Energy, Mass, Light: Unveiling the Relationship

[jnorman34]

TL;DR

Why “c” is the relationship between energy and mass?

A stupid layperson question-
while it is clear that any given quantity of mass comprises an enormous quantity of energy, I have wondered how could it be that the speed of light is involved in that relationship, rather than some very large, but random constant. It just seems so odd to me that c would just happen to be that constant. Yes, I understand the basic derivation of the equation stems from other equations which include c, but still, it boggles my mind that e, m, and c would be fundamentally related in this way. It is like some insight into the nature of reality that we “know” on the mathematical level but not quite on a philosophical or zen level. Perhaps someof you would share your thoughts on this. Thanks.

 

[Dale]

Sorry to disappoint but I don’t think there is any zen hiding here. It is just an artifact of your unit system. If you measure energy and mass in different units then you need a conversion factor with dimensions of speed squared. The speed of light is the only universal speed. So it has to be some multiple of $c^2$

 

[jnorman34]

Thank you for responding. I just wonder why speed is related to mass/energy.

 

[PeterDonis]

I just wonder why speed is related to mass/energy.

It isn't. As @Dale said, it is just that our "conventional" system of units has the units of energy being the units of mass times speed squared. So if you want a conversion factor between mass and energy in these units, it has to be the square of some invariant speed, and there is only one invariant speed, $c$.

However, there is no requirement to use different units for mass and energy, and in fact many areas of physics use "natural" units in which the units of energy and mass are the same. These units are often described as units in which $c = 1$, but a better description would be that they are units in which "speed" has no dimensions.

 

[Dale]

Thank you for responding. I just wonder why speed is related to mass/energy.

It is speed squared. By definition kinetic energy is $\frac{1}{2} mv^2$ so energy has units of mass times speed squared. So any conversion factor between mass and energy must be a speed squared.

 

[phinds]

Thank you for responding. I just wonder why speed is related to mass/energy.

when mass is converted to "energy" what that really means is that it is converted to radiation. Radiation moves at c and energy is proportional to velocity. However, when something is moving twice as fast, its energy is not twice as much it is 4 times as much. Thus it has to be c^2. And, of course, that also makes the units work out properly in the system of units you have chosen

EDIT: Ah, I see Dale beat me to it. He does that, dammit !

 

[PeterDonis]

Radiation moves at c and energy is proportional to velocity.

Sorry, but this is not valid reasoning. The energy of light, or any other radiation, is not proportional to its velocity, because it moves at the same velocity regardless of its energy.

I see Dale beat me to it.

@Dale did not "beat" you to anything, strictly speaking, since his reasoning is valid but yours is unfortunately not (see above).

 

[jnorman34]

Thank you, gentlemen - that has been helpful.

 

[phinds]

Sorry, but this is not valid reasoning. The energy of light, or any other radiation, is not proportional to its velocity, because it moves at the same velocity regardless of its energy.
@Dale did not "beat" you to anything, strictly speaking, since his reasoning is valid but yours is unfortunately not (see above).