Definitions (continued from the cosmology forum)

[neopolitan]

Then why don't you let Chrisc talk for himself? I really am not interested in an argument by proxy.

Read the first word of post #93.

 

[Dale]

Read the first word of post #93.

I read it. That is why I didn't respond to 93, I responded to 95.

Do you believe that the speed of light is different for different reference frames? If so, justify your belief.

 

[neopolitan]

I read it. That is why I didn't respond to 93, I responded to 95.

Do you believe that the speed of light is different for different reference frames? If so, justify your belief.

No, I believe that the speed of light is measured to be the same in all inertial frames in part because I see the speed of light as representing the relationship between the spatial dimensions and the temporal dimension.

What I do believe is that the time dilation/length contraction equation pair, as generally taught, is not as useful as everyone seems to think because it leads to these sorts of misunderstandings. If you think that, in an inertial frame, time is dilated and length is contracted, then it makes sense to think that you can do what Chrisc has done and say:

if

L/t=c

and the primes in the length contraction and time dilation equations are supposed to be consistent

then

\frac{L'}{t'} = \frac{{L.\sqrt{1-\frac{v^2}{c^2}}}}{\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}} = \frac{L}{t}.\sqrt{1-\frac{v^2}{c^2}} = c.\sqrt{1-\frac{v^2}{c^2}} \neq {c}

But you can't.

If you could, Chrisc would be right that there is a problem. (And I would have been right before I finally figured out where I was going wrong myself.)

cheers,

neopolitan

 

[Dale]

I believe that the speed of light is measured to be the same in all inertial frames in part because I see the speed of light as representing the relationship between the spatial dimensions and the temporal dimension.

That is exactly how I see it. The invariant speed c, also called the speed of light, is a property of the Minkowski geometry of spacetime representing the relationship between the spacelike and timelike dimensions of spacetime.

 

[Chrisc]

But you can't.

If you could, Chrisc would be right that there is a problem. (And I would have been right before I finally figured out where I was going wrong myself.)

cheers,

neopolitan

Thanks for your help neopolitan
You are coming at my point from the other end of the argument.
As a postulate of SR, c is not open to question within the theory or convention.
The problem is that I am not questioning the constancy of c.
I am pointing out that as SR defines it, the constancy of c is upheld by
the variance of dimensions between frames in motion.
This variance of dimension cannot be both true and impossible to prove.
It appears that way when as DaleSpam and others claim, you cannot mix the
evidence of frames. I know you cannot mix the evidence of frames to prove c,
but you can observe the evidence and use it to deduce the change necessary to produce it.
This requires acknowledging the evidence of time dilation regardless of the fact that
the time was marked before the length was measured, i.e. back at rest in B.

I have no issue with the convention of SR.
My problem is that too many people take the constancy of c as being a
phenomena that is explained by SR and one that is then well
understood - it is neither explained nor understood.
But in that it is upheld as a postulate of SR via the evidence of time dilation
it is evidence of a fundamental void in the laws of physics.

Some, such as DaleSpam think as long as they can wrap up their obsevations to agree with
the convention of SR's math then all is well and physics is progressing as it should.

That is the bliss of ignorance achieved when the physics of the math is ignored.

 

[Chrisc]

That is exactly how I see it. The invariant speed c, also called the speed of light, is a property of the Minkowski geometry of spacetime representing the relationship between the spacelike and timelike dimensions of spacetime.

Wholly word salad Batman...that's not even funny.
A property of a geometry of a continuum?
Representing a relationship?

It's OK to tell people the truth...we don't know why the speed of light is constant.
No one will blame you personally for this lack of knowledge.

 

[Chrisc]

This is truly funny. How did you even pass elementary school?

Yes! I most emphatically assert that 1/5 is identical to 2/10! Please check with your nearest 5th grade student for confirmation.

This certainly does not follow. See post 91.

So I asked a fifth grader to help me with fractions. I asked her to explain why
1/5 and 2/10 were not only expressions of equal quantitative value, but also
identical entities.
She said to tell you they are not identical. Identical is indiscernible - as we can
discern 1/5 from 2/10 they are not identical but express identical quantities.
So, having taken your advice I'm sure you will now see my point, the speed of light
is of identical quantitative value in every frame it is measured, but discernible
between frames.

 

[Dale]

we don't know why the speed of light is constant

I certainly agree with that. In fact I would go further than that and say that "why" questions are generally not answerable by science.

 

[Dale]

So I asked a fifth grader to help me with fractions.

Hehe! Oh, this is too funny!

 

[Mentz114]

Chrisc,

if I used the symbols 'A' and 'B' to represent the numbers 1 and 2 respectively, is 1/2 = A/B ? If not, why ?

We're not talking physics now, and I suspect your idea or whatever is eating you has no more physical content than my question above.

 

[Chrisc]

Chrisc,

if I used the symbols 'A' and 'B' to represent the numbers 1 and 2 respectively, is 1/2 = A/B ? If not, why ?

We're not talking physics now, and I suspect your idea or whatever is eating you has no more physical content than my question above.

When I take your premise as the criteria by which I am to evaluate the "=", my answer is obviously yes, as anything else would be arguing your premise which by definition (yours) is pointless.

 

[neopolitan]

Chrisc,

I remain curious. Did post https://www.physicsforums.com/showpost.php?p=2104947&postcount=87" address your issues or was I off the mark?

If you have other issues, could you try to encapsulate them in one post? (It's difficult after a while to determine what is "key" and what is "intellectual self-defence".)

cheers,

neopolitan

 

[matheinste]

Hello all.

I am not supporting the claims by Chrisc but this may be relevant, or, if not relevant, at least of some interest..

The mixing measurements between frames is mentioned in some of the posts in this thread. Is celerity or proper velocity an example of this? As an example I measure the distance to a star in our common rest frame. I travel to the star in a time measured by me in my “moving” frame. My celerity, effective velocity or proper velocity is the ratio of the two.

The following technical quote is from a thread started by JesseM entitled “An illustration of relativity with rulers and clocks” In #5 by Dr Greg.

---Although you rarely see "celerity" or "proper velocity" mentioned by name, it is in fact used, in a slightly hidden way, in 4-dimensional formulations of relativity. Celerity is just "the space component of 4-velocity" (relative to a chosen inertial frame), for anyone who understands 4-vector jargon.------

Matheinste.

 

[Dale]

Yes, celerity is similar. It is not exactly a mixed frame measurement like Chrisc is proposing because it is coordinate displacement divided by the invariant proper time. For timelike worldlines you can always find a momentarily co-moving inertial frame and make celerity into an explicit mixed frame measure, but for light there is no co-moving inertial frame with which to mix.

 

[matheinste]

Yes, celerity is similar. It is not exactly a mixed frame measurement like Chrisc is proposing because it is coordinate displacement divided by the invariant proper time. For timelike worldlines you can always find a momentarily co-moving inertial frame and make celerity into an explicit mixed frame measure, but for light there is no co-moving inertial frame with which to mix.

Thanks. I understand what you are saying.

Matheinste

 

[Chrisc]

Chrisc,

I remain curious. Did post https://www.physicsforums.com/showpost.php?p=2104947&postcount=87" address your issues or was I off the mark?

If you have other issues, could you try to encapsulate them in one post? (It's difficult after a while to determine what is "key" and what is "intellectual self-defence".)

cheers,

neopolitan

No, but thanks for the effort.
I have only one issue, the same issue, the speed of light changes between frames in motion.
It is always measured to be c, but as such must change with the change in dimensions that hold it constant.
Unfortunately, DaleSpam has managed to convince everyone I've mixed frames, which has resulted in
everyone that does post directing their attention to DaleSpam's accusations instead of reading what I've
actually posted.

Here is a conversation I've had many times. The questions (italics) are typical of someone learning SR.
The answers are mine. Please let me know where you disagree with my answers and why.

Why is the speed of light constant?

No one knows.

Why is the constancy of the speed of light significant to physics?

Because it requires the motion of light is independent of the motion of the source and the observer.

Being independent of the motion of the source is not significant is it?

Not necessarily, but being independent of the motion of the observer is very significant,
for it is the observer that measures the laws of physics. If light remains a constant speed for two observers
that are moving with respect to each other, the equations of the laws will fail. When the equations fail the laws are no longer valid laws.

How are the equations upheld?

For the equations to be upheld when the speed of light is constant, the dimensions Length and Time must change between frames in motion.

Do we have proof of this change?

Yes we have the proof of the change in the rate of time in the clocks that show time dilation.

Do we have proof of a change in the dimension Length?

We have circumstantial evidence of it. When the speed of light is measured to be constant the evidence of time dilation
requires the dimension Length must change accordingly.


If the dimensions Length and Time change with motion, then the speed of light does not change, but our measurement of it
does?

Our measurement of the dimensions Length and Time is empirical evidence of Length and Time. If our measurements of them
change, it is because they have changed.

If the dimensions Length and Time have changed with our motion and we measure the speed of light to be constant then
we are actually saying the speed of light has changed between frames?

Yes, it must change in order to remain the same when the dimensions that comprise it have changed.


Why does motion change the dimensions Length and Time?

No one knows.
Actually I do know, but unless you've understood this thread, you won't understand the answer.

 

[matheinste]

Quote:-
-----Yes, it must change in order to remain the same when the dimensions that comprise it have changed.------

That is the bit I do not understand. The statement is not logical. How can something change and stay the same?

Matheinste

 

[neopolitan]

Chrisc,

It is 11pm where I am, so my reply will have to wait until tomorrow.

cheers,

neopolitan

 

[Chrisc]

Quote:-
-----Yes, it must change in order to remain the same when the dimensions that comprise it have changed.------

That is the bit I do not understand. The statement is not logical. How can something change and stay the same?

Matheinste

Ask yourself the same question with respect to what you think is constant.
How can the dimensions Length/Time change and the Length /Time that is light speed not change?†

The Length/Time that is the motion we call light remains constant or the same quantitative value for all frames, by changing with the dimensions Length and Time such that the Length/Time for each frame = c.
The change occurs between frames and the constancy remains within each frame.

If the Length/Time that is the motion light did not change with the change in dimension between frames in motion, light would be an Absolute physical measure - it would be the eather.

† This is not the same question as - how does the speed of light remain the constant? DaleSpam keeps insisting it is and that he has answered this by stating the dimensions Length and Time both change in such a manner as to hold the speed of light constant. That is correct, but it does not answer the question.

 

[Dale]

Yes, it must change in order to remain the same

I love it, zen and SR-fu! I would make the kung-fu movie reference more overt: "Yes Grasshopper, it must change in order to remain the same."

Really, Chrisc you cannot expect to be taken seriously. You write nonsense like this and you try to justify it by claiming that elementary arithmetic errors like 1/5 ≠ 2/10 are actually correct if only we would discard basic logic and see your wisdom. Surely you are just joking.

 

[neopolitan]

Here is a conversation I've had many times. The questions (italics) are typical of someone learning SR.
The answers are mine. Please let me know where you disagree with my answers and why.

Why is the speed of light constant?

No one knows.

Certainly no-one can give a simple answer and no-one should give a definitive answer, since the nature of science is that all answers should be falsifiable. However, there are at least two answers you could give to this.

The first is that the speed of light is just a reflection of the relationship between spatial dimensions and the temporal dimension. That relationship, like all other physics laws, is the same in all inertial frames.

The second involves a consideration of how the universe expands. I won't go into detail here, but you can come to the conclusion that nothing can travel faster than the rate at which the universe is expanding - with an appropriate model of the universe, you find that the fastest anything can travel, the rate of expansion of the universe and the c in \gamma are all the same. (This is not to say categorically that such a model is correct, but it certainly works for this and a few other things.)

Why is the constancy of the speed of light significant to physics?

Because it requires the motion of light is independent of the motion of the source and the observer.

Being independent of the motion of the source is not significant is it?

Not necessarily, but being independent of the motion of the observer is very significant,
for it is the observer that measures the laws of physics. If light remains a constant speed for two observers that are moving with respect to each other, the equations of the laws will fail. When the equations fail the laws are no longer valid laws.

Well, it is not really the constancy of the speed of light in a vaccuum. I'd say it is the maximum speed limit/invariant speed, which happen also due to the nature of light, to be the speed of light in a vaccuum. There are quite a few derivations of the SR equations which do not rely on the second postulate.

I discussed in an earlier thread about "information speed" that Gallileo could have arrived at the equations of SR merely by realising that information is not instantaneously transmitted, or realising the implications of this fact. That would have resulted in the need for experiment to determine just what the speed of information is, and such experiments would have arrived at c (just as they did for Maxwell/Planck et al).

How are the equations upheld?

For the equations to be upheld when the speed of light is constant, the dimensions Length and Time must change between frames in motion.

This is a little back to front. As alluded above, if Gallileo had incorporated the fact that information is not instantaneously transmitted, then he would have arrived at SR equations without even knowing that the speed of light in a vacuum is constant (he had in fact evidence that speed of light on Earth is not a constant, for example the bent stick in water effect).

Therefore, without even knowing about the constancy of the speed of light in a vaccuum, Gallileo could have arrived at equations which would tell us that "the dimensions Length and Time ... change between frames in motion", I deleted "must" from the quotation because it's not any sort of obligation, it's just a fact.

Do we have proof of this change?

Yes we have the proof of the change in the rate of time in the clocks that show time dilation.

Ok, here's a potential problem. If someone doesn't fully grasp what time dilation means, then they will end up confused.

Which clock gets dilated? Or perhaps, what exactly is being dilated?

We seem have a better visceral understanding of spatial lengths than temporal length, and of spatial measurements than temporal measurements.

Think about amounts of time and amounts of length. Consider a whole frame K' which is initially at rest to you (but distinct), which has a bar with a certain amount of length and a clock which is identical to the clock in your rest frame. Now put K' into inertial motion (close your eyes during the acceleration, if you prefer).

Relative to you, the bar in K' has a lower amount of length. Similarly, relative to you, the clock in K' will be displaying a lower amount of time - the ticks and tocks in K' will be further apart according to you. This means the time between ticks and tocks has stretched out (I hate that bit, because it is counterintuitive to me, time for me is the number of ticks and tocks). To the same extent that the bar has shrunk (the distance between to distinct parts of the bar, one end and the other, has decreased), the period between ticks and tocks has dilated (the temporal distance between a tick and a tock has increased).

I see this as counterintuitive because time dilation is self-referential. A clock is used to measure the time between external two events (eg "according to me you are colocated with me" and "according to me you are ten metres away from me"), not two internal events (eg "I've ticked" and "I've tocked"). If you created an equation which talked about the number of ticks and tocks instead of period between ticks and tocks, you would end up with an equation which would suit your purposed. (I personally call it temporal contraction, but it's not widely used.)

Do we have proof of a change in the dimension Length?

We have circumstantial evidence of it. When the speed of light is measured to be constant the evidence of time dilation requires the dimension Length must change accordingly.

See two previous answers.

If the dimensions Length and Time change with motion, then the speed of light does not change, but our measurement of it does?

Our measurement of the dimensions Length and Time is empirical evidence of Length and Time. If our measurements of them change, it is because they have changed.

Sort of, but not really. The speed of light (amount of space covered divided by amount of time taken to cover that space) remains the same. Our perspective on another inertial frame which is in motion relative to us is such that space and time are changed in concert: (smaller amount of space covered divided by smaller amount of time taken to cover that space).

If the dimensions Length and Time have changed with our motion and we measure the speed of light to be constant then
we are actually saying the speed of light has changed between frames?

Yes, it must change in order to remain the same when the dimensions that comprise it have changed.

No. Simply "no". Here is where the misunderstanding of what time dilation is telling you comes into full force. I've been here before. I've railed against time dilation, I still don't think the teaching of time dilation is satisfactory because it leads to this sort of confusion. But if you have two frames, one in motion and one at rest relative to you, and you collect together your four measurements, then the appropriate equations are:

c= \frac{uncontracted . length}{dilated . time} = \frac{contracted . time}{undilated . time}

Time dilation and length contraction can only be used when comparing things, this hopefully addresses the immediate objection that it apparently makes sense to have

c = \frac{uncontracted . length}{undilated . time} ... (I KNOW THIS IS AN INVALID EQUATION - read the surrounding text.)

As soon as you even hint at contracted length and dilated time (which you do by mentioning their complementaries), then you have four values to deal with, rather than two.

Why does motion change the dimensions Length and Time?

No one knows.
Actually I do know, but unless you've understood this thread, you won't understand the answer.

See the response where I mentioned Gallileo. Really "why" questions are not within the remit of physics, except where they are misphrasing of "how" or "what is the mechanism by which" questions.

I hope you can get something from this and note that I did not mention "mixing frames" at all - damn, except just then.

cheers,

neopolitan

 

[Chrisc]

I love it, zen and SR-fu! I would make the kung-fu movie reference more overt: "Yes Grasshopper, it must change in order to remain the same."

I'm glad you find it funny.
It is unfortunate you don't understand it.

Really, Chrisc you cannot expect to be taken seriously. You write nonsense like this and you try to justify it by claiming that elementary arithmetic errors like 1/5 ≠ 2/10 are actually correct

You are quick to insult but slow to substantiate your arguments.
The fifth grade student told you 1/5 is discernible from 2/10 which is why you and I can even have this discussion - and therefore they are not identical identities.
Are now disputing that as well?
It seems you are trying to say the dimensions that change between frames in motion don't change because we can't place different numerical values on them?

...if only we would discard basic logic and see your wisdom. Surely you are just joking.

On the contrary I am asking you to use the basic logic you have either abandoned or never acquired.
The dimensions Length and Time change between frames in motion.
Fact or Fiction?
The dimensions Length and Time comprise the ratio of motion we call speed.
Fact or Fiction?
If the dimensions Length and Time do not change between frames in motion, please state so here for the record.

 

[matheinste]

Quote:-
----The fifth grade student told you 1/5 is discernible from 2/10 which is why you and I can even have this discussion - and therefore they are not identical identities. -----

Did he mean they are different representations of the same rational number. I hope he did.

Quote:-
---If the dimensions Length and Time do not change between frames in motion, please state so here for the record. ------

Yes they do but their ratio remains the same, but you say that this is not the resolution of your problem.

Matheinste.

 

[Mentz114]

chrisc;

The dimensions Length and Time comprise the ratio of motion we call speed.
Fact or Fiction?

Ratio of motion ? You've started talking in tongues. Speed is the distance ( as measured by an observer) divided by the time (as measured by the same observer ) taken to traverse the distance.

I really can't see what you're trying to say. This is from your first post

If identical clocks were used by A and B to measure 1/300000s of a light signal to mark their meters, would the discrepancy in their clock times at rest after constructing their rulers, indicate light speed varied between them while marking their meters?

The thing you call 'light speed' that varies between frames is not defined. You don't seem to understand that you have to state how that thing is measured. You can't do that so nothing can be said about it. Again - the very idea of the speed of light in someone else's frame is a non-starter if you can't state how it's measured.

The fact that their elapsed times differed for the constructors cannot be used to argue your point. It ain't relevant.

 

[Dale]

The fifth grade student told you 1/5 is discernible from 2/10 which is why you and I can even have this discussion - and therefore they are not identical identities.
Are now disputing that as well?

Most certainly I am disputing that absurd and illogical claim.

1/5 = 2/10. They are equal, identical, equivalent, congruent, the same, etc. They are the same thing written different ways, e.g. "six of one half-dozen of another" or "a rose by any other name". It doesn't matter if you are talking about wages, speed, or just numbers, that doesn't change the meaning of division. If you brain-washed your 5th grader (mental child endangerment IMO) then try a calculator.

Frankly, if you don't see that then you have no business even posting here since it is not possible to have any logical discussion with someone like you who rejects the most basic operations of arithmetic. This is not the forum to be seriously arguing against elementary arithmetic and it is a waste of time.

 

[Dale]

On the contrary I am asking you to use the basic logic you have either abandoned or never acquired.
The dimensions Length and Time change between frames in motion.
Fact or Fiction?
The dimensions Length and Time comprise the ratio of motion we call speed.
Fact or Fiction?
If the dimensions Length and Time do not change between frames in motion, please state so here for the record.

We have been over this before in posts 50 and 51, but I will derive it using conventional notation for clarity:

From the Lorentz transform:
t' = γ(t-vx/c²)
x' = γ(x-vt)

From the definition of velocity:
u=dx/dt
u'=dx'/dt'

We want to find if any velocity is the same in two different frames so we can set u=u' and see if there are any solutions
dx/dt=dx'/dt'
dx/dt = γ(dx-vdt)/(γ(dt-vdx/c²))
which has the solutions
v=0 and dx/dt=c

Therefore, the speed of light is the same in both frames. QED.

 

[Chrisc]

The first is that the speed of light is just a reflection of the relationship between spatial dimensions and the temporal dimension.

That would be true of all speed.
What is it about light that holds this relationship constant?

No. Simply "no". Here is where the misunderstanding of what time dilation is telling you comes into full force. I've been here before. I've railed against time dilation, I still don't think the teaching of time dilation is satisfactory because it leads to this sort of confusion. But if you have two frames, one in motion and one at rest relative to you, and you collect together your four measurements, then the appropriate equations are:

c= \frac{uncontracted . length}{dilated . time} = \frac{contracted . time}{undilated . time}

I think you are talking about a different issue here, simultaneously attributing time dilation and length contraction to A?

Our perspective on another inertial frame which is in motion relative to us is such that space and time are changed in concert: (smaller amount of space covered divided by smaller amount of time taken to cover that space).

Space and Time do change, it is not just a perspective of inertial frames.

Time dilation and length contraction can only be used when comparing things,

I assume you mean when comparing the very real changes of Time and Length.

My response to DaleSpam below should make it more clear.

 

[Chrisc]

Most certainly I am disputing that absurd and illogical claim.

1/5 = 2/10. They are equal, identical, equivalent, congruent, the same, etc. They are the same thing written different ways, e.g.

What is "they"?
You speak of "they" - more than one - two things distinguishable from each other .
Then you claim there is no distinction between them.
Start with a slice of pie that is 1/5 of the whole pie.
Cut it in half and tell me the resulting two pieces have no physically significant distinction from the one piece.
That would be a simple, grade 5 example of the difference between 1/5 and 2/10, a physical difference,
a physically significant distinction for someone interested in seeing beyond the math to the PHYSICAL evidence of observation.

If you brain-washed your 5th grader (mental child endangerment IMO) then try a calculator.

Frankly, if you don't see that then you have no business even posting here since it is not possible to have any logical discussion with someone like you who rejects the most basic operations of arithmetic. This is not the forum to be seriously arguing against elementary arithmetic and it is a waste of time.

Comments like this only persuade the rest of us to become less interested IYO.

 

[Chrisc]

We have been over this before in posts 50 and 51, but I will derive it using conventional notation for clarity:

No we have not been over this in posts 50 and 51. You have been over it because you assume that I am claiming the speed of light is not constant in all frames.

Here is your problem:

We want to find if any velocity is the same in two different frames so we can set u=u'

NO! The principle of relativity tells us how the speed of light will ALWAYS be the same in different frames.

We want to find if a quantity of the dimensions Length and Time in one frame, the ratio of which is axiomatically constant in all frames,
is the same quantity in a second frame when the second frame is in motion.
We know from the success of Lorentz transformations it cannot be, for if it were we would not need nor use the Lorentz transformations.
In using the Lorentz transformations we transform the numerical values to equality(your claim) which holds the equations true which hold the laws valid.
BUT, we know this numerical equality is brought about by TRANSFORMING otherwise UNEQUAL quantities of dimension BETWEEN frames.
The UNEQUAL quantities of dimension retain the same ratio of Length/Time but are indisputably different quantities of dimension.

You and Mentz114 (post #124) say this difference cannot be claimed or proven and is of no consequence to the laws.
This is such an irrational position I can only assume I have misinterpreted it.

I am claiming this difference in the quantities of dimension between frames is evident in the time marked by the clocks of each frame.
A fact that can ONLY be considered evidence when the clocks of both frames are at rest.
Before then or while in motion all of your argument holds, there is no evidence available to even question the measures of each frame.
But, once back at rest the time dilation of A's clocks is very real evidence that the speed of light they measured while in motion, while their
clocks ran slow, was the same ratio of Length/Time as that measured by B, but NOT the same Length/Time as that measured by B.
How do you reconcile the loss of dimension in A with the laws of conservation?
If A had returned to rest with a Mass that had changed or if they had returned with a Ruler that was shorter would you ignore this evidence?

 

[Mentz114]

How do you reconcile the loss of dimension in A with the laws of conservation?

What are you talking about now ? You're raving.

But, once back at rest the time dilation of A's clocks is very real evidence ...

It's irrelevant.

that the speed of light they measured while in motion, while their
clocks ran slow, was the same ratio of Length/Time as that measured by B, but NOT the same Length/Time as that measured by B.

You've written B twice, but whichever way you cut this is wrong. They measure the same speed of light. There's more to be said ( well, sensibly, anyway ).

 

[Chrisc]

What are you talking about now ? You're raving.

You will never know as long as you keep saying this...

It's irrelevant.

You've written B twice, but whichever way you cut this is wrong.

Yes, I have written B twice. Had you read it you would have known why and you would not have stated this again ...

They measure the same speed of light.

Which has never been in question.