Brad Klee <bradklee(a)gmail.com> wrote:
> If you haven't gone to college, shouldn't you be more inclined to
> argue with the entitlement crowd? What gives them the right to vote
> and not you?
Good question. Thanks for asking it. My answer is complicated,
and has little to do with math or even physics, so I will respond
off-list, probably this weekend. (Anyone else who wants to be CCd
on my reply, please email me. Thanks.)
> The gist of Ralston's argument is that classical quantities energy
> and mass are not useful in the quantum regime, and that they should
> not appear in formal equations of quantum mechanics, such as
> Schroedinger equation.
My understanding is that mass and energy are equally useful concepts
at every scale. The only major issues I can think of offhand are
whether mass and rest mass should be distinguished from each other,
and whether the energy of the vacuum can really be usefully defined
as zero.
> Now if we measure photoelectric nu2 on a Hydrogen standard nu1, we
> get photoelectric band gap E2 relative to hydrogen standard E1,
> *without mentioning Planck's constant*.
For any concept, no matter how useful, we can always work around it,
using circumlocutions. In some cases, which things are considered
fundamental is completely arbitrary. In other cases, working around a
lack would be as awkward as abolishing money and using barter instead.
I think the Planck constant is somewhere between those two extremes.
> That is to say, the photo-electric effect is another version of the
> Rydberg Hydrogen experiment (with a hell of a lot more uncontrolled
> variables and uncertainties. Also with less of an intelligible
> level structure.).
We could certainly use the Rydberg constant in place of the Planck
constant, but most equations would be more unwieldy.
> Once the hangup with photoelectric effect is sidestepped, there is
> still often an objection about electron mass. This is a concept
> that makes some amount of sense in terms of the oil drop experiment.
Are you sure? I thought Millikan was balancing the force from the
electron's *charge* in a known electric field against the force from
the *oil drop's* mass in a known gravitational field. You can't get
the electron's mass from that.
Measurement of how much a moving isolated electron's trajectory is
bent by a known electric or magnetic field gives you the electron's
charge-to-mass ratio. (And, as a side effect, invents television.)
And if you already know the charge, it gives you the electron's mass.
Assuming those two experiments were the only ways of measuring those
quantities, the electron's charge-to-mass ratio would always be known
to a higher precision than its mass. Similarly, each planet's GM
(product of the gravitational constant and the planet's mass) is known
to a much higher precision than either G or M alone. I assume NASA
uses each planet's GM for navigation. But that's no reason to deprecate
the concept of a planet's mass. Or of an electron's rest mass.
> Again, this is not a direct measurement of electron mass, it is
> an inference of electron mass from classical physics involving
> gravitational and electric fields. Thus the extracted parameter
> is a mess of other constants besides m_e.
I didn't know there was any issue about an electron's rest mass (other
than, as with every measured quantity, the measurement having some
error). There is an issue about its charge being larger close up,
apparently without limit. It can be modeled as an extreme negative
charge surrounded by a cloud of positive charge which almost but not
quite cancels it out.
I can understand objecting to the concept of the classical electron
radius, which comes from assuming the electron's rest mass "comes
from" the energy it would classically take to assemble infinitely many
infinitesimal like charges (whose total charge sums to that of an
electron) from an infinite distance into a small radius. There's a
unique value for which the numbers balance, and that's the classical
electron radius. Very likely it has no physical significance
whatsoever.
> Section 2 of the paper does an admirable job showing that Planck's
> constant (1900) was over-promoted relative to the fine structure
> constant (Sommerfeld 1916), and and the Compton wavelength (1923).
> It all drives to the conclusion of equation (24) that: including
> Planck's constant and electron mass introduces an extra, perhaps
> delusional, degree of freedom.
I'm not convinced that it's meaningful to count degrees of freedom
in a system in which things can't vary.
> In electron experiments, we only need Compton wavelength to
> set scale, and fine structure constant to search through the
> perturbation hierarchy (alpha as an expansion parameter is
> discussed in most QM textbooks).
Perhaps we can do without the Compton wavelength too, and only count
dimensionless parameters as degrees of freedom.
> This analysis of quantum pre-history doesn't exactly answer the
> question about generality.
It would certainly be nice if we could contact another advanced
civilization and compare notes. I would bet that they would also have
the concept of the Planck constant. And the concept of prime numbers.
I'd love to be proven wrong.
I'm reminded of the Hugo and Nebula winning "Story of Your Life," a
1998 science fiction story by Ted Chiang. A race of aliens turn out
to be familiar with variational principles in physics, but completely
ignorant of cause-and-effect explanations, not just in physics, but
also in daily life. (In 2016 it was made into a movie, "Arrival.")
> PS. QM has "Symplectic symmetry", so position and momentum are
> treated as fully equivalent variables.
They're equivalent in some senses, but not in the sense of being
the same thing. Whether a person is guilty of trespassing depends
entirely on his position, and not at all on his momentum.
> The Schroedinger EQ itself can be written in either position or
> momentum basis, and nothing much changes.
The uncertainty in one is the Fourier transform of the uncertainty in
the other (if you ignore signs -- the FT of an FT is not the original
function, but its negative). Similarly with looking at radio signals
in the time domain vs. the frequency domain. An FT simply rotates a
waterfall display by 90 degrees. But that doesn't mean that time and
frequency are the same thing.
>> Anyhow, the Planck constant would still exist, though it would
>> become a mere conversion factor, the number of hertz in a joule, ...
Of course I meant the number of joules in a hertz.
I'll agree that it's just as technically accurate to say the
Titanic broadcast its distress call at 500 kilohertz or at 0.00033
yoctojoules. (Sorry, there's no prefix smaller than yocto.)
Actually, both are ahistorical, as they called it 600 meters.
Or rather metres, as it was a British ship.
Sorry I'm rambling. It's past my bedtime.
