The burn mark problem

[Pete]

OK, first "the distance light travelled" is the most primary concept in SR. The distance light traveled is the primary logic used for clock synchronization and LT is based on that.

No, "the distance light travelled" is not even well defined, let alone a primary concept.
Clock synchronization is based on a distance defined by a ruler, and the time taken for light to traverse that distance. The ruler defines the distance, not the light.

I really don't follow why you seem to think that special realtivity relies on the poorly defined concept of "the distance light travelled".

 

[Pete]

Here's some graphs of distance against time for each frame. Can you see what's going on?

 

[iceaura]

Correct I am not using time. I only measure distances in the stationary frame.
- - - -
Next, I use the logic, while the light emission points of the frames move apart by d*(v/c), light moves d.

There is no "stationary", or reference, frame. You have to use time to measure distance, and can only do so from within a frame of reference. "The logic" is in error, because it pretends to measure the distance the points of the frames move apart in some standard reference, or absolute, frame independent of either one of the frames of reference specified.

 

[James R]

Now, the control I am using is co-location and the motion of the frames from point A to point B.

Do you know what a reference frame is? It is NOT the same thing as an object. A reference frame extends throughout the whole of space and time. It is not like an object that is located at one point in space at any given instant.

When you say things like "a frame moves from point A to point B" you make no sense. Only objects can move from point A to B. A reference frame is a complete coordinate system, not an object.

Understand?

Hint from me to you.

Self consistency is not a concept.

Hint from me to you: Yes it is.

A theory is consistent iff it has a model. This is Godel's completeness theorem.

Please give an example of a theory that has a model and is consistent. I have no idea what you mean by "a model" in this context, and I see no link to Godel's theorem. Please explain what you mean.

Now, GPS does not support reciprocal*time dilation, it is absolute in one direction only. That is a problem for SR.

GPS is an application of general relativity. Special relativity is a subset of general relativity. Since special relativity "supports" "reciprocal time dilation", so does GR, and hence so does GPS.

This is assuming, of course, a particularly understanding of the term "reciprocal time dilation". You haven't explained what YOU mean by that term, yet.

Also, SR contends the further away a moving clock, the more out of sync the clock is to a co-located moving clock with a stationary frame.

I'm not sure what you mean by this. Please give an example.

 

[Pete]

But, for low orbits if Sagnac and gravity effects were programmed into the frequency of the clocks for the GPS satellite then they would beat too slowly. Now that is fine taking the earth frame as stationary.

But, when you take the GPS orbit as stationary, then the earth frame is moving and the earth clocks should beat slowly. That is not what happens. It is not a reciprocal relationship and should be.

No, it should not not be a reciprocal relationship, according to special relativity. In SR, the GPS orbit rest frame is non-inertial. In non-inertial frames, the usual rules don't apply. For example, light doesn't always move at speed c.

Relationships between inertial frames (such as the Earth Centered Inertial frame in which GPS clocks are synchronized) and non-inertial frames are not reciprocal, although it is a common mistake to suppose that they are. That mistake is the basis of the twin paradox.

 

[Jack_]

No, "the distance light travelled" is not even well defined, let alone a primary concept.
Clock synchronization is based on a distance defined by a ruler, and the time taken for light to traverse that distance. The ruler defines the distance, not the light.

I really don't follow why you seem to think that special realtivity relies on the poorly defined concept of "the distance light travelled".

Yea, but I am not letting the distance light travels stand on its own. I connect it to the motion of a frame.

So, in reality I am saying, given the standard configuration, the origin of the moving frame moves a distance (v/c)d iff light moves a distance d.

Then, I assume the moving frame moves (v/c)d and conclude light moves d.

 

[Jack_]

Here's some graphs of distance against time for each frame. Can you see what's going on?

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.

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.

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

DL' = ( DL - DF )λ

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?

 

[Jack_]

Do you know what a reference frame is? It is NOT the same thing as an object. A reference frame extends throughout the whole of space and time. It is not like an object that is located at one point in space at any given instant.

When you say things like "a frame moves from point A to point B" you make no sense. Only objects can move from point A to B. A reference frame is a complete coordinate system, not an object.

Understand?

OK, poor wording on my part.

The moving frame moves from point A to point B in the stationary system of coordinates.

Hint from me to you: Yes it is.

OK, please explain.

Please give an example of a theory that has a model and is consistent. I have no idea what you mean by "a model" in this context, and I see no link to Godel's theorem. Please explain what you mean.

Peano arithmetic is a theory and the natural numbers are a model for the theory.

GPS is an application of general relativity. Special relativity is a subset of general relativity. Since special relativity "supports" "reciprocal time dilation", so does GR, and hence so does GPS.

OK, can you show reciprocal time dilation in GPS? Thanks.

This is assuming, of course, a particularly understanding of the term "reciprocal time dilation". You haven't explained what YOU mean by that term, yet.

It means if O and O' co-locate and then some time elapses from that co-location, then give t for O as that time, O will believe O' will elapse t/λ.

Taking O' as stationary, if the time period is t', then O' will believe O will elapse t'/λ.

I'm not sure what you mean by this. Please give an example.

Yes, poor wording, I should have said, given the light sphere, the more positive the x coordinate up to the radius of the light sphere, the slower the clocks beat in the moving frame compared to a stationary clock located at the common co-location of the origin at light emission.

The clocks remain slower until the x coordinate is decreased to the x coordinate x=vtλ/(1+λ) and this is where t' = t. Lower values of x to the -r of the light sphere will produce faster clocks compared to the stationary clock.

 

[Jack_]

No, it should not not be a reciprocal relationship, according to special relativity. In SR, the GPS orbit rest frame is non-inertial. In non-inertial frames, the usual rules don't apply. For example, light doesn't always move at speed c.

Relationships between inertial frames (such as the Earth Centered Inertial frame in which GPS clocks are synchronized) and non-inertial frames are not reciprocal, although it is a common mistake to suppose that they are. That mistake is the basis of the twin paradox.

Well, GR effects, Sagnac effects, arc path effects are one way and should be.

If those are programmed into GPS, this corrects GPS and effectively makes the two frames inertial.

Then there will exist consistent one way time dilation according to the equations used in GPS programming.


When taking the GPS orbital frame as stationary, its clocks will beat slower than the moving earth frame.


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

 

[Jack_]

No, "the distance light travelled" is not even well defined, let alone a primary concept.
Clock synchronization is based on a distance defined by a ruler, and the time taken for light to traverse that distance. The ruler defines the distance, not the light.

I really don't follow why you seem to think that special realtivity relies on the poorly defined concept of "the distance light travelled".

Assume the standard configuration.

x' = ( x - vt )λ
What is x? The distance light traveled.

Is t a free variable? No, t is controlled and known by the distance light traveled which is x.

Hence, t = x/c

x' = ( x - vx/c )λ.

Divide by c to artificially implement time.

x'/c = ( x/c - vx/c² )λ.

Thus,

t' = ( t - vx/c² )λ.

 

[Jack_]

________

OK I think I will summarize this thread.

This thread proved there exists two contradictory light path lengths between two frame for SR for one light beam.

If anyone disagreed, which no one did, then one contradicts SR immediately as LT admits this physical contradiction.

So, what SR wants you to do is accept a clock value from the moving frame that is beating faster than the stationary frame even though it is moving and should be time dilated.

Then, you are to take this fast beating clock against the longer contradictory light path length of one light beam and use this fast beating clock to forget the physical contradiction of two light path lengths for the same light beam.

Not me.

 

[Pete]

OK I think I will summarize this thread.

This thread proved there exists two contradictory light path lengths between two frame for SR for one light beam.

Of course there are two different path lengths! There are infinitely many different path lengths, because the light beam is growing with time!

The different path lengths are expected, and not contradictory.

Your mistake is in ignoring time, and pretending that the length of the light beam is a fixed ruler that undergoes length contraction. It doesn't.

 

[Pete]

Assume the standard configuration.

x' = ( x - vt )λ
What is x? The distance light traveled.

Careful. x is the space coordinate of one end of the light beam. To get a length, you need two different values for x.
This is very important for length contraction - note carefully that length contraction is its simple form only applies to to lengths that are defined by two constant values for x. If one end of the length is changing with time, then you get the wrong result if you apply simple length contraction.

Is t a free variable? No, t is controlled and known by the distance light traveled which is x.

Hence, t = x/c

x' = ( x - vx/c )λ.

Divide by c to artificially implement time.

x'/c = ( x/c - vx/c² )λ.

Thus,

t' = ( t - vx/c² )λ.

Yes... what's your point?
What this demonstrates is that SR fundamentally relies on the speed of light being the same in all inertial frames of reference.
"The distance light travelled" (whatever meaning you choose to give it) can be derived from that - it's not fundamental.

 

[Jack_]

Of course there are two different path lengths! There are infinitely many different path lengths, because the light beam is growing with time!

The different path lengths are expected, and not contradictory.

Your mistake is in ignoring time, and pretending that the length of the light beam is a fixed ruler that undergoes length contraction. It doesn't.

You are not understanding there are two co-located observers that disagree on a single light path length. Both agree on the difference. So, you are at some point and so am I and we cannot agree on the length of one light beam.


I am not sure how you can even write that. But, I know that is LT.

Then, one introduces a clock, in this case from O, to O' that is moving but beating faster than the clock of O'.

Then, you are supposed to use this clock to "change" the length of the O light beam.

Here is the key though. Both agree there is a light path distance differential that cannot be resolved by length contraction/expansion. Imagine trying to sell the idea that sometimes you use a fast beating clock to resolve it and sometimes you use a slow beating clock.

But, the key for the normal person is that one light beam is agreed to be two different lengths and confessed as such by LT.

Finally, I thought I demonstrated conclusively the main difference in the light path differential was the switching from the light emission points of the two frames. Hence, there are two different light emission points for this thought experiment.

Do you deny this?

Think about the Pythagorean Theorem derivation of time dilation.

I am curious more than anything to see your response to this.

 

[Pete]

You are not understanding there are two co-located observers that disagree on a single light path length. Both agree on the difference. So, you are at some point and so am I and we cannot agree on the length of one light beam.

You don't seem to have a problem with two observers disagreeing over the length of a ruler. Why is disagreeing over the length of a light beam a problem?

Then, one introduces a clock, in this case from O, to O' that is moving but beating faster than the clock of O'.

Then, you are supposed to use this clock to "change" the length of the O light beam.

Umwhat? Let me catch up. I don't know what you're thinking here.

Here is the key though. Both agree there is a light path distance differential that cannot be resolved by length contraction/expansion. Imagine trying to sell the idea that sometimes you use a fast beating clock to resolve it and sometimes you use a slow beating clock.

Length contraction is a special case of the Lorentz transform. It only applies when the two ends of the length in question are stationary in the same reference frame.
When one end is moving with respect to the other, you need a better tool. The difference in the length of the light path can be resolved if you use SR properly - ie use the Lorentz Transform.

Finally, I thought I demonstrated conclusively the main difference in the light path differential was the switching from the light emission points of the two frames. Hence, there are two different light emission points for this thought experiment.

I haven't read that post yet. I'm working backwards through the thread.

 

[Jack_]

Careful. x is the space coordinate of one end of the light beam. To get a length, you need two different values for x.
This is very important for length contraction - note carefully that length contraction is its simple form only applies to to lengths that are defined by two constant values for x. If one end of the length is changing with time, then you get the wrong result if you apply simple length contraction.

Nopt, I assumed the standard configuration and a start of
x=x'=t=t'=0.

x is the light path length emerging from the start point.

Yes... what's your point?
What this demonstrates is that SR fundamentally relies on the speed of light being the same in all inertial frames of reference.
"The distance light travelled" (whatever meaning you choose to give it) can be derived from that - it's not fundamental.

Hey, I did not give it a meaning, LT did.

I am simply exploiting the two light emission points to create a physical contradiction on one light beam's length.


What this demonstrates is that SR fundamentally relies on the speed of light being the same in all inertial frames of reference.
This statement is false.

Light can proceed through space at one speed c and that part is true.

Then, SR claims to measure c, simply take the light emission point in the frame to the light receiver and time that and you will get c.

I am challenging this light speed measurement technique. It fails and I have proven that.

 

[Jack_]

You don't seem to have a problem with two observers disagreeing over the length of a ruler. Why is disagreeing over the length of a light beam a problem?

I do not have a problem with the two different lengths of a single light beam as long they obey the rules of length contraction,. I tend to force a theory to obey its own rules of measurement.


Umwhat? Let me catch up. I don't know what you're thinking here.


Length contraction is a special case of the Lorentz transform. It only applies when the two ends of the length in question are stationary in the same reference frame.
When one end is moving with respect to the other, you need a better tool. The difference in the length of the light path can be resolved if you use SR properly - ie use the Lorentz Transform.

I haven't read that post yet. I'm working backwards through the thread.

Do you deny this?[/QUOTE]

Of course I deny this.

There is no provision for this logic of measure of a rod in SR. It is length contracted only.

Take your time on reading. If you feel I did not answer the question fully, feel free to make that known.

 

[Pete]

Nopt, I assumed the standard configuration and a start of
x=x'=t=t'=0.

x is the light path length emerging from the start point.

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.

What this demonstrates is that SR fundamentally relies on the speed of light being the same in all inertial frames of reference.
This statement is false.

Light can proceed through space at one speed c and that part is true.

Then, SR claims to measure c, simply take the light emission point in the frame to the light receiver and time that and you will get c.

I am challenging this light speed measurement technique. It fails and I have proven that.

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.

 

[Pete]

I do not have a problem with the two different lengths of a single light beam as long they obey the rules of length contraction,. I tend to force a theory to obey its own rules of measurement.

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?

Of course I deny this.

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

There is no provision for this logic of measure of a rod in SR. It is length contracted only.

A light beam is not a rod.

 

[Pete]

Think about the Pythagorean Theorem derivation of time dilation.

I am curious more than anything to see your response to this.

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.