= 27d567bc2d48d9f40e9ccc20ea370b15)
Thomas comments on What are your contrarian views? - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (806)
The centrifugal force can be arbitrary small. Say that we have only the outer rim of the pie, but as large as a galaxy. The centrifugal force at the half of speed of light is just negligible. Far less than all the everyday centrifugal forces we deal with.
Now say, that the rim has a zero around velocity at first and we are watching it from the centrer. Gradually, say in a million years time, it accelerates to a relativistic speed. The forces associated are a millionth of Newton per kilogram of mass. No big deal.
The problem is only this - where's the Lorentz contraction?
As long as we have only one spaceship orbiting the Galaxy, we can imagine this Lorentzian shrinking. In the case of that many, that they are all around, we can't.
If you have a large number of spaceships, each will notice the spaceship in front of it getting closer, and the circle of spaceships forming into an ellipse.
At least, that's assuming the spaceships have some kind of tachyon sensor to see where all the other ships are from the point of reference of the ship looking, or something like that. If they're using light to tell where all of the other ships are, then there's a few optical effects that will appear.
The question is what the stationary observer from the centre sees? When the galactic carousel goes around him. With the speed even quite moderate, for the observer has precise instruments to measure the Lorentzian contraction, if there is any.
At first, there is none, because the carousel isn't moving. But slowly, in many million years when it accelerate to say 0.1 c, what does the central observes sees? Contraction or no contraction?
He will see each spaceship contract. The distance between the centers of the spaceships will remain the same.
But no, those ships are just like those French TGV's. A whole composition of cars and you can't say where one ends and another begins.
It's like a snake, eating its tail!
Then they stretch. Or break.
Or they stay the same but the radius of the train as measured by the observer in the centre will shrink.
They mustn't. All should be smooth just like those Einstein's train. No resulting breaking force is postulated.
But everything boils down to the "a microscope which enlarges the angles"
How do you then see two perpendicular intersecting lines under that microscope?
Can't be.
This Lorentz contraction has the same fundamental problem. How it would look like?
The force is due to chemical bonds. They pull particles back together as their distance increases. These chemical bonds are an example of electromagnetism, which is governed by Maxwell's laws, which are conserved by Lorentz transformation.
Granted, whether a field is electric or magnetic depends on your point of reference. A still electron only produces an electric field, but a moving one produces a magnetic field as well. But if you perform the appropriate transformations, you will find that looking at a system that obeys Maxwell's laws from a different point of reference will result in a system that obeys Maxwell's laws.
In fact, Lorentz contraction was conjectured based on Maxwell's laws before there was any experimental evidence of it. Both of those occurred before Einstein formulated special relativity.
Lorentz transformation does not preserve angles Euclidean distance or angles. It preserves something called proper distance.
This is what Lorentz transformation on 1+1-dimensional spacetime looks like: https://en.wikipedia.org/wiki/Lorentz_transformation#mediaviewer/File:Lorentz_transform_of_world_line.gif. There's one dimension of space, and one of time. Each dot on the image represents an event, with a position and a time. Their movement corresponds to the changing point of reference of the observer. The slope of the diagonal lines is the speed of light, which is preserved under Lorentz transformation.
Here's my question for you: with all of the effort put into researching special relativity, if Lorentz transformation did not preserve the laws of physics, don't you think someone would have noticed?
Then how are you accelerating them up to c/2?
With a tiny force of 1 micro Newton per kilogram of mass over several million years.
This was the acceleration force.
The centrifugal force is much less.
This is the force that will serve as the breaking force.
Each piece of the ring is longer as measured by an inertial observer comoving with it than as measured by a stationary one (i.e. one comoving with the centre of the ring). But note that there's no inertial observer that's comoving with all pieces of the ring at the same time, and if you add the length of each piece as measured by an observer comoving with it what you're measuring is not a closed curve, it's a helix in spacetime. (I will draw a diagram when I have time if I remember to.)
The inertial observer in the centre of the carousel measures those torus segments when they are stationary.
Then, after a million years of a small acceleration of the torus and NOT the central observer, the observer should see segments contracted.
Right?
During the million years of small acceleration, the torus will have to stretch (i.e. each atom's distance from its neighbours, as measured in its own instantaneous inertial frame will increase) and/or break.
Specifying that you do it very slowly doesn't change anything -- suppose you and I are holding the two ends of a rope on the Arctic Circle, and we go south to the Equator each along a meridian; in order for us to do that, the rope will have to stretch or break even if we walk one millimetre per century.
I don't see any reason this very big torus should break.
Forces are really tiny, for R is 10^21 m and velocity is about 10^8 m/s. That gives you 10^-5 N per kg of centrifugal force. Which can be counterbalanced by a small (radioactive) rocket or something on every meter.
Almost any other relativistic device from literature would easily break long before this one.
If breaking was a problem.
It's not the centrifugal force that's the problem. It's the force you are using to get the ring to start rotating.
Both forces are of the same magnitude! That's why we are waiting 10000000 years to get to a substantial speed.
If one is so afraid that forces even of that magnitude will somehow destroy the thing, one must dismiss all other experiments as well.
Ehrenfest was right, back in 1908. AFAIK he remained unconvinced by Einstein and others. It's a real paradox. Maybe I like it that much, because I came to the same conclusion long ago, without even knowing for Ehrenfest.
The question of the OP was about contrarian views. I gave 10 (even though I have about 100 of them). The 10th was about Relativity and I don't really expect someone would convert here. But it's possible.
Yes, and over 10000000 the forces can build up. Consider army's example of the stretching rope. Suppose I applied force to one end of a rope sufficient that over the course of 10000000 years it would double in length. You agree that the rope will either break or the bonds in the rope will prevent the rope from stretching?
The same thing happens with the rotation. As you rotate the object faster the bonds between the atoms are stretched by space dilation. This produces a restoring force which opposes the rotation. Either forces accelerating the rotation are sufficient to overcome this, which causes the bonds to break, or they aren't in which case the object's rotation speed will stop increasing.
(or stretch)
In the case of the ring there's another possibility.
Irrelevant. How many tiny forces are inside a street car? They don't just "build up".
Nonsense.
No one's saying that forces "just build up" by virtue of applying for a long time. Azathoth123 is saying that in this particular case, when these particular forces act for a long time they produce a gradually accumulating change (the rotation of the ring) and that as that change increases, so do its consequences.
Can you see why the rope in my example would break or stretch, even if we're moving it very very slowly?
Your example isn't relevant for this discussion.
Why not?
Look!
Not every relativistic projectile will be broken. And every projectile is relativistic, more or less.
Trying to escape from the Ehrenfest's paradox with saying - this starship breaks anyway - has a long tradition. Max Born invented that "exit".
Even if one advocates the breaking down of any torus which is moving/rotating relative to a stationary observer, he must explain why it breaks. And to explain the asymmetry created with this breakdown. Which internal/external forces caused it?
Resolving MM paradox with the Relativity created another trouble. Back to the drawing board!
Pretending that all is well is a regrettable attitude.
Why wouldn't that also apply to my rope example?