Eli5 Why can’t we “know” the speed and position of an electron simultaneously? Why can we only measure one of these properties at a time?

Question

This always confuses me and I’m not sure how it works. Please explain…

In: 252

Answer 1

In a sense, we don’t really know why. We merely notice that it seems impossible.

Not just in practice (e.g. if you look at it, that means striking it with light and watching the reflection, which would push it around), but mathematically in principle our theories can’t even imagine a way to measure both.

You might wonder, ‘why not develope a better theory’? Well, the theories have to agree with all our current experimental results, and the weird world of Quantum Mechanics seems to force us to adopt a theory with features like the “Uncertainty Principle”, which in turn leads to the inability to know the speed & position of something to high precision.

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Note that the Uncertainty Principle in this case is that we cannot know **both** *to arbitrarily high precision* at **the same time**. We can measure both, but at each moment the measurements will share between them some uncertainty.

For instance, in-principle, maybe we can get:

* a decent estimate of both position and velocity
* a great estimate of position, and a bad estimate of velocity
* a great estimate of velocity, and a bad estimate of position
* absolute 100% certainty of position, but total 100% ignorance of velocity
* absolute 100% certainy of velocity, but total 100% ignorance of position

For instance, in simple Quantum Mechanics practice problems, we sometiems deal with a perfect ‘plane wave’ of an electron. This sort of toy-idea of an Electon’s Wavefunction lets us easily read-off the velocity*, there is essentially a nubmer that tells us exactly what it is. However, this toy-idea of a wavefunction is spread out equally across the whole universe, so we forefeit literally any clue as to where it is.

In such examples, it turns out that if we want to be accurate at predicting quantum behaviour, the *only* ways that we know to successfully describe an electron is to resort to using something like a wavefunction, and any wavefunction (or similar) we use to describe it will have one of the uncertanities above. It isn’t just part of our measurement-method, but part of how the wavefunctions behave.

And, like I mentioned earlier, we can’t just use a ‘better’ wavefunction without these features, because then they don’t work (they don’t help us predict the results of experiments).

[* technically it is ‘momnetum’ rather than ‘velocity’, but that isn’t too important a differnece].