Novice question on Quantum Mechanics

[Gunner B]

Hello, I am a junior in high school and I thought it would be great to study Quantum Mechanics at an earlier age to prepare me for future classes in college and in hopes of becoming a particle physicist. I have understood most of the basic concepts of QM up until now. Please help explain this excerpt:

"In Quantum Mechanics, it turns out that only specific p extra values are allowed. That leads to a discrete "tower" of observed masses for every fundamental particle! (If the extra dimension is very small, we will see that these "internal momentum" states are very heavy, which would explain why we have not yet observed them in particle accelerators.)"

The parts I don't completely understand is how exactly the professor is putting 'dimension(s)' into context. It may be that I just don't understand the definition or concept of dimensions fully, yet. (I understand the 3 dimensions we live in are basically; x-axis, y-axis and z axis and then time.) It's hard to visualize an extra dimension, if that is what I'm supposed to do. Also the part where he says

"(If the extra dimension is very small, we will see that these "internal momentum" states are very heavy, which would explain why we have not yet observed them in particle accelerators.)"

I thought if the particles are "heavy" they would be easier to observe and more noticeable than the less heavier particles. Obviously, this is not the case. I know that the LHC at CERN (where I want to work some day) is having trouble finding the Higgs boson because it is described as the professor has said "heavy". This I don't understand, please explain. Also, any other advice is greatly appreciated!

 

[Matterwave]

What book/article are you reading? The context of that statement might help us get what he is talking about...

 

[The_Duck]

Understand that this is not anywhere near a "basic concept of QM" but rather an attempt to describe for laymen a somewhat speculative theory in which there are more than 3 spatial dimensions.

Heavy particles are difficult to create in particle accelerators because they have to come out of the kinetic energy of colliding lighter particles like electrons or protons from E=mc^2. c is large, so if m is also large you have to give your colliding particles /lots/ of energy, which requires gigantic accelerators. Even when you have enough energy, heavier particles are produced less often than lighter possibilities in these collisions, so you have to do more work to find them.

 

[homology]

Its great that you've taken an interest in quantum mechanics. Its a beautiful bunch of physics and mathematics. The best first book you can read (in my opinion) is "The Meaning of Quantum Theory" by Jim Baggot (https://www.amazon.com/dp/019855575X/?tag=pfamazon01-20).

There's history and a discussion of the different interpretations, BUT, he also runs through basic calculations with spin and polarization and so deals only with two state systems and systems of pairs of particles. The 'math' is pretty basic but a good dry run. You learn about 'bras' and 'kets' and some of the probabilistic approach but its kept very accessible.

If you complete that book and are hungry for more then you MUST learn calculus, and in particular some differential equations. You need to know how to differentiate and integrate and have a passing knowledge that infinite series exist and they might be useful along with some basic familiarity with differential equations. That's the bare minimum then you can start the next step.

But do not be fooled by books for the lay public, you will never learn quantum mechanics from them any more than you'd learn French by reading about Napoleon.

In fact...if you're really interested in physics, just start with classical mechanics, that'll pay for itself over and over and over again :)

Good luck

 

[Gunner B]

Thank you for the great replies. I posted this question on yahoo answers and got a similar reply to what The_Duck said. I'm sorry I did not provide more information on the subject of the question. I also left out that the lesson was titled 'An Introduction To String Theory' and the professor was trying to connect the dots between the subjects. You can find his lesson here: http://www.slimy.com/~steuard/research/StringIntro/slide10.html
Also, I'm lucky to ask embarrising questions I don't fully understand and receive great answers. Thank you.

To Homology: I have watched lectures by Leonard Susskind on bras and kets and quantum entanglement but I will look into it more. Also, I am currently taking pre-calculus in high school (I'm already a year ahead in math) and I have all A's. I'm choosing to study physics, philosophy and mathematics outside of school. Not only to prepare me but because I think the subjects are interesting. I will be taking calculus AP next year (my senior year). I hope I'm on the right track, thanks for all of your advice!