Are Physics Models Truly Simple or Inherently Complex?

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Discussion Overview

The discussion revolves around the complexity and simplicity of mathematical models that describe the laws of physics, with a focus on various domains such as general relativity, quantum mechanics, and classical mechanics. Participants explore definitions of simplicity and complexity in the context of physical laws and their interactions.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants argue that the complexity of physical laws varies significantly depending on the specific laws being discussed, with quantum physics and fluid dynamics being labeled as complex, while Newton's laws and special relativity are considered simpler.
  • One participant suggests that general relativity might be viewed as simpler than complex, but questions the definitions of "simple" and "complex" in this context.
  • Another participant emphasizes that physical constants are not laws of physics, which are instead defined as statements about physical reality that must be falsifiable.
  • There is a viewpoint that while the laws themselves may be relatively simple, their interactions can lead to complex phenomena, such as in weather systems, which require extensive computational resources to model accurately.
  • A participant humorously notes that the term "complex" in mathematics refers to having an imaginary component, highlighting the need for clear definitions of "simple" and "complex."
  • Concerns are raised about the perceived simplicity of general relativity, citing the lengthy time it took for physicists to understand and accept it, and the ongoing debates about its mathematical formulation and interpretations.
  • One participant reflects on the idea that while formulas may be computable, this does not necessarily mean they are understandable by humans, indicating a distinction between calculability and comprehension.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the definitions of simplicity and complexity in physics. There is no consensus on whether the laws of physics can be categorized as simple or complex, as interpretations vary widely based on context and specific laws discussed.

Contextual Notes

Participants highlight the ambiguity in defining "simple" and "complex," which affects the discussion. Additionally, there are unresolved questions about the nature of physical laws and their relationships to physical constants.

revo74
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Are the mathematical models which describe the laws of physics considered simple or complex?
 
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revo74 said:
Are the mathematical models which describe the laws of physics considered simple or complex?
It depends. What laws of physics are you referring to?

If you are talking about quantum physics or fluid dynamics the laws are very complex. If you are talking about Newton's laws of motion and gravity, the laws are much simpler. General relativity is quite complex but special relativity much simpler. Etc. Etc.

AM
 
Andrew Mason said:
It depends. What laws of physics are you referring to?

If you are talking about quantum physics or fluid dynamics the laws are very complex. If you are talking about Newton's laws of motion and gravity, the laws are much simpler. General relativity is quite complex but special relativity much simpler. Etc. Etc.

AM

I'm talking about the laws of physics at the level of general relativity, not quantum mechanics. In general they would be considered more simple than complex right?

The physical constants are the laws of physics, however, are there any laws of physics which are not physical constants?
 
revo74 said:
I'm talking about the laws of physics at the level of general relativity, not quantum mechanics. In general they would be considered more simple than complex right?

The physical constants are the laws of physics, however, are there any laws of physics which are not physical constants?
You will have to define what you mean by simple and complex.

Your definition of a law of physics is not correct. A physical constant is simply a number, not a law of physics.

A law of physics is a statement of how some aspect of physical reality behaves under a certain range of conditions, or in general. The law must be falsifiable (in the sense that the law predicts behaviour that is capable of being observed) but not falsified (no physical evidence has been found that conflicts with the law).

AM
 
I think the actual laws are "relatively simple", but the way they all interact can get mindboggingly complex. Like weather for example...it might arize from a few simple rules, but when you try to add it all up on a global scale and in decent detail, you'll need a pretty damn big supercomputer to even try to scratch the surface of a model that replicates reality.
 
Complex in mathematics = possessing an imaginary component.

The theories that describe physics are indeed complex!

(A cheeky answer, I know, but this highlights the need to properly define what you mean by "simple" and "complex".)

Claude.
 
No one should claim general relativity is "simple' when it took physicsts some 20 years at it's introduction to gain a reasonably full understanding and general acceptance...

Just read some of the LENGTHY discussions in these forums about the mathematics formulation of GR and how to interpret what they mean.

From SR comes the idea that space and time are interchangeable entity components; from GR, that gravity is really the curvature of space and time...I don't believe anybody thinks those concepts are "simple"...but ARE understandable when someone explains them...

If either GR or QM were simple they would have been unified by now within quantum gravity...and we'd know what dark matter and dark energy is.

On the other hand Feynman said "Nobody understands quantum mechanics" and "shut up and compute" meaning follow the rules and formulas and donl't get side tracked trying to figure out what they mean...because you'll never get agreement on what they mean...scientists still argue about the "meaning" today...
 
I guess when I said "relatively simple" I meant that you can plug the formulas into a computer and it will be able to "understand" them...and the formulas don't require volumes of space (although honestly I'm not sure about that).

Still, I left it in quotes because "relatively simple" is highly debatable, especially since, as has been mentioned, "simple" hasn't been defined.

And also, just because they're calculable doesn't necessarily mean they have to be understandable by humans. Which, as has been said, a lot of them aren't.
 

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