Uncertainty Definition and 1000 Threads

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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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?
  6. X

    How Do You Calculate the Uncertainty in the Derivative of y = a / (x - b)^3?

    y = a / (x - b)3 a = 77.1 ± 15.2 b = -1.78 ± 1.18 x = 21 ± 1 --- y' = -3a / (x - b)4 How do I find the uncertainty of y'? Thanks.
  7. J

    Calculating Uncertainty: What is the Effect of θ?”

    Homework Statement Homework Equations Absolute uncertainty in θ = δθ/θ The Attempt at a Solution I know that smaller θ gives smaller actual uncertainty, thus leaving B and D out. The answer is C. but what about option A?
  8. Summer95

    Ground state wavelength and uncertainty Bohr/deBroglie model

    A check my work question... Homework Statement Louis de Broglie tried to explain Bohr’s hydrogen atom electron orbits as being circles of just the right circumference such that an electron of the Bohr energy going around the circle will interfere constructively with itself. This seems to...
  9. Summer95

    What does "minimum range of uncertainty" mean in QM?

    Homework Statement [/B] The problem on where the photon will hit a screen, after passing through a single horizontal slit. I know the wavelength, slit width, magnitude of momentum of incoming photon (calculated), and distance between screen and slit. Homework Equations I just don't...
  10. R

    Absolute uncertainty of calculated density

    Homework Statement An experiment to measure density, d, of a cylindrical object uses the equation d=m/(pir^2l) where m=mass=0.029 +-.005kg r=radius=8.2 +-.1mm l-length=15.4+- .1 What is the absolute uncertainty of the calculated value of the density? Homework Equations above The Attempt...
  11. H

    Uncertainty principle and double slit

    sir, what if we use Heisenberg's uncertainty principle to explain double slit experiment? i was reading about uncertainty principle for last few days n i was reading about double slit experiment and i realize that we can explain why we get electrons everywhere on the screen (getting...
  12. DanielleG

    Experimental Uncertainty - uncertainty in impact position

    Homework Statement The diagram shows the impact of 20 projectiles launched at the same speed and angle. What is the uncertainty in the impact position? (see attached file for picture of diagram) Homework Equations No equations, my lab instructor said through an email that I can get it "just by...
  13. T

    A time-energy uncertainty relation

    I am reading this: http://arxiv.org/pdf/quant-ph/0609163.pdf And Demystifier claims that "The time-energy uncertainty relation is not fundamental" However the proof is done in non-relativistic QM, where t and x are treated differently. My question is, what's about relativistic QM?
  14. M

    How is uncertainty presented in physics?

    Homework Statement How is uncertainty presented in physics? If we have: 5.76 m rounded-->wouldn't the range of uncertainty be between the lower and upper bound: 5.755m - 5.765 m However, my physics teacher said that, as the ruler you are measuring with in this scenario goes down to 0.01 m, you...
  15. K

    What are the units for ΔxΔp in the uncertainty principle?

    Hi all, I am reading an article about uncertainty principle. If we consider a Gaussian wave packet which standard deviation of momentum ##\sigma_p##. The uncertainty principle states that the multiplication of variance of x and variance of p is larger or equal to half ##\hbar## ##\Delta...
  16. G

    Uncertainty principle if position is restricted

    Hi. Assume we have a large number of identical boxes of some finite length ##l## and with infinite potential walls. Let's prepare them all in the same momentum eigenstate. Since for eigenstates ##\Delta p=0##, by the uncertainty principle ##\Delta x## should go to infinity. However, since the...
  17. B

    Understanding Heisenberg's Principle: x and p instead of delta x and p

    Homework Statement I don't get how you can use x and p instead of delta x and p in Heisenberg's principle. Also why is it just h bar? Isn't it supposed to be h bar/2? Problem 2-iv Homework Equations delta x* delta p >= h bar/2 The Attempt at a Solution I tried to deal with this problem but I...
  18. ZapperZ

    Insights Misconception of the Heisenberg Uncertainty Principle - Comments

    ZapperZ submitted a new PF Insights post Misconception of the Heisenberg Uncertainty Principle Continue reading the Original PF Insights Post.
  19. L

    Heisenberg uncertainty question

    I read this article by Hawking which includes this quote " In classical mechanics one can predict the results of measuring both the position and the velocity of a particle. In quantum mechanics the uncertainty principle says that only one of these measurements can be predicted; the ob server can...
  20. M

    What Are the Momentum Characteristics of a Quantum Wave Packet?

    The problem stated below is from Liboff "Introductory Quantum Mechanics" (2nd Edition), exercise 5.4. Homework Statement A pulse ## 1m ## long contains ##1000 \alpha ## particles. At ## t=0## each ##\alpha## particle is in the state: \psi (x,0)=\frac{1}{10}\exp (ik_ox) for |x|\leq 50cm and...
  21. T

    Uncertainty Principle and dart of mass

    Homework Statement A dart of mass ##m## is dropped from a height ##l##. Formulate the uncertainty principle and estimate the minimum limitations, set by the uncertainty principle, of the accuracy that can be achieved in the lateral ##x## position after falling, given an original uncertainty...
  22. Vannay

    Is this statement about the Uncertainty Principle correct?

    I was reading the Feynman Lectures awhile back and I remember reading something he said about the Uncertainty Principle and it seemed slightly odd to me. I don't remember the exact quote and combing through some of the lectures online I can't quite find it. I've heard it more than once from...
  23. C

    Index of Refraction Measurement Uncertainty

    Hello All, I am having some issues with calculating the measurement uncertainty when there is a mismatch in the index of refraction between a fluid and an interface. If am using an unobtrusive measurement technique such as Laser Doppler Velocimetry, how would I be able to quantify the...
  24. Shailesh Pincha

    What are the failed experiments to determine electron's position?

    What are some of the failed experiments to determine electron's position? One could be by electromagnetic radiation of suitable wavelength (here X rays) but that tears apart the atom. I want to know the different views tried to determine electron position.
  25. F

    Heisenberg Uncertainty in wavelength and position

    Homework Statement Show that ## \Delta\lambda\Delta\ x>lamdba^2/4*pi## The Attempt at a Solution When I substitute de Broglie's p=h/lambda I get the equation of ##\frac {\Delta\x}{\Delta\lambda} > 1/(4*pi )##
  26. H

    Calculating Uncertainty for Focal Length: 50mm + 3mm & 200mm + 5mm

    Hi! So I've stumbled upon this question asking us to calculate the uncertainty associated with the focal length. 1/u + 1/v = 1/f u = 50mm with uncertainty 3mm v= 200mm with uncertainty 5mm F is calculated as 40mm, what's the uncertainty in this value? My first approach was to rearrange...
  27. C

    IOR Uncertainty Quantification for PIV/LDV Measurements

    Hello All, I am running some experiments using Particle Image Velocimetry and Laser Doppler Velocimetry techniques. There is a slight mismatch in the Refractive Index of the fluid and my model (Approximately 5% difference) which is creating some uncertainty in my measurements. I was wondering...
  28. H

    B Why is the uncertainty in position equal to the wavelength?

    Why is the uncertainty in position of an object which is determined by a wave equal to the wavelength of the object? I don't get it. Isn't the wave diffracted at the surface of the object? we can then calculated the distance from velocity and time accurately, can't we? is it because we must...
  29. E

    What is the relationship between uncertainties in position and momentum?

    Homework Statement Homework EquationsThe Attempt at a Solution
  30. J

    Heisenberg Uncertainty Principle clarification

    I found these two examples in a books which demonstrate Heiseberg's uncertainty relation...
  31. T

    How can potentials be well-defined without violating U.P.?

    Tried searching for equivalent question but couldn't find it. Presumably, a potential (like a Coulomb one) comes from another particle, which has its own momentum/position uncertainty, but in the Schroedinger equation the potential is well-defined either in terms of some coordinate system or...
  32. J

    Heisenberg uncertainty principle calculations

    I am having some trouble understanding what to use for the uncertainties in the Heisenberg principle. My chemistry book has two problems on this principle. One asks to find the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known within +- 1.0 mm/s. The...
  33. A

    Minimum uncertainty of the momentum of a small particle

    Homework Statement Find the minimum uncertainty of the momentum of a small particle with mass m=1g, which is confined within a region of width a=1cm. Homework Equations Delta(p)*Delta(x)>=hbar/2 The Attempt at a Solution Delta(p)*Delta(x)=hbar/2 Delta(p)*10^(-2)=hbar/2 Delta(p)=10^2*hbar/2...
  34. Z

    Comparing the Uncertainty Principle: Griffiths vs. Shankar

    The general Uncertainty Principle is written in Griffiths' Intro to Quantum Mechanics 2nd Ed. Section 3.4, Page 109, Eq. (3.139) without dependence on the wave function itself. While it is written in R. Shankar's Principles of Quantum Mechanics 2nd Ed., Section 9.2, Page 239, Eq. (9.2.12) with a...
  35. B

    Energy-time uncertainty principle

    I feel there are several non-eqivalent interpretations of energy-tme uncertainty principle.It is right?And if so,what are those corrects?In particular one that sees it (the uncertainty energy-time ) as a chance of violate conservation of energy for a time sufficently small.I would be grateful if...
  36. J

    Improving Accuracy in Measuring Density: Tips and Techniques

    Homework Statement How would you reduce uncertainty when measuring the density of a material Homework EquationsThe Attempt at a Solution I'm guessing you have to reduce the uncertainty in the mass and volume of the material
  37. S

    Generalised uncertainty Principle Can't get rid of the i?

    Homework Statement The Attempt at a Solution As you can see where I have got up to... However I am stuck... In the solution there is no i. In mine there will be. I am unsure how you make the complex number drop out at this stage. I think I'm missing a mathematical trick here... The...
  38. CAH

    Uncertainty in ammeter and voltmeter?

    I set an ohm meter to record current in mA, smallest 0.01mA, I took three readings for several different resistances.. What would the uncertainty be? And the same for the voltmeter but reading in volts, smallest 0.01V
  39. wood

    Time independent Schrodinger equation and uncertainty in x

    Homework Statement Is the gaussian $$\sqrt{\frac{\pi}{2\alpha}}e^{-\alpha x^{2}}$$ an eigenfunction of ## \widehat{T} = \frac{\hat{p}^{2}}{2m}## ? If so, what is the corresponding eigenvalue? If not, find a P.E. operator ##\widehat{U} = U(\hat{x}) ## which gives rise to a Hamiltonian...
  40. davidbenari

    Understanding E/t uncertainty and ##\vec{L}## uncertainty

    Warning: I am taking a modern physics course, and haven't taken QM. I know nothing of "commutators, operators, hilbert spaces, etc." I understand ##\Delta E \Delta t >= \hbar /2 ## to mean that I can't know the energy of a system and the time at which that energy takes place exactly. These two...
  41. R

    What is the percentage uncertainty in V when L1-L2 is 30?

    Homework Statement My homework question says: the uncertainty in length 1 is +/- 0.1 and in length 2 is +/- 0.1 : calculate the percentage uncertainty in V where V L1-L2 is 30Homework Equations V= (1/(L1-L2))^0.5 where L is the length[/B]The Attempt at a Solution So what I did was add...
  42. J

    Heisenberg's Microscope Derive Exactly Uncertainty Principle

    Can the Heisenberg's Gamma Ray Microscope thought experiment derive the Uncertainty Principle precisely? Most derivations I find, the uncertainty is roughly 2h, whereas the uncertainty principle is "hbar over 2". Is there anywhere where there is more precise calculations to obtain "hbar over 2"...
  43. M

    Determine uncertainty of collection of data

    Hello, I work in a liquid calibration Lab and we are applying for ISO 17025. Basically we verify customers flow meters against our standard and capture the data onto our calibration report. An example is I would perform 4 tests of a specific flow rate and calculate the error in % for each test...
  44. Avatrin

    Velocity of neutron using uncertainty principle

    Homework Statement A neutron in the nucleus of an atom can move in a range which is about five femtometers long. Use Heisenberg's uncertainty principle to calculate what velocities one can expect to measure. Homework Equations \sigma_p \sigma_x \geq \frac{\hbar}{2} p = \hbar k Probably others...
  45. A

    Uncertainty of position in an infinite potential well

    The ground state energy of a particle trapped in an infinite potential well of width a is given by (ħ2π2)/2ma2. So the momentum is given by (2mE)1/2 = ħπ/a. Since this is a precise value, doesn't that mean that we know momentum with 100% certainty? And if that is the case shouldn't the...
  46. A

    Explaining Probabilities in a deterministic world

    Let's assume we're living in a mechanical deterministic world. Now do you agree that any uncertainty is a result of lack of knowledge? We flip a symmetric coin. The equations of movement are deterministic, but the outcome is uncertain, with probability 50% tail or head. Thus, it's the initial...
  47. R

    Application of Heisenberg Uncertainty Principle

    Homework Statement A parallel beam of electrons traveling in x- direction falls on a slit of width d. If after passing the slit, an electron acquires momentum py in the y direction then for a majority of electrons passing through the slit A. |py|d ≈ h B. A. |py|d > h C. |py|d < h D. |py|d >> h...
  48. StrangeCharm

    Uncertainty about Pursuing Physics

    Hello! Did you always know you wanted to study physics? How did you make the decision to major in physics? Do you regret your choices? I'm an undergraduate freshman who is thinking of majoring in physics. Nevertheless, although I enjoy physics, I sometimes wonder whether it's the right path...
  49. T

    Maximization of an Uncertainty Product

    Homework Statement [/B] Sakurai problem 1.20: find the linear combination of spin-up and spin-down S_z eigenkets that maximizes the uncertainty product \langle(\Delta S_x)^2\rangle\langle(\Delta S_y)^2\rangle. Homework Equations [/B] In general, we can write a normalized spin-space ket as...
  50. J

    Time Uncertainty and the Collapse of the Wavefunction

    I'm having a hard time understanding why it makes sense to say that the particle has an uncertain position to which it can collapse, but not to say that the particle has an uncertain time to which it can collapse. Similarly, why do we consider when the particle collapses as when we measure it...
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