Thread: Special case: a rotating body with velocity near C . Any clues as how to solve ?

Originally Posted by Pyraxus

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By any chance, do you know of any links you could share concerning this particular topic? ...

This is a good place to start. You may start here if you prefer.

And here's a chart showing the relationship between them.

Originally Posted by Jeffrey DreamKing

I thought lorentz contraction/transformation only dealt with the appearance of a speeding object to an outside observer, and not an actual physical change in the structure of the speeding object. I really don't think there would be an actual physical change.

This would be the case if an object were moving in a straight line, not accelerating. In a spaceship that is (to us) moving at 0.999 times the speed of light, the ship (as seen by its occupants) would not change shape, stretch or shrink, or anything strange like that.

But in a rotating object, every part of the object (except those on the axis) are constantly accelerating, they do not stay in the same inertial reference frame. So it is an entirely different situation.

Regarding the non-existence of spacetime, I'm not sure if you are challenging the predictions of special relativity, or simply saying that you don't like the space-time way of describing them (which is not the only way, but as I understand it, it's the most convenient way when moving on to general relativity). So I don't think I can provide any answers to the later questions without clarification on this point.

Originally Posted by Jeffrey DreamKing

... now consider an electron traveling at the speed limit of light around an atom...

The speed of an electron in a hydrogen atom is 1/137 of c. It will not be anywhere near c in any vaguely stable sized nucleus.

Originally Posted by MisterMe

This problem is a lot more complex that you have any idea. Objects spinning fast enough for certain points to become relativistic can no longer be treated as rigid bodies.

They could, but you're in for a lot of mathematical fun for sure. On the other hand, you're also in for some interesting stuff about non-euclidean geometries in SR.

Originally Posted by Coelacanth

This would be the case if an object were moving in a straight line, not accelerating. In a spaceship that is (to us) moving at 0.999 times the speed of light, the ship (as seen by its occupants) would not change shape, stretch or shrink, or anything strange like that.

But in a rotating object, every part of the object (except those on the axis) are constantly accelerating, they do not stay in the same inertial reference frame. So it is an entirely different situation.

In a rotating object, the velocity would remain the same. It is accelerating, but in another direction. It is not accelerating in the same direction, so it is not gaining velocity in the previous velocity's direction. This acceleration is not like the acceleration that occurs as an object follows a straight line. A change in velocity is equated as being caused by acceleration, and changes in velocity with lorentz transformation, but I don't think acceleration should equate to lorentz transformation, if the acceleration causes no absolute velocity increase or decrease, as with centripetal acceleration, there should also be no transformation, just like when it traveled a straight line.

I still don't see how propulsion and acceleration forward would stretch a spaceship. If anything, I would think that there would be compression back towards the rockets, like during takeoff when the astronauts are pressed into thier seats. So, if something undergoes acceleration, then it undergoes a physical change ? I would think that's a hard thing to prove, because you'd have a hard time measuring something that is accelerating a lot or moving for that matter from the speeding objects frame. That's like trying to measure an airplane propellor. Maybe this applies to a slinky, but eventually the slinky recoils. I still think that the Lorentz transformation is only a visual or optical effect. If you take a photograph of something in 1 second exposures, the object will appear longer in the photograph as it moves faster. The object occupies more space in one second as it speeds up. This is a measure of the distance covered by the object during a change in time. This is observed, but the actual object should not change in it's physical makeup during an instant in time. Instant meaning that there is no change in time. Zero.

Originally Posted by Coelacanth

Regarding the non-existence of spacetime, I'm not sure if you are challenging the predictions of special relativity, or simply saying that you don't like the space-time way of describing them (which is not the only way, but as I understand it, it's the most convenient way when moving on to general relativity). So I don't think I can provide any answers to the later questions without clarification on this point.

To answer that, I would have to remember what the predictions of special relativity are.
My problem with spacetime is... that I've been told that spacetime is acting upon matter and that spacetime has replaced gravity and that gravity is being explained as being caused by spacetime's affect on matter. I'm saying, that only matter acts upon other matter, space does not act upon matter, and matter does not act upon space. Ideal space is nothing. It cannot act upon anything. Time is a measurement of speed and the study of time is a comparison of these speeds. If you could move all objects back to their previous positions, it is just that, and not time travel. If If everything in the universe was motionless, there would be no way to measure speed or time, and there would also be no perception of time since our brains would be 'frozen' and no thinking action could occur. It may be easier to think of the units of time in reverse, the day is how long it takes for the earth to make a revolution, the hour is how long it takes for the hour-hand to move a certain distance, and the second is also a measure of the speed and distance of the second-hand of the clock, which we then use to compare to other moving things. There is no time, only the now with things moving. By observing the things in motion now, we can predict what the now will be or what it was, but there is only the now. The future and past are a part of human perception.
By extension, I think space-time is a cure-all solution and a snake oil that people have been sold on. Einstein used the twin star images around massive bodies to support the existence of spacetime but it is due to the gravitational lensing of light and not due to the warping of space-time. I believe in meters / per seconds but not space-time. Space-time is a repackaged version of the Luminiferous Aether. http://en.wikipedia.org/wiki/Ether_(..._and_astronomy)

For objects that move side to side, the lorentz transformation simply traces the outline of the trajectory that a vibrating object will take. For a object that does not move side to side, the lorentz transformation should not apply. Except, nothing is exempt from this because all atoms have moving parts or waveforms or whatever.
What I've initially have been trying to figure out from this post, is what kind of transformation will occur for an object that is not just vibrating side to side, but also moving forward and backward at the same time. I think of this as two waves, one going forward to back, and one going side to side, that constructively interfere to form an elliptical trajectory. Kind of like how light has an x and y component, and travels in the z direction. Or am I wrong, and light does not spiral like this? Polarization (waves) - Wikipedia, the free encyclopedia
Can I treat the electron in the same manner ? I thought it would help simplify the solving of the initial problem I presented. I should also explain, that there is no acceleration forward in the z direction, only constant velocity. At the speed of light, the electron would not be able to move at all, since it is already traveling at c beside the atom. As the atom begins to travel less than c, the electron with be able to move again at whatever the difference is. Spinning CCW around the atom, with the atom traveling in the z direction toward 3 o'clock, the electron shall move at the 6 o'clock position with 'C minus the atomic velocity' and at the 12 o'clock position the electron shall move at C. So, do you see the problem now, the electron would be alternating speeds, in order to adhere to the rule that nothing can go faster than light. Now if the electron was the hand of a clock, I'm am wondering what kind of time dilation would be occuring. Does dilation predicted by the lorentz transformation apply only to 'side to side' objects or does it covers elliptical paths like this one. Applying the lorentz transform to the 12 to 6 motion and adding it to the 3 to 9 motion would not be the same as the combination of the two motions. That would be like adding 'a + b to get c' , when it should be 'a^2 + b^2 to get c^2.

Actually, I think everything has a north and south pole. Like waves, electrons, protons, neutrons, quarks, preons..... everything magnetic or electromagnetic, or anything that attracts should have two poles. "For every reaction, there is an opposite reaction" so for every pole, I say there is an opposite pole. Monopoles are fine when working on paper, but it doesn't mesh with electro-magnetism. How is anyone supposed to unify everything if one keeps thinking in monopoles ?

From Special relativity - Wikipedia, the free encyclopedia

"It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be.[3]"

I argue that there is a defined absolute rest. This absolute rest should be determined by measuring the speed of light in opposite directions. When those two speeds are equal in ALL directions relative to the measurer, than the measurer has found absolute rest. It's that simple. There's (-C, 0) to (0,C+) along an axis. At (0,0) is absolute rest along that axis. If the C measured is equal in both directions, but less than nominal C, than you are still moving along some other axis than the one measured.

And then I read things like this,

"The presence of gravity becomes undetectable in a sufficiently small, free-falling laboratory."

Which is not entirely correct. If you are falling, it's because of gravity. Just because you don't feel it, or if it isn't detected, doesn't mean that it isn't there. Gravity exists between all matter, you just need more sensitive equipment to measure such a thing. Only in the center of balance of the mass of the Universe will a person have no net movement, and gravity would be immeasurable, ignoring that the measuring device is also attracted to you. Even if you could achieve absolute rest as mentioned above, it would be hard to remain that way, since you would have to be going against the currents to stay that way and counteract everything as you move through everything.

It has been pointed out to me as well, that if you are in the center of a spherically uniform mass, the gravity will cancel out and you will feel nothing. But I argue, that if the mass of the spherically symetrical shell had mass densities of that of black holes, your body would be ripped apart in every direction and form a thin film on the inside of the shell. No net force from gravity only applies if you can occupy the very center point, which is infinitesimally small, and a body is not.

And then I read about length contraction, at Length contraction - Wikipedia, the free encyclopedia

which gives the equations, which I could not copy and paste,

"where
L0 is the proper length (the length of the object in its rest frame),
L is the length observed by an observer in relative motion with respect to the object, "

So it seems that the proper length's value does not change in the equation, but the length observed does.

I'll have to leave an explanation that accounts for gravitational time dilation for another time. I'm still working that one out.

Originally Posted by MisterMe

The OP of this thread appeared to be about rapidly rotating rigid bodies.

I have a five minute video here describing one situation involving a rapidly rotating rigid body.

As MisterMe said, "Relativity calculations require knowledge and understanding of Minkowski 4-vectors and how to transform them." This video basically generates the 4-vectors of every event on the two-dimensional body (spokes and rim) as parametric equations in one variable each. And then the parametric equations are transformed via function composition, and rendered using a surprisingly versatile "ParametricPlot3D" function.

Click for Video: Relativistic-Wheel - JDoolin's library