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A quantum head scratcher

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Steve Conner

Thu Feb 16 2012, 01:09PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Quantum mechanics, the more you think about it, the worse it gets.

We all know the famous Young's slits experiment.

If we assume that the wavefunction of a photon (or other particle) somehow represents it in reality, then it explains the experimental results. And, taking the amplitude of the wavefunction gives us the EM field intensities in the classical case.

But if we run with this analogy between the probability amplitude and the EM field intensity, it takes us to some even more confusing places.

1. The uncertainty principle implies that the more monochromatic a photon is, the bigger it must be. It is easy to make a laser with a coherence length of several meters. Does that mean that, if we could persuade it to emit photons one at a time, each individual photon would be several meters long? If not, why not?

2. Let's take one of these hypothetical 10 foot long photons and pass it through a large telescope configured as a beam expander. Say we used a really big telescope, like 12". Does it make sense to say that the photon is now 10 feet long by 12" in diameter? If not, why not?

3. From a classical electromagnetic point of view, the field intensity at the telescope's output is much less than at the input, because the beam was expanded to a bigger area. So, classical intuition tells us that the EM field intensity at the output should be much less than "one photon's worth" at any small point. But from a quantum point of view, since the photoelectric effect works irrespective of intensity, it must be possible for this several cubic feet of "photon" to be swallowed up by a single atom.

You might argue that the wavefunction just represents the probability for the photon to be found at a particular place, not its actual reality. EM field intensity then only makes sense as a macroscopic quantity: something like "photon detections per square meter per second". Asking what is the intensity of a single photon makes as much sense as asking what is the gas pressure due to a single gas molecule.

4. But then you're left with the following. Every day in astronomy, a photon leaves a distant star and lands on an Earthly camera or eyeball. (For the sake of poetic license, I'll ignore the fact that a human eyeball needs about 7 photons to register any sense impression.) I have a mental picture of a photon that expands as it travels, and by the time it reaches the Earth, it could be many light years across. But somehow all of it "fits" into the telescope and deposits its energy in your eyeball, and not on a grain of dust near Alpha Centauri.

Of course, if photons were little billiard balls, none of the above would be worries. But then the Young's slits experiment wouldn't work the way it does.

Answers on a postcard please.

Sulaiman

Thu Feb 16 2012, 01:41PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

I bought a Hamamatsu photomultiplier that is supposed to be able to count individual photons
with the intention of doing the single-photon double-slit experiment
- I failed
...how do you generate single photons?
...how do you know that photon-pairs or more aren't generated?
...anyone want a Hamamatsu photomultiplier?

Steve Conner

Thu Feb 16 2012, 02:49PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

The guy from Teralab has done it...

Proud Mary

Thu Feb 16 2012, 04:15PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Sulaiman wrote ...

...how do you generate single photons?

Electrically Driven Single-Photon Source
Zhiliang Yuan,1 Beata E. Kardynal,1 R. Mark Stevenson,1
Andrew J. Shields,1* Charlene J. Lobo,2 Ken Cooper,2
Neil S. Beattie,1,2 David A. Ritchie,2 Michael Pepper1,2

which is here:

Steve Conner

Thu Feb 16 2012, 04:50PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Thanks for the link!

It looks like Hanbury Brown and Twiss actually did something not unlike my telescope experiment.

I'm going to have a look for their original 1956 paper. Edit: Found it!

Access seems to be free, although that could be because I'm at work.

Proud Mary

Thu Feb 16 2012, 05:12PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Steve Conner wrote ...

Thanks for the link!

It looks like Hanbury Brown and Twiss actually did something not unlike my telescope experiment.

I'm going to have a look for their original 1956 paper. Edit: Found it!

Access seems to be free, although that could be because I'm at work.

It is because you're at work!

But for the lumpenproletariat, there's a wikipedia entry for the Hanbury Brown and Twiss effect

Ash Small

Thu Feb 16 2012, 06:50PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Steve, the simple answer is that it is the ENERGY from the photon that is detected by the 'reciever', not necessarily the photon itself.

In the same way that it takes a certain amount of ENERGY to produce a photon, DETECTING a photon DESTROYS it, imparting that energy to the RECIEVER.

We're dealing with waves here, or 'fields', if you like.

The particle nature of photons (or electrons, or anything else, for that matter) is an 'illusion' created by the 'Higgs field', and so serves no practical use as far as analysis is concerned.

(Just my 2 cents worth

)

Steve Conner

Thu Feb 16 2012, 07:34PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

That's all well and good, but my argument implies that the energy from the photon can be spread very thinly over a huge area one moment, and the next moment it can all be detected in one atom-sized place.

In particular, if it really were "all waves", the double slit experiment would imply that half of the photon's energy goes through each slit.

I find that annoyingly non-local. And besides, quantum field theory says that the field itself is quantized: you can't have a half-photon worth of energy anywhere.

Or, you can't detect a half-photon worth of energy anywhere, which is not quite the same as saying that such a thing can't exist.

Ash Small

Thu Feb 16 2012, 08:13PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

But if you accept that the slits are also wavelike, and only have the illusion of being particulate due to the Higgs field, it all reduces to 'interference patterns'.

The photon doesn't actually 'split in two', it's effects are just 'dispersed'.

The 'energy' of the photon is a 'wave' or 'field'. Also, the energy is 'harvested' by the reciever.

Recent theories suggest that everything in the universe is connected to everything else, and that the 'empirical' notion that 'matter' exists only in one place is false. It just 'appears to', due to the Higgs field.

To put it another way, the energy of the photon is transferred from the source to the reciever at the speed of light, but it can manifest other effects on the way. Once it has been absorbed by the reciever, it can no longer exhibit these effects.

Steve Conner

Thu Feb 16 2012, 08:44PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

OK, let me try again. If everything is a wave, then the energy of each individual photon ought to disperse with distance according to the inverse square law.

So, how does the energy undisperse itself at the detector, so much so that all of it is focused onto a single atom? That's what a photon needs to do in order to get itself detected, and the wave model can't explain it.

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