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Can you disprove this please because it's been bugging me and I don't know much about physics at all as I'm only in 10th grade. It's one of those weird thoughts but I would like confirmation to keep it off my mind: at first there were the laws of math which are fundamental and simple not complex like arithmetic. Like 2+2=4. It is universal because always 2 apples and 2 apples will give you 4 apples exactly not 5 or 6. Same for atoms. This concept exists always and is absolute. So we have something absolute. This absolute knowledge of mathematics give rise to physical laws which are compatible with these mathematical laws. Like conservation and other laws since in conservation before and after everything is conserved just like both sides of the equation in math. So math gives rise to physical laws. And these specific physical laws compatible with math gives rise to our universe.

Qmechanic
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Soha
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    Can you tell me a single physical law that was given rise to by math without having been experimentally observed or confirmed at some point ? – Kurt G. Aug 06 '23 at 19:08
  • Physics without math is speculative, an example is an ansatz. You can use an ansatz without math to reach to derive a physical law by using math. – M06-2x Aug 06 '23 at 19:15
  • my answer here might help https://physics.stackexchange.com/q/399086/ – anna v Aug 06 '23 at 19:16
  • Math is no necessarily fundamental to physics. There are attempts to build physics using more general systems of rules, such as things that look more like computer programs. See for instance https://www.wolframphysics.org/ . Math is just an extremely convenient way to express rules (laws) and find their consequences (predictions of the laws), and it is not guaranteed to always work for physics (but it is doing relatively great so far) – Pato Galmarini Aug 06 '23 at 19:21
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    Math doesn't "give rise" to physical laws. Scientists make observations, plot things like motion over time, draw straight lines through the observed points. The straight lines have corresponding equations which suggest an underlying equation, ie a Law. They postulate that math equation and compare it to predictions, then use math to derive new equations from it and continue to compare with observations, making corrections or abandoning the law of it doesn't predict well. So math is a tool to model and predict reality, but doesn't "cause" reality (that we know of) – RC_23 Aug 06 '23 at 19:23
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    There has been much discussion among scientists and thinkers on the "Unreasonable Effectiveness of Mathematics" – RC_23 Aug 06 '23 at 19:27
  • @RC_23 You could have posted those comments as an answer. – StephenG - Help Ukraine Aug 06 '23 at 19:43
  • By "physical laws", do you mean the laws that govern the universe, or the laws that govern physicist's models of the universe? Those might be very different things. – WillO Aug 06 '23 at 20:53
  • @Soha you might have said "And these specific physical laws compatible with math give rise to our model of the universe," and I think most people on this site would agree. – RC_23 Aug 07 '23 at 01:41
  • I should know better. I started this yesterday. The question was closed before I finished this morning. So I will post a series of comments. – mmesser314 Aug 07 '23 at 14:40
  • First let us draw a distinction. There is the universe. It has stuff like rocks and things in it. This stuff has repeatable patterns of behavior. For example, Earth goes around the Sun. Every orbit takes the same amount of time. – mmesser314 Aug 07 '23 at 14:41
  • Then there is physics. Physics is a description of the behavior of the universe. We call the repeatable patterns laws, and we use math to describe them. – mmesser314 Aug 07 '23 at 14:41
  • So math doesn't give rise to the behavior of the universe. But it is a very important part of how we describe it. In this sense, you could sort of say that math does give rise to the laws of physics. But it might be better to think of it as a tool used to give better descriptions. – mmesser314 Aug 07 '23 at 14:41
  • Math has been used to measure things since antiquity. Some complex results were derived. For example, Archimedes used geometrical reasoning to find the volume of two intersecting cylinders. He nearly discovered calculus. Good book: The Archimedes Codex – mmesser314 Aug 07 '23 at 14:41
  • Engineering used math. But engineering was empirical rules of thumb, not based on an understanding of properties of matter or forces. For example, here is the geometrical rule used to figure out how thick the walls of an arch need to be. Building a Cathedral without Science or Mathematics: The Engineering Method Explained. The video compares the cathedral to the Pantheon. Here is more on that. Why hasn't the Pantheon's dome collapsed? – mmesser314 Aug 07 '23 at 14:41
  • But math was not used to describe the behavior of the universe, or discover things about the behavior. That was a branch of philosophy. Aristotle said all things are made from the 4 elements. The elements had natures. Earth rolled downhill and fire flowed up because that was their nature. Earth moved until you stopped pushing because its nature was to be at rest. Without mathematics, that kind of thinking is about as far as you can take descriptions of behavior. – mmesser314 Aug 07 '23 at 14:42
  • This was largely the state of natural philosophy until Galileo. Galileo discovered mathematical relationships could be used to describe motion. This fundamentally changed how we look at the world. The Biggest Ideas in the Universe | 1. Conservation – mmesser314 Aug 07 '23 at 14:42

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Math doesn't "give rise" to physical laws. Scientists make observations, plot things like motion over time, draw straight lines through the observed points. The straight lines have corresponding equations which suggest an underlying relationship, i.e. a Law. They postulate that relationship in the form of a math equation (e.g. gravity: $F=GMm/r^2$) and compare it to predictions, then use math to derive new equations from it and continue to compare with observations, making corrections or abandoning the law of it doesn't predict well. So math is a tool to model and predict reality, but doesn't "cause" reality (that we know of).

There has been much discussion among scientists and thinkers on the "Unreasonable Effectiveness of Mathematics," which may be a topic of further inquiry for you.

You might have said "And these specific physical laws compatible with math give rise to our model of the universe," and I think most people on this site would agree. Although "model of the universe" is a misleading idea, as is the term "Theory of Everything" often used, because we really do not have a mathematical or computer model of the who universe, or anything close to it. In truth we cannot even faithfully model the turbulent airflow over a single airplane wing. What we have is a collection of models that cover incredibly simple situations, which we can stitch together to predict most types of physical systems or events, as long as they are not too complex.

Quantum mechanical models tell us how a single electron in a single atom will interact with an incoming photon, or how a proton/anti-proton pair will interact in empty space, or even how a set of electrons will behave as a group in an ideal uniform conductor lattice.

General relativity can model a system of 1 or 2 astronomical bodies, or the entire "universe" idealized as a completely uniform soup of distributed matter. But there is no model that accounts for an entire galaxy of individual stars.

So physics is a patchwork of such simple models, which have been shown to be incredibly precise when the real system observed closely matches the simple model. But the complexity quickly grows to unmanageable levels in real systems, and we resort to predictions using broad approximations (which can be quite good, if done right).

RC_23
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  • "The straight lines have corresponding equations....". I'm not sure how you're going to reconcile this with "math does not give rise to physical laws", since your description of the rise of physical laws explicitly invokes pre-existing mathematics. – WillO Aug 06 '23 at 20:51
  • It's hard for me to interpret the original question exactly, but the sentence "And these specific physical laws compatible with math gives rise to our universe." suggests the idea that mathematics creates reality, or that electrons do math as they travel and interact. I was eschewing this notion, since mathematics allows us to make predictions about physical events, but physical events to not "do math" in order to work (at least as far as we know). – RC_23 Aug 07 '23 at 01:39