# Why doesn't this experiment violate the Uncertainity Principle?

Is it possible to slow an electron in such a way(for example using a cyclotron to decelerate the electron ) that it completely stops. And since we created the slowing mechanism we might be able to predict its position when it is in rest. But this is in violation to the uncertainty principle. Can anyone help me with this? Thanks.

Thank you for your answers, they all made me learn something new. As you wanted me to give a clearer explanation of what I had in mind: A cyclotron is used to accelerate particles right. If we use the same mechanism but send an electron in through the original exit of the cyclotron and reverse the direction of B field and apply the electric field in such a way as to decelerate the electrons between the 2 Ds of the cyclotron ,then, after a long time the electron would still be going in circles and its speed would go on decreasing.so if we wait long enough we might be able to violate the uncertainty principle? Am i right?

• You seem to answer your own question. "Is it possible...?" ... "But this is in violation to the uncertainty principle". – lemon Jul 4 '16 at 10:27
• my point is why should the uncertainty principle not be violated. Also the situation seems completely possible as far as I can see. Can someone tell me what I am missing? – lifelong_student Jul 4 '16 at 11:38
• Try to give more details about your proposed mechanism. You may quickly see where the flaws are... – lemon Jul 4 '16 at 11:57
• Whenever you will try to see that electron which is at rest you have to provide some light because of which it will get some momentum – Mr. Robot Jul 4 '16 at 14:33

## 2 Answers

Firstly, as an aside, note that there is nothing special about bringing the electron to 'rest', as there is no such thing as absolute rest or motion. What you want to do is get the electron in a state of any precise velocity (and hence momentum).

Now the way the accepted (thoroughly tested) quantum mechanical framework works is that if you tell me the state wave-function of a particle in momentum-space (e.g. a momentum eigenstate in your case), the particle's state wave-function in position-space is automatically determined mathematically (by a Fourier Transform, to be precise). And it just so happens that a narrowly defined function in momentum-space corresponds to a spread out function in position-space.

If you want to construct a thought experiment to violate this principle (and that is a very good learning exercise, by the way) you need to give a reasonably clear description of an apparatus which would pin down an electron's momentum (e.g. by a filtering potential) whilst at the same time physically stopping the particle's wave-function from spreading out (e.g. by an essentially infinite potential barrier).

Many people have tried to come up with such schemes, but they all fail.

That's not to say you shouldn't try, because seeing what goes wrong with such proposals provides more insight into what the uncertainty principle really means.

However, just proposing to 'stop' an electron in its tracks provides no reason to doubt that its spatial wave-function will spread out in the process. You need to tell us how you will stop this spreading out from happening, since there is plenty of evidence that it really does happen.

Quantum mechanics states that an object in its lowest energetic state still has energy (https://en.wikipedia.org/wiki/Zero-point_energy), so it would not be possible to slow the electron to zero velocity. Consequently, the uncertainty principle is not violated.