Difficulty Imagining things a possible setback?

[interhacker]

I'm a high-school graduate, on my way to college this September. I have this problem. I like mathematics and physics a lot, and, at least up to high-school level I've been getting good grades in it (I won the Cambridge Outstanding Learner's Award for topping A-Level Physics in my region). In mathematical terms, I think I comprehended most of the stuff in my Physics curriculum.

Lots of people say that one can understand things better if one visualizes them in the mind. However, I feel that I lack the imagination (or am not intelligent enough) to visualize or better understand some of the concepts in Physics. For example, the Kinetic model of matter which was taught in my freshman year, was easy to understand for me as I imagined tiny little spheres randomly jiggling around. The Rutherford model wasn't that difficult either. I believe I comprehended electron shells and sub-shells too. But I got stuck at orbitals. I understood the concept at face-value and was able to answer questions about it but I just couldn't visualize it. The same thing happened for the concept of light being quantised. Once again I understood the equations perfectly (I think) but couldn't visualize the process.

I understand pretty much most other subjects such as Biology etc. via visualization and this worked in Physics for about the first two years in high-school, but after that the concepts became difficult to visualize. Firstly, is there any way to visualize concepts like the ones I mentioned? Are there concepts in Physics that cannot be visualized at all? Can this difficulty prove to be a setback for me later in my Physics career?

 

[axmls]

While I have limited knowledge of the subject, I'm sure you won't really be able to intuitively visualize certain things in physics until you have a better understanding of the math behind them. Just like calculus aids in the understanding of many things in early-level physics (kinematics, work, impulse, etc.), things will probably be easier to visualize as you gain mathematical knowledge.

 

[micromass]

Don't worry, you're not the only one with this problem. The great physicist Richard Feynamn has said that nobody understand quantum mechanics. This deserves some comments of course. I mean, of course Feynman understood the theory of quantum mechanics and he could answer many questions about it. But what he really meant is that nobody can really understand it on a level that we understand our current world. Nobody can really visualize quantum mechanics.

There is the famous saying "Shut up and calculate", which tells us that you shouldn't bother about the intuition and the visualization, but just do the math. This is a popular approach to QM, but hardly a satisfying one.

Why is QM so incredibly counterintuitive? It's simple, we don't live in a quantum world. We live in a world of macro-structures, so the world we are used to is classical. We have evolved this way to understand our world. We have never have to deal with the tiny world of QM, so our brain isn't adapted for this. The world we live in is an illusion. But it's also an illusion that we can really intuitively grasp the real world!

So no, not being able to visualize orbitals or wave-particle duality is not a problem. If it were, I don't know if we would have physicists now! Maybe once you'll create an intuition for it, but only after you've been exposed to the math and to many mindblowing contradictions!

Some stuff to watch (yes, I'm a huge Feynman fan):

https://www.youtube.com/watch?v=hUJfjRoxCbk

https://www.youtube.com/watch?v=DUjgzmGAODc

https://www.youtube.com/watch?v=wMFPe-DwULM

https://www.youtube.com/watch?v=eLQ2atfqk2c

 

[verty]

About orbitals, one way to think of them is some kind of jiggling, so an s-orbital could be just normal rotation, a p orbital could be a vibration in one axis, there are 3 axes so there are 3 p orbitals. The other orbitals could be higher modes of vibration. 2p versus 1p, that could be like harmonic frequencies. As long as you think about stuff in some way that helps you, that should be good enough.

Or for example the double split experiment. Think of a photon as something like a bell curve, it has some maximum amplitude and smooth ramps each side. When this wave hits the double split, it diffracts in the way you would expect because it is a wave, sort of like a moving hill.

Or consider that a neutron weighs more than a proton, the difference is close to the mass of an electron IIRC, and a neutron can decay into a proton, emitting an electron (and smaller particles and energy). So one way to intuit this is that a neutron is like an electron orbiting really close to a proton, so close that the charges cancel for all intents and purposes. When that electron gets too far from the proton, it is ejected for whatever reason. This is pretty naive but it serves the purpose. You can always replace it later with something more advanced but I always think that intuition is helpful to tie things together.

My favourite intuition is about gravity. Here is one way to intuit gravity, suppose we have two atoms. They have orbiting electrons of course. Now the electrons should repel each other, so perhaps the rotations synchronize with each other so that the electrons always try to be on opposite sides. When one electron is on the near side of the atom, the corresponding electron is on the far side. So there is a slight charge differential between the atoms, positive and negative or negative and positive, similar to polar bonds but on the electron level. This should be a very weak attraction and gravity is very weak.

This intuition suggests that gravity could be just the same charge attraction that attracts charged particles but in a similar way to polar bonds. It also suggests that gravity between two atoms could be proportional to the number of electrons in those atoms. We know gravity is proportional to mass, and the number of electrons is proportional to mass, so this is a very interesting intuition indeed.

This does however suggest some odd things, like if we place four magnets at the corners of a square, the forces between them will be somehow different than with only two magnets because the electrons can't synchronize as well with four magnets. I don't claim that this is perfect but until one learns better, intuitions have an important role.

And besides, science would usually not even try to explain why things work the way they do, but only how. So whatever intuition you have or invent, if it doesn't go against what you know, it should be just fine. It's probably wrong but it's good enough.

 

[AlephZero]

Don't worry about it, and in particular don't worry that you can't "instantly" visualize things. To paraphrase a Zen koan:

Before you study them, mountains are mountains and water is water. When you start to study, you discover that mountains are not mountains and water is not water. But finally you learn that mountains really are mountains, and water really is water.

But the "finally" part can take most of a lifetime, not a few days or weeks at university. I'm still discovering new insights into "elementary" things 40 years after I started to learn about them!

 

[interhacker]

Thank you everyone (especially micromass) for all the wonderful replies.

 

[mal4mac]

Great post micromass!

Another common gripe is people saying they can't visualise curvature in 4D space time and worrying they will, thereby, never be "smart enough" to handle GR. Hawking's response was that he had enough difficulty visualising events in 3D space! But he reckons he can, just about, fully visualise 21/2 dimensions (i.e. 2D with the realisation that some things are on top of each.) It's all about the math, though a few diagrams to provide snapshots of certain situations sure does help!

 

[third-object]

I found this to be true as well. I'm in high school going into my senior year, and while I'm probably the expert in my school, I have a very hard time visualizing any of the science.

I hope that, as many have said, it will get easier with more mathematical knowledge (I have yet to take Calculus), but I also often find my visualizations to be wrong. Anything that comes easily is an abstraction, it seems.