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

I need help in understanding and exploring the relationships in the model of a rotating body that is traveling near the speed of light. I'm great with thought experiments, but I could use some help with the math involved.

I would like to go through some examples first, and then I'll show you what I've come up with math-wise.

The first thought experiment is a macroscopic kind of analogy. Lets say that a car is traveling, and must obey the speed limit or the police (the law) will slow him down. The car is already traveling at the speed limit and experiences a huge side wind. The side wind combined with the car's original speed, would send the car on a new path in which it would be traveling slightly faster than the speed limit. In order to obey the speed limit, the driver must slow down his car.

Secondly, microscopically, now consider an electron traveling at the speed limit of light around an atom . Whenever the atom is shifted in any direction, the electron must slow down to obey the speed limit. Of course, the electron has no brakes, but still cannot go faster than the speed limit of light. So, if an atom were traveling at or near the speed of light, and the electron rotates arount it, then the electron would have to slow down considerably and then speed back up to the speed limit on the opposite side. ( I have diagrams attatched below. ) At speeds before the speed of light, in the same direction of atom's travel, an electron will be allowed to move the remainder of motion allowable. In the direction of travel, the allowable motion would be: ((the speed of light) minus (the velocity of the traveling atom)). Relatively, opposite the direction of travel, the allowable motion would be the speed of light.
I made a sketch of the models, as the electron orbits the atom, traveling in the x-positive direction: in the xz-plane, xy-plane, and yz-planes . I figured an easy way to start solving this problem would be to break it up in this manner, and then maybe find some way to combine the results.

I've attached my sketches of the electron as it orbits in these planes here,

x-z plane.jpgy-z plane.jpgx-y plane.jpg

I understand how to calculate the kinematic time dilation for bodies moving perpendicular to the direction of travel, with the application of the pythagorean theorem as seen here,

http://en.wikipedia.org/wiki/Time_dilation

where it states,

" Time dilation by the Lorentz factor was predicted by Joseph Larmor (1897), at least for electrons orbiting a nucleus. Thus "... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio :" (Larmor 1897). Time dilation of magnitude corresponding to this (Lorentz) factor has been experimentally confirmed, as described below. "

This is alot like that, but I think my model described differs because of the speed limits imposed and the special case of a rotating body slowing down and speeding up as it trys to obey the invariance of the speed of light.

There are a couple of givens that I've figured out already. .

Assuming the electron travels the speed of light,

The electron travels at ((the speed of light) minus (the velocity of the traveling atom)) in the x-positive direction at point B in the x-y plane.
The electron travels the speed of light in the x-negative direction at point D in the x-y plane.

The velocity at points C and E are equal and can be found using pythagorean theorem in the x-y plane.

For the y-z plane, the velocity at all points is equal to the velocity at C and E in the x-y plane.

For the x-z plane, the values mirror that of the x-y plane.

I'm confused about whether I can simply average the velocity of the points or not. If I do, I get (C minus (C minus the velocity of the atom)) / 2 for all planes. This way of thinking would suggest that the maximum time dilation that can occur is between 0 and 50%. Which differs from the established 0 to 100% (?) , which only considers kinematic effects of the motion perpendicular to the direction of travel before the motion reaches the speed limit.

Also, I'm sure some pretty wierd things start happening when the electron and the proton start traveling at the same speed, near the speed of light. The path of the electron may get tighter on the forward side and elongated on the trailing side, or atomic structure just starts decaying at certain speeds and the electron usually escapes or collides with the proton and whatever.
And I'm sure that some people will point out that the matter is going to increase in mass somehow as it approaches the speed of light, but I think that's a big load of baloney and highly counter-intuitive to the conservation of matter. Inversely, maybe I can lose weight by slowing down. What a joke.

Originally Posted by Jeffrey DreamKing

What a joke.

Hahahah, good one.

Originally Posted by Jeffrey DreamKing

I need help in understanding and exploring the relationships in the model of a rotating body that is traveling near the speed of light. ...

The path of the electron may get tighter on the forward side and elongated on the trailing side, or atomic structure just starts decaying at certain speeds and the electron usually escapes or collides with the proton and whatever.
And I'm sure that some people will point out that the matter is going to increase in mass somehow as it approaches the speed of light, but I think that's a big load of baloney and highly counter-intuitive to the conservation of matter. Inversely, maybe I can lose weight by slowing down. What a joke.

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. A spinning sphere is probably simpler as "rigid bodies" go, but it is not trivial.

A few things to consider:

• Only the spin axis is an inertial reference frame.
• Moving objects are shorter than stationary objects. Therefore, the spinning equator must have a smaller diameter than the spin axis. The spinning sphere becomes an elliptical spheroid spinning about its major axis.
• The speed of each part of the sphere will depend on its distance from the spin axis. [This is similar to Newtonian physics.]
• The rotation frequency will depend the speed of each part of the spinning sphere. [It can no longer considered to be a solid. Newtonian physics cannot account for this.]

The takeaway message is that this is not a problem that you can solve with thought experiments and sketches. Relativity calculations require knowledge and understanding of Minkowski 4-vectors and how to transform them.

If you look very closely at 'Mr me's post #3. You might understand why I am now a quivering mass of terror filled jelly, hiding behind the couch... I can read between the lines., and in this case there is mathematics for Christmas. I can see it now 'calculations of complexity previously unimagined...'

When this is all over would you drop me a line... over the back of the afore mentioned couch... time for coffee.

Please feel free to comment ( because it is both free and you can )...' Finding a star that is not rotating would be difficult. I know of none.

Which is not to say there are none. I just have not knowledge of such..

That being of some rotational velocity would seem to be the normal state of stellar formation.

That as the gavity of a massive star contracted the size of the mass the rotation would accelerate, spin up...

That we know of Neutron stars that spin very fast. Rapidly. That a Black Hole could attain velocities near to c. Why not ?

Could the rule be broken near to or inside a BH.. exceeding c.

I think I read that there is some sort of max rotational velocity but I am not sure why ... I remember asking questions about spinning a black hole in order for the centrifugal force to release mass trapped inside. Although this site states speed of light as a possibility:

What is the maximum possible rotation speed of a black hole?

When the event horizon is rotating at the speed of light in a 'maximal Kerr' black hole. The geometry of such holes is different from a non-rotating 'Schwarschild' black hole because the event horizon and the surface of infinite redshift do not coincide and you end up along the equatorial plane, with two 'horizon like' surfaces. Only the inner event horizon is 'fatal'. The zone between the outer surface and the inner horizon, called the 'ergosphere' is traversable and has some interesting physical aspects to it where you can extract energy from the black hole. The above image is a ray trace of what the emission from an accretion disk of gas would look like around a Kerr black hole viewed at an inclination of 30 degrees from face-on. (figure courtesy of C. Perez, Stanford University)

Originally Posted by astromark

Please feel free to comment ( because it is both free and you can )...' Finding a star that is not rotating would be difficult. I know of none.

Which is not to say there are none. I just have not knowledge of such..

That being of some rotational velocity would seem to be the normal state of stellar formation.

That as the gavity of a massive star contracted the size of the mass the rotation would accelerate, spin up...

That we know of Neutron stars that spin very fast. Rapidly. That a Black Hole could attain velocities near to c. Why not ?

Could the rule be broken near to or inside a BH.. exceeding c.

Originally Posted by astromark

Please feel free to comment ( because it is both free and you can )...' Finding a star that is not rotating would be difficult. I know of none.

Which is not to say there are none. I just have not knowledge of such..

That being of some rotational velocity would seem to be the normal state of stellar formation.

That as the gavity of a massive star contracted the size of the mass the rotation would accelerate, spin up...

That we know of Neutron stars that spin very fast. Rapidly. That a Black Hole could attain velocities near to c. Why not ?

Could the rule be broken near to or inside a BH.. exceeding c.

The OP of this thread appeared to be about rapidly rotating rigid bodies. Stars like our Sun are not rigid bodies. They are balls of gas. As such, different parts of stars are free to rotate at different rates and they do. The accepted differential rotation rate is given by the empirical formula:

where is the angular rotation rate, is the co-latitude angle, and , , and are unique constants for each star. These constants may not have the same sign. The constants for our own Sun have different signs which means that some parts of the Sun rotate clockwise while other parts rotate counterclockwise.

The point is that we start with a gaseous rather than a rigid body. It spins more like smoke than a billiard ball. It also rotates slowly, taking several days for any part of it to complete a single rotation. When a star collapses to a neutron star, its rotation will accelerate. However, its rotation speed will not approach the speed of light.

Only a black hole can rotate near the speed of light. In 2007, researchers at the University of Maryland reported measurements of a supermassive black hole spinning at 98.7% of the speed of light. However, we do not know the structure of the blackhole. It is believed to be have its entire mass in a singularity at its center. If this is the case, then the event horizon is strongly warped empty spacetime. The mass outside the event horizon is not part of the black hole.

A black hole at 98.7% , whoah ! So at 100%, there is a big bang? Hopefully nowhere close to us...

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.

And all that 4-D stuff about extra dimensions... I think it looks good on paper but is not empirically proven. For example, if black holes are wormholes of space time, then white holes would also be seen, but no one has ever seen a white hole. So yeah, I don't believe in spacetime. Only down to earth Euclidean space. Heck, I don't even believe in time ...

how long does "now" last?

Okay, Mister Me. Here it goes.

About those Michelson-Morley type of experiments, which are supposed to confirm spacetime ... I think that the shift from the lasers is only a measure of the shift against the sidereal absolute rest relative to the invariance of light in opposite directions. I think what needs to be done to settle my dispute, is to take two of these drift measuring setups and pair them both alongside atomic clocks. Then monitor and compare the difference in drifts with the difference in the clocks. For me, this would give a measure of how much time dilation occurs relative to the sidereal and would be much more convincing than using only the clocks.

And if you want to say that the lensing of light around massive bodies is proof of spacetime, I'll say it's not proof. Light bends around electromagnets, and bends with gravity, which I predict is an electromagnetic force. Although that's not proven yet, and the actual mechanical cause of gravity is not figured out yet, I reason that gravity must be an electromagnetic force in order for it to be unified. And it needs to be electromagnetic in some way in order for it to interact with other electromagnetic things, namely, light. In fact, if you take Coloumbs Law equation and place it directly beside the Gravitational Law equation, they look quite the same. The k co-efficient of induction found in Coloumbs Law equation should not be equated with the gravitational constant G, because I think that space will have no induction, since space has nothing in it for induction to occur. The k co-efficient in the Gravitational Law equation should be zero, and the gravitational constant G is only a measure of the average charge of attraction per unit of mass.

I guess more specifically, there are conditions of what I'm asking:
if there is no more than 3 dimensions and no spacetime, when a rotating rigid body approaches the speed of light, will torsional force occur from resistance with space upon the outermost part of the rotating body when it is propelled to spin and move forward at a rate faster than the speed of light from the addition of the forward velocity vector and the rotational velocity vector ?

Would atomic structure continue to hold near the speed of light, if the subatomic particles cannot move ? Maybe if they cannot move anymore, they cannot mechanically produce any electromagnetic effects (strong, weak, gravitation ) on each other.

Could one design a spaceship around this? The bridge is in the core and the rotation creates workable gravity in the mantle, with time dilation induced suspended animation towards the crust. Of course, it would have to fly behind a spearheaded shield that could be built upon from behind. Perhaps if the shield was clear, or made of diamond, the shield could also act as a lens which would be used to form a shockwave of projected light to burn a hole through advancing space debris.

Anyways, I'm still looking for some math to go with my sketches. It's not a textbook situation so I'm not expecting anybody to know offhand. I thought about treating the electron as an inertial body that is going upriver, so to speak. Or like a boat, if you took the steering wheel and tied / fixid it in place so that the boat made a circle, on a river that is flowing uphill... where gravity is acting as the resistance, and either the uphill angle or the gravity becomes higher. At least, some kind of similiar scenario that I could apply equations to.

Originally Posted by Jeffrey DreamKing

...

Okay, Mister Me. Here it goes.

...

Wow! I have never before read so many misconceptions in single post on this forum.

Several points:

1. The Big Bang has nothing to do with spinning black holes. A black is considered to have all of its mass concentrated at a singularity at its center. A black hole whose equator is spinning at the speed of light has no mass on its equator. There would be nothing to explode.
2. Any physical object or phenomenon that can be represented as a function of space and time is subject to the Lorentz transformation.
3. Most atoms within a spinning object do not have inertial reference frames. They also have different accelerating reference frames. If they have different accelerating reference frames, then they have different time dilations and length contractions.
4. Spacetime as a concept has nothing to do with relativity. Spacetime combines 3-D space and 1-D time into a single 4-D space. The great science fiction novelist H. G. Wells wrote about it in his 1895 novel The Time Machine. This novel was written ten years before Einstein published his Special Theory of Relativity. 4-D spacetime is no less proven than 3-D space or 1-D time because it is simply the combination of the two.
5. The Special Theory of Relativity showed that moving reference frames mixed the spatial components of spacetime with the temporal component. The General Theory of Relativity replaced gravity as a force with gravity as the curvature of spacetime. Spacetime in the Special Theory is Euclidian. Spacetime in the General Theory may be non-Euclidian.
6. The Michelson-Morley experiment did not prove spacetime, nor did it attempt to prove spacetime. The Michelson-Morley experiment showed that the speed or light was a constant that was independent of reference frame.
7. Gravitational lensing is not proof of spacetime. It is evidence of the curvature of spacetime near a massive body.
8. Gravity is not an electromagnetic force. Period.
9. No part of a moving object can exceed the speed of light.
10. All inertial frames are equivalent. The fact that an object may be moving at a speed near that of light is irrelevant. If different parts of an object have speed differences that are significant fractions of the speed of light, thenthe structural integrity of the object is in question. However, many physical objects will fly apart if they spin at speeds that are too slow to be considered relativistic.
11. The electromagnetic force, weak nuclear force, and strong nuclear force are different manifestations of the same force. TOE (Theory of Everything) or GUT (Grand Unified Theory) will bring gravity into the fold.
12. It is well understood that artificial gravity can be created on a spacecraft by spinning it slowly.
13. Resistance in physics is a physical phenomenon that retards an object and removes energy from it.

Originally Posted by MisterMe

Wow! I have never before read so many misconceptions in single post on this forum.

LOL, I thought I had that title. :-)

Originally Posted by MisterMe

[*]The electromagnetic force, weak nuclear force, and strong nuclear force are different manifestations of the same force. TOE (Theory of Everything) or GUT (Grand Unified Theory) will bring gravity into the fold.

By any chance, do you know of any links you could share concerning this particular topic? I would really be interested in reading more along those lines besides where it is addressed in "The Elegant Universe".