How do I use math to back up my theories in physics?

[rmoh13]

Because I'm only in pre-calculus right now (I'm still not in ninth grade yet), I haven't been able to find a way to back up my theories on physics which are mostly based off of reason and logic (I know this is a bad way to back up my theories, I just want to know what you think of them and how I can improve it). So my next question is: how do I apply mathematics to my own theories? How do I back my theories up with math? How do I make novel mathematical models in physics?

 

[russ_watters]

I'm sorry, but if you don't have any math, you don't have any theories, just ideas. There are no shortcuts here: in order to do physics, you need the math. So it would be best to set your ideas aside for 5-10 years while you learn the current state of physics and its math.

 

[rmoh13]

I'm sorry, but if you don't have any math, you don't have any theories, just ideas. There are no shortcuts here: in order to do physics, you need the math. So it would be best to set your ideas aside for 5-10 years while you learn the current state of physics and its math.

I know that, but my question was, how do I apply math in physics? How does one create mathematical models of their own, to back up their ideas and turn them into actual theories? Thank you.

 

[russ_watters]

I know that, but my question was, how do I apply math in physics? How does one create mathematical models of their own, to back up their ideas and turn them into actual theories? Thank you.

That is a very broad question, but the simples answer is that there are two paths:

1. You start with an unsolved problem - an unexplained phenomena - and find the mathematical relations that describe it. Galileo rolled balls down a ramp and observed that they all accelerate at the same rate. Then he (and more so Newton) used math to describe what he was seeing.

2. You start with an existing equation/model and apply it in a new situation to see what it predicts. Stephen Hawking did this with black holes, predicting Hawking Radiation.

 

[rmoh13]

That is a very broad question, but the simples answer is that there are two paths:

1. You start with an unsolved problem - an unexplained phenomena - and find the mathematical relations that describe it. Galileo rolled balls down a ramp and observed that they all accelerate at the same rate. Then he (and more so Newton) used math to describe what he was seeing.

2. You start with an existing equation/model and apply it in a new situation to see what it predicts. Stephen Hawking did this with black holes, predicting Hawking Radiation.

Thank you, that answered my question!

 

[axmls]

I know that, but my question was, how do I apply math in physics? How does one create mathematical models of their own, to back up their ideas and turn them into actual theories? Thank you.

A theory is useless unless you can show that

1. In certain limited regions, the theory behaves like currently accepted theories (i.e. In certain limiting cases, the equations of Einstein appear in the theory if you use it as an approximation).

2. The theory predicts (successfully) something new that current theories can't predict.

Neither of these is possible without first knowing the currently accepted theories and their math behind them. Trust me--physicists know what they're doing. They don't accept theories until it's well documented that the theories make very accurate predictions.

 

[TomServo]

They don't accept theories until it's well documented that the theories make very accurate predictions.

This isn't necessarily true for all physicists, as many "believe in" string theory for example despite no new predictions, or am I wrong?

 

[mfb]

I would not say "believe in". Some consider it as plausible option.
The mathematical tools developed there certainly helped even outside string theory.

 

[axmls]

This isn't necessarily true for all physicists, as many "believe in" string theory for example despite no new predictions, or am I wrong?

String theory is not a "scientific theory", and probably 99% of physicists never deal with it. String theory is a collection of hypotheses that does show some promising results when it comes to producing a theory of quantum gravity, but it hasn't really made any predictions yet.

In the case of string theory, I believe (though I'm no expert) that it has been shown that general relativity (and maybe QM, but like I said, I'm not an expert) can be a lower energy limit for string theory. Yet it hasn't made any new predictions.

But regardless, in order to work on string theory, physicists need a thorough knowledge of both General relativity and quantum field theory just to begin. This is because you don't create a physics revolution without knowing what physics is out there first. Einstein turned the physics world over by coming up with relativity (among other things), but he also had a Ph.D in physics and was well aware of the current theories at the time.

It's great to show interest in solving physics problems, but I recommend you channel your energy into seeing and learning about what's been done, because physics works incredibly well (quantum electrodynamics has been verified out to 10 decimal places or so). Then you can make breakthroughs.