Re: Question regarding c^2
- From: Randy Poe <poespam-trap@xxxxxxxxx>
- Date: Sun, 14 Oct 2007 12:41:13 -0700
On Oct 14, 3:28 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'm not sure I understand the question. It represents
multiplying a number by itself.
I ask this because squaring is an operation the
results of which will be totally different depending on the
(arbitrary) units you use.
The resulting units will be the square of the
units you started with.
I can say that the area of a square is s^2,
where s is the length of a side. The number
will be totally different depending on what
units I measure s in, but nevertheless that
does not change the area. If I find out a
square has area 10,000 square cm by starting
with s = 100 cm, or A = 1 square meter by
starting with s = 1 m, that isn't a "totally
different result". One square meter and
10,000 square cm are the same thing.
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. Physical equations such as E = gamma*mc^2
better be true in all units, since units are
human inventions and two humans can choose
different units.
The relation A = s^2 for a square does not
assume particular units for s.
- Randy
.
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