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I'm a computer science major and I want to learn Physics. I can create computer simulations of any type. I'm not good at math that is required to learn QFT or GR,but I'm thinking is it possible to learn Physics(QFT and GR) by creating computer simulations of mathematical equations in GR and QFT and then make new discoveries in QFT and GR using computer simulations?

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closed as too broad by ACuriousMind, user36790, Carl Witthoft, John Rennie, Bill N Oct 15 '15 at 17:56

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    $\begingroup$ I suspect the easiest and quickest way to understand QFT and GR is to learn the maths. That's why people do that. Also it's no good making discoveries if you have no suitable language (i.e. maths) in common with the people you wish to communicate with. $\endgroup$ – RedGrittyBrick Oct 15 '15 at 9:47
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    $\begingroup$ Similarly along the lines of the above comment, wouldn't you have to learn the math of QFT or GR in order to write the necessary programs based on the relevant equations? $\endgroup$ – Kyle Kanos Oct 15 '15 at 11:38
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    $\begingroup$ Ummm.. no, you can't create useful simulations without understanding why the set of equations you're given are used to model the real world. $\endgroup$ – Carl Witthoft Oct 15 '15 at 13:59
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    $\begingroup$ Working in a computational field, I would say that you think you can create computer simulations of any type. The reality of it is experts in these fields sometimes struggle to make codes that work. And I see a lot of advice on StackOverflow that is completely off-base in scientific computing; knowing general purpose software practices/design does not always translate very well to scientific software practices/design (and vice versa). So if you do make the dive into physical simulations, don't be discouraged if you have to relearn a lot of the computer science things too in addition to math. $\endgroup$ – tpg2114 Oct 15 '15 at 14:51
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    $\begingroup$ Doing numerical simulations of equations and getting good results requires that you not only understand the math of the simulation, but the mathematical limitations of the methods you are programming. You can't simply take an equation and treat it like some formula that always works. Like Dirty Harry said, "A man has got to know his limitations." $\endgroup$ – Bill N Oct 15 '15 at 17:56
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Yes, you can make discoveries based on computer simulations. But you have to learn some kinds of math to do it. Lucky for you, it can be different math than is usually used.

For instance when most people learn General Relativity they learn it in a frame independent version which makes sense from a physical point of view. But most people doing simulations for General Relativity use the 3+1 formulation. So if the math used for the simulations is different than the math used regularly you get a second shot to see if you can join the field.

What kind of discoveries can be made with simulations? An example is universality, scale invariance and power-law scaling during black hole formation. Let me quote James Healy and Pablo Laguna from the preprint version of "Critical Collapse of Scalar Fields Beyond Axisymmetry" DOI:10.1007/s10714-014-1722-2

Without a doubt, one of the triumphs of numerical relativity occurred two decades ago, when Choptuik discovered universality, scale invariance and power-law scal- ing at the threshold of black hole formation. This remarkable body of work is commonly known as critical phenomena in gravitational collapse. Computa- tionally, Choptuik’s work was also revolutionary because it was the first instance in which adaptive mesh refinement techniques were used in numerical relativity. Without mesh refinement adaptivity, one could argue that unveiling gravitational collapse criticality in such an exquisite detail would have been an insurmountable enterprise.

But note the discoveries happened when a new computational science approach was applied to General Relativity for the first time. Also, you do have to be a real expert to be able to distinguish mere artefacts of the numerical method from a discovery. And others need to be able to verify your work. So cutting edge but understandable by others, which means you basically need to be on a popular enough bleeding edge that you can be new but have others understand you.

Sometimes it is unclear to me if there really is enough peer review of some numerical based discoveries. For instance the time dependent methods of reducing exotic matter requirements for warp drives (which still don't reduce it to zero exotic matter required) seem to be numerical and not really confirmed by peer review. But the flip side is that you could try to confirm existing numerical based research. Which is really an essential part to numerical based discoveries. And you'd have to write all new code on your own based on the reported results without looking at the old code in order to not accidentally redo some subtle mistake in the original code. But if you do that, they you can confirm that this arrangement with this dynamics does have the reported effect. And peer review is more essential for simulations than it normally is, and peer review (even post publication peer review) is indeed always essential to any research.

Now if you compare General Relativity to Quantum Field Theory, then General Relativity has the advantage that as a theory, we have a specific known mathematical family of objects. Whereas Quantum Field Theory is still a bit of an unknown as to what (if any) mathematical object it is. And that partly means that everyone is doing approximations so a numerical version isn't really going to be different. So I'm not sure how much success is possible there if someone enters with more computational science but without more physics knowledge.

Also, you can help other scientists make discoveries by making tools. And some tools are professionally designed simulators an experimentalist can use when investigating a setup or design before they make it. So you could make the tool an experimentalist uses to make the tools they use to make their discoveries. That might not be what you are looking for, but science is a team effort and that's important too. And if you make a tool that helps a lot of people you could potentially have a bigger overall impact on science by doing that if you do it well.

Your impact personally is more about how you do something well then exactly what you do.

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