Physics Stack Exchange
Physics Stack Exchange

Questions tagged [heisenberg-uncertainty-principle]

This tag is for Heisenberg's quantum mechanical uncertainty principle. DO NOT USE THIS TAG for uncertainty in a non-quantum measurement.

This tag is for Heisenberg's uncertainty principle in quantum mechanics. DO NOT USE THIS TAG for uncertainty in a non-quantum measurement: Use the tag instead.

The Heisenberg Uncertainty Principle (HUP) states that $\sigma_x\sigma_p\geq\frac{\hbar}2$. This comes from the non-commutativity of matrix multiplication in Heisenberg's & Pauli's matrix mechanics.

1510 questions
141
votes
8 answers

What is $\Delta t$ in the time-energy uncertainty principle?

In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to infinity. What does the $\Delta t$ mean, since…
Hobo
  • 1,435
118
votes
18 answers

Can the Heisenberg Uncertainty Principle be explained intuitively?

I have heard several pseudoscientific explanations about the Heisenberg Uncertainty Principle and find them hard to believe. As a mathematician mainly focusing on functional analysis, I have a considerable interest in this matter. Although I still…
D1X
  • 1,290
100
votes
9 answers

Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I correct? Veritasium/Minutephysics video on Youtube.
TBBT
  • 2,777
67
votes
10 answers

Is the uncertainty principle a property of elementary particles or a result of our measurement tools?

In many physics divulgation books I've read, this seems to be a commonly accepted point of view (I'm making this quote up, as I don't remember the exact words, but this should give you an idea): Heisenberg's uncertainty principle is not a result of…
Saturnix
  • 805
58
votes
14 answers

Why is it impossible to measure position and momentum at the same time with arbitrary precision?

I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is sharply peeked its fourier transform will be…
catmousedog
  • 728
47
votes
6 answers

Does Heisenberg's uncertainty under time evolution always grow?

Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting question of my own. I guess the answer should be…
Marek
  • 23,981
46
votes
5 answers

How do I interpret uncertainty in velocity greater than the speed of light?

I just studied Heisenberg's uncertainty principle in school and I came up with an interesting problem. Assume an electron which is moving very slowly and we observe it with a distance uncertainty of say $\Delta x=1\times10^{-13} \text{ m}$ if we…
Thulashitharan D
  • 595
46
votes
3 answers

What is the decay width and why is it given in energy units?

I'm reading Thomson, Modern Particle Physics, and in chapter 16 author says that the decay width of the Z boson is $\Gamma_Z =2.452 \pm 0.0023 \,\mathrm{GeV}$. He also says the total width of the decay is the sum of the partial widths,…
Patrick
  • 1,955
41
votes
6 answers

What constitutes an observation/measurement in QM?

Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle. What is the technical definition of an observation/measurement? If I look at a QM system, it will collapse. But how is that any different from…
ThisIsNotAnId
  • 953
  • 7
  • 16
40
votes
7 answers

Isn't the uncertainty principle just non-fundamental limitations in our current technology that could be removed in a more advanced civilization?

From what I understand, the uncertainty principle states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on equipment but just a natural phenomenon. However, isn't…
user8791
40
votes
5 answers

How does non-commutativity lead to uncertainty?

I read that the non-commutativity of the quantum operators leads to the uncertainty principle. What I don't understand is how both things hang together. Is it that when you measure one thing first and than the other you get a predictably different…
vonjd
  • 3,801
39
votes
10 answers

Is there a notion of causality in physical laws?

I was reading "A Few Useful Things to Know about Machine Learning" by Pedro Domingos and towards the end of the paper he makes this statement: "Many researchers believe that causality is only a convenient fiction. For example, there is no notion of…
covfefe
  • 483
35
votes
5 answers

Heisenberg Uncertainty Principle Applied to an infinite square well

I appreciate the statement of Heisenberg's Uncertainty Principle. However, I am a bit confused as to how exactly it applies to the quantum mechanical situation of an infinite square well. I understand how to apply Schrödinger's equation and…
DJA
  • 1,038
35
votes
7 answers

Is there something behind non-commuting observables?

Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no simultaneous basis of eigenvectors of each of them.…
Gold
  • 38,087
  • 19
  • 112
  • 289
33
votes
3 answers

Why doesn't the uncertainty principle contradict the existence of definite-angular momentum states?

We know that for a position variable $x$ and momentum $p$, the uncertainties of the two quantities are bounded by $$\Delta x \Delta p \gtrsim \hbar$$ Now, this is usually first explained with $x$ being a simple linearly measured position and $p$…
bob.sacamento
  • 893
1
2 3
…
99 100