Wave-particle interpretations

[hobz]

I have been under the idea that experiments either shows the wave nature or particle nature of things, never both at the same time.

 

I recently watched a shows called "The Mechanical Universe" in which a professor demonstrates an experiment with light and Polaroid.

He explains the phenomenon in which no light passes through two cascaded polaroid lenses, polarized perpendicular to each other. He then turns the second lens at an angle of 45 degrees, and now some light passes through.

 

He says: ".. It is very easy to understand so long as we believe that light is a wave. But remember, light is also a particle, and there must be a particle explanation of how this occurs as well."

 

He explains the particle nature as follows.

 

The first filter lets all vertical polarized photons through, and rejects all other. The probability is 50% of either event.

The second filter only lets through horizontal polarized photons, of which there are none.

 

When he then turns the second polaroid oblique to the first, he states that the photons thought they were either up or down, but now are either oblique along the way of the polaroid or perpendicular to that.

 

What kind of explanation is that? "You thought you were"?

How does this really work?

 

It seems to me as though he claims that all phenomena have a wave explanation and a particle explanation, although the double slit experiment cannot be explained be either, but is explained as experiencing wave-particle behavior.

[timo]

Are you sure he rotates the 2nd filter at an angle of 45° and not adds a 3rd filter at an angle of 45° between the previous two? The latter experiment is much more impressive.

 

How it really works:

The free electromagnetic field (i.e. light) can be mathematically cast into a sum of different addends each having a wavelength, a direction of travel and a polarisation vector that is perpendicular to the direction of travel. The square of the amplitude is the intensity (for that respective wavelength for that respective direction). Let's assume the travelling direction was the z-direction so that the relevant degrees of freedom for the amplitude are all vectors of the xy-plane [math]\vec A = \left( \begin{array}{c} A_x \\ A_y \end{array} \right).[/math].

A filter projects the amplitude onto some direction (i.e. cuts out all shares in the perpendicular direction). A filter on the x-direction would mathematically be applying the matrix [math]P_x = \left[ \begin{array}{cc} 1 & 0 \\ 0 & 0 \end{array} \right] [/math], correspondingly a filter on the y-direction would be [math]P_y = \left[ \begin{array}{cc} 0 & 0 \\ 0 & 1 \end{array} \right] [/math]. So if you apply both filters on the incoming light, the resultant amplitude on the other end of the filters would be [math]\vec A_{\text{after}} = P_y P_x \vec A_{\text{before}} = \vec 0[/math] and hence the intensity would also be zero. A projection on a 45° rotated direction would be [math]P_{45} = \frac{1}{2} \left[ \begin{array}{cc} 1 & -1 \\ -1 & 1 \end{array} \right] [/math].

Now the rather boring thing is that when you rotate one of the two polarisation filters to a 45° position you get

[math]\vec A_{\text{after}} = P_{45} P_x \vec A_{\text{before}} =\frac{1}{2} \left( \begin{array}{c} A_x \\ -A_x \end{array} \right)[/math]

which will not always be zero (meaning that there's some part of the light that shines through). The much more interesting thing happens when you put a 3rd 45°-rotated polarisation filter between the two perpendicular ones:

[math]\vec A_{\text{after}} = P_y P_{45} P_x \vec A_{\text{before}} =\frac{1}{2} \left( \begin{array}{c} 0 \\ -A_x \end{array} \right)[/math]

That is usually also not equal to zero.

[hobz]

Thanks for answering.

 

You are right, he puts on a third filter.

However, your explanation assumes wave nature?

[timo]

Yes and no. For getting waves you'd add some term like exp[i(kx-wt)] as a factor to the polarisation vector. That factor does not play any role here. For getting particles you'd additionally restrict each addend to initially have a polarisation vector of a definite magnitude (where bigger magnitudes are then achieved by just having more of those addends) and call those addends particles. Restriction of the polarisation vector to some length is not necessary here, either. So I'd say it's neither particle nor wave nature that plays the crucial role. You can of course add either phenomenon (i.e. seperately or both) and still get the same result just with a few additional complications.

[lakmilis]

Thank you for the explanation Atheist... very nice and helpful

 

Although a German atheist can only make me think of Nietsche which I personally thought was a bit of a gimp but alas... it is beides the point ,)