Is PBS's Layman Explanation of E=mc^2 Accurate?

[trewsx7]

Newbie here with a question on an article I read on the PBS website regarding the e=mc^2 equation and whether or not it is factualy accurate (yet extremeley simplified) for a non-mathematical layman's description of the equation.


Regarding the reasoning for the speed-of-light in the equation, the article in part reads:

"So why would you have to multiply the mass by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a piece of matter to pure energy, the resulting energy is by definition moving at the speed of light. Pure energy is electromagnetic radiation—whether light or X-rays or whatever—and electromagnetic radiation travels at a constant speed of roughly 670,000,000 miles per hour."


The article, of course, then explains the reasons for squaring and so forth, but in regards to the aforementioned paragraph on c, is it correct on a layman's level? If not, what parts of the preceding description is wrong (or right)?

Thanks

 

[lbrits]

Roughly. There's an explanation over at http://en.wikipedia.org/wiki/Mass–energy_equivalence under the section "Einstein: Mass–energy equivalence".

The derivation I remember has to do with the work energy theorem, but I can't for the life of me remember it. I'll have to consult an old first-year text.

 

[tiny-tim]

… the article in part reads:

"So why would you have to multiply the mass by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a piece of matter to pure energy, the resulting energy is by definition moving at the speed of light."

… but in regards to the aforementioned paragraph on c, is it correct on a layman's level? If not, what parts of the preceding description is wrong (or right)?

Hi trewsx7!

I think that part of the article is rubbish.

The simple explanation is that energy has dimensions of mass times velocity-squared.

In Newtonian dynamics, energy was proportional to 1/2mv², which is zero for zero velocity (so the rest energy is zero), and already incorporates a velocity-squared.

In relativity, energy is proportional to 1/√(1 - v²/c²), which is not zero for zero velocity (so the rest energy is not zero), and is a dimensionless number, and so must be multiplied by a velocity-squared constant, which is obviously the rest energy.

Furthermore, 1/√(1 - v²/c²) = 1 + 1/2v²/c² for small v, so the constant must be mc² to agree with Newtonian dynamics and obvious low-speed experiments.

So the rest energy must have a factor of c².

 

[nrqed]

Newbie here with a question on an article I read on the PBS website regarding the e=mc^2 equation and whether or not it is factualy accurate (yet extremeley simplified) for a non-mathematical layman's description of the equation.


Regarding the reasoning for the speed-of-light in the equation, the article in part reads:

"So why would you have to multiply the mass by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a piece of matter to pure energy, the resulting energy is by definition moving at the speed of light. Pure energy is electromagnetic radiation—whether light or X-rays or whatever—and electromagnetic radiation travels at a constant speed of roughly 670,000,000 miles per hour."


The article, of course, then explains the reasons for squaring and so forth, but in regards to the aforementioned paragraph on c, is it correct on a layman's level? If not, what parts of the preceding description is wrong (or right)?

Thanks

To me this sounds completely wrong. The equation is valid even when massive particles are produced and they do not move at the speed of light at all. I am sorry, but it sounds like someoen trying to justify an equation by using a totally unjustified argument. Sometimes people use "layman arguments" to explain some aspects of physics which are more or less correct but still useful to get the basic idea across. This example is completely wrong even at the simplest qualitative level. I am surprised of that from PBS.

 

[pmb_phy]

Newbie here with a question on an article I read on the PBS website regarding the e=mc^2 equation and whether or not it is factualy accurate (yet extremeley simplified) for a non-mathematical layman's description of the equation.

Note: That expression only holds in the special case of a closed system. The mass and inertial energy of a rod under stress may not obey that relationship.

Pete