Uncertainty Definition and 1000 Threads

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...

Summary:: I'm trying to understand the meaning behind the answer of 2.34... but I haven't taken a quantum class yet so I'm utterly lost. So I took this physics class that's teaching us python and for our final project our teacher assigned random problems to work out, well I got stuck with a...

I'm doing a lab report where I manually measure the time taken for a bifilar pendulum to do 10 oscillations. Is there a rule or a method that I should follow to calculate its uncertainty? Or is the uncertainty just an estimation of human reaction time and judgment? I also need to know the...

In quantum mechanics it is impossible to prepare an electron in a state where both position and momentum are known with arbitrary accuracy. In classical physics such states do exist, but can they be prepared? If we assume that the electron is a classical particle (small ball of charge) can we...

So i have a folder with a lot of data/information. Basically what i have is approximatelly 2k 2upla of x and y, because i need to find the function that describe the behavior of these data. Of course, i can use a program/software to fix/adjust the curve using the concept of OLS... BTW. The...

I realize that it is impossible to know both the speed and position of a particle because of the uncertainty principle. I also know that this is because if you send a photon at the particle to detect its position you alter its momentum. But does that mean that when you measure position it has no...

I have done this question and gotten: Vmin = 4pi/3(19.18)^3=29555.2 V = 4pi/3(19.31)^3=30160.3 Vmax = 4pi/3(19.44)^3=30773.5 Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong... Could someone please help me find out where I went wrong, or tell me if I went the wrong...

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##...

Let Q be a time-independent operator. ##[H,Q] = iħ[\frac{d}{dt},Q]## Since Q is time-independent, ##[H,Q]=0## And from the uncertainty principle : ##\Delta H\Delta Q \ge |<\Psi|\frac{1}{2i}[H,Q]|\Psi>|## From ##[H,Q] = 0##, I concluded that ##\Delta H\Delta Q \ge 0## But by evaluating d<Q>/dt...

Hello everyone, I calculated the matrix element of a parton level process and determined the total cross section via a MC-simulation. Then I wanted to look at some differential distributions like the differential cross section with respect to the energy of one of the particles in the final...

I know how to do the individual uncertainties but just not sure of the order.

While I will not be showing the graph here, I am trying to dissect what the question even means. While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any...

Background Information: I am working on a pulsed NMR lab project that involves graphing out a semi-log graph of free induction decay amplitude as a function of time. After graphing out the semi-log graph, I am to determine the apparent spin-spin relaxation time (##{T_2}^*##) through the...

Hi folks, This is my first post so be gentle :) I've heard the uncertainty principle before - ΔxΔp ≥ ħ/2 I've seen it demonstrated with the single slit experiment where the x position is constrained (measured?). I was wondering what happens when light is split by a prism. Since the wave...

A water cooled plate condenser, condensing refrigerant. Heat exchanger (condenser with plates) characteristics: Description symbol value value (converted) number of plates np 28 number of channels nc 27 number of water channels nwc 14 number of flowing channels for refrigerant...

I need to calculate the overall uncertainty of the value I have obtained for the speed of sound in water, using Mackenzies equation... I am not sure in what way to combine the above uncertainties. Any help would be greatly appreciated! Lloyd

How do you prove Heisenberg uncertainty relations for mixed states (density matrix), only from knowing the relation is true for pure states?

Is there an uncertainty between amplitude and phase in classical quasi-monochromatic light?(E(t)=a(t)cos(phi(t)-omega_0*t))If it exist, what is the relation between classical and quantum uncertainty(delta I* delta phi>=1/2)?

This is from Halliday et al Physics 4e, p9, sample problem 3. Problem: My question: Why do the authors say that the weight of the cat has 1lb uncertainty rather than 2lb? Isn't it between 127.5-119.5=8lb, and 10lb, hence 9lb+-1lb ie uncertainty of $$\frac{2}{9}\times 100 = 22\%$$ rather...

Hi, Would it be reasonable to have uncertainty in your independent variable (e.g. uncertainty of mass measured by electronic balance)? For processing raw data: does each processed answer just have the same number of sigfigs as each raw datum it is calculated from, or do I need to keep track of...

Hi, I have a question that I am quite confused about. Please note this is at the undergraduate level. Question: Given the transfer function with inverse multiplicative uncertainty \bar G (s) = \frac{G(s)}{1+\Delta \cdot W(s) \cdot G(s)} and the fact that the system is connected in feedback...

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

a) Consider a dust grain of mass 0.1µg whose position is known to a distance of 1µm. How precisely can its velocity be known? b) A company claims to have invented a device that can measure the momentum of objects inside it with extreme accuracy. The device fits within a matchbox, and the...

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...

It is supposed to find it with the uncertainty propagation, so i tried by it. $$\delta _{n} = \delta_{\theta}\frac{dn}{d\theta}=\frac{\delta _{\theta}\pi sec(\theta )^{2}}{180} = sec(59,3)^2*\pi*1.2/180$$ $$n = 1.68 \pm 0.08$$ But this uncertainty is quite low, so i am trying to understand if i...

For Example: Trial 1: 5.36 ± 0.03 Trial 2: 5.42 ± 0.04 Trial 3: 5.35 ± 0.01 Trial 4: 5.38 ± 0.03 Trial 5: 5.45 ± 0.02 What I did was take the average of the best estimates and the uncertainties. Best Value 5.39 ± 0.03 (0.03+0.04+0.01+0.03+0.02)/5=0.026=0.03

Hi guys can someone look at my work for uncertainty and let me know if it makes sense.

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...

By definition , ##\ket{+x} = \alpha \ket{+z} + \beta \ket{-z}.## Therefore we proceed , \begin{align*} \langle S_{x} \rangle &= \lvert \alpha \rvert^{2} \left(\frac{\hbar}{2}\right) + \lvert \beta\rvert^{2} \left(-\frac{\hbar}{2}\right) = (\alpha^{2} - \beta^{2})\left(\frac{\hbar}{2}\right).\\...

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...

My initial guess was to calculate the upper and lower value, and then average those two values, but I don't know whether this is correct to make the uncertainty interval symmetric. After I calculated the average value, I subtracted it form the upper and lower value, and obtained the symmetric...

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...

##\frac{1}{f}=\frac{1}{u}+\frac{1}{v}## ##f = \frac{u.v}{u+v}## Let: u + v = w → w = 250 mm ± 8 mm Percentage uncertainy of v = (3/50) . 100% = 6% Percentage uncertainty of u = (5/200) . 100%=2.5% Percentage uncertainty of w = (8/250) . 100% = 3.2% Percentage uncertainty of f = 6 % + 2.5 %...

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?

Often a calibration certificate for an instrument has the error found during the calibration as well as the uncertainty associated calibration itself. I'm reasearching uncertainty calculations using the GUM 1995 method and I haven't found one yet that includes the uncertainty of the calibration...

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...

I know option (a) and (c) are wrong but I don't know the difference between option (b) and (d) because I think they are the same (taking average to get more accurate reading and reduce random error). My guess is (b) because I think for (d) the fractional uncertainty maybe can stay the same...

Good Morning When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative). I do understand that this is allowed: we are trying to find...

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 have an Textronics oscilloscope with 500 MHz sampling rate and using an 50 ohm cable for the measurement. I can’t find the measurement uncertainty in the manual or the calibration sheet. In the calibration sheet it says an ‘uncertainty’ for the used channel in divisions, for example 1m up to...

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...

The uncertainty principle tells us that there is no state that a particle can be in such that we can predict with certainty both what the result of a position measurement will be and what the result of a momentum measurement will be. This statement is not the same as saying we can't measure the...

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say ##\hat{z}##-direction. But to not violate...

I am following this: avntraining.hartrao.ac.za/images/Error_Analysis.pdf I have a ruler with an uncertainty of ± 0.5mm. I made a calculation subtracting one measurement of the ruler, from another measurement, making the uncertainty for the data ± 1.0mm. As I have four trials, I calculated the...

Hello there! This is my first post, so I apologise for any faux pas I am about to commit. I have recently bumped into a few situations where I'm uncertain about my uncertainties. Especially where the value is a product of multiple variables. Please see the attatched table, where g is a function...