Perspective on Relativity and Length Contraction

[universal_101]

(my emphasis)

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

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

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

 

[universal_101]

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

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

Such planets do not have the effect at all.

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

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

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

 

[Mentz114]

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

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

 

[universal_101]

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

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

 

[Doc Al]

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

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

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

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

 

[Mentz114]

No, rather what is the physical nature of the terms used for a coordinate dependent quantity. Even though it is easy to see their apparent nature, everybody seems to ignore it,

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

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

I think you might have misunderstood someting.

 

[universal_101]

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

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

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

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

 

[Dale]

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

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

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

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

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

 

[universal_101]

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

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

 

[TheBC]

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

My bold.

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

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

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

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

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

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

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

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

 

[TrickyDicky]

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

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

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

 

[Mentz114]

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

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

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

 

[universal_101]

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

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

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

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

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


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


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


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

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

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

 

[Histspec]

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

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

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

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

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

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

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

 

[universal_101]

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

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

What principle, please elaborate.

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

 

[Mentz114]

What principle, please elaborate.

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

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

 

[Dale]

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

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

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

 

[Dale]

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

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

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

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

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

 

[universal_101]

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

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

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

 

[ghwellsjr]

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

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

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

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

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

 

[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.

 

[phyti]

the muon scenario for anyone's consideration (without all the fluff)

In the left figure, the Earth observer E records the avg. travel time of the muon for the distance x (altitude to ground) as t. E calculates the travel time for M the observer moving with the muon as t', resulting from time dilation. M's clock shows t' at the ground, yet his position is x. He calculates his position should be vt' = x'. Since M experiences time dilation to the same degree as his clock, his sense of time agrees with his clock. To reconcile the distance disparity, he concludes the universe outside his frame of reference has contracted in the x direction, as shown in the right figure.

If time dilation and length contraction are motion induced phenomena, then
this large scale length contraction is not a consequence of em field deformation, but the interpretation of the observers own time dilation. The observer's motion cannot alter the form of distant objects, but can alter his perception.

 

[TheBC]

Ghwellsjr, thanks for again putting so much effort in discussing diagrams.

I do not agree with you that the simultaneous green car events are 'really' 'physically' out there.

Then please tell me which events of the short green car are out there for Red between his red hands. (Definitely not the green rest car events!)

The simultaneity of the green car events are frame variant. Same with the red car events. Simultaneity is a coordinate effect.

I'm asking you: which events of the short green train are between the red hands of the observer? The events of the green rest train? No. So, which events are between his hands? Please tell me.
I don't like at all you call it an 'effect'. The frame (any frame) indicates which events out of 4D spacetime existence form a 3D space of simultaneous event, i.o.w. the 3D world as it 'exists' at one moment in time.
You will tell me that that 3D world is 'arbitrarily 'chosen... I don't care less. Point is that an observer considers some events frome 4D spacetime as his 'real world now'. And because of relativity of simultaneity green's 3D world is different from red's 3D world. The content of events is completely different. The only invariant in this exercise is the full picture: all the 4D spacetime events, the 4D spacetime world.

Only the first diagram is "as seen from the railway track".

I cannot see this. For me it's what red measures. In your first diagram I read that horizontally you give length12 for red car at rest and length 6 for short green car.

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

Because Loedel shows you in one diagram the same proper rest length in both frames.
What is astonishing is that apparently you use your 3 rd diagram for other purposes that I would do. Because in no time I make it a loedel diagram. Your 3 rd diagram with coordinate distances is about a frame I am not interrested in. Because you don't show any of the 12 proper length or 6 long contracted cars in your 3 rd diagram. But the information is in your drawing, so why not showing it? Drop your irrelevant horizontal and vertical margins and read directly what red and green measure in their respective 3D space. Piece of cake. In next post I will mark up your diagram so it can be read as loedel.

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.

I don't need this. Both cars are traveling relative to each other at same speed (0;866c). I don't need anything else.

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.

I don't need the 57.7%c. Once more: it's about reciprocal length contraction between the 2 cars. They are traveling at 86.6%c relative to each other. And that's all I need.
Your first diagram shows red's frame: a 12 long red car for red observer and a 6 long green car.
Your second chart shows green's frame: 12 long green car for green observer and a 6 long red car.
Your 3 rd diagram is a loedel diagram only if you also indicate the green and red frames in which you read proper and contracted lengths on both axes with one and 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 never said is is 'easy' to read. But let's be honnest; do you find a Minkoski diagram, with different unit lengths for time and space 'easy' to read reciprocal length contraction and time dilation? Forget it.
I find loedel A LOT easier to read than your or Minkowski... But it has it's limitations. More than 2 frames f.ex. Because then not all frames keep same unit lenghts...
But for most exercises where only two relative moving systems are used loedel is sublime.

I just prefer separate clearly marked diagrams.

This is where we disagree. Dalespam too does not see any advantage of one loedel over 2 separate diagrams because it does not show more raw date than your two diagrams. In that sense raw data written on a piece of paper, cut to pieces and thrown on the floor also 'contains' all the information. But Loedel shows clearly how all rest and shorter 'moving' length are part of one full 4D spacetime diagram. With one ruler.

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

There we are. With loedel you do not have to calculate it. You just measure it all with one and the same ruler. And believe it or not, it's on your diagram but apparently you are not aware of it.

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.

(In first diagram) Then what represents the distance between your two vertical red lines of the red car (at rest for red)?

And E-G is the proper length between green's fingertips, not the green train in the second diagram.

Correct. Sorry about that. My mistake.

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.

I saw them full scale, but they are not what I asked.
Once more: quote<<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.>>
In fact you should draw a line between E-G en continue to the green worldlines of the front and rear of green car. The line is 'made of'/represents all the events that are simultaneous for green at one moment of time on green's wristwatch.
Similar reasoning for red. That red line is 'made of'/represents all the events that are simultanoeus for red.
Dalespam may call this this clutter, but I find this essential to understand 4D of SR.
See my comments to his quote:

The only possible addition is to label the two moving frame's axes. Personally, I think that would just add clutter,

You call that clutter? Waw! Interesting. I rather call the extra frame in which both cars have equal contracted length completely obsolete. Totally irrelevant for reciprocal length contraction.

but I think that is what he considers to be missing.

That's indeed a good start.

 

[TheBC]

Ghwellsjr,
I quickly transformed your 3rd diagram into a full Loedel diagram, with lots of dots representing the events of 4D spacetime existence of red and green car. Please take the time to scrutinize this sketch before it is considered clutter and deleted from the thread... ;-)

 

[nitsuj]

Love the Festive coloring!

 

[PAllen]

Love the Festive coloring!

Yep, a SAD case (Seasonally Appropriate Diagram)

 

[pervect]

Very christmassy, but unfortunately I can't tell what it's supposed to represent.

I guess the vertical axis is some coordinate time t, and the horizontal axis is some coordinate position x. There's some grey lines through the labels, but I can sort of make out the text anyway. I don't understand the motivation for the wiggly grey lines.

Then the red car apparently at t=2 was at x=4, and at t=3 was at x=-5.5.

If we assume c=1, this would be FTL. Presumably c then has some other value than 1.

are the thin diagonal lines supposed to be "lightcones"? Hard to say, but if so, then I guess c is supposed to be near 2, but it doesn't seem to be exactly. Perhaps this choice was explained in some post in the thread I didn't read, but it seems like a strange choice. Why not make c=1? Or at least tell us what it is.

"Space-time existence" isn't a familiar standard term, I don't know what the author is trying to imply by it. It looks like it may be a future light cone for the green line, and a past lightcone for the red line? It seems to have philosophical overtones, rather than being a statement of where the coordinate chart is valid.

 

[ghwellsjr]

Ghwellsjr, thanks for again putting so much effort in discussing diagrams.

You're welcome.

I do not agree with you that the simultaneous green car events are 'really' 'physically' out there.

Then please tell me which events of the short green car are out there for Red between his red hands. (Definitely not the green rest car events!)

Just to make it clear, my issue with you is characterizing the simultaneity of certain events as 'really' 'physically' out there.

But to answer your question: one of the events is labeled "A" in my three diagrams and the other one is labeled "C". In each diagram, the event labeled "A" is the same event. It has different coordinates in each diagram and once we know the coordinates in one diagram, the Lorentz Transformation process is how we determine what the coordinates for the same event are in another diagram. The event occurs 'really' and 'physically' out there when the "left" end of the green car becomes coincident with red's "left" fingertip. The coordinates that we apply to this event are totally arbitrary and do not have the attributes of 'really' or 'physically'.

Similar comments for event "C".

Thus, if it happens in a particular Inertial Reference Frame that they have the same time coordinate, then we say that they are simultaneous in that IRF. Events "A" and "C" have the same time coordinate in my first diagram and are therefore simultaneous in that IRF. In the other two IRFs depicted in the other two diagrams, events "A" and "C" have different time coordinates and are not simultaneous.

As far as I know, the foregoing is mainstream Special Relativity. I don't think it is just my opinion. If you don't accept it, then I don't think you are accepting mainstream Special Relativity.

The simultaneity of the green car events are frame variant. Same with the red car events. Simultaneity is a coordinate effect.

I'm asking you: which events of the short green train are between the red hands of the observer? The events of the green rest train? No. So, which events are between his hands? Please tell me.

In the second frame depicted in the second diagram, it is the same events labeled "A" and "C" which are also on the ends of the green rest train, or, as I prefer to say it, it is the frame in which the green train is at rest, or it is the green train's rest frame.

I don't like at all you call it an 'effect'. The frame (any frame) indicates which events out of 4D spacetime existence form a 3D space of simultaneous event, i.o.w. the 3D world as it 'exists' at one moment in time.
You will tell me that that 3D world is 'arbitrarily 'chosen... I don't care less. Point is that an observer considers some events frome 4D spacetime as his 'real world now'. And because of relativity of simultaneity green's 3D world is different from red's 3D world.

I think the problem is that you consider an observer in a scenario to be locked into one particular frame, namely the frame in which he is at rest. I'm trying to point out that there is nothing that this observer can measure, observe or see that will force him to that conclusion. He must apply Einstein's simultaneity convention, which is what your red and green observers did in your scenario to arrive at the conclusion that what they felt on their fingertips occurred simultaneously. There's no dispute on that issue. What is in dispute is that Einstein's simultaneity convention is real and physical. In other words, two events are only simultaneous because we define them to be simultaneous. It is not a physical thing that we could let nature (the physical world) decide for us or that we could discover by only measurements or observations.

The content of events is completely different. The only invariant in this exercise is the full picture: all the 4D spacetime events, the 4D spacetime world.

I don't know what you mean by this. What is the content of an event? The closest thing I can think of is its coordinates but you don't seem to be to appreciative of coordinates so I'm wondering if you mean that some events belong exclusively to a particular object and some other events belong exclusively to another (and some other events can belong to both objects). Is that what you mean, or something like that?

Only the first diagram is "as seen from the railway track".

I cannot see this. For me it's what red measures. In your first diagram I read that horizontally you give length12 for red car at rest and length 6 for short green car.

Yes, the grid lines going to the coordinate markings tell you that. Since the red car is at rest on the railway track and both are at rest in this IRF, we can say it is "as seen from the railway track". Those are your words. I would rather say that it is the mutual rest frame of the railway track and the red car because neither the railway track (or any observers stationed along it) nor the red car (or any observers stationed within it) can actually see most of the details that we can see when we look at the completed diagram. Of course, as I have repeatedly said, they can construct those details by sending and receiving radar signals and images from remote objects and applying Einstein's convention and doing a lot of calculations after the scenario is all done.

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

Because Loedel shows you in one diagram the same proper rest length in both frames.
What is astonishing is that apparently you use your 3 rd diagram for other purposes that I would do. Because in no time I make it a loedel diagram. Your 3 rd diagram with coordinate distances is about a frame I am not interrested in. Because you don't show any of the 12 proper length or 6 long contracted cars in your 3 rd diagram. But the information is in your drawing, so why not showing it? Drop your irrelevant horizontal and vertical margins and read directly what red and green measure in their respective 3D space. Piece of cake. In next post I will mark up your diagram so it can be read as loedel.

I never said it was a Loedel diagram. I only provided the third diagram as a basis for making a Loedel diagram. Remember, I said that a Loedel diagram depicts three frames on the same diagram--all three of my diagrams get squeezed on to the one diagram by providing additional grid lines and markings--if you want to make it clear. As the wikipedia article says:

...there is a frame of reference between the resting and moving ones where their symmetry would be apparent. Such a frame of reference is a Loedel frame. In this frame, the two other frames are moving in opposite directions with equal speed.

Count them: there are three frames jammed into one diagram. I show all three frames as separate diagrams because it is so much easier to read and in this day of computers, they are so easy to generate. My problem with the Loedel diagram is providing the three sets of grid lines and three sets of markings. Since you leave them all out, I don't know how you can tell what is going on.

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.

I don't need this. Both cars are traveling relative to each other at same speed (0;866c). I don't need anything else.

I can easily see that each car is traveling at 57.7%c relative to the coordinates of the frame but how can you tell that each car is traveling at 0.866c relative to the other car?

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.

I don't need the 57.7%c. Once more: it's about reciprocal length contraction between the 2 cars. They are traveling at 86.6%c relative to each other. And that's all I need.
Your first diagram shows red's frame: a 12 long red car for red observer and a 6 long green car.
Your second chart shows green's frame: 12 long green car for green observer and a 6 long red car.
Your 3 rd diagram is a loedel diagram only if you also indicate the green and red frames in which you read proper and contracted lengths on both axes with one and same ruler.

I agree, if you transformed the grid lines for the first two diagrams so that you could actually indicate the 12-foot Proper Length of each car and the 6-foot Contracted Length from the other car's rest frame but instead, you have a magic ruler. How do you "calibrate" this ruler? How do you know how to lay it on the diagram to get the measurements. Do the red and green observers have access to this 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 never said is is 'easy' to read. But let's be honnest; do you find a Minkoski diagram, with different unit lengths for time and space 'easy' to read reciprocal length contraction and time dilation? Forget it.

No, I don't find the typical Minkowski diagram, with or without grids and markings easy to read. But I understand their historical significance--and Loedel diagrams--because it was fairly difficult to make any diagram by hand but with our computers, it is easy to make interactive diagrams where the user can "dial" in any speed he wants to see how the Lorentz Transformation process creates additional IRF's.

I find loedel A LOT easier to read than your or Minkowski... But it has it's limitations. More than 2 frames f.ex. Because then not all frames keep same unit lenghts...
But for most exercises where only two relative moving systems are used loedel is sublime.

That's only one exercise. Two inertial observers. It can't even show the most popular of all scenarios, the Twin Paradox. My diagrams are trivially easy to read (as you have already demonstrated) and can be used with any in-line scenario. And I can even expand to non-inertial frames using the exact same techniques that observers can use to construct Inertial Reference Frames. They are truly sublime.

But I don't object to a properly drawn and marked Loedel diagram with enough explanation to make its interpretation clear. I do object to the idea that it conveys anything more than any other properly drawn diagram.

I just prefer separate clearly marked diagrams.

This is where we disagree. Dalespam too does not see any advantage of one loedel over 2 separate diagrams because it does not show more raw date than your two diagrams. In that sense raw data written on a piece of paper, cut to pieces and thrown on the floor also 'contains' all the information. But Loedel shows clearly how all rest and shorter 'moving' length are part of one full 4D spacetime diagram. With one ruler.

Again, you are giving preference to each observer's rest frame and concluding that both are in operation at the same time and ignoring the fact that any other frame is just as valid.

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

There we are. With loedel you do not have to calculate it. You just measure it all with one and the same ruler. And believe it or not, it's on your diagram but apparently you are not aware of it.

I'm not aware of where you got the 12-foot length of the ruler that you can place in just the right spot to measure both the Proper Length of one car and the Contracted Length of the other car. How do you determine that it's 12 feet long and not 8? Where do you get the information from that it is 12? And how do you know what angle to draw the two sets of lines at? And where do you show the relative speed between the two observers?

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.

(In first diagram) Then what represents the distance between your two vertical red lines of the red car (at rest for red)?

If you're asking about the two outside vertical red lines, then, yes, they are 12 feet apart, but you were not talking about those two lines, you were talking about the proper red length between A and C, which is 6 feet. Here's what you said:

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).

And E-G is the proper length between green's fingertips, not the green train in the second diagram.

Correct. Sorry about that. My mistake.

And you made the same mistake regarding A-C, correct?

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.

I saw them full scale, but they are not what I asked.
Once more: quote<<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.>>

Now this one is my mistake. I didn't do what you asked but here it is now:

But I still don't understand why you want this drawing, please explain.

In fact you should draw a line between E-G en continue to the green worldlines of the front and rear of green car. The line is 'made of'/represents all the events that are simultaneous for green at one moment of time on green's wristwatch.
Similar reasoning for red. That red line is 'made of'/represents all the events that are simultanoeus for red.

The second diagram already has a grid line corresponding to simultaneous events that include events E and G and the first diagram has a grid line corresponding to simultaneous events that include A and C.

Dalespam...

I'll let him comment if he wants to.

 

[ghwellsjr]

Ghwellsjr,
I quickly transformed your 3rd diagram into a full Loedel diagram, with lots of dots representing the events of 4D spacetime existence of red and green car. Please take the time to scrutinize this sketch before it is considered clutter and deleted from the thread... ;-)

I never heard of events belonging to just one object.

How did you determine the values of 12 and 6? Where did you get this ruler from that has those markings?

Where do you see on this diagram that the two observers are traveling at 0.866c relative to each other?

 

[TheBC]

O.K. guys, this is getting out of hand. It's really too ridiculous to waste more time on this.
I'll get back to this forum the day you know what events are, how loedel works, and what SR is about.
Untill then; good luck with your coordinate effects.

 

[ghwellsjr]

O.K. guys, this is getting out of hand. It's really too ridiculous to waste more time on this.
I'll get back to this forum the day you know what events are, how loedel works, and what SR is about.
Untill then; good luck with your coordinate effects.

How do you expect me to know how loedel works if you won't answer my simple questions:

How do you portray the relative speed of 0.866c between the two observers in your diagram?

How do you calibrate your ruler?