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Theory of Relativity

Imagine a Silver ball spinning at a very high angular velocity such that every point that is at a distance R/2 from the center is moving with speed of light. How would motion of points that are at a distance between R/2 and R from center would appear from an initial frame? (R is radius of ball)

Give your views without any hesitation.

Note by Lokesh Sharma
4 years, 6 months ago

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Actually, since nothing can travel faster than \(c\), and no object with mass can travel at, but only infinitely close to \(c\), this implies that there are no rigid objects. The angular velocity will actually vary with the distance \(r\) from the center, so that \(\omega(r)<\frac{c}{r}\). If I have time, I'll maybe do the maths to acquire the formula for \(\omega (r)\), or I'm certain someone else here could do that

Mattias Olla - 4 years, 6 months ago

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I am a bit confused. You said two things - One that there are no rigid objects and second that there is restriction to angular velocity. If the former case is true then I guess there is no need for the later case to be true. Can you explain how these two things are related?

Lokesh Sharma - 4 years, 6 months ago

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The condition is that nothing can travel faster than light. This, in this case, implies that the angular velocity has to decrease (otherwise it would eventually become faster than light), which means the object can't be rigid. This is the same problem as the following idea of transmitting information faster than light: Take a metal rod and make it one light-year long. If you then move the rod back and forth, you could send signals via morse code, and thereby faster than light. The solution is, once again that since information can't move faster than light, the rod can't be perfectly rigid. This means that if you push the rod forward, the other end won't move instantly. In fact, this information would only travel with the speed of sound in the rod, since the rod being pushed forward is actually a longitudinal compression wave.

Mattias Olla - 4 years, 6 months ago

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the principle of special relativity applies to inertial frames of reference only this is not an inertial reference frame

Dave Johnson - 4 years, 6 months ago

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Hmm... I don't know. See, we are observing the rotation in an inertial frame that is attached to free space around the ball not on the ball. Isn't it the inertial frame?

Lokesh Sharma - 4 years, 6 months ago

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but the sphere is accelarating !! we cant apply str in conditions like this !

Dave Johnson - 4 years, 6 months ago

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@Dave Johnson i mean the sphere is not inertial the masses are changing their velocities..they are undergoing accelaration .. the sphere is accelarating was a wrong way to write it !

Dave Johnson - 4 years, 6 months ago

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@Dave Johnson that is why is has the name -- SPECIAL !!

Dave Johnson - 4 years, 6 months ago

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@Dave Johnson I think special relativity can deal with accelerating particles and sphere is just bunch of accelerating particles. I can't see the reason why special relativity can't be applied here. So I did a little search on google and found out this article by "Philip Gibbs 1996".

It says - "It is a common misconception that Special Relativity cannot handle accelerating objects or accelerating reference frames. It is claimed that general relativity is required because special relativity only applies to inertial frames. This is not true. Special relativity treats accelerating frames differently from inertial frames but can still deal with them.

Special relativity gives a completely self-consistent description of the mechanics of accelerating bodies NEGLECTING GRAVITATION, just as newtonian mechanics did."

Lokesh Sharma - 4 years, 6 months ago

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@Lokesh Sharma there is one thing the writer forgot to mention .. when dealing with noninertial frames the str can only give us answer approximately .. we have to use gtr for the complete soln.. read any standard book on gtr/str .. the geometry of the 2 are totally .. the author points out in the second line "This error often comes up in the context of the twin paradox when people claim that it can only be resolved in general relativity because of acceleration. This is not the case." -- only an APPROXIMATE answer can be found by applying str .. but after applying gtr a complete soln is found and the paradox resolved COMPLETELY .. for the problem in this case --> lets say we want to solve it by str.. then 1st --> str geometry is not the same as euclidian geometry .. 2ndly --> the whole notion of rigid bodies is lost in case of str .. you have to use metric tensors called ( Langevin-Landau-Lifschitz metric) and use the concept of Born Rigidity to fully understand that nothing is violated .. it is a very good question but with a very complicated answer

Dave Johnson - 4 years, 6 months ago

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This is an impossibility, as no mass can travel the speed of light. There are formulas to find the velocity of an object from different reference frames traveling near the speed of light. Moreover, if the R/2 sphere is moving near the speed of light, the R sphere would be moving faster, but still under the speed of light.

Bob Krueger - 4 years, 6 months ago

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i agree with Bob but with my incomplete logics...:(

Riya Gupta - 4 years, 6 months ago

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A big blur.

Michael Sheng - 4 years, 6 months ago

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Although the Special Theory of relativity is applicable only for an object in an inertial frame of reference, the above question could be thought-off in a completely different manner....According to Special theory of relativity, the if the centre of a body is at rest, although the particles around it move, the theory is applicable. Therefore, At the centre of the ball, the point is at rest...At the point next to the centre point, suppose (R-x), the particle is at it's fastest...At R/2, it moves with an unaccelerated motion in a particular line..while at R, the particle moves with a further lesser velocity than the point at R/2.. I know...I'm fully wrong(Please send in corrections as a 'reply' to my explanation...Thank You...

Souvik Paul - 4 years, 6 months ago

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i am thinking of two things. time dilation and length contraction.. apply these two with the mathematics and you will be able to see how it is impossible for any object to reach speed of light in any reference frame.. so here too this willl happen and as said by Mattias the body will not seem to be rigid. i think so.. but i am not so sure.. :)

Sarvo Singh - 4 years, 6 months ago

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There is no way for a sphere to be spinning at a constant angular velocity about an axis such that all points at a certain distance from the centre will be moving at the same speed.

Jiahai Feng - 4 years, 6 months ago

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This is my view on Special Relativity. Einstein proved nothing can travel faster than light. I really appreciate what he and other scientist did. But I am not convinced that nature has put a limit on speed of objects. This is just an unjust law. Why speed of light? Why not speed of sound? What's the difference. This is what I think - "There is no limit to speed with which an object can travel. Objects CAN travel faster than light. But we cannot perceive such a thing at all. Because there is a limit to which we can see how fast objects are moving. That's why its speed of light which is key to relativity not speed of sound or any other sound. Further, its worthwhile to keep theory of relativity the way it is because its what we perceive is all what matters. I might give an example later to explain how this is true."

Does anyone agree with me?

Lokesh Sharma - 4 years, 6 months ago

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I agree with you Sir Lokesh.

Souvik Paul - 4 years, 6 months ago

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Sir Lokesh, Einstein never universally declared that anything cannot travel faster than light, instead he deviced a theory that work even at speeds faster than light...This is what we call the ultimate theory of Relativity...

Souvik Paul - 4 years, 6 months ago

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i think...there will be differences i mean a total ring of particles...at a distance R/2 from centre will be invisible....as it will be converted into energy....at speed of light and we will be able to view a sphere partitioned into two portions.......(i am most probably wrong...:/ )

Riya Gupta - 4 years, 6 months ago

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If you think you are right or wrong, either way you are right - Old proverb. Belive in yourself.

Lokesh Sharma - 4 years, 6 months ago

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is my logic even a bit true?

Riya Gupta - 4 years, 6 months ago

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@Riya Gupta I think you need to be clear why ring of particles at distance R/2 will be invisible. Its true mass is equivalent to energy but that doesn't mean that every thing that travels at speed of light will be converted into energy if that what you are thinking.

Lokesh Sharma - 4 years, 6 months ago

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@Lokesh Sharma then???

Riya Gupta - 4 years, 6 months ago

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