Is hf=mc2 a Valid Equation in Physics?

[adamh]

Hi all you physicists out there.

I am just a physics enthusiast and have a question. I have seen this equation (hf = mc2) bandied about at a lot of places. Recently I read Mark Perakh's following passage in an essay where he discredits this equation (the essay is a criticism on Gerald Schreoder). Here's the passage

On page 38 of his book Schroeder suggested the following equation:

hf=mc2......(1)

where h is Planck's constant, f is the frequency of deBroglie's wave for a particle, m is the particle's mass and c is speed of light.

Whereas equation (1) is absurd, it is easy to figure out how Schroeder derived it. He read somewhere about the following correct equations [4]:

1) E=hf.....(2)

and 2) E=mc2......(3)

Equation (2) was originally suggested by Planck (in 1900) for the quantum of energy emitted by a black body. In 1905, Einstein applied that equation to the energy of photons regardless of whether they are emitted, traveling or absorbed by a material. In 1923 de Broglie suggested to expand the application of that equation to all particles, either massless as a photon or having a rest mass m. As to equation (3), it is probably the most widely known equation of science derived by Einstein in 1905 as a part of his special theory of relativity.

In both equations (2) and (3) E denotes energy of a particle. Obviously lacking proper understanding of these two equations, and seeing the same letter E on the left side of both, Schroeder mechanically combined the equations (2) and (3) into one equation (1).

Unfortunately for Schroeder, he obviously did not know that E in equation (2) and E in equation (3), while both denoting the energy of a particle, actually denote two different energies. E in equation (2) denotes the variable energy of a moving particle, related to that particle's momentum. E in equation (3) is a constant for a given particle, which denotes the so-called rest energy. These two types of particle's energy have little to do with each other. The absurdity of Schroeder's equation (1) is immediately obvious when we notice that it equalizes a variable quantity to a constant. Indeed, the frequency f of de Broglie wave for a particle is not a fixed constant but depends on the particle's momentum, i.e. on its velocity.

Schroeder could have easily realized the senselessness of his equation (1) if he thought for a minute what are the values of the quantities in that equation.

Planck's constant equals about h=6.626.10-34 J.s while the speed of light equals c=2.997.108 m/s. Let us apply Schroeder's equation (1), for example, to the electron. The mass of an electron is close to 9.1x10-31kg. Then the right side of equation (1), i.e. the electron's rest energy is about 8.17x10-14 Joule, or about 5.1x105 eV (electron-volt). Hence, if Schroeder's equation (1) were correct, all electrons in the world would always have the same energy of about 5.1x105 eV. To have such level of energy, free electrons must be accelerated by a voltage a little more than half a million volt. Of course, different electrons (as well as any other particles) actually possesses different levels of energy in a wide range rather than all having the same energy of about half a million electron-volt.

What do you guys say? Is Perakh right or is hf=mc2 is a valid physical construct?

Cheers.

Adam

 

[pervect]

Hi all you physicists out there.
I am just a physics enthusiast and have a question. I have seen this equation (hf = mc2) bandied about at a lot of places. Recently I read Mark Perakh's following passage in an essay where he discredits this equation (the essay is a criticism on Gerald Schreoder). Here's the passage
What do you guys say? Is Perakh right or is hf=mc2 is a valid physical construct?
Cheers.
Adam

Take a look at

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

The big question is whether Schroder is guilty of simply poor word choice or whether he is about to make some further unfounded leap. One cannot tell from the material presented which is the case, though it is very common for a semantic confusion over the issue of "rest mass vs invariant mass' to lead to further, more serious, errors.

 

[adamh]

hf=mc2

Thanks for the reply. Ignoring for a second what Schroeder is going to do with the construct, I just wanted to know if Perakh is right that hf=mc2 cannot be derived from E=hf and E=mc2.

Thanks

Adam

 

[rbj]

Thanks for the reply. Ignoring for a second what Schroeder is going to do with the construct, I just wanted to know if Perakh is right that hf=mc2 cannot be derived from E=hf and E=mc2.
Thanks
Adam

Adam, can you try to use the tex markup so we can read your equations?

i take it that you're saying that Perakh is saying that Schroeder is saying that

$$E = m c^2$$

and

$$E = h \nu$$

and equates them to say

$$h \nu = m c^2$$ .

the issue simply is what does Schroder mean by $m$ and by $E$? if he means "rest mass" and "rest energy" it's wrong. if he means total relativistic mass and energy, he right. if fact, in my 30 year old physics book, this very equating of the two E's is what is done to derive the deBroglie wave velocity and the wave equation and eventually make a stab at Schrodinger's Eq.

r