evidence since it involves length contraction of the object moving relative to the lab.

 

[universal_101]

Nonsense. All measurements are local measurements in a rocket inertial frame. We measure speed of a passing beacon, and time between one passing and then the other. One pair of local clocks, one ruler, all on/in rocket are all that are used.

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..

 

[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.