This tag is for Heisenberg quantum mechanical uncertainty principle.
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260 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 ...
19
votes
2answers
541 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 ...
18
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5answers
1k 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 ...
12
votes
3answers
996 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 ...
12
votes
8answers
575 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.?
11
votes
1answer
284 views
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 ...
10
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2answers
1k views
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} ...
9
votes
2answers
206 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 ...
8
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5answers
567 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 ...
8
votes
1answer
348 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 ...
7
votes
6answers
298 views
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 ...
7
votes
2answers
251 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?
7
votes
3answers
306 views
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 ...
7
votes
2answers
592 views
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 ...
7
votes
2answers
271 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 ...
6
votes
6answers
803 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?
6
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4answers
2k views
Heisenberg Uncertainty Principle scientific proof
Heisenberg's uncertainty principle states that: if the x-component of the momentum of a particle is measured with an uncertainty
$$\Delta \vec p_x$$
then its x-position cannot, at same time, be ...
6
votes
3answers
179 views
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 ...
6
votes
3answers
562 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 ...
5
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6answers
627 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 ...
5
votes
3answers
176 views
Does a ball thrown in the air really stop at its apex, and if it does, wouldn't that violate the uncertainty principle?
When throwing a ball straight up, most experts say that it momentarily comes to a stop at its apex before its return fall. If it stops, wouldn't we know its velocity and position and wouldn't this ...
5
votes
4answers
286 views
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?
...
5
votes
3answers
520 views
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 ...
5
votes
2answers
324 views
The Uncertainty Principle and Black Holes
What are the consequences of applying the uncertainty principle to black holes?
Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
5
votes
1answer
209 views
Is there any uncertainty between mass and proper length or time?
I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
5
votes
1answer
197 views
Relativistic contraction for a wave packet and uncertainty on momentum
Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
4
votes
4answers
361 views
Uncertainty Principle for Information?
I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question:
While we have Heisenberg uncertainty principle on measuring coupled observables, ...
4
votes
6answers
314 views
Why is Heisenberg's uncertainty principle not an experimental error since it is the error created by photons striking on elementary particles?
Why is Heisenberg's uncertainty principle not an experimental error since it is the error created by photons striking on elementary particles?
4
votes
4answers
502 views
Uncertainty Principle for a Totally Localized Particle
If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, ...
4
votes
5answers
299 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 ...
4
votes
5answers
333 views
Would something like the uncertainty principle arise even if the universe was built on something like Newtonian mechanics?
I am thinking of a (greatly simplified) computer simulation of a universe that followed something like Newtonian rules. Inside the simulation are A.I.s that are made from those same rules, and can ...
4
votes
3answers
394 views
Very simple example of the way the Fourier transform is used in quantum mechanics?
According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples ...
4
votes
2answers
98 views
Do viruses suffer from quantum de-localization?
Consider some microscopic life form. It should obviously be localized in space, in the quantum-mechanical sense, if it is treated as a single particle (though it is composite). If its characteristic ...
4
votes
4answers
371 views
What is the meaning of uncertainty in Heisenberg's uncertainty principle?
The Heisenberg's uncertainty principle states the following:
$$\Delta p \cdot \Delta x \ge \frac{h}{4\pi}.$$
While studying for my high school physics exams, I fooled myself into believing that I ...
4
votes
3answers
1k views
Proof of Canonical Commutation Relation (CCR)
I am not sure how $QP-PQ =i\hbar$ where $P$ represent momentum and $Q$ represent position. $Q$ and $P$ are matrices. The question would be, how can $Q$ and $P$ be formulated as a matrix? Also, what is ...
4
votes
1answer
205 views
Uncertainly Principle in orthogonal directions
The Heisenberg Principle states that for each direction, $\Delta x\cdot \Delta p_x \ge \hbar , \Delta y\cdot \Delta p_y \ge \hbar$ and $\Delta z\cdot \Delta p_z \ge \hbar$.
But, can anything be said ...
4
votes
3answers
111 views
uncertainty of fields with many harmonic modes
In most basic level introduction to the quantum harmonic oscillator formulation of fields, it is assumed that the commuting variables for the fields $p_m$, $q_m$ are
$$ \lbrack p_m , q_n \rbrack = ...
4
votes
3answers
348 views
Generalizing Heisenberg Uncertainty Priniciple
Writing the relationship between canonical momenta $\pi _i$ and canonical coordinates $x_i$
$$\pi _i =\text{ }\frac{\partial \mathcal{L}}{\partial \left(\frac{\partial x_i}{\partial t}\right)}$$
...
4
votes
2answers
258 views
Heisenberg uncertainty principle derivation - unexplained factor of $4 \sigma_k^2$ in Gaussian
I did a Fourier transform of a gaussian function $\scriptsize \mathcal{G}(k) = A \exp\left[-\frac{(k-k_0)^2}{2 {\sigma_k}^2}\right]$
$$
\scriptsize
\begin{split}
\mathcal{F}(x) &= ...
4
votes
2answers
170 views
How does QM allow imaging of individual electron orbitals?
Question: Why does the uncertainty principle allow probing of characteristics specific to the electron orbital distribution? If you measure an electron's position/momentum, then after you measure ...
4
votes
1answer
72 views
Simple uncertaintly calculation of the center coordinates of a Landau Level
I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long.
In equation 2.39, the ...
3
votes
11answers
2k 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 ...
3
votes
4answers
183 views
Are photons deterministic?
I propose the following scenario:
At $t=0$, a photon is emitted from a star. At $t=n$, said photon is received and interpreted by some detector.
My question is whether or not it is accurate to say ...
3
votes
4answers
819 views
What is meant by “Nothing” in Physics/Quantum Mechanics(QM)?
I am not a phycisist, so please forgive my ignorance. This is related to my posts and this.
I am trying to undertand what is meant by the term "Nothing" in physics or Quantum Mechanics since it seems ...
3
votes
1answer
123 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 ...
3
votes
2answers
161 views
Why does $i ( LK-KL )$ represent a real quantity?
According to my textbook, it says that $i( LK-KL )$ represents a real quantity when $K$ and $L$ represent a real quantity. $K$ and $L$ are matrices. It says that this is because of basic rules. ...
3
votes
2answers
350 views
Calculating lifetime of a pi meson via Heisenberg uncertainty relationship?
This is a problem from my textbook:
"A proton or neutron sometimes 'violates' conservation of energy by emitting and then reabsorbing a pi meson, which has a mass 135MeV/$c^2$. This is possible as ...
3
votes
2answers
562 views
Who first realized the uncertainty principle allows for virtual particle pair production?
For all I've read about Quantum Field Theory I've never seen the concept of the living vacuum accredited to someone in particular. Given the importance of this very application of the uncertainty ...
3
votes
2answers
561 views
The complementary variable to the qubit and spin-1/2
The qubit is a big topic of quantum information theory. A qubit is a single quantum bit. Physical examples of qubits include the spin-1/2 of an electron, for example, see page 39 of Preskill:
...
3
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2answers
316 views
Creation of particle anti-particle pairs
I was reading some QFT notes and there is one point that I don't understand, they are justifying why we need QFT saying that the number of particles is not preserved once we consider special ...
