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Hands-On Quantum Uncertainty

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

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

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

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

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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?

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

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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.

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

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

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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.

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

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

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

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

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= 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

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Classical Polarization of Light

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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?

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What if the filters are at 45 o ?

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How can we explain this?

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

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

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

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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.

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

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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.

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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.

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

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Up close. Far away.

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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.

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

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

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Only electrons near the metal plates were detected. metal plates

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

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

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

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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?

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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.

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

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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.

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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.

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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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