The Nomological Character of Physical Laws

tom

As noted by Russell, the dynamical Laws of Nature are functional relations without any intrinsic direction of determination.

Russell (1913 p1)writes:

Certain differential equations can be found, which ... given the configuration and velocities at one instant, or the configurations at two instants, render the configuration at any other earlier or later instant theoretically calculable. That is to say, the configuration at any instant is a function of that instant, and the configurations at two given instants. this statement holds throughout physics and not only in the special case of gravitation.

There is no direction or asymmetry in the determination. Later events determine earlier ones, as surely as earlier ones determine later ones. Russell thought that these laws to be so different from causal relations as traditionally conceived that it is misleading to think of them in causal terms at all.

Russell gave two main reasons for rejecting the causal interpretation of the dynamical laws:

1. Causal relations incorporate temporal asymmetry - dynamical laws do not.
2. Causal beliefs relate to localised events - dynamical laws relate global system states.

Russell continues:

The laws of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm

While our fundamental physical theories are globally deterministic and thus automatically time-symmetrical, it is interesting to note that the nomological character of physical law persists even if physical law is not deterministic:

A law L is time-reversal invariant just in case, for every trajectory (S_i, S_1, S_2, s_3 ... S_f) there is a history (S_f, S_f-1, S_f-2 ... S_i) which reverses the sequence, that is also compatible with L. If L is not time-reversal invariant, then there are physically possible trajectories whose time-reversal is physically impossible. But this does not help us recover causality into physical law, or an intrinsic direction of determination in nature. We still are unable to declare whether the nomological predecessor, or successor that determines the other.

Nomological relationships do not have an intrinsic direction of determination, they are just constraints on the joint values of variables.

Just thought this needed to be clarified, due to intense confusion revealed in other threads.

apokrisis

Russell gave two main reasons for rejecting the causal interpretation of the dynamical laws:

1. Causal relations incorporate temporal asymmetry - dynamical laws do not.
2. Causal beliefs relate to localised events - dynamical laws relate global system states. — tom

Yes, but "laws" are a calculational machinery and so they have to represent the holism of nature indirectly. You get time-reversal because time itself has to be taken for granted as a backdrop dimension not accounted for by law.

So in QM, you almost have a time~energy complementarity, but not quite as QM still needs to presume time as background dimension. And to get to quantum gravity, that is why we would need an emergent story on time - one that explains its irreversibility in first principles fashion. We kind of have that already with statistical mechanical models of thermal time, but that too has to presume a fixed basis rather than being a fully emergent story. Somehow a state of low entropy must be rigged to create a start point down which time then flows.

So the story is just that time - representing change itself - has eluded its own fundamental theory. We need it as a globally fixed backdrop to make a local calculational approach possible. But we also know that time must be an emergent property of the cosmological system.

It is right to say a certain understanding of causality - as localised/deterministic chains of cause and effect - is thus an over-idealisation. Newtonian mechanics is certainly a powerful calculational framework despite its time-symmetry. Likewise SR, GR, QM and even statistical mechanics. But the metaphysics of physics already tells us that something bigger has to be going on. We know we can't just believe time-symmetry applies in the global fashion that is implied by its local presence.

Physics is founded on three general principles - the principles of locality, cosmology and least action. So standard "causation" is represented in the principle of locality. But then the cosmological principle speaks to a global symmetry - the rules of physics are the same everywhere. And the principle of least action then wires in a directionality - events take the energetically shortest path. You thus now have a holistic or systems metaphysics where there is a global tendency or finality. Everything is constrained to head in the direction that expresses the least action.

So we are working our way back towards the fuller four causes view of causality set out by Aristotle. Causality became closely identified with local chains of cause and effect through Newtonian mechanics. In taking space and time for granted as fixed backdrop dimensions, that seemed to confirm local determinism. But there was a price paid for that helpful calculational shortcut. Space and time fell outside the material dynamics being measured. They became the a-causal void, a simple unexplained stage for all the action.

That really works for us humans, living in an era when the Universe is so cold and large and classical. But as we work our way to more fundamental theories, we have to make sense of the other two principles - the cosmological and least action. And while quantum theories can make space and emergent feature, they have not yet managed to absorb time as a further emergent property of the collective. That has to be the next step.

tom

Yes, but "laws" are a calculational machinery and so they have to represent the holism of nature indirectly. You get time-reversal because time itself has to be taken for granted as a backdrop dimension not accounted for by law. — apokrisis

I was tempted to go a bit further into the global determinism of our fundamental theories, but decided not to, because the point was made, that our "calculational machinery" is nomological, it does not capture, or attempt to capture anything relating to causation.

General relativity tells us that reality is a static 4D block - quite a feat for a mere calculating machine, I think you'll agree. Quantum mechanics, when interpreted realistically and freed of metaphysical baggage, slightly disagrees. It tells us that reality is, approximately, a countably infinite set of static 4D blocks. Again, not bad for a calculating machinery. Then of course, there are theories of quantum gravitation, such as Wheeler-DeWitt, where time is completely absent.

So, no, time is not a "backdrop dimension" and is accounted for, and these accounts have experimental support.

https://medium.com/the-physics-arxiv-blog/quantum-experiment-shows-how-time-emerges-from-entanglement-d5d3dc850933

apokrisis

General relativity tells us that reality is a static 4D block - quite a feat for a mere calculating machine, I think you'll agree. — tom

You mean SR? And you mean that SR is a physical model that hardwires in a global time symmetry by treating time as a spatialised dimension? So having made this big metaphysical presumption - time being a direction in which you can go backwards and forwards just as happily as any of the three spatial dimensions - you then have this extraordinary metaphysical consequence of a block universe when you extrapolate the said model beyond its limits of usefulness?

This seems to be the same mindset in which you approach all your physics. If some bit of calculational convenience works for certain modelling purposes, you then happily believe whatever ridiculous scenario appears to be the case if the model is extrapolated to be the whole ontic story.

But the map is not the territory. It's just the map.

tom

You mean SR? And you mean that SR is a physical model that hardwires in a global time symmetry by treating time as a spatialised dimension? — apokrisis

No, I typed general relativity, because I meant general relativity, according to which, we inhabit a 4D static bloc universe.

MetaphysicsNow

↪tom

Moving things on to another thread does not make you any more correct.
As Uber pointed out to you there are differential equations used in mechanics which are not time-invariant and so do display asymmetry that one would require for them to be modelling causation.

But this does not help us recover causality into physical law,

Maybe, maybe not. If you take the view that - whatever might have motivated their construction - physical laws are purely formal models, of course they have nothing to say about causation, since the issues about causation only become relevant when dealing with interpretations of those models. However, you think that physical laws must be more than merely formal models, then it will depend on the interpretation you feed into the purely formal parts that will determine whether or not there is causal asymmetry involved.

Philosophy of science has moved on since Russell. I suggest you do a little catching up.

apokrisis

↪tom

The block universe was consequence of Minkowski space, so no idea what you are on about in emphasising GR as your speculative basis here.

tom

The block universe was consequence of Minkowski space, so no idea what you are on about in emphasising GR as your speculative basis here. — apokrisis

Literally the first Google result.

https://plus.maths.org/content/what-block-time

and the second

https://plus.maths.org/content/stuff-happens-block-time

and the third

https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)

...

apokrisis

↪tom

So to be clear, you mean to deny that the block universe was already a consequence of SR? We had to wait for GR?

The Nomological Character of Physical Laws

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