question about mass-energy equivalence

[vuquta]

E=mc^2

where

E=energy

M=mass

c= the speed of light

 

What value of c is used in a rotating frame?

http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

[ajb]

The article states that c is the velocity of light, which by itself could be ambiguous. However, as a standard it will mean the speed of light in vacua as measured with reference to any inertial frame of reference. So, 299,792,458 m/s (or whatever other units preferred.)

[vuquta]

The article states that c is the velocity of light, which by itself could be ambiguous. However, as a standard it will mean the speed of light in vacua as measured with reference to any inertial frame of reference. So, 299,792,458 m/s (or whatever other units preferred.)

 

Nope does not work.

 

Look at section 6.

 

http://www.fourmilab.ch/etexts/einstein/specrel/www/index.html#SECTION21

 

You can go one way or the other.

 

Einstein uses these SR Maxwell equations to derive the mass energy equivalence. However, each requires a constant measured value of c. But, in a rotating frame, measured c is directionally and v dependent and not a constant.

 

If that is not enought, you cannot sync clocks in a rotating frame. Note Einstein takes partial derivatives with respect to tau.

 

You cannot take the derivative unless you have a free and consistent variable. But, since you cannot sync clocks in a rotating frame, then you do not have a free variable tau and hence you cannot take the partial derivative.

Edited September 6, 2010 by vuquta

[swansont]

The article you linked to in the OP was not about rotating frames. c is, by definition, a constant, and ajb's answer is quite correct. Asking what c is and what the speed of light is when measured in a rotating frame are two different questions.

[vuquta]

The article you linked to in the OP was not about rotating frames. c is, by definition, a constant, and ajb's answer is quite correct. Asking what c is and what the speed of light is when measured in a rotating frame are two different questions.

 

Einstein takes the partial derivative with repect to tau for the Maxwell transformations.

 

How are you going to do this in a rotating frame?

 

Why are we getting off task? This is a simple question.

Edited September 8, 2010 by vuquta

[swansont]

Einstein takes the partial derivative with repect to tau for the Maxwell transformations.

 

Yes, and he does this in an inertial frame.

 

How are you going to do this in a rotating frame?

 

Why are we getting off task? This is a simple question.

 

Even though you can't synchronize clocks, the rate (i.e. frequency) is offset by a constant amount. You would probably have to approach this by accounting for this offset, much like one would add in a pseudoforce to make a non-inertial system "look" inertial (Coriolis or centrifugal) in analyzing forces.

[vuquta]

Yes, and he does this in an inertial frame.

 

 

 

Even though you can't synchronize clocks, the rate (i.e. frequency) is offset by a constant amount. You would probably have to approach this by accounting for this offset, much like one would add in a pseudoforce to make a non-inertial system "look" inertial (Coriolis or centrifugal) in analyzing forces.

 

No, this is wrong. The offset is not constant since it can involve a sphere.

 

The only way you can sync the clocks is using a resursive function and convert it to a Cauchy sequence to prove it converges to the correct rotational direction. Then and only then can you sync clocks. And the synchronization is a function of direction. Perpendicular, they are synched and parallel to the rotation they are max unsynched. This is fact is a cosine function and certainly not a constant.

 

This implies the partial derivatives are wrong for a rotating frame and should be using some form of the chain rule but only after the direction has been established.

[swansont]

No, this is wrong. The offset is not constant since it can involve a sphere.

 

It works for GPS.

[vuquta]

It works for GPS.

 

Exactly, I told you how they do it.

 

You have to know the rotation of the earth.

 

If you check the GPS constants and such, you will find this "value" of the speed and rotation of the earth.

It is built into all calculations.

 

But, when you boot this system, you need a method to determine the rotational speed and exact direction/axis of rotation.

 

That is what I was giving you.

[swansont]

It can't both work and not work. The frequency offset in GPS clocks is a constant.

[vuquta]

It can't both work and not work. The frequency offset in GPS clocks is a constant.

 

I never said it does not work.

 

I am saying, you must know the absolute rotation of the earth to correctly calculate the rotatiuonal sagnac. That should be obvious.

[swansont]

I never said it does not work.

 

I guess I was confused by your assertion that the frequency offset cannot be a constant. You obviously meant something else by that.

 

I am saying, you must know the absolute rotation of the earth to correctly calculate the rotatiuonal sagnac. That should be obvious.

 

And one uses the standard value of c in those calculations. So, do you have a point here?

[vuquta]

I guess I was confused by your assertion that the frequency offset cannot be a constant. You obviously meant something else by that.

 

 

 

And one uses the standard value of c in those calculations. So, do you have a point here?

 

Absolutely you must use c for those calculations. That way, depending on the direction you can use the below to calculate the t. You then compare this to the t you would have if no rotation occured. The difference between the two is the sagnac correction.

 

[math]

t = r/\sqrt{c^2+v^2-2cvcos(\theta)}

[/math]

 

So, all my logic was doing was establishing the absolute rotation of the earth since you cannot use ESP to figure it out.

Edited September 13, 2010 by vuquta

[eclectic`]

E=mc^2

where

E=energy

M=mass

c= the speed of light

 

What value of c is used in a rotating frame?

http://www.fourmilab...tein/E_mc2/www/

 

Excellent question!

 

Einstein's theory of relativity was based on spherical radiation. I question that assumption, but for spherical radiation, there is a radius and and angle that affects what you see at various points along the frame. In addition, this variation is not constant but varies with distance.