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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 ...
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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 ...
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67 votes
10 answers
7k views

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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21 votes
3 answers
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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
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30 votes
3 answers
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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
10 votes
4 answers
28k views

Heisenberg Uncertainty Principle scientific proof

Heisenberg's uncertainty principle states that: $$\sigma(x)\sigma( p_x )\ge \frac {\hbar}{2}.$$ What is the scientific proof of this principle? Operators Uncertainty
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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
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22 votes
2 answers
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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 ...
Asciiom'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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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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11 votes
4 answers
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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 ...
Ryker'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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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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22 votes
2 answers
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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, ...
Yashbhatt'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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7 votes
3 answers
2k views

Uncertainty principle and measurement

I would like to really understand how the uncertainty principle in QM works, from a practical point of view. So this is my narrative of how an experiment goes, and I'm quickly in trouble: we prepare ...
Frank's user avatar
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8 votes
1 answer
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Energy conservation of Virtual Particles - Quantum Fluctuation?

I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?...
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6 votes
2 answers
8k views

Absolute zero and Heisenberg uncertainty principle

I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position ...
Four Seasons'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
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
39 votes
6 answers
9k views

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
58 votes
14 answers
8k views

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
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
2 votes
1 answer
1k views

Heisenberg relation

Given that $A(k)=\frac{N}{k^2+\alpha^2}$, show that $\Delta k \Delta x >1$. Considering the above example, according to my textbook, it is written that I must square the above function and ...
amir's user avatar
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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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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
14 votes
2 answers
3k views

Uncertainty principle in quantum field theory

Can the uncertainty principle be derived in quantum field theory? If yes, does is have a different interpretation than quantum mechanics because the coordinates $x_i$ are now parameters and not ...
SRS'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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14 votes
5 answers
4k views

Why can't the Uncertainty Principle be broken for individual measurements if it is a statistical law?

The Heisenberg Uncertainty Principle is derived for two operators $\hat A$ and $\hat B$ as $$\Delta \hat A\ \Delta \hat B \geq \dfrac{1}{2}|\langle[\hat A, \hat B] \rangle|$$ where $\Delta$ denotes ...
Physiker's user avatar
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12 votes
1 answer
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Phase space in quantum mechanics and Heisenberg uncertainty principle

In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state. In my book about statistical physics ...
yarnamc's user avatar
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6 votes
3 answers
5k views

What is the meaning of natural line broadening?

I have recently found one exercise in an exercise book: During the transition from the first excited state of a hydrogen atom into the ground state, photons with a wavelength of 121.5 nm are ...
korinn's user avatar
  • 85
6 votes
4 answers
3k views

Is uncertainty principle a technical difficulty in measurement? [duplicate]

Is the uncertainty principle a technical difficulty in measurement or is it an intrinsic concept in quantum mechanics irrelevant of any measurement? Everyone knows the thought experiment of measuring ...
Gotaquestion's user avatar
  • 2,725
4 votes
3 answers
558 views

Scientific determinism and the Heisenberg's uncertainty principle

I'm reading Brief Answers to the Big Questions by Stephen Hawking. In chapter 4, it discusses whether we can predict the future. As many have known that Laplace put forth that if we knew the positions ...
Khanh's user avatar
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1 vote
3 answers
2k views

Do black holes violate the uncertainty principle?

If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?
Alex's user avatar
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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
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
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14 votes
6 answers
3k views

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?
pablasso's user avatar
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9 votes
1 answer
3k views

What physical significance has the Heisenberg Group?

I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, ...
Kai's user avatar
  • 201
7 votes
5 answers
11k views

Interesting relationship between diffraction and Heisenberg’s uncertainty principle?

I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens’ construction but instead relies on Heisenberg’s uncertainty principle: The uncertainty ...
hb20007's user avatar
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3 votes
3 answers
1k views

Uncertainty principle and multiple observers

My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa. Say there is ...
James's user avatar
  • 33
1 vote
4 answers
4k views

Why is the Bohr's idea of defined circular orbits overruled?

If we consider a thought experiment for determining position of an electron by using photons of light. According to principles of optics, if we use light of wavelength $\lambda$, then the position of ...
Sensebe's user avatar
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1 vote
1 answer
741 views

Virtual particles with almost infinite energy?

I'm reading A Universe From Nothing by Lawrence M. Krauss, and I encountered a paragraph that I found confusing: The source of the infinity is easy to describe. When we consider all possible ...
The Pointer'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
  • 473
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
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
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
12 votes
6 answers
5k views

Why can't we use entanglement to defy Heisenberg's Uncertainty Principle?

In principle, it is possible to entangle any property of two particles, including speed and momentum. Surely then, this could be used to defy the Uncertainty Principle, which states that the momentum ...
ODP's user avatar
  • 4,597
10 votes
2 answers
2k views

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?
excitedaboutphysics's user avatar
9 votes
2 answers
1k views

Why don't quantum effects invalidate the speed of light barrier?

While proving that no matter can reach the speed of light (a fact which I call the kinetic energy barrier), Einstein uses the fact that he can calculate the velocity and position of an electron. ...
nikhil bachhawat's user avatar
8 votes
3 answers
10k views

'The size of an atom' using Uncertainty Principle

Suppose we have a hydrogen atom, and measure the position of the electron; we must not be able to predict exactly where the electron will be, or the momentum spread will then turn out to be infinite. ...
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