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. U

    Calculating Energy Uncertainty for a Particle Described by a Wave Function

    Homework Statement Determine the energy uncertainty \Delta E = \sqrt{<E^2> - <E>^2} for a particle described by a wave function \Psi (x) = c_1 \psi (x)_1 + c_2 \psi (x)_2 where \psi_1 and \psi_2 are different (orthonormal) energy eigenstates with eigenvalues E_1 and E_2. Homework...
  2. G

    When do I use these equations for calculating linewidths?

    hi i am looking for the correct equation, that gives me the linewidth by knowing the time of the emission process. so far, i found in the internet: Δf=1/(Δt), Δf=1/(4πΔt) and Δf=1/(2Δt) can you tell me, when i have to use which of these equations and maybe whether you think that...
  3. D

    A thought on Heisenberg Uncertainty Principle

    Let me first start off by saying that I am somewhat new to physics and it's understanding. But I was looking over the Hiesenberg Uncertainty Princple and a thought occurred to me. The Heisenberg Unvertainty Principle states "More precisely the position is determined, the less precise the...
  4. C

    Expectation value of uncertainty

    Homework Statement Show that, if [H,A] = 0 and dA/dt = 0, then <&Delta;A> is constant in time. Homework Equations d<A>/dt = <i/ℏ[H,A] + dA/dt> The Attempt at a Solution I am trying to use the above equation to show that d<&Delta;A>/dt is 0, and I can get to d&Delta;A/dt = 0, but I...
  5. S

    RMS uncertainty using a Trend Line

    Homework Statement Find the acceleration of gravity. Using the trendline equation of Force v. hanging mass, find the RMS uncertainty for the force. Trend line equation: y = 9.8968x - 0.0342 R² = 0.9493 Data Values: Hanging mass is the first number. Force is the second number...
  6. C

    Uncertainty in Energy an ground state energy

    I'm asked to show that in the ground state, a particle trapped in a potential well approximately equal to its lowest allowed energy. I know the expression for the energy is h^2/8mL^2 for a finite well, and ΔEΔt~h/2π. But I'm at a loss as to how I'm supposed to even begin to start this...
  7. K

    Linewidth of emission and the uncertainty principle

    Homework Statement The linewidth of a certain fluorescing dye molecule is 60nm and the peak emission wavelength is 600nm. The lifetime of the dye molecule in the excited state is 1ns. Determine whether the linewidth of the emission is a result of the uncertainty principle. (it may be helpful...
  8. V

    Is Heisenberg uncertainty principle a problem of our measuring techniques?

    Hello I know this topic must have been done to death already, but i can't seem to find a satisfying answer. As the title suggests, my question is, what experiment proves that the uncertainty principle is not just a result of our flawed measuring techniques? From what i understand, when we...
  9. W

    Using uncertainty principle to estimate ground state energy

    Homework Statement Use the uncertainty principle to estimate the ground state energy of a particle of mass "m" is moving in a linear potential given by V(x) = ∞ for x≤ 0 V(x) = αx for x ≥ 0 Homework Equations ΔxΔp ≥ h/2 The Attempt at a Solution I've looked at a similar problem...
  10. A

    What's the kinetic energy uncertainty for gaussian wave packet?

    What's the kinetic energy uncertainty for gaussian wave packet ψ(x)=((α/pi)^(1/4))exp(-αx^2/2)?
  11. J

    Heisenberg Uncertainty Principle

    Homework Statement An electron is confined within a region of atomic dimensions on the order to 10-10 m. Compute the uncertainty in its momentum. Homework Equations N/A The Attempt at a Solution I know this problem involves a simple application of Heisenberg's uncertainty...
  12. S

    Propagation of errors addition numbers without uncertainty

    Homework Statement I am having trouble calculating uncertainty when a number is added to a value with uncertainty. M = 350g a = 0.624 \pm 0.001 µk = 0.07 g = 9.80 m/s2 Homework Equations T = M*a + µk*M*g The Attempt at a Solution T = (350g)*(0.624 m/s2) +...
  13. B

    Calculate the uncertainty on the values of m

    Homework Statement m 7.29 7.31 7.3 7.31 7.27 7.28 7.31 7.29 7.28 7.27 7.26 7.3 87.47 mean 7.289166667 using the values in the table calculate the uncertainties on the mean values of m The Attempt at a Solution I thought finding the difference between the...
  14. R

    Heisenberg's Uncertainty Principle, Determinism and Free Will

    Heisenberg's uncertainty principle only seems to have implications for our understanding of the body of knowledge produced by science, not reality itself. The uncertainty comes from the inability to make two separate measurements, since each measurement will disturb the system and change the...
  15. G

    Heisenberg's uncertainty principle, find uncertainty in position

    Homework Statement Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of a proton moving at a speed of (5.00±0.01) x 10^4 m/s. Homework Equations Δx\geq \frac{h}{4mΔv\pi} The Attempt at a Solution x\geq (6.626*10^-34)/(4pi(1.6726*10^-24)(5±0.01 *...
  16. A

    (easy) Uncertainty Analysis question

    Homework Statement If I measure A=50, with a minimum value of 48, and a maximum value of 51, and measure B=100, with a minimum value of 92, and a maximum value of 115, and I add the two (C=A+B) together, what is the resulting minimum and maximum value of C? Homework Equations If A...
  17. R

    Trying to understand Heisenberg Uncertainty Principle in a physical sense

    I'm trying to understand the Heisenberg Uncertainty Principle, as it relates to experimental measurements, because it's kind of confusing me. We just learned the derivations for it in my QM class -- basically it's two standard deviations multiplied together (corresponding to measurements of...
  18. R

    Calculating uncertainty using the least squares method.

    Can someone point me in the right direction or give me a rundown on how to use the least squares method in calculating the uncertainty in a gradient of a graph? We have been given a theoretical experiment with data and so on supplied and we need to find the uncertainty of the graph we have...
  19. A

    Absolute Uncertainty - Enough Information?

    Homework Statement If an electronic scale reads 502.4 g, what is the absolute uncertainty in the mass reading. Homework Equations Not sure The Attempt at a Solution Not a clue, it seems that there isn't enough information given. How am I supposed to figure out the absolute...
  20. A

    Uncertainty with a simple pendulum

    A simple pendulum is used to measure the acceleration of gravity using T=2pi(sqrt(L/g)) . The period T was measured to be 1.24 ± 0.02 s and the length L to be 0.381 ± 0.002 m. What is the resulting value for g with its absolute and relative uncertainty? So the first thing I did was to isolate...
  21. F

    Uncertainty In a Physics Experiment

    Hello, I'm trying to figure out a way to calculate a suitable uncertainty value for the accuracy of a human measuring timing values during an experiment. The experiment was designed to determine the frictional force acting on a trolley as it is pulled along by a string attached to a...
  22. A

    How can the uncertainty principle and relativity coexist?

    The uncertainty principle says that you can't simultaneously measure position and momentum with arbitrary precision. So you can measure one at a time t1 and the other at a time t2 with t2 > t1, thus not measuring both simultaneously, but relativity tell us that there exists a frame of reference...
  23. M

    Please check solutions to Error Uncertainty calculations

    Please check if my solutions are correct or if I am totally wrong. Thank you! 1. Homework Statement [/b] In an experiment to measure the density of a steel ball. The diameter of the ball is d= 1.76 +- 0.02 cm and the mass to be m= 22 +- 1g. (include error calculations and report values with...
  24. C

    Large Scale Uncertainty Principle

    Hi, I was watching Through the Wormhole two weeks ago (I think it was a re-run), and they were talking about the uncertainty principle, and how it was impossible to prove due to the change in momentum of a particle when hit with an observation device, such as light. I think the guy was using...
  25. T

    MATLAB Uncertainty in values from Matlab Curve Fitting

    Hi- I apologize if this has been covered elsewhere, but after much searching with no luck... I am taking a lab class, the first in a while, and am using Matlab's Curve Fitting tool to fit data to exponential curves. My question is how to translate (if possible) the "goodness of fit"...
  26. C

    Approximate uncertainty in area of circle

    Homework Statement What is the approximate uncertainty in the area of a circle of radius 5.3 * 104 cm? Express your answer using one significant figure. Homework Equations A = pi*r2 The Attempt at a Solution Using the given radius, I found the area to be 8.8 * 109 cm2. And since...
  27. W

    Centripetal force + uncertainty

    Homework Statement The centripetal force is given by F= (mv2) / r. If the mass is measured to be 2.8 +/- 0.1 kg, the velocity is 14 +/- 2 ms^-1, and the radius 8.0 +/- 0.2 m, find the force on the mass, including the uncertainty. Homework Equations F= (mv2) / r The Attempt at a...
  28. C

    Do we have Any idea why the uncertainty principle occurs?

    I understood the Delayed Eraser experiment, and the Eraser experiment and the basic double slit experiment. And all I can conclude is, why? Why is there such a necessity? I now understand that it's most probably impossible to learn the 2 properties at the same time but I don't see any...
  29. C

    Question on Uncertainty Principle

    If Uncertainty Principle is a result of 'fiddling' of an apparatus with what is being observed (for example light particle/wave of a detector fiddling with particles/waves being observed), then wouldn't uncertainty principle cease to apply if in the future a 'smaller' or 'less interfering'...
  30. A

    Uncertainty Propagation Argument

    A while back, one of my undergraduate physics professors gave an argument for why the uncertainty in a function or quantity F is given by \Delta F = \sqrt{^{N}_{i-1}\sum(\frac{\partial F}{\partial x_{i}})^{2}(\Delta x_{i})^{2}} He argued to think of a right triangle and think of...
  31. J

    Question on estimated uncertainty and significant digits

    Question on "estimated uncertainty" and significant digits Homework Statement The value is 136.52480, and the "estimated uncertainty" is 2. How many digits should be included as significant? Homework Equations Not sure whether estimated uncertainty refers to a 1σ (68.26%) confidence...
  32. R

    Uncertainty principle and electrons

    I've been exposed to two different interpretations of the uncertainty principle. 1) If an electron is in a certain state, a measurement of its position will yield a definite result. However, if after the measurement the electron could be returned to the same state, then a repeated measurement...
  33. B

    Calculating uncertainty in a experiment

    Homework Statement Finding uncertainty in magnetic field strength. N=2, i=1.00\pm0.005 A, R=0.1 m, \tan \theta=0.49\pm0.008 Homework Equations The equation B_{coil}=\frac{\mu_0 N i}{2 R \tan \theta} The Attempt at a Solution I am assuming that the radius R and number of turns N are exact. I...
  34. S

    Variable Uncertainty: Solving Equations with Empty Sets

    Homework Statement Ok, I don't have a problem with the question, but what I believe to be an empty set variable is used which I have not covered in a course before. My problem is that I do not know the relevance of an empty set in part b) of the equation. Homework Equations The equation and...
  35. K

    Non-linear least-squares: Uncertainty estimates including non-fitted parameters

    Hi all, I have a question regarding least-squares, and I'm certain I can't be the first one to encounter it, but I've had no luck searching the literature for a solution. Here it is: Say we have a non-linear least-squares optimisation problem. We have data points y_i and a model y(x_i;{\bf...
  36. L

    Does the Uncertainty Principle Make Precise Momentum Measurement Impossible?

    Hi all, I am sure this is a quite simple question but I just can't figure it out, any helps would be greatly appreciated. If a particle stay in a state in a very short time, then by energy time uncertainty relation, it's energy must has a great uncertainty. Also because of energy is propotion...
  37. P

    Uncertainty of room mode frequencies

    Hi - I'm new here - I'm just writing a paper based on an acoustical analysis of a rock/pop performance venue in a college I work at, and I'm up to my uncertainties section. I've read up on uncertainties, and feel confident in working out uncertainties for simple additions, multiplications...
  38. I

    How Do Uncertainties Affect Calculations in Cookie Volume and Size Ratios?

    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+-0.02cm and a thickness of 0.050+-0.005cm. Homework Equations a. Find the average volume of of a cookie and the uncertainty in the...
  39. BWV

    Uncertainty principle discrete operators

    couple of questions a) the operators not commuting would also be true of position and momentum operators in classical mechanics (x d/dx -d/dx x) f(x) so the non-commutation does not inherently constitute a proof for the uncertainty principle, or do you just not care about the uncertainty at...
  40. J

    The Heisenberg Uncertainty of Bowling Balls

    I was recently thinking about the Heisenberg Uncertainty Principle which states that we can not know a subatomic particle's position and momentum at any instant. We can know one or the other measure but not both at the same time. The more we know about one, the less we know about the other...
  41. S

    Heisenberg's Uncertainty Principle

    Here's how I understand it: The light of a shorter wavelength disturbs the momentum of the electron, but shows the electron's position. Why doesn't the light of a longer wavelength disturb the momentum of the electron?
  42. M

    Paradox: The infinite square well vs. the Uncertainty Principle

    I've come across an apparent paradox in elementary quantum mechanics, and after a little Googling, haven't found a reference to it. Here goes, The 1-D infinite square well is a classic problem in introductory QM. We find that the position-space eigenfunctions of the Hamiltonian (the "allowed...
  43. J

    Exploring Heisenberg's Uncertainty Principle: Intuition & Explanations

    You are no doubt familiar with Heisenberg's uncertainty principle, putting a limit on the accuracy with which we can measure a particle's position and momentum, \Delta x \Delta p \geq \hbar/2 On my course I was shown the derivation, it popped out of a few lines of mathematics involving the...
  44. I

    Uncertainty and The Double Slit Experiment

    While reading Feynman's 6 Easy Pieces, I see he talks about bouncing photons off of the electrons that are passing through two slits. According to Feynman, when a photon strikes an electron near one of the slits, it bounces (sometimes back at the observer) and registered as a sharp point of...
  45. 0

    Uncertainty in measurement (GRE question)

    This is actually a GRE problem, I'm just trying to go through and understand them all for studying purposes, but I don't understand how to do this one at all. Homework Statement A student makes 10 one-second measurements of the disintegration of a sample of long-lived radioactive isotope and...
  46. S

    Heisenberg's Uncertainty Principle: Exploring Possibilities

    Hello everyone. This is my first post, but I enjoy reading all the forums. I have a simple question that I thought about recently: Would Heisenberg's Uncertainty Principle still hold up if we could somehow observe a particle without the aid of instruments? I know it is entirely...
  47. M

    Help calculating uncertainty of slope & intercept of cal. curves. uncertainty ?s

    Homework Statement I need assistance in learning the proper way to calculate error/uncertainty in a few things for my undergrad thesis.Homework Equations 1) how to calculate the uncertainty in the slope and intercept of calibration curves (peak area vs mol of compound) I have made via excel...
  48. K

    Photon flight times and the uncertainty principle

    Ok I feel a bit silly asking about this, but I have gotten myself confused and need some help sorting something out. In QFT the operators of observable quantities commute over space-like intervals, so we cannot propagate effects faster than light, causality is safe, cool. But I have somewhat...
  49. N

    What is the meaning of uncertainty principle in QTF?

    Please teach me this: In Quantum Mechanics the Heizenbeg principle holds for one particle.In QTF Theory,the creation and annihilation operators corresonding to coefficients of Fourier components of transformation,so it seem that each quantum(particle) has a definite momentum.Then it seem that...
  50. stevmg

    Explaining the Heisenberg Uncertainty Principle and Electron Orbits

    It is stated that electrons orbit the nuclei of atoms not as particles. By the Heisenberg Uncertainty Principle (whatever that is) one cannot pinpoint their actual location and one cannot track the motion of an electron as it orbits the nucleus. What is that all about? Please use 10th...
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