# Hands-On Quantum Uncertainty. Quantum uncertainty is present in the diffraction, polarization and interference of light.

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Hands-On Quantum Uncertainty

Quantum uncertainty is present in the diffraction, polarization and interference of light.

Classical Diffraction of Light You will look at a bright spot of light through the slit between two pencils. Sketch what you will see.

Why does the light spread more when you make the slit narrower? How do you explain this spreading of the light?

A laser beam will be pointed through the small slit. Sketch what you will see.

The one slit can be viewed as many tiny slits side-by-side. Each of these interferes with the others. Why does it form an interference pattern?

The half width of the central maximum, is given by x = L/w. This is similar to the double-slit.

Quantum Diffraction of Light Draw this diffraction pattern. Below it, draw the pattern we would get if you used really, really, really, really faint light.

http://phys.educ.ksu.edu/vqm/html/singleslit.html

Diffraction is a wave phenomenon that can be seen with photons. It is an example of wave-particle duality.

It also demonstrates measurement-disturbance. The slit measures where the photon is and this disturbs where it goes next.

The amount of disturbance is governed by Heisenberg’s Uncertainty Principle. The more certain we are of where a photon is, the less certain we will be of where it is going.

The uncertainty in position is determined by the slit width, w, and so  x is roughly +/- w/2. xx

The photon has a momentum perpendicular to the slits of p = h/.

pp After the slit, it may be deflected up or down, producing an uncertainty in its momentum of +/-  p.

The uncertainty in momentum can be found using similar triangles. L x1x1 p = h/ pp  p = p x 1 /L = h x 1 / L

= w/2 * x 1 h / L = w/2 * L/w * h/ L = h/2 The Heisenberg Uncertainty Principal restricts the product of these two uncertainties,  x *  p

Classical Polarization of Light

Put on the glasses, close one eye and then look at your neighbour's eyes. Try tilting your head. What do you observe? How do you explain this?

What if the filters are at 45 o ?

How can we explain this?

What if you put a third filter in between two crossed filters?

Quantum Polarization of Light Will the photon go through the second filter? Yes, No or ?????

How do you explain this? Will the photon go through the second filter? Yes, No or ?????

What is detected on the far side of a filter is either a photon or no photon. However, whether it gets through or not is calculated using components of a wave. This is another example of wave-particle duality.

The photon’s state of polarization is disturbed by a filter. This is also an example of measurement-disturbance.

If the photon gets through a vertical polarizer, then we are certain it will go through a vertical filter but not a horizontal one. This is also an example of Heisenberg’s Uncertainty Principle.

However, we are uncertain about any other basis. We are reduced to probabilities. It will have a 50:50 chance of going through a filter at 45 0.

Classical Interference A laser beam is aimed at a pin. Sketch what will you see up close and far away.

Up close. Far away.

Quantum Double-Slit Interference Does a photon go through one slit, neither or both? If the light is really, really low intensity, we have another example of wave-particle duality and measurement-disturbance.

What happens with electrons? This was tested in Tubingen in 2006. top view metal plates

Electrons that induced a current in one of the metal plates, showed which slit they went through. side view metal plates

Only electrons near the metal plates were detected. metal plates

Electrons far from the metal plates were not detected. Electrons near the metal plates were detected.

If you are uncertain, the two possibilities can interfere. If you are certain which path it took, there will be no interference pattern.

What will you see if you put horizontal and vertical polarizers on either side of a double slit?

The polarizers allow us to be certain as to which slit the photons went through, so the interference pattern disappears. What will happen if you add a third polarizer after the slits?

If the polarizer is at 45 o, the pattern returns. Why? After a photon passes through a 45 o filter, we are uncertain whether it was vertical or horizontal. We don’t know which way it went.

The polarizer is acting as a quantum eraser. It erases our knowledge of which way the photon went.

So, which way does the photon go? If we are certain which way it went, it acts like a particle. There is no interference pattern.

So, which way does the photon go? Only if we are uncertain of its path, does acts like a wave and make an interference pattern. We can’t be certain.

Measurement produces certainty of a photon’s polarization in one basis and destroys it in all others. Diffraction is a result of the uncertainty in momentum caused by a slit measuring position. Certainty of which slit a photon goes through destroys the interference pattern.

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