Definitions (continued from the cosmology forum)

[Dale]

Hi Chrisc,

To be explicit you should write (2) and (3) as follows:
x1 = ¥(x-vt)

(2)​

t1 = ¥(t-vx/c^2)

(3)​

(7) is only true for the specific cases of x/t = c or v = 0. Since I don't believe you are interested the case v = 0 then to be explicit you should write:
c = x/t = ¥(x-vt)/¥(t-vx/c^2)

(7)​

Equation (8) is also an equality for the specific case of x/t = c and can be derived by substitution of (2) and (3) into (7):
c = x/t = x1/t1

(8)​

For clarity:
c = x/t = 300,000km/1s

(9)​

c = x1/t1 = ¥(x-vt)/¥(t-vx/c^2) = 13,413.0735135km/0.044710245045s

(10)​

And again, to be explicit:
c ≠ 300,000km/0.044710245045s = x/t1

(14)​

c ≠ 13,413.0735135km/1s = x1/t

(15)​

which makes it clear, as I said earlier, that you only get your inequality by mixing frames and by treating time differently from space.

 

[Chrisc]

...And again, to be explicit:
c ? 300,000km/0.044710245045s = x/t1

(14)​

c ? 13,413.0735135km/1s = x1/t

(15)​

which makes it clear, as I said earlier, that you only get your inequality by mixing frames and by treating time differently from space.

Hi DaleSpam
I'm afraid you are not making any sense.
You've essentially restated what I said and claimed your restatement somehow makes it clear I am mixing frames.

It appears you think that stating by c does not equal x/t1 and c does not equal x1/t helps your argument.
If you mean that it shows that x is of B and t1 is of A you are right.
But I hope you don't think that cross referencing the evidence is somehow a mistake?
How would you check the claims of equality in any frame if you did not cross reference their evidence?

If there were NOT any change in the magnitude of motion that is c in A and B as you claim
then the statements:
c = x/t = x1/t1 = x/t1 = x1/t = 300,000km/1s
would all be true.
That they are not and you agree that you've made this point in (14) you are then stating my point.

 

[atyy]

Not sure this works, nor that it will convince Chrisc, but let me try. A and B should mark off lengths on the *same* infinitely long ruler (instead of constructing a ruler, this way the we have a record of the *accumulated* length, just as we have a record of the *accumulated* time). This way A and B can cross check that though their clocks now tick at the same rate, and the lengths they are marking off are the same, neither the rate nor lengths were the same when they were in relative motion. ?

 

[Dale]

I'm afraid you are not making any sense.
You've essentially restated what I said and claimed your restatement somehow makes it clear I am mixing frames.

It appears you think that stating by c does not equal x/t1 and c does not equal x1/t helps your argument.
If you mean that it shows that x is of B and t1 is of A you are right.

Back in https://www.physicsforums.com/showpost.php?p=2076072&postcount=47" you said that you were not mixing frames and that I was. What exactly do you think it means to "mix frames" if not to use expressions like x/t1 and x1/t?

 

[Chrisc]

Not sure this works, nor that it will convince Chrisc, but let me try. A and B should mark off lengths on the *same* infinitely long ruler (instead of constructing a ruler, this way the we have a record of the *accumulated* length, just as we have a record of the *accumulated* time). This way A and B can cross check that though their clocks now tick at the same rate, and the lengths they are marking off are the same, neither the rate nor lengths were the same when they were in relative motion. ?

Thanks atyy,
Unless I'm mistaken this is not the issue DaleSpam and others have with my claim.

 

[Chrisc]

Back in https://www.physicsforums.com/showpost.php?p=2076072&postcount=47" you said that you were not mixing frames and that I was. What exactly do you think it means to "mix frames" if not to use expressions like x/t1 and x1/t?

In #47 I said you were mixing the evidence gathered between frames.
It appears I am wasting your time.
I'll keep it short, are you in agreement with the following?

I claim A measured the speed of light to be 300,000km/s
So do you.
I claim B measured the speed of light to be 300,000km/s
So do you
I claim A's ruler was shortened and A's clocks were dilated during their measuring.
So do you.
I claim this change in A's measuring devices reflects a change in what A measured wrt
what B measured - given both measured a constant.

You claim this change in A's measuring devices has no bearing on A's claim of c.

If this is the case, please explain how A's ruler and clocks can change without reflecting a change in what they measure.

 

[Mentz114]

You claim this change in A's measuring devices has no bearing on A's claim of c.

If the change in the measuring instruments is such as to give the same answer, it is possible.

 

[Dale]

In #47 I said you were mixing the evidence gathered between frames.

Right, and what did you mean by that?

Look Chrisc, I was very clear about what I meant: when I said you were mixing frames I meant that you were using expressions like x/t1. What did you mean by "mixing evidence gathered between frames"? What kinds of expressions does that involve?

The reason that mixing frames (e.g. x1/t) is incorrect is that it is not a velocity in any frame. You cannot take something that is not a velocity in either frame and use it to conclude that the speed of light changed between frames. You yourself derived the constancy of c, and the only way you got something that was not c was to mix frames to give something that was not a velocity in either frame.

If this is the case, please explain how A's ruler and clocks can change without reflecting a change in what they measure.

Because the measurement of the rulers and the clocks "changed" by the same amount such that the ratio c stayed constant. You derived this yourself in (7).

 

[Chrisc]

Right, and what did you mean by that?

You said because A's ruler was the same as B's and because
A's clock runs at the same rate as B's, taking both into account
A gets c = 300,000km/s.
I pointed out that although A's ruler is the same as B's
A's clock was not running at the same rate as B's when
A constructed their ruler.

Because the measurement of the rulers and the clocks "changed" by the same amount such that the ratio c stayed constant. You derived this yourself in (7).

You (and Mentz114)have misunderstood my question.
I do not want to know how the ratio of the quantities of what is measured remains unchanged, as you said I have already stated that myself.

I want you to explain how a ruler and a clock can change without that change representing a change in what rulers and clocks measure.

 

[Dale]

Chrisc, I have already answered that question several times and I am simply not masochistic enough to go down that road yet again with you.

I tried to communicate using English; I tried to communicate using math. I told you the same thing using both English and math, I clearly connected the two, and I pointed out your error both ways. You seem to have a very difficult time forming a cogent argument in either English or math. I am not the only one who has voiced this communication difficulty, so I don't think it is due to stolidness on my side.

The bottom line is that despite several pages of attempts you have simply failed to make your case that "they have little option but to conclude the speed of light differs between the labs when they are in motion". Every attempt to do so has involved taking an expression like x/t1 or x1/t and trying to pass it off as a velocity.

 

[atyy]

Thanks atyy,
Unless I'm mistaken this is not the issue DaleSpam and others have with my claim.

No, I'm trying to figure out why you have a problem with what eg. DaleSpam is saying. I can't figure out why you feel the need to take, as DaleSpam says, x1/t or x/t1. I guess you somehow feel that the clock presents evidence that it has changed rate, while the ruler doesn't present evidence that it has changed length? However, the quantity on the clock that shows the change is an integral - the final rate of A and B's clock is the same, but the integrated time is not. So I am suggesting you look at the integral of the measured length so that the "ruler" also presents evidence that it was different (maybe, I haven't really thought this through).

 

[Chrisc]

Chrisc, I have already answered that question several times and I am simply not masochistic enough to go down that road yet again with you.

I tried to communicate using English; I tried to communicate using math. I told you the same thing using both English and math, I clearly connected the two, and I pointed out your error both ways. You seem to have a very difficult time forming a cogent argument in either English or math. I am not the only one who has voiced this communication difficulty, so I don't think it is due to stolidness on my side.

The bottom line is that despite several pages of attempts you have simply failed to make your case that "they have little option but to conclude the speed of light differs between the labs when they are in motion". Every attempt to do so has involved taking an expression like x/t1 or x1/t and trying to pass it off as a velocity.

DaleSpam, I too am finding this an exercise in futility.
You are I think, quite aware of the meaning of my question.
Why you are avoiding it I don't know.

If you really do think that the evidence of clocks and rulers can change without
that change indicating a change in what clocks and rulers measure - Length and Time -
then this discussion certainly is futile.

I am grateful for your time and effort.

 

[Chrisc]

No, I'm trying to figure out why you have a problem with what eg. DaleSpam is saying.

I do not have a problem with what DaleSpam has said in general.
He is employing the convention of SR to show me that c is constant in all frames.
I do not disagree with that, I never have.
It is DaleSpam who has a problem with what I've said.

I can't figure out why you feel the need to take, as DaleSpam says, x1/t or x/t1.

Taking x1/t or x/t1 is simply a cross reference of L/T of A and B.

I guess you somehow feel that the clock presents evidence that it has changed rate,

Yes, it is evidence that A's clocks have changed rate wrt B's.

while the ruler doesn't present evidence that it has changed length?

I am not concerned that the ruler does not present evidence of changing length.
The evidence of c by A during the experiment is indication that Length did change.
If it did not A would not have found c = 300,000km/s.

 

[Dale]

Why you are avoiding it I don't know.

I didn't avoid it, I already answered it. The point is that you are the one making the unorthodox claim and so it is up to you to substantiate it, which you have failed to do.

 

[Chrisc]

I didn't avoid it, I already answered it. The point is that you are the one making the unorthodox claim and so it is up to you to substantiate it, which you have failed to do.

My claim is unorthodox?

You agree time dilates between frames in motion.
You agree speed requires a measure of time.
Yet you deny the time dilation will affect the measure of speed.
Why - because length contraction makes it impossible to detect.

Do you not see you are denying the existence of a deduced
state of physical dimension by inferring the validity of the deduction
precludes its own existence?
You claim Time dilation and Length contraction are physically real
effects of motion, yet deny any change of Time and Length because as
they change they make it impossible to detect that they have changed.

Are you familiar with the story of the Emperor's New Clothes?

 

[Mentz114]

Chrisc:

the discrepancy in the total time marked by their clocks leads them to reason the speed of light differs between their labs when in motion, but is constant wrt any "measure" of length/time in either lab.

This is your original assertion.

You seem to be saying that there is an underlying objective reality in which there is something called 'the speed of light'. This thing may vary between frames - but we never measure this thing, whenever we try we always come up with the same number, because nature conspires to alter our instruments to hide this difference.

If this were so, then the 'underlying speed of light' has no effect of the laws of physics, cannot be empirically falsified or detected, and so is irrelevant. The thing just contradicts itself - why are you so convinced it has any meaning ? Your arguments are mathematically naive - you cannot 'prove' that it exists after admitting it can't be measured.

You may be interested to know that there's a theory of gravity called PV gravity that postulates that matter changes \epsilon_0 and \mu_0 and thus the locally measured speed of light. There's an excellent summary here
http://en.wikipedia.org/w/index.php?title=Polarizable_vacuum&oldid=56603531

 

[Dale]

My claim is unorthodox?

Yes.

Do you not see you are denying the existence of a deduced
state of physical dimension by inferring the validity of the deduction
precludes its own existence?

No, I don't see that, and you have failed to demonstrate it as indicated above.

Are you familiar with the story of the Emperor's New Clothes?

Yes, are you familiar with the story of the boy who cried wolf?

 

[Chrisc]

Chrisc:

This is your original assertion.

You seem to be saying that there is an underlying objective reality in which there is something called 'the speed of light'. This thing may vary between frames - but we never measure this thing, whenever we try we always come up with the same number, because nature conspires to alter our instruments to hide this difference.

No, I am not the one claiming immeasurable mechanics. I am the one claiming the time dilation of A's clocks is VERY REAL, VERY MEASURABLE evidence of a change in the dimensions of A while in motion.
DaleSpam is claiming the dilation of A's clocks is evidence that should be IGNORED or worse considered proof of his claim that the dimensions of A were NOT CHANGED while A was in motion wrt B.
Think about that for a second. A physically real, measurable CHANGE in a fundamental dimension of physics should be IGNORED, or considered evidence of NO CHANGE.
Now explain to me why I'm the conspiracy theorist, why my arguments are naive, why I should suffer the burden of proving to reasonable people that a physically measurable change in a fundamental dimension is evidence of a physically measurable change in a fundamental dimension?

Thanks for the link.

 

[Chrisc]

No, I don't see that, and you have failed to demonstrate it as indicated above.

One last appeal to your ...
10/20 = 1/2
If I gave you 10 dollars over twenty days or 1 dollar over 2 days, I would in each case give you the same thing, a ratio of money/days that is a constant $0.50/day.
I think you will agree the ratio of money/days remains constant and if all you could ever look at was the money/day you would argue (as your are now) that there is no difference in the money/day in either case.
I am simply arguing that since you can look at more than the money/day in that you can see that the time of A is different than the time of B, you must consider the magnitude of the ratio they both agree on is different between them. One gets a total of 10 dollars, the other a total of 1 dollar.

Yes, are you familiar with the story of the boy who cried wolf?

I am, and I've enough confidence to leave it at that.
Again, I thank you for your time and hope someday you will see this beyond the math.

 

[Dale]

One last appeal to your ...
10/20 = 1/2
If I gave you 10 dollars over twenty days or 1 dollar over 2 days, I would in each case give you the same thing, a ratio of money/days that is a constant $0.50/day.
I think you will agree the ratio of money/days remains constant and if all you could ever look at was the money/day you would argue (as your are now) that there is no difference in the money/day in either case.
I am simply arguing that since you can look at more than the money/day in that you can see that the time of A is different than the time of B, you must consider the magnitude of the ratio they both agree on is different between them. One gets a total of 10 dollars, the other a total of 1 dollar.

I actually like this example quite a bit. The amount of money a worker earns divided by the amount of time that they worked is called the worker's wage. The fact that A earned $10 and B earned $1 does not in any way contradict the fact that they were paid the same wage of $0.50/day (must be a "sweat shop").

Additionally, the amount of money earned by A divided by the time worked by B is not a wage and vice versa. So the fact that those numbers are not equal to $0.50/day also does not in any way contradict the fact that they were paid the same wage. There is, in fact, no logical way for them to conclude that they were paid different wages, despite the fact that they earned different amounts of money.

All of your assertions in this thread have been based on this type of mistake as I have pointed out long ago.

I thank you for your time and hope someday you will see this beyond the math.

That "see beyond the math" is an interesting phrase. Math is the language of logic, so what that phrase means is that you hope I will just discard logic and blindly accept your claims.

 

[Mentz114]

Additionally, the amount of money earned by A divided by the time worked by B is not a wage and vice versa. So the fact that those numbers are not equal to $0.50/day also does not in any way contradict the fact that they were paid the same wage. There is, in fact, no logical way for them to conclude that they were paid different wages, despite the fact that they earned different amounts of money.

All of your assertions in this thread have been based on this type of mistake as I have pointed out long ago.

Good thinking, Dalespam.

 

[Chrisc]

All of your assertions in this thread have been based on this type of mistake as I have pointed out long ago.

No, all of your answers have been this same misconstrued take on what I've said.
But as you like this analogy...

Consider two workers meet in a bar and claim to have earned the same wage $0.50/day.
They put their pay cheques on the table and see they are exactly the same amount.
All is well until they notice that one of their watches shows that worker only worked half as many days.
As their pay cheques match, is there some answer you can offer other than the worker whose watch ran slow was paid $1.00/day relative to the other?

That "see beyond the math" is an interesting phrase. Math is the language of logic, so what that phrase means is that you hope I will just discard logic and blindly accept your claims.

No, I said "see beyond" the math not exclusive of or regardless of or instead of...
you are not doing yourself any justice by twisting my words to suit your argument.

 

[Mentz114]

Consider two workers meet in a bar and claim to have earned the same wage $0.50/day.
They put their pay cheques on the table and see they are exactly the same amount.
All is well until they notice that one of their watches shows that worker only worked half as many days.
As their pay cheques match, is there some answer you can offer other than the worker whose watch ran slow was paid $1.00/day relative to the other?

They can't have the same total and the same rate, if one worker worked less time than the other. It doesn't make sense. Someone in that scenario is mistaken.

 

[Chrisc]

They can't have the same total and the same rate, if one worker worked less time than the other. It doesn't make sense. Someone in that scenario is mistaken.

Let me rephrase what you've just said in context of what this thread has been discussing.
They can't have the same Length of ruler and the same speed of light if A's time ran slower than B's.

Are you suggesting the physicists in A were mistaken when they measured c to be 300,000km/s?
Perhaps you think that the numbers on the pay cheques "changed" from when they worked to when they met in the bar?

Or perhaps you are beginning to see my point... the rate is, was and always will be the same, the same ratio, the same rate of pay, the same rate of motion or the same speed. What changes is the dimensions by which these are measured. When Length contracts and Time dilates BETWEEN two frames in motion, then that which is defined by the quantities of these CHANGED measures, is itself changed BETWEEN these same frames.

 

[Dale]

is there some answer you can offer other than the worker whose watch ran slow was paid $1.00/day relative to the other?

Sure, one is a full-time employee and the other is a part-time employee.

 

[Dale]

Good thinking, Dalespam.

Thanks!

 

[Chrisc]

Sure, one is a full-time employee and the other is a part-time employee.

Funny, useless, but funny.

 

[Dale]

Funny, useless, but funny.

Hehe, thanks!

Of course there are some obvious limitations with your analogy: there is no "invariant wage", time worked and money earned don't Lorentz transform, and inflation isn't really analogous to length contraction.

But even so I was making the point that proper time is not the same as "time worked" which is in the definition of wage. Only working time is relevant, which is generally different from wristwatch or calendar time.

Similarly with your original point. Regardless of how you object, it remains clear that your assertions result from mixing frames or equivalently from using the wrong time in calculating a speed.

 

[Chrisc]

Regardless of how you object, it remains clear that your assertions result from mixing frames or equivalently from using the wrong time in calculating a speed.

It is clear from this statement that you still don't understand what I've said.
You are stuck on the notion that I've mixed frames with x/t1 and x1/t.
I've explained the inequality of this cross reference shows a change in
MAGNITUDE of dimensions measured NOT the inequality of the speed of light.

It is this change you are failing to see, or ignoring or for some reason denying.
Until you acknowledge a very real change of dimension between A and B you will
not understand what I've said.

Think of this distinction as the difference between dimensional and dimensionless physical constants.
You posted a very lucid account of this distinction a while ago.
Use your reasoning there to see and define the difference here.

The speed of light is a physical constant in all frames.

The magnitude of the dimensions that comprise this constant change...between frames.

A change in the numerical value of c would have no affect on the laws, it would be an imperceptible change.

A change in the ratio of dimensions that is c would have significant affect on the laws.

I'll leave the rest for you to reason through, but I would be very interested in your results.

 

[Dale]

It is clear from this statement that you still don't understand what I've said.
You are stuck on the notion that I've mixed frames with x/t1 and x1/t.

Perhaps I don't understand your new argument if it has been modified from your previous derivation. Can you derive your new assertion without mixing frames with expressions like x/t1 and x1/t?

 

[atyy]

Chrisc, I don't even understand the assertion, let alone the argument. I'm especially confused since you agree with DaleSpam, yet you seem to be saying something different. So if you can state what you mean in a simple way, I would be much less confused.

 

[Chrisc]

Perhaps I don't understand your new argument if it has been modified from your previous derivation. Can you derive your new assertion without mixing frames with expressions like x/t1 and x1/t?

I've not changed my argument, I am offering another perspective that I thought you'd be more familiar with.

 

[Chrisc]

Chrisc, I don't even understand the assertion, let alone the argument. I'm especially confused since you agree with DaleSpam, yet you seem to be saying something different. So if you can state what you mean in a simple way, I would be much less confused.

From the beginning my assertion has stemmed from the fact that the constancy of the speed of light is empirical evidence.
As malawi-glenn said, "we can never prove the light speed to be constant."
Upon SR surviving falsification, the postulate is considered sound, but still not prove-able as it is a postulate or axiom of the theory.
SR holds the speed of light constant by formulating a change in the dimensions that comprise it.
In other-words, when the theory does away with absolute rest, it simultaneously does away with the notion of all absolute measures including those of the dimensions Length, Time and Mass.
This is interesting - the lack of absolute measure affords a universal constant of measure "c".
It should be clear from this that between frames in constant linear motion, there exists a very real, verifiable CHANGE in the dimensions that comprise the motion of light.
How can we verify a physical change in dimension yet not use it to prove the constancy of the speed of light?
Because its constancy is relative to the dimensions in which it is measured. When these dimensions change as SR predicts they do, the speed of light changes with them which holds it constant in every frame it is measured.
How does the speed of light change? (which is DaleSpam's argument)
It changes with and "as" the dimensions that comprise it. This does not mean we can measure the change directly any more than we can measure the change in dimensions directly. But as the evidence of this change is empirically verified by the clocks of A, then the validity of SR demands we acknowledge this change is equally valid evidence of the change in light speed necessary to hold it constant for the frame in which the change of dimension occurred.

This is where DaleSpam jumps up yelling "Hand Waving, Hand Waving, it's all a bunch of Hand Waving.
Show me the math"
I've tried to explain the math is just as he has seen it a thousand times before. There is nothing new in the math. It is essentially a case of understanding what it means to apply the math, specifically the Lorentz factor.
1/sqrt(1-v^2/c^2)
This is a ratio of dimension, 1 over a function of CHANGE of dimension. A function driven by the relative measure known as v and the constant (axiomatic) measure known as c.
I can't rewrite this any differently without it meaning something else. So how I am expected to show DaleSpam math he has not already seen is beyond me.

 

[Dale]

I've not changed my argument

Then your argument still stands refuted. You simply cannot derive a change in c without erroneously mixing frames, as we showed above.

 

[Fredrik]

LOL, is this still going on?

\uparrow​

(rhetorical question)

 

[Dale]

Derive that! You're mixing frames!

Oh, sorry, it is getting to be a reflex.

 

[neopolitan]

One last appeal to your ...
10/20 = 1/2
If I gave you 10 dollars over twenty days or 1 dollar over 2 days, I would in each case give you the same thing, a ratio of money/days that is a constant $0.50/day.
I think you will agree the ratio of money/days remains constant and if all you could ever look at was the money/day you would argue (as your are now) that there is no difference in the money/day in either case.
I am simply arguing that since you can look at more than the money/day in that you can see that the time of A is different than the time of B, you must consider the magnitude of the ratio they both agree on is different between them. One gets a total of 10 dollars, the other a total of 1 dollar.

Oi, is someone using my economic theory without attribution?

Chrisc, maybe the problem here is that you are only thinking of one factor. I discussed a sort of economic theory of spacetime with DaleSpam a while back.

Think of it this way, you have a constant income of spacetime dollars - ct spacetime dollars per t. You can spend it just sitting around doing nothing, which means you spend it in terms of time (c.t_{you}). You might notice that I split mine up and spend part of my income on moving from one place to another (distance of v_{me}.t_{me}) and the remainder goes up in time (c.t_{me}) . The exchange rate depends on how long I take to move from one place to another, but the end result is that the spacetime dollars I spent my distance traveled and my time elapsed will equal the spacetime dollars you spent on your time elapsed (and your distance traveled which was zero (v_{you} = 0) ):

\sqrt{v.t_{me}^{2} + c.t_{me}^{2}} = c.t_{you}

The same sort of equation can be used for a rod at rest. A rod at rest has simultaneous ends, the value of the simultaneous ends of a rod which has a length of x is x spacetime dollars.

Relative to you, that rod can convert some of that length into motion (this is not rational economics here) - this is giving the rod a time component, and will make the ends of the rod non-simultaneous to you. The magnitude of the non-simultaneity (MNS) and the length of the rod will vector sum to the resting length of the rod:

x_{at rest} = \sqrt{x_{in motion}^{2} + MNS_{in motion}^{2}} ... (1)



Finally, the same sort of equation can be used for a clock. A clock at rest, with colocal ticks and tocks, has a time value of ct_{at rest} - where t_{at rest} is the number of ticks and tocks, not the period between each tick and tock. The clock can convert some of that, relative to you, into motion but the ticks and the tocks will not be colocal. The vector sum of the values, time value in motion plus the extent of non-colocality (ENC) of the clock in motion will add up to the rest time value:

ct_{(at rest)} = \sqrt{ct_{(in motion)}^{2} + ENC_{in motion}^{2}} ... (2)


...


Equations (1) and (2) can be more balanced, if one considers a zero MNS_{at rest} and a zero ENC_{at rest}:

\sqrt{x_{at rest}^{2} + MNS_{at rest}^{2}} = \sqrt{x_{in motion}^{2} + MNS_{in motion}^{2}}

and

\sqrt{ct_{(at rest)}^{2} + ENC_{at rest}^{2}} = \sqrt{ct_{(in motion)}^{2} + ENC_{in motion}^{2}}

Leaving these out is possibly where a lot of confusion comes in.

Anyways, in conclusion, if you "make" the ticks and tocks of a clock non-local or you "make" the ends of a rod non-simultaneous, by giving them motion relative to you, then you will reduce the number of tick and tocks or contract the rod to an extent equivalent to the extent to which the ticks and tocks are non-local or the ends of the rod are non-simultaneous.

...


No-one but me may understand this "economic theory", but the by the state of the world economy, no-one understands the real thing either

cheers,

neopolitan

PS In terms of the quoted section, you could say that one guy got $10 for just sitting there, the other got only $1 but did get to do some very fast, mind broadening travel (since the traveling one spends less spacetime money on time, he could arrive back home after twenty days of the $10 guys time having only 2 days on his clock, qualifying for only 2 days' pay).

 

[Mentz114]

Going back to mixing quantities across frames. If we calculate x'/t we get

\frac{x'}{t}=\frac{x\cosh(\beta)+t\sinh(\beta)}{t}=c\cosh(\beta)+\sinh(\beta)

The across frame quantity x'/t which Chrisc claims represents a velocity can be greater than c so it is not governed by relativity and has no physical significance within the framework of SR.

 

[Chrisc]

Going back to mixing quantities across frames. If we calculate x'/t we get

\frac{x'}{t}=\frac{x\cosh(\beta)+t\sinh(\beta)}{t}=c\cosh(\beta)+\sinh(\beta)

The across frame quantity x'/t which Chrisc claims represents a velocity can be greater than c so it is not governed by relativity and has no physical significance within the framework of SR.

Thanks Mentz114, that is a problem, but not what I've said.
It seems DaleSpam's insistence that I have mixed frames has convinced everyone.

 

[Chrisc]

Then your argument still stands refuted. You simply cannot derive a change in c without erroneously mixing frames, as we showed above.

You are not listening.
Go back and read post #50, lines 14 and 15.
They state that c DOES NOT EQUAL x/t1
and c DOES NOT EQUAL x1/t

It is because c ≠ x1/t
and c ≠ x/t1
which is to say c ≠ BLength/ATime
and c ≠ ALength/BTime
that one can say
BLength ≠ ALength
BTime ≠ ATime
therefore
BLength/BTime ≠ ALength/ATime
and
c = BLength/BTime ≠ ALength/ATime = c

 

[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.