How Can Action Be Understood in Human Terms?

[Siv]

Objective evidence is always followed by a subjective interpretation. Without such an interpretation there is no "evidence". The very term "evidence" implies a subjective presupposition. Thus there is no point of denying subjectivity. The important question is how to make it less vulnerable to errors. I am suggesting that this can be done by increasing, expanding and utilizing knowledge - one of the most important factors along with seeking as much objectivity as possible.

Well, we seek consistency, that's all.
It could all be a Matrix scenario. But this scenario has some patterns which are independently verifiable.
Far far better than subscribing to something based on anecdotes.

 

[jambaugh]

I don't think the "least action principle" is fundamental per se. In studying graduate physics I was surprised to discover that we can essentially map any physical laws into an extremum problem. Lagrange multipliers show how to incorporate constraints into the action and so you can see the Lagrangian as merely an "action principle" formulation of the dynamic constraints (dynamical laws). It is one elegant and useful formulation but I think it manifests more as "the way we find most useful to think about things" as opposed to "the way things are deep down".

That having been said, Let me try to answer the OP's question, starting with the deeply mathematical and surfacing to a layman's definition if possible. As a background my graduate work was in deformations of physical theories through the deformation of their assumed Lie group/Lie algebra structures.

Any physical activity involves the changing of physical systems. These activities when involving continuous change we can express mathematically in terms of Lie groups. Take as an example the rotation of an object and the rotation group.

Now consider Noether's theorem and the correspondence of symmetries and conserved quantities. The corresponding quantities still exist if the symmetries are broken, they are just no longer conserved. So look upon it as a deeper correspondence between group actions and measurable quantities.

In expressing the transformation of our physical description of an object we see this correspondence in the exponentiation of a Lie algebra element to yield a group element in the form:
g(\theta) = e^{\Gamma \theta}
where the Gamma is the generator of the action and corresponds to a physical observable and the theta corresponds to a dual coordinate. The product must in general be unitless but typically we have conventional units for the components whose product is action units and we divide by Plank's constant to get a unitless exponent. E.g.
\Gamma \cdot \theta =\frac{1}{\hbar}\cdot p\cdot \Delta x
Even if this exponent is unitless there is a question of scale. Is there a (somewhat) natural scale to the group action \Gamma \cdot \theta?

For simple groups the answer is yes. There is a natural metric and measure on the simple Lie groups. This is how we get for example radian measure for rotations. If we assume that all the physical groups are singular deformations of some simple group then the natural units carry into the singular case and we can assume the (typically extreme) unit constants we find are manifestations of the extreme deformation, becoming (like c) simple unit conversion factors when we recognize the proper simple group structure.

Now let us review radian units for a moment. We typically use the arclength of the unit circle but a more easily generalized unit is the corresponding sector area (times a factor of 1/2 to get agreement but that's just a choice of convention). This half-area generalizes nicely to the hyperbolic pseudo-rotations of SR boosts. We then see it manifest in the limiting case between the two where in Galilean relativity we simply translate velocities.

If one asserts that all of the non-simple transformation groups are singular limits of actual simple or semisimple underlying groups then all group transformations has a natural unit we can call action which will be the product of a generalized momentum (generator of transformation) and generalized coordinate (transformation parameter) be it:

angular momentum times angle
energy times time
momentum times distance
pseudo-angular momentum (mass moment times c) times boost parameter
et cetera

As to why we get these units, we actualize a given amount of transformation in an object, say a relative change at some future time, by exciting the object into motion, then waiting for that motion to manifest. This excitation has energy units because of the Nother correspondence. Energy is what holds constant as we "do nothing" over time thus preserving time translation symmetry for that period. We can re-parametrize by expressing energy as some form of momentum times a rate of change for the corresponding parameter. Then the time times the rate of change gives the change in parameter and you have generic momentum times dual parameter units.

Note that the "larger" the object the more "excitation" required so the more action per parametric translation.

So for the layman action is the amount of physical transformation a system goes through "measured" in such a way that it sums over components and is independent of "how quickly" we effect the change.

 

[bayak]

Action can not be a length of path in space-time. It has a wrong physical dimension.

But it has a right metaphysical dimension. In fact, S=m*s, where mass (m) has dimension [absolute length]/[absolute time] and length between two events of this mass (s) has dimension [absolute time].

 

[jambaugh]

But it has a right metaphysical dimension. In fact, S=m*s, where mass (m) has dimension [absolute length]/[absolute time] and length between two events of this mass (s) has dimension [absolute time].

If you double the mass of an object you double the action for the same transition. That is not what "space-time distance" means. "Metaphysical dimension" sounds like you're trying to change reality to fit your "facts".

 

[ThomasT]

Nice discussion, and perhaps I'll return to some of the, er, peripheral considerations -- however, wrt arkajad's OP:

A friend, humanist by profession, asked what is "power"? Well, that was easy to explain in human terms. You do a certain amount of work, you use a certain amount of calories, you can do you work slowly, during one day, or you want to do it in one hour. Then you need more power.

Right, power refers to a certain amount of work done in a certain amount of time. The more work you can do per unit of time, the more powerful you are. I would say that the word power in ordinary language means basically the same as the word force in quantitative physics.

But the next question was about "action". To say action is energy times time, or momentum times displacement does not fly. That is good in formulas, but it tells nothing to a humanist.
To say "Planck constant is the quantum of action" does not help either.

So, how to explain what is action so that it will be understood and "felt" by a humanist or engineer? How we can relate it to our daily experience and/or engineering?

What is action philosophically?

Any ideas?

Well, is this correct? Power = Force = Mass x Acceleration. Energy = Force x Distance. Action = Energy x Time.

What mechanisms in us, human beings, are directly sensitive to action? Are there any? We are sensitive to time in an obvious way, through the rythms around us and in us. We are sensitive to energy we spend. Do we have sensors for action?

Yes, we directly detect force vis inertia.

So, what is the essence of force, or inertia? My guess? It's simply the expansion of the universe. It's why, when you drop a pebble into a calm pool of water, the wavefront travels, omnidirectionally, outward from the initial disturbance. It's the fundamental 'direction' of motion, the 'arrow of time', and kinetic energy imparted via the Big Bang. It's the fundamental wave dynamic of the universe. It's how and why, over countless iterations and interactions, we are what we are. And why, because of future countless iterations and interactions, we will eventually cease to be.

Sorry if I got a bit metaphysical there.

 

[bayak]

If you double the mass of an object you double the action for the same transition. That is not what "space-time distance" means. "Metaphysical dimension" sounds like you're trying to change reality to fit your "facts".

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

 

[ThomasT]

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

From the OP:

So, how to explain what is action so that it will be understood and "felt" by a humanist or engineer? How we can relate it to our daily experience and/or engineering?

What is action philosophically?

 

[bayak]

OP also is:

Let's leave our human affairs for a while, isn't it funny that action is energy multiplied by time or momentum multiplied by displacement while at the same time we have uncertainty relations between these quantities. Can action be strictly defined and measured even when we have uncertainties as regards its components? Can action be directly measured at all? How?

 

[ConradDJ]

So for the layman action is the amount of physical transformation a system goes through "measured" in such a way that it sums over components and is independent of "how quickly" we effect the change.

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.

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.

But quantum physics is based on the notion that there is a certain minimum of action that has to happen in any physical event... so instead of a world of continuous change we have a world made of tiny events. And it appears that they always occur in the form of moments of connection between two things, i.e. interactions in which a mutual “transformation” occurs.

From a philosophical standpoint, this suggests the possibility of a relational ontology based on connection-events, rather than the traditional “objects” or “substances” that last through time. The interesting thing about that is that the world we actually experience, in real time, and the world through which we communicate with each other, is evidently a world made of interaction. But our intellectual tradition has always treated “the appearances” of things to each other as something secondary, compared with their “reality” in and of themselves.

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. I suspect that what we have to learn from QM and Relativity will never become clear until we learn how to imagine the physical world that we actually experience, the world of “action” in the moment. At least as a complementary viewpoint to the classical space-time picture.

 

[ThomasT]

OP also is:

Ok. Thank you.

 

[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.