Does the equation E=mc2 prove that energy and mass are equivalent?

[DavidF]

Please excuse my ignorance re. this subject. I know that there will be an obvious answer to this question (and that it has probably been asked a thousand time before) - apologies in advance.

Question is concerning e=mc2

As I understand it, the essence of this equation is that energy and mass are equivalent. In Einstein's own words: "It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamilar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned before. This was demonstrated by Cockcroft and Walton in 1932, experimentally."

I also understand from previous reading that as an object (with mass) accelerates towards c it takes more and more energy until it requires an infinite amount of energy for any mass to travel at c.

So, if a photon has energy, then according to e m equivalence it must have mass - but it takes an infinite amount of energy for a body with mass to travel at c - which is obviously the definition of a phot.

Please help me understand.

Again, I am sorry for this stumbling question.

Cheers

D

 

[The hermit]

The Einstein's equation is right for inert particle only. Yet a photon has a kinetic energy only, so a nil energy at pause.
The complete equation is E²=m²c4+p²v²

 

[DavidF]

Cheers...knew it would be straight forward...

 

[jtbell]

The complete equation is E²=m²c4+p²v²

Correcton: E^2 = m^2 c^4 + p^2 c^2

or as I prefer to write it, E^2 = (mc^2)^2 + (pc)^2

to reflect more clearly that mc^2 and pc both have units of energy.

 

[pmb_phy]

Please excuse my ignorance re. this subject. I know that there will be an obvious answer to this question (and that it has probably been asked a thousand time before) - apologies in advance.

Question is concerning e=mc2

As I understand it, the essence of this equation is that energy and mass are equivalent. In Einstein's own words: "It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamilar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned before. This was demonstrated by Cockcroft and Walton in 1932, experimentally."

I also understand from previous reading that as an object (with mass) accelerates towards c it takes more and more energy until it requires an infinite amount of energy for any mass to travel at c.

So, if a photon has energy, then according to e m equivalence it must have mass - but it takes an infinite amount of energy for a body with mass to travel at c - which is obviously the definition of a phot.

Please help me understand.

Again, I am sorry for this stumbling question.

Cheers

D

Once again we're set back to the question which must be asked a priori before an answer can be given to your question. If by "mass" you are referring to "proper mass" then the proper mass "m" of the photon is zero due to the relationship E^2 - (pc)^2 = [mc^2]^2. Since for a photon E = pc it follows that m = 0. However if by "mass" you mean "relativistic mass" (aka "inertial mass") then yes. The photon has an inertial mass, "m" of m = p/c = E/c^2.

For all the gruesome details please see
http://www.geocities.com/physics_world/mass_paper.pdf

Pete

 

[Doc Al]

The complete equation is E²=m²c4+p²v²

That should be: E²=m²c4+p²c²

(jtbell gave a complete correction, but for some reason Latex is not displaying.)

 

[loom91]

This is why it is not adviced to use the word mass in relativistic physics until you are sure you know what you are talking about. Either say rest mass or inertial mass.