Relativity, Quantum Mechanics, & the Link Between Energy & Time

[daniel_i_l]

Is there an intuitive explanation for the fact that in both relativity (time part of 4vector) and qm (frequency) energy is related to time and momentum to space?
Thanks.

 

[lalbatros]

Well by counter examples you can find some intuition:

if the interaction changes with time, energy will change
(switching on slowly some high voltage for example)

if the interaction changes with position in space, the momentum will change
(a piece attached by a spring cannot maintain its momentum)

 

[pervect]

Is there an intuitive explanation for the fact that in both relativity (time part of 4vector) and qm (frequency) energy is related to time and momentum to space?
Thanks.

There is an explanation, but it may not be "intuitive". Momentum can be defined as space translation symmetry, and energy as time translation symmetry. This happens because of "Noether's theorem".

You can google a bit for this, or check out http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html and maybe even the Wikpedia.

Noerther's theorem requires that the laws of physics be expressed in terms of an action principle, but this requirement is generally met (Newtonian physics with or without gravity and General Relativity are both expressible in terms of an action principle, for instance).

 

[masudr]

Momentum can be defined as space translation symmetry, and energy as time translation symmetry. This happens because of "Noether's theorem".

Perhaps you mean "momentum can be defined as the quantity that is left invariant under space translations (given the space translation symmetry of the Lagrangian)," and similarly with energy and time, respectively.