Alexander defines cosmology, explains loop quantum theory, and compares loop quantum theory with string theory.
Stephon Alexander: I would definitely make a distinction and say that humans have always done cosmology, meaning that we’ve always wanted to understand our origins, you know, even going right back to creation stories or creation myths, you know. I would say that- I would go as far as saying the Adam and Eve story- how that started- in the beginning, you know, the earth was without, you know, form and we were in this void. I forget the exact statement of that, but- so we’ve always been doing cosmology. I would say that cosmology is now a branch- is basically a branch of physics, of the physical sciences, that correlates or looks at phenomenon that physics- or the everyday physics that we study- and in a sense applies that to the universe as a whole. And, you know, as we do that, we learn that we can actually account for a lot of things, such as how stars and galaxies and planets are sort of formed on larger scales, but we also learn new physics. We also can use this by looking at the universe as a whole, and the largest distances we can imagine- we can learn something about the smallest things. Here- like, you know- like atomic physics, particle physics, physics in a sub-nuclear domain- so, it really is- cosmology is a physics that connects the smallest things in the universe to the largest things in the universe.
Question: What is loop quantum gravity?
Stephon Alexander: Okay. So, loop quantum gravity- you can break this up into actually the title of this particular theoretical framework- the word loop- and when you think of loop, you literally think of a hula hoop. Think of that shape. So you have a hula hoop. And I can imagine linking a bunch of those hula hoops together and making, you know, some sort of fabric of hula hoops, when I look from far away. That’s the loop part. Quantum, of course, is quantum, as in quanta discrete quantum mechanics that, you know- one of the things we learn from quantum mechanics is that how the electron actually occupies itself in the hydrogen atom is through quanti’s positions and energy levels- discrete jumps in positions and energy levels. That’s sort of, you know, of course a very bastardized way of talking about quantum mechanics, but that’s one way we can think about it. So that’s the quantum part. And the most important part about loop quantum gravity is the gravity part. So, really what loop quantum gravity is is a theory of quantum gravity, of unifying quantum mechanics that’s been so successful. Most of our technology, for example, uses quantum mechanics with the other successful paradigm of physics, which is Einstein’s theory of general relativity, having to do with matter and energy being able to warp the very fabric of space and time. And loop quantum gravity- if you- another way of combining the quantum with the gravity part, now that I gave you the Einsteinian view, that the fabric of space and time can be warped- now, imagine you say, okay, therefore, I have an atom of space and time. So let’s forget the time part now. But I have an atom- a piece of space- that appears to be continuous on large scales- distance scales. But when I actually go to very, very small scales- how small? Put thirty-four zeroes in front of a centimeter, okay? Decimal points- and we’re talking about that distance scale, okay? So call it the Planck Distance Scale- we actually start seeing that space- the fabric of space- comes in atomistic chunks,
just like the atom- or like the hydrogen atom was a quantum- became a quantum entity. So we move from this continuous description of space and time to atomistic description of space and time. And that’s- and the loops themselves- if you wanna think of them- are the objects, okay? That, you know, when they link up together, those are the atomistic objects in a sense of the fabric of space-time- and when they link up together, there is some sort of weave, a fabric that I see, just like you look at my shirt- seems to be smooth, but when I go in, I actually see the fabric, the threads, that link up together. In that case, it’ll be the hula hoops of the fabric of space and time. One weird concept of loop quantum that I think is pretty cool is that the loops themselves define space. So, in other words, if I give you a loop, in loop quantum gravity, space only exists in the loop. But outside the loop, there is no space. So loop quantum gravity also incorporates the idea of there being no space- empty space is still something in loop quantum gravity. But there is actually a notion of no space.
Question: How does loop quantum theory relate to string theory?
Stephon Alexander: Yes, that’s a- how does loop quantum gravity compare to string theory? Is very much actually an active role- active line of research- for some people right now, in that they are trying to connect or think of ways in which string theory and loop quantum gravity could actually be unified- not unified, but related to each other. Because as it stands right now, there are different pictures, so to speak, of quantum gravity, of how you marry quantum physics with gravity- how you link space-time, the arena that matter works/moves in, with actually quantum mechanics, which does so well at describing matter. So, they differ in a sense. One way to contrast them is that string theory is based on a form of matter, in a sense- that it’s string-like rather than point-like- like atomistic. So, you take matter- I don’t wanna cut my finger up- but use that as an example, but- yeah, I can divide the molecules of my finger down to- the Planck link- string theory says when I get to that link scale, that atomistic point actually resolves itself to be a string-like vibration of energy. And depending on the different vibrational frequencies, or how the string rotates maybe, all right- or how it wraps onto itself, I get the appearance of different types of matter. But it’s a theory really of, fundamentally of, matter moving in space-time, so in a sense we call that a background-dependent formulation of quantum gravity versus loop quantum gravity, which doesn’t require a background space-time- it itself defines the background.
Yes. So, string theory is a theory that starts out positing a form- a string-like form of matter. But that string-like form of matter propagates or moves in a background space-time. Now, in loop quantum gravity, there is no background space-time. It’s the loops themselves that define the background space-time, because there can- outside of these loops, okay?- there is no space-time. So, loop quantum gravity is set to be a relational theory. If I depend on how I link these loops- quantum loops- of space-time together,
will give me space-time relationships. Okay? So that’s more the so-called Leibnizian viewpoint of space-time, that it’s relational. This sense is nothing more than, you know- not just about some space in between you, but a sense of farness and nearness. That’s a relationship. And so loop quantum gravity takes it to that viewpoint- where it doesn’t require a background space-time, which is one of the fundamental postulates of Einstein’s theory of general relativity, but the laws of physics should not care about the positions, or the background space-time, that an observer, say like you and I or a planet, is situated. They should be invariant under one state of motion or position, where string theory starts out with that as an assumption, and then they can actually get gravity back from that assumption. So that’s one way in which they’re different.