This tag is for Heisenberg quantum mechanical uncertainty principle.

learn more… | top users | synonyms

23
votes
5answers
2k 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 ...
23
votes
7answers
579 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 ...
20
votes
2answers
895 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 ...
19
votes
8answers
988 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.?
16
votes
3answers
1k 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
5answers
954 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 ...
12
votes
3answers
658 views

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
votes
1answer
320 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 ...
11
votes
4answers
1k 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 ...
11
votes
2answers
2k 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} ...
11
votes
2answers
376 views

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 ...
10
votes
5answers
934 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 ...
9
votes
6answers
2k views

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 ...
9
votes
2answers
335 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
votes
3answers
616 views

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 ...
8
votes
4answers
703 views

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. ...
8
votes
2answers
570 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 ...
8
votes
1answer
418 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 ...
8
votes
1answer
154 views

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 ...
8
votes
5answers
434 views

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) = - ...
7
votes
3answers
408 views

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 ...
7
votes
6answers
307 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
3answers
1k 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 ...
7
votes
4answers
1k 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
426 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
375 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 ...
6
votes
6answers
1k 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
votes
3answers
231 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
6answers
1k 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 ...
6
votes
3answers
464 views

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 ...
6
votes
2answers
2k views

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 $\Delta x \Delta p \geq \hbar$ ...
6
votes
4answers
391 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? ...
6
votes
1answer
84 views

In calculations with uncertainty principle why could you equate the uncertainty in momentum with the actual momentum of the system

This website is trying to calculate the confinement energy of a electron starting from the uncertainty principle, but it does this: $\Delta p=p$. Why is this valid?
6
votes
1answer
371 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
4answers
4k 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 ...
5
votes
3answers
273 views

Uncertainty principle and the energy-momentum 4-vector

In each of the uncertainty relations $$\Delta p_x \Delta x \geq \hbar/2$$ $$\Delta p_y \Delta y \geq \hbar/2$$$$\Delta p_z \Delta z \geq \hbar/2$$$$\Delta E \Delta t \geq \hbar/2$$ the second term on ...
5
votes
3answers
238 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
765 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 ...
5
votes
1answer
364 views

Does the uncertainity principle violate the law of conservation of energy?

What is the scientific view of the beginning of universe? Quantum fluctuation seems to contradict with the law of conservation of energy. Uncertainity Principle does seem to violate the Law of ...
5
votes
3answers
248 views

How can particles travel in a straight line?

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to ...
5
votes
1answer
254 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
12answers
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 ...
4
votes
4answers
353 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 ...
4
votes
6answers
554 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
550 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
4answers
708 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
343 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
435 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
3answers
184 views

Does the uncertainty principle make simulation of systems impossible?

Is it possible to fully define a system, then be incapable of simulating or calculating its future states due to the Uncertainty Principle? If it can be done, how?
4
votes
4answers
277 views

Is uncertainty principle a technical difficulty in measurement?

I have searched for an answer to this question on physics SE but I have not seen a question in which it is addressed properly. Please let me know if there is an answer already. My question briefly ...