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. P

    What is the uncertainty in area and volume for a right circular cone?

    Uncertainty partial derivatives Homework Statement 1 a) Give expressions for the uncertainty in both the area and volume of a right circular cone with radius R and height H and side length S. Assume that the radius has uncertainty σR and the height has an uncertainty σH. <----First part...
  2. 0

    How Does Error Propagation Affect Calculations in Physics?

    A position of a particle in linear motion is given by: x = vt + 0.5at2 Calculate x with the error for: t = 25.3 ± 0.5s v = 10.1 ± 0.4m/s a = 2.5 ± 0.3m/s2 So for calculating vt: q = (10.1) (25.3) = 255.53 (exact) Δq = (10.1)(25.3) * √ (0.4/10.1)2 (0.5/25.3)2 = 11.31... Therefore, vt =...
  3. lep11

    How Do You Calculate Uncertainty in the Volume of a Cookie?

    Homework Statement As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio...
  4. E

    Percent uncertainty in Volume of a beach ball?

    Homework Statement What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r=5.60±0.05m? Homework Equations ∏r^2 The Attempt at a Solution
  5. E

    What is the approximate uncertainty in the area of a circle

    Homework Statement Approximate uncertainty in the area of a circle of radius 5.5×10^4 cm? Homework Equations πr^2 The Attempt at a Solution
  6. Y

    Find the average and uncertainty?

    "5 students time a bowling ball traveling from point A to point B. They record the following times": 2.45s 2.49s 2.58s 2.55s 2.51s "7 students measure the length of a car. They record the following lengths": 4.5 m , 4.7 m , 4.4 m , 4.6 m , 4.8 m , 4.5 m , 4.6 m Homework Equations...
  7. G

    Heisenberg uncertainty principle and wavelength of light

    I read somewhere that Heisenberg described his uncertainty principle by saying that you can't measure position more accurately than the wavelength of light (which makes sense), so Δx > λ. This is what I don't get. He then says that p=h/λ, so Δp > h/λ2 Δλ. He the multiplies and sets Δλ ≈ λ to...
  8. D

    Generalized uncertainty principle

    Homework Statement A spin-half particle is in a known eigenstate of Sz. Show that the product <S^2_x> < S^2_y> is consistent with the Uncertainty principle Homework Equations The Attempt at a Solution I know that the generalized uncertainty principle gives ΔS_x ΔS_y ≥ |<[S_x...
  9. C

    Finding Absolute Uncertainty Using Formulas

    Homework Statement Hello, I have solved the problem, but not the way the writer intended. I need help figuring out how they wanted me to do it. Here's the problem: The circumference of a sphere is found to be 0.98 m +/- 0.01 m. Calculate the volume and absolute error with five digits...
  10. D

    Uncertainty Principle textbook equation

    I have been going through my Physics textbook to brush up on my Quantum Mechanics before starting my next QM course next academic year and the Heisenberg uncertainty principle for position and momentum is written as ΔxΔp ≥ h-bar when I thought it was ΔxΔp ≥ (h-bar)/2. Other sources say it is...
  11. C

    How to combine instrument uncertainty with deviation

    Here's my problem: I have been using a digimatic indicator tool to measure the thickness of a somewhat uneven film. The digimatic indicator has a digital screen that shows up to 1 um, but according to specifications the accuracy is only 3 um. To account for the uneveness I have taken 10...
  12. K

    Detector Characterization Uncertainty -Poisson

    Hi to all, I have the following problem: I want to characterize two lots of detectors in order to retrieve their mean cross section and standard deviation for a proton beam. For cross section I mean the number of counts respect the fluence of particle (fluence = integral of the particle flux...
  13. S

    How Do You Calculate Uncertainty in Ammeter Readings?

    Homework Statement The manufacturer of a digital ammeter quotes its uncertainty as ±1.5% ±2 digits. a. Determine the uncertainty in a constant reading of 2.64 A b. The meter is used to measure the current from a d.c. power supply. The current is found to fluctuate randomly between 1.58 A and...
  14. 7

    Calculating uncertainty of energy if all we know is dimension of box

    Homework Statement Homework Equations \begin{align} \Delta p \Delta x &\geq \frac{\hbar}{2}\\ \langle p \rangle &= \sqrt{\langle p^2 \rangle - \langle p \rangle^2}\\ \langle x \rangle &= \sqrt{\langle x^2 \rangle - \langle x \rangle^2} \end{align} I allso know that a wavefunction of a...
  15. 7

    Uncertainty of an electron in a core

    Lets say we put an electron in a box (spherical) which has a radius ##r##. I want to know if position uncertainty ##\Delta x = r## or is it ##\Delta x = 2r##? I need to know this to corectly calculate 1st the momentum uncertainty ##\Delta p=\frac{\hbar}{2\Delta x}## and 2nd that kinetic...
  16. N

    Boson statistics and the uncertainty principle

    This question is regarding the boson statistics and it’s relation to the uncertainty principle. Consider we have a vacuum state and we apply a field operator on it to create a particle at position x, we end up with state like \begin{array}{l} \left| \psi \right\rangle = {\psi ^\dag...
  17. M

    Can someone prove the uncertainty principle for me

    My qm textbook, aptly named "quantum mechanics", is by McIntyre, though it omits the proof for the uncertainty principle and simply states it as ∆A∆B ≥ 1/2|〈[A,B]〉|. In words, if that's unclear, this is 'the product of the rms deviations of A and B is greater than/equal to one half the absolute...
  18. B

    How Do You Calculate the Uncertainty in Kinetic Energy?

    Homework Statement An object of mass m = 2.3 ± 0.1 kg is moving at a speed of v = 1.25 ± 0.03 m/s. Calculate the kinetic energy (K =(1/2)mv2) of the object. What is the uncertainty in K?Homework Equations Δz = |z| ( Δx/x + Δy/y ) - Multiplication Δz = n (xn-1) Δx - Power The Attempt at a...
  19. H

    Why is there a small variation in the spectrum of the same element?

    why doesn't the uncertainty principle lead to small discrepancies in the spectrum of the same element in different situations? I think that since there is a whole area for the electron to jump from and to and therefore a small range of values of possible jumps for a single shell, so there...
  20. B

    Heisenberg uncertainty for noob

    Hey guys, I saw a joke about this in the jokes thread. So I went to see what it is exactly. But the thing is I didn't understand it fully. Could anyone please simplify and comprehend to me? Also I saw that it's only for particles. What is the importance of this theory. I hope non complicated...
  21. B

    Propagation of uncertainty for no-load voltage

    Need help propagating the uncertainty of Es = Ex ×(x+xo/xs+xo) . I understand all of the rules and can do it for a formula such as vo+ at. But I am having trouble with the (A+B)(/A+C)
  22. B

    Propagation of Uncertainty in non-load voltage

    Need help propagating the uncertainty of Es = Ex ×(x+xo/xs+xo) . I understand all of the rules and can do it for a formula such as vo+ at. But I am having trouble with the (A+B)(/A+C).
  23. K

    The Uncertainty Relation for Position and Momentum

    Homework Statement The position of a 60-gram golf ball sitting on a tee is determined within +- 1μm. What is its minimum possi- ble energy? Moving at the speed corresponding to this kinetic energy, how far would the ball move in a year?Homework Equations ## K\geq\dfrac {\hbar ^{2}} {2ma^{2}}...
  24. E

    Measurement uncertainty and error

    Suppose we have x plates of wood of thickness (0.0150 \pm 0.0002) \text{ m} and we wish to stack them into a pile of height (1.000 \pm 0.001) \text{ m}. The number of plates x required is then x = \dfrac {1.000 \pm 0.001}{0.0150 \pm 0.0002} \, . How many plates will certainly fit in the...
  25. N

    Reconciling quarks and the uncertainty principle

    As a result of some precise experimental data, we now know that the mass of the quark is not naively 1/3 the mass of the proton. The most recent estimates for the mass of the quark is: Masses of the current quarks: = 2 - 8 MeV/c2 = 1.0 - 1.6 GeV/c2 = 168 - 192 GeV/c2...
  26. coktail

    Uncertainty Principal: Limit of measurement, or the nature of things

    Hi! I found a few old threads lying around regarding this, such as this one, but I thought I'd start a new one asking the question in my own way. So here goes. Is the uncertainty described by the Uncertainty Principal a result of the fact that by measuring something we affect it, or a...
  27. U

    Beam width uncertainty, deflection

    Homework Statement In a scanning electron microscope, a 0.3 keV electron beam, collimated by an aperture of width ∆xi, is directed towards a target 1 m away from the aperture. Assuming a field-free region from aperture to target, the uncertainty ∆xf in the transverse coordinate of the...
  28. L

    I need all the information about theHeisenberg's uncertainty principle

    I really can't understand the uncertainty principle,and now there are some experiment that violate the uncertianty principle, I need deepen understanding of quantum uncertainty,who can give me all the information about the uncertainty principle,such as new ideas,related study or books,thanks
  29. A

    Find the percentage uncertainty of a wooden block

    Homework Statement I have to find the percentage uncertainty of a wooden block for its volume and density. Using 3 different types of measurements for length, width, and height. Let's say that this is my data (cm): Instrument 1: L= 1.1 W= 1.1 H= 1.3 V=1.573 Instrument 2: L= 1.13 W= 1.13...
  30. N

    Bumblebee uncertainty question

    Homework Statement A bumblebee is flying around your kitchen with an average speed of 5.0 m/s. You very carefully measure its position to be 3.01 m in the x direction, 0.25 m in the y direction and 1.23 m in the z direction. What is the approximate theoretical uncertainty in its...
  31. D

    Uncertainty Product for a hydrogen-like atom,

    Homework Statement Calculate the uncertainty product ΔrΔp for the 1s electron of a hydrogen-like atom with atomic number Z. (Hint: Use <p> = 0 by symmetry and deduce <p^2> from the average kinetic energy) Homework Equations All I have is the wavefunction. For a 1s, it takes the form...
  32. G

    Exploring the Energy-Time Uncertainty Relationship

    This is from Hogdson's book the Mind Matters Does anyone know what the actual equation he is talking about and I was wondering if anyone could give me a few more details regarding the energy-time uncertainly relationship.
  33. nomadreid

    From statistical to ontological: uncertainty principle

    The derivation of the momentum/position Heisenberg Uncertainty Principle (HUP) is based on the statistical interpretation which says that if we have a lot of quantum systems in identical states, and measure the momentum in half of them and get a distribution with standard deviation σp, and...
  34. B

    Uncertainty principle regarding a narrow optical fibre?

    If we take a narrow aperture(such as the one used in the double slit experiments) and attach a length of optical fibre to it, surely now we know the position (confined by the width of the fibre) and also the momentum(defined by the direction of the fibre). How does the uncertainty principle...
  35. L

    The uncertainty principle and the measurement postulate

    Hi everybody. I have a quick question regarding the relationship between the uncertainty principle and the measurement postulate. According to the former, the higher our certainty is about the position of a particle, the lower our certainty is regarding its momentum, and vice versa. This...
  36. R

    Uncertainty with sine of angles?

    Homework Statement I'm in a Year 10 Physics class, and we have been doing an experiment about Snell's Law (θincident = θrefracted). The experimental design is fairly simple: a beam of light (from a ray box with a single slit in front of it) is shone into a glass block. The angles of the...
  37. P

    Uncertainty principle using 2 detectors

    This may be a dumb question, but I am still new the the concept of the quantum world... If we can't measure position and momentum precisely at the same time, why can't we use 2 detectors? One to measure position, and one to measure momentum. Have them take the measurement at the same time, and...
  38. V

    What do I do if my uncertainty is larger than the actual value?

    It's .22 ± .026s I know it's wrong to have an uncertainty mor eprecise than the value, but this uncertainty was obtained through the standard deviation methos ( with the sqaure) root? What should I do?NVM I fugured it out myself.
  39. Q

    Estimating Atom Size using the Uncertainty Principle

    The typical energy needed to ionise an atom is around 5 eV. Use the Uncertainty principle to estimate the size of an atom. Homework Equations E=mc^2 E = p^2/2m Δx.Δp ≥ h/4π The Attempt at a Solution So I got the mass rearranging E = mc^2 m = 5*1.6*10^-19 / (3*10^8)^2...
  40. T

    Photons Moving Through a Single Slit (Uncertainty)

    Homework Statement The diagram is attached. Photons are being beamed with momentum \rho_{0} and mass m at a slit of width A Estimate the uncertainty \Delta p_{y} emerging from A Sketch spot size at B as a function of slit width using the uncertainty principle Determine minimum spot size...
  41. A

    Problem about uncertainty principle

    We have an electron pulse of width 1 nanosecond and with kinetic energy of 1keV. We have to calculate Δx and Δp. I have a question regarding this problem. If they give us the kinetic energy of the electron pulse then we know exactly the momentum right? And so the uncertainty of momentum would...
  42. C

    Heisenburgs Uncertainty Principle in a narrow tube?

    The principle states: δxδp≥h/4π I understand what it means and I've seen in proven both theoretically and expiamentally, so I am not questioning the inequality here. My question is: If there was a very narrow tube that had a vacuum inside it and a laser attached at one end that shoots...
  43. D

    Given the uncertainty in momentum, calculate the uncertainty in Energy

    Homework Statement I am given that E = (hbar)^2 k^2 / 2m. I am suppose to calculate the uncertainty in energy(ΔE). I am also given the wave equation. I am given Δp (uncertainty in p), Ko (wave number). and that Δp << hbar Ko. Homework Equations I believe the equation is ΔE = sqrt(<E^2> -...
  44. H

    Uncertainty of experiment relative or absolute

    I calulated the time(s), then i found the uncertainty as a percentage of my results. Later on i calculated 1/time and used the uncertainty % which i originally calulated. Could somebody tell me if it is relative or absoulte uncertainty and why?
  45. B

    Uncertainty of energy in a quantum harmonic oscillator

    Homework Statement Find the uncertainty of the kinetic energy of a quantum harmonic oscillator in the ground state, using \left\langle p^2_x \right\rangle = \displaystyle\frac{\hbar^2}{2a^2} and \left\langle p^4_x \right\rangle = \displaystyle\frac{3\hbar^2}{4a^2} Homework Equations...
  46. M

    Propagation of uncertainty in an experiment

    I performed an experiment using different wavelength lasers to calculate the distance between the pits of a DVD by measuring the angles formed by the resulting diffraction pattern,but now I'm unsure on how to calculate the uncertainty of the final result. I took 9 measurements each with their...
  47. M

    Time-energy uncertainty (question after reading FAQ)

    Hi, The FAQ is a good answer, but it leaves me wondering about something. From what I read, the jist is that a short enough measurement sees no difference between an energy eigenstate and a quantum superposition which mostly comprises of that energy eigenstate but also has a few other...
  48. C

    Practical physics questions - Pressure & Uncertainty

    Hey guys, I have a few questions I would like to ask if that is okay First off: I was doing an experiment regarding Boyle's Law, and there are some questions that accompany it. I had a syringe filled with gas and I had to add mass on the syringe so that the piston moved down. I had to convert...
  49. D

    Heisenberg Uncertainty Maximum Lifetime of Photon

    Homework Statement In special conditions, it is possible to measure the energy of a gamma ray photon to 1 part in 10^15. For a photon energy of 50 keV, estimate the maximum lifetime that could be determined be a direct measurement of the spread of photon energy. Homework Equations...
  50. S

    Uncertainty about Heisenberg Uncertainty Principle

    I'm not certain as to the true meaning of the Heisenberg Uncertainty Principle, and wonder if anyone can provide insight. I understand that there is a reciprocal relation between the certainties as to the position and momentum of a particle such as an electron; the more precisely position is...
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