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. B

    How to Combine Gradient Uncertainty with other Uncertainty?

    Homework Statement I did an experiment to measure the speed of sound(using two microphones and a hammer). I changed the distance between the two mics and calculated(using a fast timer) the time taken for the sound to reach from the start mic to the end mic. I made a graph(distance on x axis...
  2. A

    Uncertainty in Measurements: Understanding Multiplication Factors

    Hello, guys! (And girls, but.. you know..) There are several things I do not quite understand, so, can you help me clear my doubts? ^^ 1) How do I know when to multiply the value of calculated data when it comes to determining the uncertainty of the data? 2) When do I multiply the percentage...
  3. L

    How Should Uncertainty Be Handled When Averaging Measurements?

    Homework Statement This isn't a specific problem. It's more of something that I have encountered before and I have been unable to find an answer to by looking online or through notes. Hopefully this thread might serve others with similar problems in the future. Say for example, you want to...
  4. C

    Schools Uncertainty about graduate school

    Hello, my name is Charles and I am experiencing some doubts about my physics career; I am hoping that other people here have felt the same and can give me some advice. I am presently at a crossroads career-wise and am rather lost. I have just accepted an admissions offer with very good funding...
  5. 123leo

    Finding the random uncertainty of a set of values

    Ok, for the switch-on voltage of a red LED I have the readings as follows, all in volts: 1.45, 1.46, 1.46, 1.44, 1.45. The mean of these readings, in volts, is 1.45 (I rounded up to 2 decimal places as my scale reading uncertainty was +/-0.01V, and my teacher told me to round them up since to...
  6. phys-student

    Quantum harmonic oscillator, uncertainty relation

    Homework Statement Consider a particle with mass m oscillates in a simple harmonic potential with frequency ω. The position, x, and momentum operator, p, of the particle can be expressed in terms of the annihilation and creation operator (a and a† respectively): x = (ħ/2mω)^0.5 * (a† + a) p =...
  7. A

    What constant p.d. should be used in a potentiometer?

    Homework Statement I am trying to use a slide wire potentiometer and a galvanometer to find the electromotive force of an unknown cell. I have heard that the balance point at which the galvanometer needle has zero deflection should be towards the centre of the slide wire as this reduces...
  8. Anithadhruvbud

    Understanding the Uncertainty Principle: Microscopic vs. Macroscopic Examples

    Can anybody give me a simple example of uncertainty principle in both microscopic and microscopic level so that I can recall it every time I read about this topic ?
  9. T

    I Uncertainty in Scale Measurement

    Having a bit of trouble estimating total scale uncertainty. In this experiment, I used four precision weights (error << scale resolution). Each weight has a known mass and is weighted on a scale 20 different times. Therefore, for each weight, I have a mean scale measurement, a standard...
  10. L

    Simple (Constant) Wavefunction -- Find Uncertainty In p^2

    Homework Statement Given the following wave function valid over -a \le x \le a and which is 0 elsewhere, \psi(x) = 1/\sqrt{2a} Find the uncertainty in \left<\left(\Delta p\right)^2\right> momentum, and the uncertainty product \left<\left(\Delta x\right)^2\right>\left<\left(\Delta...
  11. G

    What is the Uncertainty of Human Hearing Frequency?

    what can be the uncertainty of the frequency that humans can hear ? I'm aware that there are many ways,but i tried google-ing to find them but i couldnt. if you could help me it would be great.
  12. DrPapper

    I Expression for Uncertainty of Arbitrary Operator

    Hello all, as far as I can see this question is not posted already, my apologies if it is and please provide a link. But I'm watching this video on youtube: And at 22:38 there's an expression given for the uncertainty of an arbitrary operator Q, however I'm concerned the expression is incorrect...
  13. L

    How to Calculate Resistors in Parallel Uncertainty

    Homework Statement We are told that resistor 1 has a resistance of 4700Ω ± 5% and resistor 2 has a resistance of 6800Ω ± 5% and the equivalent series and parallel resistances are to be calculated with an estimate of uncertainty. Homework Equations RSeries = R1 + R2 RParallel = R1 × R2 / R1 +...
  14. Thanshin

    I Relativity & Uncertainty: Exploring the Impossible

    There's something I don't manage to understand in the union between the relativity of simultaneity and the uncertainty of a quantum system's state. Observer A is in a lab on Earth. Observer B is approaching Earth at half the speed of light. On Earth, we build an experiment that gives a result...
  15. H

    I How can I calculate uncertainty in my lab report data?

    Hi, I'm doing a lab report and for every number we need to calculate the uncertainty. I tried to calculate by using the SQRT of the number but i didn't get the same answer as my partner had? could you help me! These are the numbers and the uncertainty of my partner which i could not figure out...
  16. Jonathan Densil

    What is the Uncertainty of Weight Flow Rate in a Discharging Water Experiment?

    Homework Statement I know this is more of a physics question, but I tried there and wasn't successful. I have done a physics experiment measuring the weight as a function time of the discharge of water from a cylindrical bottle with a pinhole at the bottom. What I ultimately want to get at is...
  17. H

    I Are physical constants subject to the uncertainty principle?

    Are physical constants, such as the elementary charge or the gravitational constant, subject to Heisenberg uncertainty principle, theoretically and empirically? Theoretically in the sense that infinite precision of these constants will directly violate HUP. Empirically in the sense that, for...
  18. ognik

    How to Understand Position Uncertainty in Quantum Mechanics?

    Homework Statement I don't understand how the following works:Homework Equations I follow ## \Delta \nu_0 = \frac{\hbar }{2 m \Delta x_0} ## easily, but then ## \Delta x = \frac{\hbar }{2 m \Delta x_0} t ## ;leaves me puzzled - I understand multiplying through by t, but how does ## \nu_0 t =...
  19. nikoladjal

    Demostration of the Uncertainty Principle from a given ket

    1. Homework Statement I have to demonstrate the Uncertainty Principle Starting from the expression of the following ket: |Ψa>=(ax^+ibp^)|Ψ> where a and b are complex numbers and the ^ denotes that x and p are unitary vectors. 2.Relevant equations I must use the bra-ket notation, but I...
  20. B

    Is Weighing Quarters Individually More Precise Than Together?

    Homework Statement What is a more precise way of finding the total mass? Weighing 5 individual quarters or weighing them all together? 2. Relevant equation individual weights n1+n2+n3+n4+n5 = total weight total weighed together N = total weight The Attempt at a Solution I think weighing...
  21. H

    Increase of Uncertainty over Time

    Looking at the literature it appears that the increase in the variance of the wave function over time is proportional to (1+t^2)1/2. Is that right?
  22. ognik

    MHB Uncertainty relationship

    Trying to follow some text: Given a Gaussian-like distribution for a wave packet, ie a symmetric distribution of $k_x$ about a mean value $ \bar{k}_x $. Making the change of variable $u=k_x - \bar{k}_x$, they write the Fourier transform as: $\psi(x,0) = \frac{1}{2 \pi} e^{i\bar{k}_x...
  23. entropy1

    Difference/similarity between superposition and uncertainty

    What is the relation between "superposition" and "the Heisenberg uncertainty relation"?
  24. Nick tringali

    Determining the uncertainty of the coefficient of friction

    Homework Statement So far i know that the uncertainty of the force of friction is +/- 0.1 and the uncertainty of the force normal is +/- 0.1 also. Homework Equations Force of friction=(myoo)(force normal) Myoo= force friction / force normal The Attempt at a Solution My data is Force of...
  25. F

    Use the uncertainty principle for momentum vs. position to e

    Homework Statement Please see the attachment for a better picture The energy of an electron in a hydrogen atom is: E = p^2/2m - αe2/r; where p is the momentum, r the orbital radius, me the electron mass, e the electron charge, and α the Coulomb constant. Use the uncertainty principle for...
  26. R

    What is the Total Uncertainty in Measuring Force with a 0-10 lbf Load Cell?

    Say I have a 0-10 lbf load cell that can measure the force it takes to lift an object. The load cell is accurate to 1% of the full scale. I take 5 measurements and get the following readings: 5.2, 5.1, 4.9, 5.0, & 4.8, all in lbf. Now I am asked to give the mean with the associated...
  27. T

    Understanding proof for Heisenberg uncertainty

    I've uploaded a proof of the Heisenberg uncertainty principle from Konishi's QM. I just don't quite understand one part: what is the significance of the discriminant being less than or equal to 0? Wouldn't this just result in ## \alpha = R \pm iZ ##? Why would this be desired in this proof?
  28. C

    Finding the overall uncertainty

    Homework Statement How do I find the overall uncertainty of R when R = (h2+l2)/2h Homework Equations uncertainty in h = ±0.57% uncertainty in h2=±1.14% uncertainty in l2=±7% The Attempt at a Solution √1.142+72+0.572
  29. Zeeboozoo

    Tangibly Explaining HUP to General Chemistry Students

    I understand this topic has been brought up before, however there appears to be "truth" or "lies" and very little in between when it comes to explaining the Heisenberg Uncertainty Principle (HUP) to students of freshman chemistry. I'm teaching university general chemistry to students who've had...
  30. weezy

    How is the uncertainty relation preserved in this experiment

    For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...
  31. Negatratoron

    Pairs of observables in uncertainty principle

    Observables are paired up in the uncertainty principle such that we can't measure both to a high degree of accuracy. Specifically, ## \sigma_x \sigma_y>\frac{\hbar}{2} ## where ## \sigma_x ## and ## \sigma_y ## are the standard deviations of our measurements. I've got two lines of questions...
  32. C

    Signal to noise ratio and uncertainty in magnitude

    1. The problem statement, all variables and given/known dat Show that if you have a signal f and noise σf for a stellar flux measurement, then the uncertainty on the observed magnitude is given by σm = 1.0875 x σf / f Homework Equations (you should use the fact that when ε<<1 then log(1±ε) ≈...
  33. Q

    Calculating Uncertainty in Scientific Measurements

    Homework Statement [/B] a=12.26 +/- 0.08 b=0.25 +/- 0.05 e=1.2 +/- 0.2 Evaluate the uncertainty of following calculations Part 1. z= 5(ab/e) Part 2. p= 3e - b The Attempt at a Solution I attempted part 1 like this Δz/z = 5 (Δa/a + Δb/b + Δe/e) ... Calculated Δz to be 20 but the answer is...
  34. D

    Uncertainty of temperatur and pressure

    Somebody who can explain the question How big a error must there be at the temperature for the error on the pressure measurement is not more than 5 % ? thanks in advance
  35. preitiey

    Uncertainty principle at the macroscopic level

    what will be the scenario if Heisenberg's uncertainty principle is applied at macroscopic level?
  36. R

    Calculating Uncertainty for Gravitational Potential and Kinetic Energy Equations

    Homework Statement I am writing a lab report and I need to calculate the uncertainty error for Gravitational Potential Energy and Kinetic Energy. The Professor told us that the margin of uncertainty for time is +- 0.025 seconds, margin for height is +- 0.001 meters, margin for mass is +-0.001...
  37. AstroKeith

    Solving Uncertainty in Lab Report Calculation

    Hello, I am working on a lab report and am unsure about how to express the uncertainty of one of my calculations. I am calculating the volume of a cylindrical disk with height = 0.0258 ± 0.0001 m radius = 0.0767 ± 0.0002m Using V=π(r^2)h and the upper/lower bound method, I find: V= 0.000476205...
  38. AstroKeith

    Finding Uncertainty Using Upper/Lower Bound

    Hello, I'm working on a lab report and am having a bit of trouble when it comes to figuring out uncertainty. Trial 1 Acceleration: 0.93 ± 0.14 m/s^2 Trial 2 Acceleration: 0.83 ± 0.35 m/s^2 Trial 3 Acceleration: 0.93 ± 0.14 m/s^2 I have three values listed above and and wanted to find the...
  39. nazmus sakib

    Uncertainty principle (stationary state)

    I have to derive I did all the way but stuck with the ">=" to "=" sign. what is the logic behind it ? is it safe to write "approximate" while taking the square-root on both side ? or the energy term "V" has gone during the calculation so it has only momentum "p" ?
  40. T S Bailey

    Cosmological expansion and uncertainty

    Firstly, I assume that I'm correct in assuming that since expansion is accelerating it will increase to any arbitrarily large value at some point in the future. If this is true, there must be some point at which particle/antiparticle pairs (due to uncertainty) are carried away from one another...
  41. W

    Uncertainty Principle And Collapse Wavefunction

    Upon a measurement of the position, the wavefunction collapses to a spike centered at x0 https://farside.ph.utexas.edu/teaching/315/Waveshtml/img3240.png I encounter similar spike pictures numerous times, but there is an uncertainty in position , it can't be a spike right. First thing I see...
  42. M

    Estimating uncertainty for a probability

    If I flip an old coin with irregularities 100 times and get side a up 55 times and side b 45 times I say that the probability is 55% that side a comes up. But how can I estimate the uncertainties in this experiment? For example can I say something like "with 95% confidence the probability is...
  43. A

    How can the uncertainty relation be written as such

    Homework Statement Show that the uncertainty relation can be written as Δλ Δx >= λ^2 /4π Homework EquationsThe Attempt at a Solution Ok the uncertainty relation is ΔpΔx >= h/2π , also p = h/λ , so substituting that I have Δh/λ Δx >= h/2π , then divide both sides by h, and multiply both sides...
  44. Multiple_Authors

    Does the Heisenberg Uncertainty Principle Imply Energy Nonconservation?

    Multiple_Authors submitted a new PF Insights post Does the Heisenberg Uncertainty Principle Imply Energy Nonconservation? Continue reading the Original PF Insights Post.
  45. L

    Error propagation with dependent variables

    Homework Statement Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra. I am having trouble finding information on how to calculate and propagate errors when the quantities in my equations are not independent...
  46. A

    What is the Minimum Energy of a One-Dimensional Linear Oscillator?

    Homework Statement The (classical) energy of one-dimensional linear oscillator is a) show, using the uncertainty relation, that the energy can be written as b) Show that the minimum energy of the oscillator is Where Homework Equations Δp Δx >= ħ/2 p ≈ ħ/2x The Attempt at a Solution I'm...
  47. snoopies622

    Can one derive the photon number / phase uncertainty relation

    In an earlier thread of mine, another physics forums member was nice enough to point out that there is an uncertainty relation between photon number and wave phase for light. https://www.physicsforums.com/threads/is-there-a-frequency-eigenstate-for-light.727141/ Now I am wondering, where does...
  48. G

    Uncertainty in Radioactive Decay Dating Calculation

    Homework Statement Charred wood remains were found in Conimbriga, probably with Roman origin. When measured at 14C activity in these remnants, it afforded 10.8 disintegrations per second per gram. The half-processing 14C is 5730 ± 30 years and the activity of this isotope in the atmosphere and...
  49. nmsurobert

    How to Calculate Uncertainty for Spin-1/2 Eigenstates?

    Homework Statement Calculate ΔSx and ΔSy for an eigenstate S^z for a spin-1/2 particle. Check to see if the uncertainty relation ΔSxΔSy ≥ ħ|<Sz>|/2 is satisfied. Homework EquationsThe Attempt at a Solution I'm confused on where to start. As I am with most of this quantum stuff. From what...
  50. A

    Heisenberg's Uncertainty Principle in quantum computing

    My question is how does the uncertainty principle relate to quantum computers? Does it hinder the theoretical production of a quantum computer?
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