Planck's Constant

#REDIRECT Planck's constant

Planck's constant

'''Planck's constant''', denoted ''h'', is a physical constant that is used to describe the sizes of quantum. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory. Its value is :

h=6.626\ 069\ 3(11) \times10^{-34}\ \mbox{J}\cdot\mbox{s}

or with electronvolts as energy unit: :

h=4.135\ 667\ 43(35) \times10^{-15}\ \mbox{eV}\cdot\mbox{s}.

Planck's constant has Physical unit of energy multiplied by time, which are the units of action (physics). These units may also be written as momentum times distance (Newton·metre·second), which are the units of angular momentum. A closely-related quantity is the reduced Planck constant (sometimes called ''Dirac's constant''): :

\hbar\equiv\frac{h}{2\pi}=1.054\ 571\ 68(18)\times10^{-34}\ \mbox{J}\cdot\mbox{s},

where π is the constant pi. This constant is pronounced as "h-bar". The figures cited here are the 2002 CODATA-recommended values for the constants and their uncertainties. The 2002 CODATA results were made available in December 2003 and represent the best-known, internationally-accepted values for these constants, based on all data available through 31 December 2002. New CODATA figures are scheduled to be published approximately every four years. Planck's constant is used to describe quantization, a phenomenon occurring in microscopic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than assuming a continuous range of possible values. For instance, the energy ''E'' carried by a beam of light with constant frequency ''ν'' can only take on the values :

E = n h \nu \,,\quad n\in\mathbb{N}

It is sometimes more convenient to use the angular frequency ''ω'' = 2 π'' ν'', which gives :

E = n \hbar \omega \,,\quad n\in\mathbb{N}

Many such "quantization conditions" exist. A particularly interesting condition governs the quantization of angular momentum. Let ''J'' be the total angular momentum of a system with rotational invariance, and ''J_z'' the angular momentum measured along any given direction. These quantities can only take on the values :

\begin{matrix}
J^2 = j(j+1) \hbar^2,  & j = 0, 1/2, 1, 3/2, \ldots \\
J_z = m \hbar, \qquad\quad & m = -j, -j+1, \ldots, j\end{matrix}

Thus,

\hbar

may be said to be the "quantum of angular momentum". Planck's constant also occurs in statements of Werner Heisenberg uncertainty principle. The uncertainty (more precisely: the standard deviation) in any position measurement, Δ''x'', and the uncertainty in a momentum measurement along the same direction, Δ''p'', obeys :

\Delta x \Delta p \ge \begin{matrix}\frac{1}{2}\end{matrix} \hbar

There are a number of other such pairs of physically measurable values which obey a similar rule. On some browsers, the Unicode symbol ℎ (ℎ) is rendered as Planck's constant, and the symbol ℏ (ℏ) is rendered as Dirac's constant. == See also == * Electromagnetic radiation * Natural units * Schr�dinger equation * Wave-particle duality * Quantum Hall effect ==Reference== *[http://physics.nist.gov/cgi-bin/cuu/Value?h NIST] link to CODATA value Fundamental constants lv:Planka konstante vi:Hằng số Planck

Planck's constant

h means: energy is related to time. Is there an upper or lower limit of energy or time? User:ErNa 09:17, 9 Jun 2005 (UTC) Article says: :Similarly, the amount of time it takes a photon to travel one Planck length is Planck time: 10^-43 seconds. This is the smallest meaningful division of time. Shouldn't that be more accurately the amount of time it takes for a particle travelling at the speed of light in a vacuum one Planck length? Photon's can travel slower than the speed of light in a vacuum in some circumstances, can't they? -- User:SJK I don't think that the photons actually slow down. I believe that the slow down in a refractive material is due to the absorbtion and re-emission of the photons; slowing down the wave as a whole. I may, of course, be wrong. --BlackGriffen :You are correct. Incidentally, the unqualified phrase "speed of light" almost always refers to the speed of light in a vacuum. -- User:CYD

Shouldn't the title of the article contain an apostrophe, or is that not possible? --BlackGriffen ----- Also could someone post the equation for Planck's length and explain in detail why two points separated by less than Planck's length are indistingushable? I think it has something to do with heisenberg's uncertainty principle? :Moved --User:maveric149 Thanks for the suggestion! The formula for the Planck length is: SQRT(h-bar G/c³) There is currently a buzz in physics surrounding this length because general relativity and quantum mechanics are glaringly incompatible at Planck scale. This is a temporary condition. The theories of gravity and matter will be adjusted so they don't contradict each other, the buzz will stop or be about something else. The Planck units will still be there as natural units implicit in light and gravity explainable in simple terms without all the heavy talk about theories breaking down, just as they have been there for a hundred years. They're nice because they make the constants you use all the time come out to be one. But yes!!!! maveric. The current clash of theories DOES have to do with HUP! The prevailing theory of gravity (Gen. Rel.) allows for black holes of any mass, consisting of a point of singularity surrounded and hidden by an event horizon whose size (the halfradius) is proportional to the hole's mass. For a non-rotating black hole of Planck mass the halfradius would be Planck length. But in the prevailing theory of matter (Qua. Mech.) every mass has a Compton wavelength which imposes a limit on localization and the Compton for something with Planck mass is also equal to Planck length. This trashes the model of a black hole because how can the point of singularity be surrounded and hidden by the event horizon when the point is so spread out that it barely fits inside? there is not enough ability to localize for the trim geometry of the black hole model to work convincingly. So physicists (as a professional class very subject to tunnel vision, thinking only about the Problem of the Day) tell you that Planck scale IS where the theories break down. Right now that is the significance of the Planck scale for them. I think in the long run it is more significant that the people who seem to be making the most progress at FIXING the problem (String Theorists) actually do their work in Planck units. In other words they are handy units to work in when you are trying to unify gravity and the other forces of matter and build a general theory, so that when there finally is some theory that works it will very likely be written in Planck units. I see them as the units of the future rather than as the place where current theories collide. But you are right to point out that aspect. == Updated 2002 CODATA values == I've replaced the old 1998 CODATA-recommended values with the new 2002 CODATA-recommended values. These values became available in December 2003, and are the new internationally-recommended values for these constants. The U.S. National Institute of Standards and Technology's excellent reference site has the updated CODATA international data. References to 2002 CODATA Values: * [http://physics.nist.gov/cgi-bin/cuu/Value?h CODATA value for h] * [http://physics.nist.gov/cgi-bin/cuu/Value?hbar CODATA value for hbar] --Alan Eliasen

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