• Question: Does Quantum physics deal with the toughest part of mathematics?

    Asked by rajathjackson to Jack, Dave on 17 Jun 2013.
    • Photo: Jack Miller

      Jack Miller answered on 17 Jun 2013:

      Hi Rajathjackson,

      Maths is a big field, and quantum mechanics uses a large chunk of maths. I think it’s fair to say that some of the maths involved in particle physics is undoubtedly the hardest I’ve ever encountered in my life, but that doesn’t mean that there isn’t more maths out there that I’d find more difficult! Also, I should stress that what people find “easy” and “hard” varies — which is a good thing, as you can often get mathematicians to do your difficult calculations for you!

      I think it’s also important to say _why_ the maths behind quantum mechanics is hard. In the quantum world, particles aren’t individual little things at a given point in space and time, but rather they’re something that you have a certain probability of measuring at a given point in space and time. If you’re looking at something happening, then there are many, many different ways that the thing you’re looking at could occur. In fact, there are often infinitely many different ways for it to happen, each with an associated probability, and each resulting in an outcome with a set of properties. To get an answer for what you’re interested in, you then have to do a pretty horrible infinite sum, where you look at the infinitely many different ways that something can happen, and add them all up to get an answer that relates to something you can measure. Fortunately, there are mathematical techniques for doing this, but it often gets a bit nasty, as I’m sure you can imagine!

      Hope this helps,

      — Jack

    • Photo: Dave Farmer

      Dave Farmer answered on 17 Jun 2013:

      Hi rajathjackson,

      I agree with Jack, everyone finds different areas of maths hard/easy. That being said some of the more advanced quantum mechanics stuff I imagine gets a bit challenging for most!

      I think the main issue with quantum mechanics is that, without maths, it’s very hard to describe at all. The probability functions that Jack describes are much easier to describe when you can write them down mathematically, however, that relies on the person you’re speaking to understanding the language of maths. Feynman once said “I think I can safely say that nobody understands quantum mechanics!”. Without an intuitive understanding, we have to rely on maths, which I think is why quantum physics has a reputation for being so maths-heavy. It’s currently the way we learn it.

      I don’t think that’s any reason to be put off though. Learning to express physical problems mathematically arms you to solve them, which is where all the fun is!

      Dave

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