DocuWatch on Facebook
Art America Britain History Science Societies War Shop
DocuWatch

Uncertain Principles

« Time Trip

Uranium Goes Critical - (1979) »

Description

From Wikipedia

Uncertain Principles

In quantum mechanics, the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the other can be known. This statement has been interpreted in two different ways. According to Heisenberg its meaning is that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle with any degree of accuracy or certainty. According to others (for instance Ballentine) this is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but it is a statement about the nature of the system itself as described by the equations of quantum mechanics.

In quantum mechanics, a particle is described by a wave. The position of the particle is regarded as being where the wave amplitude is greatest and the momentum is determined by the wavelength. The position is uncertain to the degree that the wave is spread out (well-defined wavelength), but the momentum is certain (well-defined) only to the degree that the wavelength is well-defined. Thus, position and momentum for a particle have opposite requirements for good definition, so that both position and wavelength cannot simultaneously be well-defined.

The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength. Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there are no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

The uncertainty principle can be restated in terms of measurements, which involves collapse of the wavefunction. When the position is measured, the wavefunction collapses to a narrow bump near the measured value, and the momentum wavefunction becomes spread out. The particle's momentum is left uncertain by an amount inversely proportional to the accuracy of the position measurement. The amount of left-over uncertainty can never be reduced below the limit set by the uncertainty principle, no matter what the measurement process.

This means that the uncertainty principle is related to the observer effect, with which it is often conflated. The uncertainty principle sets a lower limit to how small the momentum disturbance in an accurate position experiment can be, and vice versa for momentum experiments.

A mathematical statement of the principle is that every quantum state has the property that the root mean square (RMS) deviation of the position from its mean (the standard deviation of the X-distribution):

Delta X = sqrt{langle(X - langle X
angle)^2
angle} ,

times the RMS deviation of the momentum from its mean (the standard deviation of P):

Delta P = sqrt{langle(P - langle P 
angle)^2
angle} ,

can never be smaller than a fixed fraction of Planck's constant:

Delta X Delta P ge {hbar over 2}.

Any measurement of the position with accuracy scriptstyle Delta X collapses the quantum state making the standard deviation of the momentum scriptstyle Delta P larger than scriptstyle hbar/2Delta x.

Tags

 

Other videos in channel "Atoms":

 Atoms Old and New Atoms Old and New An Expensive Theology - (1992) An Expensive Theology - (1992) Atom Atom
Atoms and their Electrons Atoms and their Electrons Chemistry Chemistry
Chemistry - A Volatile History Chemistry - A Volatile History Chemistry 1A Chemistry 1A Cold Fusion ? - (2005) Cold Fusion ? - (2005)
Copenhagen Fall Out - Niels Bohr & Werner Heisenberg Copenhagen Fall Out - Niels Bohr & Werner Heisenberg Do You Know what time It Is? - (2008) Do You Know what time It Is? - (2008)
E=mc2 - Einstein and the World's Most Famous Equation E=mc2 - Einstein and the World's Most Famous Equation Einstein Einstein Einstein, Albert Einstein, Albert
Einstein's Biggest Blunder Einstein's Biggest Blunder Einstein's Brain Einstein's Brain Einstein's Equation of Life & Death - (2005) Einstein's Equation of Life & Death - (2005)
Einstein's Miracle Year - (1996) Einstein's Miracle Year - (1996) Einstein's Unfinished Symphony - (2005) Einstein's Unfinished Symphony - (2005) Elementary Particles and the Laws of Physics - Richard Feynman Elementary Particles and the Laws of Physics - Richard Feynman
Faster Than the Speed of Light Faster Than the Speed of Light Feynman On Quantum Mechanics Feynman On Quantum Mechanics Fundamentals of Physics with Ramamurti Shankar Fundamentals of Physics with Ramamurti Shankar
Great Ideas of Classical Physics 02 - 08 Great Ideas of Classical Physics 02 - 08 Greatest Discoveries - Chemistry Greatest Discoveries - Chemistry Greatest Discoveries - Physics Greatest Discoveries - Physics
Hitler's Bomb - (1992) Hitler's Bomb - (1992) How Long Is A piece Of String ? How Long Is A piece Of String ? Introduction to Chemical Engineering Introduction to Chemical Engineering
Molecules With Sunglasses Molecules With Sunglasses Most Of Our Universe Is Missing Most Of Our Universe Is Missing Nanoutopia Nanoutopia
Nikola Tesla - Master of Lightning Nikola Tesla - Master of Lightning Our Friend The Atom Our Friend The Atom Particle Physics 01 Particle Physics 01
Particle Physics 02 Particle Physics 02 Project Poltergeist Project Poltergeist Quantum Mechanics Explained Quantum Mechanics Explained
Six Billion Dollar Experiment  Six Billion Dollar Experiment Strangeness Minus Three Strangeness Minus Three String Theory String Theory
String Theory and M-Theory String Theory and M-Theory Superconductivity Superconductivity The Big Bang Machine The Big Bang Machine
The Birth Of Liquid Crystals The Birth Of Liquid Crystals The Good German The Good German The Hunt for Higgs The Hunt for Higgs
The Man Who Loved Trees The Man Who Loved Trees The Mysterious Mr. Tesla The Mysterious Mr. Tesla The Path To Nuclear Fission The Path To Nuclear Fission
The Riddle of AntiMatter The Riddle of AntiMatter The Secret Life of Waves The Secret Life of Waves Time Lords Time Lords
Time Trip Time Trip Uncertain Principles Uncertain Principles Uranium Goes Critical - (1979) Uranium Goes Critical - (1979)
Visions Of The Future 03 - The Quantum Revolution Visions Of The Future 03 - The Quantum Revolution What Gives Particles Mass? What Gives Particles Mass? What is One Degree? What is One Degree?
What On Earth Is Wrong With Gravity? What On Earth Is Wrong With Gravity? Zero G Zero G  
Video channels
Videos in this channel
Adsense
Featured
Featured
Featured
Featured
Featured
Featured