Police Inspection in a "Quantum" car

The Joke

Our two "quantum" friends, Schrodinger (on the left) and Heisenberg (on the right), are getting bored in the office and they decide to take a ride with the car.


Heisenberg is driving very fast down the motorway when a policeman pulls them over for inspection. The police walks up to the window and asks Heisenberg



-Hello Sir, do you know how fast you were going?

Heisenberg replies immediately,

-No, but I know exactly were I was.

The policeman finds the reply too weird and decides to further investigate the car, so he tells Heisenberg to open the boot of the car.

-Hey you, do you know there is a dead cat in here, the policeman shouts,

 and Schrodinger replies

-Well ,we weren't sure, but know we do know!

Background
That was a double joke in a package of one. The first part of it is related to Heisenberg's so called uncertainty principle. This principle is in the origin of quantum mechanics, the theory that describes nature at the sub-atomic scales, and has profound physical and philosophical implications. In other words we could write for hours about the uncertainty principle. In a glimpse, in quantum mechanics some physical quantities cannot be measured with infinite accuracy, in other words cannot take exact values. One example of such quantities is the position and momentum (velocity times the mass) of a particle. As we know this is in contrast to classical mechanics, where we can have statements about the exact position of a particle at some time t, and its exact momentum at the same time. However this is no longer true in quantum mechanics.

One way to understand it is the following. At sub-atomic scales, in order to measure the momentum (velocity times mass) of a particle we have to send a signal, in the same way that the police uses its speed-guns to measure the speed of passer-by cars; it sends an electromagnetic signal to the car, the signal (or wave) is reflected to the car and comes back to the speed-gun. In the same fashion, we send an electromagnetic wave (signal) to the particle under question. But if we want a precise measurement of momentum, we have to send a low-energy wave (otherwise a high-energy wave would ''disturb" the particle and change its moment; it is like throwing a fast ball into another ball, the former would change the velocity of the latter by a great amount). But low energy waves have big wavelengths (the length of a wave in a period time). This implies that this wave which measures the momentum precisely has a huge uncertainty in position. In order to understand why waves with big wavelength cannot identify the position of a particle think the following. Imagine you have huge hands and you would like to grope something extremely small. Obviously you will never grope all the details of that object. You can barely say what it is, or where it is. However you need tiny fingers to be able to probe all its details and find it. In the same way the smaller wave(length) the more precise we measure the position and vice versa.

On the other hand if we sent a wave with small wavelength we would be able to measure the particle's position with great accuracy, but small wavelength implies that the wave has large energy. And the latter implies  that the energetic wave would "disturb" the momentum of particle a lot, without being able to measure its exact value.

The moral of this thought experiment is that in the realm of quantum physics,

The more precise the position is determined the less precisely the momentum is known in this instant, and vice versa. - Heisenberg, uncertainty paper, 1927. 

More about the origins of the uncertainty principle here. This statement usually comes with the mathematical formula

$\Delta x \Delta p \geq \hbar$

where $\Delta x$ and $\Delta p$ are the uncertainties in position and momentum respectively and $\hbar$ is a constant (the Planck constant).
For the advanced readers the fact that these two quantities cannot be measured exactly at the same time comes from the fact that their commutator is not vanishing, i.e.

$[\hat x, \hat p]= i \hbar$.

So, back to the joke, when the police stops Heisenberg, he doesn't know how fast he goes, but he knows exactly his position because of the uncertainty principle. (Now please laugh)

The second part of the joke is the well-known Schrodinger's thought experiment with the cat which is both dead and alive (with equal probabilities). We only know the outcome only after observing it. We are not going to describe it, since you can read about it everywhere  (see for example here). A very nice and related thought experiment is the double slit experiment, which is described excellently in this video

(Now please laugh again! :P )

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