time dilation???

jilfe · Aug 1, 2015

Here is a good one to think about, according to the theory of special relativity, time slows down, at high velocities.
Ok, using only theoretical apparatus such as a chain and sprocket drive, with a chain that has the miraculous ability to stretch infinitly to maintain a constant sprocket teeth to chain relationship, such that a motor connected to one sprocket is stationary on the earth, and on the other end of this miraculous chain is a identical sprocket connected to a shaft fixed onto the body of a rocket ship.
Also both sprockets have a light beam interuptor, that allows counting of revolutions, per minute to be displayed on board the ship and another one on the earth.
Now lets say the rocket is at a stand still, and the motor is turned on, and is now spinning at 60 rpm's, the light beam interuptor shows a tach reading of 60rpm's on both the ships tachometer, and the earthbound tachohmeter.
Now an inspection is made and seen that this miraculous lengthening chain, is keeping track with the sprocket drive, as would normally be in a mechanical system containing a sprocket chain drive.
according to the laws of physics, the driven sprocket is keeping track with the driving sprocket due to the chain links connection between them.
So far it all fits in to mechanical laws.
Now lets suppose the rocket takes off and is approaching the speed of light, this miraculous lengthening chain is stretching so as to keep all the links in synchronization with both sprockets.
Now the motor on the earth is turned on and is given to rotate for 3 minutes, so the motor is rotating its earthboun sprocket 60 rpms, for a total of 3 (earth minutes), the tachometer reads exactly 60 rpm's, and the interuptor shows 180 rotations on its display and immediately the hypothectical motor is able to shut down.
The earthbound display shows 180 revolutions in 3 earth minutes of time, how many revolutions would the display show on the rocket ship, in other words the earthbound sprocket revolved 180 times in 3 earth minutes, but what would be the total amount of revolutions the sprocket onboard the high speed rocket show???

RC1970 · Aug 1, 2015

You lost me at "Here is a good one..." :scratch:

Gracchus · Aug 1, 2015

I think the problem arises with the "miraculous chain".

sidney-harris-i-think-you-should-be-more-explicit-here-in-step-two-cartoon.jpg

pmb · Aug 2, 2015

jilfe said:
The earthbound display shows 180 revolutions in 3 earth minutes of time, how many revolutions would the display show on the rocket ship, in other words the earthbound sprocket revolved 180 times in 3 earth minutes, but what would be the total amount of revolutions the sprocket onboard the high speed rocket show??

There's a problem with your stretching chain idea. There are a set number of links in the chain and each link corresponds to a sprocket. I think this contributes to making the problem unrealistic and therefore without a solution. I'm not 100% certain though.

[serious] · Aug 2, 2015

These usually work better with a diagram.

lesliedellow · Aug 2, 2015

Many many years ago, when I was doing a course in Special Relativity, we were given a problem. I can't remember the details now, but I did the mathematics, and got the right answer, but it wasn't obvious what that answer physically implied. So I asked the lecturer whether relativity implied that there was no such thing as an infinitely rigid rod, and the answer was yes. One might have suspected that there was no such thing as an infinitely rigid rod anyway, but it isn't immediately obvious that Special Relativity implies it.

I would guess that Special Relativity might also imply that there is no such thing as an infinitely elastic chain.

[serious] · Aug 2, 2015

OK, no math, since we aren't dealing with numbers, but I sketched it out and here's what I get.

Ship moving such that clocks move half as fast.
Chain links near the ship are also lengthed relativistically due to moving away. Hence, the gear will be moving half speed and being fed with double length links. The gear would be oval as it would be lengthened too.

sfs · Aug 5, 2015

[serious] said:
OK, no math, since we aren't dealing with numbers, but I sketched it out and here's what I get.

Ship moving such that clocks move half as fast.
Chain links near the ship are also lengthed relativistically due to moving away. Hence, the gear will be moving half speed and being fed with double length links. The gear would be oval as it would be lengthened too.

Moving objects look shorter, not longer.

Loudmouth · Aug 5, 2015

lesliedellow said:
Many many years ago, when I was doing a course in Special Relativity, we were given a problem. I can't remember the details now, but I did the mathematics, and got the right answer, but it wasn't obvious what that answer physically implied. So I asked the lecturer whether relativity implied that there was no such thing as an infinitely rigid rod, and the answer was yes. One might have suspected that there was no such thing as an infinitely rigid rod anyway, but it isn't immediately obvious that Special Relativity implies it.

I would guess that Special Relativity might also imply that there is no such thing as an infinitely elastic chain.

The rigidity of a rod depends on the interactions between molecules, specifically the electromagnetic interactions. Since this force propogates at the speed of light it would limit the rate at which a pulse of force can move down the rod. This means that movement at one end of the rod will always be delayed at the other end of the rod.

lesliedellow · Aug 5, 2015

Loudmouth said:
The rigidity of a rod depends on the interactions between molecules, specifically the electromagnetic interactions. Since this force propogates at the speed of light it would limit the rate at which a pulse of force can move down the rod. This means that movement at one end of the rod will always be delayed at the other end of the rod.

The point is that disparate areas of physics, such as Special Relativity and electromagnetism, throw up relationships between different aspects of the physical world, when there is no obvious reason why they should be related. It is possible to find that mysterious.

Another example. The number pi crops up all over the place in physics, and yet there is no obvious reason why the ratio of the diameter to the circumference of a circle should be in any way related to the frequency of a radio wave. Sure you can do the mathematical derivation, but it still seems mysterious.

sfs · Aug 5, 2015

lesliedellow said:
The point is that disparate areas of physics, such as Special Relativity and electromagnetism, throw up relationships between different aspects of the physical world, when there is no obvious reason why they should be related. It is possible to find that mysterious.

Except that in the case of Special Relativity, the theory was largely motivated by the equations of electromagnetism.

lesliedellow · Aug 5, 2015

sfs said:
Except that in the case of Special Relativity, the theory was largely motivated by the equations of electromagnetism.

It is motivated by the fact that Maxwell's equations seem to imply that the speed of light - sqrt(1/ε0μ0) - is relative to nothing, because those other two constants are relative to nothing.

ddubois · Aug 6, 2015

jilfe said:
Here is a good one to think about, according to the theory of special relativity, time slows down, at high velocities.
Ok, using only theoretical apparatus such as a chain and sprocket drive, with a chain that has the miraculous ability to stretch infinitly to maintain a constant sprocket teeth to chain relationship, such that a motor connected to one sprocket is stationary on the earth, and on the other end of this miraculous chain is a identical sprocket connected to a shaft fixed onto the body of a rocket ship.
Also both sprockets have a light beam interuptor, that allows counting of revolutions, per minute to be displayed on board the ship and another one on the earth.
Now lets say the rocket is at a stand still, and the motor is turned on, and is now spinning at 60 rpm's, the light beam interuptor shows a tach reading of 60rpm's on both the ships tachometer, and the earthbound tachohmeter.
Now an inspection is made and seen that this miraculous lengthening chain, is keeping track with the sprocket drive, as would normally be in a mechanical system containing a sprocket chain drive.
according to the laws of physics, the driven sprocket is keeping track with the driving sprocket due to the chain links connection between them.
So far it all fits in to mechanical laws.
Now lets suppose the rocket takes off and is approaching the speed of light, this miraculous lengthening chain is stretching so as to keep all the links in synchronization with both sprockets.
Now the motor on the earth is turned on and is given to rotate for 3 minutes, so the motor is rotating its earthboun sprocket 60 rpms, for a total of 3 (earth minutes), the tachometer reads exactly 60 rpm's, and the interuptor shows 180 rotations on its display and immediately the hypothectical motor is able to shut down.
The earthbound display shows 180 revolutions in 3 earth minutes of time, how many revolutions would the display show on the rocket ship, in other words the earthbound sprocket revolved 180 times in 3 earth minutes, but what would be the total amount of revolutions the sprocket onboard the high speed rocket show???

I think I read some time ago that as time slows down for the rocket ship, mass increases, and most importantly for your question, length shortens. So the end of your miraculous sprocket would probably shorten to the same extent that time was dilated. It seems weird, but that is what I remember.

lesliedellow · Aug 6, 2015

ddubois said:
I think I read some time ago that as time slows down for the rocket ship, mass increases, and most importantly for your question, length shortens. So the end of your miraculous sprocket would probably shorten to the same extent that time was dilated. It seems weird, but that is what I remember.

The foreshortening of a body in the direction of travel is called the Fitzgerald Contraction.

Gracchus · Aug 7, 2015

lesliedellow said:
The point is that disparate areas of physics, such as Special Relativity and electromagnetism, throw up relationships between different aspects of the physical world, when there is no obvious reason why they should be related. It is possible to find that mysterious.

The universe is one thing. It would be strange if it didn't all relate.

Another example. The number pi crops up all over the place in physics, and yet there is no obvious reason why the ratio of the diameter to the circumference of a circle should be in any way related to the frequency of a radio wave. Sure you can do the mathematical derivation, but it still seems mysterious.

Pi is not just the relation of the diameter to the circumference of the circle. It turns up in all periodic functions such as electromagnetic waves, and in the inverse-square law of gravity. And by Euler's Formula (e^(ix)=cos(x)+iXsin(x))it can be found as a factor in asymptotic limits. Since Pi is absolute, it determines the possible ratios between physical constants, hence the "fine tuning" of the universe. You can't get around the math.

:wave:

Chriliman · Aug 7, 2015

lesliedellow said:
Many many years ago, when I was doing a course in Special Relativity, we were given a problem. I can't remember the details now, but I did the mathematics, and got the right answer, but it wasn't obvious what that answer physically implied. So I asked the lecturer whether relativity implied that there was no such thing as an infinitely rigid rod, and the answer was yes. One might have suspected that there was no such thing as an infinitely rigid rod anyway, but it isn't immediately obvious that Special Relativity implies it.

I would guess that Special Relativity might also imply that there is no such thing as an infinitely elastic chain.

Correct, there's also no such thing as an infinitely dense singularity.

sfs · Aug 7, 2015

lesliedellow said:
It is motivated by the fact that Maxwell's equations seem to imply that the speed of light - sqrt(1/ε0μ0) - is relative to nothing, because those other two constants are relative to nothing.

Right. Put more formally, Maxwell's equations are Lorentz-invariant. So the equations imply Special Relativity, which isn't really surprising, since the speed of light (an EM phenomenon) is central to SR. So I don't see anything surprising about SR being involved with EM.

lesliedellow · Aug 9, 2015

Chriliman said:
Correct, there's also no such thing as an infinitely dense singularity.

A singularity is a notion which physicists pinched from the mathematicians. Therefore a singularity is a product of the mathematics; it is not a physical something. It implies that the mathematical model of a physical system is not 100% perfect, although it is extremely good for most purposes.

Chriliman · Aug 9, 2015

lesliedellow said:
A singularity is a notion which physicists pinched from the mathematicians. Therefore a singularity is a product of the mathematics; it is not a physical something. It implies that the mathematical model of a physical system is not 100% perfect, although it is extremely good for most purposes.

Exactly, this idea of a singularity is unprovable, similar to how God is unprovable. So essentially physicists are saying our universe came from an unprovable singularity and somehow they think they can get away with this claim simply because the mathematics point to it, but can't prove it. Just an interesting observation I've had when thinking about what physics is actually claiming about the origins of the universe.

FrumiousBandersnatch · Aug 9, 2015

Chriliman said:
..So essentially physicists are saying our universe came from an unprovable singularity and somehow they think they can get away with this claim simply because the mathematics point to it, but can't prove it.

Well not really, no. If you extrapolate the physics back far enough, you reach a hypothetical singularity. You can't do physics with a singularity, so you start at the earliest point you can, and go from there. As far as I'm aware, most physicists who work in early universe cosmology don't think there really was a singularity - mainly because it's an invalid physical solution - and while most will say they just don't know what happened, there is a range of different ideas about what might have happened. See 'Did the Universe Begin with a Singularity?'

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