[quote=xilman;169227]I disagree. I believe that converting mass into energy is [B]exactly[/B] as simple as it is sometimes portrayed.

In my view, mass [B]is[/B] energy. No conversion is necessary. What is necessary is a scaling factor to convert between units of kilograms and units of joules. That conversion factor is c^2, but we're converting the units in which we measure a quantity, not converting the quantity itself.


Paul[/quote]
A recent problem was posed on Physics Forums:
A particle decays into two photons, which are observed to
have energies of 500 GeV and 600 GeV, and their directions were
60 degrees apart. What was the rest mass of the particle?

The "Homework Helpers" suggested choosing the x axis to be
the direction of the original particle.

I suggested taking the momenta of the photons to be
500[B]i[/B] and 600 (cos(60)[B]i[/B] + sin(60)[B]j)[/B]
and finding the square of the magnitude.

Admittedly that wasn't my only contribution that went over their
heads, but I have been banned for ten days:(((

Of the three, I think it was probably this contribution that got you banned:
[url]http://www.physicsforums.com/showpost.php?p=2200186&postcount=10[/url]

[QUOTE=xilman;169227]I disagree. I believe that converting mass into energy is [b]exactly[/b] as simple as it is sometimes portrayed.[/QUOTE]

"Mass is just energy at rest"

[quote=davieddy;139254]Onomatopea (can't spell it)[/quote]
Shouldn't that be as it sounds?

[QUOTE]MAFFS - The study of numbers.[/QUOTE]
The mispronunctiation I can't stand is is the singular "Math".

[quote=plandon;174446]Shouldn't that be as it sounds?[/quote]

The correct spelling is "onomatopoeia". (My English teacher always used to get it wrong.)

[quote=plandon;174448]The mispronunctiation I can't stand is is the singular "Math".[/quote]

That's the American way of doing things.

[QUOTE=ewmayer;174418]"Mass is just energy at rest"[/QUOTE][b]No![/b] Energy [b]is[/b] mass. A photon has mass even though it is not at rest in any reference frame. If you want to rescue your statement, you should rephrase it as (the rather tautologous) "Rest mass is just energy at rest".

Consider how in practice one can measure the mass of a system, that is to give the word "mass" a physical meaning. There are two fundamental ways --- measuring its acceleration under a force (the inertial mass) and the effect it has on local test masses (the gravitational mass). Very precise measurements have shown that both forms of mass are independent of the internal state of the systems and that the two forms of mass are strictly proportional to each other.

Exercise: use similarly precise statements to show how the word "energy" is defined and how "energy" may be given a physical meaning through measurement of the "energy" of a system.


Paul

[quote=xilman;174484]

Consider how in practice one can measure the mass of a system, that is to give the word "mass" a physical meaning. There are two fundamental ways --- measuring its acceleration under a force (the inertial mass) and the effect it has on local test masses (the gravitational mass).
Paul[/quote]

It wasn't until I started teaching Newton's Laws to schoolchildren
that I fully realized how circular they were, and how they obscured crucial,
simple, and empirical facts of Classical Mechanics.

Eddy's Laws:

1) There are frames of reference in which ALL isolated particles
travel with constant velocity. (Intrigingly their orientation is
fixed relative to the stars).

In such a frame:

2) When two particles A and B interact, their changes in velocity are
in opposite directions and the magnitude of the changes are in a
constant ratio AkB.

3) AkC = AkB * BkC
This enables us to ascribe a "mass" (inertial) to each particle,
s.t. massA*accelerationA = -massB*accelerationB

Define the "force" exerted by A on B as massB*accelerationB
So AforceB = - BforceA.

4) Forces superimpose.

David

[QUOTE=xilman;174484][b]No![/b] Energy [b]is[/b] mass. A photon has mass even though it is not at rest in any reference frame. If you want to rescue your statement, you should rephrase it as (the rather tautologous) "Rest mass is just energy at rest".[/QUOTE]

I was speaking tongue-in-cheekily, Paul - thoughts of a certain [i]Dead parrot sketch[/i] were in my mind: "He's really quite energetic, he's just resting", that sort of thing.

Anyway, as well you know, a photon has no rest mass, reflective of the fact that it can never be brought truly to rest without being destroyed (I mean destroyed in the sense of it losing its photonic identity, by being converted into some other form of mass/energy). One could argue that it has relativistic mass m[sub]r[/sub] proportional to its energy, but the usual m[sub]r[/sub] = gamma(v/c) * m[sub]0[/sub] formula gives infinity * 0 (or perhaps best to just say "undefined", since one can also argue that the rest mass of a photon is undefined rather than zero), so at that point one must *define* the relativistic mass by rearranging Herr Einstein's famous formula as m[sub]r[/sub] := E/c[sup]2[/sup]. For a photon to contribute to the *rest* mass of something, it has to be brought to rest (and thus destroyed/converted), so in that sense my quip was true. The more-accurate "Rest mass is just energy at rest" doesn't roll off the tongue as well, due to the repetition of the word "rest".

[quote=ewmayer;174506]I was speaking tongue-in-cheekily, Paul - thoughts of a certain [I]Dead parrot sketch[/I] were in my mind: "He's really quite energetic, he's just resting", that sort of thing.

Anyway, as well you know, a photon has no rest mass, reflective of the fact that it can never be brought truly to rest without being destroyed (I mean destroyed in the sense of it losing its photonic identity, by being converted into some other form of mass/energy). One could argue that it has relativistic mass m[sub]r[/sub] proportional to its energy, but the usual m[sub]r[/sub] = gamma(v/c) * m[sub]0[/sub] formula gives infinity * 0 (or perhaps best to just say "undefined", since one can also argue that the rest mass of a photon is undefined rather than zero), so at that point one must *define* the relativistic mass by rearranging Herr Einstein's famous formula as m[sub]r[/sub] := E/c[sup]2[/sup]. For a photon to contribute to the *rest* mass of something, it has to be brought to rest (and thus destroyed/converted), so in that sense my quip was true. The more-accurate "Rest mass is just energy at rest" doesn't roll off the tongue as well, due to the repetition of the word "rest".[/quote]

The most helpful equation (a la Physics Forums:smile:) to remember is

E[sup]2[/sup] = (pc}[sup]2[/sup] + (m[sub]0[/sub]c[sup]2[/sup])[sup]2[/sup]

[QUOTE=ewmayer;174506]I was speaking tongue-in-cheekily, Paul - thoughts of a certain [i]Dead parrot sketch[/i] were in my mind: "He's really quite energetic, he's just resting", that sort of thing.[/quote]I guessed as much, but there are enough folk who are badly confused about what Albert had to say that it seemed worthwhile drawing the distinction.

[quote]Anyway, as well you know, a photon has no rest mass, reflective of the fact that it can never be brought truly to rest without being destroyed (I mean destroyed in the sense of it losing its photonic identity, by being converted into some other form of mass/energy). One could argue that it has relativistic mass m[sub]r[/sub] proportional to its energy, but the usual m[sub]r[/sub] = gamma(v/c) * m[sub]0[/sub] formula gives infinity * 0 (or perhaps best to just say "undefined", since one can also argue that the rest mass of a photon is undefined rather than zero), so at that point one must *define* the relativistic mass by rearranging Herr Einstein's famous formula as m[sub]r[/sub] := E/c[sup]2[/sup]. For a photon to contribute to the *rest* mass of something, it has to be brought to rest (and thus destroyed/converted), so in that sense my quip was true. The more-accurate "Rest mass is just energy at rest" doesn't roll off the tongue as well, due to the repetition of the word "rest".[/QUOTE]Two things:

a) a photon undoubtedly has inertial mass (or, more precisely, momentum) and you do not need quantum mechanics to show it theoretically. Measuring it experimentally, by photon scattering experiments for instance, shows that QM is required. Experiment also shows that if something emits a photon, the (inertial) mass of the initial something and the final something differ by precisely the predicted mass of the photon.

b) I concede that the gravitational mass of a photon, or collection of photons, has not yet been measured by experiment (as far as I know). Given that every experiment yet conducted suggests very strongly that inertial masses and gravitational masses are strictly proportional, I doubt that any serious physicist believes that a photon (or collection of photons) does not have a gravitational mass too.

(The famous 1917 eclipse observation indicated that photons are influenced by a "gravitational field" but that in itself was no great surprise. Newtonian gravity also predicts the same effect. The difference between the two theories is that GR predicts twice the deflection as Newtonian gravity. The observations were much better in accord with GR and, to that extent, they suggested that Einstein came closer to "the truth" than Newton.)



Paul