# B Double Slit & Momentum

1. Sep 13, 2017

### fanieh

How true is this? Do you believe that in the double slit experiment, what is subsequently measured at the detection screen is actually the particle’s momentum?? How does this differ to the normal double slit explanation of the particle being deflected left or right of the slit, etc.?

http://www.users.csbsju.edu/~frioux/diffraction/s00897040748a1.pdf

"In Marcella’s quantum mechanical analysis of the double slit experiment, what is subsequently measured at the detection screen is actually the particle’s momentum. In other words, the well-known diffraction pattern created by the double-slit geometry is the particle’s momentum distribution in the plane of the detection screen. Therefore, to calculate the diffraction pattern one needs a momentum wave function, and this is obtained by a Fourier transform of eq 1 into momentum space"

2. Sep 14, 2017

### Simon Bridge

There is no difference between this momentum description and saying a particle is deflected. The use of this approach is that "momentum" is well defined while "particle deflection" is, at leats in this context, not.
Marcella's paper, Quantum interference at slits ( https://arxiv.org/abs/quant-ph/0703126 ), has other problems.
See followup paper: Rothman and Bouhm, Quantum interference at slits revisited ( https://arxiv.org/abs/1009.2408)

3. Sep 14, 2017

### fanieh

Say. Can the wave properties of any particles or fields be detected without using any material detector? Can anyone give an example proving the wave properties is inherent in the particles or fields? Thanks.

4. Sep 14, 2017

### DrChinese

As a matter of fact, they can. The example I like is using polarizers in front of each of the 2 slits. When the polarizers are parallel, there IS interference. When the polarizers are perpendicular, there is NO interference.

The only relevant variable here is the relative orientation of the 2 polarizers. Each individual polarizer's absolute orientation makes no difference. This is effectively a situation in which there is no material detecting the which path information.

5. Sep 14, 2017

### vanhees71

Well, the with-way information is simply in the polarization state of the particles. If you have, e.g., photons and the relative orientation of the polarization filters is $\pi/2$, then you have no interference at all, because the polarization states of the photons runing through slit 1 are perpendicular to thouse of slit 2. If the relative orientation is $0$ (i.e., parallel oriented polarizers) you have full interference contrast. For all relative angles between these extrems you get interference patterns with less than the maximal contrast.

6. Sep 14, 2017

### fanieh

The first paper was shared by Bill Hobba for over 50 times in the PF archives.. he summarized it thus:

"Here is the double slit experiments explanation without using that myth: http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf Whats going on is this. Each slit is a position measurement. After the slit it has a definite position so by the Heisenberg uncertainly relation it momentum is unknown. It's kinetic energy is still the same so the magnitude of its velocity doesn't change - its scattered in an unpredictable direction. When you have two slits the wavefunction is a superposition of the the wavefunction at each slit and when you work through the math as detailed in the above link you get interference. Thanks Bill"

Reference https://www.physicsforums.com/threa...lit-experiment-questions.799522/#post-5020416

I'd like to know. Is this momentum context of the explanation the consensus or 100% followed by all physicists.. but then Simon shared the second paper which gives the explanation as somewhat misleading.. so I'd like feedback from super experts on this. Thanks.

7. Sep 14, 2017

### Mentz114

Yes this is fine for light, which can be in physical superposition.

How does this help with 'matter waves' ?

8. Sep 14, 2017

### fanieh

I have polarized sunglasses so I know what it can do able to suppress all horizontal light waves. If you just put one polarizer in any slit in the double slit.. won't it cause a darkening of the interference pattern? But putting for example the polarized sunglasses in one of the slits would suppress all horizontal photons in that slit.. won't this create a which way path for the horizontally polarized photon or electron?

9. Sep 14, 2017

### Staff: Mentor

Yes, but not for the vertically polarized photons; these still have both paths available so will interfere.

10. Sep 14, 2017

### fanieh

It is said if you have two perpendicular polarizer.. there is no interference pattern because it can tell which path the photon passes (because one of them will pass it 100% and the other 0%). But if the photon has polarization photon oriented 45 degrees.. won't it pass thru both slits and polarization without giving any which way path?

11. Sep 14, 2017

### Mentz114

The polarizers argument is true but overcomplicated.

The general principle is that the two parts of the superposition must remain coherent for interference to happen.

If anything happens on one path that is different from the other - the coherence is lost and there is no interference.

12. Sep 15, 2017

### fanieh

Polarizer can prove the wave part of is in the particle being emitted and not in the detector as hidden pattern. See this New Scientist article shared by a science advisor here:

https://www.newscientist.com/article/mg21128241-700-beyond-space-time-welcome-to-phase-space/

"Smolin’s hunch is that we will find ourselves in a place where space-time and momentum space meet: an eight-dimensional phase space that represents all possible values of position, time, energy and momentum. In relativity, what one observer views as space, another views as time and vice versa, because ultimately they are two sides of a single coin – a unified space-time. Likewise, in Smolin’s picture of quantum gravity, what one observer sees as space-time another sees as momentum space, and the two are unified in a higher-dimensional phase space that is absolute and invariant to all observers. With relativity bumped up another level, it will be goodbye to both space-time and momentum space, and hello phase space."

Some question whether having objective phase space means there is a hidden interference guide in an object. This can give another view of how the double slit experiment can work. Using this particular phase space duplex-space perspective, one can see an entirely different explanation for the very famous Young's double slit experiment from the era of the classical mechanics paradigm. The conventional, single-space explanation (the old space and time explanation) saw the result as the interference of the light waves entering the two parallel slits. In that model, the slit structure itself contributes nothing but the two, parallel gap openings. This phase space duplex-space perspective says the slit structure itself, without the light waves, already has an Phase space substance interference pattern existing around the slit regions of the physical space structure. The model is that it is this objective phase space pattern that guides the light into its maxima and minima ordinary space intensity locations behind the slits.

Polarizer can help refute the idea. Anyway. If you are hit with electron beam (with electron matter wave).. and you use a polarizer.. would it filter some of the electron matter wave too? Or does polarizer only work for photons?

13. Sep 15, 2017

### vanhees71

Not true! As a single person I'm a tiny fraction of physicsts, but not 0% I think this paper is a didactical desaster and should not be used, and I told so in this forums several times. I can't help that nobody seems to take this criticism seriously. At least there is a published paper in Eur. J. Phys. also criticizing this paper, and this should be taken seriously.

14. Sep 15, 2017

### fanieh

But note that for all relative angles between these extremes of parallel and perpendicular, how can you get interference patterns when the polarizer can tell where the photon passes thru because it can make the pattern brighter.. for example. the right slit with the photon say 25 degree orientation closer to one of the polarizer vertical or horizontal.. do you get what I mean..i planned to draw to illustrate it but I think you get the idea...

15. Sep 15, 2017

### fanieh

Let's say you put the 2 polarizers outside the 2 slits of the double slit as DrChinese tried. The one on left is oriented vertical.. while the one on right is oriented 60 degrees. Now assume you have photon passing thru the slit with polarization of 25 degrees.. It's closer to the left (25 degrees) than the right polarizer which has 35 degrees from the nearest horizontal. Therefore the right polarizer would be brighter.

1. Wouldn't this produce a which way path to the 25 degrees photons producing lack of intereference for the 25 degree photons?
2. If yes. Does it mean only 30 degree photon can cause interference (since this is middle to the vertical and 60 degree oriented polarizer)?
3. In double slit, in one at a time photon or electron emission.. what degree of polarization does it use?

Thanks a lot!

16. Sep 15, 2017

### vanhees71

As I said, then you get interference patterns with reduced contrast. The point is that the polarization states for not perpendicular to each other oriented polarizers are not orthonal, i.e., $\langle \psi_1|\psi_2 \rangle \propto \cos \alpha \neq 0$, and thus you get some interference but with some function of the relative angle $\alpha$ of the polarizer orientation.

17. Sep 15, 2017

### Staff: Mentor

The incident photons have no polarization before they encounter the filter (because we haven't yet measured it). Thus, no matter what the angle of the filter, every photon has a 50% chance of passing the filter, and both polarizers are equally "bright".

18. Sep 15, 2017

### vanhees71

The point is not, how many photons run through the slits but whether there is interference between the two alternative paths. If the filters are in 90-degree relative orientation you have no interference, if they are in 0 (or 180)-degree relative orientation you have interference with full contrast. For any angle in between you have interference with reduced contrast.

19. Sep 15, 2017

### fanieh

You mean before measurement, the polarization is also in superposition just like the position or momentum? I thought only the position and other observables don't have values before measurement. I didn't know even the polarization didn't have definite degrees before measurement (?) Why is polarization not an observable in QM?

20. Sep 15, 2017

### vanhees71

Of course, polarization is an observable in QM. The standard basis are the helicity states ($\pm 1$ for photons), corresponding to left- and right-circular polarized modes of the em. field.

21. Sep 15, 2017

### Mentz114

I did not read the article because it is a popularization.

Electrons have quantum spin alignment and they can be filtered like polarizised photons in a Stern-Gerlach filter. They can also be in a superposition of spin states.
This reference has details ( maybe too much math for a basic thread)

http://www.if.ufrj.br/~carlos/fismod/seminarios/SternGerlach/SternGerlach_programas/SpinBook02.pdf

22. Sep 15, 2017

### fanieh

Yes. I just remember in the aspect experiment.. they can change the spin or polarization after the entangled photon or electron are at a distance and they can change the setting (like angle) and after the results are compared, they match...

Do classical photons or electromagnetic wave also have polarization in superposition?

23. Sep 15, 2017

### Staff: Mentor

There is no such thing as a "classical photon".

Classical electromagnetic waves, like all waves, obey the principle of superposition: If $x$ and $y$ are solutions of the wave equation, then so is $\alpha{x}+\beta{y}$. In particular, this works when $x$ and $y$ are the solutions to Maxwell's equations corresponding to two different polarizations.

24. Sep 15, 2017

### fanieh

In other words, or for short.. when classical electromagnetic waves are emitted by the sun.. do they have definite polarization already as they travel in space or do the polarization only pop up when we measure them or it hits detectors or objects on earth?

25. Sep 16, 2017

### Staff: Mentor

Although understanding the behavior of classical electromagnetic fields is essential for understanding the quantum electrodynamic behavior of photons, there are no simple correspondences between the two. Measuring the polarization or energy of a single photon generally tells you nothing about the incident electromagnetic radiation. (For an analogy, consider that knowing that a single molecule in a container of gas struck the wall of the container at a particular point and with some energy tells you nothing about the pressure or temperature of the gas). Only if the incident light is monochromatic and already polarized can we sensibly talk about its frequency and polarization.

Classical electromagnetic radiation is described by functions that give the electric and magnetic fields as a function of position and time; at every moment the two fields have some definite value at every point in space (very different from quantum mechanical observables). These functions obey the wave equation derived from Maxwell's equations. Because the wave equation is linear, these solutions to Maxwell's equations can be written as a sum (superposition!) of the infinite number of various solutions that describe monochromatic plane waves with various polarizations and frequencies; and writing them in this form is helpful in solving many problems in classical physics.

However, you should not confuse these superpositions with the superpositions of quantum mechanics. We're working with similar-looking differential equations so the solutions take vaguely similar forms and share the property that the sum of two solutions is also a solution so they can be superimposed - but despite the similarities it's a completely different physics involving completely different things.