Is There a Discrepancy Between Inertial and Gravitational Mass in Relativity?

[K8181]

I have a fundamental question. I am reading this modern physics book, and it says that an electron and a proton that are released and come together into a bound state release a photon. Fine. But the explanation given is that the sum of the individual masses of the proton and electron is greater than the mass of the bound system, and that the extra rest mass was converted to energy in the release of the photon. I am confused because it seems that an equally good explanation is that the electron and proton have a potential energy when they are apart, and it is this energy that is released as a photon. Here there would be no conversion of mass into energy needed to save conservation of energy. Does the bound system behave as though it has less mass than the constituent particles, or is the second explanation just as good? Please help.

 

[LURCH]

Hello and welcome to the Forums K8181!

I think that a fundamental part of your question may be flawed. This statement:

...the electron and proton have a potential energy when they are apart, and it is this energy that is released as a photon. Here there would be no conversion of mass into energy needed to save conservation of energy...

seems self-contradicting. If there is potential energy, and that energy has mass, and that energy is converted to EM radiation, so that its mass is lost from the electron-proton system, then the system has lost mass, and that mass is the photon, so the mechanism you propose is still conversion of mass from the atom to energy in the photon, isn't it?


P.S.
You should only post a thread once; just pick the forum that seems to best suit your topic, and if the Mentors think you'd get better results in a different Forum, they'll move it for you.

 

[K8181]

Yes, that does sound self-contradicting. Let me try to clarify. What I have proposed with the potential energy being released as a photon seems to me as energy being converted to energy, if you will. Sure you could think of the potential energy as mass, but that won't solve my problem. Consider the energy before and after. Before, there is the rest mass energy of each particle m1 and m2, and the potential energy due to their interaction (they "know" about each other). After, there is a bound system with some total mass M, and a photon that was released. The book says that M < m1 + m2 because the photon took away some mass, but I don't see why this is necessary. Why can't M = m1 + m2 and the potential energy "create" the photon?

 

[pmb_phy]

Please note: The answer to this question is dependant on the definition of the term "mass." Since there are two commonly used definitions then there are two ways to describe this. But under either definition the mass of the system remains constant. What changes is the makeup of the system.

Simply stated - You start off with mass in the form of potential energy. That mass is converted to a photon which also has a mass m = E/c^2.

I have a fundamental question. I am reading this modern physics book, ...

which book is that?

...and it says that an electron and a proton that are released and come together into a bound state release a photon. Fine. But the explanation given is that the sum of the individual masses of the proton and electron is greater than the mass of the bound system, and that the extra rest mass was converted to energy in the release of the photon.

I don't particularly like that description myself.

I am confused because it seems that an equally good explanation is that the electron and proton have a potential energy when they are apart, and it is this energy that is released as a photon.

Sounds good to me.

Here there would be no conversion of mass into energy needed to save conservation of energy.

I disagree since in this context the term "converted" means " to change from one form or function to another."

Does the bound system behave as though it has less mass than the constituent particles, or is the second explanation just as good? Please help.

Sorry but I don't understand what that means. Do snowflakes behave differently than a snowball? Please clarify.

This might be of some help to you
http://www.geocities.com/physics_world/sr/nuclear_energy.htm

Peted

 

[K8181]

Thanks for the website, it was very helpful and I think I am understanding this better. But I am still a little bothered...

Consider a case of spontaneous fission. Before the split, the forms of mass-energy are the rest masses of the constituent particles, and the potential energy. After, there is the rest mass of each particle and their kinetic energy.

I am learning that you can look at all mass-energy as mass, in which case mass is conserved, or all mass-energy as energy, in which case energy is conserved. So say we choose the mass option. Then one would say that the original particle, before it splits, has a mass greater than the sum of the rest masses of the constituent particles because of the potential energy being counted as mass. My question is, does the particle really act like it has that extra mass? Say, under gravity? I mean, we can call potential energy "mass" if we want, but does it really behave like extra mass?

 

[K8181]

ps

The book is Modern Physics for Scientists and Engineers by John R. Taylor and Chris D. Zafiratos.

 

[pmb_phy]

My question is, does the particle really act like it has that extra mass? Say, under gravity? I mean, we can call potential energy "mass" if we want, but does it really behave like extra mass?

Excellant question: Consider the 3 aspects of mass

(1) Inertial mass - that aspect of mass which opposes changes in momentum
(2) Passive gravitational mass - that aspect of mass which gives a body weight or allows gravity to act on it
(3) Active gravitational mass - analogous to electric charge, i.e. that aspect of mass which generates a gravitational field (in fact there is an analogy in general relativity called gravitomagnetism).

Since you speak of kinetic energy contributing to the mass of a particle then you're speaking of inertial mass aspect I think and that definition which some people call relativisitic mass (which I simply call "mass").

According to aspect (1) given two particles with the same proper mass (aka rest mass) the one with the greater kinetic energy will be able to oppose changes in momentum more than the one with less kinetic energy. Heuristically you can think of that as saying "it gets harder to push as it moves faster." Mass in this sense is defined such that mv is a conserved quantity. From that definition it can be shown that m is also a conserved quantity (no need to invoke conservation of energy to prove this either!)

According to aspect (2) a moving particle weighs more than an identical particle which is at rest.

According to aspect (3) the faster a particle is moving the stronger the gravitational field generated.

Pete

 

[K8181]

So is it possible for a particle to have inertial mass and gravitational mass that are not equal? I am recalling Einstein's equivalence principle, but maybe I am missing some information? I am very curious about this.

 

[K8181]

This thread has greatly helped me clarify my question. I am starting a new thread that is more to the point. Feel free to offer more insight there...and thanks for all the help.

K

 

[pmb_phy]

This thread has greatly helped me clarify my question. I am starting a new thread that is more to the point. Feel free to offer more insight there...and thanks for all the help.

K

There is much more at

http://www.geocities.com/physics_world/sr/sr.htm

There is a large paper on this topic that I wrote at

http://www.geocities.com/pmb_phy/

See "On the concept of mass in relativity"

So is it possible for a particle to have inertial mass and gravitational mass that are not equal?

Relativity states that they can't be unproportional. But I guess relativity could be wrong if that's what you mean. There is no evidence to that though.

I am very curious about this.

Cool! Admirable attitude

Pete