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| Action | |
|---|---|
Common symbols | S |
| SI unit | joule-second |
Other units | J⋅Hz−1 |
| In SI base units | kg⋅m2⋅s−1 |
| Dimension | |
In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects.[1] Action and the variational principle are used in Feynman's formulation of quantum mechanics[2] and in general relativity.[3] For systems with small values of action similar to the Planck constant, quantum effects are significant.[4]
In the simple case of a single particle moving with a constant velocity (thereby undergoing uniform linear motion), the action is the momentum of the particle times the distance it moves, added up along its path; equivalently, action is the difference between the particle's kinetic energy and its potential energy, times the duration for which it has that amount of energy.
More formally, action is a mathematical functional which takes the trajectory (also called path or history) of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths.[5] Action has dimensions of energy × time or momentum × length, and its SI unit is joule-second (like the Planck constant h).[6]
- ^ Neuenschwander, Dwight E.; Taylor, Edwin F.; Tuleja, Slavomir (2006-03-01). "Action: Forcing Energy to Predict Motion". The Physics Teacher. 44 (3): 146–152. Bibcode:2006PhTea..44..146N. doi:10.1119/1.2173320. ISSN 0031-921X.
- ^ Ogborn, Jon; Taylor, Edwin F (2005-01-01). "Quantum physics explains Newtons laws of motion" (PDF). Physics Education. 40 (1): 26–34. Bibcode:2005PhyEd..40...26O. doi:10.1088/0031-9120/40/1/001. ISSN 0031-9120. S2CID 250809103.
- ^ Taylor, Edwin F. (2003-05-01). "A call to action". American Journal of Physics. 71 (5): 423–425. Bibcode:2003AmJPh..71..423T. doi:10.1119/1.1555874. ISSN 0002-9505.
- ^ Cite error: The named reference
FeynmanIIwas invoked but never defined (see the help page). - ^ Goodman, Bernard (1993). "Action". In Parker, S. P. (ed.). McGraw-Hill Encyclopaedia of Physics (2nd ed.). New York: McGraw-Hill. p. 22. ISBN 0-07-051400-3.
- ^ Stehle, Philip M. (1993). "Least-action principle". In Parker, S. P. (ed.). McGraw-Hill Encyclopaedia of Physics (2nd ed.). New York: McGraw-Hill. p. 670. ISBN 0-07-051400-3.