Blake, as often happens, I’m going to need to do a half-hour of reading to even appreciate the invitation to consider what’s on the other end of the links. AdS/CFT correspondence? Sheesh. I’m guessing that CFT stands for ‘constant fine tuning’ or ‘cosmic fine tuning’, but really, I’m clueless.

I appreciate it, though! Keep it up! (skull…is….on….fire….)

“…as often happens, Iâ€™m going to need to do a half-hour of reading to even appreciate the invitation to consider whatâ€™s on the other end of the links.”

I know that feeling well. Of course, I keep coming back for more, so I must just be a sucker for punishment or something.

“AdS” stands for “anti-de Sitter,” and “CFT” is short for “Conformal Field Theory.” I’ll poke around for a reasonable lay explanation of the topic; I haven’t really seen a great one yet, but I suspect something worthwhile is out there.

Edit to add: Luckily for me, Clifford Johnson just wrote a good backgrounder, here.

OK,thanks, but you’ll now excuse me so that I can study maths for a year in order to appreciate the ‘explanation.’ ….:)

Yep, math matters! And so does “maths,” for our friends across the Atlantic.

I can try to unpack a few of the things in Johnson’s explanation; there are several concepts which he employs without introduction, probably because it would take too long to explain them all from scratch and still discuss the physics he wants to talk about! For example, this “symmetry group” thing. To us, a “symmetry” means that we can transform an entity and have it look the same as it did before. A vase is symmetrical, because we can rotate it around an axis running through its center, and after the rotation it looks the same. A person’s face is typically symmetrical under left-right reflection, or roughly so.

More deeply, we can say that physical laws are symmetrical under certain transformations. Imagine yourself riding in an airplane, in smooth and level flight. Unless the plane encounters some unexpected turbulence, you can’t really tell you’re moving without looking outside. Soda pours from a can into a cup just like it does on the ground, and so forth. Just as a vase is symmetrical under rotation, so are the behaviors of physical phenomena symmetrical when we go from a state of rest into uniform motion in a straight line. This is clearly tied up with Einstein’s theory of relativity, and in fact the mathematical construction of that theory involves something called the “Lorentz symmetry group.”

Why “group”? Well, a group is a way of generalizing the notions of arithmetic. We can combine symmetries, for example, in much the same way that we combine numbers: instead of adding or multiplying, we just perform one rotation and then apply the other. This “composition” of rotations means that the whole set of possible symmetry transformations is a group. John Armstrong has an introduction to group theory here, and I wrote a little about what considering rotations will get you into, here.

All that talk about [tex]SU(2)[/tex] and [tex]SU(N)[/tex] refers to particular symmetry groups which are built out of matrices. I wrote a little about matrices here; although I didn’t say so at the time, I was really building the Lie group [tex]SO(3)[/tex] and its associated Lie algebra!

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"no matter how gifted, you alone cannot change the world"

Blake, as often happens, I’m going to need to do a half-hour of reading to even appreciate the invitation to consider what’s on the other end of the links. AdS/CFT correspondence? Sheesh. I’m guessing that CFT stands for ‘constant fine tuning’ or ‘cosmic fine tuning’, but really, I’m clueless.

I appreciate it, though! Keep it up! (skull…is….on….fire….)

“…as often happens, Iâ€™m going to need to do a half-hour of reading to even appreciate the invitation to consider whatâ€™s on the other end of the links.”

I know that feeling well. Of course, I keep coming back for more, so I must just be a sucker for punishment or something.

“AdS” stands for “anti-de Sitter,” and “CFT” is short for “Conformal Field Theory.” I’ll poke around for a reasonable lay explanation of the topic; I haven’t really seen a great one yet, but I suspect something worthwhile is out there.

Edit to add:Luckily for me, Clifford Johnson just wrote a good backgrounder, here.OK,thanks, but you’ll now excuse me so that I can study maths for a year in order to appreciate the ‘explanation.’ ….:)

Yep, math matters! And so does “maths,” for our friends across the Atlantic.

I can try to unpack a few of the things in Johnson’s explanation; there are several concepts which he employs without introduction, probably because it would take too long to explain them all from scratch and still discuss the physics he wants to talk about! For example, this “symmetry group” thing. To us, a “symmetry” means that we can transform an entity and have it look the same as it did before. A vase is symmetrical, because we can rotate it around an axis running through its center, and after the rotation it looks the same. A person’s face is typically symmetrical under left-right reflection, or roughly so.

More deeply, we can say that

physical lawsare symmetrical under certain transformations. Imagine yourself riding in an airplane, in smooth and level flight. Unless the plane encounters some unexpected turbulence, you can’t really tell you’re moving without looking outside. Soda pours from a can into a cup just like it does on the ground, and so forth. Just as a vase is symmetrical under rotation, so are the behaviors of physical phenomena symmetrical when we go from a state of rest into uniform motion in a straight line. This is clearly tied up with Einstein’s theory of relativity, and in fact the mathematical construction of that theory involves something called the “Lorentz symmetry group.”Why “group”? Well, a group is a way of generalizing the notions of arithmetic. We can combine symmetries, for example, in much the same way that we combine numbers: instead of adding or multiplying, we just perform one rotation and then apply the other. This “composition” of rotations means that the whole set of possible symmetry transformations is a group. John Armstrong has an introduction to group theory here, and I wrote a little about what considering rotations will get you into, here.

All that talk about [tex]SU(2)[/tex] and [tex]SU(N)[/tex] refers to particular symmetry groups which are built out of

matrices.I wrote a little about matrices here; although I didn’t say so at the time, I was really building the Lie group [tex]SO(3)[/tex] and its associated Lie algebra!