The burn mark problem

[Jack_]

Yes, I realise that. I'm pointing out that calling a single value of x a length is not strictly true. The other x value is important even if it is zero.



No, deriving the Lorentz transform does not involve measuring c, it assumes that c is constant.
There is no light speed measurement involved. I'm not sure why you think it is.

The reason I say the speed of light is measured c and that is fundamental is because of the clock sync of SR.

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

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

This is the hidden "measure at c" postulate that is actually the third postulate of SR

Can you see it proposes a method of measuring c?

This is completely different from the light postulate.

 

[Jack_]

You don't appear to understand the rules of length contraction, since you are attempting to naively apply it to a light beam with one end fixed and the other moving.
Length contraction doesn't work in that case.
Do you understand why?


Whoops, I left the tag end o your post in my reply. I didn't mean to post that sentence.


A light beam is not a rod.

Of course I understand what you are saying.

Now, understand what I am saying.

The difference in the light beam lengths are length contraction and the difference in length of the two emission points in the frame when light travels x.

Do you see this?

 

[Jack_]

Is that the one where a light beam bounces off a mirror?
In one frame, it goes straight up and down again (distance d, time d/c)
In a frame moving horizontally, the light goes diagonally up and down (longer distance, longer time)?

I can't see the relevance yet, but wait while I go back to your argument about two emission points.

No problem, I will wait.

 

[Pete]

Time dilation then causes the moving clocks' frequencies to be slow by
http://www.ipgp.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf

Not in the GPS orbit rest frame. In that rotating (non-inertial) reference frame, you can't use Lorentz transforms to transform events from other reference frames - the LT only applies between inertial reference frames with a common origin and orientation - so the simple rules of time dilation (which are a consequence of the simple Lorentz transform) don't work.

In the GPS orbit rest frame, the frequency of clocks depends on their distance from the centre of rotation as well as their speed.

I can't see anything in the linked article that says otherwise.

Perhaps you are confusing a satellite's rotating orbital rest frame with the satellite's instantaneous inertial rest frame?

 

[Pete]

The reason I say the speed of light is measured c and that is fundamental is because of the clock sync of SR.

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

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

This is the hidden "measure at c" postulate that is actually the third postulate of SR

Can you see it proposes a method of measuring c?

This is completely different from the light postulate.

No, I don't see that at all. Can you be more explicit about what this hidden postulate postulates? Is it that "All measurements of the speed of a light beam will necessarily result in a value of c?" If so, this is logically equivalent to the postulate of the constancy of the speed of light.

 

[Jack_]

Is that the one where a light beam bounces off a mirror?
In one frame, it goes straight up and down again (distance d, time d/c)
In a frame moving horizontally, the light goes diagonally up and down (longer distance, longer time)?

I can't see the relevance yet, but wait while I go back to your argument about two emission points.

This is Einstein's logic to set this up and it is one way without a mirror.

An analogous consideration--applied to the axes of Y and Z--it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √( c² - v²) gives us

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[Jack_]

Not in the GPS orbit rest frame. In that rotating (non-inertial) reference frame, you can't use Lorentz transforms to transform events from other reference frames - the LT only applies between inertial reference frames with a common origin and orientation - so the simple rules of time dilation (which are a consequence of the simple Lorentz transform) don't work.

In the GPS orbit rest frame, the frequency of clocks depends on their distance from the centre of rotation as well as their speed.

I can't see anything in the linked article that says otherwise.

Perhaps you are confusing a satellite's rotating orbital rest frame with the satellite's instantaneous inertial rest frame?

No, the articles use the phrase time dilation which in SR is reciprocal.

 

[Jack_]

No, I don't see that at all. Can you be more explicit about what this hidden postulate postulates? Is it that "All measurements of the speed of a light beam will necessarily result in a value of c?" If so, this is logically equivalent to the postulate of the constancy of the speed of light.

Your statement above is false.

Here is the correct statement.

All correct measurements of the speed of light will be c.

You are implicitly implying the SR measurement technique is absolutely true.

First, to explore this, we need to resolve this multiple light emission points issue.

If SR confesses multiple light emission points, then it confesses it cannot measure the speed of light with absolute certainty.

Hence, the clock sync method fails. LT is based on the clock sync.

[Edit I already know SR cannot do this. It is the theory of relativity. It would need to know the absolute motion of the frame to know the actual light path].

 

[Pincho Paxton]

This is Einstein's logic to set this up and it is one way without a mirror.

An analogous consideration--applied to the axes of Y and Z--it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √( c² - v²) gives us

http://www.fourmilab.ch/etexts/einstein/specrel/www/

I'm bookmarking that Einstein paper. Thanks! (I swear you could solve the magnet / Conductor problem with an Aether)

 

[Pete]

Yes, I can see what is going on.

But, you have a time axis and we are not controlling this thought experiment with a clock.

It is being controlled by the co-location of a burn mark.

Of course there is a time axis! This experiment involves events happening at different times. You can not analyse it without considering the times involved. The lack of a clock is irrelevant.

Then two co-located observers in different frames differ by length contraction plus the distance (v/c)d with lenght contraction/expansion.

Clocks cannot alter these distance differentials of one light beam.

The first sentence isn't clear, but the second is just misguided. Clocks are irrelevant. Time is the critical factor.

Now, watch me hide this truth of a physical contradiction of the length of one light beam in the clocks.

First, let me check that I understand your notation.

DL = the distance (in frame O) that the light travels between time zero and the time when O' reaches the burn mark.
DL = d
DF = the distance (in frame O) that O' has travels between time zero and the time when O' reaches the burn mark.
DF = dv/c

DL' = the distance (in frame O') that the light travels between time zero and the time when the burn mark reaches O'.
DF' = the distance (in frame O') that O travels between time zero and the time when the burn mark reaches O'.

Good so far?

DL' = ( DL - DF )λ

I get:
DL' = d/λ
I didn't use length contraction to get this result. I applied the Lorentz transform to the event at which O' meets the burn mark:
(x, t) = (-vd/c, d/c)
(x', t') = (0, d/cλ)

...and thus calculated the location of end of the light beam at that time to be x'=d/λ.
And since the light beam started at x'=0, DL' = d/λx


Your logic for calculating DL' seems to involve applying length contraction to things other than rulers, which is not what SR says.

DF = (v/c)DL

DL' = ( DL - (v/c)DL )λ

Divide by c to change this to time.

DL'/c = ( DL/c - (vDL/c²) )λ

t' = ( t - (vDL/c²) )λ

Now give the term (vDL/c²) a pretty name like, say, simultanerity shift.

The reality is that SR uses LT to switch between the origins of the frames and the reason for this is the origin of each frame is that frame's light emission point.

LT is actually switching between light emission points.

This is the cause of the light travel distance differentials I am exposing.

Do you agree that is what LT is doing?

No, I don't agree. I think that you are confusing yourself about what SR says by trying to apply length contraction where it doesn't apply. You might also be confusing locations (the light emission point) with events.

The emission of the light beam is an event. It happened at a particular position at a particular time. Events are unambiguous things, they can't be fundamentally altered by a transform. The light was emitted at the time and place where O and O' met, and that is true in all frames of reference.

A location is the set of all events that occur at a given place at different times. A location is ambigous; it depends on your chosen frame of reference.
In frame O, the light was emitted at x=0. x=0 is the light emission point.
In frame O', the light was emitted at x'=0. x'=0 is the light emission point.
Note well that the lines x=0 and x'=0 are different lines - O and O' disagree on where the light emission point is at all times except t=0.

Is that what you mean when you say that there are two emission points?

 

[Pete]

Your statement above is false.

Here is the correct statement.

All correct measurements of the speed of light will be c.

That is of course implied.

You are implicitly implying the SR measurement technique is absolutely true.

What measurement technique? Where in the derivation of SR is a distance and time used to calculate c rather than the other way around?

 

[Pete]

No, the articles use the phrase time dilation which in SR is reciprocal.

Can you be more specific? Perhaps cut and paste a quote?
The article linked does not mention the word "reciprocal" at all, and only refers to time dilation of satellite clocks, as far as I can tell.

 

[Pete]

This is Einstein's logic to set this up and it is one way without a mirror.

An analogous consideration--applied to the axes of Y and Z--it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √( c² - v²) gives us

http://www.fourmilab.ch/etexts/einstein/specrel/www/

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.

 

[Pete]

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.

 

[Jack_]

Of course there is a time axis! This experiment involves events happening at different times. You can not analyse it without considering the times involved. The lack of a clock is irrelevant.

The first sentence isn't clear, but the second is just misguided. Clocks are irrelevant. Time is the critical factor.

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

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'.

First, let me check that I understand your notation.

DL = the distance (in frame O) that the light travels between time zero and the time when O' reaches the burn mark.
DL = d
DF = the distance (in frame O) that O' has travels between time zero and the time when O' reaches the burn mark.
DF = dv/c

DL' = the distance (in frame O') that the light travels between time zero and the time when the burn mark reaches O'.
DF' = the distance (in frame O') that O travels between time zero and the time when the burn mark reaches O'.

Good so far?

Intelligent.

I get:
DL' = d/λ
I didn't use length contraction to get this result. I applied the Lorentz transform to the event at which O' meets the burn mark:
(x, t) = (-vd/c, d/c)
(x', t') = (0, d/cλ)

...and thus calculated the location of end of the light beam at that time to be x'=d/λ.
And since the light beam started at x'=0, DL' = d/λx

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.

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.

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.

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

So, you made a mistake.

I think you would have seen this since first you confessed multiple light path lengths and clocks necessary to resolve it and then you claim the light paths are not different.

Perhaps, you have been working with SR too long.

No, I don't agree. I think that you are confusing yourself about what SR says by trying to apply length contraction where it doesn't apply. You might also be confusing locations (the light emission point) with events.

Let me be specific.

Here is the light path conversion.

x' = ( x - vt)λ.

Since t = x/c because of the light path, then

x' = ( x - vx/c)λ.

OK, so tell me exactly why the term vx/c exists.

Of course, that is exactly the divergence distance of the two frame origins/light emission points.

So, you have to explain this specifically otherwise to refute that.

 

[Jack_]

That is of course implied.

What measurement technique? Where in the derivation of SR is a distance and time used to calculate c rather than the other way around?

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?

 

[James R]

Jack_

If SR confesses multiple light emission points, then it confesses it cannot measure the speed of light with absolute certainty.

Pete is right. I think you're confusing coordinate systems or locations with spacetime events. The coordinates of any spacetime event vary among different reference frames. Is this what you mean by "multiple emission points" - that the spatial location (coordinate) of the emission of a light pulse can vary? That is something that SR readily "confesses" - it applies to every event, not just emission of light.

Hence, the clock sync method fails.

Which clock sync method?

Edit I already know SR cannot do this. It is the theory of relativity. It would need to know the absolute motion of the frame to know the actual light path.

SR says there is no absolute motion of a frame.

 

[Jack_]

Can you be more specific? Perhaps cut and paste a quote?
The article linked does not mention the word "reciprocal" at all, and only refers to time dilation of satellite clocks, as far as I can tell.

Good point.

In SR, time dilation is reciprocal.

 

[Jack_]

Jack_

Pete is right. I think you're confusing coordinate systems or locations with spacetime events. The coordinates of any spacetime event vary among different reference frames. Is this what you mean by "multiple emission points" - that the spatial location (coordinate) of the emission of a light pulse can vary? That is something that SR readily "confesses" - it applies to every event, not just emission of light.

This is not resolving this thought experiment. Yes, SR says that. Agreed.

Which clock sync method?

The SR simultaneity convention.

The Einstein clock synchronization method.

SR says there is no absolute motion of a frame.

I could not agree with you more.

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".

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

I am proving it is not logically decidable.

That should be perfectly natural if you cannot know the absolute motion of the frame.

 

[Pete]

Good point.

In SR, time dilation is reciprocal.

Only between inertial reference frames. Rotating frames are not inertial.