I hear a lot of fluffy terms. Do you mean action as in choice?

What immediately comes to my mind are Planck's constant, and Angular momentum, measured in Joule-seconds, or kg m^2/second.

It comes up in Heisenberg's uncertainty principle as

Delta E * Delta t (Uncertainty of energy * Uncertainty in time)

or

Delta p * Delta x (Uncertainty of momentum * Uncertainty of position)

It's also describe for a particle by integrating its "Lagrangian" over it's path length. The Lagrangian is sort of a combination of kinetic and potential energy of a particle.

https://en.wikipedia.org/wiki/Action_(physics)

I think there have been other definitions that might not be the same as the one I'm offering though

• Gottfried Leibniz, Johann Bernoulli and Pierre Louis Maupertuis defined the action for light as the integral of its speed or inverse speed along its path length.
• Leonhard Euler (and, possibly, Leibniz) defined action for a material particle as the integral of the particle's speed along its path through space.
• Pierre Louis Maupertuis introduced several ad hoc and contradictory definitions of action within a single article, defining action as potential energy, as virtual kinetic energy, and as a hybrid that ensured conservation of momentum in collisions.[4]

Liebniz/Bernoulli definition would have units m^2/s, or just seconds, depending on whether you used speed or inverse speed.

Euler's definition would be in m^2/s

Maupertis apparently used Action as a generic term to describe several different quantities.

to @Frederik:

No, I mean action from the principle of least action.

to @Jonathan:

Thanks for the historical digression, but what do you think about interpreting the action as a projection of length from a multidimensional space into observer space.

to @Jonathan:

Thanks for the historical digression, but what do you think about interpreting the action as a projection of length from a multidimensional space into observer space."

What do I think? Hey, that's a question I'm actually qualified to answer, though you might find my thoughts a bit bit tangential to whatever are your expectations, but I'll take this opportunity to muse.

I'm not entirely sure what to think about that, because I don't know what ideas you're intending with "multidimensional space" One idea of a space is a region on which two or more variables can be plotted against one another. This has little or nothing to do with Euclidean space, except we draw the graph in Euclidean space, representing a relation of quantities that have little do do with space.

We could speak, for instance, of a Pressure vs Volume space, or a Temperature vs Entropy space, both being, in some sense, two dimensional spaces describing macroscopically observable quantities of a system.

I've been thinking, well, a couple of days ago, I spent some time thinking about Action as it relates to phase changes in matter, and gasses, and plasmas. In particular, consider this specific question...

I have two particles colliding with one another. Their (positive) kinetic plus (negative) potential energy integrated over time might either stay ABOVE planck's constant, or it will be BELOW planck's constant. If it is below planck's constant, perhaps the particles could combine to form a molecule. If it is above planck's constant, the two particles will bounce elastically. (I'm not 100% sure this is the way the physics works, by the way, but I've been trying to muse out something called the equipartition theorem, and this seems involved with the partition function.)

If they combine, then the number of particles in the system drops by one, and perhaps the degree of freedom of one of the particles increases. This would have an effect on the entropy in the system.

If the system were roughly homogeneous, there could be a situation where particles went from colliding with a median action slightly above Planck's action, to a median action just slightly below the Planck Action. This would effect a phase change in the substance, or a chemical reaction.

So, if action can be described as a length in some abstract space, the place to look here would be where I was comparing the kinetic + potential energy over time of a pair of particles, to the measure of Planck's constant.

For the moment, I am not, in particular imagining this quantity of "kinetic + potential energy over a time of interaction" as a coordinate of any space. But could it constitute a sort of "fifth dimension"?

What I can imagine, in the universe, as a whole, is a sort of changing of the average properties of the particles as the particles move apart, and the density goes down. Because as the density decreases, there would be changes in the number and degrees of freedom of particles in the system, which would give rise to changes in Pressure, Volume, Entropy, and Temperature at various epochs. One could also probably add "action per particle pair" as a sort of thermodynamic quantity. But "per particle pair" may have a sort of multidimensional aspect to it, because we would have many different types of particles, and each pairing could have a different average action associated with it, with each possible pairing offering a sort of "dimension" in action space. So it might, in principle, be possible to create a multidimensional space to represent that idea, but these would not be dimensions of space or time--just abstract dimensions one might use for graphing purposes.

As an example, one might consider the Action of the triple-alpha process in the sun, vs the action of the triple-alpha process in Betelgeuse. The kinetic energy is very high, but because of how closely packed the particles are, they have a longer time to interact at the deepest potentials., which brings the action below a certain cutoff where the Carbon atoms form.

If things can be described as "multidimensional" here, I think it would be a sort of form of the partition function. One dimension of the partition function. The standard partition function has Z_i where i represents the different possible quantum states of a pair of particles--for instance, a proton and an electron in ground state and i'th excited states. A multidimensional partition function could have hydrogen molecules, hydrogen atoms, electrons, and protons, alpha particles, neutrons, singly ionized Helium atoms, all kind of mixed up together in one mixture.