Can all the laws of nature always can be written in simple single equations alone?

[shivakumar]

TL;DR

can all the laws of nature always can be written in simple single equations alone?

do we have laws of nature discovered that form a set of equations which use different formula in different set of parameters?

 

[PeroK]

TL;DR Summary: can all the laws of nature always can be written in simple single equations alone?

do we have laws of nature discovered that form a set of equations which use different formula in different set of parameters?

How do you define simple, single and different?

 

[Albertus Magnus]

I don't know if there is anything we can't understand with Hamilton's principle of least action and the law of increase of entropy.

 

[Dale]

You can always take any system of arbitrarily complicated equations and write it as $A=0$ where $A$ is defined as some sequence where each element is defined by one of your complicated equations.

For example, Maxwell's equations can be written as $A=0$ for $$A\equiv \left\{ \nabla \cdot D - \rho, \nabla \times H - J - \frac{\partial D}{\partial t}, \nabla \cdot B, \nabla \times E + \frac{\partial B}{\partial t}, D - \epsilon_0 E - P, H -\frac{1}{\mu_0}B + M\right\} $$

So does $A=0$ count as a "simple single equation"?

 

[sophiecentaur]

TL;DR Summary: can all the laws of nature always can be written in simple single equations alone?

do we have laws of nature

The word "law", when used in Science, is not the same as a law of a government or a church. Scientific Laws are principles which have emerged from observations and experiment. The laws we use and apply involve the simplest model that can be used for phenomena. All our laws of Science operate over a limited range; there's always some other factor that interferes with the basic law in practice. That is no reason to discard the statement of a law.

"Nature abhors a vacuum" is a pretty crude statement. It's a principle that can be seen to operate in many situations but it falls down because there no numbers associated with it. We can do better.

 

[phinds]

do we have laws of nature discovered that form a set of equations which use different formula in different set of parameters?

No. At the very least, we still have no idea how to formulate quantum gravity.

 

[DaveC426913]

No. At the very least, we still have no idea how to formulate quantum gravity.

Or reconcile GR with QM (which another way of saying what phinds said).

They are two excellent, extremely well-verified, rigorous theories. But they are incompatible.

 

[fresh_42]

You can always take any system of arbitrarily complicated equations and write it as $A=0.$

Yes, but $F\sim \ddot x$ is so much nicer than $F-m\ddot x=0.$

No. At the very least, we still have no idea how to formulate quantum gravity.

I had to think about, IIRC Bine's comment about "the dictate of beauty" that rules physics. As a mathematician, I am convinced that theorems or physical laws have to be beautiful - like my example of $F\sim \ddot x$ or Maxwell's equations above - or we wouldn't have completely understood the matter otherwise. However, there is a chance that this idealistic point of view is incorrect and Bine is right that such a theory might not be beautiful and this is what hinders us from finding it.

 

[Tom.G]

I am convinced that theorems or physical laws have to be beautiful

Or do we consider them beautiful simply because we ourselves are a product of those laws?

(remember that 'Beauty is in the eye of the beholder.')

 

[sophiecentaur]

we ourselves are a product of those laws

I'm not sure about that. There have been many Scientific theories which have been proved incorrect but they were often regarded as beautiful despite our not being 'built' according to them. I'd say, rather that a statement (including statements of Scientific relationships) will appeal if it manages to condense / paraphrase an explanation / rule in a concise form. Our brain spends all its time trying to do this with al its input so there's no wonder we feel smug when we read E=mc² and we 'get' what it stands for.

 

[fresh_42]

(remember that 'Beauty is in the eye of the beholder.')

I do not share this opinion. I think that beauty is objective, not subjective.

 

[sophiecentaur]

I think that beauty is objective,

Admitted, there are often 'points' allotted in the assessment of beauty but no two people agree about beauty. How then is it objective?

 

[javisot20]

I do not share this opinion. I think that beauty is objective, not subjective.

If you relate beauty to symmetry and symmetry to conservation laws, and further demand that "objective" means "experimentally confirmable," then yes, beauty is objective.

(if you use another definition, no)

 

[fresh_42]

Admitted, there are often 'points' allotted in the assessment of beauty but no two people agree about beauty. How then is it objective?

This is difficult to discuss here without drifting into philosophy or into an argument. It is my opinion, and even a personal opinion is apparently hard to tolerate for some users here. Some here always comment with skepticism as soon as things are not conform to their own opinions. Sad.

If you relate beauty to symmetry and symmetry to conservation laws, ...

For example. However, the golden ratio is beautiful but not symmetric. At least not visually. There are mathematical symmetries though.

and further demand that "objective" means "experimentally confirmable," then yes, beauty is objective.

Not really, since mathematical beauty doesn't require experiments. I don't understand enough about physics to assess the relevance of experiments concerning beauty. I tend to refuse this part of your definition since measurements always have an ugly noise.

(if you use another definition, no)

I do. I think beauty is a matter of education, not a matter of taste. However, I cannot rule out that both could be related.

 

[PeroK]

This is difficult to discuss here without drifting into philosophy or into an argument. It is my opinion, and even a personal opinion is apparently hard to tolerate for some users here. Some here always comment with skepticism as soon as things are not conform to their own opinions. Sad.

Saying that beauty is objective is just another way to say that what you think is beautiful is objectively beautiful and what anyone else finds beautiful is objectively wrong. The fact that we disagree (unless I'm being wilfully contrary) is proof that these things are subjective.

You might find your family beautiful and I might see them as ordinary human beings. There is nothing wrong in that unless you demand that they are objectively beautiful to the whole world.

 

[fresh_42]

Thinking about it, I think that the experimental confirmation part can be called beautiful. That would be decoupled from noise and only emphasize that the discrepancy between ideal formulas and observations is negligible. A real world confirmation of what can be called an idea in Plato's sense. Yes, I think that's beautiful.

You see, things become automatically philosophical when discussing terms that cannot be rigorously defined.

 

[gmax137]

You see, things become automatically philosophical when discussing terms that cannot be rigorously defined.

Beautifully said

 

[fresh_42]

Saying that beauty is objective is just another way to say that what you think is beautiful is objectively beautiful and what anyone else finds beautiful is objectively wrong.

That is my opinion, yes. It needs understanding to call something beautiful (aesthetic) or not. Without this understanding, it is simply a worthless opinion that led to the beholder's eye idiom.