Definitions (continued from the cosmology forum)

[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 When the equations fail the laws are no longer valid laws.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.