Re: Time-dependence of Double-Slit experiment


<David.Paterson@xxxxxxxx> wrote in message
news:1155598949.682215.321920@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|I don't understand quantum mechanics.
|
| Some wise person said that it you understand the double slit experiment
| then you understand quantum mechanics. While trite, there is some truth
| in that, I can follow the logic from the double slit experiment to the
| path integral formulation heavily used by Feynmann.
|
| I don't understand the double-slit experiment.
|
| I understand parts of it, such as how a single photon can interfere
| with itself, but I don't understand the time-dependent aspect.


Okay....


| Consider the following gedanken experiment. Have an asymmetric
| arrangement of two slits, say 1 light second apart, one near and one
| far. Arrange the experiment so that the light through the distant slit
| has a significant relative amplitude.
|
| Light travels at a finite speed, so the light passing through the
| nearer slit will get to the screen before that passing through the
| further slit. So my common sense says ... taking into account what
| Einstein said about common sense being a prejudice I should rephrase
| that ... my prejudice says that we should expect to see no interference
| fringes for approximately the first second, until the light has had
| time to take the longer path, and then after that interference fringes
| should appear.
|
| Has this ever been checked experimentally?

Yes, light diffracts at the edge of a single slit.
http://scienceworld.wolfram.com/physics/Half-InfiniteScreenDiffraction.html
http://www.ph.unimelb.edu.au/~ssk/fresnel/edge.html

|
| In quantum mechanics the amplitude to propogate from from point x_I to
| point x_F in time T is governed by the operator e^(-iHT), where H is
| the Hamiltonian. The amplitude in question is just <x_I | e^(-iHT) |
| x_F>.
|
| I don't yet understand how to get the switch from no fringes at short
| times to fringes at longer times from <x_I | e^(-iHT) | x_F>. What have
| I missed?

You missed this:
"my prejudice says that we should expect to see no interference
fringes for approximately the first second" . That is exactly what
it is, prejudice.

Common sense may be the set of prejudices acquired by the age of 18,
but John Goodricke was 18 when he "discovered" Algol was a binary star
and did not take into account the finite velocity of light relative to the
source.
The poor kid was dead by the age of 22 and his prejudices lead to
thought experiments (notably Einstein's thought experiments)
that are paradoxical and ridiculously wrong.
Algol is an ordinary star moving around a barycentre in common
with a planet. The speed of light from Algol is added to the speed
of Algol and produces the light curve we see, a 52 degree wide
minima in 360 degrees of orbit. An eclipsing star would need to
have a separation of 4.5 radii of the larger OR LESS, and that
violates the Roche limit. Hence Einstein's prejudice was his second
postulate.
As far as QM is concerned, double slit is not all that much help in
understanding quanta IMHO.
By quanta we mean particles and we think of electrons as particles.
Electrons diffract, but that doesn't help much in explaining what a quantum
is, or its mechanics.
We think of photons as quanta, but we are tempted into thinking
of them as being very small, but in reality they can be any size.
A radio transmitter emits a train of photons, one photon per cycle, and
they spread. They can be focussed into beam with a parabolic
dish and sent to Cassini at Saturn instead of being broadcast.
That is true quantum mechanics. Photons are pulses of finite
energy, and intrinsic oscillators.
http://www.androcles01.pwp.blueyonder.co.uk/AC/AC.htm
Planck's prejudice is very like Einstein's prejudice.
Where Planck said
E = hf
he should have said
E =hf at the single speed of 300,000 km/sec,
because the frequency of a photon will not change if you should
travel alongside one. In other words, photons, like all objects,
have a relative speed which is indepent of time.

Androcles





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