How Can Action Be Understood in Human Terms?

[arkajad]

Dividing the world up into “events” is rather arbitrary, in classical physics. All happening is continuous, and there's always more going on in the vicinity that you could include as part of whatever "event" you're talking about. It usually makes more sense to divide up the world into objects and regions in space and time, or regions in phase space.

And yet the "least action principle" mysteriously is at the foundations of classical mechanics. Sure, we do not understand "why?". It looks somewhat teleological there. Perhaps QM can help us to get rid of this teleological thinking. But at what price? Mysterious "spooky action at a distance?" Yes, something seems to be still missing.

 

[ThomasT]

Basically, the idea of action corresponds to the idea of an event. If you designate a certain related set of changes as "an event" then it makes sense to quantify "how much happened" in that event -- which is the action.

So, "action" refers to configurational incongruencies, ie. positional, changes? If so, then is "action", at least in that manner of speaking, synonymous with "time"?

My own view is that the lack of a well-developed picture of the world of real-time interaction is the main reason why quantum physics remains conceptually so problematic.

Well, your statements make sense to me. But I'm not sure how they contribute to answering the OP's question. Keep in mind that I'm writing this in the morning after little sleep, so it's quite possible that I've missed your point. But, thank you.

Anyway, I see that arkajad is online now, so maybe he will clarify.

And I must confess that I don't entirely understand how jambaugh's statements answer arkajad's questions, although I have greatly benefited from jambaugh's contributions in many threads and hopefully will, eventually, in this one also.

 

[ConradDJ]

And yet the "least action principle" mysteriously is at the foundations of classical mechanics. Sure, we do not understand "why?". It looks somewhat teleological there. Perhaps QM can help us to get rid of this teleological thinking. But at what price? Mysterious "spooky action at a distance?" Yes, something seems to be still missing.

I'm no expert in the field, but my understanding is that the classical "least action principle" can be understood as arising from quantum mechanics in the following way.

Essentially, in any physical situation, anything can happen. Per Feynman's lovely book QED -- if an interaction takes place between a system that emits a photon and another system that absorbs it, then the photon takes every possible path between the two systems... including all kinds of bizarre paths that involve gigantic quantities of "action" or hop around all over the universe.

There aren't any rules about how the photon can behave -- but for every path there is a certain associated "quantum phase". And for all the weird paths, the phase is canceled out by other weird paths that have an opposite phase-angle. The only paths where the phases reinforce each other instead of canceling each other are those that are very close to the classical straight-line path between the systems... i.e. the path with "least action".

I’m not sure how to make sense of this, but it’s a way of describing how the precisely lawful world of classical physical physics emerges out of the craziness of QM, that seems to be very generally applicable. That is, everything that happens in classical physics can be described in terms of the canceling out of the phase-angles of the weird, unlawful possibilities.

A recent thread in the “Beyond the Standard Model” forum quoted this blog on this subject –
http://motls.blogspot.com/2010/10/dont-mess-with-path-integral.html"

 

[ConradDJ]

So, "action" refers to configurational incongruencies, ie. positional, changes? If so, then is "action", at least in that manner of speaking, synonymous with "time"?

Hi Thomas -- To try to clarify, "action" might refer to anything that can happen in any kind of "event". For example, my son leaving home and going off to college... to me that's a big, complicated “event” in my life that "happens" over a couple of years. But it can be broken down into lots of smaller, simpler events, like his writing an essay for a college application, or my dropping him off at the airport. And those can be broken down into smaller, simpler physical events, that can actually be quantified.

This is similar to breaking physical objects down into smaller, simpler objects, until you get down to the level of atoms. In this case the smallest unit-events are quantum interactions – “atoms of happening”.

But if you try to specify what happens at the quantum level in terms of positional changes or time-intervals, you run into ambiguity, due to the uncertainty principle. For example, a quantum interaction doesn't "take time” to happen – there’s generally an instantaneous “quantum jump” between states. But it doesn’t happen at any specific point in time, either (unless the energy involved is completely indeterminate, in which case there’s no limit to how localized it can be in time.)

So yes, in a sense action is profoundly connected with time – in that time is meaningful only if something happens. But it appears that happening is in some sense more fundamental than “time” in the classical sense of clock-time or calendar-time. I imagine it may be related to the time we actually experience in this ongoing present moment “now”.

 

[arkajad]

then the photon takes every possible path between the two systems... including all kinds of bizarre paths that involve gigantic quantities of "action" or hop around all over the universe.

And here you have the mysterious nonlocality. It's a lot of work for the Nature to take into account "all possible paths" - isn't it? From this point of view classical theory, where the lest action principle can mysteriously be converted from the nonlocal "shortest path" to a local "straigthest path" (Euler-Lagrange equations) is conceptually much simpler.

 

[jambaugh]

It is because my metaphysical space-time is wound on a sphere's product S³xS¹.

That doesn't address the point. Toridal space-time or flat space-time. Saying action is simply space-time distance doesn't address the additivity of action for objects which as a group travel the same space-time distance. Adding a "metaphysical" qualifier doesn't change anything and really isn't helpful. If the topological space to which you refer is "space-time" then it is "space-time" if it is something else then be clear with the definition.

You can always construct a space in which a quantity resides (momentum space, hilbert space, phase space, etc) but that gives no information about the quantity. If on the other hand you express it in terms of an a priori defined space then it can connect to the quantities that space was constructed to represent. Example:

"Action is area in phase space." a beautifully intuitive definition in a 1 dimensional system but problematic as we add degrees of freedom. But understand phase space a the representation space for the group of canonical transformations and it becomes less so.

BTW With regard to Quantum Action Principle to Classical:

It really is quite well thought out in the literature. Swinger's quantum LAP is simply a manifestation of the interference we see in quantum phenomena. When you sum over histories the path with extremal "action" is the path on which the phase is stationary and so no destructive interference occurs.

The action can then be understood as the measure of complex phase rotation for a given path.

You then find that in the quantum setting the "path" in question is the path followed by the expectation values of the principle observables through the classical configuration space. It is indeed a type of distance.

There are however problems. This complex phase is not quite the same U(1) phase of e-m gauge. (Otherwise "action" would just be E-M potential times charge and = 0 for neutral particles) There are multiple distinct imaginary units in QM which we can understand as emerging as distinct U(1) subgroups of a larger gauge+dynamic group. Again my assertion (in abbreviated form) that:
action is distance in "group space".

Or for the layman, "how much transformation of the system has occurred". The fact that this seems to be an unambiguous (or nearly so) quantity hints at some fundamental unification which has yet to be fully achieved.

A final note to the OP, I understand your desire for a simple "gut level" definition of action. But it isn't an observable quantity like momentum or energy. I can't give you an "action" ruler you can put in your pocket. To appreciate it you need to do a little math.

 

[ConradDJ]

It's a lot of work for the Nature to take into account "all possible paths" - isn't it? From this point of view classical theory, where the lest action principle can mysteriously be converted from the nonlocal "shortest path" to a local "straigthest path" (Euler-Lagrange equations) is conceptually much simpler.

I wonder... classical physics does seem much simpler conceptually and mathematically. But is it a "practical" way to run a universe? When you have more than two particles involved, actually computing their classical paths gets very complicated, and can generally only be done to some approximation (using perturbation methods). The complexity increases exponentially the more particles you have interacting. And approximation is really not ok, since in most physical systems very tiny differences in position or momentum at one point can make a huge difference in the state of the system later on ("butterfly effect").

The quantum method seems to be -- just let everything happen... and an approximately "lawful" path will just emerge by chance, 99.9999% of the time -- because of the way quantum probabilities operate with phase-angles. There's no need for an infinitely precise determination of the particle's position and momentum at each point on its path, and no need to combine a bunch of separate classical calculations for all the particles involved.

This is just hand-waving, of course, but it does seems conceivable that QM represents a method of information-processing that's far simpler and infinitely more efficient at dealing with complex systems than classical physics.

 

[arkajad]

I can't give you an "action" ruler you can put in your pocket. To appreciate it you need to do a little math.

You see, I have no problems with the math. However, in order to do math in a creative way (and not only passively appreciate what has already been done) one needs an intuition. And it is good to have an intuition that is somewhat different from the intuition of other physicists - then there is a chance that you will be able to see something that others do not see.

Concerning the concept of "action" I am seeking for such an intuition - thus my question. But it is not because I am selfish, I thought that such an discussion may help other participants as well.

 

[jambaugh]

And here you have the mysterious nonlocality. It's a lot of work for the Nature to take into account "all possible paths" - isn't it? From this point of view classical theory, where the lest action principle can mysteriously be converted from the nonlocal "shortest path" to a local "straigthest path" (Euler-Lagrange equations) is conceptually much simpler.

This is a means of expressing the behavior in old classical terms "photon taking a path". Photons do not take classical paths. Sum over histories is not fundamental but this is a nice way of translating from prior classical concepts. It is a manifestation of Huygen's principle for waves. Even a classical wave "takes all paths" but it doesn't invoke any non-locality or "spooky action at a distance".

What we're talking about here is descriptions of "what goes on between measurements". In the quantum setting this can only be understood as a conceptual device or calculative device, not a statement about the nature of reality.

 

[arkajad]

I wonder... classical physics does seem much simpler conceptually and mathematically. But is it a "practical" way to run a universe?

Well, each particle is just looking at the local geometry (gauge fields, gravitational fields), checks its position and speed, and calculates the next step. Runge-Kutta of some order works well for a small number of particles and not too long times.

That's the whole point: in classical physics least action is equivalent to second-order differential equations.

In quantum theory the computation is enormously more complicated. That is why people have hope in quantum computers since Nature does it seemingly effortlessly.

 

[Upisoft]

But, to give an example, out of my free will, I am choosing "otherwise" - that is not to continue my participation in this particular thread, even if I have started it.

Your example failed.

 

[arkajad]

Your example failed.

Of course. Did you expect otherwise? After all I am a human being not some perfect machine.

 

[ConradDJ]

Well, each particle is just looking at the local geometry (gauge fields, gravitational fields), checks its position and speed, and calculates the next step. Runge-Kutta of some order works well for a small number of particles and not too long times.

That's the whole point: in classical physics least action is equivalent to second-order differential equations.

In quantum theory the computation is enormously more complicated. That is why people have hope in quantum computers since Nature does it seemingly effortlessly.

The calculation is more complicated for us, when we try to compute probabilities in quantum physics. But I doubt that Nature is doing any numerical computations -- it certainly doesn't appear to be set up to do that.

Quantum "computation" seems to work in a different way. When two particles interact, everything that could possibly happen happens, but nearly all the possibilities get "taken out" in some sense by other possibilities with opposite phase. Of the remaining possibilities for interaction where the phases reinforce, the two particles randomly agree on one, as what "really happens" between them.

Actually the superposition of possibilities never gets "reduced" to a single, classically well-defined reality. In QM there is definite information only to the extent it's "relevant" -- i.e makes a measurable difference.

But without getting into the whole question of measurement -- my point is that this quantum set-up can maybe determine the dynamics of very complex systems "by feel", so to speak -- through a combination of phase-cancellation and random selection. No numerical calculation required.

A fanciful thought, but easier for me to imagine than your particle doing the equations "in its head."

 

[Upisoft]

Of course. Did you expect otherwise? After all I am a human being not some perfect machine.

I did not expect otherwise. You thought you can choose otherwise, but you couldn't. You were controlled by your imperfectness.

 

[arkajad]

Perfect things are essentially dead or dying - so they are not that perfect after all. The universe is alive because the perfect symmetry is broken. And that is why it is interesting rather than dull.