# Tag Info

8

The link about superluminal neutrions you cite is missing the fact that later on an error was discovered, and neutrinos do not, in fact, travel faster than light (see e.g. the Wikipedia article). To date, nothing that travels faster than light is known. The uncertainty principle does not "allow for the creation of virtual particles". The idea of such pairs ...

5

As usual, you can re-express the wave-function in momentum space (it's just a Fourier transform away from the spacial wave-function for bound state which is really nice). But that does not tell you how the electron moves anymore than the spacial wave function tells you where it is. Instead, it tells you the probability distribution function for results of ...

5

The uncertainty principle says something a deeper than "it is impossible to measure both position and momentum to arbitrary accuracy". It says 1) The accuracy is precisely limited by $\Delta x \Delta p > \hbar/2$. 2) In fact, this is not a limit of our measuring procedure, but a limit of reality. If something has well-defined position, it does not have ...

5

It is perfectly possible to use wavelets to analyse quantum mechanical situations. The wavelets are localised in both time and frequency but they are themselves subject to the uncertainty principle - if you want a better time resolution, you need to pay for it with a coarser frequency resolution. The uncertainty principle is a universal wave phenomenon and ...

3

As ACuriousMind says in a comment, this isn't the approach Yukawa used in his 1935 paper (Yukawa H 1935 Proc. Phys. Math. Soc. Japan 17 48) though whether he did that calculation in the privacy of his own notebook only he knows. The calculation you describe is a rather arm waving sort of justification for the relationship between the mass of the mediating ...

2

The uncertainty principle doesn't say anything about simultaneous measurements of a particle - that's just a myth which originated from Heisenberg's interpretation of it. Let us first describe the basis of quantum physics and let's start with the most innocent looking object: the quantum state. We can see a quantum state as a prescription to prepare a ...

2

According to the Quantum Mechanics, one cannot talk about a particle's position but about the probability of the position of the particle. A wave function is a function whose product with its conjugate gives the probability distribution of the position of the particle. Since the particle is known to be located somewhere in the range, the wave function should ...

1

In Peskin's introduction to quantum field theory, he talks about this in chapter 2, section 4 in a subsection titled causality, which is on page 27 in my book. He explains that yes, there is some non-zero probability that a particle will move faster than the speed of light. However, he shows any two local operators that are separated by a spacelike ...

1

tl;dr In general no, but for bound systems the RMS momentum is within a small factor of the momentum width Let's start with the title question: Is the momentum of a microscopic particle always equal to or less than the error of momentum Certainly not. For example, when you set up a beam of electrons in a CRT their momentum far exceed the uncertainty ...

1

In order to measure an object's speed, you need at least two measurements of its position at different times. This is not the case. The radar guns used by police to determine if you are exceeding the speed limit do not use position measurements. They instead measure the frequency difference between the outgoing and reflected signals. No position ...

1

I agree with the first half of your question, but I think you have wandered astray in the second part. The theory of quantum mechanics is based on a number of axioms. A thorough description of these can be found in this paper, though this is a rather greater level of detail than would be useful for most non-physicists. If you construct the theory of quantum ...

Only top voted, non community-wiki answers of a minimum length are eligible