Question

How would you relate Diffraction and Heisenberg's Uncertainty Principle? Is Diffraction just a special case of Heisenberg's Uncertainty Principle?
http://www.youtube.com/watch?v=a8FTr2qMutA

Answer 1

I think one of the comments there makes sense.. uncertainty principle says if you know position of a particle to some great accuracy you ll have a minimum amount of inaccuracy in determining its momentum.. and vice vers

so when you are confining a particle to go through a very very narrow slit.. any particle that goes through it.. m very certain about its position right??.. (cause the slit is very narrow and hence the particle must have been somewhere in that slit and hence somewhere in that extremely small gap.. and hence i have a high degree of accuracy on the position of the particle).. so Heisenberg comes in.. and particle will now have a crazy momentum.. so it can go in any direction .. infact now its momentum will have so many possibilities that it ll make sure that your error in calculating is more than that min. :D.. did that make sense??

Answer 2

i mean't crazy momentum possibilities

Answer 3

If you plug in values for the typical momentum for light (remember P=E/c for a photon with E=3eV) and compare it to h/2pi= 0.66x10^-15 eV-sec you find the slit with for which the Heisenberg uncertainty principle in appropriate is 0.00022 mm. Diffraction is observed at slit widths of 0.1 mm way larger, almost 500 times, than the HUP would predict importance. Also if the HUP where important wouldn't the uncertainty in momentum and therefore energy produce aberrant frequency changes in the exiting light spectra which should easily be seen. The HUP gives a boundary between classical and quantum effects and is not a mechanism for producing effects, it does not make things happen.

Answer 4

Well for starters no one says that it makes things happen.. we say things happen that way and HUP would predict it.. lemme check your calculations and get back to you! :)

Answer 5

if i consider the slid width to be .1mm.. then i would the max uncertainty in position to be .1mm hence now ... i plug in the value

\[\Delta x \Delta p \ge h/4 \pi \]

i would get \[\Delta p \ge h10^{4}/4 \pi \]
so that would be the min. uncertainty.. now i consider momentum of a photon of frequency say 500nm

then \[p = h \nu/c\]

that yields \[500h \times 10^{-17} joules\]
so since the light photon has such a small momentum it can vary a lot to match that uncertainty! right?

Answer 6

m not sure whether what i did is right.. or horribly pelletty .. please bare with me :D

Answer 7

You are correct that there is a relationship between single-slit diffraction and the uncertainty principle - well done :) It is a very interesting phenomenon as it almost allows us to see quantum stuff going on with our own eyes.

You can show quite easily that this is the case by calculating the diffraction pattern as the absolute square of the fourier transform of the slit. You may know that the fourier transform of something narrow is something wide... you can see that it makes sense in a vague way. Actually proving that the diffraction pattern is always the fourier transform of the aperture (slit) is more involved. Take it on faith for now.

Once you have the fourier transform it will be in momentum space. You define the uncertainty in momentum as half the width of the 0th order peak. Calculation actually shows the product of this with the width of the slit to be 2pi*h. Thus, not only are the effects qualitively similar, they are of the same magnitude (contrary to what gleem calculated above).

See here: http://pubs.acs.org/doi/pdfplus/10.1021/ed082p1210

Answer 8

@Mashy your calculation seems weird.. frequency isn't measured in nm.. Wavelength is.. and then did you put value of c correctly in your calculations?

Answer 9

oh damn lol.. yea sorry about that :D

Answer 10

min uncertainity would be 5.27E-31
and the obtained uncertainity with 500 nm is 1.32E-27 (which is gretaer) so, it makes sense..

Answer 11

\[p = hc/\lambda \]

so the momentum would be of the order of

h*10^17 .. which is way way higher than h*10^4.. so i guess it really doesn't make much sense :O

Answer 12

momentum=h/\(\lambda\)=h/500nm=2h*10^6
makes sense..

Answer 13

OMG... what am i DOING!!!.. m really sleepy!!!

Answer 14

the order of that momentum is 10^2 higher than the min. uncertainty right?

Answer 15

we require uncertainity greater than or equal to \[\frac{h10^4}{4\pi}\] and 2h*10^6 is greater than that.. so, i guess it makes sense..

Answer 16

no no its not like that.. see if the energy is higher.. then the obviously the uncertainty is high enough.. and the photons wouldn't behave crazily.. only if the energy was lower then the photons would behave crazy and we would get the diffraction

Answer 17

where does energy come from? We are not concerned about energies.. or are we?

Answer 18

This is weird.. Can't make anything out of it..

Answer 19

i mean't momentum sorry.. i mean if the momentum is so high anyways.. then obviously we would have high enough certainty .. and there is no need for crazy behavior .. thats why we don't see such crazy things at a macro level... cause our order of calculations are so high that we have high uncertainties.. and really don't see the effect of it

Answer 20

waiting for a simple yet profound reply from @experimentX

Answer 21

haha ... these days I'm having math exams!!

Answer 22

Oops!! I didn't know that.. haha..

Answer 23

ha.. great i suck at quantum mechanics :P.. right now i am really trying to understand how max planck came up with quantum theory.. really.. everywhere they explain the theory but no where am i able to understand how planck thought of it.. or why did he think of it.. exactly what connection he saw between that and the black body radiation.. i mean if we start with quantum theory its now easy to understand the radiation curve.. but going the other way around is difficult.. anyone knows exactly what and how he must have thought of it?

Answer 24

energy is emitted from black body in certain packets.. which was later called photons.. that's where it all began..
And no one knows why scientists think that way..
The most weird of all is De-broglie.. why should matter behave as waves?? But unfortunately they do... Accept it... :\

Answer 25

no no.. people do know it.. there are articles on it.. but its difficult to understand.. i am reading this one article in which they have explained what was probably going in planck's mind with examples :D

and De-broglie.. well he just thought of symmetry in physics.. if light that was thought of waves could behave as particles.. why can't particles behave like waves.. and so he went about his hypothesis

Answer 26

Hold it guys. One has to be careful when taking about momentum of a photon. Unlike a particle it has no mass and more importantly has a constant velocity C in any reference frame or direction. The only way the momentum can be determined is by frequency or wavelength or energy. The formalisms that have "demonstrated" the applicabilty of the HUP to a slit experiment have used a transverse momentum across the slit opening and have derived a velocity but it is not C. So for that formalism all bets are off.

The only way to determine any uncertainly in the momentum of light ( and therefore the energy) is to determine a shift in frequency of the transmitted light from the incident light .
ΔE≥hc/2πΔx
Δf=ΔE/h

For our case a slit width of 0.1mm photon energy of ~ 2 ev. f ~ 500 THz. wavelength ~ 600nm (orange light) and h=4.137x10^-15 eVsec, the uncertainty in the frequency which can be take as its spreading comes out to 5 THz ( 2.5THz high and 2.5 THz low) which is the far infrared . I suppose it might be measurable but not as shift in spatial information.

Its fun to play with HUP but it is a limit a boundary not an exact relationship. In at least on "demonstration" of its consequences to macroscopic phenomena it was used to provide a photon with an incremental change in momentum ( and erroneously velocity) as if HUP caused it. And it just occurred to me how is a photon localized?. A particle has a diameter, How big is a photon It seems HUP is even harder to apply.

Answer 27

There is no connection between diffraction and the uncertainty principle. Diffraction is a classical mechanics result, the uncertainty principles is strictly quantum.