Solving E=MC2: What Does C2 Imply?

[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.

 

[Doc Al]

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.

 

[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! :)

 

[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).

 

[TR14L]

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

 

[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.

 

[JesseM]

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.

No, natural units don't get rid of the fact that c is a constant with "dimension" different from a dimensionless constant like the ttp://en.wikipedia.org/wiki/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)

 

[jtbell]

Just curious because the concept of C² would imply faster-than-light velocity of something in my mind.

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?

 

[Klockan3]

No, natural units don't get rid of the fact that c is a constant with "dimension" different from a dimensionless constant like the ttp://en.wikipedia.org/wiki/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)

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.

 

[Dale]

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".