The Math of Physics: Exploring Physical Phenomena

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In summary, the goal of physics is to make quantitative predictions. Any physical phenomena that exists can be represented with mathematical equations.
  • #1
thetexan
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Since math is such an important part of physics I was wondering...

Why so? Is it assumed that any physical phenomena (and I mean any conceivable physical phenomena from quantum to cosmological) that exists, known or yet unknown, can be explained with a mathematical formula or equation thus necessitating the endless math involved?

Or...and in conjunction with the above...the math will prove the phenomena or at least predict it. Take e=mc^2 for example. Was Einstein searching for a formula or did it reveal itself by accident? (retorical question)

Let's say string theory as another example. Why all the math? What is the purpose? (this is more than a stupid question). Is the goal to find a formula that works each time it is applied to string ideas thus making a prediction that works every time thus proving the theory?

It just seems to me that there is a universal belief that there will be a math equation or formula for anything. Or better stated...anything that can be observed can be modeled with math, and if that math hasn't been found...YET...it will be with enough research? In other words, all puzzles CAN be solved with math given enough effort. Is this the idea?

tex
 
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  • #2
thetexan said:
Since math is such an important part of physics I was wondering...Why so?
Because the goal of physics is to make quantitative predictions.
 
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  • #3
I think, you're overthinking it. Maths is just a hardcore approach to logical reasoning. And if your goal is to describe reality in a rigorous fashion, what else would you use? Faulty reasoning? Illogical reasoning? Magical thinking?

The only assumption necessary for this approach is that the universe is indeed logical.
 
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  • #4
I guess I made my question more complicated than it needed to be. Here is the real issue that I think will answer my main wonderment...

Is it assumed to be a fact that any physical phenomena, regardless of what it is, from quantum physics to the biggest cosmological physics, can be represented with mathematical equations?

It seems that if any phenomena, known or unknown, exist, then it exists and works in some way that must, as you say, be logical. And if it operates logically, then the language of logic, mathematics, must, by definition, be able to represent it. It just becomes a matter of figuring out the representation.

Is this correct?

tex
 
  • #5
thetexan said:
Is it assumed to be a fact that any physical phenomena, regardless of what it is, from quantum physics to the biggest cosmological physics, can be represented with mathematical equations?
Nobody assumes this. A physical phenomena is something which can be measured or in general be observed. A measurement is by its nature a comparison with a scale, which gets numbers and units involved. It is furthermore often a change of state, so time as a parameter comes in. The requirement to express all these as uniquely as possible, and at the same time as understandable as possible, brings in logic, numbers and mathematics in a natural way. And the big advantage is: If there is no mathematical language to express an observation, no problem, then a calculus will be developed. Such mathematics is not at the beginning of physical observations as your statement suggests, but their natural fellow traveler.
 
  • #6
thetexan said:
Is it assumed to be a fact that any physical phenomena, regardless of what it is, from quantum physics to the biggest cosmological physics, can be represented with mathematical equations?
Firstly, when considering well known classical Physics, situations are just better explained using Maths. When you read the laboured way that phenomena used to be described 'just' in words, it is not surprising that Science was highly esoteric. You could say that, literally, "word's cannot express" some things. Appropriate Maths was devised to make such descriptions possible. Over the years, Maths has developed to follow the demands of Science. Trust me, they didn't invent maths just to annoy you. :wink:
 
  • #7
There are cases when math was developed to "follow the demands of Science". The most famous example is possibly the "calculus of fluxions" invented by Newton.
However, most of the time the math was developed for its own sake and physicist just found more and more parts of it to be "useful". A real mathematician cannot care less about the applications of the new concepts he develops. If he does, he is not a "real" mathematician. :)
I think there are also cases when physicists developed "new" mathematical methods just because they did not know they were already known to mathematicians.
 
  • #8
Eugene Wigner wrote a very famous philosophical essay called "The unreasonable effectiveness of mathematics in the natural sciences" that might interest you:

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
 
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  • #9
nasu said:
A real mathematician cannot care less about the applications of the new concepts he develops. If he does, he is not a "real" mathematician. :)
I hope this is ironic, but I fear that it is not.
 
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  • #10
As a physicist, I like to believe that math is developed for the sake of applications, especially in physics. Or even that math was developed by physicists.
However this is not the case. I did not intend to be disrespectful to mathematicians. Just to give them what is theirs.

To put it in a mathematical format, there are (and were) at least some mathematicians who believe that math is done for its own sake, for its beauty and for the intellectual satisfaction. Do you disagree with this?

Sure, the part with being or not real was a joke.
If you are a mathematician developing applications of mathematical methods, of course you are a real mathematician. Without quotes. :)
 
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  • #11
nasu said:
To put it in a mathematical format, there are (and were) at least some mathematicians who believe that math is done for its own sake, for its beauty and for the intellectual satisfaction. Do you disagree with this?
No, on the contrary.
 
  • #12
It's not always physics. It wasn't QM that started probability theory. It was in fact simple gambling :wink:
And RSA might be related to ERH, but they didn't induce each other. I still find my picture of traveling companions more suitable than any implications are, in which direction ever and how well hidden ever. And who expected to find graded algebras or cohomology theory in modern physics? Lie theory on the other hand arose from the need to solve differential equations which again likely had their origin in physical requirements, but not exclusively.
 
  • #13
thetexan said:
Since math is such an important part of physics I was wondering...

Why so? Is it assumed that any physical phenomena (and I mean any conceivable physical phenomena from quantum to cosmological) that exists, known or yet unknown, can be explained with a mathematical formula or equation thus necessitating the endless math involved?

Or...and in conjunction with the above...the math will prove the phenomena or at least predict it. Take e=mc^2 for example. Was Einstein searching for a formula or did it reveal itself by accident? (retorical question)

Let's say string theory as another example. Why all the math? What is the purpose? (this is more than a stupid question). Is the goal to find a formula that works each time it is applied to string ideas thus making a prediction that works every time thus proving the theory?

It just seems to me that there is a universal belief that there will be a math equation or formula for anything. Or better stated...anything that can be observed can be modeled with math, and if that math hasn't been found...YET...it will be with enough research? In other words, all puzzles CAN be solved with math given enough effort. Is this the idea?

tex

This is rather puzzling.

Would you ask a mechanic why he/she needs all those "tools" to repair a car? Or would you ask a linguist why we need all these words just to convey a message or an idea?

Zz.
 
  • #14
nasu said:
I did not intend to be disrespectful to mathematicians. Just to give them what is theirs.
You need not worry. Mathematicians (the really hot ones) do not care what we lessor mortals say or think about them. They are only worried about what their fellow mathematicians think. They tend to get just as excited about solving Rubic's Cube as with developing some Maths that is of use to Science or Engineering. But we would be lost without them so we have to treat them gently.
thetexan said:
Is it assumed to be a fact that any physical phenomena, regardless of what it is, from quantum physics to the biggest cosmological physics, can be represented with mathematical equations?
I think that may be far too much to hope for. There will be problems that can never be solved with Maths to a level that is entirely satisfactory. For a start, there are many Differential Equations which relate to Physical processes which do not have Analytical solutions. For instance, the only way to solve the Equation that describes 'simple Frequency Modulation is by using numerical methods. There are many more instances of that and it must really upset non pragmatic users.
Also, the mathematical models are only as good as the evidence that's used to build them, which is down to measurement, in the end.

But, if you want a world with No Maths in it, the level of Scientific understanding will be very low.
 
  • #15
sophiecentaur said:
But we would be lost without them so we have to treat them gently.
That was the reason for my post. I was afraid that some of the hot ones will read this thread and get offended by the idea that they work for the benefit of these scientists back there.
https://imgs.xkcd.com/comics/purity.png
 
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  • #16
nasu said:
That was the reason for my post. I was afraid that some of the hot ones will read this thread and get offended by the idea that they work for the benefit of these scientists back there.
https://imgs.xkcd.com/comics/purity.png
I think they 'know' they are smarter than 'us' and wouldn't care. Most of them are aware of the esteem in which they are held.
 
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  • #17
Not all are so self-reassured. There was one of them who felt the need to "apologize" for the applied math. :)
https://en.wikipedia.org/wiki/A_Mathematician's_Apology
(Available online)

"Any genuine mathematician must feel that it is not on these crude achievements that the real case for mathematics rests, that the popular reputation of mathematics is based largely on ignorance and confusion, and there is room for a more rational defence."

The "crude achievements" are the practical applications of math. He mentions Einstein's relativity between them.
 
  • #18
Why all the math? Because it works. The rest is philosophy, so thread closed.
 

1. What is the relationship between math and physics?

The relationship between math and physics is very close and intertwined. Math is used as a language to describe and understand the physical phenomena that occur in the universe. Many physical laws and theories are expressed and derived using mathematical equations, and understanding these equations allows us to make predictions and understand the behavior of the physical world around us.

2. Why is math important in physics?

Math is important in physics because it allows us to quantify and describe the physical world in a precise and systematic way. Without math, we would not be able to fully understand and explain the complex phenomena and relationships that exist in the universe. It also allows us to make accurate predictions and develop new theories and concepts.

3. What are some key mathematical concepts used in physics?

Some key mathematical concepts used in physics include calculus, algebra, geometry, and trigonometry. Calculus is used to describe the rate of change in physical systems, while algebra is used to solve equations and express relationships between variables. Geometry and trigonometry are used to understand the shapes and angles of objects in space and their movements.

4. How does math help us understand the laws of physics?

Math helps us understand the laws of physics by providing a way to express and quantify these laws in a universal language. By using mathematical equations, we can describe the behavior of physical systems and make predictions about how they will behave in different situations. This allows us to test and refine our understanding of the laws of physics.

5. Can physics be understood without using math?

While some basic concepts in physics can be understood without using math, a deeper understanding of the subject requires the use of mathematical tools. Math allows us to make precise and accurate predictions about the behavior of physical systems, and without it, our understanding of the laws and theories of physics would be limited. Therefore, math is an essential component of understanding physics.

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