The Heisenberg Uncertainty Principle

[Vitruvian]

full-size video here

"We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power."
--Bertrand Russell

[KBCraig]

Is that really an accurate portrayal of the Heisenberg (Uncertainty) Principle?

Narrowing the opening through which light passes has been known for centuries as as way to produce a lens effect. Being near-sighted, I learned 30 years ago how to create tiny apertures between my fingers that would allow me to see the blackboard or distant objects in perfect focus. Pinhole cameras, anyone?

I'm no physicist, so perhaps I'm confusing Heisenberg's work with the "observer effect", which is commonly credited to Heisenberg.

[Jacobus]

I agree with KBCraig.  This demonstration is a better depiction of diffraction than Heisenberg's Uncertainty Principle. 

The spatial distribution of the light after passing through a slit can be derived by treating each point of light emanating from the slit as a point source of light that produces a spherical (or circular, if working in 2D) wave.  Further out from the slit, the effects of each of these point sources add up and interfere with each other to produce some pattern.  Thinking in this way, you can see how as the slit approaches zero width, only a spherical wave would emanate from it that would completely spread out.

If you do some geometry you can set up an integral formula to describe the spatial distribution of light at any plane beyond the slit.  The near field formula is the Fresnel formula and is difficult to use.  But as you get further from the slit, yuo can use approximations and you get the Fraunhofer equation, which is actually a Fourier Transform.

Using Fourier Transforms is fun and easy.  Now, the cool thing about a laser beam is that its spatial distribution can be described by a Gaussian (i.e. normal) distribution.  And one of the cool properties of a Gaussian distribution is that any linear operation on one produces yet another Gaussian distribution (including integration and Fourier Transforms).  It is the only such distribution with this property I believe.  This is one way of seeing why a laser beam continues to propagate as a laser beam (so long as it is not passed through a slit).

As for slits, if you know anything about Fourier Transforms, then you know that an impulse (i.e. a zero-width energy input) in one domain yields a unit distribution (i.e. even across all values) in the other domain.  In fact, there is an inverse relation between the "width" of the distribution in one domain and the "width" of it in the other.  So as a slit narrows, the distribution in the first plane better approximates an impulse, and as a result the distribution in a plane further out better approximates a unit response.

Now, I think this inverse relationship about the localization of the field in one plane (the one with the slit) and in a plane further out from the slit might have relation with the uncertainty principle.  I seem to recall the uncertainty principle defines inverse relationships between properties (i.e. localization of a particle and its momentum).  So maybe if you define the uncertainty principle as applying anywhere there is an inverse relationship between two quantities you are trying to measure, it applies here.       

[Puke]

"You ruined the outcome by measuring it!"

Which Professor of a canceled sci-fi animated show said that?

[Vitruvian]

The principle states, in part, that an increasingly precise determination of one property (either position or momentum) of a given particle will render determination of the other property increasingly imprecise.  The experiment in the video seems to demonstrate this phenomenon.  When the slit is made extremely narrow, the (horizontal) position of the laser's photons can be determined.  Following the uncertainty principle, therefore, one should be unable to determine the photons' momentum, otherwise the beam would appear as a point on the projection screen no matter how narrow one made the slit.

[KBCraig]

"You ruined the outcome by measuring it!"

Which Professor of a canceled sci-fi animated show said that?

Ron Jeremy?

[Puke]

Ron Jeremy?

Ron Jeremy was in a cancelled sci-fi animated TV show?!

[KBCraig]

Ron Jeremy?

Ron Jeremy was in a cancelled sci-fi animated TV show?!

Sorry. Lame joke about "measuring it".

[ReverendRyan]

Professor Farnsworth, of course.

And personally, I use the chicken to measure it.

[Puke]

Professor Farnsworth, of course.

And personally, I use the chicken to measure it.

Booyah!