What is Uncertainity principle: Definition and 50 Discussions

In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions.
Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified.
Introduced first in 1927 by the German physicist Werner Heisenberg, the uncertainty principle states that the more precisely the position of some particle is determined, the less precisely its momentum can be predicted from initial conditions, and vice versa. The formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:

where ħ is the reduced Planck constant, h/(2π).
Historically, the uncertainty principle has been confused with a related effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the system, that is, without changing something in a system. Heisenberg utilized such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty. It has since become clearer, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer. Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number–phase uncertainty relations in superconducting or quantum optics systems. Applications dependent on the uncertainty principle for their operation include extremely low-noise technology such as that required in gravitational wave interferometers.

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  1. physical_chemist

    A Angular momentum uncertainty principle and the particle on a ring

    By considering a particle on a ring, the eigenfunctions of ##H## are also eigenfunctions of ##L_\text{z}##: $$\psi(\phi) = \frac{1}{\sqrt{2\pi}}e^{im\phi}$$ with ##m = 0,\pm 1,\pm 2,\cdots##. In polar coordinates, the corresponding operators are $$H =...
  2. J

    B Relationship between a material wave and the uncertainty of position and momentum

    I'm just an ordinary person who's very interested in physics. I'm posting a question because I'm curious about quantum mechanics. The wavelength of the material wave that can be obtained when a baseball with a mass of 150 g is thrown at 40 m/s is 1.1×10^-34m by the h/mv formula. As you can see...
  3. V

    I Uncertainty Principle in QFT & Early Universe Conditions

    I have a question related to the uncertainty principle in QFT and if it is related to the early universe conditions. Do we still have four-vector momentum and position uncertainty relation in relativistic quantum theory? I have been following the argument related to the early universe and the...
  4. R

    B Why exactly do Virtual Particles not violate Conservation of energy?

    Recently I've read more about virtual particles and at first I tought that there were only doubts that virtual particles are not interpretable with the help of uncertainty principle. Furthermore it can't be used an an "excuse" for the temporary violation of the conservation of energy. Can...
  5. patric44

    Proof of the generalized Uncertainty Principle?

    hi guys i am trying to follow a proof of the generalized uncertainty principle and i am stuck at the last step : i am not sure why he put these relations in (4.20) : $$(\Delta\;C)^{2} = \bra{\psi}A^{2}\ket{\psi}$$ $$(\Delta\;D)^{2} = \bra{\psi}B^{2}\ket{\psi}$$ i tried to prove these using the...
  6. patric44

    Is this a valid derivation of the Uncertainty Principle?

    Homework Statement:: i saw this simple derivation of the uncertainty principle in my college introductory quantum book Relevant Equations:: Δp.Δx = h hi guys i saw this derivation of the uncertainty principle in my college quantum book , but the derivation seems very simple and sloppy , i...
  7. N

    I Is it possible to explain Quantum tunneling with the HUP?

    I'm a student in South Korea(It is my first English question ever). I found descriptions of quantum tunneling explained by the uncertainty principle in Korea. There are two kinds of descriptions to explain quantum tunneling; position-momentum and time-energy uncertainty principle. First...
  8. SEYED2001

    B Can we measure any two of the energy, momentum or mass simultaneously?

    I want to know between which two quantities of energy, momentum, and mass there is an uncertainty principle going on. Can I measure any two of those at the same time? If yes, which ones? Thank you in advance
  9. R

    A question related to de Broglie wavelength and the Uncertainty Principle

    "Now, if an electron has a definite momentum p, (i.e.del p = 0), by the de Broglie relation, it has a definite wavelength.A wave of definite (single) wavelength extends all over space. By Born’s probability interpretation this means that the electron is not localised in any finite region of...
  10. NoctusPartem

    How can I calculate the smallest speed of a proton in a nucleus?

    My approach: Assuming non-relativistic velocity: $$p = mv$$ $$mvL = \frac{\bar{h}}{2}$$ $$v = \frac{\bar{h}}{2mL} = \frac{h}{4\pi mL}$$ $$v = (6.626*10^-34) / (4pi * 1.67*10^-27 * 4.3*10^-15)$$ $$v = 7.34*10^6 = .0245c$$ This answer is incorrect. What have I done wrong? --- Edit: My...
  11. usehn

    How to get the Uncertainty of a percentage change

    I have a measurement with uncertainties for two years. Say Year 1 Rain : 100mm(80-120mm) Year 2 Rain : 120mm(103-131mm). Now I get the percentage change in rain in Year 2 w.r.t Year 1 as 20%. Is there a way to get the uncertainty associated with this percentage change?
  12. Michael Price

    A Resolving power of a radio telescope array: Quantum or classical?

    My question is: is the resolving power of an array of radio telescopes a quantum or a classical effect? The increase in resolving power of a single telescope, as aperture size increases, is easy to explain in terms of Heisenberg's uncertainty principle. But when we go an array of telescopes are...
  13. Sushmita

    "Uncertainity Product for Particle in 1-D Box

    Homework Statement For the ground state of a particle moving freely in a one-dimensional box 0≤x≤L with rigid reflecting end points, the uncertainity product (Δx)(Δp) is (A) h/2 (B) h√2 (C) >h/2 (D) h/√3Homework Equations The uncertainity principle says that - (Δx)(Δp) ≥ ħ/2 Ground state energy...
  14. F

    I Heisenberg - Uncertainty principle - lifetime of a particle

    I have seen that the more a particle has a high energy, i.e ##E##, the more its lifetime is short, respecting so the uncertainty principle. But by the definition of this uncertainty principle : ##E\,\Delta t \geq \dfrac{\hbar}{2}##, I can write : ##\Delta t \geq \dfrac{\hbar}{2E}##, then...
  15. P

    I What's the significance of HUP if Ψ collapses?

    If I understand it correctly, a particle doesn't have a definite momentum and a definite position, but is in a superposition of multiple positions and momenta. And when we measure either of the two quantities, say, position, the wavefunction collapses to tell us where the particle is. Now when...
  16. P

    I Why is the Uncertainty principle inherent to particles?

    If we have a particle, say, an electron and we shoot it straight through an empty box. This box is surrounded by light sources on its two sides: So, if you consider the above cube, if we shoot a particle in a straight line such that it crosses the face ABEF and it crosses the face HGDC through...
  17. J

    I Are the energy fluctuations in space real or virtual?

    Heisenberg's uncertainty relation says: $$\Delta x \Delta p \ge \hbar$$ If we assume a massless quantum object then we have the relationship ##\Delta E = c\Delta p## so that the above uncertainty relationship becomes $$\Delta E \ge \frac{\hbar c}{\Delta x}.\tag{1}$$ I understand that if we have...
  18. A

    I Finite universe, quantized linear momentum, and the HUP....

    Hi all, Yet another question: if the universe is finite, then linear momentum should be quantized (I assume in a similar manner to an infinite potential well since there are boundary conditions). My question is, then, if one computes a value for ##\Delta p## (momentum variance), is the variance...
  19. G

    I What is the origin of Van der Waals force?

    Hello. What I know about the Van der Waals force is that it comes from an instantaneous electronic cloud flucutation of the netural atom. This instantaneous electric dipole of the atom attracts electrons in nearby neutral atoms so other electric dipoles are induced on those atoms. As a result...
  20. M

    A Can a Point-Like Particle Defy the Uncertainty Principle?

    Imagine a spatial frame of reference attached to a point-like particle. It has x=0 since it is at the origin and p=0 since it is at rest. Having definite position and momentum is normally considered a violation of the uncertainty principle. How would you resolve this paradox? 1. Position frames...
  21. W

    B Are vertical lines from squinting a Quantum phenomenon?

    When looking at a night light with almost closed eyes, I notice that the light becomes a vertical line. When tilting my head 90 degrees, the line becomes horizontal. Can this be explained by Heisenberg's Uncertainty principle? This question has been asked in another thread : "Squinting at...
  22. H

    Single slit with minimum uncertainty

    Homework Statement A horizontal beam of laser light of wavelength 474 nm passes through a narrow slit that has width 5.80×10−2 mm . The intensity of the light is measured on a vertical screen that is 2.40 m from the slit. Use the result of part A to estimate the width of the central diffraction...
  23. M

    Why Does the J/psi Meson Detection Show Large Standard Deviation in CMS Graphs?

    Homework Statement See Image The bit about Spectral lines, I couldn't explain why[/B] Homework Equations ΔEΔt≈h The Attempt at a Solution I expected the histogram to peak at the given mass in question and to have a width of about 0.08 MeV calculated as ΔE from the Energy-time uncertainty...
  24. 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.
  25. Stephanus

    Determinism and Uncertainity Principle

    Dear PF Forum, Determinism. 1. Is there determinism? 2. Because we can't measure the electron position, it doesn't mean there's no determinism? Heisenberg uncertainity principle states, per wiki: But because we can't measure it, it doesn't mean that the universe itself is indeterministic...
  26. weezy

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  27. 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...
  28. Praveen Vijayan

    Uncertainity Principle: possible to know the momentum and position?

    The principle states it is impossible to 'simultaneously' know the position and momentum(velocity)of an object. Position is something that can be noted at a particular instant, as from a photograph whereas velocity is something that can only be measured over a period of time,as from a movie. The...
  29. P

    That Heisenberg Uncertainity Principle

    Does the Heisenberg Uncertainity Principle mean: 1) If a particle is confined within a length x then it must jiggle around with a momentum given by p ~ h/2x PI OR 2) If we measure the position of a particle to an accuracy of x then its momentum will be uncertain by ~ h/2x PI
  30. B

    When does ΔxΔp equal h/4pi in the uncertainty principle?

    When it actually 'equal to' in uncertainty principle? For example under what conditions: ΔxΔt = h/4pi
  31. Y

    Virtual particles and the Uncertainity Principle

    Recently, I was reading about Hawking Radiation in A Brief History of Time. It says that at no point can all the fields be zero and so there's nothing like empty space(quantum fluctuation etc.). Now, the reason mentioned was that virtual(force-carrier) particles cannot have both a precise rate...
  32. T

    Helicity and the Uncertainity Principle

    Hi all! So rumor has it, that the spin of a particle is preferably aligned opposite to the direction of the particle's momentum, whereas an antiparticle spins along the direction of motion. For the sake of simplicity let us assume that the (anti-)particle is massless and hence it is an...
  33. S

    Can uncertainity principle be tweaked

    I am new to quantum mechanics. By hitting a particle with photon in vacuum we find its momentum and then again hit it with another photon to find its position . can we calculate backwards using conservation of momentum the position an momentum of that particle in both two states ( since we know...
  34. I

    The uncertainity principle, a new take?

    http://www.livescience.com/18567-wac...principle.html are these once again bold claims? they are saying the uncertainty principle isn't just in measurement but in the very nature of the quantum. It seems to be bold claims and not reperated anywhere on any other sites and certainly doesn't...
  35. B

    Heisenberg s uncertainity principle

    existence of protons, neutrons nd alpha particles in the nucleus.
  36. 1

    Heisenberg's Uncertainty Principle: Philosophical Implications

    I've been reading extensively around the internet and haven't been able to find a website which describes the philosophical implications of Heisenberg's uncertainty principle. Would appreciate if someone would explain these implications or provide a link in which describes them. thx
  37. 1

    Heisenberg's uncertainity principle

    Can someone please explain the history of Heisenberg discovered his uncertainty principle? Was he trying to physically measure the position and momentum of an electron to disprove the old atom model or did he just do it hypothetically?
  38. D

    Heisenbergs uncertainity principle for an electron

    Homework Statement The speed of an electron is measured to within an uncertainty of 2e4 m/s. What is the size of the smallest region of space in which the electron can be confined? Homework Equations Diracs Constant=ΔxΔp p=mv The Attempt at a Solution what I did was (Diracs...
  39. A

    How would this universe be if there's NO UNCERTAINITY PRINCIPLE

    how would this world appear like if energy,time &&& momentum,distance can commuate...and anyone please describe relation between energy and time
  40. N

    Heisenberg uncertainity principle

    i am not getting the interconnection between probability wave function of particle with particle's momentum,can anyone help? i don't want any mathematical equations,any theoretical explanation would suffice
  41. D

    Understanding the Uncertainty Principle and Its Effects on Atomic Particles

    According to uncertainty principle, it's not possible to measure the position and momentum of an atomic particle ( say electron) simultaneously. Now, suppose a scientist grows so small in size that an electron is the size of a big ball (or planet) for him. Is uncertainity principle...
  42. V

    Understanding the Uncertainty Principle in Quantum Physics: A Beginner's Guide

    I am a beginner to the part of quantum physics and I am not getting the ideas well enough.I am reading it on the Feynman Lectures. But the uncertainity principle does not give any hint and it does not reveal itself at all in our day to day lives. Suppose a man starts to run at uniform...
  43. B

    Uncertainity Principle , particles and antiparticles

    Is Uncertainity Principle is applied during particle antiparticle generation and is it a deterministic principle related to their positions and momentum in space ?
  44. C

    Violating uncertainity principle

    Suppose in a double slit experiment, we place a machine that traps the gravitons emitted by the electrons and hence gives us the exact trajectory of the electrons(this would have no effect on the experiment as gravitons are liberated in any double slit experiment, just that we are able to...
  45. M

    The Uncertainity Principle

    1)Consider a beam of electrons in a CRO striking the phosphor screen.How does the uncertainity principle pan out here? Technically, we are getting the exact position of the electron due to the point made on the screen.And, we can most certainly calculate the velocity by estimating the time in...
  46. M

    IS THIS the Heisenberg uncertainity principle?

    I read that the Heisenberg uncertainty principle arises for stuff like electrons simply because the observer affects the observed . That is,because photons (or what ever the observer uses to detect the position) will affect the trajectory of the particle... That doesn't make much sense to...
  47. S

    Did photon obey Uncertainity Principle?

    Photon has no mass.So when we apply Uncertainity principle to photon position*velocity*mass=greater than Plancks constant So when we use mass as null,the equation implies that 0<h. That is h is negative.But h is positive. Please explain me this.
  48. L

    Fourier transform and uncertainity principle

    To find the frequency, Why do you need to consider the signal over long period of time? For example - if you look at a sine wave from 0-360 with two cycles, isn't it enough to get the frequency? I get the second part - you need a short time window to see sudden changes in frequency.
  49. G

    Uncertainty Principle: Position Uncertainty of Electrons

    In application of uncertainity principle i read,if we suppose electron in a sphere of radius r then we assume unertainity of position as delta 'r',instead of taking diameter as uncertainity.Though it will not effect the calculations at all,but conceptually and physically what could be the reason...
  50. I

    Help Uncertainity principle problem

    in my problem i am told that the x-component of the velocity of a 2x10^-4 kg mass is measured to an accuracy of +_ 10^-6 m/s. i need to find the limit of the accuracy with which the particle can be located along the x-axis. the uncertainity principle delta(x) * delta(Px)>= h/4pi i have...