# Math behind Theoretical Physics

I look around the internet and there are theories about a lot of different aspects of physics such as various alternative theories on gravitation from GR, M-Theory, Quantum Theory. My question is, if math is used in physics to make sense of the world we see, and a lot of mathematical equations seen on paper can be seen in the real world. How can the math point to various theories ?? , cant the math follow a order and that be the end of it since its proven on paper or can the math be absolutely perfect but still wrong in reality assuming specific constants and observed numerical data ??

Sorry if I'm not clear in what I'm asking, if there are doubts just ask

Thanks,
Will

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jedishrfu
Mentor
math is used to model the world. it doesn't mean the world will always work like the math says. The orrery is a good example of a machine of gears and cogs that models planetary motion but the planets don't use gearing to move. So the machine allows useful predictions of where planets will be.

The same goes for math, we use it to model a system meaning we use it to predict what the system will do. When the system something outside the math then we need to patch up the math model or develop a new one.

Historically, planetary motion was first modeled by Ptolemy's cycles with in cycles theory but later Copernicus proposed a simpler theory of planetary motion. Later Kepler deduced the math to describe planetary motion and Newton derived his theory of gravitation from it.

However, Newton's gravitation couldn't explain the precession of the orbit of Mercury. It took a whole new theory, General Relativity to describe everything Newton described and provide a description of the motion of Mercury. In a sense we learn from our desire to explain everything via math and we learn from the mistakes of our theories crafting new and better theories.

I look around the internet and there are theories about a lot of different aspects of physics such as various alternative theories on gravitation from GR, M-Theory, Quantum Theory. My question is, if math is used in physics to make sense of the world we see, and a lot of mathematical equations seen on paper can be seen in the real world. How can the math point to various theories ?? , cant the math follow a order and that be the end of it since its proven on paper or can the math be absolutely perfect but still wrong in reality assuming specific constants and observed numerical data ??

Sorry if I'm not clear in what I'm asking, if there are doubts just ask

Thanks,
Will
Mathematics is a language; it's used to describe certain aspects of the natural world. Describing something does you no good unless you choose your words properly, which takes a great deal of work.

math is used to model the world. it doesn't mean the world will always work like the math says. The orrery is a good example of a machine of gears and cogs that models planetary motion but the planets don't use gearing to move. So the machine allows useful predictions of where planets will be.

The same goes for math, we use it to model a system meaning we use it to predict what the system will do. When the system something outside the math then we need to patch up the math model or develop a new one.

Historically, planetary motion was first modeled by Ptolemy's cycles with in cycles theory but later Copernicus proposed a simpler theory of planetary motion. Later Kepler deduced the math to describe planetary motion and Newton derived his theory of gravitation from it.

However, Newton's gravitation couldn't explain the precession of the orbit of Mercury. It took a whole new theory, General Relativity to describe everything Newton described and provide a description of the motion of Mercury. In a sense we learn from our desire to explain everything via math and we learn from the mistakes of our theories crafting new and better theories.
Mathematics is a language; it's used to describe certain aspects of the natural world. Describing something does you no good unless you choose your words properly, which takes a great deal of work.
Thanks guys.
Take a look at the Standard Model, it predicted certain particles that had not been observed in nature at the time and then we discovered them as predicted in the mathematical equations which is interesting.

Also GR is a great attempt at understanding gravity but thinking rationally could nature really contain space time curvature and so forth, or could it be simpler but the math is just not known to us. Sure GR provides great insight into former unknown gravitational behavior but it still is not complete so could it be wrong ?, and be just a theory that seems to work much like Newtonian gravitation where it seemed to work good and the math looked good but it was still WRONG no matter how you looked at it. Is it possible to formulate a mathematical equation/s that could fully seem to explain all of the gravitational behavior but still be wrong according to nature.

Nabeshin
Also GR is a great attempt at understanding gravity but thinking rationally could nature really contain space time curvature and so forth, or could it be simpler but the math is just not known to us. Sure GR provides great insight into former unknown gravitational behavior but it still is not complete so could it be wrong ?, and be just a theory that seems to work much like Newtonian gravitation where it seemed to work good and the math looked good but it was still WRONG no matter how you looked at it. Is it possible to formulate a mathematical equation/s that could fully seem to explain all of the gravitational behavior but still be wrong according to nature.
This is a pretty philosophical issue, but my stance is that one needs to view ALL theories in this way. If we come up with some theory which supersedes GR, perhaps even uniting it with quantum mechanics, I would still treat the theory the same: just a model for the physical world. The notion that there is some fundamental, unifying, absolute description of nature doesn't seem to have much basis if you ask me. All we've ever done, and all we can do, is make models for the phenomenon we observe and fit to within the error bars.

jedishrfu
Mentor
So far math is always an approximation to reality. When doing experiments we can only get so accurate. Our accuracy needs to be enough to say our measurement proves theory A but disproves theory B otherwise we can't know which is the better theory. Because GR described the motion of Mercury but Newtons didn't we can say GR is a better theory. When QG comes thru experiments will have to show that it's a better theory than GR the current gold standard that it describes all the things GR describes and then some new stuff that GR fails at.

This is a pretty philosophical issue, but my stance is that one needs to view ALL theories in this way. If we come up with some theory which supersedes GR, perhaps even uniting it with quantum mechanics, I would still treat the theory the same: just a model for the physical world. The notion that there is some fundamental, unifying, absolute description of nature doesn't seem to have much basis if you ask me. All we've ever done, and all we can do, is make models for the phenomenon we observe and fit to within the error bars.
I agree and i don't think we will have a perfect theory just a good one that still retains errors here and there, but the extent that physics goes to explain the natural world is crazy, it started with curvature of space, uncertainty principle, string theory (multiverse and etc). I know this goes deep into it but just bare with me, isnt it crazy how these theories try to explain reality

So far math is always an approximation to reality. When doing experiments we can only get so accurate. Our accuracy needs to be enough to say our measurement proves theory A but disproves theory B otherwise we can't know which is the better theory. Because GR described the motion of Mercury but Newtons didn't we can say GR is a better theory. When QG comes thru experiments will have to show that it's a better theory than GR the current gold standard that it describes all the things GR describes and then some new stuff that GR fails at.
That is true, i guess that is why they are all called theories and you are right QG might just be a better theory. So why is there a big push to unify relativity with quantum mechanics ?, wouldn't a new mathematical approach disregarding one like GR and trying to formulate another using quantum mechanics at its base a more feasible approach ?

Chronos
Gold Member
Figures don't lie, but, liars figure - so go figure.

jedishrfu
Mentor
I agree and i don't think we will have a perfect theory just a good one that still retains errors here and there, but the extent that physics goes to explain the natural world is crazy, it started with curvature of space, uncertainty principle, string theory (multiverse and etc). I know this goes deep into it but just bare with me, isnt it crazy how these theories try to explain reality

That is true, i guess that is why they are all called theories and you are right QG might just be a better theory. So why is there a big push to unify relativity with quantum mechanics ?, wouldn't a new mathematical approach disregarding one like GR and trying to formulate another using quantum mechanics at its base a more feasible approach ?
Scientists have a dream that all of reality can be modeled by a single theory. GR uses a geometric view a smooth and continuous view at all levels but QM has shown that there are limits to how precise we measure making a more pixelated view at the smallest level. How do we combine the two theories to make one? You can't without some new fundamental idea like what superstring theory or Loop QG are trying...

Scientists have a dream that all of reality can be modeled by a single theory. GR uses a geometric view a smooth and continuous view at all levels but QM has shown that there are limits to how precise we measure making a more pixelated view at the smallest level. How do we combine the two theories to make one? You can't without some new fundamental idea like what superstring theory or Loop QG are trying...
Ya i see where your coming from, but maybe that just cant happen, there just might be different laws for the macro and micro respectively. In my personal opinion i think GR is flawed, sure it has been shown to work in many test throughout the century but maybe gravity is a particle and not just an observed effect of the curvature of space time. I am by no means a theoretical physicists but i just think a theory will come along or already is present that better explains gravity and maybe ties in with QM but without the hassle of 11 dimensions and so forth.

Figures don't lie, but, liars figure - so go figure.
Excellent description. Trying to use pure math to come up with a theory and then prove that it's the only theory is like using a refrigerator to remove a splinter - pure math just isn't designed to model the Universe, one would need to know how to apply the math correctly. One would get an infinity of theories, each with results that conflict completely with observational evidence and even some that predict 7-dimensional Universes where every rainbow unicorn can teleport at will and solid unicorns are doomed to have to walk everywhere.

I look around the internet and there are theories about a lot of different aspects of physics such as various alternative theories on gravitation from GR, M-Theory, Quantum Theory. My question is, if math is used in physics to make sense of the world we see, and a lot of mathematical equations seen on paper can be seen in the real world. How can the math point to various theories ?? , cant the math follow a order and that be the end of it since its proven on paper or can the math be absolutely perfect but still wrong in reality assuming specific constants and observed numerical data ??
Thanks,
Will

This is a well known and well-discussed part of Philosophy of Science, and I belive most people these days follow a viewpoint called 'objective realism'. (This name I cannot remember and might be wrong).

This states - simply - that person only knows only what one can detect. If i turn my back on someone I can no longer say with certaincy what he is doing unless I have a mirror.

Therefore we know only about the world what we observe and we invent a model (physics) that can explain this observation. For exmaple we invent 'law of XYZ'.

We don't know for sure if 'law of XYZ' is true but all we know is that everytime we test it, the measurements from experiment match the predictions of the law.

That is the best we can do. We do not know if : for example : we are brain in jar in advanced computer simulation? We cannot know this for sure if we cannot see out side of their simulation

So all we can say is that model can explain observed results therefore we can think of model as true and use it in our lives ... and we don't *need* to know if it's not true since we can't know if we can see the "real" truth or not.

Obviously this cannot be "proved" true or false but is very popular view these days amongst science types. Science is based on explaining your observations and STOPS as soon as you get into stuff you cannot observe. So by this definition science sees only observable things ... but most people argue that is it 'crazy' to deal with non-observable things. If I imagine elephant in my room, I am nuts and must call head doctor! I *must* accept the result of eyes which say no elephant until the point at which i detect elephant by other means e.g. noise or smell or being stepped on or weird footprints. Only then I can change model to accept invisible elephant, and only if that is most likely explanation. But in truth most likely explanation is joke made by lab worker.

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This is a well known and well-discussed part of Philosophy of Science, and I belive most people these days follow a viewpoint called 'objective realism'. (This name I cannot remember and might be wrong).

This states - simply - that person only knows only what one can detect. If i turn my back on someone I can no longer say with certaincy what he is doing unless I have a mirror.

Therefore we know only about the world what we observe and we invent a model (physics) that can explain this observation. For exmaple we invent 'law of XYZ'.

We don't know for sure if 'law of XYZ' is true ...
Very well said, anyone else want to throw their 2 cents please feel free to do so, i would love to hear other point of views

My question is, if math is used in physics to make sense of the world we see, and a lot of mathematical equations seen on paper can be seen in the real world. How can the math point to various theories ??
Math gives you precise answers which you can test. If a theory says I should measure 5 +/- 1 and I measure 10, then the theory is worng.

Cant the math follow a order and that be the end of it since its proven on paper or can the math be absolutely perfect but still wrong in reality assuming specific constants and observed numerical data ??
YES. And that's *GOOD* when it happens.

If you come up with a theory, and you do the maths, and the maths say that you should get answer 5, but you do the measures and you get 500, then that's *GREAT*. You've just shown that your theory is wrong.

One mistake that people is about what theorists do. People assume that the job of the theorist is to figure out the universe. It isn't. The job of a theorist is to come up with new ideas about how the universe works and to come up with predictions about what what the consequences of those ideas are.

If you do that and the numbers don't work out, then you've *won*. You've shown that the universe can't work in a certain way.

Also GR is a great attempt at understanding gravity but thinking rationally could nature really contain space time curvature and so forth, or could it be simpler but the math is just not known to us.
One of the reasons that physicists like general relativity is that mathematically, it's *extremely* simple. The problem is that it's weird.

Sure GR provides great insight into former unknown gravitational behavior but it still is not complete so could it be wrong ?
Or it could be wrong, because it's just wrong. Now what we *do* know is that the true theory of gravity is *similar* to GR. We know this because we can do experiments. We take the numbers that GR says we get, and look at the actual numbers and they are close enough so that GR could be correct. Or it could be wrong and the real theory is something close.

Most people have an incorrect idea of what theoretical physicists do. The job of a theoretical physicist is often to work out the consequences of an idea. So I have an alternative theory of gravity. How close is it to GR? That can take months to figure out.

Is it possible to formulate a mathematical equation/s that could fully seem to explain all of the gravitational behavior but still be wrong according to nature.
That's a philosophical question which different people will answer differently. My answer is NO. If you get all of the right answers, then by definition the theory is *correct* because the definition of *correctness* is getting the right answers.

Scientists have a dream that all of reality can be modeled by a single theory.
No. Some scientists that write lots of popular books have this dream. Personally, I don't think it's possible, and a lot of scientists would agree with me.

How do we combine the two theories to make one? You can't without some new fundamental idea like what superstring theory or Loop QG are trying...
And I don't think the problem is lack of ideas. The problem is lack of observations.

In my personal opinion i think GR is flawed, sure it has been shown to work in many test throughout the century but maybe gravity is a particle and not just an observed effect of the curvature of space time.
This is where the math and numbers comes in. Suppose gravity is a particle? What is that particle like? It's a massive? How does it interact with other particles? Without numbers, you have something vague, untestable, and useless.

Now if I start saying that "gravity is particle with properties X, Y, and Z" then I can do tests to show whether or not it's true.

I am by no means a theoretical physicists but i just think a theory will come along or already is present that better explains gravity and maybe ties in with QM but without the hassle of 11 dimensions and so forth.
Everything is easy until you find out that it's hard.

The basic problem is that whenever you start doing the math, you find out that you can't get any numbers out. The problem with gravity is that "gravity produces gravity". So when you try to do calculations, you end up with an infinite number of particles and it's a mess.

This is all a general summary, but to show exactly what happens, you have to do the math.

Very well said, anyone else want to throw their 2 cents please feel free to do so, i would love to hear other point of views
The problem with "objective realism" is that you run into problems figuring out happens when the observation changes the thing that you are viewing. Which is a *BIG* problem with quantum mechanics.

The problem with "objective realism" is that you run into problems figuring out happens when the observation changes the thing that you are viewing. Which is a *BIG* problem with quantum mechanics.
It's not really a problem as such for me.

It just means that you, yourself, are a component of the whole universe, and the whole thing is interdependent on some level. It still doesn't mean that can you ignore the result of observation, or make claims about things you cannot observe. Or am I misunderstanding you?

It does imply the universe is not completely deterministic, but I am OK with that, and it's not any different from what QM says. Also if it's non-deterministic on a scale we can't perceive, that's not really relevant to us if something happens that we can't predictably influence.

Basically I assume that anything huamns can't detect doesn't exist until proven otherwise. Otherwise all unobservable phenomena are equally valid.

And if it is a problem, and this being a science site, I have to ask what you do propose to fix it.

It just means that you, yourself, are a component of the whole universe, and the whole thing is interdependent on some level. It still doesn't mean that can you ignore the result of observation, or make claims about things you cannot observe.
There are several different interpretations of QM. One of them is the Bohm interpretation in which every particle is interconnected with every other particle in the universe. That didn't bother David Bohm, but it did bother Einstein a great deal.

Also if it's non-deterministic on a scale we can't perceive, that's not really relevant to us if something happens that we can't predictably influence.
Except that it's not hard to get QM non-determinism to affect things at macro-scopic scales. There is a problem in dividing the world in "classical" and "quantum" because then you have problems figuring out what to do at the boundaries, and that's an area of active physics research.

Basically I assume that anything huamns can't detect doesn't exist until proven otherwise. Otherwise all unobservable phenomena are equally valid.
I can't do that since I have to deal with "undetectable" objects in my daily life (i.e. money).

And if it is a problem, and this being a science site, I have to ask what you do propose to fix it.
No idea. But that's good. Sometimes the job of a theorist is to bring up a problem, with no clue as to how to fix it. The thing about mathematical logic is that it invariably creates a choice. If you assume A, B, and C, D *MUST* be true. If D isn't true, you *MUST* reject either A, B, or C. Some of the best theory papers have been of this form, and if you ask the writer if they reject A, B, or C, then the answer is "I dunno."

Money is a concept that exists in the minds of the people that understand it. It is observable.

I don't know anything about quantum mechanics but if it is true that classical systems are an emergent property of the quantum, then your life is an illusion (albeit a very persistent one).