Thread: Electromagnetic phase cancellation

During the double slit experiment the probability waves cancel and reinforce each other to produce a certain fringe pattern. What I want to know is, can two photons at the same frequency but out of phase cancel each other out? Does this occur at all during that experiment?

My guess is that two photons will have different frequencies at a fixed position or the same frequency at different positions, given Heisenberg uncertainty wrt position and energy. However the double split experiment shows constructive and destructive interference of a photon with its self - a good question though.

I remember a "thought experiment" some time ago that related the idea of measuring which slit the photon went through by placing a detector over one slit - this detector had 100% "chance" of detecting a photon (and destroying it) if it passed through the slit. Equally, it would not register if the photon passed through the other slit. The target was a photographic plate that could record each photon and build up an interference pattern.

Obviously this arrangement would destroy a 2-slit interference pattern as only 1 slit would be available. Such a pattern is the result of cumulative in phase and out of phase contributions. However what if we ran the experiment 2 times - i.e. we let one photon travel towards the slit at 1 per second say. It would have 50 % chance of being detected and 50% chance of not being detected. Lets say we repeat the experiment photon by photon providing no photon is detected on the monitored slit. Perhaps we get 5 photons not detected - then we get one. So we close the experiment and repeat again.

Lets say we repeat the procedure as often as need until, say, 100 photons are released but none are detected. We would imagine then that all had passed through the non monitored slit, but that we had not influenced them in any way. Had we influenced even one, the detector would have registered the photon and destroyed it - causing the experiment to be repeated again and again from scratch until the photon quota was reached.

Given that no photon had been "detected" would we have the 2 slit interference pattern? In the 2 slit experiment we assume the photon has a probability density and goes through both slits simultaneously to subsequently interfere with itself. If we don't influence the "photon" by performing a "non measurement" in this way, shouldn't the outcome be the same interference pattern as the 2-slit case?

It appears however that this is not the case - even a non measurement affects the probability function and collapses the field to become a measured particle. The act of knowing which slit the photon did not transverse is equivalent, in a measurement sense, to knowing which slit the photon did transverse. Either measurement collapses the wave function and destroys the interference pattern.

So if I have understood this correctly, or at least adequately, I doubt that 2 photons will interfere (unless you pass them through a non linear optical material and produce frequency mixing i.e. sum and difference photon frequencies as some laser arrangements can demonstrate).

If we consider photons to "cancel" then their energy must be conserved - i.e. converted to some other form such as heat. However cancellation at one point in space results in summation at another. In acoustic analogy, noise canceling headphones are available for jet pilots and cause a local cancellation of noise. However it would be impracticable to design "noise canceling speakers" as cancellation will only occur at spot frequencies and positions in a room depending on the wavelength of each noise spectral component.

I agree though that the idea of a photon by photon interpretation is intriguing. A photon can definitely be absorbed by an atom for example, if its energy change corresponds to the photon's wavelength (as in a laser for example) but can one photon be "absorbed" by another?

If energy is conserved, the combined duo-photon would have twice the energy and therefore half the wavelength. I have read that non linear optics can be used to convert long wavelength (red) laser emissions to shorter wavelength (blue) emissions by "frequency doubling" - similar to radio frequencies and harmonic distortion in audio amplifiers. However does this non linear mixing combine one photon to another or each photon with itself?

If two photon frequencies are mixed in a non linear optical material, then sum and difference frequencies will be produced (i.e. c/wavelengths). If both photons have the same frequency then the sum will be a second harmonic and the difference will be DC (perhaps a static charge?). So frequency doubling would require two photons merged into one + DC.

On a related conjecture, say we mixed blue and green laser light in a non linear optical material, producing say infra-red photons as the difference product. Say we introduce these "conceptually" pair by pair. Since the difference frequency photons have less energy per photon, would there be a lot more of them to conserve energy?

For example, say the difference frequency was only a few GHz - compared to the light photon frequencies the energy difference would be massive. Would we expect two photons to go into the non linear optical material and find millions and millions of microwave photons coming out?

Thanks for the question Cold Fusion, I hope it spurns some interesting conjecture :wink:

Originally Posted by Cold Fusion

During the double slit experiment the probability waves cancel and reinforce each other to produce a certain fringe pattern. What I want to know is, can two photons at the same frequency but out of phase cancel each other out? Does this occur at all during that experiment?

In the standard double slit experiment, light of the same colour goes through the slits and forms an interference pattern. This does not actually require the invocation of probability waves at all, but can be explained in terms of regular light-as-a-wave physics.

Probability waves, as I understand it, enter the picture when you are trying to do clever thingies like produce paradoxes such as having a single photon interfere with itself (which sounds like something that would have been illegal a few decades ago ) when, with both slits exposed, the probability wave function shows signs of interaction with both slits. When only one slit is available, the individual photons pass through showing no signs of intereference.

So in sum, the answer is yes - what you are asking about is the standard double-slit intererence experiment where light of the same colour, not necessarily in phase, interferes in a wave-like fashion as it passes through the double slits. It is, by all accounts, an experiment you can perform yourself with a sufficiently monochromatic light source, whereas the photon by photon probability wave experiment is not as easy to do...

Originally Posted by Cold Fusion

During the double slit experiment the probability waves cancel and reinforce each other to produce a certain fringe pattern. What I want to know is, can two photons at the same frequency but out of phase cancel each other out? Does this occur at all during that experiment?

With light I see no different effect on light, from a double slit, as opposed to a single slit. No wave effect at all.

Just particles electrons in my part of the universe.


Sincerely,


William McCormick

As sunshinewarrior posted, the light has to be (reasonably) monochromatic for the interference patter to be observed. Macroscopically the path lengths from each slit to a central target point are equal, therefore the two light waves add in phase. As we move, say to the right, the path from the right slit is shorter than the light path from the right slit. When this path length difference equals one half the light wavelength where the two wavefronts will be in anti-phase and cancel leaving a dark region. Moving further along, the path length will become equal to one wavelength and the waves will add again. This repeats causing a row of light, dark, light, dark spots etc.

This "interference pattern" requires two slits for light to pass through. Since the light wavelength is related to its color, non monochromatic light will not produce an easily viewed pattern; the peaks and troughs will be further apart for red light than blue light components for example.

Originally Posted by Vaedrah

As sunshinewarrior posted, the light has to be (reasonably) monochromatic for the interference patter to be observed. Macroscopically the path lengths from each slit to a central target point are equal, therefore the two light waves add in phase. As we move, say to the right, the path from the right slit is shorter than the light path from the right slit. When this path length difference equals one half the light wavelength where the two wavefronts will be in anti-phase and cancel leaving a dark region. Moving further along, the path length will become equal to one wavelength and the waves will add again. This repeats causing a row of light, dark, light, dark spots etc.

This "interference pattern" requires two slits for light to pass through. Since the light wavelength is related to its color, non monochromatic light will not produce an easily viewed pattern; the peaks and troughs will be further apart for red light than blue light components for example.

Even with laser light I see no effect whatsoever. No strange wave pattern. Even at angles. The only way to create a problem or strange effect like in that movie. Is to have variables.

If you create multiple sources of light, within your light source. Then yea, sure you will get strange patterns. But you have to have different energy level areas within your source creating the light. A none uniform light source. But this would be elementary school light experiment variables.



Sincerely,


William McCormick

William, very interesting. I guess that real world observation rules over text book theory!

That is the point, if this were possible then energy would have to be conserved, but in which way? If the interacting photons were surrounded by an "entropic" material then heat could be generated, but what about in space or in a vacuum? Would it produce matter, more light, or maybe even a new type of particle?

I have read that non linear optics can be used to convert long wavelength (red) laser emissions to shorter wavelength (blue) emissions by "frequency doubling" - similar to radio frequencies and harmonic distortion in audio amplifiers. However does this non linear mixing combine one photon to another or each photon with itself?

A very interesting point. These crystals that they use are apparently at best only 30% efficient. The questions is, how is the energy lost? Are photons arbitrarily chosen to be eliminated, or is the frequency of each photon reduced by 70%, then multiplied by 6 or 7 times to get the resulting doubled frequency?

Originally Posted by Cold Fusion

That is the point, if this were possible then energy would have to be conserved, but in which way? If the interacting photons were surrounded by an "entropic" material then heat could be generated, but what about in space or in a vacuum? Would it produce matter, more light, or maybe even a new type of particle?

I have read that non linear optics can be used to convert long wavelength (red) laser emissions to shorter wavelength (blue) emissions by "frequency doubling" - similar to radio frequencies and harmonic distortion in audio amplifiers. However does this non linear mixing combine one photon to another or each photon with itself?

A very interesting point. These crystals that they use are apparently at best only 30% efficient. The questions is, how is the energy lost? Are photons arbitrarily chosen to be eliminated, or is the frequency of each photon reduced by 70%, then multiplied by 6 or 7 times to get the resulting doubled frequency?

Frequency is only the effect of rays of light, or any other ray, even gravity rays.

When light changes from red to blue, it is because its velocity has increased. When you shine a parabolic reflected light off into the distance and it disappears into the distance. It was not stopped or blocked. It was accelerated to velocities faster then light.

That is all they are doing if they are changing red light to blue light. Positively accelerating it.

I take a red laser light and accelerate it to yellow light, and even get little flashes of blue. Through amber liquids, and glass.

It is natural for all light to accelerate as it passes through dark gases. Through a red rose laser light turns yellow almost white.

Sincerely,


William McCormick