Perspective on Relativity and Length Contraction

[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.

 

[universal_101]

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".

The reason I introduced "muon gun" is that we can get rid of atmosphere. Now instead of focusing on muons created you are hanging with the gun!

Forgive me to be so blunt but I think you are deliberately not addressing the issue, there is no reason length contraction should involve the muon gun, instead it is the distance between the muons created and the Earth(and these two objects are moving w.r.t each other).

 

[Dale]

instead it is the distance between the muons created and the Earth(and these two objects are moving w.r.t each other).

The source of the muons (the top of the atmosphere or the muon gun) is not moving wrt the earth. The important distance is the distance betweed the source and the detector. That is the distance (together with the closing speed) which determines how much time passes between the creation and the detection in any frame.

 

[ghwellsjr]

The reason I introduced "muon gun" is that we can get rid of atmosphere. Now instead of focusing on muons created you are hanging with the gun!

Forgive me to be so blunt but I think you are deliberately not addressing the issue, there is no reason length contraction should involve the muon gun, instead it is the distance between the muons created and the Earth(and these two objects are moving w.r.t each other).

If you would define whatever scenario you want precisely enough so that I and everyone else can understand it (without unending questions about what you meant) then I will draw a diagram and transform it to any other frame you want and then maybe we can see where the problem is. Just remember, you need to specify all times, locations and speeds according to a single Inertial Reference Frame and make it be along one dimension, otherwise, I can't draw a spacetime diagram for it.

OOPs: I guess it's too late. Oh well, keep reading threads on this forum and maybe you'll clear up your misunderstanding that way. For example, this one:

www.physicsforums.com/showthread.php?t=659658

 

[ghwellsjr]

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.

My bold.

This seems wrong. Correct me if I do not read you correctly.

You only quoted my last sentence of the paragraph. I put in the whole paragraph to keep the last sentence in context.

Simultaneity is frame dependent. Speed is frame dependent (except for the speed of light). Length is frame dependent. Time is frame dependent. Measurements, observations, sensations, and appearances are not frame dependent. An event in different frames has different time and spatial coordinates. We set up the coordinates of events for a scenario in one frame and we use the Lorentz Transformation process to determine the coordinates of each event in any other arbitrary selected frame. As a result, all the measurements, observations, sensations, and appearances will come out the same in all these frames but the coordinates and thus the simultaneities, speeds (except the speed of light), lengths and times will come out different. These comments explain all the rest of your questions and concerns.

I think the problem is that you consider the rest frame of each observer to be preferred and it's not. The rest of my post is just elaboration on this one point.

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?

The event of the arrival of the two sensory feelings are simultaneous because they happen at the same location. It is one event. In any coordinate system, it will continue to be one event. But the two events at the two fingertips of an observer are not at the same location which is why they are two separate events. The time coordinates of those two events determines whether they are simultaneous or not. In the rest frame of the observer, they are simultaneous but in other frames, they have different time coordinates and are not simultaneous. These concepts are well-established definitions in Special Relativity and I didn't think they were debatable.

This does not make sense.
Red's arms have equal length. Period.

True in all frames.

The signals (let's take light speed) travel for him at same speed. Period.

True only for light in all frames.
For other signals (the feelings conducted by nerve signals) it is true only in red's rest frame. In other frames, it's not true.

Hence both signals left simultaneously. Period.

True only in red's rest frame, not true in other frames.

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... )

The measurements that each observer makes, that is, the raw data that shows up on his instruments are exactly the same in every frame. He cannot determine simultaneity of remote events by just passively making measurements and observations. He must also be proactive and emit radar signals and wait for their echoes, and if he is going to follow Einstein's convention, he must assume that those signals took the same amount of his measured time to reach the target as it did for the echo to return. Then, from all this data, he can construct a frame and make a spacetime drawing and if he wants he can transform to any other frame and if he follows the edicts of Special Relativity, he will not claim that anyone of these frames is preferred, in the sense that it is more correct or contains more information or is more closely aligned with reality, than any other frame.

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.

Well, if correctly reading a full 4D spacetime diagrams means concluding that simultaneous events are 'really' 'physically' out there, then you are not wrong.

By the way, by "full 4D spacetime diagram" do you mean a Loedel diagram of the type that you drew earlier? If so, that to me is nothing more than a 2D spacetime diagram just like the ones I make with 1D of time and 1D of space. If you are saying that a Loedel diagram shows reality in a way that diagrams for other frames does not, then this is exactly the point of disagreement, as I said earlier.

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.

OK, I've added in light paths and labeled the important events for all three of my previous diagrams for both red and green (more than you asked--but I don't know your point):

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...

What if we have just a single train with a Proper Length of 1000 feet, nobody in it or out of it, it's sitting motionless on a track. We establish coordinates for it for the rest frame of the track and the train and draw a spacetime diagram for the train, which will appear as two vertical lines (if we want, it really doesn't matter). Then we transform it to a different frame moving at 60%c with respect to the first frame. Now the length of the train is 800 feet and the two vertical lines are closer together. We continue to transform to a frame moving at 80%c with respect to the original frame. Now the train has a length of 600 feet. Transform to 93.6%c, the train is 352 feet long. Transform to 96%c, the train is 280 feet long.

Do you agree with all of the foregoing? If so, how does a Loedel diagram help understand what's going on?

 

[phyti]

Begin with a space-time drawing with U as a reference. A and B are moving in identical ships 4 units long, at .4c and .8c respectively in the x direction. Each ship has a transmitter at the front, radiating 360º perpendicular to the x axis. As the ships pass each other, A and B record the interval of reflected signals according to their clocks.

A hyperbolic curve of constant time is formed at an arbitrary time (10.00), copied and scaled to intersect an event of interest. By making the front of one ship coincident with the back of the other at the origin, only one time axis is required. Since the front and back clocks are synchronized for each ship, the events can be shifted to the end passing thru the origin.

A records the B ship passing from e1 to e2, or 5.50 time units.
B records the A ship passing from e0 to e1, or 5.50 time units.

A measures the speed of B as (.8 - .4)/(1 - .32) = .588.
A calculates 1/ = .809.
A calculates length of B ship as 4/ = 3.23 = .588*5.50

B measures the speed of A as -.588.
B calculations are equal to those of A.

The results are symmetrical and equal.

As noted by others, the misinterpretation is A and B making their observations simultaneously.
As noted by ghwellsjr, two observers with relative motion do not measure time dilation or length contraction, but a general form of doppler shift, i.e. a varying frequency shift of light signals. Each observer is present at emission and detection of their signal, and calculate (per SR convention) the time (and subsequent position) of the reflection event.

 

[TheBC]

You only quoted my last sentence of the paragraph. I put in the whole paragraph to keep the last sentence in context.

Simultaneity is frame dependent. Speed is frame dependent (except for the speed of light). Length is frame dependent. Time is frame dependent. Measurements, observations, sensations, and appearances are not frame dependent. An event in different frames has different time and spatial coordinates. We set up the coordinates of events for a scenario in one frame and we use the Lorentz Transformation process to determine the coordinates of each event in any other arbitrary selected frame. As a result, all the measurements, observations, sensations, and appearances will come out the same in all these frames but the coordinates and thus the simultaneities, speeds (except the speed of light), lengths and times will come out different. These comments explain all the rest of your questions and concerns.

I think the problem is that you consider the rest frame of each observer to be preferred

Definitely not, but this is irrelevant. Relativity of simultaneity events is what is important.

and it's not. The rest of my post is just elaboration on this one point.The event of the arrival of the two sensory feelings are simultaneous because they happen at the same location. It is one event. In any coordinate system, it will continue to be one event. But the two events at the two fingertips of an observer are not at the same location which is why they are two separate events. The time coordinates of those two events determines whether they are simultaneous or not. In the rest frame of the observer, they are simultaneous but in other frames, they have different time coordinates and are not simultaneous. These concepts are well-established definitions in Special Relativity and I didn't think they were debatable.

correct

True in all frames.True only for light in all frames.
For other signals (the feelings conducted by nerve signals) it is true only in red's rest frame. In other frames, it's not true.

You are correct, but you are nitpicking now. I consider the nerve signal light speed transportation of contact event.

True only in red's rest frame, not true in other frames.

Same remark

The measurements that each observer makes, that is, the raw data that shows up on his instruments are exactly the same in every frame. He cannot determine simultaneity of remote events by just passively making measurements and observations. He must also be proactive and emit radar signals and wait for their echoes, and if he is going to follow Einstein's convention, he must assume that those signals took the same amount of his measured time to reach the target as it did for the echo to return. Then, from all this data, he can construct a frame and make a spacetime drawing and if he wants he can transform to any other frame and if he follows the edicts of Special Relativity, he will not claim that anyone of these frames is preferred, in the sense that it is more correct or contains more information or is more closely aligned with reality, than any other frame.

correct

Well, if correctly reading a full 4D spacetime diagrams means concluding that simultaneous events are 'really' 'physically' out there, then you are not wrong.

thanks. So you agree that the red car between green's hands is a different train than any green rest train? O.K.?

By the way, by "full 4D spacetime diagram" do you mean a Loedel diagram of the type that you drew earlier? If so, that to me is nothing more than a 2D spacetime diagram just like the ones I make with 1D of time and 1D of space. If you are saying that a Loedel diagram shows reality in a way that diagrams for other frames does not, then this is exactly the point of disagreement, as I said earlier.

What is this third diagram about? I don't know. Is it as seen from the railway track? I am not interested at all in that information, because it's irrellevant for reciprocal length contractiion.
Does that IRF chart combine previous two? In that case I cannot find the reciprocal contraction length 6 as shown on separate first two diagrams.
One loedel diagram (one and the same the same ruler) does give you reciprocal contraction length 6. And with one and the same ruler.

Furthermore in your third chart I can not read the proper length of the red and green car (12 length) .
In a loedel diagram you would measure -with one and the same ruler- the proper red length (12) between A and C; i.e. the line (not drawn in your IRF charts but essential in Loedel -and SR!) between A and C because that line is the collection of events the shorter train is made of. Same remark for proper green length between E and G (12).

(I won't discuss reciprocal time dilation here, because at this stage off topic in our exercise, but on loedel that too is read with that same ruler. Proper times and lengths, reciprocal contraction and reciprocal time dilation, all in one diagram with one ruler only. Your charts can not get this wright.)

Because in your diagram there is no line drawn between A and C, nor between E and G, you do not highlight the events a contracted train car between the hands is made of. And that's precisely the point I want to make.
Only then you will see what happens 4-dimensionally.
I find you first chart even a bit disturbing, alhough it does give you the correct contraction length. In that first diagram (red with a shorter green) the rest length of red AND green are measured horizontally, which in 4D spacetime is problematic because it looks as if there's one preferred frame where in fact bith red and green cars have same length 12 -the horizontal one-.
For all above reasons I do not consider your IRF charts real 4D diagrams... They are more IRT charts. Loedel gives you a far better picture how 4D spacetime works, but obviously/apparently not everybody agrees with this? ;-)

OK, I've added in light paths and labeled the important events for all three of my previous diagrams for both red and green (more than you asked--but I don't know your point):

I asked: <<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.>> You didn't draw this.

-

 

[TheBC]

What if we have just a single train with a Proper Length of 1000 feet, nobody in it or out of it, it's sitting motionless on a track. We establish coordinates for it for the rest frame of the track and the train and draw a spacetime diagram for the train, which will appear as two vertical lines (if we want, it really doesn't matter). Then we transform it to a different frame moving at 60%c with respect to the first frame. Now the length of the train is 800 feet and the two vertical lines are closer together. We continue to transform to a frame moving at 80%c with respect to the original frame. Now the train has a length of 600 feet. Transform to 93.6%c, the train is 352 feet long. Transform to 96%c, the train is 280 feet long.

Do you agree with all of the foregoing?

yes

If so, how does a Loedel diagram help understand what's going on?

see my comments about loedel in previous post.

 

[Dale]

For all above reasons I do not consider your IRF charts real 4D diagrams.

Of course they are not 4D, neither are Loedel diagrams. Both are 2D and both contain the exact same information.

 

[phyti]

A calculates 1/ = .809.
A calculates length of B ship as 4/ = 3.23 = .588*5.50

post 125
characters translated incorrectly, should read

A calculates 1/γ = .809.
A calculates length of B ship as 4/γ = 3.23 = .588*5.50

 

[Simon Bridge]

I have a feeling that everyone has started talking past each other.

Perhaps all parties could use a position statement from each POV along with some sort of definition of terms used? Then we can check what someone is trying to say against what we think they have been saying. It also allows for shifts in position as a result of effective arguing gone by.

Lets pick a situation ... the argument revolves around basic simultaniety.

Two observers in separate railway carriages [Alice Red and Bob Green], with equal rest-lengths [of the carriages: Alice and Bob are not comparing their own lengths], pass each other.

They [Alice and Bob] each measure the length of the other carriage.

They also observe the process of the other person making the measurement ... this last part seems to be where a lot of the debate is.

They make a careful record of all their observations, then meet up in a railway cafe later on to compare notes.
How does each observer describe the events on the journey ... we can allow them to make allowances for the finite speed of light when they report things.

It will probably help to have an unambiguous measuring device so we don't have to rely on biology ... they each have a pair of boxes that have a brush-contact and a light bulb. The bulb flashes when the contact brushes something.

Rig so the brushes will contact the other carriage.
Just using one box: the other carriage leading end passes <pulse1> then the other carriage trailing end passes <pulse2> the time between pulse 1 and pulse 2, and knowledge of the relative speed, gives the measured length of the other carriage.

To get the speed, we want two of these boxes set a known distance apart.
Time for the lead end to from one box to the other, with the known distance, tells you the speed.

This would be the first set of measurements.
To avoid having to take the observer's fallable word for things - we can set up very accurate light detectors half way between the boxes - as measured in the frame in which the boxes are at rest - hooked to a recording device. The detector needs to be able to tell which light is which - maybe they can be different polarizations, different colors, or there are two detectors, or whatever. It's a solvable technical problem.

i.e. In Alice's notebook:
the time the green carriage front-end triggers a pulse on box a is $[t_{a1}]_A$
the time the green carriage front-end triggers a pulse on box b, known distance $[d_A]_A$ away, is $[t_{b1}]_A$
the time the green carriage back end triggers a pulse on box a is $[t_{a2}]_A$

Notice how careful I am being with notation?
For those who may not follow: $[X_{yn}]_Z$ indicates quantity the nth measurement of X on device y in the rest-frame of Z.
Usually some sort of shorthand gets used so it is not always obvious without careful reading which is being done where. i.e. $[d_A]_A$ may not actually be clear - so I'll explain - d_A is the length between Alices boxes, so $[d_A]_A$ is the proper length between Alices boxes. I want to distinguish this measurement from $[d_A]_B$ - the distance between Alice's boxes measured in Bob's rest-frame... and so on.

Thus: The earlier requirement that the rest-lengths of the trains be the same translates to $[L_R]_A=[L_G]_B$.

Alice gets to do the calculations: $$v_A=\frac{[d_A]_A}{[t_{b1}]_A-[t_{a1}]_A}\\ [L_G]_A = v_A([t_{a2}]_A-[t_a1]_A)$$ ... here $L_G$ is the length of the green carriage (Bob's carriage) made by Alice.

The proper length of Bob's carriage is, of course $[L_G]_B$.

Notice how tempting it is to ditch the subscripts?

Bob has a similar set of results and calculations.
When they compare notes, they find, for instance, that: $v_A=v_B$ ... i.e. they agree about their relative speed.

We can also ask them, how does $[L_R]_B$ compare with $[L_G]_A$ ?

They have noticed that $[L_R]_B \neq [L_R]_A$ ... but there is a simple relationship between them. Alice and Bob could, quite legitimately, say that they disagree about the length of each other's carriage, OR they can choose to conclude that assigning their particular measurement to the concept "the length of the other's carriage" was naive and not especially helpful and that this way of thinking about lengths should be abandoned.

In the former, they are both right; and in the latter, they were both wrong... but they can discover a non-naive way of assigning a measure. The former is easy, the latter is hard(er).
The former is how special relativity is commonly introduced to students but the latter is where the student's understanding should be headed.

...

But the observers try to get clever ... after the first experiment, they set the known distance between the boxes so that it is the same as the measured length of the other carriage.
So: $[d_A]_A=[L_G]_A$ etc.

Ten the experiment is repeated.

The idea is that $[t_{a2}]_A=[t_{b1}]_A$ ... i.e. the lights go off simultaneously.
I think this is the situation that the original diagram was supposed to be trying to show us.

The fun part is when you describe what happens with the time values in this setup.
You find, for instance, that $[t_{a2}]_B\neq [t_{b1}]_B$

The above is by no means exhaustive.

Using this setup and notation it should be possible to be fairly clear about what each of us are talking about - and we can vary the setup according to the particular details we want to bring out.

By comparison, the original trains diagram is designed to highlight (apparent) contradictions ... if you were in the situation, you won't experience any contradiction ... and the math, when the numbers are crunched, bears that out.

Notice that Alice and Bob do their comparing notes in a third rest frame.
The rest frame of the cafe $[]_C$ need not be the same as either the other rest frames.
This can be important.

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

Aside: ... $[t_{a1}]_A$ may be the time that the pulse leaves the 1st box in Alices frame as determined by Alice, but it would arrive at a detector at another time $[t_{a1}]_A+\frac{1}{2c}[d_A]_A$

That's the time it arrives at Alices detector, as measured by Alice ... but the pulse from Alices boxes will also arrive at Bob's detector ... and the notation gets messy if we want to find a way keep them straight.

This can get very messy indeed - i.e. the detectors can be rigged to give a flash of light and we can ask what time alice notices that bob has detected the pulse from her box... she pushes a button to flash a light when this happens and bob sees that light and it never ends.

Something like this is probably a major part of the confusion evident in the previous posts. I want people to be aware of this when they make adjustments to the thought experiments.

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

Disclaimer: I have probably made some mistakes - typos etc. Maybe messed up a relation or something. Be alert for this please. It has also been written for people in the future who may have googled here ... so some statements will appear insulting to current participants like I'm treating you like you're stupid or something. This is unintentional. The main purpose is to standardize notations and definitions so that people have a chance of being understood. It probably won't work - but it should be more fun for everyone. :)

 

[jartsa]

Fast moving muons suggest length contraction is at least as real as time dilation unless you want to claim there is something less preferred about the the muon frame. In the muon frame, the only possible explanation for how it reaches the ground is that the atmosphere is extremely thin it its (the atmosphere's) direction of net motion. That muons reach the ground is an invariant fact. SR then states that explanation is frame dependent, but that time dilation and length contraction are on the same footing as explanations. If one is 'real', so is the other.

Usually planets are quite spherical in their rest frame. That is a problem.

When the myon "sees " a planet that is not spherical, then the myon "thinks" that the planet is contracted.

So I suggest that we replace the planet with a stick ... no not stick but just some pebbles lined up.

Alternatively we may decide that the myon is a very skeptical myon.

 

[ghwellsjr]

Well, if correctly reading a full 4D spacetime diagrams means concluding that simultaneous events are 'really' 'physically' out there, then you are not wrong.

thanks. So you agree that the red car between green's hands is a different train than any green rest train? O.K.?

No, it's not O.K. You have once again used a partial quote to totally come to a wrong conclusion. Here's the full quote:

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.

You are not wrong in your assessment of my position. I do not agree with you that the simultaneous green car events are 'really' 'physically' out there. The simultaneity of the green car events are frame variant. Same with the red car events. Simultaneity is a coordinate effect.

What is this third diagram about? I don't know.

It's the frame that a Loedel diagram is based on. I'm surprised that you don't know.

Is it as seen from the railway track?

No, it's simply the first diagram transformed to a speed such that both trains are traveling in the opposite direction at the same speed. Only the first diagram is "as seen from the railway track". The tracks are moving in the second and third diagrams.

I am not interested at all in that information, because it's irrellevant for reciprocal length contractiion.

Then I don't see why you would think a Loedel diagram is relevant for reciprocal length contraction.

Does that IRF chart combine previous two?

No, we start with the first IRF chart based on your picture of the two trains and the two passengers from post #12. I just applied some specific lengths (12-foot cars and 6-foot arm span). I also applied a speed of 86.6%c since at that speed, gamma =2. Then I transformed it to the second IRF chart using the same speed of 86.6%c to get to the rest frame of the green car. Then I transformed the first chart to a speed of 57.7%c which is the speed at which both trains are traveling at the same speed.

It's important to understand that all three IRF diagrams contain exactly the same information. There is nothing in anyone of them that isn't in the other two. They just have different coordinates for the events.

In that case I cannot find the reciprocal contraction length 6 as shown on separate first two diagrams.

And why should you? Since both trains are traveling at the same speed, they are contracted to the same length. There's nothing sacrosanct about the length of 6 feet. You only get a contraction to 50% of the Proper Length of 12 feet when the speed is 86.6%c. Since these trains are traveling at 57.7%c, they are contracted to 1/1.22 or just under 10 feet as the diagram shows.

One loedel diagram (one and the same the same ruler) does give you reciprocal contraction length 6. And with one and the same ruler.

That's because you are adding the coordinates from two other frames to the original frame. Nothing wrong with that, as long as your audience understands how to read the diagram. If the two added sets of coordinates are not drawn on the diagram, then it becomes very difficult to understand how to read it. I just prefer separate clearly marked diagrams.

Furthermore in your third chart I can not read the proper length of the red and green car (12 length) .

But you can easily calculate it using the formula for the spacetime interval.

In a loedel diagram you would measure -with one and the same ruler- the proper red length (12) between A and C; i.e. the line (not drawn in your IRF charts but essential in Loedel -and SR!) between A and C because that line is the collection of events the shorter train is made of. Same remark for proper green length between E and G (12).

As I see it, the Proper Length between A and C is the distance between red's fingertips (6 feet) in the first diagram. I don't know where you got the 12 from. And E-G is the proper length between green's fingertips, not the green train in the second diagram.

(I won't discuss reciprocal time dilation here, because at this stage off topic in our exercise, but on loedel that too is read with that same ruler. Proper times and lengths, reciprocal contraction and reciprocal time dilation, all in one diagram with one ruler only. Your charts can not get this wright.)

My charts show everything correctly, for any particular frame. I didn't show the Proper Times as dots on these charts because they are irrelevant and would only clutter up the diagrams. But if you want to see a Proper Length, you just transform to the frame in which the object is at rest. If you want to see contracted lengths, you transform to a frame in which the object is moving at any speed you want. You seem to think that in your example, only a length contraction of 50% is valid, and it's not.

Because in your diagram there is no line drawn between A and C, nor between E and G, you do not highlight the events a contracted train car between the hands is made of. And that's precisely the point I want to make.

There is a coordinate line between A and C in the first diagram and a coordinate line between E and G in the second diagram. Only one car is contracted and the other one is its Proper Length.

Only then you will see what happens 4-dimensionally.

How am I supposed to see what happens 4-dimensionally on a 2-dimensional chart?

I find you first chart even a bit disturbing, alhough it does give you the correct contraction length. In that first diagram (red with a shorter green) the rest length of red AND green are measured horizontally, which in 4D spacetime is problematic because it looks as if there's one preferred frame where in fact bith red and green cars have same length 12 -the horizontal one-.

No, there's no frame in which both trains have the same length of 12 feet. If you want them to have the same length, it will be in the frame in which they are traveling at 57.7%c in opposite directions (my third diagram) and then their lengths are both slightly less than 10 feet.

For all above reasons I do not consider your IRF charts real 4D diagrams... They are more IRT charts. Loedel gives you a far better picture how 4D spacetime works, but obviously/apparently not everybody agrees with this? ;-)

Like I said before, a Loedel diagram combines just three specific charts, the ones in which both objects are at rest to the one where they are traveling at the same speed. You seem to be giving preference for each object's own rest frame. And I don't see any concepts that lead to 4D that require a Loedel diagram in a way that individual frame diagrams don't.

I asked: <<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.>> You didn't draw this.

I thought I did what you wanted. Did you see the line segments A-D-C and E-H-G? Maybe you're looking at it on a small screen.

EDIT: Here are a repeat of the three diagrams to avoid flipping between pages to see them:

 

[Dale]

Usually planets are quite spherical in their rest frame. That is a problem.

Why would that be a problem?

 

[jartsa]

Why would that be a problem?

Objects that give us the illusion that we know if those objects are contracted or not are a "problem".


If we manage to reduce the intuitiveness of the fast myon experiment, we will end up with a thought experiment where length contraction is reciprocal. (That's my theory anyway)

Reciprocal in such way that if myon "sees" a contracted measuring stick extending from the surface of the Earth to the myon, then the myon may deduce that the distance to the surface of the earh is contracted ... and reciprocally the Earth may deduce that the distance to the myon is contracted.

Or if that does not work, then it does not work for the myon and it does not work for the earth.

 

[Simon Bridge]

Reciprocal in such way that if myon "sees" a contracted measuring stick extending from the surface of the Earth to the myon, then the myon may deduce that the distance to the surface of the earh is contracted ... and reciprocally the Earth may deduce that the distance to the myon is contracted.

It's been done that way. You can watch it for yourself.
http://www.scivee.tv/node/2415

The demonstration deals with the reciprocity - so should help you.

niggle: it's a muon, not a myon. After the Greek letter mu.
The movie is old enough that they called it the mu-meson.

 

[Dale]

Objects that give us the illusion that we know if those objects are contracted or not are a "problem".


If we manage to reduce the intuitiveness of the fast myon experiment, we will end up with a thought experiment where length contraction is reciprocal. (That's my theory anyway)

Reciprocal in such way that if myon "sees" a contracted measuring stick extending from the surface of the Earth to the myon, then the myon may deduce that the distance to the surface of the earh is contracted ... and reciprocally the Earth may deduce that the distance to the myon is contracted.

Or if that does not work, then it does not work for the myon and it does not work for the earth.

How so? I don't get what you think the problem is.

Regarding reciprocal, in the Earth's frame the muon is contracted, in the muon's frame the Earth is contracted. Again, no problem. Just apply the Lorentz transform from one frame to get the other. No problem.

 

[ghwellsjr]

What if we have just a single train with a Proper Length of 1000 feet, nobody in it or out of it, it's sitting motionless on a track. We establish coordinates for it for the rest frame of the track and the train and draw a spacetime diagram for the train, which will appear as two vertical lines (if we want, it really doesn't matter). Then we transform it to a different frame moving at 60%c with respect to the first frame. Now the length of the train is 800 feet and the two vertical lines are closer together. We continue to transform to a frame moving at 80%c with respect to the original frame. Now the train has a length of 600 feet. Transform to 93.6%c, the train is 352 feet long. Transform to 96%c, the train is 280 feet long.

Do you agree with all of the foregoing?

yes

Then there is no disagreement between our understandings of Length Contraction. You agree it is purely a coordinate effect. The length of an object is dependent on the frame in which it is described. Or another way of saying the same thing is that if we know the Proper Length of an object in its rest frame, we know its length in any other frame in which it is moving. That allows us to put any number of objects moving at any arbitrary speeds in a frame and we can trivially calculate what their lengths are by dividing their Proper Lengths by the gamma factor at each of their speeds. From this we can set up any scenario according to a single frame and use the Lorentz Transformation process to see what the same scenario looks like according to any other frame moving with respect to the original defining frame. We don't have to limit ourselves to the rest frame of any particular object. That is what I have done in this thread.

If so, how does a Loedel diagram help understand what's going on?

see my comments about loedel in previous post.

I'm sorry, but none of your comments in the previous post help me understand how you make a Loedel diagram for any of the frames in which the train is moving. Can you please be more specific?

 

[ghwellsjr]

I have a feeling that everyone has started talking past each other.

Perhaps all parties could use a position statement from each POV along with some sort of definition of terms used? Then we can check what someone is trying to say against what we think they have been saying. It also allows for shifts in position as a result of effective arguing gone by.

I stated my position (it's actually not mine, it's just the standard explanation provided by Special Relativity) in my previous post.

I would add that there are many ways for any observer to use radar signals, apply Einstein's simultaneity convention (radar signals take the same amount of time to get to a target as they take to return to the observer which results in the observer making calculations for his own rest frame), and calculate the speeds and the Length Contractions of moving objects and all of these methods get exactly the same results in any frame that is used to define or describe a scenario or any other transformed frame. Length Contraction is never directly observable since it depends on the frame but can be determined by the application of Einstein's convention.

 

[Dale]

I'm sorry, but none of your comments in the previous post help me understand how you make a Loedel diagram for any of the frames in which the train is moving. Can you please be more specific?

You already made a Loedel diagram, your third diagram. A Loedel diagram is simply a spacetime diagram in the frame where they are moving at equal speeds in opposite directions, which is what you drew. The only possible addition is to label the two moving frame's axes. Personally, I think that would just add clutter, but I think that is what he considers to be missing.

 

[ghwellsjr]

You already made a Loedel diagram, your third diagram. A Loedel diagram is simply a spacetime diagram in the frame where they are moving at equal speeds in opposite directions, which is what you drew. The only possible addition is to label the two moving frame's axes. Personally, I think that would just add clutter, but I think that is what he considers to be missing.

I'm asking how to do it for a single train.