Definitions (continued from the cosmology forum)

[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?

:rofl: 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.