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

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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 ...
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9answers
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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 ...
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9answers
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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): ...
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8answers
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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 ...
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6answers
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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 ...
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7answers
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An entropy of the Wigner function

Is there an entropy that one can use for the Wigner quasi-probability distribution? (In the sense of a phase-space probability distribution, not - just von Neumann entropy.) One cannot simply use $\...
24
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3answers
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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 ...
23
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3answers
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Is there an actual proof for the energy-time Uncertainty Principle?

As I understand, the energy-time uncertainty principle can't be derived from the generalized uncertainty relation. This is because time is a dynamical variable and not an observable in the same sense ...
22
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6answers
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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 ...
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6answers
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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 ...
22
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8answers
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Why do quantum physical properties come in pairs?

Why do quantum physical properties come in pairs, governed by the uncertainty principle (that is, position and momentum?) Why not in groups of three, four, etc.?
21
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4answers
402 views

Heisenberg's uncertainty principle for mean deviation?

The Heisenberg uncertainty principle states that $$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$ However, this is only for the standard deviation. What is the inequality if the mean deviation, defined as ...
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2answers
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Theoretical penetration limit for evanescent waves

Consider a problem in classical electrodynamics, when a monochromatic beam experiences total internal refraction when traveling from a medium with $n>1$ to a medium with refractive index $1$ - see ...
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4answers
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Uncertainty in Uncertainty?

I was reading about how the Planck's Constant can be measured with LEDs, which made me think about this question. The Heisenberg Uncertainty Principle states that: $$\Delta x \Delta p \ge {\hbar\...
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1answer
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Is the Uncertainty Principle valid for information about the past?

My layman understanding of the Uncertainty Principle is that you can't determine the both the position and momentum of a particle at the same point in time, because measuring one variable changes the ...
17
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2answers
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Is the uncertainty principle just saying something about what an observer can know or is it a fundamental property of nature?

I ask this question because I have read two different quotes on the uncertainty principle that don't seem to match very well. There are similar questions around here but I would like an explanation ...
16
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3answers
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Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?

Thought experiment: what happens if we measure momentum of a particle so precisely, that the uncertainty of its position becomes absurd? For example, what if the uncertainty of the position exceeds 1 ...
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4answers
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Does the uncertainty principle apply to photons?

Wikipedia claims the following: More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being ...
14
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3answers
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Is there a prediction of quantum mechanics that could be construed as representing an “energy-time uncertainty relation?” [duplicate]

As the title suggests. Is there a prediction of quantum mechanics that could be construed as representing an "energy-time uncertainty relation?" Does there exist any reference to such a prediction, or ...
13
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4answers
927 views

Can momentum have a complex expectation value?

I'm making examples of wave functions to incorporate in a QM exam. I came up with the following wave function, which gives me some troubles: $$\psi(x,0) = \begin{cases} A(a-x), & -a \leq x \leq a\...
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6answers
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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 ...
13
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2answers
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Meaning of the anti-commutator term in the uncertainty principle

What is the meaning, mathematical or physical, of the anti-commutator term? $\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle [ A,B ] \rangle \vert^{2} ...
12
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3answers
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Heisenberg's uncertainty principle - $ \Delta p $

So I was reading this paper, "Limits to Binary Logic Switch Scaling—A Gedanken Model". The following is the paper's abstract: In this paper we consider device scaling and speed limitations on ...
12
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1answer
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Quantum uncertainty of particle falling in black hole

A stationary observer at infinity sees a particle of mass m falling in a supermassive Schwarzschild black hole. He observes an increasing redshift and sees the particle ceasing to progress when it ...
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2answers
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Virtual particles and physical laws

Recently, I was reading about Hawking Radiation in A Brief History of Time. It says that at no point can all the fields be zero and so there's nothing like empty space(quantum fluctuation etc.). Now, ...
11
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1answer
925 views

What exactly does the Hamiltonian operator tell us?

I'm confused about how energy and time are linked. On the one hand, the Hamiltonian seems to describe the time evolution of the system because in the time dependent Schrodinger equation, $$ \hat H \...
11
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2answers
642 views

Do stationary states with higher energy necessarily have higher position-momentum uncertainty?

For simple potentials like square wells and harmonic oscillators, one can explicitly calculate the product $\Delta x \Delta p$ for stationary states. When you do this, it turns out that higher energy ...
11
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2answers
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Why uncertainty principle is not like this?

In Griffiths' QM, he uses two inequalities (here numbered as $(1)$ and $(2)$) to prove the following general uncertainty principle: $$\sigma_A^2 \sigma_B^2\geq\left(\frac{1}{2i}\langle [\hat A ,\hat B]...
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6answers
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If I drop a leaf twice from the height of a tree in a completely controlled environment, will the trajectory in each case be the same?

Putting my question in other words, can earth form again if a similar initial universe condition is given? The uncertainty principle says that we cannot tell with certainty the position of a particle ...
10
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6answers
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Will Determinism be ever possible?

What are the main problems that we need to solve to prove Laplace's determinism correct and overcome the Uncertainty principle?
10
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1answer
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Question on Uncertainty Principle

I have read about the uncertainty principle. And it applies to electrons. Then how is it that we can get exact tracks of electrons in cloud chambers?? That is to say that how is it that the position ...
9
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3answers
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Eigenstate of position+momentum?

I'm studying Quantum Mechanics on my own, so I'm bound to have alot of wrong ideas - please be forgiving! Recently, I was thinking about the quantum mechanical assertion (postulate?) that states with ...
9
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5answers
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Are there any practical applications of the uncertainty principle

I believe GPS works because of extremely small time differences between the satellites. Because of how small the time differences are, it needs to take into account gravity's effect on time. ...
9
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2answers
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How do tracking detectors in particle accelerators create the pretty pictures we see?

I have read several sources about tracking detectors used in particle accelerators like LHC, but still have not found a more detailed source that can still be understood by a layperson like myself. I ...
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Concept of a point particle in quantum mechanics

A point particle is usually thought of as structureless and without dimension. However, given that Heisenberg's uncertainty principle prohibits us from knowing the position of a particle exactly, what ...
8
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4answers
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Is it possible for $\Delta x$ ($\sigma_x$) of any free particle wave packet to be decreasing at any time?

Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens ...
8
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4answers
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What does it mean “not to have a definite trajectory”?

In a comment to my question someone stated the following: "photons do not travel at some definite number of oscillations per second. In fact, they do not "travel" at all, no more than electrons ...
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4answers
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Is the uncertainty principle axiomatic or derived?

To take an example, Feynman Lectures Vol 3 13-1 Let's think of an electron which ban be in either one of two positions [...] There are two possible states of definite energy for the electron. ...
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6answers
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Does the HUP alone ensure the randomness in QT?

This answer of mine has been strongly criticized on the ground that it is no more than a philosophical blabbering. Well, it may well be. But people seem to be of the opinion that HUP alone does not ...
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2answers
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Heisenberg Uncertainty Principle: Which formula is correct?

Some websites and textbooks refer to $\Delta x \Delta p \geq \frac{\hbar}{2}$ as the correct formula for the uncertainty principle whereas other sources use the formula $\Delta x \Delta p \geq \hbar$ ....
8
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2answers
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Was uncertainty principle inferred by Fourier analysis?

I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
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Conjugate Variables, Noether's Theorem and QM

What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
8
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3answers
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An electron falling into a black hole

If an electron falls into a black hole. How can the Heisenberg uncertainty principle hold? The electron has fallen into the singularity now so it has a well defined position which means that it doesn'...
8
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5answers
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Why doesn't a quantum particle in an attractive 1D potential accumulate at the center?

I have two questions regarding (possibly counter intuitive results) Schrodinger equation and its application to two (strictly hypothetical) scenarios. Consider the 1D potential $V(x) = - \frac{\...
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1answer
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Uncertainty Principle Intuition

So, as your usual physics undergrad, I read Griffiths's derivation of the general uncertainty principle. I understood it but there was no physical intuition given behind it in the book. It was ...
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3answers
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Connection between $\Delta x \Delta p \geq \frac{\hbar}{2}$ and $\Delta E \Delta t \geq \frac{\hbar}{2}$

Is there a way to derive second equation from the first one? I mean is there a connection between those two uncertainty relations? \begin{align} \Delta x \Delta p &\geq \frac{\hbar}{2}\\ \Delta ...
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7answers
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Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes ...
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Is the uncertainty principle valid?

The uncertainty principle says that the product of the uncertainties in position and momentum can be no smaller than a simple fraction of Planck's constant $h$. Several articles lately suggest this ...
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Does uncertainty imply noncommutativity?

We already know that non-commutativity of observables leads to uncertainty in quantum mechanics cf. e.g. this and this Phys.SE post. What about the opposite: Does uncertainty imply noncommutativity? ...
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Why is the Heisenberg uncertainty principle stated the way it is?

I spent a long time being confused by the Heisenberg uncertainty principle in my quantum chemistry class. It is frequently stated that the "position and momentum of a particle cannot be ...