I have pulled this message from the 3 Clocks thread and started a new thread here for two reasons.

1 - It doesn't relate to the 3 Clock topic.

2 - I have asked what I feel is a bonified and important question to which the responders have yet to provide a direct explanation to the question.

In the 3 Clock string there were arguements about if the circumference contracts or if the radius contracts by Relativity when a disk rotates.

While virtually everything I have seen says the circumference contracts in the vector of motion due to velocity by:

Lr = L0 * (1 - (v/c)^2)^.5

and while I know that gravity curves time-space, I have never seen it claimed that the radius contracts due to acceleration (gravity), until it came up in that string. The arguement there was that the circumference does not contract and that the radius does.

Also, my question was and still is "How do you justify claiming that Pi changes, regardless of what contracts. The reason is that whatever relavistic affect there may be on the ruler, it must also affect the rotating disk.

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Rotating Disk


Thanks for the link. I'm posting this portion for xxxx's benefit.


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Let's consider a huge disk above which are drawn two concentric circles, one very small and the other one as huge as the disk:

Our observer is on the disk, which rotates at a very high speed. Another man, in a galilean frame, measures the circumferences (P) of the two circles, and their diameters (d) with a ruler. This man then does the following calculus: P/d. He finds: P/d = p. For him, euclidean geometry is true. (True means here that it describes reality.)

The observer on the disk measures the circumferences and the diameters WITH THE SAME RULER. For the measurement of the diameters, the ruler is not contracted (from the point of view of the man in the galilean frame) in its length. (See special relativity for this.) Thus, the observer on the disks will find the same results as the man in the galilean frame.

Now, the observer measures the circumference of the small circle. For the man outside the disk, the rule is not contracted in its length because it goes very slowly (it's close to the center of the disk). Therefore, the observer finds again the same result.

However, things are going to be different for the fourth measurement. When the observer on the disk measures the circumference of the big circle, he goes very fast compared to the man outside the disk. Hence, from the point of view of this man, the rule is contracted in its length and the observer won't find the same result. For him: P/d does not equal p. Euclidean geometry doesn't describe reality in this case.
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Another error I suppose. Since it says the diameter doesn't change and the circumference does.

And the same error in that it fails to give any explanation as to how the affects of Relativity shortened the ruler without shortening the circumference.

Since, in my example, the circumference is made of the same material. Indeed the circumference was built using a series of short measuring rods or rulers. So if the circumference is made of rulers, the circumference and the measuring rod both shrink equally and hence there is no measurable change in Pi.

My complaint is, and has been, that this is a false illustration of Relativity and says nothing about my view of relavistic contraction.

As yet nobody has addressed the issue of seeing any (measureable) affect at all.

Do you (xxxx) actually not see that any affect by any geometry you impose means the ruler will always measure the same?
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I'm reposting this portion here because I truly would hope somebody out there has a direct answer. The correct answer actually has nothing to do with relativity or geometries as has been attempted to cram down my throat.

The issue is by what justification or physical process do you say Pi changes when any force, any geometry, any affect , by any theory must change not only the ruler but the rotating disk in equal fashion and hence I argue the changing Pi illustration is invalid.

The observer on the disk measures the circumferences and the diameters WITH THE SAME RULER. For the measurement of the diameters, the ruler is not contracted (from the point of view of the man in the galilean frame) in its length. (See special relativity for this.) Thus, the observer on the disks will find the same results as the man in the galilean frame.

How about explaining how one can measure both circumference and diameter "WITH THE SAME RULER" without TURNING the ruler? As several people have pointed out, the observer on the disk will, in fact, arrive at the fact that "circumference equals 2 pi r" since, from his point of view, he is not moving. The "man in the galilean frame" will arrive at the same radius as the man on the disk because that is measured perpendicular to the motion. He will measure the circumference as being smaller than 2 pi r because he is now measuring along the direction of motion. From his point of view, the man on the disk CANNOT "measure with the same ruler" because when he turns his ruler to measure the circumference of his disk, he turns it in the direction of the motion and so (from the point of view of the stationary man) it shrinks by exactly the same factor as the circumference.

By the way, no one is claiming "pi changes". pi is a number and not dependent on physics. What is true is that the circumference of a rotating disk is not equal to "2 pi r".

Finally, simply repeating over and over again "the fault is not mine" does not make it so.

HallsofIvy,

Finally sombebody speaks out. We are in 100% agreement here. "No change in Pi".

And Pi by definition is the ratio of the diameter of a circle vs its circumference, not the radius of a sphere vs some circle on the surface of a sphere. I made that very point in the other string.

I think you mis-stated the fact when you said nobody says Pi changes. Virtually all relavist do. It is one of their selling points explaining Relativity. The article in the link provided also says so.

This variable Pi is the crux of my complaint.

I did not however get your meaning to the following:

Finally, simply repeating over and over again "the fault is not mine" does not make it so.

Thanks.

Actually Mac, he is disagreeing with you. The arguement is with pi the number and pi the variable. Pi the number is 3.142..., and is just a mathematical entity. What you are talking about is Pi the variable i.e c/2r. Pi the variable changes, obviously Pi the number doesn't. Don't change tact and make it out as if you were talking about Pi the number either.

Hey, and Old man Mac

it is relativists, not relavists.

MacM:

<i>I think you mis-stated the fact when you said nobody says Pi changes. Virtually all relavist do.</i>

As I explained elsewhere, nobody says pi changes. What changes is the ratio of the measured circumference to the diameter. It changes from pi in Euclidean geometry to something else in non-Euclidean geometries.

James R.,

OK. We have been there on this issue. Please note my statement.

"Whatever component is contracted, circumference, radius and/or both, the invocation of any affect of relativity, geometry used, etc has to affect the rotating object in the same manner and magnitude as it will affect a ruler, hence no change in measurement, hence no change in the results of calculated pi."

Mac, can you see my arguement? If acceleration is not included, this is just a rectilinear motion problem

MacM:

Let's set out the situation carefully.

Imagine I place a whole bunch of rulers on the ground just outside the circumference of the merry-go-round (MGR). Let's suppose the MGR has radius 10 metres (measured when stationary). Then, the number of 1 metre rulers which fit around the circumference (on the ground) is 2 pi times 10 = approximately 63 rulers. Above the MGR, we rig up a stationary cross-bar, and lay out 1 metre rulers along it, so the rulers remain stationary when the MGR rotates beneath them. Exactly 10 rulers lie along this bar.

Now, our observer jumps onto the MGR, with some metre rulers. The MGR is set spinning. The observer notices that he can fit 10 rulers along the radius of the disk whilst it is spinning. Similarly, if he compares the lengths of each of his radial rulers to the ones on the bar above (as it goes past), the lengths are the same.

The observer on the disk now takes his meter ruler to the outer edge of the disk and lays it down on the (rotating) edge. As the rulers on the ground go past him (from his point of view), he compares the length of one of the ground rulers to the length of his disk ruler. He discovers that the ground rulers are shorter than his disk ruler due to the rotation.

He also counts the number of ground rulers there are, and discovers that there are 63 rulers on the ground - each of them less than 1 metre long.

So, the disk observer concludes that

circumference = 63 rulers times length of one ruler,

which is less than 63 metres. He also concludes that the radius of the disk is 10 metres.

Therefore, the observer on the disk concludes that the circumference length is less than 2 pi times the radius.

James r.,

We agree. But that hasn't been the problem. All presentation until yours has dealt with the claim by presentation of Relativity which state the moving observer and "his" ruler at the circumference is shortened and therefore Pi changes.

That has been my arguement. The ruler in motion measures no change in Pi because it and the rotating disk change by the same amount.

ryans,

Yes I see your argument for a change due to "gravity". I even think it may be thee but it is never referred to by any presentation I have ever read on Relativity. You are the first to have mentioned it.

It has been my view in fact that that must happen otherwise as Crisp stated you have a shrinking circumference upon a fixed diameter. You would soon have a broken m-g-r.

If both velocity and gravity affect the circumference and radius by the same amounts then everything works. No measurabel change in Pi and no broken m-g-r.

Originally posted by MacM
James r.,

We agree. But that hasn't been the problem. All presentation until yours has dealt with the claim by presentation of Relativity which state the moving observer and "his" ruler at the circumference is shortened and therefore Pi changes.

No. Other than me none had said circumference contracts. They all gave you the GR explanation. But you only insisted on C contracts knowingly or unknowingly. my question to you & logical (not necessarily the correct) answer too,as i had already said, was along your line.

Even now you have not realised that the moving observer doesn't observe directly that the circumference of the m-g-r alongwith the ruler really contracted. He measures that with the stationary rulers kept along the circumference. This is what SR talks about length contraction along the direction of relativistic motion. For the moving observer there is no direct evidence (his own ruler) that C & ruler contracted. hence for him there is no change in pi, if he depends on his ruler alone. He needs the stationary rulers to know that the C contracted.

That has been my arguement. The ruler in motion measures no change in Pi because it and the rotating disk change by the same amount.

Reduction in C is due to SR and your presumed change in radius is due to GR (curved space) and they don't follow the same rate of reduction to keep pi constant.

James explained in clear SR terms, if i understand properly, that :

(1) change in pi is due to the moving observer refers the stationary ruler to measure C.

(2) no change in pi if he depends on his ruler alone.

(i know, using the term 'change in pi' is wrong understanding of what is pi..!, just for ease of argument)

everneo,

Ah but Yes.

Re: Ah but No

quote:
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Originally posted by MacM
James r.,

We agree. But that hasn't been the problem. All presentation until yours has dealt with the claim by presentation of Relativity which state the moving observer and "his" ruler at the circumference is shortened and therefore Pi changes.
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No. Other than me none had said circumference contracts. They all gave you the GR explanation. But you only insisted on C contracts knowingly or unknowingly. my question to you & logical (not necessarily the correct) answer too,as i had already said, was along your line.

Even now you have not realised that the moving observer doesn't observe directly that the circumference of the m-g-r alongwith the ruler really contracted. He measures that with the stationary rulers kept along the circumference. This is what SR talks about length contraction along the direction of relativistic motion. For the moving observer there is no direct evidence (his own ruler) that C & ruler contracted. hence for him there is no change in pi, if he depends on his ruler alone. He needs the stationary rulers to know that the C contracted.


quote:
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That has been my arguement. The ruler in motion measures no change in Pi because it and the rotating disk change by the same amount.
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Reduction in C is due to SR and your presumed change in radius is due to GR (curved space) and they don't follow the same rate of reduction to keep pi constant.

James explained in clear SR terms, if i understand properly, that :

(1) change in pi is due to the moving observer refers the stationary ruler to measure C.

(2) no change in pi if he depends on his ruler alone.

(i know, using the term 'change in pi' is wrong understanding of what is pi..!, just for ease of argument)

ANS: NOW WE ARE IN COMPLETE AGREEMENT; except when you say I contested or didn't believe the circumference contracted.

Please read my post more carefully. I said at the outset that I accepted Lorentz Contraction but that the issue was that claiming the ruler shortened and hence pi measured differently was false. Pi to the moving observer does not change.

James R., is the first either from this forum or of all the reference link statements that refered to a change as viewed against a stationary ruler. To the contrary ryans, chroot and others have only said the problem was my understanding and "ignorance".

I bent over backwards to accomdate ryans assertion that the raidus changed due to acceleration but stated I had never seen anybody ever claim that but lthat if it did (and I thought it might) that it still would not produce a measurement change in pi by the moving observer.

So I seem to be in complete agreement with you and James R., on this issue.

The following is a reprint of one of many of my statements, followed by the kind of responses made wheich failed to address the issue or address it properly:

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Question: "Assuming some form of relavistic dimensional change either at the circumference or at the radius and/or both, what is your explanation for claiming Pi changes when measured by a ruler? That is to say any dimensional affect on the rotating object, regardless of geometry imposed, is going to also affect the ruler and no change can be measured and hence no change in Pi.?"



report | quote | edit | 05-13-03 at 09:21 PM


ryans
275 posts
Whatever Mac.

1/ Chroot and I gave you the reason, you chose to ignore it.

2/If the radius does not contract relative to the observer, he will calculate himself as going faster than c. Since this is not possible, the observer on the m-g-r MUST measure Pi to be smaller.

You cannot see the wood from the trees Mac.
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One final point:

Reduction in C is due to SR and your presumed change in radius is due to GR (curved space) and they don't follow the same rate of reduction to keep pi constant.


ANS: I agree with your point of differing rates but it still will not result in a different calculation for Pi. It does shift geometry but any affect at the circumference changes the ruler in like amounts.

A different amount of change at the radius by a different function will still change the ruler by the same amount and no measurement change can be determined hence no change in the calculated value of Pi for the moving observer.

The space is changing, the length of the ruler does not change with it. Take for example the expansion of the universe. Space time is expanding, but the objects in it aren't. If the objects in space expanded with the space, then we would not see the universe as expanding. But we do. The radius changes length, the ruler doesn't

ryans,

Give it up.

The radius changes length, the ruler doesn't

You lose and everything you say now is just stacking aginst you.

I'll ask once again. "By what justification do you say the radius changes but the ruler subjected to the same dynamics and geometery will not be changed.?"

As James R., everneo AND I (the ignorant old man) have already told you "There is no measurable change in Pi to the moving observer", which was my argument from the first entry into this subject.

So now, since you have choosen to wrongfully call me all sorts of names, I damn well dare you to say that to James R., or everneo.

The ratio of the circumference to the radius changes. Do you even listen to my arguments?

ryans,

The ratio of the circumference to the radius changes. Do you even listen to my arguments?

ANS: Oh, I listen but fortunately I have been wise enough to not accept what you have put out.

The ratio between the circumference and the diameter "DO NOT CHANGE" as measured by the moving observer and his ruler. that has been my arguement and it seems now that James R., and everneo have also agreed with that fact.

Now that you still want to insist otherwise let me once more "Teach" you some facts.

Regardless of the motion, regardless of the geometry invoked, regardless of any affect of motion or acceleration (gravity) by any theory of relativity, the ruler used by the observer on the rotating device will find no change in measurement because any such affect will also be applied to the ruler and rotating device in like and equal amounts.

There is no mearureable change, hence no change in Pi calculations.

Try to get it through your head. Nobody says there is no contraction. Only that the presentations being made are invalid.

The presentations, as you state above, that claim there is measurable difference between the ratio of the circumference and the diameter - That simply is not so. Whatever affects the disk, affects the ruler. NO CHANGE.

PS: By the way, James R. does discuss the radius and you assume to much again when you assume I not only don't know these things but couldn't understand them.

If I were you I would start to worry about your reputation here and stop this attack nonsense. You have stepped in quicksand and just haven't realized it yet.