JohnDenker
commented
8 years ago The aforementioned "next message" is item #199.
See also item #107 for a catalog of issues related to mass, inertial, gravitation, et cetera. See item #201 for a catalog of issues related to special relativity.
@JohnDenker wrote:
1) In hydrogen, the electrons are marginally relativistic.
2) In lead, the electrons are more relativistic. The gamma-factor is larger (compared to hydrogen).
3) The book claims that inertia has a gamma-factor whereas gravitational mass does not.
4) This cannot possibly be correct. -- In theoretical terms, it is inconsistent with the equivalence principle. -- In experimental terms, it is inconsistent with the results of Eötvös experiments that compare paraffin to lead ... inconsistent beyond the uncertainty of the experiment by many orders of magnitude.
Suggestion: This is easy to fix. There is much to gain and nothing to lose by fixing it. Executive summary:
1) Mass is mass. Inertial mass is exactly the same thing as gravitational mass. The equivalence principle guarantees it. Einstein's elevator argument.
2) The attempt to simplify the equations of motion by distinguishing inertia from gravitational mass has failed. However, this is no cause for regret, because there are other ways of simplifying the equations. For details, see next message.
This is tangential to the main discussion, but still important:
1) We agree that electrons are identical particles. They do not wear name tags. We cannot assign them social-security numbers.
2) I insist there is a concept of "shells" that applies to the electron wavefunctions in atoms. (There are also shells for the nucleon wavefunctions in the nucleus, but that's not the topic for today.)
3) This concept (suitably fleshed out) can be used as a /basis/ for describing the wavefunctions.
4) Each person is free to choose whatever basis he likes, while recognizing that others may choose differently.
We can't say that the atom "has shells" or "does not have shells". The basis vectors are not the only vectors ... and the shells are not even the only basis.
5) If I choose to use the shell basis for estimating the gamma factor for atomic electrons, you should not complain too much. The calculation can be done in any basis that seems convenient. If you wish to redo the calculation using some other basis (or no basis at all) you are free to do so. The answer will be the same no matter what basis (if any) is chosen.