what is c^2

[gre]

A proton, and an anti-proton will collide to release both of their mass-energies, and c^2 is just considered a conversion factor. But is it possible c^2 represents something, why not? For example, a velocity of an object (like a quark) times the velocity of something else (i.e. electron), or the centripetal acceleration (m/s^2) of something times a distance (m). Is it possible to break c^2 down into something else?

How is it described in special relativity?

Edited January 10, 2009 by gre

[ajb]

The way to think of [math]c[/math] in relativity is as some universal conversion factor that allows you to equate space and time. I mean the objects [math]cdt[/math] and [math]dx[/math] (t-space, x-time) have the same units.

 

The amazing thing is that [math]c[/math] is the speed of light.

[Mr Skeptic]

c was first calculated as [math]c^2 = \frac{1}{\epsilon_0 \mu_0}[/math] where

[math]\epsilon_0[/math] is the permittivity of free space or the electric constant and

[math]\mu_0[/math] is the permeability of free space or the magnetic constant.

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There's definitely lots of meaning to c, but I doubt I know all the meaning.

[gre]

That is an interesting equation.

 

Does it imply the speed of light is dictated by vacuum permittivity, and vacuum permeability?

[ajb]

That is an interesting equation.

 

Does it imply the speed of light is dictated by vacuum permittivity, and vacuum permeability?

 

Absolutely. You can derive all this from Maxwell's equations, which are the first relativistic equations written down.

[gre]

Thanks! Next question : ).

 

Does it dictate the rate which time passes as well?

 

[math]c^2 = \frac{1}{\epsilon_0 \mu_0}[/math]

[ajb]

In the sense that it appears in just about all equations of relativity. What was you thinking of?

[gre]

I was just wondering if since time is dependent on velocity, maybe vacuum constants are as well.

[swansont]

I was just wondering if since time is dependent on velocity, maybe vacuum constants are as well.

 

That would be problematic in regard to the postulates of relativity — the laws of physics are the same in all frames and there is no preferred frame. If the constants depended on the frame, you could tell what your speed was with respect to some arbitrary frame, without measuring anything in that particular frame. And then there's the effect this would have on c.

[gre]

That would be problematic in regard to the postulates of relativity — the laws of physics are the same in all frames and there is no preferred frame. If the constants depended on the frame, you could tell what your speed was with respect to some arbitrary frame, without measuring anything in that particular frame. And then there's the effect this would have on c.

 

 

If everything scales down equally at relativistic velocities, including: mass, energy, time, and all the constants and rules. How would you know if they change at all?

 

 

At relativistic speeds does a mass's density increase?

[devrimci_kürt]

Why is c the symbol for the speed of light?

reason?

constant or celeritas ?

[swansont]

If everything scales down equally at relativistic velocities, including: mass, energy, time, and all the constants and rules. How would you know if they change at all?

 

You wouldn't. But science doesn't like ad-hoc-iness; if you can't test it, why bother assuming it?

 

At relativistic speeds does a mass's density increase?

 

In whose frame? That needs to be specified. In the mass's frame, no. In the observer's frame, yes, because of length contraction.

[ajb]

If everything scales down equally at relativistic velocities, including: mass, energy, time, and all the constants and rules. How would you know if they change at all?

 

If you cannot measure the change then is there any change? Philosophically, you should think of the only "real" things as being what you can measure (see Occam's razor). Thus, it would be completely consistent to say that there is no change.

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Why is c the symbol for the speed of light?

reason?

constant or celeritas ?

 

You can find an answer here.

 

Maxwell used V and not c.

 

Apparently the first use of c originally meant constant by Kohlrausch and Weber (1856) [1].

 

It is believed that it was Max Planck and Hendrik Lorentz who really popularised the notaion c.

 

Einstein use V in his original papers, only turning to c 1907 [2].

 

After that people started to use c to mean a variable speed and hence the "celeritas". (Mathematically, there is no reason why you would not want to think of c as "some" parameter in the Lorentz group and not really fix it*.)

 

 

*I am being lose here, remember that the Lorentz group is non-compact.

 

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[1]R. Kohlrausch and W.E. Weber, "Ueber die Elektricitätsmenge, welche bei galvanischen Strömen durch den Querschnitt der Kette fliesst", Annalen der Physik, 99, pg 10 (1856)

 

[2]A. Einstein, "On the Relativity Principle and the Conclusions Drawn From It", Jahrbuch der Radioaktivität und Elektronik 4, pgs 411--462 (1907)

Edited January 14, 2009 by ajb
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[gre]

Well mass density is something that we can determine.... If an object's density decreases as it's velocity increases maybe the mass density from your specific frame would be directly related to your "time" . For example, a photon has 0 mass and 0 density, and it's time rate is also 0.

 

The density of a hydrogen is pretty close to the density of the earth, maybe since we are all moving through space at similar velocities?

Edited January 14, 2009 by gre

[swansont]

Well mass density is something that we can determine.... If an object's density decreases as it's velocity increases maybe the mass density from your specific frame would be directly related to your "time" .

 

Hydrogen masers, cesium clocks and rubidium clocks all exhibit the same time dilation effects. This would seem to rule that conjecture out.