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. tomwilliam2

    Simultaneity of Uncertainty Principle

    All of the statements of Heisenberg's uncertainty principle that I've read seem to state that there is a fundamental limit on the precision to which you can measure the values of conjugate pairs (like position and momentum) at the same time. So is this simultaneity necessary? I ask because...
  2. L

    Uncertainty principle in terms of expectations values in Dirac notatio

    Homework Statement Show that (\Delta A)^{2} = \langle \psi |A^{2}| \psi \rangle - \langle \psi |A| \psi \rangle ^{2}\\ \phantom{(\Delta A)^{2} }=\langle \psi | (A - \langle A \rangle )^{2} | \psi \rangle , where \Delta A is the uncertainty of an operator A and \langle A \rangle is the...
  3. 7

    Gaussian function to derive Heisenberg's uncertainty principle

    At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves ##\psi = \psi_0(k) e^{i(kx - \omega t)}## over wave numbers ##k##. We do it at ##t=0## hence ##\psi = \psi_0(k) e^{ikx}## \psi = \int\limits_{-\infty}^{+\infty} \psi_0\!(k) \cdot...
  4. N

    A question about Heizenberg uncertainty.

    In some QFT books they say:If we consider momentum p of particle being very great,then the physics is at short scale.Then how can we apply Heizenberg uncertainty principle when the momentum p of particle having a certain value?What do they imply when they say that?
  5. Q

    Heisenberg's uncertainty principle invalidated?

    Heisenberg's uncertainty principle asserts a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously. The more you know about one, the less you know about the other. Why does the following...
  6. K

    Uncertainty on best fit gradient

    Hi everyone, I have a plot of some data points that have error bars on the y axis. A bit of software I am using gives me the best fit gradient and a "Standard Error", but it doesn't take the size of error bars into consideration. I'm assuming that it just looks at how well the gradient...
  7. H

    Pre Lab, how to find uncertainty

    Hello, I have been stuck on this prelab all day.I have finished all the questions except for the last one, where it asks you to find the uncertainty (or standard deviation) of Fave. I have tried every resource and nothing has helped so far. Any help would be great! Thanks
  8. Q

    What is the concept behind the Uncertainty Principle?

    I'm trying to understand the uncertainty principle. ΔxΔp >= h/4∏ from my understanding of the concept, its not possible to know the value of the position and the momentum simultaneously. yet the problems that i see floating around on the internet seem to just plug in values for mass and...
  9. S

    Photons violate Uncertainty Principle?

    A photon is considered as a quantum particle, right? However since we know the speed of a photon(speed of light) and hence can predict its position, isn't it violating the Heisenberg Uncertainty Principle? Where am I going wrong? Is it false to believe that a photon is a quantum particle?
  10. P

    Quantum entanglement and the uncertainty principle

    This question may have been posted before, but I didn't have much luck finding it. We can't know the momentum and position of a particle at the same time, but if one were to entangle two particles (I.e. photons), wouldn't it be possible to measure one quality on each and thus deduce both the...
  11. P

    Implications of Heisenberg uncertainty principle

    Hi does anyone know how bogulobov transformations are related to the Heisenberg uncertainty principle?
  12. T

    Sensitivity and Uncertainty in measurements

    Greetings fellow members, I have some queries on a laughably rudimental topic regarding measurements. Say you have a metre rule with sensitivity of 0.1cm, and you are measuring a wire which stretches from the 0.0cm starting point to the middle point between 7.3 cm and 7.4cm. My...
  13. A

    R through a wire: What's the max error in diameter if your R has 1% uncertainty?

    Homework Statement I have a wire of some resistance, resistivity, and length. What is the maximum error in measuring the diameter that you can have if the resistance is to have 1% uncertainty? Homework Equations R = \frac{ρ*l}{\pi*r^{2}} for which I substituted the area as \pi(.5...
  14. liometopum

    Does GR produce the Planck relation and uncertainty principles?

    Can the Planck relation, and the Heisenberg and the time-energy uncertainty principles be derived, or produced, from the equations of General Relativity?
  15. vanhees71

    Heisenberg-Robertson uncertainty relation vs. noise-disturbance measures

    Finally I found the time to write my account on the interpretation of the Heisenberg uncertainty principle vs. the question whether it can be interpreted as Heisenberg did in his very first paper on the subject. Although it is well known that this interpretation is not compatible with quantum...
  16. M

    Uncertainty with regards to a science career

    For two years now, I have been on PF. I spent many of those months checking PF - largely the academic and career guidance forums - just about every other day, and I learned a great deal about academia, and careers in science and engineering. A few months ago, when I posted in the Mathwonk's...
  17. ShayanJ

    Uncertainty principle,examining the «principle» part

    In some experiments like Heisenberg's microscope and Davisson–Germer experiment,we see that by using light to understand the actual path of electrons,the electrons are disturbed and so the result is changed(in the second case,the interference pattern is replaced by the distribution of classical...
  18. M

    Has the Uncertainty Principle been defeated?

    According to this article, scientists were able to bypass the Heisenberg Uncertainty Principle, creating relative certainty in measurement of both position and momentum. Any thoughts, objections, comments?
  19. F

    Uncertainty, Symmetry, and Commutators

    It seems the uncertainty principle, the commutator between operators, and the symmetry of the action integral are all related. And I wonder how universal this is. For example, the action integral is invariant with respect to time, and this leads to conserved quantity of energy. This means...
  20. trollcast

    Uncertainty of measurements

    Homework Statement The experiment set up is a steel ball bearing is held from an electromagnet and above a switch at the bottom. When the electromagnet is switched off a timer starts and stops when it hits the switch. The height from the bearings initial position to the switch is measured...
  21. A

    How Should Uncertainty Be Reported for the Square Root of a Measurement?

    Homework Statement Book: Introduction to error analysis, Taylor In page 66, quick check 3.8 If you measure x = 100\pm 6, what should you report for \sqrt{x}with its uncertainty. Homework Equations Rule for uncertainty as power: \frac{∂q}{|q|} = |n|\frac{∂x}{|x|}where q = x^{n} 3...
  22. S

    Heisenberg's Uncertainty vs Virtual Particle Fluctuations

    I notice that many physicists say that virtual particle fluctuations occur in space "because Heisenberg's Uncertainty Principle allows them" Is this really the best form of reasoning? Isn't it actually the other way around - that because virtual particle fluctuations happen, then there is a...
  23. snoopies622

    The uncertainty principle and electric field strength

    As my knowledge of an electric field strength becomes more precise, what physical quantity becomes correspondingly less precisely known?
  24. ShayanJ

    A peculiarity in uncertainty principle

    Consider two hermitian operators A and B. Imagine a system is in state |\psi\rangle ,then we have: \langle \psi|[A,B]|\psi\rangle=\langle \psi|AB-BA|\psi\rangle=B^{\dagger}A^{\dagger}|\psi\rangle-BA|\psi\rangle=BA|\psi\rangle-BA|\psi\rangle=0 This just seems a little strange,for example...
  25. C

    Uncertainty in some observable A

    Why do we define the uncertainty in some physical quantity ##A## as: $$\delta A = < \sqrt{<A^2> - <A>^2} > .$$ I know that it can be derived by computing the variance of ##A##, but what is the physical meaning? Thanks!
  26. B

    Particle in a box and Heisenberg Uncertainty principle paradox?

    Say you have a particle in a one-dimensional box of length L. The particle can only have momentum values of the form p_{n} = \frac{nh}{2L} according to the De Broglie standing wave condition. Now say I don't measure the position of the particle, but I know for certain that it is in the box...
  27. A

    Uncertainty of distance measurements for regions between 50-250 pc away

    Hi, I am in the middle of a project dealing with the mass loss rate of protostars and hence I am working with the distance that these sources are away from us. I need to find the error in these distance measurements, however I cannot. In any paper (I find) that cites distances it just gives...
  28. H

    Energy-Time Uncertainty Relation

    I was trying to Go from the uncertainty principle to its energy-time counter part. i know the maths is a bit off,but the idea is correct? dx=position p=momentum e=energy \upsilon=frequency \lambda=wavelength c=velocity of electromagnetic radiations dt=time now , \lambda=h/p....(i)...
  29. D

    Energy-time Uncertainty principle

    hi pf, i am so confused with this energy time uncertainty principle. Somewhere i find that this means law of conservation of energy can be violated for a while and somewhere i find this still being a mystery? please help me out.
  30. E

    Energy uncertainty of an atom in an excited state

    Homework Statement A Na atom is in an excited state for a mean time of 1.6 \times 10^{-8}s. Then it jumps to the ground state emitting a photon with 2.105 eV of energy. Find the energy uncertainty of that excited state. Homework Equations The Attempt at a Solution I don't even...
  31. B

    Energy time uncertainty principle

    Hi, Consider a laser source of frequency f. This source is projected to a target at a distance D, so that the light needs time T = D/C to reach the target. I will consider the particle behavior of light in this situation. I will study the motion of one of the photons. At the exact time T/2...
  32. C

    Doubts about heisenbergs uncertainty principle.

    Doubts about wave particle duality I know that a wave packet is formed by superposition of several individual waves having different wavelength.And the resultant wave has varying amplitudes.And from these amplitudes we can find the likeliness of the object to be in that position. My doubt is...
  33. B

    Statistical uncertainty of weighted mean

    Hello! I am using physical data to do an analysis (~30k measurements). These measurements include energies, momenta, angles... of particles. I am calculating a value (call it v) at the end after a lengthy process, and if I introduce all the data into my program I did, the result is v±σ...
  34. I

    Uncertainty equal to zero

    could we able to measure the velocity for a free particle with uncertainty equal to zero, could we able to have a certain values for its velocity, and let the uncertainty of the position to be infinity is there any theoretical restrictions on having a certain value for the velocity? is there...
  35. T

    Minimum Uncertainty in Electron Position: Rectangular Wave in k-space

    Homework Statement In the case of an electron wave packet, the function A(k) has a rectangular shape, i.e. it is equal to A0 if k0-a<k<k0+a, and zero everywhere else. (a) Find the minimal uncertainty of electron position. (b) Find the electron wavefunction. Homework Equations ΔxΔp=h/4pi...
  36. A

    Heisenberg uncertainty principle

    Hello! I have a doubt about Heisenberg uncertainty principle. Suppose that a particle moves along x-axis with a given uncertainty in velocity. Can I say something about its motion along y-axis? Thanks
  37. ElijahRockers

    Basic Energy and Time Uncertainty Problem

    Homework Statement A pi zero meson is an unstable particle produced in high energy particle collisions. It has a mass-energy equivalent of about 135MeV, and it exists for an average life-time of only 8.7x10^-17 seconds before decaying into two gamma rays. Using the uncertainty principle...
  38. S

    Understanding Heisenberg's Uncertainty Principle

    Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. Homework Equations Δx = λ/sinθ Δp_x = 2h/λ sinθ The Attempt at a Solution In the equation given in the problem (Δx = λ/sinθ), why is the uncertainty of the ELECTRON written as a function of the...
  39. N

    Does anyone know how to calculate absolute uncertainty?

    Does anyone know how to calculate absolute uncertainty?? A student repeatedly measures the time taken by an object to cover a certain distance and obtains the following data: t1 = 2.432 s, t2 = 2.393 s, t3 = 2.402 s, t4 = 2.412 s, t5 = 2.424 s The instrument uncertainty is 0.001 s What...
  40. T

    Propagation of Uncertainty with Angles

    Homework Statement I conducted an experiment which involves measuring two distances (Y and L) and have used tan to determine the angle, then finally calculated the sine of the angles for use in my analysis. I have uncertainties in both length measurements and am unsure how to propagate the...
  41. Z

    Formula relating to Uncertainty Principle

    Homework Statement I was looking at a solution inmy notes which begins: ΔE = hc/λ -1st eqn ΔEΔt ~ (h-bar)/E -2nd eqn Δt ~ (h-bar)/ (hc/λ) Δt ~ λ/2∏c (where 'c' is the speed of light) What formula has been used to go from: Δt ~ (h-bar)/ (hc/λ) to Δt ~ λ/2∏c...
  42. P

    Could uncertainty be that big?

    Another question I have concerns a table's surface area. If L=122.14±0.14[cm] and W=24.30±0.57[cm], I got that S=2968.00±69.70[〖cm〗^2], using ∆S=√((∂S/∂L)^2 〖∆L〗^2+(∂S/∂W)^2 〖∆W〗^2 ). Would you kindly confirm this result? Is it plausible that ∆S would be nearly 70 cm^2??
  43. Z

    What is Heisenberg Uncertainty Formula?

    What is the Heisenberg Uncertainty Principle Formula? Here: http://www.people.vcu.edu/~rgowdy/mod/122/xmp4.htm It is quoted as Δx(Δmv) ~ h/2∏ which is ΔxΔp ~ (h-bar) Here: https://en.wikipedia.org/wiki/Uncertainty_principle It is quoted as ΔxΔp ~ (h-bar)/2
  44. I

    Question about the uncertainty principle and unit cell in phase space

    In statistical mechanics, nearly all the textbooks say that the volume of the smallest cell in the phase space of a N-particle system is h^{rN} where h is the Planck Constant, r is the degree of freedom. Also these books say that this comes from the uncertainty principle. However, the...
  45. L

    Uncertainty for least squares fit

    I am fitting data to a parabolic equation using the least squares fit method. Each data point that goes into the fit is the average of 5 data points at that x value, so that each point has error bars that come from the standard deviation of those 5 y values. I have a fitted equation, and I...
  46. A

    Using uncertainty principle to find minimum Kinetic Energy expectation value

    Homework Statement Assume that a particle travels with a certain known (average) velocity ##v = \left\langle\hat{p}/m\right\rangle##. You know it's position with an uncertainty ##Δx##. Use the uncertainty principle to determine the least possible value for the article's kinetic energy...
  47. W

    Uncertainty in position for eigenstates (Liboff 3.10)

    Homework Statement From Liboff edition 4: For the state ψ(x,t)=A exp(x-x0)2 / {4a2} * exp(ip0x)/hbar * exp (-iω0t) show that (Δx)2 = a2 then argue the consistency of this conclusion with the change in shape that |ψ2| suffers with a change in the parameter a Homework...
  48. E

    Lagrangian visualisation and Uncertainty Principle

    Probably, the essence of quantum theory (QT) is principle of uncertainty (HUP). The essence of QT is also the fact that Fourier transformation of wave function in phase(?) space gives wave function in momentum space. If one wave function is Gaussian (and so both ones) this gives HUP. Very...
  49. S

    Prove Heisenberg Uncertainty Principle for Ground State Harmonic Oscillator

    Ground State Wave Equation: ψ0=(a/∏)(1/4)e(-ax2/2) Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values. First I found <x>=0 because it was an odd function then I found <Px>=0 because it was an odd function Then <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of...
  50. S

    Rejecting the Semiclassical Bohr Model: Examining the Uncertainty Relation

    "Show that the uncertainty relation forces us to reject the semiclassical Bohr [...]" Homework Statement The problem along with the solution is attached as TheProblemAndSolution.jpg. Homework Equations Uncertainty principle/relation. The Attempt at a Solution Why is it the consideration of...
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