Why is the Constant in Mass-Energy Equivalence C^2?

[Manel]

Hello everyone,
How does Einstein established the equivalence between mass and energy, or in other words what is the fact that proves this.And why the constant is not just C but C square. Why C anyway ??

 

[Orodruin]

This can be answered on many different levels. To start with, the speed of light has the physical dimensions length/time. It simply cannot be c instead of $c^2$, the dimensions would not match.

The modern view is that c is simply a conversion factor between different units of space-time. In many situations, the easiest is to simply select units of time and length such that c = 1.

 

[Herman Trivilino]

Hello everyone,
How does Einstein established the equivalence between mass and energy, or in other words what is the fact that proves this.

There is no way to prove these types of assertions. He established it by explaining that theoretically when a light beam bounces off a mirror the mirror recoils.

It's just a statement that two things that were previously thought to be different are instead the same. There is an overwhelming amount of experimental evidence to support the assertion, so it is accepted as a fact.

And why the constant is not just C but C square.

It's a conversion factor that has to have units of velocity squared rather than velocity. Think of it this way. There are 231 cubic inches in a gallon. Why does the conversion factor have units of cubic inches instead of units of inches?

Why C anyway ??

It has to do with the relationship between electricity and magnetism. This is the speed at which electromagnetic waves travel. And the fact that neither this propagation nor anything else can be used to distinguish between a state of rest and a state of steady speed in a straight line. Or maybe the reason is deeper than that.

But anyway, it doesn't matter because you can always choose a system of units where $c=1$.

 

[jssamp]

The prove of energy matter equivalence can be seen in nuclear reactions. The enormous energy released in an atomic blast is bound up in the matter before it causes such a fuss.

If you are asking why the letter c is used instead of another letter, I believe it is for celeritas the latin word for speed.

 

[rootone]

'Why' c has a particular value (depending on chosen co ordinate system), is probably not within the realm of science.
Why is the value of Pi what it is?, it just simply is, it's not something which could up for debate.

 

[Manel]

There is no way to prove these types of assertions. He established it by explaining that theoretically when a light beam bounces off a mirror the mirror recoils.

Do you have any resources that detail this?
Also i don't get the relation beween the choice of C and the movement in a staight line?
Very grateful for your answer.

 

[Herman Trivilino]

Do you have any resources that detail this?

Wikipedia is a good place to start. Are you looking for something nontechnical?

Also i don't get the relation beween the choice of C and the movement in a staight line?

The Principle of Relativity is an assertion that these two things are the same:

1. A state of rest.
2. Motion in a straight line at a steady speed.

Galileo is credited for introducing it and you can easily find his detailed nontechnical explanations, such as the one where he describes being inside the hold of a ship. Newton included it in his treatise as his First Law. Einstein asserted it as a postulate of special relativity in 1905.That's a span of nearly three centuries.

In the decades prior to 1905, following Maxwell's treatise on electromagnetism in the 1860's, physicists were trying to find a way to incorporate the propagation of electromagnetic waves into the Principle of Relativity. Those waves travel at speed c and Einstein's 1905 treatise is now accepted as the way to do it.

One cannot understand all of this without delving into it in great depth. There are lots of books and web articles that provide the details. The Wikipedia article can get you started, but you will have to look at the references cited there, and the references cited in those references, until you find something that hits your particular sweet spot.

These are all alternatives to a formal study of physics at a college and this particular topic is typically covered by the second or third year of undergraduate study. There have been attempts to introduce it to students in their freshman year, and there may be colleges and universities still doing that. The textbook Spacetime Physics by Taylor and Wheeler was part of one of those efforts. It's a thin book written in the 1960's and is written in a conversational style. It does require a knowledge of trigonometry and calculus. I highly recommend it.

 

[Manel]

I will check the book for sure. Thanks a lot for your help. I really appreciate that.