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[Phys-L] what's quantized and what's not

Sometimes people aren't very good at critical reasoning.
I've heard physics teachers say explicitly that they don't
know how to teach critical reasoning.

Well, here's a first step: Whenever you hear a new idea,
mull it over, checking to see in what ways it is consistent
(or inconsistent!) with other stuff you know. This makes
the new idea vastly more useful, because it establishes
more ways of recalling the idea when needed.

This approach to learning -- based on understanding, not
mere rote -- has been known in the pedagogical psychology
literature for well over 100 years (James, 1898).

«Everybody» knows that energy is quantized. If you look up
the definition of quantum in the dictionary, it will tell
you this. Einstein wrote a paper about it in 1905.
http://www.colorado.edu/physics/phys2170/phys2170_sp15/Library_files/A.%20Einstein,%20Ann.%20Phys.%2017,%20132%201905.pdf
He got the Nobel prize for this (not for relativity) in 1921:
http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/

Einstein emphasized quantization of light i.e. electromagnetic
radiation, but the idea was soon applied more generally.

There's only one problem. The basic idea is wrong. Anybody
who thought carefully about it in 1921, or even in 1905,
should have known it was wrong. The title of Einstein's
paper was carefully understated:

"Über einen die Erzeugung und Verwandlung des Lichtes
betreffenden heuristischen Gesichtspunkt"
^^^^^^^^^^^^^
"Concerning a Heuristic Point of View Toward
the Emission and Transformation of Light"

Planck in particular was skeptical and warned people to be
careful. However, more-or-less everybody except Planck
swallowed the bait, hook, line, and sinker.

Let's apply some "Critical Reasoning 101" techniques here.
Einstein offered a hypothesis and a fair bit of supporting
evidence. So what's the next step?

Answer: The next step is to
a) check the theory against additional evidence
b) check the evidence against competing theories.

a) Conflicting evidence:

In the years before 1921, and even before 1905, there was a
boatload of conflicting evidence. People had been building
heterodyne radio receivers since 1901 (Fessenden, patented
1902). Marconi was awarded the Nobel prize in 1909. Radios
were common aboard ships in 1912 (e.g. Titanic). Superheterodyne
was invented in 1918.

I mention all this radio technology because if you build a
radio receiver to be a photon counter for radio-frequency
photons, it will be a reeeeally lousy radio. It's an easy
calculation:
-- The voltage coming from the antenna is on the order of
nanovolts.
-- Energy goes like voltage squared. Ditto for photon
number, roughly speaking.
-- A heterodyne receiver does not multiply the antenna
voltage times itself, but rather multiplies it by the
local oscillator (LO) signal, which is on the order of
volts. So the energy in the intermediate-frequency (IF)
signal is about a billion times larger than what you
would get just by receiving the photon energy.
-- As if that weren't bad enough, the photon energy is
small compared to kT, so if you tried to build a photon
counter it would explode due to thermally-activated
dark current, even with no antenna attached.

b) Alternative theories:

Einstein's quantization calculations, and Planck's even
earlier quantization calculations, depend on counting the
number of basis states. Note the contrast:
-- Counting the basis states is easy in the energy-eigenstate
basis.
++ HOWEVER any other basis set works just as well. Energy
states are not the only states. The energy basis is not
even the only basis!

Seriously, folks, energy is not quantized. The EM field is
not quantized. Planck's constant doesn't even have dimensions
of energy. You can choose whatever basis you like.
-- If you build a photodetector, it will measure photon number
(a†a) and will see quantized energy levels, but this has more
to do with the structure of the detector than the intrinsic
properties of whatever the antenna is looking at.
-- If you build a voltmeter, it will measure (a† + a) and you
will see a voltage with no quantization whatsoever. Here
a† is the field creation operator, in second-quantized
language.

BTW here is an instructive example of the /opposite/ of critical
reasoning:
Einstein is smart, Einstein says something seems to be
quantized, therefore everything is quantized.
I reckon that sort of thinking set physics back 50 years.
Eventually Glauber and others cleaned up the mess.
http://www.nobelprize.org/nobel_prizes/physics/laureates/2005/glauber-bio.html

This is relevant to the recent brief discussion of gravitons.
We know exactly what gravitons are. However, they are irrelevant
to the production, propagation, and detection of gravitational
waves, for the same reasons that quantized photons are irrelevant
to AM radio. I guarantee you that the LIGO machine is not a
graviton counter.

On 04/15/2016 07:20 AM, Ludwik Kowalski wrote:
I am not familiar with textbooks printed in this century. I suspect
that their descriptions of gravitation are not different from
descriptions in previous three to five decades.

Right. They're not appreciably different AFAICT.

And these old
descriptions were often meaningful to students, as far as I know.

Is there any evidence that they were "meaningful to students"?

All evidence I've seen is that after a few years, most students
(other than physics majors) remember virtually /nothing/ from the
first-year physics course. Such evidence is easy to obtain:
just interview someone who has been out of school for a few
years. So I'm not buying the assertion that it is "meaningful".

Evidence that they learned it well enough to pass the test
does not impress me. I assume they learned it by rote and
then forgot it almost immediately. The fact that much of
what the book says is self-contradictory is powerful evidence
that students did not assign much "meaning" to it. Such
contradictions serve to remind students that critical
reasoning just gets them into trouble.

The fact that they forgot it is powerful evidence that it was
never "meaningful". Stuff that gets used gets remembered.

The same conclusion is well supported by theory, as follows:
Are there opportunities for laypersons to apply Newton's law
of universal gravitation? Opportunities where it is important
for daily life? I can't think of any. The book doesn't
provide any. The application to cosmology doesn't count,
because you don't need it for any practical purpose.
-- If you're a sailor, you can figure out when the tide
will ebb and flow based on published tables. It would be
wildly impractical to figure it out from first principles.
-- If you are a farmer, you can predict the harvest moon
based on published tables. You don't need to figure it
out from first principles.
-- If you live in town and work in an office, you have even
less pressing need for cosmology.

Furthermore, if you are interested in something practical
like centrifugal force, the explanation in the book is almost
certainly wrong, seriously wrong, so that strikes me as the
opposite of "meaningful". The fact that students can pass
tests on the topic tells us there are /two/ problems: The
exposition is no good and the testing is no good.

So I'm not buying the idea that the stuff in the book
"should" in theory be meaningful.

==============

Tangential remark: The concept of "graviton" has been well
established in the scholarly literature for 75 years that I
know of, understood at a level well beyond idle speculation:
Marie-Antoinette Tonnelat,
"Sur les Ondes planes de la Particule de Spin 2 (graviton)."
"On plane waves of a particle of spin 2 (graviton)"
Comptes Rendus Hebdomadaires des séances
de l'Académie des Sciences 212 (1941): 263-6.

http://gallica.bnf.fr/ark:/12148/bpt6k3164q/f263.image

This is just one of a bazillion things that are well established
in the scholarly literature but are not appropriate for the
introductory course.