Did nature or physicists invent the renormalization group?

In summary, the renormalization group is a systematic theoretical framework and a set of elegant (and often effective) mathematical techniques to build effective field theories, valid at large scales, by smoothing out irrelevant fluctuations at smaller scales. But does the renormalization group also describe something that nature does? If you think the question doesn't make sense, please say so but also explain why.
  • #1
Giulio Prisco
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Or in other words:

The renormalization group is a systematic theoretical framework and a set of elegant (and often effective) mathematical techniques to build effective field theories, valid at large scales, by smoothing out irrelevant fluctuations at smaller scales.

But does the renormalization group also describe something that nature does?

If you think the question doesn't make sense, please say so but also explain why.
 
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  • #2
Whether physics describes nature or not is a question for experiments and you can only test quantitative predictions. You can never test whether nature ”actually does” something. That is a purely philosophical question. All you can say is ”nature behaves in accordance with the observable predictions of the the theory”.

That being said, I think you should regard the RG as more of a computational tool than as a theory of its own.
 
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Likes bhobba, Giulio Prisco, dextercioby and 1 other person
  • #3
This question extends towards mathematics as a whole, not only some theoretical physics formalism.

Is mathematics a part of nature? Is it discovered or invented?
I actually like to think that mathematics is the underlying algorithm of the world. We do not invent it, we discover it. The only thing we invent are the symbols like for numbers or signs.

On the other hand, a mathematician can start form all kinds of crazy axioms, that he might have invented himself, and carry out the logic to get to new results. Even if the axioms themselves can't be found in nature. So it's really not that simple.
 
  • #4
Physicists are part of nature.
 
  • #5
Orodruin said:
You can never test whether nature ”actually does” something.

Right of course, but intuitive mental models of "what nature actually does' are useful thinking aids.

Orodruin said:
That being said, I think you should regard the RG as more of a computational tool than as a theory of its own.

Thanks, this is the answer I was looking for.
 
  • #6
Giulio Prisco said:
Right of course, but intuitive mental models of "what nature actually does' are useful thinking aids.
I respectfully disagree. Intuitive models serve only as thinking aids (and it is unclear what should be labled ”intuitive”). I think you should not mistake that for ”nature does this”.
 
  • #7
Orodruin said:
I respectfully disagree. Intuitive models serve only as thinking aids (and it is unclear what should be labled ”intuitive”). I think you should not mistake that for ”nature does this”.

I don't - but I am also persuaded that would be unable to think effectively without intuitive models. I need intuitive models, even if they are not entirely right or mostly wrong.

"Intuitive" is something that you understand quickly, easily and permanently. Of course, what is intuitive for me may not be so intuitive for you and vice versa.
 

1. What is the renormalization group?

The renormalization group is a mathematical framework used in theoretical physics to study how physical systems behave at different scales. It allows physicists to understand the behavior of a system at both small and large scales and is particularly useful in understanding complex systems such as phase transitions and critical phenomena.

2. How does the renormalization group work?

The renormalization group works by iteratively rescaling a system, analyzing its behavior at each scale, and then using that information to make predictions about the behavior of the system at larger or smaller scales. This process is repeated until a desired level of precision is achieved.

3. Did nature or physicists invent the renormalization group?

The renormalization group was first developed by theoretical physicists in the 1960s as a tool for understanding quantum field theory. However, the concepts behind the renormalization group have since been applied to a wide range of systems in nature, suggesting that it may be a fundamental aspect of how nature behaves.

4. What are some practical applications of the renormalization group?

The renormalization group has been used to understand a variety of phenomena in physics, including phase transitions, critical phenomena, and the behavior of complex systems. It has also been applied to other fields, such as economics and biology, to study complex systems and their behavior at different scales.

5. Can the renormalization group be used to solve all problems in physics?

No, the renormalization group is a powerful tool, but it is not a universal solution for all problems in physics. It is best suited for studying systems that exhibit scale invariance, and it has limitations when applied to highly nonlinear systems or systems with strong interactions. Other mathematical techniques and approaches are needed to fully understand and solve these types of problems.

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