[chris (OP)]

When an object moves at light speed it stretches out to the eye of the observer. So what happens when an object follows a circular path at light speed. e.g. a windmill spinning at the speed of light?

C

[alancalverd]

In order to move in a circle, the object must be subject to a centripetal force.

Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion - or indeed to change its direction at all. And even if there were an infinitely strong string, what would you attach it to?   

[PmbPhy]

When an object moves at light speed it stretches out to the eye of the observer.

Objects cannot move at the speed of light unless they have zero proper mass such as as photons.

Where did you get the notion that objects stretch out to the eye of the observer? The faster an object moves the shorter it gets in the direction of motion. I.e. objects shrink at high speeds. They don't stretch.

[evan_au]

If you could whirl a significant mass at relativistic speeds, it would radiate energy in the form of gravitational waves (or so the theory of general relativity and confirming astronomical measurements indicate).

If the object were electrically charged, it would also radiate electromagnetic waves.

[mathew_orman]

When an object moves at light speed it stretches out to the eye of the observer. So what happens when an object follows a circular path at light speed. e.g. a windmill spinning at the speed of light?

C

In my opinion based on observations there are such cases in reality...

[PmbPhy]

When an object moves at light speed it stretches out to the eye of the observer. So what happens when an object follows a circular path at light speed. e.g. a windmill spinning at the speed of light?

C

In my opinion based on observations there are such cases in reality...

You're wrong. Nothing that has mass can move at the speed of light. There are no observations which demonstrate otherwise.

[alancalverd]

In my opinion based on observations there are such cases in reality...

Please cite the observations. There's nothing better than a good experiment to demolish a theory that has been held for the last hundred years.

[jeffreyH]

When an object moves at light speed it stretches out to the eye of the observer. So what happens when an object follows a circular path at light speed. e.g. a windmill spinning at the speed of light?

C

In my opinion based on observations there are such cases in reality...

Which part are you referring to? The stretching out or the circular motion? I agree with Pete on the stretching out part. In the case of circular motion you would need a binding force to keep the object in orbit. If there were a force of such magnitude you wouldn't be posting to this forum. You would be a microscopic speck in a singularity.

[lightarrow]

In order to move in a circle, the object must be subject to a centripetal force.

Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion

Which equation are you using here?

--
lightarrow

[lightarrow]

If you could whirl a significant mass at relativistic speeds, it would radiate energy in the form of gravitational waves (or so the theory of general relativity and confirming astronomical measurements indicate).

Excepting when there are simmetries like an homogeneous disk rotating around its principal axis (or other cases).

--
lightarrow

[alancalverd]

In order to move in a circle, the object must be subject to a centripetal force.

Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion

Which equation are you using here?

--
lightarrow

m = m₀/√{1-v²/c²} is good enough for CERN and me.

[lightarrow]

In order to move in a circle, the object must be subject to a centripetal force.

Since a massive object will have infinite mass at c, there is no force that can constrain it to circular motion

Which equation are you using here?

--
lightarrow

m = m₀/√{1-v²/c²} is good enough for CERN and me.

No, I was referring to what you called "centripetal force".

--
lightarrow

[alancalverd]

The centripetal force required to maintain circular motion of a body moving at relativistic speeds is

F = γm₀v²/r

where v is the instantaneous tangential velocity.

[lightarrow]

The centripetal force required to maintain circular motion of a body moving at relativistic speeds is

F = γm₀v²/r

where v is the instantaneous tangential velocity.

Ok.
Now find the expression of the tangential force you need to accelerate the body to relativistic speeds, then I'll show you something interesting.

--
lightarrow

[alancalverd]

Any force will do if you wait long enough - the principle behind solar sails and ion rockets.

The problem is that "long enough" is infinite, whatever the force applied, if you want a massive particle to reach c. How is that "interesting"?

[PmbPhy]

Use a proton in a particle accelerator as an example. In such accelerators there is a magnetic field that keeps the protons moving in a circle. That force is the required centripetal force. This force is known as the Lorentz force.

The protons are accelerated in the direction of motion by an electric field. As the speed is increased the magnetic field is increased so as to keep the proton moving in the same circle.

[lightarrow]

Any force will do if you wait long enough - the principle behind solar sails and ion rockets.

The problem is that "long enough" is infinite, whatever the force applied, if you want a massive particle to reach c. How is that "interesting"?

Why do you think to know what I'm referring to?
Write the relation between tangential force and acceleration at relativistic speeds. If you don't know, I can write it for you.

--
BlueRay

[alancalverd]

We're not talking about "relativistic speeds" but c. Accelerating leptons to 0.99c in a circular path is an engineering problem, but the physics is no big deal. It's the recurring decimal point that distinguishes between difficult and impossible. Your equation is awaited with bated breath.

[lightarrow]

We're not talking about "relativistic speeds" but c.

In this case what you wrote here:

The centripetal force required to maintain circular motion of a body moving at relativistic speeds is
F = γm₀v²/r
where v is the instantaneous tangential velocity

is meaningless since you cannot define γ  []

Accelerating leptons to 0.99c in a circular path is an engineering problem, but the physics is no big deal. It's the recurring decimal point that distinguishes between difficult and impossible. Your equation is awaited with bated breath.

If physics "is no big deal" why didn't you write the equation I asked you?
Ok, I'll write it:

F = γ³m₀ * a

m₀ = proper mass
F = tangential force
a = tangential acceleration

Now compare the two equations:
1) F = γm₀ v²/r     (centripetal = radial force).
2) F = γ³m₀ * a     (tangential force)

and then tell me which is here the mass that goes to infinity according to the sentence you wrote:

Since a massive object will have infinite mass at c

I mean, the mass you are referring to is γm₀ or is γ³m₀?

Is it still meaningful to talk about relativistic mass, in this context? Wouldn't be better to talk about m₀ = m only and say that it doesn't change with velocity?

--
lightarrow

[PmbPhy]

]
We're not talking about "relativistic speeds" but c.

I don't understand this sentence. Are you trying to say that the speed of light is not a relativistic speed? If so then you're wrong since the term relativistic speed is defined as follows. From:
https://en.wikipedia.org/wiki/Relativistic_speed [Links inactive - To make links active and clickable, login or click here to register]

A relativistic speed is a speed which is a significant proportion of the speed of light.

It's reasonable to say that the speed of light itself is a significant proportion of the speed of light. Saying otherwise without elaborating is confusing.

[alancalverd]

m_v =  m₀(1 - v²/c²)^−1/2

This works for "relativistic speeds" but clearly raises problems when v = c, as Einstein remarked. And who am I to disagree? 

[PmbPhy]

m_v =  m₀(1 - v²/c²)^−1/2

This works for "relativistic speeds" but clearly raises problems when v = c, as Einstein remarked. And who am I to disagree?

That didn't help me understand your sentence, i.e. what did you mean when you wrote "We're not talking about "relativistic speeds" but c."?

[alancalverd]

Pretty much the same as the difference between "green-ish" and "λ = 520 nm". 0.99c is a relativistic speed in most people's language. c is c.

The point is that all and only photons travel at c, whereas any particle with nonzero mass could in principle travel at any speed less than c. That makes c rather special, and 0.999c rather ordinary.

[lightarrow]

Pretty much the same as the difference between "green-ish" and "λ = 520 nm". 0.99c is a relativistic speed in most people's language. c is c.

c is not relativistic speed? I don't know if laughing or crying...

The point is that all and only photons travel at c, whereas any particle with nonzero mass could in principle travel at any speed less than c. That makes c rather special, and 0.999c rather ordinary.

Your problem is the obstination to want to use  equations which are valid only for velocities different from c. If you used those which are always valid, for all velocities included c, you wouldn't need to "climb on the mirrors"  []

--
lightarrow

[evan_au]

what happens when an object follows a circular path at light speed?

We're not talking about "relativistic speeds" but c.

what did you mean when you wrote "We're not talking about "relativistic speeds" but c."?

I think we may be talking at cross purposes here.

The OP was asking about swinging an object around at lightspeed=c.
The discussion moved on to discussing what happens at relativistic speeds < c.

Alan was just reminding us that the OP was asking about traveling at speed=c, which is infinitely harder than traveling at "relativistic speeds" < c...

[alancalverd]

Your problem is the obstination to want to use  equations which are valid only for velocities different from c. If you used those which are always valid, for all velocities included c, you wouldn't need to "climb on the mirrors"  []

--
lightarrow

I don't have a problem! I'm trying to answer the original question. By all means choose any equation you like that consists with experimental evidence, and tell us how much energy we need to expend to accelerate an object for which m₀≠ 0 to the speed of light, then how much force is required to constrain it to a circular path with a constant tangential speed c.

[lightarrow]

Tangential Radial (centripetal) force. In modulus: F = (E/r)*β²

E = energy.
β = v/c

For a body with mass: E = mc²γ; γ = (1-β²)^-1/2
For a body moving at c: β = 1.

About the energy needed to accelerate a body to light speed, see "E" up. For a photon you can write E = h*f if you like.

--
lightarrow

[jeffreyH]

If we take the value we end up with . How do you come to this determination? Beta may equal 1 according to your previous post but then you are taking the square root of zero and dividing it into 1. How is that valid? None of this has a bearing upon c.

[PmbPhy]

Tangential force. In modulus: F = (E/r)*β²

E = energy.
β = v/c

For a body with mass: E = mc²γ; γ = (1-β²)^-1/2
For a body moving at c: β = 1.

About the energy needed to accelerate a body to light speed, see "E" up. For a photon you can write E = h*f if you like.

--
lightarrow

Did you know that in his 1905 paper on special relativity Einstein got the expression for the transverse mass wrong? Ohanian explains the error in his book Einstein's Mistakes located at http://www.newenglandphysics.org/other/Ohanian_Einstein_error_1905.pdf [Links inactive - To make links active and clickable, login or click here to register]
http://www.newenglandphysics.org/other/Ohanian_Einstein_error_1905.pdf [Links inactive - To make links active and clickable, login or click here to register]

[lightarrow]

If we take the value we end up with . How do you come to this determination? Beta may equal 1 according to your previous post but then you are taking the square root of zero and dividing it into 1. How is that valid? None of this has a bearing upon c.

Sorry, I'm a bit "slow" in these days, what do you mean exactly? Are you referring to the equation F = m*a when F is in the same direction of velocity?

--
lightarrow

[alancalverd]

Tangential force. In modulus: F = (E/r)*β²

E = energy.
β = v/c

For a body with mass: E = mc²γ; γ = (1-β²)^-1/2
For a body moving at c: β = 1.

Agreed, so as v→c, E → ∞ if m ≠ 0

And the radial force required to maintain circular motion of a massive body at v = c is?

[lightarrow]

Tangential force. In modulus: F = (E/r)*β²

E = energy.
β = v/c

For a body with mass: E = mc²γ; γ = (1-β²)^-1/2
For a body moving at c: β = 1.

Agreed, so as v→c, E → ∞ if m ≠ 0

And the radial force required to maintain circular motion of a massive body at v = c is?

Ehm, I wrongly wrote "tangential" force but it clearly was "radial" force. Sorry for the mistake and thank you to have noticed it!
I am correcting it.

--
lightarrow

[lightarrow]

Tangential force. In modulus: F = (E/r)*β²

E = energy.
β = v/c

For a body with mass: E = mc²γ; γ = (1-β²)^-1/2
For a body moving at c: β = 1.

About the energy needed to accelerate a body to light speed, see "E" up. For a photon you can write E = h*f if you like.

--
lightarrow

Did you know that in his 1905 paper on special relativity Einstein got the expression for the transverse mass wrong? Ohanian explains the error in his book Einstein's Mistakes located at http://www.newenglandphysics.org/other/Ohanian_Einstein_error_1905.pdf [Links inactive - To make links active and clickable, login or click here to register]
http://www.newenglandphysics.org/other/Ohanian_Einstein_error_1905.pdf [Links inactive - To make links active and clickable, login or click here to register]

Very interesting.
So, after all, Albert Einstein wasn't that "super mind" being we are used to think, but just a common person which makes the same kinds of mistakes you and me can make too  []

--
lightarrow

[alancalverd]

Ehm, I wrongly wrote "tangential" force but it clearly was "radial" force. Sorry for the mistake and thank you to have noticed it!
I am correcting it.

--
lightarrow

Correction noted, and as I stated way back in this thread, F → ∞ if v → c and m ≠ 0. Glad we settled that.