What is Uncertainty: Definition and 1000 Discussions

Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, psychology, sociology, engineering, metrology, meteorology, ecology and information science.

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  1. mncyapntsi

    Uncertainty, volume, and measurement

    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...
  2. Wannabe Physicist

    Exploring the Time-Energy Uncertainty Relation to Solve a Schrodinger Equation

    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##...
  3. Ebi Rogha

    I Uncertainty principle equation for virtual particles

  4. F

    I Uncertainty principle##\Delta H\Delta Q##, where Q is time-independent

    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...
  5. M

    I Uncertainty of histogram bins from MC-simulation

    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...
  6. M

    Oscillating spring experiment uncertainty

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

    Finding the Relative Uncertainty for the Standard Error of the Mean

    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...
  8. Athenian

    Calculating Numerical Uncertainties in an Equation

    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...
  9. S

    I Uncertainty and light through a prism

    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...
  10. M

    Condenser calculations - uncertainty

    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...
  11. L

    Uncertainty of Speed of Sound in water, using Mackenzie's Equation

    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
  12. Jamister

    A Heisenberg Uncertainty Relation for mixed states

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

    I Is there an uncertainty between amplitude and phase in an EM wave?

    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)?
  14. W

    Uncertainty in cat's weight

    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...
  15. I

    Chemistry Uncertainty and Significant Figures

    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...
  16. M

    Engineering Robust Stability: criterion for inverse multiplicative uncertainty

    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...
  17. B

    B The relativistic uncertainty principle

    Could this statement be the first step towards quantum gravity? Or is it trivial or not true at all?
  18. vintagelover007

    Quantum Uncertainty Questions (HUP)

    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...
  19. Axel Togawa

    I Double slit experiment and the Uncertainty Principle

    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...
  20. LCSphysicist

    Calculating the uncertainty with this measurement

    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...
  21. WannaLearnPhysics

    Uncertainty of the Best Value from a Multiple-Trial Experiment

    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
  22. aatari

    Finding the Uncertainty in the motion of a pendulum

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

    I Is the Heisenberg-Robertson Uncertainty Relation Always Consistent?

    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...
  24. patric44

    Proof of the generalized Uncertainty Principle?

    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...
  25. patric44

    Is this a valid derivation of the Uncertainty Principle?

    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...
  26. P

    Verifying that the uncertainty is 0 for a QM state

    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).\\...
  27. peguerosdc

    I Understanding the meaning of "uncertainty" in Heisenberg's UP

    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...
  28. E

    Asymmetric uncertainty intervals in astrophysical data

    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...
  29. P

    I Possible paradox in the uncertainty principle?

    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...
  30. S

    Uncertainty in the measurement of the focal length in this experiment

    ##\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 %...
  31. iVenky

    I Maxwell's Demon and the Uncertainty Principle

    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?
  32. F

    When does the calibration uncertainty contribute to a measurement uncertainty?

    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...
  33. H

    B Uncertainty Principle versus spin alignment

    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...
  34. S

    Correct statement about error and uncertainty

    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...
  35. T

    Heisenberg and Varying the Velocity

    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...
  36. tanaygupta2000

    Help With Heisenberg's Energy-Time Uncertainty Principle

    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...
  37. Souma

    I Using general relativity to violate the uncertainty principle

    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...
  38. N

    How to estimate the measurement uncertainty of an oscilloscope ?

    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...
  39. B

    B What happens to the uncertainty principle if....

    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...
  40. SamRoss

    B Uncertainty versus impossibility of measurement

    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...
  41. Coltrane8

    I Neutrino Helicity and Spin Uncertainty

    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...
  42. U

    B Calculating Uncertainty of Mean for 0.5 mm Ruler Measurements

    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...
  43. T

    Determining uncertainty in an experimental value of g

    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...
  44. Cheesycheese213

    Propagation of uncertainty with tangent function?

    For a lab, I needed to calculate the uncertainty of a refractive index that was found using Snell's law. I found an equation online for propagation of error for any general function, which was I thought that since my equation was I could just get rid of the variable y, and have After...
  45. cemtu

    I Heisenberg Uncertainty: simple explanation required please

    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??
  46. jim421616

    Help with uncertainty calculation

    This is from an online quiz. I thought the answer would be 0.6/5 = 0.12 0.12*0.6 = 0.072 ∴ 7.2% but apparently this is wrong. Can anyone help me out please?
  47. K

    I What is the name for the Heisenberg uncertainty principle?

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

    Standard deviation vs measurement uncertainty

    Using the above formulas, we can arrive at an unbiased estimate of the standard deviation of the sample, then divide by sqrt(N) to arrive at the standard deviation of the average. What I'm confused about it where the measurement uncertainty comes into the equation. Is it being ignored? Say I...
  49. Saptarshi Sarkar

    Uncertainty in wavelength and position

    In my attempt to solve the problem, I used the formula for de-Broglie wavelength ##p=\frac h λ## and differentiated both sides to get ##Δp = \frac {hΔλ} {λ^2}##. Plugging this equation into the Heisenberg's position and momentum uncertainty principle formula and calculating the minimum...
  50. V

    A question involving the Uncertainty Principle

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