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

AI Thread Summary
The discussion centers on whether all laws of nature can be expressed as simple, single equations. Participants argue that while complex equations can be simplified to a form like A=0, this does not necessarily qualify as "simple." The conversation also touches on the nature of scientific laws, emphasizing that they are derived from observations and operate within specific limits. Additionally, the concept of beauty in scientific equations is debated, with some asserting that beauty is objective and linked to symmetry and conservation laws, while others argue it is subjective. Ultimately, the dialogue highlights the ongoing challenge of reconciling different scientific theories, such as quantum mechanics and general relativity.
shivakumar
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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?
 
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shivakumar said:
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?
 
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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.
 
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"?
 
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shivakumar said:
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.
 
shivakumar said:
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.
 
phinds said:
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.
 
Dale said:
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.##

phinds said:
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.
 
fresh_42 said:
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.') :rolleyes:
 
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Tom.G said:
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.
 
  • #11
Tom.G said:
(remember that 'Beauty is in the eye of the beholder.') :rolleyes:
I do not share this opinion. I think that beauty is objective, not subjective.
 
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  • #12
fresh_42 said:
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?
 
  • #13
fresh_42 said:
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)
 
  • #14
sophiecentaur said:
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.

javisot20 said:
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.
javisot20 said:
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.
javisot20 said:
(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.
 
  • #15
fresh_42 said:
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.
 
  • #16
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.
 
  • #17
fresh_42 said:
You see, things become automatically philosophical when discussing terms that cannot be rigorously defined.
Beautifully said
 
  • #18
PeroK said:
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.
 
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