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M3L15o.txt
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#
# File: content-mit-8-421-3x-subtitles/M3L15o.txt
#
# Captions for 8.421x module
#
# This file has 101 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
Colin.
So when you derive the amplitude of the electric fields
due to the single photon?
Yep.
I always get the factor of 2 wrong.
So you wrote h bar omega is 2 epsilon 0 V e squared?
Now, there's a contribution that comes
from the electric field and magnetic field that
can be one factor too.
Then there's always that other factor of 2.
Are you getting that from using 1/2 h
bar from the vacuum fluctuations?
I'm not going back to the formula,
because I run the risk that it was wrong.
[LAUGHTER]
But all I want to say is, what I really mean is,
use Jackson, put in a volume
V, an electromagnetic field with h bar omega energy.
And the electric field squared of this photon,
that's what I mean.
And if you find a factor of 2 mistake in my E square,
I can still get out of the rear exit, the rear entrance door,
by saying that there is also a difference
whether E square is E square RMS,
or whether E square is the amplitude.
[LAUGHTER]
You know?
I mean, there are those factors of 2 everywhere.
But what I mean is, really, is THE electric field
caused by one photon.
And of course, the argument stands,
I don't need any factors of 2 or any subtleties
of the electromagnetic field energy.
We know that the energy is n plus 1/2,
but emission is n plus 1.
And this shows that the stimulation by the vacuum field
cannot quantitatively account for spontaneous emission.
So the quantity that you set equal to is h bar omega,
and not 1/2-- not the fluctuation, but the real--
OK.
If you want to know-- let's not compare apples with oranges.
You want an electric field.
And you can pick whether it's the RMS field,
or whether it is the maximum amplitude.
You can pick what you want.
But now, we are comparing what is the E square for the vacuum,
for single-mode vacuum, and what is
the E square for single photon.
The two answers differ by a factor of 2.
A single photon is twice as strong in E square
as the vacuum fluctuations in the same mode.
That's what it means.
Yes?
I have a question about the spontaneous emission rate.
The explanation that you have, quantum mechanical derivation
that we have, did people not know
how to describe spontaneous emission .... before the field was quantized?
I think so.
I have not gone deeply back into the history,
but a lot of credit is given to Einstein.
And as I mentioned last week, that Einstein actually
had spontaneous emission in his derivation for the Einstein A
and B coefficient in this famous paper.
And so, he found that there must be spontaneous emission
based on a thermodynamic argument.
It's only spontaneous emission which
brings the internal population of an atom into equilibrium.
So I think it is correct to say ....
Can you derive it from that stat mech condition
of getting equilibrium?
That's what Einstein did.
And the answer is, by comparison with the Planck law,
you get an expression for the Einstein A and B coefficient.
Now, of course, you can go the other way around.
You can say, if you just use classical physics,
you would actually expect-- now, it depends, if you use the Bohr
model, you would expect that the electron is radiating,
and it was a mystery, how can you have an atom in the ground
state which is circling around a nucleus,
and not radiating at all.
On the other hand, in quantum mechanics,
we are not assuming that the atom is circulating,
and we have an accelerated charge which is--
and we have a time-dependent charge distribution,
we use a steady state wave function.
So I'm not sure if there is, maybe, an argument
which would say there should be some spontaneous emission,
based on a purely classical argument.
But this would not be the whole story,
because a classical argument would then deal with the difficulty,
why is there difference between n
equals 1 ([in hydrogen], which does not radiate, and n=2 which radiates?
So my understanding is that it is only the physics,
either through the perspective of Einstein,
by just using equilibration or our microscopic derivation,
using field quantization, which allows
us to understand the phenomenon of spontaneous emission.
Other questions?