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Thomas comments on What are your contrarian views? - Less Wrong
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I have two photos of two different pies, one of rotating one and one of not rotating. Photos are indistinguishable, I can't tell which is which.
On the other hand, both pies have one-to-one correspondence with photos an one should be slightly deformed on the edge.
Even if it is, on the photo can't be. The photo is perfectly Euclidean. I have measured no Lorentz contraction.
Just to clarify, is the spinning pie a set of particles in the same relative position as with a still pie, but rotating around the origin? Is it a set of masses connected by springs that has reached equilibrium (none of the springs are stretching or compressing) and the whole system is spinning? Is the pie a solid body?
What exactly we're looking at depends on which of the first two you picked. If you picked the third, it is contradictory with special relativity, but there's a lot more evidence for special relativity than there is for the existence of a solid body. Granted, a sufficiently rigid body will still be inconsistent with special relativity, but all that means is that there's a maximum possible rigidity. Large objects are held together by photons, so we wouldn't expect sound to travel through them faster than light.
The spinning set of particles is a toroidal with let say 1 million light years across - the big R. and with the small r of just 1 centimetre. It is painted red and white, differently each metre.
The whole composition starts to slowly rotate on the signal from the centre. And slowly, very slowly accelerate to reach the speed of 0.1 c in a several million years.
Now, do we see any Lorentzian contraction due to the SR, or not due to the GR?
(Small rockets powered by radioactive decay are more than enough to compensate for the acceleration and for the centrifugal force. Both incredibly small. This is the reason why we have choose such a big scale.)
I'm going to assume mass is small enough not to take GR into effect.
From the point of view of a particle on the toroid, the band it's in will extend to about 1.005 meters long. Due to Lorentz contraction, from the point of reference of someone in the center, it will appear one meter long.
The question is ONLY for the central observer. At first he sees 1 m long stripes, but when the whole thing reaches the speed of 0.1 c, how long is each stripe?
One meter.
I just want to clarify. I'm assuming the particles are not connected, or are elastic enough that stretching them by a factor of 1.005 isn't a huge deal. If you tried that with solid glass, it would probably shatter.
Come to think of it, this looks like a more complicated form of Bell's spaceship paradox.
I think you're right, but you're interpreting “sees” literally I'm not 100% sure of that, because of light aberration (the Terrell-Penrose effect).
I wasn't interpreting "sees" literally, but it wouldn't make much of a difference. Since the observer is in the center of the circle, the light lag is the same everywhere. The only difference is that the circles bordering the bands will look slightly slanted, and the colors will be slightly blue-shifted.
In other news, the earth is really flat because photographs of the earth are flat.
Place red and white equilength rulers on the edge of the cylinder. The rotating cylinder will have more and shorther rulers. Thus the photos are not the same. Even better have the cylinder slowly pulse in different colors. The edges will pulse more slowly thus not being in synch with the center.
Related phenomenon is that moving ladders fit into garages that stationary ones would not.
They will multiply as the orbital speed increases? Say that Arab numerals are written on the rulers. Say that they are 77 at the beginning. Will this system know when to engage the number 78?
Or will there be two 57 at first? Or how is it going to be?
I was thinking of already spun cylinder and then adding the sticks by accelerating them to place.
If you had the same sticks already in place the stick would feel a stretch. If they resist this stretch they will pull apart so there will be bigger gaps between them. For separate measuring sticks they have no tensile strenght in the gaps between them. However if you had a measuring rope with continous tensile strenght and at a beginning / end point where the start would be fixed but new rope could freely be pulled from the end point you would see the numbers increase (much like waist measurements when getting fatter). However the purpoted cylinder has maximum tensile strenght anywhere continously. Thus that strenght would actually work against the rotating force making it resist rotation. a non-rigid body will rupture and start to look like a star.
So no there would not be duplicate sticks but yes the rope would know to engage number 78.
If you would fill up a rotating cylinder with sticks and spin it down the stick would press against each other crushing to a smaller lenght. A measuring rope with a small pull to accept loose rope would reel in. A non-rigid body slowing down would spit-out material in bursts that might come resemble volcanoes.
Saying that a moving ladder "fits" means that the start of the ladder is in the garage at the same time that the end of the ladder is. If the ladder is moving and contracted because of relativity, these two events are not simultaneous in all reference frames. Thus, you cannot definitely say that the moving ladder fits--whether it fits depends on your reference frame. (In another reference frame you would see the ladder longer than the garage, but you would also see the start of the ladder pass out of the garage before the end of the ladder passes into it.)
Why have that definition of "fit"? I could eqaully well say that fitting means that there is a reference frame that has a time where the ladder is completely inside.
If you had the carage loop back so that the end would be glued to the start you could still spin the ladder inside it. From the point of the ladder it would appear to need to pass the garage multiple times to oene fit ladder lenght but from the outside it would appear as if the ladder fits within one loop completely. With either perspective the one garage space enough to contain the ladder without collisions. In this way it most definetly fits. Usually garages are thought to be space-limited but not time limited. Thus the eating of the time-dimension is a perfectly valid way of staying within the spatial limits.
edit: actually there is a godo reazson to priviledge the rest frame oft he garage as the one that count as ragardst to fitting as then all of the fitting happens within its space and time.
In that case, the ladder fits.
Each rung of the ladder has a distinct reference frame. "From the point of the ladder" is meaningless.
If the ladder point of view is ildefined so is the garage point of view as the front and back of the garage have distinct reference frames. Any inertial reference frame is equally good. The ladder is not accelerating thus inertial. In the sense that we can talk of any frame as more than a single event or world line the ladder frame is perfectly good.
In the normal example, where the ladder is straight and moving forward, it has only one reference frame. Strictly speaking, each rung has a different reference frame, but they differ only by translation.
From what I understand, you modified it to a circular ladder spinning in a circular garage. In this case, each rung is moving in a different direction, and therefore at a different velocity. Thus, each rung has its own reference frame.
ah, I meant to glue the end and start together without curved shape/motion. But I guess that is physically unrealisable and potentially more distracting than explanatory.
Actually that's not a big deal. Technically you need general relativity to do that, but it's just a quotient space on special relativity. In any case, it works out exactly the same as an infinite series of ladders and garages.
There is one thing you have to be careful about. From the rest frame, the universe could be described as repeating itself every, say, ten feet. But from the point of view of the ladder, it's repeating itself every five feet and 8.8 nanoseconds. That is, if you move five feet, you'll be in the same place, but your clock will be off by 8.8 nanoseconds.
Actually from the point of view of the ladder the universe still repeats at every ten feet. It is just that from it's point of view it takes the space of two carages at any one instant.Both the garage and ladder are in a state of rest and show equally good times. Yes they read different but doesn't mean they are in error.
I am not sure whether it would see other instances of itself. I only spesified a spatial gluing and not that the garage be split into timeslices. I guess that the change of the point of view has changed some of that gluing to be from future to past. For if the ladder would be too long the frontend would not crash to the same ladder time backend but to a future one. (ignoring the problem of how you would try to slide the ladder into too small a hole in the first place)
If the rotating pie is a pie that when nonrotating had the same radius as the other one, when it rotates it has a slightly larger radius (and circumference) because of centrifugal forces. This effect completely dominates over any relativistic one.
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?
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.
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?