boit
A cylinder is rotating in its own axis at relativistic speed. A point on its circumference is moving at say 0.8666c will the cylinder's diameter (as well as its circumference obviously) shrink in half? We are assuming centrifugal forces are somehow eliminated.
Sithdarth
Rotating in special relativity is difficult. Mostly because rotation is an acceleration. A rigid disk in special relativity.

To summarize a bit the circumference is subject to Lorentz contraction but the diameter isn't resulting in, lets say interesting, things happening.
boit
Thanks Sithdarth. I usually post a question then remembers to consult google later (any psychologist major to analyse me?). My search term was: ''cylinder rotating at relativistic speed shrink in diameter, circumference.'' It turns out there is no new question under the sun. I found out this paradox is called Ehrenfest paradox. I then followed a thread in physforum and some guy there was equally perplexed. I find it difficult to figure. There was once an inconclusive argument in this forum about the importance of acceleration vis a vis time dilation. Some said it was a must for it to occur. Others were of a different opinion. Anyway I see you point about acceleration. In rotation it is always there but a point gets to a speed, stops then turns back. It seems there is wanning and waxing of dilation, contraction and if we average things settle where they were (i.e. same diameter and circumference). I this an over-simplification? Anyway let me read more.
boit
Ach! The more I read the more I discover how little I know or thought I knew. I used to think a space traveller travelling at relativistic speed will see us guys back on earth living as if we're in a fast moving motion picture. We on the other hand will see the travellers acting in a slow motion fashion. An article am reading seems to suggest both of us will see the other slowing up! Ai?!
NymphaeaAlba
QUOTE (boit+Jul 15 2011, 10:06 PM)
I then followed a thread in physforum and some guy there was equally perplexed. I find it difficult to figure. There was once an inconclusive argument in this forum about the importance of acceleration vis a vis time dilation. Some said it was a must for it to occur. Others were of a different opinion.

Cool! Will you provide the link to the thread that's in here?

Thanks, Boit!
boit
Now I get it, almost. http://galileoandeinstein.physics.virginia...s/time_dil.html
Confused1
As far as I can make out:- length contraction and time dilation only make sense as a property of spacetime.*
-C2.

*Edit.
boit
QUOTE (NymphaeaAlba+Jul 16 2011, 10:35 PM)
Cool! Will you provide the link to the thread that's in here?

Thanks, Boit!

First a correction. The perplexed guy was in physicsforum. I guess you noticed my mistake. As for the link from this forum this is the closest I got http://www.physforum.com/index.php?showtopic=5080
What am searching for exactly was posted between '09 and '10. On the other hand if photons trully experience time dilation then acceleratio isn't necessary for time dilation to occur. Why do I boldly say that? Cause it was pointed to me that light (and all things without mass) don't accelerate.
synthsin75
The only thing necessary to time dilation is either a relative velocity or different gravity potentials. No acceleration required.
boit
QUOTE (synthsin75+Jul 19 2011, 06:29 AM)
The only thing necessary to time dilation is either a relative velocity or different gravity potentials. No acceleration required.

I totaly agree with you there though I will be hard put to argue with someone who says the only way to solve the twin paradox (as in which twin ages more) is by introducing the element of acceleration. The space bound twin had to fire his engines hence accelerated. I have been convinced more than once by their argument. Let me read more to get more ammunition to counter that argument.
synthsin75
QUOTE (boit+Jul 19 2011, 12:46 AM)
I totaly agree with you there though I will be hard put to argue with someone who says the only way to solve the twin paradox (as in which twin ages more) is by introducing the element of acceleration. The space bound twin had to fire his engines hence accelerated. I have been convinced more than once by their argument. Let me read more to get more ammunition to counter that argument.

That's simply a matter of how the two reach their relative velocity, and determining which actually changed their time rate relative to the other. Thus which one was actually in the slower time frame.
Sithdarth
To explain it more clearly. By the rules of relativity it is equally valid to say either one was in the slower frame while traveling inertially. The twin that goes out while moving at a constant velocity sees his twin slow just as much as the twin that stayed home. The difference is that the acceleration acts like a gravitational potential and introduces a time dilation that happens in addition to the time dilation due to the relative velocity. Special relativity tells us that during the inertial phases of the trip neither frame is the slower frame. The difference between the twins is that the one in the ship when the ship turns around experiences a gravitational potential and sees his stay at home twin as at a much higher potential. Thereby the twin in the ship sees the stay at home twin moving much faster during the turn around.
Montec
Hello bolt
From the perspective (frame) of an observer located on the rim of a cylinder, as the angular velocity increases the circumference shrinks. This happens because the time-rate relative to the center of rotation is decreasing and the time the observer measures for a complete revolution gets smaller. IE it takes less time to measure a period so the circumference is smaller.

From an observer not in the rotating frame there is no change in the circumference.

As a side note there is a time-gradient set up between the center of rotation and the rotating/moving frame on the cylinder's circumference. So there is a "pseudo force" generated on any rotating mass interacting with the time-gradient set up by the rotation.

Sithdarth
QUOTE
From the perspective (frame) of an observer located on the rim of a cylinder, as the angular velocity increases the circumference shrinks. This happens because the time-rate relative to the center of rotation is decreasing and the time the observer measures for a complete revolution gets smaller. IE it takes less time to measure a period so the circumference is smaller.

From an observer not in the rotating frame there is no change in the circumference.

It's a tad more complicated than that as the link I posted at the beginning of the thread shows.
boit
I have re-read Sith's original link and Montec's summary and I think I get the gist of it. Both the observer at the centre (who by the way is always perpendicular to the traveler) and the disk rider will agree on the diameter of the circle but disagree on the circumference.
What will the traveller conclude? That he is in a non-Euclidean surface? Rieman's perharps? Like the surface 'radius' from the poles is 10,000 but circumference is only 40,000 drawing the conclusion that this is a curved surface? On a side note this guy will know he is the one undergoing time dilation. If turning back was the crucial thing in frame shifting this guy is always turning round. . . Wow!
Confused1
A clock on the circumference will have to decide whether it is going to:-
a/ run slow relative to a clock at the centre because it's moving round the central point
b/ stay the same because the distance from the centre is constant.
c/ something else.

-C2.

boit
Since things perpendicular to direction of motion do not undergo Lorentz's contraction and time dilation, I imagine a long tunnel several light years long that is once every minute. We mark the inside with longitudinal black and white stripes numbered 1 to 60. Now our space craft shoots in at 86.6r% c. If this traveler could see us guys back home he'll say our clock slows because we're directly behind him. But if looks to his side (90 degrees) he sees the tunnell still turning at the same radians as at rest. Since his onboard clock will be at variance with the tunnel's he will know he's undergoing time dilation. Or he may wrongly conclude that the tunnel is turning twice as fast.
Another questions, how much do object 30 and 60 degrees to the traveller behave? Do clocks at those angles slow to between half and one the rate of the traveler's?
AlexG
While length contraction occurs along the axis of motion, time dilation occurs regardless of orientation.
boit
QUOTE (AlexG+Jul 23 2011, 07:43 PM)
While length contraction occurs along the axis of motion, time dilation occurs regardless of orientation.

I know the onboard clock will undergo time dilation. What I want to know is if a spot on the inner surface of the lenghthy tunnel will continue to appear once every minute to the traveller as it does to us guys on earth.
In the second question I should have said that those clocks at 60 and 30 degrees were not on board but on earth's frame (let's place them at infinity for ease). I am tempted to think since they are on earth's frame they will behave the same. The traveller will conclude that these clocks are twice as fast as his. Am I on the right track? I tried the relativity FAQs but didn't get a clearly asked question fit to answer this.
boit
. . . I imagine a long tunnel several light years long that is ROTATED once every minute. . .
Oops! I just realized in my post preceding the one above I failed to write the word rotated. I hope it now makes sense.
boit
Aha. I see what puzzles me is being tackled in another thread. 'Twin paradox and Aluminium ion clock.' I'll read along.
boit
QUOTE (boit+Jul 29 2011, 07:35 PM)
Aha. I see what puzzles me is being tackled in another thread. 'Twin paradox and Aluminium ion clock.' I'll read along.

This thread made me search the net for a nice explanation fit for dummies and guess what? I finaly get what you guys have been trying to put across. I now understand simultenious and synchronizing talk. In my hypothetical tunnel, the end of the tunnel will be observed to have twisted earlier than the mouth. Instead of seeing longitudinal lines in the inside surface of the tunnel the traveler (let's call him Prime) will see a helix. Unprime (that's the home twin sees the tunnel as normal and if Prime had a smaller cylinder rotating inside the ship (faithful to the tunnel) he will see it as turning slower. Isn't that right?
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