What is Fluctuation: Definition and 57 Discussions

In quantum physics, a quantum fluctuation (or vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. They are tiny random fluctuations in the values of the fields which represent elementary particles, such as electric and magnetic fields which represent the electromagnetic force carried by photons, W and Z fields which carry the weak force, and gluon fields which carry the strong force. Vacuum fluctuations appear as virtual particles, which are always created in particle-antiparticle pairs. Since they are created spontaneously without a source of energy, vacuum fluctuations and virtual particles are said to violate the conservation of energy. This is theoretically allowable because the particles annihilate each other within a time limit determined by the uncertainty principle so they are not directly observable. The uncertainty principle states the uncertainty in energy and time can be related by




{\displaystyle \Delta E\,\Delta t\geq {\tfrac {1}{2}}\hbar ~}
, where 1/2ħ ≈ 5,27286×10−35 Js. This means that pairs of virtual particles with energy


{\displaystyle \Delta E}
and lifetime shorter than


{\displaystyle \Delta t}
are continually created and annihilated in empty space. Although the particles are not directly detectable, the cumulative effects of these particles are measurable. For example, without quantum fluctuations the "bare" mass and charge of elementary particles would be infinite; from renormalization theory the shielding effect of the cloud of virtual particles is responsible for the finite mass and charge of elementary particles. Another consequence is the Casimir effect. One of the first observations which was evidence for vacuum fluctuations was the Lamb shift in hydrogen. In July 2020 scientists report that they, for the first time, measured that quantum vacuum fluctuations can influence the motion of macroscopic, human-scale objects by measuring correlations below the standard quantum limit between the position/momentum uncertainty of the mirrors of LIGO and the photon number/phase uncertainty of light that they reflect.

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  1. Leandro Bolonini

    I How do quantum fluctuations affect the formation and evolution of structures in the Universe?

    How do quantum fluctuations affect the formation and evolution of structures in the universe on large scales?
  2. ergospherical

    I The Good Guy Fluctuation: Is Sheldon's Second Line Making Sense?

    Can anybody comment on whether the second line of Sheldon's work makes sense...? I don't see it. :oldeyes:
  3. piyushverma

    Ansys Maxwell: Transient generator simulation torque fluctuation

    I am working on an axial flux generator design, I consisits of 2 rotors and one stator, there are 6 pole pairs and 9 coils. Here is my simulation setup The three phase windings are connected in star configuration through Maxwell circuit. I created two bands enclosing each rotor and then united...
  4. Y

    A Contribution of vacuum fluctuation to the self-energy of the electron

    In the book" The Quantum Theory of Radiation", Heitler derived the transverse self-energy of the electron(Chapter III, Section18, Eq.(23)) $$\frac{{{e^2}}}{{\pi m}}\int_{\text{0}}^\infty {kdk} $$ which is the energy of the electron under the action of the vacuum fluctuation of the radiation...
  5. phun_physics

    I Derivation of Average Square Energy Fluctuation in a Canonical System

    The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...
  6. A

    A Quantum vacuum fluctuation in BEC

    Hi, I have some problems with visualization (I'm trying to understand Jeff Steinhauer's experiment, but my questions are general). Why the quantum vacuum fluctuations are guaranteed by the underlying pointlike atoms composing a BEC? And if vacuum fluctuations generate excitations (i.e...
  7. K

    I Quantum fluctuation and classical physics

    Hi, Can we derive an equivalent concept of quantum fluctuation in classical physics using correspondence principle? Also, how can we account for transfer of energy back and forth at the quantum and classical border? Thanks
  8. TeethWhitener

    I Derivation of Crooks's Fluctuation Theorem

    I'm reading through Crooks's paper: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.60.2721 as well as a review paper by Mansour et al.: https://aip.scitation.org/doi/10.1063/1.4986600 trying to figure out their derivation of the fluctuation theorem (section II of both papers). I had a...
  9. mark!

    B Was the Big Bang a quantum mechanical vacuum fluctuation?

    It has been proposed by Edward P. Tryon that the Universe may be a large scale quantum mechanical vacuum fluctuation where positive mass-energy is balanced by negative gravitational potential energy, as a consequence of the early inflationary launch of the expansion of the Universe, in which...
  10. N

    Mean Square Fluctuation (Q.M.)

    Homework Statement A state of a particle in the potential box of width a with infinitely high walls is described by the wave function: Ψ(x)=Ax(x-a) Find the probability distribution of various value of particle energy, mean value and mean square fluctuation of energy. Homework Equations...
  11. R

    I Is nuclear fission a quantum fluctuation

    Nuclei of unstable isotopes spontaneously fission in a way that is measured in half-life. So for a particular nucleus at a given time, it is a probability of some amount, thus is a QM fluctuation? Then what is going on in reactors which in effect modify the nucleus half life by introducing extra...
  12. A. Neumaier

    Insights The Vacuum Fluctuation Myth - Comments

    A. Neumaier submitted a new PF Insights post The Vacuum Fluctuation Myth Continue reading the Original PF Insights Post.
  13. wolram

    B What is a quantum fluctuation....

    One reads a lot about quantum fluctuations but what exactly are they and how do they make a seed for galaxy formations ?
  14. I

    Destructive Interference in Water but not Air

    Homework Statement Consider a given monochromatic component of sunlight. The electric field drives a given air molecule. Each oscillating charge of the air molecule radiates waves in all directions, some of which travel to the eye of a given observer. But, for a given molecule (call it No.1)...
  15. w0_0dy

    The big bang was a fluctuation of what?

    I have read that the total energy of the universe is zero and that the big bang might have emerged from a quantum fluctuation. Also that there is a chance (extremely low) of another big bang occurring in the quantum vacuum energy fluctuations. As far as I understand the vacuum energy / dark...
  16. D

    Quantum fluctuation and quantum mysticism

    Hello, searching for information about debunking quantum mysticism I stumbled upon this article: http://www.csicop.org/si/show/quantum_quackery/ , where one of the main arguments seems to be based on quantum fluctuation to explain Einstein´s famous "spooky effect on a distance". You can check...
  17. F

    Fluctuation Dissipation Theorem

    Homework Statement We have a system of two coupled Langevin equations dr/dt=kr-yrr+nr(t) dp/dt=kpr-ypp+np(t) where the ki,yi are constants and ni(t) are noise terms satisfying <ni(t)>=0 and <ni(t')ni(t'')>=qiδ(t'-t'') (this is zero if the two indices differ). The physical background of these...
  18. S

    Number density: Initial fluctuation strength and more....

    Dear all, I am trying to understand the physics behind the "number density" formula given by Weinberg. Is there anyone who can explain these parameters to me: 1- "Initial fluctuation strength": \begin{equation} \rho_1= \lim_{t \to 0}\frac{\Delta \rho_M^3}{\bar{\rho}^2_M}\end{equation} However...
  19. wolram

    What is the Role of Quantum Fluctuations in the Formation of Black Holes?

    What is a quantum fluctuation and how do they form a seed for black holes?:
  20. onkel_tuca

    Discretizing a Fluctuation Dissipation Theorem

    Hey! I want to discretize a fluctuation dissipation theorem for the white noise ζ of a stochastic differential equation on a 2D domain (sphere). For that I integrate over "Finite Volume" elements with area A and A' (see below). \begin{eqnarray*} \int_{A} d A \int_{A'} d A'...
  21. D

    How to design discrete circuits for transistor beta changes?

    In my circuits/active devices course we had to make amplifier designs with various type of transistors (BJT, JFET, MOSFET). In each design the transistor beta parameter played an important role in deciding which resistors to use in the final amplifier circuit. This beta parameter changes widely...
  22. Jimster41

    QM and Crook's Fluctuation Theorem

    Is there a bridge from QM to Crook's Fluctuation Theorem and/or the Jarzynski Equality? More ambiguously, but maybe more directly, Is there thought to be a relationship between the QM-entanglement/decoherence/interference, and the SLOT? I am worried I may be missing a discussion of this, due...
  23. Jimster41

    AdS/CFT w/out Holography and SLOT - Fluctuation Work Theorem

    http://arxiv.org/abs/1507.00591 AdS/CFT without holography: A hidden dimension on the CFT side and implications for black-hole entropy H. Nikolic (Submitted on 2 Jul 2015) We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its...
  24. C

    Automotive How to calculate 1.5 order wheel torque fluctuation (3 Cylin

    Hi all, I have the raw data in .csv file which has Engine speed, wheel torque value and main shaft speed (Please refer to below image - raw data_screen shot) I have to find the logic for the above raw data, to get 1.5 order wheel torque value, which is close to resulted value as attached...
  25. S

    Fluctuation operator and partial wave

    Can someone please explain to me why the expression ##[-\Box + U''(\Phi(r))]## is called the fluctuation operator? I was also wondering how to derive the following for the ##l^{th}## partial wave of the above operator: ##-\frac{d^2}{dr^2}-\frac{3}{r}\frac{d}{dr} + \frac{l(l+2)}{r}+...
  26. Jimster41

    Confusion: Fluctuation Theorem, Poincare Recurrence Theorem

    Is Poincare' Recurrence Theorem (PCRT) considered a possible explanation for the "low entropy" initial conditions of the universe? Is the following a roughly correct paraphrasing of it? For a phase space obeying Liouville's theorem (closed, non-compress-able, non-decompress-able), the...
  27. J

    Term to express a range of fluctuation

    I am trying to make a term for a function equipped on an image sensor. The term is to express "the upper limit of fluctuation allowance in image size which is specified in %" The value of percentage does not express the ratio of the enlarged image size compared to the original image size, so...
  28. J

    Dissipation function in fluctuation dissipation theory

    Hello every: Actually, there are 2 questions. The first one is how to understand the dissipation function used in the fluctuation dissipation theory. I notice that for a dielectric material with a complex dielectric function, this dissipation function will be the imaginary part of the...
  29. B

    Do quantum fluctuation particles create gravitational effect?

    Do particles popping in and out of existence due to quantum vacuum fluctuations create a gravitational effect? My thought is yes If so, considering all the quantum particles in existence at one time at a given moment in the universe, added to the mass of the universe as well as the mass of...
  30. U

    Can BLDC Technology Solve Voltage Fluctuation Issues for Domestic Water Pumps?

    Hi there, I have spent quite some time on PF as an unregistered user reading through various stuff and have learned a lot. Just registered now to seek help on something that's been bothering me a lot and to which I haven't managed to find a solution yet. Please let me know if this is not the...
  31. N

    Why Do Voltage Fluctuations Occur in Renewable Energy Systems?

    why voltage fluctuation is there? since all the houses are in parallel,so all of them receive same voltage..then why voltage fluctuation is there? and why not current fluctuation? why voltage stabilizers are used ?
  32. J

    Understanding Entropy and Fluctuation: The 2nd Law of Thermodynamics Explained

    The 2nd law of thermodynamics state that entropy increases with time and entropy is just a measure of how hard it is to distinguish a state from another state (information theoretical view) or how hard it is to find order within a system (thermodynamic view). There are many ways to view entropy...
  33. M

    Density Fluctuation: What Is It & How Does Hydrogen Bonding Enhance?

    Anyone know how hydrogen bonding in water can enhance "density fluctuation" ? And in first place What is "density fluctuation" ?
  34. J

    Hydraulic oil not susceptible to temperature fluctuation

    Im having an issue with a manual pump opening an actuator. It opens fine and holds pressure until the temperature starts to drop. My question is does anyone know of any hydraulic oil that is not susceptible to condensing when temperature drops?
  35. danihel

    Couple of quantum fluctuation related questions from a curious layman

    Hi, is it true that: 1. when virtual particles/antiparticles come to existence every billionth particle survives? is it the reason why the universe consists of particles rather than antiparticles? 2. when virtual particles annihilate the energy gets absorbed by the vacuum in contrast...
  36. S

    What is Maxwell Distribution, Thermal Equilibrium, Fluctuation and Wein's law?

    I was reading a book, 'Introducing Quantum Theory' by J.P.McEvoy, and I find it difficult to understand in details of Maxwell Distribution, Thermal Equilibrium, Fluctuation, Wein's law and Planck's quantum theory, so I am finding it difficult to follow Einstein's explanation of photoelectric...
  37. R

    What exactly is a quantum fluctuation

    This comes from Paul Davies' the Cosmic Jackpot: I just assumed a quantum fluctuation was more or less what a fluctuation in normal English is like: something that goes up and down. So I thought a quantum fluctuation was the act of some magical pure energy going up and down. But from the...
  38. T

    Flywheel effect on torque fluctuation of an IC engine

    How does a flywheel reduce torque fluctuations in a IC engine? Of course the more inertia you have, the less rotational speed fluctuation you get. But how does more inertia lead to less 'torque' fluctuation?
  39. D

    Wireless Signal Fluctuation. Weird Results.

    Hi there, I'm taking some measurements of a wireless signal using InSSIDer 2.0. Sometimes the signal fluctuation is upwards of 20 dBs, and sometimes the fluctuation is almost nothing. It is a very short range signal. There is minimal fluctuation in the signal shown when I'm 10 metres...
  40. N

    Virtual particles and quantum fluctuation

    the virtual particles that are created are the result of a quantum fluctuation ..but the energy of this fluctuation must be zero so 1 particle has positive mass and the other has negative mass ...so that if they annihilate the mass is zero and they go back to not existing but if the one with...
  41. N

    How to quantize the ''mathematical'' fluctuation field in statistics?

    Please teach me this: The general effort is to quantize the fields of elementary particles and gravitons.But I wonder about ''mathematical'' fields such as the fluctuation fields in statistical physics.I think there may be many ''continuous'' fields in physics.Could the functional integral...
  42. A

    Why is it called fluctuation conductivity in superconductors?

    Why is it called "fluctuation conductivity" in superconductors? Hello, In the work of Aslamazov-Larkin and many more, conductivity of a superconductor is calculated from the time dependent Ginzburg-Landau (TDGL) theory. They call it "fluctuation conductivity" bellow and above critical...
  43. maverick_starstrider

    Fluctuation Terms in Landau Theory

    Alright, here is something that is driving me insane. I feel like I've looked through every stat mech book on the planet and not a one discusses this stuff properly. My difficulty is in the study of phase transitions when one applies Landau's approach of expanding the free energy about the...
  44. N

    Voltage Fluctuations: Protecting Electrical Appliances in Stormy Weather

    how can voltage fluctuation arm electrical appliances... say fluctuation on a stormy night...
  45. N

    Voltage Fluctuation: Causes & Solutions

    What is te reason of voltage fluctuation in our home power supply?
  46. P

    Calculating Average Fluctuation

    Homework Statement I have been asked find the average fluctuation in a certain value. But I don't know what that means. Say x fluctuates about a mean. (\overline{(\Delta V)^{2}})^{1/2}? But that's the root mean square fluctuation, which isn't the same. Then how about...
  47. C

    Fluctuation in terms of Hilbert space formalsm

    This will sound like a very amateur question but please read: I have been puzzled for a while about the *precise* mathematical meaning of "quantum fluctuation". I know what a classical fluctuation is (as found in classical statistical dynamics). I also know what a superposition is. These seem...
  48. U

    Quantum Fluctuation: Exploring the Origins of Our Universe

    Indeed, the entire universe may have arisen from a quantum fluctuation in a vacuum, through a combination of inflation and a curious property of gravity. This curious property is that the severity of negative energy store. When something falls in a gravitational field there is a release of...
  49. S

    Vacuum Fluctuation: Exploring Interaction with EM Field

    recently i listened something about vacuum fluctuation.i don't know what exactly is it.but from that fluctuation is it possible to say that there is some width of the energy eigenvalue of a system where the particles are interact with em field.i don't know anything about field theory.
  50. A

    Mathematical principle for decomposing metric fluctuation

    What's the underlying principle to demonposite metrict fluctuation as scalar ,vector and tensor? Is this decomposition complete?unique? for scalar mode, \begin{equation} \delta g_{\mu \nu}=a^{2} \left( \begin{array}{cccc} 2\phi & -B,_{i} \\ -B,_{i} & 2(\psi \delta_{ij}-E,_{i,j})...