How should I imagine quantum mechanics?

Like Einstein, I struggle a bit with some things about quantum mechanics. For example, I can’t imagine what this really means: “Something isn’t real until it’s measured, otherwise you just have a wave of probability.”

When I was thinking about this, I thought maybe I could compare it with the following situation. We take a random street where many people walk. Suppose we now want to know at the end of the day which of the people who have walked down the street in the past 24 hours has the most hair on their body. We can make an estimate (“probability”) based on how many people walk through the street on average per day and how much hair a person has on his body. For example, from this we could conclude that the person with the most hair probably had about 600,000 hairs. But if we really want to know (“reality”), we have to stand in the street and count everyone’s hair.

So now I would like to know if this representation is useful. Can I really imagine quantum mechanics like this? Thanks!

Asker: Sebastian, 17 years old

Answer

Indeed, quantum mechanics contains a number of concepts that are counterintuitive and go against our day-to-day experience.

Classically we assume that a particle always has a well-defined position and speed. You may be left with an uncertainty (measurement error) if you want to determine that position, but you assume that you can determine that position with arbitrary accuracy as long as your measuring instrument is accurate enough. In quantum mechanics we have to give up those certainties.

The example you give is essentially still a ‘classic’ example in the sense that you can determine all the data infinitely accurately at any time when you take a measurement. The uncertainty relation from quantum mechanics is more fundamental than that: it says that you CANNOT determine all parameters together infinitely accurately, regardless of the measuring instrument you use. It’s like looking at your street through the fog.

Actually, the uncertainty relationship is not so strange in itself: it simply comes from the classical theory of waves. What is special about quantum mechanics is that we are going to describe the behavior of particles as if they were wave packets. And immediately you get the uncertainty relation on top of it.

That (small) particles (eg electrons) have a wave character is overwhelming experimental evidence, so we MUST accept that. As soon as you look at a particle as a wave packet, the uncertainty relationship becomes somewhat more understandable.

Suppose you throw a rock into the water. You see a wave package propagating on the water surface. Where exactly is the wave? You can’t answer that. You can indicate approximately where the water is disturbed, you can indicate the point with the highest amplitude, you can indicate where the disturbance of the water surface is negligible, but you quickly come to the conclusion that the term ‘exact position’ makes no sense here. has.

Suppose you want to determine the exact frequency of a wave. The wave must therefore be a perfect sine wave. To determine that frequency exactly, you have to make sure (measure) that it is a perfect sine wave and does not stop at a certain moment or change into a signal of a different shape. In other words, you have to measure indefinitely. The result is that you know the frequency infinitely accurately, but you have no idea where that wave is: it is infinitely long and is therefore everywhere.

Suppose you have a wave packet whose position you can determine with infinite precision: such a packet could for example be a very sharp peak (what we call a delta function). You can now determine the position of that package extremely accurately at a certain moment, but a delta function is actually the sum of infinitely many sines: your uncertainty about the frequency is infinitely large.

You see that the uncertainty relation is not so strange in itself, what our minds protest against is that we apply these properties, which are typical for waves, to particles.

Answered by

Prof Walter Lauriks

Physics Acoustics

Catholic University of Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/

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