What is the ACTION?

lightarrow

I know how Action is defined, the fact the planck's constant h is an action, the variational theorems associated with it, as the principle of stationary action, and, mostly, the important facts that from this principle comes the relations between space homogeneity and linear momentum conservation, space isotropy and angular momentum conservation, time homogeneity and energy conservation.

My question is: what physically, intuitive meaning can have the action? Is it possible to visualize it in some way or to relate it directly to some property of space or of something else?

I think we should investigate more this concept, if we want to understand better the connection between the space (time?) structure and the constant h, that is, between General Relativity and quantum mechanics.

Do you agree?

pervect

You might enjoy reading http://www.eftaylor.com/pub/call_action.html

Taylor also advocates using Feynman's "sum over paths" formalism to show how QM reduces to the classical limit.


Note that GR can be understood in terms of variational principles (look up "Hilbert action").

The incompatibility between GR and quantum mechanics has sometimes been overstated a bit. Basically, at low energies, we already know how to quantize gravity, as an "effective field theory". It's only at high energies that we don't know how to marry the two. Unfortunately, the energies needed to really study this matter are probably not going to be experimentally accessible.

Planck's constant can be thought of as representing the way that the universe varies with scale. IIRC this remark was originated by Hermann Weyl.

Consider, for example, the transition from geometric units to Planck units. Geometric units make c=G=1, and unify time, distance, and mass - they can all be measured in a common unit, usually cm.

Planck units get rid of the cm and have no units at all - this is done by fixing the scale factor appropriately. This is an example of how Planck's constant can be thought of as setting the scale factor of the universe.

http://en.wikipedia.org/wiki/Planck_units
http://en.wikipedia.org/wiki/Geometrized_units
http://en.wikipedia.org/wiki/Natural_units

go into some of the various "natural" units, if this brief description wasn't too clear.

lightarrow

Thank you for your answer and for the file you indicated to me.

I have understood that a body moves in a geodesic of curved space-time according to the maximum proper time and this is equivalent to follow the minimum-action path.

So, there is a relation between action and proper time?

pervect

Yes - the action is the proper time expressed in different variables. Part of the Lagrangain formalism is to find the value of the function L in terms of the variabes t,x,dx/dt, i.e. to find L(t,x,dx/dt).

lightarrow

Ok. So, since the action has h as minimum value, would it be correct to say that proper time must be quantized as well?

lightarrow

So, since the action is quantized, would it be correct to say that proper time must be quantized as well?

lightarrow

If proper time is quantized, that would be an interesting subject, isnt'it?