The burn mark problem

The Burn Mark Problem

The below experiment will avoid clocks and use light distance travel and frame distance travel. Since the SR clock synchronization method uses distance and light travel for its implementation, then distance and light travel are more fundamental than clocks.

Assume a stationary light source O a moving frame O’ moving at v in the direction of the negative x-axis.

When O and O’ are co-located, O emits a light pulse. O concludes when light moves a distance d, the observer O’ moves to the x coordinate –vd/c.

O decides to place a burn mark at that x location. Therefore, when O’ and the burn mark are co-located, O concludes light has traveled such that it is a distance vd/c + d from the burn mark.

O concludes O’ must measure this distance light traveled with a length contracted rod and hence, O’ will measure this distance light traveled as
(vd/c + d)/λ.

O’, on the other hand, draws different conclusions when taken as stationary. O’ sees the burn mark coming toward it from the left at v.

Also, when O and O’ are co-located at light emission, the burn mark is a distance (vd/c)/λ from O’. While light travels d/λ, the burn mark travels (vd/c)/λ toward O’. Hence, O’ concludes it is co-located with the burn mark when light travels d/λ from the light emission point O’ since O’ is taken as stationary for this set of conclusions. Hence, O’ concludes when it is co-located with the burn mark, light has traveled a distance d/λ from the burn mark. Also, O’ concludes O will measure this distance as d/λ2.

To summarize, when the burn mark and O’ are co-located.

O stationary
1) An O observer co-located with the burn mark concludes the one light beam is a distance vd/c + d from the burn mark.
2) O concludes O’ will measure this distance as (vd/c + d)/λ.

O’ stationary
1) An O observer co-located with the burn mark concludes the one light beam is a distance d/λ from the burn mark.
2) O’ concludes O will measure this distance as d/λ2.

Obviously, sans length contraction, frames cannot disagree on the length, from a co-located point, of a single light beam.

 

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I wonder who is best here. Would that be AN or Rpenner.

Would not matter to me.

The results would be the same.

Is there someone better?

 

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Uhhh, that is the experiment.

If you are willing to concede SR is false then so be it.

Where is rpenner or AN?

 

Not right, James - the burn mark is not at the light source.
I think Jack deserves more respect than our long-term antirelativity cranks - he seems to be coming from firmer grounding, and may be interested in learning something.

 

i like the way you talk.

the only problem with me is you will learn something.

i suggest you all team up.

 

Hi, Jack, and welcome to Sciforums.

All good so far.

Careful... "the distance light travelled" isn't yet well-defined enough to unambiguously transform it to the O' rest frame.
First, let's be clear that the burn mark (B) is at rest with respect to O, right?
Now, let O add a second marker, an apple (A), at rest with respect to O, on the x-axis at distance d from the origin. The distance in question is from Burn to Apple, OK?
As you say, O notes:

• that the light passes A at the same time as O' passes B,
• that the distance from A to B is vd/c +d, and concludes
• that O' will measure the distance from A to B to be (vd/c + d)/λ.

Right.

Once again, we need to carefully define the distance in question.
Let O' place a marker (a carrot, C) to show the distance the light has travelled. O' notes that B passes O' at the same time as the light passes C, and notes that at that particular instant, the distance from B to C is d/λ.
Now, take extra care... remember that according to O', B is moving. So in order to make B-C a meaningful ruler, we need to make sure that C is moving in the same way as B. So, O' must place the carrot so that it is at rest with respect to O, A, and B.
Why is this important? Because now the B-C ruler is moving in the frame of O', and will be longer in the frame of O.
So, O’ in fact concludes that O will measure this distance B-C as d.

Of course, O' could place C to be at rest with respect to O', but then B-C would not be a good ruler and we'd have to be very careful about specifying times if we wanted to know what O measured.


Now, to summarize:
B, O, C, and A are all markers placed in that order on the x axis, at rest with respect to each other.
O says that when O' passes B, the light beam is passing A.
O' says that when O' passes B, the light beam is passing C.

We conclude that according to special relativity, O and O' disagree about the order of events.

O says that events occur in this order:

• O and O' co-located, light emitted
• O'and B colocated, light passes A
• light passes C

O' says that events occur in this order:

• O and O' co-located, light emitted
• light passes A
• O'and B colocated, light passes C

And that's why I italicised the phrases indicating simultaneity - O and O' disagree about which events occur at the same time.

It seems that they can. Length contraction applies to rulers, with the key feature of a ruler being that the two ends are at rest with respect to each other.
The length between things that are moving with respect to each other (like the source of a light beam and its end) is not easily transformed between reference frames, and gives different results at different time references.

As an exercise, you might think about O' placing their own set of markers at rest with respect to O'. What events will occur in which order?

 

I do science to become right, not to show I'm right.

If I'm not open tothe possibility of learning something, I'll never get any smarter.
The same applies to you.

 

Yes, I am playing. Thanks for the welcome.

Agreed with the above.

 

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.

Hence, I do not want nor need another mark.

Here is specifically why. I am circumventing clocks on purpose and that 2nd mark would introduce a clock by neccessity.

So, if I cannot depend on the logic of the light path length, then SR cannot do clock synchronization and hence LT falls.

Now, the control I am using is co-location and the motion of the frames from point A to point B. I realize, when the frame moves from A to B, light must move a certain distance by the constancy of light. See how I am getting around clocks?

Now, why am I doing this.

I have realized the clock argument in SR is a red herring.

Here is the actual logic.

DL - distance light travels.
DF - distance the frame travels

DL' = (DL - DF)λ

The λ is necessary because the primed frame sees the distances of the unprimed frame as length contracted.

So, with this I am confessing the distance light travels is the distance from the light emission point in the frame to some coordinate.

OK, so, while the frame moves DF, light moves DL.

So, while the frame moves vd/c, light moves d. For the sake of communication, let's say x instead of d.

Now, we have,

DL' = ( x - vx/c )λ.

The above is exactly what I am doing.

Then, you want to do this unnecessary step.

Divide by the frame to frame constant c,

DL'/c = ( x/c - vx/c² )λ

t' = ( x/c - vx/c² )λ

x/c is simply the time light took to travel to x.

t' = ( t - vx/c² )λ.

Hence, when the burn mark and O' are co-located, the distance light traveled in each frame cannot be correctly resolved with length contraction simply because LT/SR is actually the science of multiple light emission points which is inconsistent with nature, IMHO.

 

Hint from me to you.

Self consistency is not a concept.

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

Since SR is based on the clock sync, one would need a model that tests one way light transfer in various frames using light travel and clocks.

For example, (I do not believe in light emission theory) to prove Ritz's theory is false, you need clocks of accuracy of 10-14 seconds at one mile.

So, as of yet, SR does not have a model and is supported only by some indirect evidence.

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

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.

This also is not supported by GPS either.

 

Correction: You should have written \(DL'=(x+vx/c)\lambda\)

Taking my sign correction into account, you should actually get \(t'=(t+vx/c^2)\lambda\)

Are you not aware of the Lorentz time contraction/simultaneity shift? It's not just a spatial contraction, there's also an equation for time transformations, which is exactly what you wrote above. The Lorentz transformations, being fully self-consistent, require that in the O' frame, the arrival at the burn mark and the measurement O makes of the light beam's travel distance occur at distinct times, even though these events are simultaneous in the O frame. That's an implicit self-consistency requirement fully accounted for in SR, so where's the contradiction?

I don't see how your claim has anything to do with Godel's Completeness Theorem. Please elaborate.

Why? The only clock synching you need to worry about is what the clocks and metre sticks for each observer read for one single event. If O sees an event at x=5, t=3 and O' sees this same event at x=-12, t=-4, and you know their relative velocities, that's all you need to determine what their relative measurements are thereafter.

I call BS on your claim and ask what you consider to be mere "indirect evidence". I also question what you mean by "model" and whether it really has any relation whatsoever to Godel's work.

That's nonsense and we've already dealt with claims like this many times before- see MacM's threads in the Pseudoscience section. Time dilation is reciprocal at any given moment, gravity and acceleration aren't.

??? That sentence doesn't even make sense, you talk about a moving clock being "further away" from a "co-located" stationary clock. Godel would be stirring in his grave.

 

Not sure what you mean by that, but the speed of light in a vacuum is fixed, while distance is mutable, in SR.

 

1) but the speed of light in a vacuum is fixed - Agreed and validated by tests of light speed from moving light sources.

2) while distance is mutable, in SR - Yes, that is what this thought experiment is showing.

There are two components to the distance one light beam travels when comparing frames.

One is length contraction.

The other is the diverging distance between the two light emission points. Each frame has its own light emission point.

However, this second component causes the frames to disagree from a certain co-located point the length of a light beam by length contraction plus d*(v/c).

How can two co-located observers disagree on the length of a light beam by anything other than length contraction?

 

I was not writing one for this experiment but one in general. In this particular thought experiment v is negative which would cause a plus sign that you have.

Hey, look what I have done though. You are not thinking about the lack of synchronicity of clocks but about light travel differentials. Once I have you thinking about that, then you will have to confess SR uses two different light emission points for LT. Once I have you to that point, then you will agree the clock synchronization method cannot know the correct and exact light emission point. But, the clock sync method claims the correct and "free from contradiction" light path is from the light emission point in the frame to the receiver/mirror. Yet, SR confesses other viable light emission points.
Hence, the clock sync method is not free from contradictions(this means a logical truth).

But, LT is constructed on the clock sync method.

We are not talking about clocks in this thought experiment. I did not use clocks. I used the logic, while the frame moves d*(v/c) light moves d.

If LT is "self-consistent", whatever that means, then you will be able to explain the light travel differentials in this thought experiment.

If you claim "while the frame travels d(v/c) light travels d" is false, then I will be able to put that to good use against LT.

Sure, someone said SR is "self-consistent".
I said a theory/set of L sentences is consistent iff it has a model.
h t t p
www
.amazon.com/Model-Theory-Studies-Foundations-Mathematics/dp/0444880542

Page 66, Theorem 1.3.21.

This has nothing to do with what I am talking about.

LT is constructed on the clock sync. I am showing the clock sync is invalid. It is a theoretical issue.

Call it what you want. Anyone familiar with mathematical logic knows if you want to contruct a theory (set of postulates), you need to have a model to back it up/ prove the consistency of the theory, preferably a mathmatical model.

A model is a set of constants, predicates and functions on a universe.

So, for example the natural numbers is a model such that
{N, +, *, S, 0} This is called the standard model

Say, why did you leave off the fact GPS proves reciprocal time dilation is one way? I am curious.

Here is a link for GPS.
http:
//relativity.livingreviews.org/Articles/lrr-2003-1/
See chapter 5 and you will see the GPS clocks are synched with time dilation and gravity differentials.

For time dilation, it only does one way.

Actually, I could care less about time dilation. I was just pointing out the facts of GPS "experiments".

Funny.

Imagine a light sphere. The point on the positive x-axis is the slowest clock compared to the stationary clock. As you alter the x coordinate while remaining on the light sphere, the clocks speed up but are still slower than the stationary clock until you reach the x-coordinate

x = (vtλ)/(λ+1). At that point, t' = t.


Anyway, once you continue decreasing x past this point, the clocks become faster than the stationary clock.

 

If you attempt to specify, in some intelligible fashion, exactly what you mean by "co-located" and "disagreement", the source of your confusion may become easier to spot and clear up. Try drawing a picture including (in the picture) the details of how you are measuring distances throughout, and being very careful with your grammar.

Right now I have no idea what you are talking about, and you are decorating your prose with assertions ("the distance light traveled is the most primary concept in SR", "There are two components to the distance one light beam travels when comparing frames", "
Imagine a light sphere. The point on the positive x-axis is the slowest clock compared to the stationary clock" ) that seem to indicate a basic confusion.

I think you are overlooking the role of time in your measurements of distance, and imagining a fixed or absolute distance relationship independent of any measurements of it. But that's just a guess.

edit in: Try this - there is no "stationary clock". There is no "stationary" distance, either.

 

Correct I am not using time. I only measure distances in the stationary frame.

This is consistent with the following,

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good.2 In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ``stationary system.''

If a material point is at rest relatively to this system of co-ordinates, its position can be defined relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean geometry, and can be expressed in Cartesian co-ordinates.
http://www.fourmilab.ch/etexts/einstein/specrel/www/


Next, I use the logic, while the light emission points of the frames move apart by d*(v/c), light moves d.

Next, co-location is defined in the exact way Einstein defined co-located origins for his LT thought experiment with mirrors. It simply means they represent the same point. If this logic is not definable, then LT false apart since co-location of the origins for light emission is not possible for the LT thought experiment.



Based on that, the problem to solve is:

When the burn mark and O’ are co-located.

O stationary
An O observer co-located with the burn mark concludes the one light beam is a distance vd/c + d from the burn mark.
O concludes O’ will measure this distance as (vd/c + d)/λ.

O’ stationary
An O’ observer co-located with the burn mark concludes the one light beam is a distance d/λ from the burn mark.
O’ concludes O will measure this distance as d/λ2.

 

You still seem to be making the mistake of assuming that the arrival of O' at the burn mark and the light beam's arrival at the mirror are coincidental. These events are only coincidental in the O frame. In the O' frame, when the burn mark arrives at the origin of O', the light beam has yet to reach the mirror. That's not a contradiction, SR requires that a set of clocks synchronized in one frame will be ticking out of sync in other frames. Doesn't matter whether you actually use clocks or not, as every event in every frame has a space and time coordinate regardless.

The Lorentz transformations in standard form require that the point x=0,t=0 describes the same point as x'=0,t'=0. That's the only synchronization required. They line their respective clocks up and agree to start them at the same time. They don't have to both call it "zero", but then the Lorentz transformations take on a slightly modified form.

Your very use of the word "while" implies synchronicity, which in turn implies clocks. Q.E.D.

My understanding of Godel's Completeness Theorem is that if you have a theory T, and a statement S, then S can be proven by deduction from the axioms of T, provided S is true for any object/"model" obeying those axioms. See here: http://mathworld.wolfram.com/GoedelsCompletenessTheorem.html

Now, I presume you're not just throwing jargon around to impress everyone, so please explain how this definition relates to what you just wrote, and to the concept of self-consistency. I think you're confusing the Completeness Theorem with the Incompleteness Theorems, but if that's indeed the case, you shouldn't be using such esoteric concepts in the first place.

And how does SR not satisfy all these requirements? It assumes elements of Real Number theory, linear algebra, etc. and all of its postulates are framed in terms of this language. For SR to be self-contradicting, the mathematical foundations on which it was built would have to be wrong.

I did mention it. I said time dilation was reciprocal (i.e. you can treat each clock as if it were stationary at a given point in time and apply the exact same equations), but because the two clocks are undergoing different accelerations and gravity, they will both agree that one clock registers more ticks than the other over time.

No, I don't see how you've demonstrated anything here. I don't even understand your setup, because you're doing a bunch of internet handwaving as if I were looking at a blackboard with you and could see what you're doing. Please specify all the position and time coordinates of the events in your scheme, otherwise it's impossible to figure out what you're trying to demonstrate.

 

I am not using a second point or mirror.

You seem to imply clocks control the light path length. You are caught in circular reasoning since the clock sync depends on the light path from A to B equalling the light path from B to A for a mirror experiment and hence the elapsed time for light travel is the same for each path.

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

The issue is not what happens with clocks.

It is how co-located observers measure one light beam length.

O stationary
An O observer co-located with the burn mark concludes the one light beam is a distance vd/c + d from the burn mark.
O concludes O’ will measure this distance as (vd/c + d)/λ.

O’ stationary
An O’ observer co-located with the burn mark concludes the one light beam is a distance d/λ from the burn mark.
O’ concludes O will measure this distance as d/λ2.

Each frame's conclusions failed to describe correctly what is going on in the other frame in terms of measure.

SR instructs us that measurement is a contraction issue when comparing frames.

The above conclusions prove that is false.

"While" is temporal logic and does not require a clock.

How about this if that word bothers you.

Assume the standard configuration.

A frame with relative motion v moves a distance d*(v/c) iff light moves a distance d.

The above statement is true. I use the extended completeness theorem because it is more general.
http://www.amazon.com/phrase/extended-completeness-theorem

When dealing with postulates, there is no such thing as self-consistency. You need a model. You also must know, I have taken that grad course in model theory and thus it would not be me that is confused as I can tell by what you are saying you do not know this area of mathematical logic.

You know how you all chant if clocks are synched in a frame then a moving frame will claim those clocks are not synched?

Well, we chant a theory is consistent iff it has a model.

For SR to be self-contradicting

It is not self-contradicting iff light emits from different points in space as the theory claims.

Well, that is not how GPS is programmed. Low orbits time dilation is the dominant adjustment. Higher orbits gravity effects are.

Gravity effects are one way and that is fine.

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.

OK, agreed.

Initial setup. Light emits up the positive x-axis when O' and O are co-located.

Code:

BM
|           O
         v<-O'

Assume BM co-locates with O' as below,

Code:

BM
|           O
O'

Setup logic
O and O' are co-located and light is emitted in the direction of the positive x-axis.
O stationary
O marked the spot at -d*(v/c) where d is some chosen distance and v is known.

O' stationary
O' measures this distance as (d/λ )*(v/c) under the rules of SR

The following logic of motion applies based on the above setup.
O stationary
If O' moves left a distance d*(v/c), then light moves a distance d.

O' stationary
If the burn mark moves toward O' a distance (d/λ )*(v/c), then light moves a distance (d/λ ).

Now assume O' moved left a distance d*(v/c) from the view of O.

Then, the burn mark moved a distance (d/λ )*(v/c).

Conclusions:
O stationary
Since O' moved d*(v/c) then light moved d. Hence an O observer co-located with O' concludes light is a distance d + d*(v/c).
O concludes O' must measure this distance as (d + d*(v/c))/λ.

O' stationary
Since BM moved (d/λ)*(v/c) then light moved d/λ. O' concludes light is a distance (d/λ) from O'.
O' concludes O must measure this distance as (d/λ²)

SR has no logic to resolve this discrepancy in the measurements of the frame.