# C Squared=E/M?

1. Jun 9, 2010

### TR14L

So, I understand the implications (basically, anyway) of solving the equation E=MC2 for E, and solving for M. But, what is the implied outcome of solving for C2? Just curious because the concept of C2 would imply faster-than-light velocity of something in my mind. Of course, my flawed thinking is why I'm asking in the first place :)

Thanks in advance.

2. Jun 9, 2010

### Staff: Mentor

Like any other equation, you can isolate any variable you wish in terms of the others. Think of C2 as just a parameter (a conversion factor)--it has nothing to do with anything moving faster than light.

3. Jun 9, 2010

### TR14L

Yeah, that was kind of the answer I was expecting. Just seemed odd to me that you could write it in that format.

Thanks for the speedy reply! :)

4. Jun 9, 2010

### JesseM

Note that c2 has the wrong units to be a speed anyway; in SI it has units of meters2/second2, whereas all speeds have units of meters/second (even faster-than-light speeds).

5. Jun 9, 2010

### TR14L

Good point, Jesse. Kind of a silly oversight on my part.

6. Jun 9, 2010

### Klockan3

If you use arbitrary units then squaring things do nothing. If you use natural units where C is taken to be 1 then squaring it just gives 1 again, as it is now it is just a conversion factor between our arbitrarily chosen seconds and meters which should really have the same units. Velocity is just a direction in space time so it got no units.

7. Jun 9, 2010

### JesseM

No, natural units don't get rid of the fact that c is a constant with "dimension" different from a dimensionless constant like the fine structure constant. Natural units are still a system of units just like SI, but they use units of distance and time where c happens to have a value of 1, like c=1 light-second/second, or c=1 planck length/planck time (in planck units)

8. Jun 9, 2010

### Staff: Mentor

Suppose you're going down the road at 100 km/h. Square it and you get 10000 km2/h2. That's not even a velocity. It doesn't have the right units. And even if it were a velocity, what's actually moving at that velocity?

9. Jun 9, 2010

### Klockan3

No, if you define time to have the same dimension as the spatial ones then velocity is dimensionless. It is natural to have them equal since they translate into each other, separating them is just practical since that is intuitive to us but it doesn't really make sense considering the structure.

Velocity is just the projected angle in spacetime.

10. Jun 9, 2010

### Staff: Mentor

What Klockan3 is describing is the convention taken by geometrized units. What JesseM is describing is the convention taken by Planck units. Both systems are considered "natural".

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