The "Laws" of physics

kgbgru

In physics and math we often talk about the laws of nature. I have never liked to call these laws. My first diff EQ treacher felt the same. He liked to call them "really good aproximations". I perfer to think of them as equations that relate quanties in nature, or "relationships" we see in nature. I am curious to how others think of others think the math we use to describe our universe.

Q_Goest

Good question. There was an interesting article in Scientific American that can be read online here.

One description of a law I liked was here:
I wouldn't say the laws of nature are our mathematical models. We come up with models such as F=ma that are aproximations to the patterns seen in nature, but they are not the physical laws written out in mathematical form. These are only models of what is occuring.

I think the most difficult issue we deal with in defining what a law is, is separating what's controlling the physical occurances we see from the mathematical models we attribute to those causes. In other words, physical laws are the 'framework' that the patterns (or physical occurances) we see in nature must abide by. Our models are not the laws themselves, they are only our representations of the laws of nature.

Pythagorean

Here's a link that has been posted here numerously in response to similar questions:

http://www.dartmouth.edu/~matc/MathD...ng/Wigner.html

brainstorm

I find it confounding when people talk about physical "laws" as if they are causes of deterministic behavior instead of generalized observations. Just because patterns are observed to be law-like in regularity doesn't make them the functional cause of the occurrences they explain. I can't think of a good example now, but I have encountered it in the past that people confused laws extrapolated from patterned observations as the cause of the observed data.

loseyourname

Well, I don't think ordinary or scientific usage of the term "law" expresses an agent of causal origination so much as a description of constrained behavior. Certainly, in the social sense, laws don't cause human behavior, but they do constrain it or at least they attempt to. When we move down the hierarchy of complexity and predictability from human decision-making to something like the path of a struck baseball, these constraints become more and more without exception to the point that we can very accurately predict the path of a baseball from facts about the collision between it and the bat.

But even here, I don't think anyone would say the laws of aerodynamics and classical mechanics cause the path of the baseball. They just constrain it and allow us to predict it.

brainstorm

Good example. I don't know if I would even give the law causal power to "constrain." I think the law is purely a representational description of generalized observations. I don't think it exists physically in the realm of the data. Forces are a different story. Those I think actually exist as causal "forces" (lol) of physical phenomena, as would something like momentum carrying energy that it delivers through a collision to another object/particle. However, to say that the law of conservation of momentum constrains a baseball from causing a bowling ball to move faster than it after a collision is false, imo. The bowling ball would never be inclined to move faster than a baseball colliding with it in the first place, so how is it "constrained" or otherwise caused to attain whatever speed it does? To me the bowling ball just moves with whatever amount of momentum it has been imparted with by the baseball - i.e. direct determination. The laws, imo, are just representational descriptions that explain and predict regularities of observation.

loseyourname

I think you're right. Using the word "constrain" rather than "describe" or "predict" does imply a causal relationship I don't mean to imply.

apeiron

Why not go the next step and accept constraints as causal?

In "larger" models of causality - from Aristotle's four causes to systems science and holism today - there really is no problem in treating constraints as top-down causality.

Global constraints emerge via self-organisation (which is why it is tempting to treat them as secondary and non-fundamental - and so just "effects") but they are still causal in that they shape the potential for local actions. They actively restrict the local degrees of freedom - the very degrees of freedom that are supposed to be "causing" the system to be in the first place.

Dickfore

This guy called it that. Altough appeal to authority is a logical fallacy.

brainstorm

You don't see the problem with saying that the conservation of momentum "causes" a bowling ball to roll slower than a billiard ball that collides with it? The cause of the bowling ball's motion is the energy it receives from the billiard ball. Conservation of momentum is just an explanation for why the velocity results of momentum vary according to mass. There is no constraint because there is no inclination to behave in any other way than what is directly determined.

apeiron

I don't see any problem with smaller models of causality - reductionist ones that invoke just local efficient cause. You can model the world that way. But I am saying that the larger model is a truer account.

The reason for inertia is a famous problem for strictly reductionist accounts. That's why Mach suggested the universe itself must provide the reference frame, the ambient back-drop of constraint.

Calling inertia a property locally inherent in mass clearly is not an explanation that ultimately satisfies people, even though it makes for the simplest models.

brainstorm

I'm not talking about how true or false a generalization or observed pattern is. I'm talking about empirical causation verses observed patterns. Observed patterns don't cause anything empirically, regardless of how well they explain or predict observations. I think you have to be able to distinguish between empirical causes at the material level and explanations and modeling at the level of discourse. Laws are discursive, not part of the material systems they describe/explain.

apeiron

The magnetic field of a bar magnet is an observed pattern - a global state of organisation. It is caused by atomic dipoles lining up as the hot metal cools. And the emerging field is also causing the dipoles to line up. The emerging field becomes a global constraint on local behaviour.

planck

Yes, but can approximations be good enough to successfully create a self-sustaining....machine, universe, take your pick.

I think that's the main reason, at least for me, why laws must remain immutable.

Redsummers

Let's first think about the language we use to express those 'laws' (or a way to predict such and such phenomenon). I think in mathematics the formulas and the platonic forms of those concepts are equal. Take for instance a circle. No matter how even you draw it, it will never be perfect. But the equation expresses a perfect circle; and if you could make it general enough, it could also express all circles. Hence it becomes the “circleness” from the platonic form.

So in this way, mathematics becomes the tool to describe this one little aspect of the platonic realm (the circle). Nevertheless, mathematics are not the platonic form, they just help us express it, and we could have used any other language as long as we express these concepts correctly. Remember that we created the language of mathematics, in order to discover other concepts, hidden, in this platonic realm of mathematics. The number ten, as '10', does not exist in this 'platonic realm' but just the concept of ten units. Look at spiders, they reproduce with each other and they have an intrinsic number kept in their nature: they must create other spiders with exactly eight legs.

Now, going back to how do we apply this to physics (which doesn't seem to be a big deal, since physics is mainly represented by mathematics) we should first come to reality and find a mathematical model to express this phenomenon. But then this general expression, the one we made, may or may not align with the platonic form of this phenomenon.

For example, take Newtonian mechanics. We describe it in math, and the concepts expressed with math are what we believe is it's most general form –it's platonic form. We may be wrong, because we can absolutely never be 100% sure that the general form that we outlined in mathematics (our guess as its platonic form) accurately describes the perfect form of this phenomenon. And that is basically the main difference in mathematics and physics.

Due to the fact that we have to ground everything in reality, we have to check all our math physics in reality –this leads to logical induction- which is not proof. We can see a planet orbit a circle, and we think that orbit is a circle, and we can guess that it orbits a circle, and predict and check. And a million times out of a million it will always be on that circle. But that doesn’t guarantee that the millionth and 1 time it will still be a circle. It seems to us crazy that it could not be, (and I mean, it will be) but the point is it’s not proven.

In math, we lose the reality step. We create the formula for a circle –then we have the concept of a circle. We don’t really care that circles exist or not in reality, and because of that we can use deductive logic. That uses proofs. Mathematics is the only subject that
can prove it’s postulates. All other subjects use induction ( and again, logical induction is much different from mathematical induction and isn’t the same thing at all, mathematical induction unlike logical induction is a rigorous proof).

This is why the incompleteness axiom is a huge blow to math, but doesn’t really matter for physics. Because all of a sudden, the only thing ever proved might be proved on bad foundations. But physics was never proved anyway, physics is just really really really
good guesses which for the majority of it will certainly not be disproved, but that doesn’t mean its proven rigorously. So the incompleteness thing just says that it can’t be proven rigorously –well that’s no problem because physics wasn’t anyway. So at the end of the day it doesn’t really matter.

However, I don't know –I'd say nobody does– if there is really a link between physical phenomena and the mathematics realm. I'd say there is none. Still, I like Maxwell's laws, I like the mathematics of it; and I will probably keep on calling them 'laws', even if that would make me an hypocrite, I mean in this case is just a word. Another example I would like to mention is that of String theory, there is no doubt that there are 11 dimensions in the theory (of course not, in the mathematics of it is well stated), but we cannot tell whether a correct proposition of a language –in this case mathematics– corresponds directly to a true-proposition as for in the reality –the platonic form of the physical phenomenon.

Redsummers

I don't wanna be a spammer here, but I was just thinking, and instead of law, we could just use Thomas Kühn's word for this: paradigm.
He gives a nice definition of this term, and yes its definition is basically what I was explaining in that last post. But nowadays –as well as one century ago–, that most of the scientists have understood the scientific method, they still call these paradigms 'laws'. I would like to believe that in the quantum revolution, the physicists such as Heisenberg, Dirac, Bohr, etc. already had a positivist idea of science (which later evolved to the actual scientific method).

apeiron

If you don't like the term laws, there are alternatives like CS Peirce's use of "habits". From a self-organised constraints point of view, the universe evolved a set of self-consistent regularities.

But the "laws of physics" are given a commonsense interpretation based on the acceptance that science is only modelling reality - it is making a useful, rather than necessarily "truthful" map of the terrain.

So in this view, mathematics is our most precise language for making mapping-type statements - constructing formal models. We can then measure reality against our idealised concepts of it. Maths seems rather detached from physics because you can draw all kinds of maps of imaginary worlds. It is a landscape of free play that lacks constraints (edit: or rather internalises its constraints by way of axioms). But science is the activity of mapping constrained by a reality.

Wiki has a good page on what people generally understand by "physical law".
http://en.wikipedia.org/wiki/Physical_law

(I'm not agreeing with all these statements, but they show there is a considered view - something definite and coherent to argue against).