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What do the laws of physics describe? Do they describe the properties of the universe? Or does the properties of the universe described by physical theories, and laws describe how those theories work?

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Laws and properties work together in physics. The laws - such as Newton's three laws of motion and law of universal gravitation, Maxwell's equations, the laws of thermodynamics, Boyle's law, the Navier-Stokes equations in fluid dynamics and Einstein's equations of general relativity - tell us how objects in general will behave. To apply these laws to specific objects or substances we need to know some properties of those objects or substances, such as mass, momentum, charge, pressure, density, temperature, viscosity etc.

Sometimes the laws are approximations and we know they are only good approximations in certain scenarios. Newton's laws are only good approximations at non-relativistic speeds and in weak gravitational fields. The Navier-Stokes equations only apply to Newtonian fluids. Boyle's law only applies to ideal gases. Usually we know how in principle to modify approximate laws to work in more complex scenarios. The big exception to this is the conflict between general relativity and quantum mechanics, which we do not know how to resolve at present.

There is another layer behind all these separate laws. We observe that the properties of objects do not change at random. Instead, the universe conforms to certain fundamental underlying principles such as conservation of mass/energy, momentum, angular momentum, and electric charge, which restrict how the properties of objects can change. These conservation principles are related to symmetries of spacetime and symmetries of quantum fields in quantum mechanics. The link between conservation laws and symmetries is called Noether's theorem.

All of these laws and properties are based ultimately on experimental observation. If we ever observed an object whose mass/energy, momentum, charge etc. changed at random we would have to re-think some of these laws. But physicists have such a high confidence in these laws (and especially in the underlying conservation principles) that when experimental outcomes or observations appear to contradict them, the first reaction is to look for some alternative explanation that keeps the laws intact. Sometimes this leads to the discovery of new particles (such as the neutrino or the Higgs boson); sometimes the search for new particles is still ongoing (dark matter is an example of this).

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  • $\begingroup$ But still, at a fundamental level, laws do reflect the properties and behavior of the universe, right? $\endgroup$ – Arman Armenpress Nov 27 '20 at 13:12
  • $\begingroup$ @ArmanArmenpress Yes, as far as our current knowledge extends. We can never say more than that. $\endgroup$ – gandalf61 Nov 27 '20 at 13:46
  • $\begingroup$ That is, laws do not exist separately from the universe. Laws are how the universe works. $\endgroup$ – Arman Armenpress Nov 27 '20 at 13:58
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    $\begingroup$ @ArmanArmenpress I am taking about the human laws of physics that we have discovered over time and that are our best model of how the universe behaves based on our current state of empirical knowledge. I think you are talking about some Platonic ideal set of rules that the universe follows independently of human thought. We have no idea whether such Platonic laws exist, and, if they do, we have no way of revealing them - otherwise we could short-cut all of science. $\endgroup$ – gandalf61 Nov 27 '20 at 15:09
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    $\begingroup$ @ArmanArmenpress We have no idea what the "internal properties" of the universe might be. All we can do is observe its external properties - how objects behave - and then come up with models that we hope will predict how similar objects will behave in the future. The laws of physics are these models. If we find data that does not fit our models then we may have to change them, but this does not change the universe itself. $\endgroup$ – gandalf61 Nov 27 '20 at 16:25
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Predictive power. This is the answer to your question. The laws of physics are a mathematical description of the universe giving us the phenomenological power of predicting the behavior of the universe.

Now this behavior of the universe (and our laws) can be questioned whether it is the same in different places and whether it changes over time.

Do the laws of physics work everywhere in the universe?

Do the laws of physics evolve?

We then do experiments, and they justify the theories we developed over the years and some of them become laws. As we progressed over the years developing newer and newer theories, some of the old ones are replaced by new laws because the new theories have a better predictive power, and thus help us to have a better understanding of how the universe works.

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  • $\begingroup$ For me (as a German) the English term "predictivity power" is not very common. I translated from DeepL and found simply "predictability". (Curiously, the word "Vorhersagekraft" also exists in German and is also very appropriate. Only in English I can't do much with it). $\endgroup$ – HolgerFiedler Nov 28 '20 at 6:57
  • $\begingroup$ @HolgerFiedler thank you so much! $\endgroup$ – Árpád Szendrei Nov 28 '20 at 16:02
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The easiest answer is that the laws of physics sum up our experimental observations so far. For example, Maxwell's equations summarize the results of all electromagnetic experiments so far, i.e. all results of those experiments can be predicted using those equations / laws.

Insofar as "the properties of the universe" is the same as "what we have observed experimentally so far", then yes, the laws of physics describe the properties of the universe. That connection, however, is more in the realm of philosophy than that of physics.

For further reading into perspectives on the relationship between physical theories and the nature of reality, I recommend checking out the excellent essay contests hosted by the Foundational Questions institute. A personal favorite is the contest on the "mysterious" connection between math and physics.

To maybe address your question better, what makes physical theories work is that they are logically consistent due to being based on math. The logical consistency of math is real but does not seem to be a physical quality, but then that depends on whether you accept that there exists both physical and non-physical qualities of reality.

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The laws of physics are nothing but our understanding of how the universe works written in the language of mathematics that we have developed over the past.

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