The burn mark problem

[Jack_]

Wow, going right back to the seminal paper. Hard to follow and easy to misinterpret. Some vocabulary and notation has changed since that time. Clearer methods of deriving the transform have been developed.

I note that there is a mirror involved...

From the origin of system k let a ray be emitted at the time $$\tau_0$$ along the X-axis to x', and at the time $$\tau_1$$ be reflected thence to the origin of the co-ordinates, arriving there at the time $$\tau_2$$; we then must have $$\frac{1}{2}(\tau_0+\tau_2)=\tau_1$$, or, by inserting the arguments of the function $$\tau$$ and applying the principle of the constancy of the velocity of light in the stationary system:-​

I get lost in interpreting the text and equations that follow. It would take more time than I can spare.

But the principle seems clear enough - according to one reference frame, the light beam returns to its emission point, while in another it doesn't. In the first frame, the light path (the distance the light travels!) is shorter than in the second. Therefore the time taken must be longer in the second frame than the first.

All agreed.

Except, you do not need two way.

The paper clearly say the path is the same both ways.

One way is sufficient.

 

[Pete]

I already posted this.

In agreement with experience we further assume the quantity
c = 2AB/(t'A-tA)

to be a universal constant--the velocity of light in empty space.
http://www.fourmilab.ch/etexts/einstein/specrel/www/

BTW, what experience supports this measurement technique?

Ah, so you're claiming that the distance 2AB doesn't correspond to the time (t'A-tA)? Why?
If something goes from A to B and back again, leaving A at tA and returning at t'A, with a distance of AB both ways... then isn't the speed involved 2AB/(t'A-tA)?

Note that this is a calculation or definition rather than a measurement, but that's just semantic quibbling.

 

[Jack_]

It occurs to me to mention that "the distance that something travels" was frame dependent long before Einstein's relativity:

O watches O' ride by on her bike during a race.
O notes that the distance the bike travels between the start and the end of the race is 1km.
O' notes that the distance the bike travels between the start and the end of the race is 0km.

No time dilation or length contraction involved. Just Galilean relativity of motion.

Also agreed.

But, within the frame, this distance is logically decidable.

Now, to translate this distance between two frames, we use length contraction.

However, with the light path, this distance and clock beats are directionally dependent.

That is because of the switch between the two light emission points.

 

[Jack_]

Ah, so you're claiming that the distance 2AB doesn't correspond to the time (t'A-tA)? Why?
If something goes from A to B and back again, leaving A at tA and returning at t'A, with a distance of AB both ways... then isn't the speed involved 2AB/(t'A-tA)?

Note that this is a calculation or definition rather than a measurement, but that's just semantic quibbling.

No, I am not disputing this for this analysis.

But, I am disputing this as logic.

Assume you shoot a laser in your back yard toward a tree from west to east during the day.


The distance between you and the tree is d.

SR says the light path distance is absolutely d.

But, think about it.

Light abberation from distant stars shows our dominant motion is our orbit around the sun at about 18.55 miles per second.

So, when you shoot the laser, the earth moves in its orbit and the laser hits the target. The target is OK but the emission point moved with the earth and that cannot be eliminated. The light path is not d. The emission point moved.

Hence, since we really do not know the exact motion of the earth, the light path distance is not logically decidable.

That is my point.

 

[James R]

Jack_:

The SR simultaneity convention.

I'm not aware of any "convention" about simultaneity. The relativity of simultaneity is a derived result from the postulates of special relativity, not an additional "convention".

So, light emits from the emission point and hits the receiver. Yes?

So, we know where the light receiver is for the termination point of the light beam.

But, while light traveled so did the frame. The emission point is no longer where it was in "space".

I think now you're confusing locations of events with coordinate systems. The emission point of a light pulse is an event in spacetime. That event is fixed in spacetime, even though it can have different coordinates in different reference frames.

When you say "the emission point is no longer where it was in space", it is not clear what you're talking about. The event of the light pulse being emitted has one set of spacetime coordinates in the "stationary" frame and a different set of spacetime coordinates in the "moving" frame. [And note: we need both the space and time coordinates to specify an event - just the space coordinates alone are not enough.] Neither of these two sets of coordinates ever changes for the emission event, even though the moving frame moves relative to the stationary frame between the emission and detection. The detection, of course, is a separate event that has its own fixed spacetime coordinates in either frame.

What you seem to be imagining is that a reference frame somehow carries space along with it when it moves - or perhaps that "space" stays still while the moving frame moves through it. In other words, you're imagining a preferred "background", "stationary" frame in which events "really" occur, such that other frames see the "real" locations of those events moving as a consequence of the movement of the "moving" frame. There are no such preferred frames.

This thought experiment is proving the invalidity of claiming you can decide the absolute light path.

I'm not sure what you mean by the "absolute light path".

Perhaps the closest analogy to an "absolute light path" in special relativity is the spacetime interval between the emission and absorption events. Are you aware of the spacetime interval? It is the same in ANY reference frame.

Assume you shoot a laser in your back yard toward a tree from west to east during the day.

The distance between you and the tree is d.

SR says the light path distance is absolutely d.

Let's be clear. What SR says is that in YOUR reference frame, the light travels distance d from you to the tree, which is fair enough when you are measuring that distance. But there's nothing "absolute" about that. If I run past you and watch your laser shot, then SR says that the "light path distance" (distance from you to the tree) is shorter than d, as measured by me in my moving frame. The two distances are related by the Lorentz transformation.

So, when you shoot the laser, the earth moves in its orbit and the laser hits the target. The target is OK but the emission point moved with the earth and that cannot be eliminated.

In the Earth frame, the emission point is you, and you're not moving. In a frame viewing the Earth's motion, you move. But that doesn't affect the spatial coordinate at which the emission event occurred. In fact, in that other frame, you move away from the emission coordinate.

Is this all you're saying?

Hence, since we really do not know the exact motion of the earth, the light path distance is not logically decidable.

So rulers don't work? Is that your claim?

 

[Pete]

Of course time is required to resolve this contradiction of light path lengths.

Then why did you complain about having a time axis on the graphs?

That is why you want me to apply a fast beating clock from the O frame.

Please tell me why it is beating faster than the stationary clocks of O'.

I don't know what you mean.
What I want is for you to apply the Lorentz transform when you're talking about what SR does and doesn't say. Forget about time dilation and length contraction as individual effects - they are not. They are both consequences of special cases of Lorentz transformations.

Nope, this is an error.

Let's consider the O frame. Light moves from O up the positive x-axis.

Good.

Now, at the burn mark, if O' moves (v/c)d, then light moves d.

At the burn mark, light is a total distance of d + (v/c)d.

"light is a total distance"... What?
At this time, the light has travelled a total distance of d.
At this time, the light is a total distance of d + (v/c)d from O' and the burn mark.

This is then apossed to the O' frames as a distance measurement in which O' must expand.

Hences, O' uses this value as
d' = (d + (v/c)d)λ.

What? Are you applying length contraction? To what ruler?
Please remember that length contraction applies only to rulers, not to arbitrary lengths with ends defined at different times.

Try again:
In the rest frame of O, O' meets the burn mark at (x, t) = (-vd/c, d/c)
Transforming this event to the rest frame of O', we get (x', t') = (0, d/cλ)

So the length of the light path at this time in the rest frame of O' is the distance that the light has travelled between t=0 and t=d/cλ.

This is just
x' = ( x - vt)λ given that this is a light beam and t = d/c and v negative as required by the problem.

That formula transforms the x coordinate of an event (the event at the top of DL in the diagrams). When you transform the t coordinate of the same event, you will find that it does not result in the same time as the burn mark reaches O' - you can see in the diagram that this event (the top of DL) occurs well afterward. So, you have calculated the wrong distance (in the diagrams, it is the distance from the t-axis to the top of DL in the rest frame of O').

Now, in O', while the burn mark moves (v/c)d)/λ to meet I', light moves from O' a distance d/λ.

Right. As I showed, DL' = d/λ

Here is the light path conversion.

x' = ( x - vt)λ.

It's not a "light path conversion", it the transformation of the x-coordinate of a specific event, and that event is not when you think it is in the rest frame of O'

 

[Pete]

Also agreed.

But, within the frame, this distance is logically decidable.

Yes, the distance is logically decidable in both cases. For the bike, we can use either use a Galilean transform or a Lorentz transform. At low speeds, the Galilean is an extremely close approximation to the Lorentz.
For our light beam, we use a Lorentz transform.

Now, to translate this distance between two frames, we use length contraction.

No, no, and no again.
Length contraction will give you the wrong answer.
Length contraction is what you get when you apply the Lorentz transform to a moving rod.
When you apply the Lorentz transform or the Galilean transform to a light path or a bike path, you do not get simple length contraction.

However, with the light path, this distance and clock beats are directionally dependent.

That is because of the switch between the two light emission points

Do you realize that and the end of the race, the bike has two starting points?
At the end of the race, in the rest frame of O, the bike's starting point is at x=0.
At the end of the race, in the rest frame of O', the bike's starting point is at x=-1km.

Is that a problem? Is it contradictory?

 

[Pete]

No, I am not disputing this for this analysis.

But, I am disputing this as logic.

Assume you shoot a laser in your back yard toward a tree from west to east during the day.


The distance between you and the tree is d.

SR says the light path distance is absolutely d.

But, think about it.

Light abberation from distant stars shows our dominant motion is our orbit around the sun at about 18.55 miles per second.

So, when you shoot the laser, the earth moves in its orbit and the laser hits the target. The target is OK but the emission point moved with the earth and that cannot be eliminated. The light path is not d. The emission point moved.

Hence, since we really do not know the exact motion of the earth, the light path distance is not logically decidable.

That is my point.

So your point is that there is an absolute frame of reference in which all points are fixed and absolute.

The point of relativity, from hundreds of years before Einstein, from the time of Galileo, is that this is false.

If a runner runs 100m in 10 seconds, what is their speed? Do you need to consider whether they are running eas to west, whether it is morning or afternoon, or whether they are running toward the great attractor or not?

 

[Pete]

OK, I'm stepping back for while because this is getting a little heated.

Jack, you are not alone in struggling with the notion of relativity.
I recommend that before you tackle Einstein's relativity, you should make sure that you have a good grasp of why Galileo had such a struggle to convince people that the Earth wasn't fixed and unmoving, why you can bounce a ball in a train, play tennis on a ship, and juggle in an elevator.

Why? Relativity!

As long as you aren't accelerating or rotating, you might as well be stationary.

 

[Jack_]

Jack_:



I'm not aware of any "convention" about simultaneity. The relativity of simultaneity is a derived result from the postulates of special relativity, not an additional "convention".

SR's simultaneity convention is another name for Einstein's clock synchronization method.

I think now you're confusing locations of events with coordinate systems. The emission point of a light pulse is an event in spacetime. That event is fixed in spacetime, even though it can have different coordinates in different reference frames.

Nope, the SR light speed measurement of t = d/c where d is the distance between the light emission point in the frame and the receiver. When two frames are co-located, there is a common point for light emission.

However, when the receiver is struck by the light in each frame, the emission points of the frames have moved a distance apart of d(v/c). So which is the correct point? One calculation naturally would call one frame correct and conclude the emission point is a distance d + (v/c)d in the moving frame. But, its emission point is d from the target. Your logic does not address the divergence of ther emission points. If you do not have the correct emission, then you do not know the correct and absolute light path.

When you say "the emission point is no longer where it was in space", it is not clear what you're talking about. The event of the light pulse being emitted has one set of spacetime coordinates in the "stationary" frame and a different set of spacetime coordinates in the "moving" frame. [And note: we need both the space and time coordinates to specify an event - just the space coordinates alone are not enough.] Neither of these two sets of coordinates ever changes for the emission event, even though the moving frame moves relative to the stationary frame between the emission and detection. The detection, of course, is a separate event that has its own fixed spacetime coordinates in either frame.

Yes, that is exactly how SR sees it. But, unfortunately, SR also confesses two different points in the two frames that are diverging by vt after any time t each of whcih is claimed to be the correct point for the light wave. When the target is hit, and I note we are off the burn mark problem I assume because you understand the physical contradiction, each frame measures from its emission point to the target for the light path.

What you seem to be imagining is that a reference frame somehow carries space along with it when it moves - or perhaps that "space" stays still while the moving frame moves through it. In other words, you're imagining a preferred "background", "stationary" frame in which events "really" occur, such that other frames see the "real" locations of those events moving as a consequence of the movement of the "moving" frame. There are no such preferred frames.

Good now that you know there is no preferred, you will understand the start of the light path aftre time t > 0 is not logically decidable.

Now, under the absoluteness of Newtonian physics, they believed in absolute paths for light and such.

SR, retained this absoluteness of the light path in a "theory of relativity".

If claims the absolute light path is known.



I'm not sure what you mean by the "absolute light path".

Perhaps the closest analogy to an "absolute light path" in special relativity is the spacetime interval between the emission and absorption events. Are you aware of the spacetime interval? It is the same in ANY reference frame.



Let's be clear. What SR says is that in YOUR reference frame, the light travels distance d from you to the tree, which is fair enough when you are measuring that distance. But there's nothing "absolute" about that. If I run past you and watch your laser shot, then SR says that the "light path distance" (distance from you to the tree) is shorter than d, as measured by me in my moving frame. The two distances are related by the Lorentz transformation.



In the Earth frame, the emission point is you, and you're not moving. In a frame viewing the Earth's motion, you move. But that doesn't affect the spatial coordinate at which the emission event occurred. In fact, in that other frame, you move away from the emission coordinate.

Is this all you're saying?



So rulers don't work? Is that your claim?[/QUOTE]

 

[Jack_]

Then why did you complain about having a time axis on the graphs?

Because that is how SR resolves it. It asks you to forgets about the physical contradictions of the single light beam path length and "shorten" it with a fast beating clock. Well, this does not resolve the physical conflict in the light path length.

Nice graphic BTW.

I don't know what you mean.
What I want is for you to apply the Lorentz transform when you're talking about what SR does and doesn't say. Forget about time dilation and length contraction as individual effects - they are not. They are both consequences of special cases of Lorentz transformations.

OK, I will leave the burn mark problem since you cannot resolve its contradiction and will work exclusively on LT.

Here you go. This is the burn path problem.

Shoot a laser straight down the positive x-axis. It leaves a burn path of its travel.

Standard Configuration for LT
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
+---------------------------+-----------------------------------------------------x
O          vt               O'                              x'/λ

From above, x'/λ + vt = x
x'/ λ = x - vt
x' = (x - vt)λ
Since, x is struck by the light beam, t = x/cx' = (x - vx/c)λ.
The term vx/c is the distance between the two origins of the frames.Hence, LT switches between the two origins.. Why? These are the two distinct light emission points in each frame.


Now, check it out. An O observer claims a continuous burn path from O to x. This is LT Oh, watch, I will show the clock argument is a red herring.

An O' observer will claims the burn path is from O' to x' which is sligtly beyond x in its geometry.


An O' observer says there is no burn path left of O' but an O observer says there is, a contradiction of the universe.

See how the clocks cannot save SR?

What? Are you applying length contraction? To what ruler?
Please remember that length contraction applies only to rulers, not to arbitrary lengths with ends defined at different times.

I am applying it to the coordinate system of the moving frame. This is the Minkowsky space.

Try again:
In the rest frame of O, O' meets the burn mark at (x, t) = (-vd/c, d/c)
Transforming this event to the rest frame of O', we get (x', t') = (0, d/cλ)

So the length of the light path at this time in the rest frame of O' is the distance that the light has travelled between t=0 and t=d/cλ.

Nice algebra and this is how the fast beating clock makes it appear resolved.
However, this does not resolve the geometry of the diagram I made.

If it does and you understand it, then apply this logic and math to the diagram.

That formula transforms the x coordinate of an event (the event at the top of DL in the diagrams). When you transform the t coordinate of the same event, you will find that it does not result in the same time as the burn mark reaches O' - you can see in the diagram that this event (the top of DL) occurs well afterward. So, you have calculated the wrong distance (in the diagrams, it is the distance from the t-axis to the top of DL in the rest frame of O').

You are introducing clocks here. The burn mark controls the destiny of the experiment not clocks.

When the burn mark and O' are co-located there is a severe disagreement on the light path lengths.

Again, clocks are not used. The co-location of the burn mark and O' is the control in this experiment.

So, if you are able to use these clocks according to the control of the experiment, then fine use them to "shorten" the longer light path.

 

[Jack_]

So your point is that there is an absolute frame of reference in which all points are fixed and absolute.

The point of relativity, from hundreds of years before Einstein, from the time of Galileo, is that this is false.

If a runner runs 100m in 10 seconds, what is their speed? Do you need to consider whether they are running eas to west, whether it is morning or afternoon, or whether they are running toward the great attractor or not?

No, that is exactly what I did not say.

I said SR claims to know with absolute certainty the exact path of the light path.
Yet, I produced one and can produce many more experiments that prove that is false.

SR claims to know the "preferred" light path.

SR is all very Newtonian physics to me.

 

[Jack_]

OK, I'm stepping back for while because this is getting a little heated.

Jack, you are not alone in struggling with the notion of relativity.
I recommend that before you tackle Einstein's relativity, you should make sure that you have a good grasp of why Galileo had such a struggle to convince people that the Earth wasn't fixed and unmoving, why you can bounce a ball in a train, play tennis on a ship, and juggle in an elevator.

Why? Relativity!

As long as you aren't accelerating or rotating, you might as well be stationary.

I have not been talking about the motion of the frame except to prove the the light path is not logically decidable except in the world of Newtonian physics and oh in SR as well.

SR and Newtonian physics both agree, they know the exact light path length.

That is all very absolute to me.

 

[Pete]

Because that is how SR resolves it. It asks you to forgets about the physical contradictions of the single light beam path length and "shorten" it with a fast beating clock. Well, this does not resolve the physical conflict in the light path length.

What conflict?
Why do you insist that SR should dictate a single length for the light path in all frames of reference?
Why do you insist on ignoring what SR says about time, when you acknowledge that time is an important part of the problem?

Nice graphic BTW.

Perhaps you should look at it. Where, exactly, is the supposed contradiction between the two reference frames?

OK, I will leave the burn mark problem since you cannot resolve its contradiction and will work exclusively on LT.

By LT you mean Lorentz Transform, right? Why does "working on LT" mean leaving the burn mark problem, since using the Lorentz Transform it is essential to resolving the burn mark problem.
The problem is resolved to my satisfaction, and I'm waiting for you to catch up. The reason that you are still struggling is because you seem to think that length contraction is all you need to know about SR. When you analyse what SR says about the problem properly (ie by using the Lorentz Transform), then there is no problem.


Remember, Jack, we're all here to learn.

 

[Pete]

SR and Newtonian physics both agree, they know the exact light path length.

No, in both SR and Newtonian physics, the light path length is frame dependent.

 

[Pete]

I said SR claims to know with absolute certainty the exact path of the light path.
...
SR claims to know the "preferred" light path.

Wrong on both counts. The path is frame dependent, not absolute, in both SR and Newtonian physics.

 

[James R]

Jack_:

You seem to have trailed off half way through your last reply to me.

SR's simultaneity convention is another name for Einstein's clock synchronization method.

That's the first time I've heard anybody say that.

Nope, the SR light speed measurement of t = d/c where d is the distance between the light emission point in the frame and the receiver. When two frames are co-located, there is a common point for light emission.

What do you mean when you say two frames are co-located? Recall that a reference frame extends throughout the whole of space.

However, when the receiver is struck by the light in each frame, the emission points of the frames have moved a distance apart of d(v/c).

No. The emission point of a light pulse, as I explained to you, is a fixed point in spacetime. It does not move.

Yes, that is exactly how SR sees it. But, unfortunately, SR also confesses two different points in the two frames that are diverging by vt after any time t each of whcih is claimed to be the correct point for the light wave.

You're saying no more than that the same event has different coordinates in different reference frames. There's no problem with that.

Good now that you know there is no preferred, you will understand the start of the light path aftre time t > 0 is not logically decidable.

Nonsense. All you have to do is look to see where and when the light is emitted and note the coordinates.

Now, under the absoluteness of Newtonian physics, they believed in absolute paths for light and such.

What do you mean by an "absolute path for light"?

SR, retained this absoluteness of the light path in a "theory of relativity".

I've never seen the term "absolute path for light" used in any relativity text I've ever read. Do you have a reference?

....

At this point, your reply trailed off. Did you lose track of what you were doing?

 

[Jack_]

Wrong on both counts. The path is frame dependent, not absolute, in both SR and Newtonian physics.

Can you explain this?

Are you saying that light in fact has an infinite number of paths in reality based on the frame?

Then, Einstein says the light path is "free from contradictions" for the clock sync.


How do you have a light path length of many values and yet at the same time it is free from contradictions?

Can you explain this absoluteness of SR?


But, what you are really saying is that the light path has many "real" emission points divergent in space.

WOW!!!!!

 

[Pete]

This is the burn path problem.

Shoot a laser straight down the positive x-axis. It leaves a burn path of its travel.

Standard Configuration for LT
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
|                           |
+---------------------------+-----------------------------------------------------x
O          vt               O'                              x'/λ

So the laser only goes as far as x? Or does it continue burning the path indefinitely?

Is that time is on the vertical axis? If so, why is O' stationary?
If not, then how are you going to apply a Lorentz transform?

 

[Jack_]

Jack_:

You seem to have trailed off half way through your last reply to me.

That's the first time I've heard anybody say that.

so what

What do you mean when you say two frames are co-located? Recall that a reference frame extends throughout the whole of space.

I mean the same thing as is the case when Einstein with his R of S experiment claimed two frames were co-located.

No. The emission point of a light pulse, as I explained to you, is a fixed point in spacetime. It does not move.

Oh? So exactly where is this point?
We will need it because SR contends that emission point is the one used to decide t = d/c for a multitude of frames.

I want you to explain this.