# 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.

297 questions
Filter by
Sorted by
Tagged with
38k views

### 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 ...
• 1,325
7k views

### 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 ...
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): ...
• 805
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 ...
• 511
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 $x$ ...
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
18k views

• 1,028
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 ...
• 121
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 ...
• 1,875
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 ...
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 ...
• 26.6k
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 ...
• 36.3k
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 ...
• 1,461
6k views

### 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 ...
• 1,231
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 ...
• 85
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 ...
• 2,725
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 ...
• 41
1 vote
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?
• 6,015
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?...
• 575
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 ...
• 24.9k
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?
• 753
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, ...
• 201
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 ...
• 1,546
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 ...
• 33
1 vote
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 ...
• 5,789
1 vote
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 ...
• 879
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 ...
• 473
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,\...
• 331
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 ...
• 751
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 ...
• 393
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 ...
• 4,597
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?
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. ...
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. ...