Howdy!
I’m writing to announce a series of articles that will delve into the formalism behind String Theory. Specifically, we’ll start with the quantization of perturbative, bosonic strings.
This will be original material, supplemented with texts by Kaku, as well as the classics: GSW and Polchinski.
Before I get to the mathematics involved, I wanted to express why I am writing this series I’m calling String Theory without the Baggage. I hope you enjoy it.
Sean
There is No Crisis in Theoretical Physics
For reasons I still don’t fully understand, it’s become popular to demagogue String Theory and, by association the broad institution of High Energy Physics. No doubt this is a delayed response to the historic boosterism from the proponents of both String Theory and Weak Scale Supersymmetry. But within those complaints there also appears to be a willful misunderstanding of the practices of phenomenology and theory.
I’ve written about this elsewhere:
At the heart of this conflict is silence. We haven’t found a compelling need for dramatically new Physics in a while, yet the high energy theorists and phenomenologists are still working. Unfortunately, so are the journalists.
From the perspective of Science there is nothing wrong with this1. There’s no conflict or compelling, a priori need for a different way of working. There’s no institutional drama worth commenting on. It’s just that progress is slow.
Slow scientific progress only negatively impacts one class of stakeholders: those who talk about new scientific progress. With nothing to talk about, they are more than incentivized to fabricate and promote a “crisis”.
I’ve written about this too:
Of course, there are still technical criticisms worth discussing.
What Constitutes Evidence for a Hypothesis?
Recently, I got sucked2 into an interesting discussion about what Science can say about the nature of spacetime.
Olivier is an great physicist who works on really interesting stuff, inclusive of testing GR in the solar system. His complaint demonstrates a difference in thought between theorists and probably everyone else.
The point I was attempting to make was that the dimensionality of spacetime is not something you can completely restrict experimentally. As usual, Cliff made the point more clearly:
Olivier boiled the complaint down to a single question: what constitutes sufficient evidence for a theoretical hypothesis?
My thoughts on that were hopefully clear:
The dimensionality of spacetime is always going to be assumed as four-dimensional until experimentally proven otherwise. But you cannot rule the converse out, at least until we’re able to probe the Planck scale. It’s a black swan problem, which places its negation squarely outside the realm of reasonable scientific argument3.
Nevertheless, Olivier’s critique was clear: what constitutes acceptable evidence for the extraordinary claims put forward by String Theorists?
My stance on this is that the math counts as sufficient evidence to investigate they hypothesis. I totally understand how that might not fly for everyone.
Mathematically, what we call String Theory is the only known collection self-consistent quantum theories that contain Gravity. They’re models really. They are highly constrained and have very specific and surprising formal requirements. That any solution to them exists at all is worth understanding and exploring.
It’s this mathematical evidence that, in my opinion, justifies further exploration. Whether or not that is worthy of funding is a question for the funders. That is to say, it’s an opinion4.
The Claims of String Theory aren’t that Extraordinary
Sure, the past was full of immature, wild conjecture. String Theory is highly constrained and didn’t appear to have many solutions. So-called critical string theories appeared to only exist in a time-independent background5 in ten-dimensions. For a while, it looked as though there might only be one6.
But assigning these values to physical dimensions, curled up at the Planck scale is still something of an interpretation.
Phase transitions in Statistical Mechanics only occur in the continuum limit. They require either embedding on a torus or an infinite lattice. Yet we see phase transitions every day in real life, without these theoretical devices. There’s no hysteria there.
My assertion is that these mathematical details in String Theory are simply formalism. It’s weird formalism, sure, and we’re not yet comfortable with their philosophical implications. But that doesn’t mean that they’re a necessary requirement for physical interpretation.
Nobody, with a straight face, can really explain what a physical heterotic string would even look like. It’s also worth pointing out that nobody seems to care they they require twenty-six dimensions to be sensible7.
Perhaps one day we’ll have a better understanding. But until then, the only way out of this confusion is through the details. It’s time to shut up and calculate.
String Theory without the Baggage
So this is our aim. To go through the formalism of String Theory, piece by piece, for its own sake.
We’ll highlight and expand on ideas that are often understated or overlooked. We’ll also try to point out what pieces of the formalism are simply that - technical pieces - and have little if any concern for their philosophical (or frankly experiential ) meaning.
Just as many modern physicists don’t particularly care about the difference between the Copenhagen or Everett interpretation of Quantum Mechanics8, we don’t care about the meaning of extra dimensions or whether Supersymmetry is realized near the Higgs scale or not.
Those concerns are for others to deal with.
Personally, I’d encourage you to get a handle on how the formalism works before acceptation broad assertions about value, truth or other kinds of applicability. We’re here to help with that. We’ll try to send out one email a day.
Contrast this with Medicine, where slow progress equates to poor outcomes for sick individuals. Nobody will die because we haven’t found a stau or a neutralino.
Read: I inserted myself into such a discussion.
Which isn’t to say we shouldn’t look for these extra dimensions. Quite the opposite is true. Plenty of searches have already been done. It was remarkable how recently it was shown that there were no millimeter sized extra-dimensions we interact with in a meaningful way. Yes, there is a logical imbalance here. That’s the whole point.
And these can be treacherous lines to pursue. Are individuals who work to develop the formal techniques of Quantum Field Theory also not working on good science, because they lack direct, experimental justification? Certainly not, as their work ties into well-tested Physics. Ditto studies of General Relativity. Of course, how much funding goes into whose research groups is a very reasonable question to pin on the utility of experiment. Having joyfully left the world of grant proposals, I have no dog in that fight.
Of course, we know the universe isn’t in a time-independent, so this assumption still feels curious.
The completion of 11-dimensional supergravity, M-theory or whatever, modulo any duality to other models.
Sure you can wrap the details of the extra 16 bosonic dimensions as being tied up in the “gauge bundle” but how, philosophically, is that different from the 6 dimensions tied up in a Calabi-Yau?
Assuming there is any, although some experiments have been proposed to that effect.