Can Photons Interfere After Passing Through a Calcite Crystal?

[εllipse]

In Nick Herbert's Quantum Reality, he describes an experiment in which light is sent through a calcite crystal which separates the photons by their polarization. In the experiment he describes, the light has a 50/50 chance of either going up into a detector or down into a different detector. Later, when he is talking about when the wave functions representing the photons might collapse, he says they can't collapse at the calcite crystal because it would disagree with other experiments:

Using mirrors, for instance, we can combine light from the two cyrstal channels and look for wavewise interference of polarization attributes which is characteristic of [quanta] that are taking both paths. If we see such interference, then we know the wave function has not yet collapsed. In this case, when we combine beams we see interference effects between polarization attributes: immediately after the crystal, the photon evidently takes both paths.

Well this seems similar to the double slit experiment, but somehow I just can't wrap my mind around it. In the double slit experiment, atleast the photons don't touch anything, but in this experiment the photons hit this calcite crystal and are separated by it according to their polarization, but apparently Herbert is saying the photons aren't really sent on a specific path when they hit the crystal because they can still interfere with themselves later... So I guess I really don't have much of a question but am just asking for someone to corroborate this claim. Is this true? Has this experiment been performed by sending single photons through the calcite crystal at a time so there's no chance of photons interfering with each other? Quantum theory is driving me insane.

 

[DaTario]

I believe photons with different polarizations don't interfere.

Best Regards

DaTario

 

[DrChinese]

Just as with the double slits, it doesn't matter if photons are sent through singly or not: a single photon exhibits interference. Likewise, the idea of the photon "touching" something is not relevant... the photon simply interacts with the atomic field of the crystal lattice.

In essence, there are a large number of possible paths and possible interactions. But they whittle down to a few possibilities when you decide what you want to observe. If it is polarization you look at, you will have a superposition of the horizontal and vertical states. If you look at position, you can have interference effects.

 

[Antiphon]

If a single photon stikes your front window, it has a 8% chance of being detected
outside as a reflected photon and a 92% chance that it will get inside your house.

This has nothing to do with any other photons that may come towards the window.

The key is that you can set up equipment inside the house that changes this
probablility to 0% reflection. This is what he means when he says it doesn't
"collapse at the crystal".

The photon hitting your window can be made to come all the way through with 100%
probablility by positioning equipment inside the house so it can't "make the decision"
to become a reflected photon when it hits the window.

 

[DrChinese]

The photon hitting your window can be made to come all the way through with 100% probablility by positioning equipment inside the house so it can't "make the decision" to become a reflected photon when it hits the window.

That leads to an interesting question, I wonder if anyone knows if there are any optical experiments to test it...

As mentioned, you can very the thickness of the glass by varying amounts to change the reflection percentages (0 to 8% in the case described). This is done on the opposite side of the glass relative to the reflection point. So what is the latency time for this change to take effect at the point of reflection? Is it the speed of light in the medium (my guess) ?

I think the reflection and refraction of light are some of the most interesting elements of optics.

 

[Antiphon]

That leads to an interesting question, I wonder if anyone knows if there are any optical experiments to test it...

As mentioned, you can very the thickness of the glass by varying amounts to change the reflection percentages (0 to 8% in the case described). This is done on the opposite side of the glass relative to the reflection point. So what is the latency time for this change to take effect at the point of reflection? Is it the speed of light in the medium (my guess) ?

I think the reflection and refraction of light are some of the most interesting elements of optics.

Actually, it will not matter how thick the glass is (assuming an idealized
glass which does not absorb the photon in it's bulk.)

You see, in order for this to work you must prepare a photon with a very
specific wavelength, that is a definite energy. And such a photon lasts
for a very long time and is very extended in space. You can show that the
photon would have to be extended enough spatially to cover the entire
length of the glass block, even if it were a light-year deep.

It means that the spectral width of the photon would have to be
correspondingly narrow to ensure 0% reflection overall, and narrow to
the extent that the glass block is thick.

And now you see why it's not so paradoxical. The spatial extent of a photon
is determined by it's spectral purity. It cannot be treated as a point particle
which may or may not reflect from a single surface.

Edit: Incidentally, this implies rather directly that it takes a year to
form a green photon (wavelength = ~550 nm) with a frequency of
$$545 \times 10^{12} +/- ~0.00000000000000000000000545)$$ Hz

-but that's how accurate the frequency would have to be in order to ensure
proper phasing through a light-year of distance between reflectors.

 

[DrChinese]

You see, in order for this to work you must prepare a photon with a very specific wavelength, that is a definite energy. And such a photon lasts for a very long time and is very extended in space. You can show that the photon would have to be extended enough spatially to cover the entire length of the glass block, even if it were a light-year deep.

So if I understand correctly, the purity of incident photon AND the thickness of the glass are both elements in such determination (of whether the reflection rate is 0%, 8% or somewhere in between). Or did I get confused again?

 

[Antiphon]

So if I understand correctly, the purity of incident photon AND the thickness of the glass are both elements in such determination (of whether the reflection rate is 0%, 8% or somewhere in between). Or did I get confused again?

Yes. Spectral purity would be a semi-classical term to describe it.

The quantum thinking would be that any "practical" photon is in a state
of superposition in momentum space because they have to be created in
a finite amount of time (and therefore can't have inifinite spatial extent.)

The momentum can be very narrowly spiked and it usually is, but just like
with any other quantum (like say an electron) there is some indefiniteness
about this (consistent with the HUP.)

What would happen if you had a light-year thick ideal piece of window
glass tuned for perfect transmission at exactly 550nm?
Almost every actual photon you could make with a laser or any other
laboratory-grade source would have only some probability of getting
through this without a reflection. To make it through without reflection
every time, you'd have to prepare photons with a hyper-accurate
momentum,and this peparation would take about a year or more for
each and every quantum (though many could be made in parallel.)

 

[DaTario]

Is it a kind of Fabry-Perot device ?

 

[Zardoz]

Conceptual Answers. John Gribbin

John Gribbin's book "Schrödinger's Kittens and the search for Reality is a good one to explain most of these difficulties. At the end of his book he explains John Cramer's model of QM called "transactional interpretation" which is a clear easy way to conceptualize and understand these bizarre experimental results with light.

The only issue I have now is that I have read in a Discover article about Roger Penrose that they have had objects as large as buckyballs (soccer-ball-shaped carbon molecules) in a state of quantum superposition.

If anyone here has read John Gribbin's book or is familiar with "transactional interpretation" model could they tell me if this model is compatible with non photons. Works very well at clearing up all the bizarre photon interactions, but I don't see how it translates to larger objects.

Z.
… all models of the world beyond the reach of our immediate senses are fictions, free inventions of the human mind. … Reality is in a very large measure what you want it to be. Still, though, almost everybody wants to know ‘the answer’. The quest for a really real model is what drives theoretical physicists, just as it motivates other folk to study philosophy or to subscribe to a particular religion. I still have this hankering myself, even though the logical part of my mind tells me that the search is fruitless, and that all we can ever hope to find is a self-consistent myth for our times.



- John Gribbin