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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.

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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 ...
Hobo's user avatar
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117 votes
18 answers
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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 ...
D1X's user avatar
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98 votes
9 answers
24k views

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 ...
TBBT's user avatar
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67 votes
10 answers
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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): ...
Saturnix's user avatar
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58 votes
14 answers
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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 ...
catmousedog's user avatar
46 votes
6 answers
6k views

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 ...
Marek's user avatar
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45 votes
5 answers
6k views

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 ...
Thulashitharan D's user avatar
41 votes
3 answers
40k views

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 ...
Patrick's user avatar
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40 votes
5 answers
15k views

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 ...
vonjd's user avatar
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39 votes
7 answers
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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 ...
user avatar
39 votes
6 answers
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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 ...
ThisIsNotAnId's user avatar
38 votes
10 answers
5k views

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 ...
covfefe's user avatar
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35 votes
7 answers
7k views

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 ...
Gold's user avatar
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34 votes
5 answers
15k views

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 ...
DJA's user avatar
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33 votes
9 answers
7k views

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.?
user6090's user avatar
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33 votes
7 answers
2k views

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 $\...
Piotr Migdal's user avatar
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31 votes
3 answers
6k views

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 ...
TheQuantumMan's user avatar
30 votes
3 answers
3k views

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 $x$ ...
bob.sacamento's user avatar
29 votes
4 answers
5k views

Why doesn't the phase operator exist?

In many articles about quantum optics, the phase-number uncertainty relation $$\Delta \phi \Delta n \ge 1$$ has been mentioned and used as a heuristic argument, but they say that the phase-number ...
Veteran's user avatar
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28 votes
3 answers
1k 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 ...
Zach466920's user avatar
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28 votes
3 answers
1k views

Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq \left|\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\...
hyportnex's user avatar
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26 votes
1 answer
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Did I get hit by a car this morning?

Quantum mechanics allows us to describe a particle as a wave, and also a collection of particles, which a car happens to be. What separates a typical wave from a classical particle is that the ...
B. Brekke's user avatar
  • 1,772
25 votes
7 answers
6k views

What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle

Assuming a laser beam going back and forth between two mirrors, what would happen if we keep bring the mirrors closer and closer to each other? Because after a certain width, we would be knowing both ...
Xfce4's user avatar
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23 votes
11 answers
7k views

What does Heisenberg's uncertainty principle tell about nature? [closed]

I agree with the fact that the principle points out to the inaccuracy in the measurement of the two quantities of the particles (momentum and position). But measurements apart, does it explain ...
Swaroop Joshi's user avatar
23 votes
4 answers
15k views

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 ...
Pricklebush Tickletush's user avatar
22 votes
2 answers
4k views

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, ...
Yashbhatt's user avatar
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22 votes
2 answers
2k views

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 ...
Asciiom's user avatar
  • 613
21 votes
4 answers
3k views

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\...
Udit Dey's user avatar
  • 552
21 votes
3 answers
2k views

How can I solve this quantum mechanical "paradox"?

Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
user32109's user avatar
  • 511
21 votes
2 answers
5k views

What is the 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}...
Rodrigo Thomas's user avatar
21 votes
2 answers
2k views

How are cloud chamber tracks consistent with the uncertainty principle?

I have read about the uncertainty principle. As it applies to electrons, 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 is fixed?...
Pallavi Roy's user avatar
20 votes
5 answers
11k views

Can the momentum operator have an imaginary 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,\...
Nicolas's user avatar
  • 331
20 votes
3 answers
8k views

The Planck constant $\hbar$, the angular momentum, and the action

Is there anything interesting to say about the fact that the Planck constant $\hbar$, the angular momentum, and the action have the same units or is it a pure coincidence?
Isaac's user avatar
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20 votes
2 answers
4k views

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 ...
Piotr Migdal's user avatar
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19 votes
2 answers
7k views

Uncertainty principle for a sitting person

If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths. What am I missing? Do ...
Fakrudeen's user avatar
  • 751
19 votes
5 answers
5k views

If perfect blackness violates the Uncertainty Principle, how isn't dark matter a violation?

In a recent tweet, Dr. Michio Kaku stated that perfect blackness would violate the Heisenberg Uncertainty Principle, i.e. every object must emit some radiation. I have two questions regarding this ...
playdis's user avatar
  • 353
19 votes
3 answers
1k views

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 ...
mbeckish's user avatar
  • 635
18 votes
4 answers
3k views

Are "intelligent" systems able to bypass the uncertainty principle?

This paper talks about finding theoretical correlations to experiential phenomena in quantum mechanical experiments using artificial intelligence (AI). If AI applications can be sufficiently well ...
Maan's user avatar
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18 votes
2 answers
2k views

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 ...
John's user avatar
  • 393
18 votes
4 answers
18k views

Factor 2 in 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 \...
Patrick's user avatar
  • 281
17 votes
6 answers
5k views

Heisenberg's Uncertainty Principle [duplicate]

I have heard various definitions of the uncertainty principle. Yet I cannot quite comprehend how it is true. Nevertheless, something tells me, it is a consequence of the wave nature of light/electron ...
Jyotishraj Thoudam's user avatar
17 votes
5 answers
2k views

How can I accurately state the uncertainty principle?

In almost every introductory course, it is taught that the uncertainty principle happens due to disturbance in the system to be measured. Teachers give these examples that induce students to ...
1__'s user avatar
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17 votes
2 answers
798 views

Why is the uncertainty principle not $\sigma_A^2 \sigma_B^2\geq(\langle A B\rangle +\langle B A\rangle -2 \langle A\rangle\langle B\rangle)^2/4$?

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]...
user215721's user avatar
16 votes
7 answers
12k views

Heisenberg uncertainty principle in daily life

I need some examples of the Heisenberg uncertainty principle on a basic level, or if possible in daily life. Or maybe a simple explanation for validity of the principle in easier words. I cannot get ...
Akil's user avatar
  • 384
16 votes
4 answers
3k views

Why does the Heisenberg uncertainty principle apply to particles?

This might be a slightly naive question, and if so I apologize, but I am currently a little confused as to why the Heisenberg Uncertainty principle should apply to particles, i.e. our system (say an ...
Mason Giacchetti's user avatar
15 votes
7 answers
10k views

Can Heisenberg's uncertainty principle be used to prove the electron can't exist in the nucleus in this way?

This is the solution given in the textbook (my analysis below it): From my understanding, I believe this solution is wrong. My understanding is that the more accurately we know the position, the less ...
Ravi Arora's user avatar
15 votes
13 answers
6k views

Could the Heisenberg Uncertainty Principle turn out to be false?

While investigating the EPR Paradox, it seems like only two options are given, when there could be a third that is not mentioned - Heisenberg's Uncertainty Principle being given up. The setup is this (...
Ehryk's user avatar
  • 3,241
15 votes
3 answers
12k views

Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
The Quantum Physicist's user avatar
15 votes
3 answers
2k views

What are quantum fluctuations, really?

So, I have read a lot about quantum fluctuations, and how they are responsible for: Lamb shift Spontaneous emission of photons from excited atomic states Casimir effect ... and the explanation ...
SuperCiocia's user avatar
  • 24.9k
15 votes
2 answers
3k views

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 ...
Andrew Palfreyman's user avatar

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