Why does c have to be the speed of light

[drinkey]

In e=Mc2 Does c have to be exactly the speed of light? Can it not be a slightly bigger or smaller number? Or does C squared simply represent an enormous number?

 

[harrylin]

In e=Mc2 Does c have to be exactly the speed of light? Can it not be a slightly bigger or smaller number? Or does C squared simply represent an enormous number?

Welcome to physicsforums!

Your question has been thoroughly discussed recently, here:
https://www.physicsforums.com/showthread.php?t=461451

 

[tiny-tim]

welcome to pf!

hi drinkey! welcome to pf!

(try using the X² button just above the Reply box )

In e=Mc2 Does c have to be exactly the speed of light?

yes

c² is really only a conversion factor, between the units for energy and speed

if, instead of the metres and kilograms in the SI system, we used light-seconds and a similar light-based mass unit (such as is used in studying black holes), then the equation would just be e = m

 

[clamtrox]

Light moves at speed c because photons are massless.

 

[drinkey]

Thanks for your answer TT. I read the thread suggested but now my brain hurts! I am a novice that did not do physics at school but am now fascinated by the subject. I saw this somewhere where a question was asked about the energy in a kg of matter (rest)

This is determined by Einstein's equation E = mc2, where c = velocity of light = 3 x 108 meters/sec. So c2 = 9 x 1016. For 1 kg of mass therefore the equivalent energy is 9 x 1016 Joules, for 1 gram it is 9 x 1013 Joules.

Note units, in the SI system energy is in Joules, mass in kg, distances in meters. If you keep to these units you will get consistent results.

So I get the conversion I still don't know why (above example) it has to be 1016 and not say 1015...

 

[harrylin]

[..] I read the thread suggested but now my brain hurts! I am a novice that did not do physics at school but am now fascinated by the subject. I saw this somewhere where a question was asked about the energy in a kg of matter (rest)

This is determined by Einstein's equation E = mc2, where c = velocity of light = 3 x 108 meters/sec. So c2 = 9 x 1016. For 1 kg of mass therefore the equivalent energy is 9 x 1016 Joules, for 1 gram it is 9 x 1013 Joules.

Note units, in the SI system energy is in Joules, mass in kg, distances in meters. If you keep to these units you will get consistent results.

So I get the conversion I still don't know why (above example) it has to be 1016 and not say 1015...

The best answer is, I think the one by DrStupid:

https://www.physicsforums.com/showthread.php?p=3760256#post3760256

Now, this does require mathematical insight, together with know laws of physics. But then, your question was a mathematical question.

I'll try to clarify drStupid's summary:

E = m * constant, let's call that constant k. And you ask why should k be equal to c*c.

If E=m*k, then a change of energy dE = dm*k

A change of mass dm is given by Newton's force law (which is still valid):
Force is proportional to a change of momentum per time, and momentum is mass times speed. Maybe you did get that far with physics lessons.

In handy units that law is written as: F = d(m*v)/dt

After a little math drStupid got from these two equations that for a moving body, its inertial mass (resistance against acceleration) increases as follows:

m= m₀ / √ (1- v²/k)

That can only be correct if the moving body can just not be accelerated to c, which is the limit speed. Then k=c². (You can try what happens for other values of k!).

So, if the limit speed is c (and that is the case according to special relativity, because light has no rest mass), then the energy formula constant must be c².

And that, I hope, answers your question.