# 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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18. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### How is the uncertainty relation preserved in this experiment

For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...
27. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### Heisenberg s uncertainity principle

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