Re: Question regarding c^2

On Oct 14, 12:28 pm, drblitzkr...@xxxxxxxxx wrote:
Hey,

What is the significance of squaring the speed of light? c^2 is used
so much in areas such as relativity, but what does the act of
"squaring" represent? I ask this because squaring is an operation the
results of which will be totally different depending on the
(arbitrary) units you use. Ie., I just presumed until now that
squaring c will cause a larger dilation in its value if you use a
smaller unit, such as km/h, vs. a larger unit, such as miles/h. What
if you make up a unit of speed that is equal to c? Then the speed of
light would be 1, and squaring c would then just leave you with c
again, so no need for the "^2". When scientists write "c^2", are they
implying necessarily a certain unit, such as km/h?

No, but c does have to have dimensions of distance over time,
regardless of what units are chosen. Then mc^2 has dimensions of
mass*distance^2/time^2, which is energy.

You are certainly free to choose a unit if you want where c has a
numeric value of 1, but it still has dimensions. For example, let's
choose our unit of time to be the second, and our unit of distance to
be the light-second (the distance light travels in one second). Then
the value of c is one light-second per second. If we choose kilograms
as a unit of mass, our unit of energy then becomes the kg-
lightsecond^2/second^2. So you still have to use c^2 to come out with
units of energy.

.

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