Uncertainty principle Definition and 528 Threads

As I understand it, the energy-time uncertainty relation \triangle E \triangle t \geq \hbar /2 expresses a trade-off between the precision with which energy and time can be simultaneously measured. I understand that, unlike position and momentum, time is not an operator, so the relation is not...

A Qbit with up probability 1 - (10^-75) would most likely still produce a reading of up, so an up reading does not mean that the up probability is 1.0 to millions of decimal places. The spin detector is a physical device made of atoms. None of its surfaces are pure mathematical planes or...

Consider the measurement problem for an electron in a single-slit experiment done one electron at a time. There are two interlinked questions, but some consider just one of them to be the actual measurement problem. The first question is concentration - a fairly uncertain distribution condenses...

Here is my thought experiment: Let's say I attenuate a very short laser pulse to single photon intensity. Due to the uncertainty principle, I know the time of arrival of the photons, but not their energy. So let's reverse that by splitting the pulse in its spectral components with a diffraction...

I calculated the answer for question a to be about 10^-6 m/s (1 significant figure), but I am stuck on question b. It seems to me that it is a trick question because we don't know anything about the speed in the y-direction, and the answer can be everything from 0 to infinity. Am I right?

How accurate of a measurement can we make on the position of a particle? I heard you need more and more energy to get a measurement more accurate. Would the energy needed to be infinitesimal accurate create a black hole upon. Measurement?

I have a question related to the uncertainty principle in QFT and if it is related to the early universe conditions. Do we still have four-vector momentum and position uncertainty relation in relativistic quantum theory? I have been following the argument related to the early universe and the...

I understand that the uncertainty is low when you're dealing with a "macro" scale area that is much bigger than Planck's constant. But what's confusing to me is when you know with extreme precision the location, but there's so many particles involved that there is little uncertainty since the...

As I understand it the principle states that the more accurately you measure one factor of an object, for example speed, the less you can tell of any other factors, for example position. To me this seems we will every only be able to measure an approximation of reality and thus determinism...

Soo. I think this problem is too direct and easy so I think I got it in wrong way: p=h/r and then plug in the K and V and then we get E=E(r) and get derivative and we have minimum? What do you think? is there sth I am missing?

I'm studying orbital angular momentum in the quantum domain, and I've come up with the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is necessary to pay attention to the triviality problem, because in the case where the commutator is...

We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...

Per the Heisenberg uncertainty principle, a particle does not have a precisely defined location. Does such uncertainty contribute to the transfer of thermal energy (i.e. entropy)? Is uncertainty the primary means for the transfer of thermal energy at the quantum level?

Hello, 2 questions please about the Uncertainty Principle and the following scenario: I shoot at each other, 2 electrons each with equal but opposite velocity such that they repel each other? (To me, this indicates that you know the momentum of each electron and you know each position...

I am guessing time-energy uncertainty relation is the way to solve this. I solved the Schrodinger equation for both the regions and used to continuity at ##x=-a, 0,a## and got ##\psi(-a<x<0) = A\sin(\kappa(x+a))## and ##\psi(0<x<a) = -A\sin(\kappa(x-a))## where ##\kappa^2 = 2mE/\hbar^2##...

Could this statement be the first step towards quantum gravity? Or is it trivial or not true at all?

With the double slit, experiment we show the double nature of light and matter as wave and particle. In particular, the so called "which way" thought experiment illustrate the complementary principle. In my book, this experiment is analyzed putting a series of particles in front of one of the...

The general uncertainty principle is derived to be: \sigma_A^2 \sigma_B^2 \geq \left(\frac{1}{2} \langle \{A,B\} \rangle -\langle A \rangle \langle B \rangle \right)^2 + \left(\frac{1}{2i} \langle [A,B] \rangle \right)^2 Then it is often "simplified" to be: \sigma_A^2 \sigma_B^2 \geq...

hi guys i am trying to follow a proof of the generalized uncertainty principle and i am stuck at the last step : i am not sure why he put these relations in (4.20) : $$(\Delta\;C)^{2} = \bra{\psi}A^{2}\ket{\psi}$$ $$(\Delta\;D)^{2} = \bra{\psi}B^{2}\ket{\psi}$$ i tried to prove these using the...

Homework Statement:: i saw this simple derivation of the uncertainty principle in my college introductory quantum book Relevant Equations:: Δp.Δx = h hi guys i saw this derivation of the uncertainty principle in my college quantum book , but the derivation seems very simple and sloppy , i...

Hi! I am checking Zettili's explanation on the uncertainty principle and I have this confusion on what the "uncertainty" really means which arises from the following statements: When introducing the uncertainty principle, for the case of position and momentum it states that: if the x-component...

In the Heisenberg's uncertainty principle ## \triangle x \triangle p \geqslant \frac{\hbar}{2} ## what happens when the uncertainty in position becomes very small is that the uncertainty in momentum becomes very large. But what happens when the spread of the uncertainty in momentum becomes...

Maxwell's demon measures the position and velocity of the particle. How can it do that when it violates the uncertainty principle? Does that mean uncertainty principle is unavoidable otherwise we will violate II law of thermodynamics as in the case of Maxwell's demon?

Hello, So I know that the magnetic moments of atoms are dependent on the spin and orbital angular momenta of its electrons. Both of these quantities are limited by the uncertainty principle so that neither of their direction and magnitude can be known simultaneously with arbitrary precision...

In Scientific American, July 2020, the article "The Darkest Particle" by Louis and Van de Water, page 46, discussing the hypothetical sterile neutrino, there is the sentence: "Because sterile neutrinos are likely to be more massive than the regular flavors, however, particles could make the...

So according to Heisenberg's energy-time uncertainty principle, the product of accuracies in energy and time is equal to ћ/2. In this problem, I know I have to calculate ΔE. But when I'm using Δt = 1.4e10 yrs. = 4.41e17 s, I am getting ΔE = 0.743e-33 eV, which is certainly incorrect! Where am I...

Hello everyone, Heisenberg's uncertainty principle tells us that we cannot measure the position and the momentum of a particle to infinite accuracy. My question is, can we use general relativity to overcome this difficulty? From what I know, any mass can curve spacetime even if it was small, and...

I just read the Feynman Lectures about the electron gun experiment with two holes in the middle wall. It demonstrates that if we don't look at the electrons while they travel toward the detector there is an interference pattern in the probability curve of the electrons similarly to what happens...

If I understand correctly (a big caveat), one shows that if one can get from one function to the other via a Fourier transform and multiplication by a constant, then the width of the corresponding Gaussian wave of one gets larger as that of the other gets smaller, and vice-versa, and by a bit...

why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

In quantum mechanics the name is Uncertainty principle. But outside of QM, what is the name for those inequalities?

I have no idea how to approach. Hence would appreciate any help

Hi there, I'm very stuck on this problem when approaching it like this. I know I could use the Landau Criterion for rotons but that's not accepted here, it wants the approach to come from the uncertainty principle. My thinking is along these lines: There will be a change in chemical potential...

"Now, if an electron has a definite momentum p, (i.e.del p = 0), by the de Broglie relation, it has a definite wavelength.A wave of definite (single) wavelength extends all over space. By Born’s probability interpretation this means that the electron is not localised in any finite region of...

So with the \gamma=\frac{1}{\sqrt{1-\beta^2}} it seems obvious that relativistic momentum, p=\gamma m_o v is supposed to be used. Then \frac{ dp}{dv}=m_o(1-\beta^2)^{-1/2}+m_o v...

I know Heisenburg's Uncertainty Principle states that there has to be a minimum amount of uncertainty. Where the minimum uncertainty is hbar/2. My attempt at the solution Uncertainty in x = 28E-12 m (Turn pm into m) h=6.63E-34 (constant) hbar=1.055`19E-34 (constant) hbar/2 = 5.275986363E-35...

I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25. How do I derive the given equations?

I have a bit of confusion regarding the application of the uncertainty principle in the context of experiments. If a detector allows you to measure a particle's path through said detector, does that mean that you know a particle's position at all points in time, and are able to work out its...

I have been trying to see if my understanding of uncertainty principle is right. So I thought consider a circle. for this augment we will look at its diameter and it circumference. Suppose you get a length of string and make a exact measure of the circles circumference using this length of...

I am not too knowledgeable about QM, so please forgive me if this is a dumb question. I have outlined below an experiment setup for which Heisenberg's uncertainty principle seems not to apply: Imagine a particle for which we wish to collect the exact position and velocity. We have a detector d1...

The main role in quantum gravity can be played by the uncertainty principle , where is the gravitational radius, is the radial coordinate, is the Planck length. This uncertainty principle is another form of Heisenberg's uncertainty principle between momentum and coordinate as applied to the...

Hi For 2 Hermitian operators A and B using the Cauchy-Schwarz inequality and assuming the expectation values of A and B are zero I get (ΔA)2(ΔB)2 ≥ (1/4)|<(AB+BA)>|2 + (1/4)|<(AB-BA)>|2 Now both terms on the RHS are positive so why is this inequality usually just written with only the...

I have come across a paper where it is stated that if the infinity assumption in the FT is removed, the uncertainty doesn't hold. Is this a sensible argument? Thank you.

I'm a hobbyist physicist and I just started studying QM through watching Leonard Susskind's lectures on the Stanford Youtube channel. I get the idea of it being impossible to precisely know both a subatomic particle's position and momentum, but is this actually a physical limitation? Or is it...

Hello, In Griffiths (2nd edition) pgs 110-111 - deriving the uncertainty principle I have 2 questions 1) I am stuck on a point ... (h = ^ hat ) <f | g > = < ( Ah - <A>) ψ | ( Bh - <B>) ψ > = <Ψ | ( Ah - <A>) ( Bh - <B>) Ψ> FOIL = <ψ | AhBh ψ> - <B><ψ | Ah ψ> - <A>< ψ | Bh ψ> +...

To summarize, my current understanding of how Heisenberg's uncertainty principal works suggests that there would be a contradiction (somewhere down the line) with any way that it applies to (or doesn't apply to) photons, due to the fact that they must always travel the speed of light. I...

heisenberg uncertainty principle ## Δx Δp ≥ ħ## where ##Δx = \sqrt{<\hat{x}^2>-<\hat{x}>^2}## ##Δp = \sqrt{<\hat{p}^2>-<\hat{p}>^2}## I don't know. Why ##Δx## equal to ## \sqrt{<\hat{x}^2>-<\hat{x}>^2} ## and ## Δp ## equal to ## \sqrt{<\hat{p}^2>-<\hat{p}>^2} ## What can I find out about...

I apologize ahead of time for the simplicity of the question, but this has really been bothering me.Given the de Broglie relation, assuming natural units, where ##\hbar = 1##: \begin{equation} \begin{split} \vec{k} &= M \vec{v} \end{split} \end{equation}My question regards velocity and...

We are all familiar with Heisenbergs uncertainty principle. When we determine the position of a particle or wave, the uncertainty of momentum reach infinity. So let's say I have a machine that measures the position very very precisely. Then the uncertainty of this non-moving particles momentum...