3 ms·
Here's my attempt: Suppose a system evolves such that it moves forward from coordinate "c" to "c+dc" in time "dt". Since "c+dc" is similar to "c" (due to a sym
by ssivark 10y ago
Here's my attempt:
Suppose a system evolves such that it moves forward from coordinate "c" to "c+dc" in time "dt". Since "c+dc" is similar to "c" (due to a symmetry along the coordinate) the system's behavior must be repeated in the next dt interval, since different coordinate values have equivalent physics.
If we imagine a wave/wavefunction with this property, the most reasonable way to implement this is if the wave has a periodic form such as "exp(i * c * B)" such that on moving along coordinate "c", the wave retains the same form up to an overall phase, which is physically unobservable.
This is the same as saying that there is a conjugate quantity "B" that remains constant during the evolution.
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More loosely: unless there is some form of generalized force along a coordinate (eg: friction), a system with conjugate quantity B keeps moving on an on with the same value of quantity B, since the only way to change its value would be to do something non-symmetric to it at different locations in the coordinate.
- brianberns 10y agoAs a layman, this sounds very much like Newton's first law: An object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
- ssivark 10y agoYes, that allusion was deliberate on my part. Newton's first law is a manifestation of the symmetry principle when position "x" is the coordinate under consideration. Force is proportional to gradient(Potential) so any asymmetry in the way the Potential depends on the position produces a Force which changes the Momentum. So, Momentum is the conserved quantity corresponding to the symmetry that all positions are equivalent.
- brianberns 10y agoThank you, this is a very helpful explanation.
- aphextron 10y ago>As a layman, this sounds very much like Newton's first law: An object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Many equations in physics are simply restatements of other laws showing the same relationship. For instance Coloumb's law for electromagnetic attraction [0], and Newton's law of gravitational attraction [1]. [0] http://home.fnal.gov/~cheung/rtes/RTESWeb/LQCD_site/objects/coulombslaw.png http://home.fnal.gov/~cheung/rtes/RTESWeb/LQCD_site/objects/... [1] https://kaiserscience.files.wordpress.com/2015/08/force-gravity.jpg https://kaiserscience.files.wordpress.com/2015/08/force-grav...