Quantum Mechanics Still
Survives
Quantum
mechanics is the bane of many people’s existence. Anyone who has struggled to make sense of it,
and wondered how the universe could possibly be this crazy, will tell you that
quantum mechanics is the realm of the most bizarre. Furthermore, it creates many philosophical
problems about the nature of science- if the universe is inherently
probabilistic and random, how can we postulate that certain physical laws exist
at all, much less give sufficient epistemological support for them. Many people would like to see quantum
mechanics replaced by some sort of deterministic theory. While I don’t personally see any possibility
for it, I would most certainly welcome it, because I too am concerned about the
philosophical implications of quantum mechanics (although I hope string theory
can do something to limit the probabilistic nature of our fundamental physical
laws). Recently, Dr. Randell Mills has
proposed a new version of quantum mechanics that is probabilistic in its nature
(see the Guardian), but
unfortunately both his reasoning and mathematics are flawed, as pointed out by
Dr. Andreas Rathke of the European Space Agency (Read his abstract here). Below is my response to this issue, after
reading both articles.
Originally
scientists believed that there was a continuous spectrum of energy. Then
Max Planck noticed that the observed profiles of blackbody radiation can only
be explained by postulating that energy can be gained or lost only in
whole-number multiples of hv (h is Planck's constant, v is the frequency of the
light). This is the basic foundation of quantum mechanics (all the other
craziness comes out of this- surprising, isn't it? In fact the smallest
amount of energy is called a quantum, hence the name.) Although at this
time, it's only quantum theory. Classical theory of matter, because it
assumes that matter can absorb or emit any quantity of energy, predicts that
the profiles of blackbody radiation would go to infinity- they clearly don't,
no matter how you tweak them. Later, Einstein figured out that this is
because electromagnetic radiation is quantized, (these "particles"
are called photons), and this is supported experimentally by the photoelectric
effect (and this is what he actually won the Nobel Prize for, incidentally),
which again is contradictory to what classical theory predicts. This is
the phenomenon in which electrons are emitted when light strikes a metal
surface; experimentally it has been shown that: No electrons are emitted by a
given metal below a specific threshold frequency v0, for a light with the
frequency lower than v0, no electrons are emitted regardless of the intensity
of the light, for light with frequency greater than v0, the number of electrons
emitted increases with the intensity of the light, and for light with a
frequency greater than v0, the kinetic energy of the emitted electrons
increases linearly with the frequency of the light. The only explanation
of these observations is that electromagnetic radiation is quantized (made of
photons) and the threshold frequency is the minimum energy required to remove
and electron from a metal's surface.
So between Plank and Einstein we have:
Energy is quantized and con only be transferred in discrete units (called
quanta)
Electromagnetic radiation also shows certain characteristics of particulate
matter (wave-particle duality- the craziness is starting to come in)
So what does this have to do
with hydrogen and electrons? A lot, actually.
When light is passed through hydrogen, then through a slit, and then through a
prism, only certain wavelengths of light show up (the line spectrum of
hydrogen). Classical theory has no explanation of this, but quantum
mechanics does because only certain energy levels are allowed for the electron
in the hydrogen atom. Around the same time, people began to realize that
the classical idea of the atom with electrons just revolving around the nucleus
had a slight problem- revolution involves an acceleration, and by classical
physics they should constantly radiate energy, and thus spiral inwards and
crash into the nucleus. Fortunately we've noticed that atoms in general
are pretty stable, and thus they had a problem to deal with.
Enter this new quantum theory- and Bohr makes his model of the atom. The
important point here is that the model correctly fits the quantized energy
levels of the hydrogen atom, from its emission spectrum, and now these energy
levels correspond to stable circular orbits for the electrons. The only
problem is that this does not work AT ALL for any other atom than hydrogen, and
hence it was absolutely rejected. (Whatever you learned in high school,
modern atomic models are not in any way derived from the Bohr model.)
So by this time quantum
mechanics was a little more developed, by Heisenberg, De Broglie, and
Schrödinger. Thanks to relativity, people realized that not only did
waves have particle properties, but particles (like electrons) have wave-like
properties. They discovered that an electron in a stable orbit (which by
the way is not circular) is like a standing wave. To be a standing wave,
it has to have a whole number of half-wavelengths, and so therefore there are
only a few energy levels that correspond to a wave which has a whole-number of
half-wavelengths. I can't really explain this well in an email- take a
piece of paper, draw a dot on it, and then draw a sine curve while rotating the
paper. Odds are when you get back to the place you started your sine
curve won't align so that you retrace it- this would be unstable because
there's not an integer number of half-wavelengths in your circular sine
curve. If you happened to make it just right so that it retraces,
congrats, you've created a stable wave function for your electron.
Schrödinger wrote the wave functions- a specific wave function for a given
electron is an ORBITAL not an ORBIT- it does not give any information about the
movement of the electron itself, but the square of the function evaluated at a
particular point in space indicates the probability of finding an electron near
that point. So it's a probability distribution for finding electrons in
stable orbitals. (By the way, the shape of most of the
orbitals (except the s ones) aren't even circular).
So, review/summarize- Either
energy is continuous or discrete. Classical theory assumes continuous,
and predicts incorrect measurements regarding blackbody radiation, the photoelectric
effect, and line spectra. Therefore energy must be "quantized"
and hence the birth of quantum mechanics, whose first attempt to explain atoms (the Bohr model) was a miserable failure but now it
forms the only model of the atom that can explain those measured features.
Now onto Mills-
The thoughts I had going in is that he doesn't replace quantum mechanics with
anything- and if energy isn't continuous and isn't quantized, then what is
it?!!! He says something like classical quantum mechanics- which doesn't
really exist. You have the classical model and the quantum mechanics
model- the only thing between is the Bohr model, and he seems to argue to
return to the Bohr model without responding to the reasons that it was
discarded originally. Therefore he'd better have an absolutely airtight
argument against quantum mechanics- something that absolutely cannot be
explained by quantum mechanics, and preferably something that contradicts the
predictions of quantum mechanics (like what the blackbody radiation experiments
did for classical theory) in a repeatable experiment for me to have
epistemological basis to believe him.
When you go through the math of the wave function for the hydrogen atom of the
quantum mechanical model, you get that
E-sub-n =-Z2/n2*(me4/(8*epsilon-not2*h2)) =-2.178*10^-18 (Z2/n2)
Ze- Nuclear charge (Z=1 for H)
n- Principles quantum number- can only have integer values because you can only
have integer number of half-wavelengths to have a standing wave for the orbital
to be stable. So there is a minimum energy level- which is often thought
of in terms of a "radius" even though the electron doesn't really
have an "orbit". I'm not really absolutely sure why the
Guardian article says that there is an absolute prohibition on the electron and
proton getting closer- I think what they're saying is something like this-
remember hydrogen only has an s-orbital, which is circular. The amount of
energy does correspond roughly to something like a physical radius at which the
electron would be zipping around ON AVERAGE. Mills claims that he's been
able to find a closer radius which is still stable- in which case energy is not
quantized, but continuous. (Side note: It's important to notice, too,
that the physicists who investigated this are not specialists in quantum
mechanics.)
So what is Mills
fighting? He seems to say that there's another energy level, which in
current theory would correspond to a non-integral value of n, particularly to
n<1, which would be a problem, yes. But if he’s trying to revive some
version of the Bohr model, he needs to explain how his model would work for
elements other than hydrogen where the Bohr model fails. However, all the theoretical weirdness of
quantum mechanics comes from accepting that energy comes in little packets
called quanta, and he doesn't seem to be attacking that claim. In fact, I
don't even see what he's attacking- I think quantum mechanics can still explain
his observations, if they are correct, without assuming n<1. I would
just say that our value for Planck's constant, determined experimentally
anyway, may be slightly off- in which case you can have a closer orbit.
You may need more theory as to why the electrons don't go to that orbit, since
it'd be lower energy, but that's possible to explain. (In fact, as he's
explained in Rathke's article, he already has).
I guess even if he's right I don't think quantum mechanics needs to be
abandoned, and even if we completely went to his theory, I don't think he's
rejecting the idea of quantized energy, which is where the theoretical stuff
you don't like comes in anyway- at worst he's arguing for the Bohr model (with
new states), which doesn't work for anything beyond hydrogen- and I personally
think that this is what's he's thinking of as "classical quantum
mechanics"- in which he has not explained why it doesn't work for anything
other than hydrogen.
And so then I read Rathke's
critique. And while I haven't done the math myself, I have to say I am
absolutely convinced. I followed everything except the ansatz, which Rathke claims Mills
claims can be used to solve the DE. I'm accepting him on this point, and
from there it's a math error, assuming he quotes the proper separation from
Rathke's article. The non-zero angular momentum equation doesn't fulfill
the
I
agree with Rathke that there are no solutions for n<1, but I'd be a bit more
open minded that if there are "hydrino" states (of course, since
"hydrino" is typically defined as n<1, I suppose mine aren't true
"hydrino" states) it's because we've mismeasured Plank's constant-
but I have no idea how that's measured or how certain it is.
In short [ha, ha, after all
I've written] it'd be nice if he could resurrect some deterministic version of
the theory, that had a determined position of the electron, and I too would
absolutely love it. But he doesn't get rid of the assumptions that lead
to the weirdness (that energy is quantized), and I myself don't see how his
theory can be consistent with those, and he doesn't really explain it. On
top of all that, his math is indeed absolutely horrid.