Definitions (continued from the cosmology forum)

[Dale]

BLength ≠ ALength
BTime ≠ ATime
therefore
BLength/BTime ≠ ALength/ATime

Wrong.
1 ≠ 2 and 5 ≠ 10 but
1/5 = 2/10

 

[Chrisc]

Wrong.
1 ≠ 2 and 5 ≠ 10 but
1/5 = 2/10

Think about why you are putting an equal sign between 1/5 and 2/10?

To quote Dr. John Baez "every equation is a half-truth: after all, if the two sides of the equation look different, why are we saying they're the same?"

There is an expression of equality in the ratios, or fractions or proportions which can be written as:
1/5 = 2/10
which means the ratio c of A = the ratio c of B when expressed as measurements of A by A, or of B by B, but NOT of A by B or of B by A, which means -
the speed of light is always "MEASURED" to be a constant.

But do you actually think that 1/5 is identical to 2/10?
If so you are claiming the Length and Time of A is identical to B.
If that is the case why do we need Einstein's work, Lorentz transformations, or even the notion of relativity.
If not, you are agreeing with me.

 

[neopolitan]

Chrisc,

You are suffering from the same problem I have had and which I think a lot of students of relativity have, and which the "masters" of relativity seem to be reluctant to address.

Note that these two equations:

Time Dilation: t' = \frac{t}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

Length Contraction: L' = {L}.{\sqrt{1-\frac{v^{2}}{c^{2}}}}

have assumptions behind them which are rarely stated. At least one of the guys arguing here could have told you, but for some reason they love to call "mixing frames" without explaining why.

The time dilation equation applies in the frame in which two events happen at the same location. The length contraction applies in the frame in which two events happen simultaneously. Think about that, take two events which are at the same place and happen simultaneously ... they are the same event.

You can't apply time dilation and length contraction to the same frame without being trivial.

You seem to be searching for a pair of equations which apply in the same frame, that would be the Lorentz Transformations which are used to compare a number of separations between events (I won't go into detail about it but you could consider it to be about four different events, the others can argue for and against as their fancy takes them).

Perhaps you are looking for a temporal contraction equation. I personally see value in one, but the others probably don't. The time dilation equation is usually used in such a way as to say that the time between the ticks and tocks of a clock are elongated in a clock which is in motion relative to you. (In this case, those presenting the argument are possibly guilty of mixing frames, but that is another story.)

However, as you sit there looking at the clock on your wall, you don't measure how long the period between each tick and tock is to measure the passage of time - you measure the number of ticks and tocks. A clock in motion - relative to you - experiences fewer ticks and tocks than the clock which is at rest - relative to you.

Using the same frame of reference as that used in the length contraction equation, you could have an equation which is more appropriate for your purposes and has what I think is an additional benefit - consistent application of the prime (one primed frame, one unprimed frame, distance and time components primed and unprimed accordingly):

Temporal Contraction: T' = {T}.{\sqrt{1-\frac{v^{2}}{c^{2}}}}

You could use Temporal Contraction and Length Contraction to your heart's content, and you will find that the speed of light is consistent along with all velocities.

The really funny thing is, I'd not be surprised if they argue that I am wrong, even if I am trying to explain helpfully where you have gone wrong

cheers,

neopolitan

(If you want evidence in support of my argument, see http://en.wikipedia.org/wiki/Special_relativity#Time_dilation_and_length_contraction" on wikipedia. At least one of the guys you are having a discussion with is willing and able to modify that entry if he thinks it is wrong. Since it has remained largely unchanged for the past two years, and I have referred him to it before, I suspect he thinks it is right.)

 

[Dale]

Think about why you are putting an equal sign between 1/5 and 2/10? ... But do you actually think that 1/5 is identical to 2/10?

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.

If so you are claiming the Length and Time of A is identical to B.

This certainly does not follow. See post 91.

 

[neopolitan]

Yes! I most emphatically assert that 1/5 is identical to 2/10!

This is certainly true, but I don't think it is what Chrisc meant in his frustration. I'm giving him the benefit of the doubt -

\frac{1.kumquat}{5.puppies} \neq \frac{2.apples}{10.teachers}

Without units, you are perfectly right, but if I am reading Chrisc right (in what he is trying to say, right or wrong), then he thinks that:

(1) in the stationary lab the length of an uncontracted rod (L_{uncontracted}) is measured in terms of the undilated time it takes for a photon to go from one end of the rod to the other (t_{undilated}), and

(2) in the lab in motion, the length of a contracted rod (L_{uncontracted}) is measured in terms of the dilated time it takes for a photon to go from one end of the rod to the other (t_{dilated}).

( c = \frac{L_{uncontracted} }{t_{undilated}} ) \neq \frac{L_{contracted}}{t_{dilated}}

Which is right even if there is a problem because he is misusing time dilation (because time dilation can't be used for this purpose - see my earlier post).

cheers,

neopolitan

 

[Dale]

This is certainly true, but I don't think it is what Chrisc meant in his frustration. I'm giving him the benefit of the doubt -

\frac{1.kumquat}{5.puppies} \neq \frac{2.apples}{10.teachers}

Without units, you are perfectly right

You are setting up a strawman argument here that is not really relevant. Your units are dimensionally inconsistent, and I have never advocated that nor has Chrisc. He has mixed frames but not made dimensionally inconsistent equations that I have noticed.

If you set up an equation with different but dimensionally consistent units then you can get an equality. For example 1 ms ≠ 2 s and 5 mm ≠ 10 m but 1 ms/5 mm = 2 s/10 m. Similarly, your inequality in (2) does not necessarily follow.

 

[neopolitan]

You are setting up a strawman argument here that is not really relevant. Your units are dimensionally inconsistent, and I have never advocated that nor has Chrisc. He has mixed frames but not made dimensionally inconsistent equations that I have noticed.

I may have set up a strawman, but I never attacked it. I also never said you were wrong, so I don't see your problem.

If you set up an equation with different but dimensionally consistent units then you can get an equality. For example 1 ms ≠ 2 s and 5 mm ≠ 10 m but 1 ms/5 mm = 2 s/10 m.

I think you still don't understand what Chrisc was getting at. As far as I can tell, it is not about s and ms, it is about undilated seconds and dilated seconds. (I freely admit that I may still not understand what Chrisc is getting at either.)

Similarly, your inequality in (2) does not necessarily follow.

I don't understand. The (2) wasn't an equation, it was a situation. (1) = lab at rest relative to the observer, (2) = lab in motion relative to the observer.

If the inequality which follows my description of (2) does not necessarily follow, please explain how it would not follow.

Note the following:

t_{dilated} = t'
t_{undilated} = t
L_{contracted} = L'
L_{uncontracted} = L

so that:

L' = L.\sqrt{1-\frac{v^{2}}{c^{2}}

and

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

cheers,

neopolitan

(PS I know the inequality does not follow if v=0, but I did say in (2) that the lab was in motion, so I implicitly excluded v=0.)

 

[Dale]

As far as I can tell, it is not about s and ms, it is about undilated seconds and dilated seconds.

It's just a dimensionally consistent analogy.

If the inequality which follows my description of (2) does not necessarily follow, please explain how it would not follow.

See equation (8) in post 51.

 

[neopolitan]

See equation (8) in post 51.

Love it, it works but you are talking about (x and x1) and (t and t1) related by Lorentz transformations.

Note however, that Chrisc is still talking about time dilation in post https://www.physicsforums.com/showpost.php?p=2095337&postcount=68".

Note also that in posts https://www.physicsforums.com/showpost.php?p=2095337&postcount=95" I specifically refer to time dilation and length contraction.

I repeat, referring again to post https://www.physicsforums.com/showpost.php?p=2095337&postcount=95", if the inequality which follows my description of (2) does not necessarily follow, please explain how it would not follow.

cheers,

neopolitan

RE your edit, they are not my dimensions, I am trying to get to what Chrisc is trying to say, so I suspect they are his dimensions. But, I say yet again, I might be wrong about what Chrisc is getting at.

 

[Dale]

I am trying to get to what Chrisc is trying to say, so I suspect they are his dimensions. But, I say yet again, I might be wrong about what Chrisc is getting at.

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

 

[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.