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There's this idea that beauty is a powerful guide to truth in the mathematics of physical theory.
String theory is certainly beautiful in the eyes of many physicists,
but is it beautiful enough to pursue even if it's wrong?
[intro music]
Hermann Weyl once said, "If I have to choose between beauty and truth, I choose beauty."
It was in reaction to a rebuke by Einstein.
Weyl had tried to explain electromagnetism by imposing on Einstein's general theory of relativity.
the very first gauge symmetry -- Weyl invariance
Einstein pointed out that the proposal led to some absurd results, and so the idea went down in flames.
It just couldn't be true, despite the elegance of the math.
But sometimes it can be hard to let go of the sense that a beautiful theory must be right.
Could this also be the case with string theory?
As it happens, Weyl's old idea did work when translated to the very particular case of a quantum string,
which is part of what got string theory going in the first place.
We talked about this in detail in our episode on why string theory is right.
Which itself was a sequel to our primer on the basics of string theory.
In those episodes, we saw some of the remarkable ways that string theory promised to converge on a theory of everything.
It seemed so beautiful,
the effortlessness of its inclusion of quantum gravity, its promise to unify all particles under one umbrella,
and there's also the convergence of many versions of string theory into a single picture
with a very specific number of extra dimensions. I'll talk more about that today.
So why, with all of this promise of being so right
do more and more physicists think that string theory is after all either woefully incomplete or just plain wrong?
Modern string theory is the convergence of many beautiful ideas in physics, each of which feel right in their own way.
To see where string theory ultimately fails, we need to rewind to look at some of these a bit closer,
to start with, to a precursor to string theory and the origin of all this extra dimension stuff.
In 1919, not long after Einstein published his great theory of gravity,
Theodor Kaluza discovered something strange.
He was playing around with the newfangled general relativity in five dimensions, 4 space and 1 time,
because why not.
He found that in the right sort of
5-D space-time, you can separate the resulting Einstein equations into a
4-D component that looks exactly like the familiar general relativity in our universe,
plus an extra bit of math from the extra special dimension.
Crazily, that math also looked familiar. It looked like Maxwell's equations for electromagnetism.
It appeared that gravity acting in this fifth dimension looks like electromagnetism
to being trapped in our 4-D space-time.
Einstein himself was supposedly jubilant at the idea -- a rather better reaction than was received for the
electromagnetism of poor old Hermann Weyl.
The mild inconvenience of their very clearly being no extra special dimension was solved by Oskar Klein in the late 1920's.
Klein realized that you can get a sensible quantum theory if you compactify that extra dimension.
Shrink it down to around 10 to the power of negative thirtieth of a meter,
so it's only visible to things equally miniscule.
In the resulting in Kaluza–Klein theory, the fifth dimension is looped into a tiny circle.
At every point in space, there's another direction to move: up, down, left, right, forward, back, and around.
Momentum in that loop dimension has the exact behavior of
electric charge, with the direction of rotation
determining the sign of the charge.
It was an incredible discovery and a beautiful one. It even made a prediction:
the ratio between the mass of the electric charge and the electron.
Assuming the experimentally measured value for the electric charge, the corresponding electron mass should be around five
kilograms?
Probably wrong, and it's not the only problem with the first version of Kaluza–Klein theory.
It also predicted an unknown field,
the dilaton field, and a corresponding particle that had never been seen.
It also didn't give anything beyond electromagnetism,
but, to be fair, the other fundamental forces hadn't even been discovered at that stage.
These may have seemed like fatal flaws,
but we can thank this wrongness for the later development of string theory.
People tried various things to fix these issues.
For example, adding more compact dimensions of various shapes and, of course, strings.
There are many Kaluza-Klein inspired theories out there.
String theory is just the most famous.
So, start with Kaluza-Klein, add vibrating strings and exactly the right extra special dimensions, and you have string theory.
The last critical ingredient is
supersymmetry.
This is a theoretical symmetry between bosons and fermions, which very elegantly explains certain
anomalies, like the vast differences in strengths between the fundamental forces.
It also introduces fermions to the boson only version of string theory to give super string theory.
The introduction of supersymmetry along with the discovery of the right symmetries for the extra dimensions
sparked the first superstring revolution of the mid 80s,
roughly coinciding with the theatrical release of Weird Science.
Just saying.
Superstring started out with incredible promise, and so there was a proliferation of different versions of super string theory.
It turns out there are five ways to tie superstring: Type 1, Type 2 (A and B),
heterotic SO32, and E8 by E8.
Five different approaches to getting all of the desired particles out of the basic premise of strings wiggling in ten dimensions.
All required six compactified extra dimensions of space.
What differs is the detailed geometries and symmetries of those spaces, and the way strings vibrate within them.
In fact, these versions appeared fundamentally different from each other,
divergent, rather than convergent,
contradictory even.
Hardly elegant, one might even say ugly,
or wrong.
But the key to their convergence and the return to beauty had already been glimpsed.
The various superstring theories exhibited what we call
dualities.
A duality in physics is when two apparently different
mathematical theories proved to represent the same physical process.
These dualities reveal that certain classes of string theory
were actually the different ways of expressing exactly the same theory.
Perhaps there was a glimmer of hope for these divergent versions of string theory after all.
To give you a sense of what a duality looks like,
let's go back to the good old simplicity of Kaluza–Klein theory,
or at least at the simplicity of just one extra circular spatial dimension.
In fact, let's simplify even further.
Imagine
only one extended and one compactified spatial dimension.
If the latter is circular,
we can get a tube.
Our tiny quantum strings can roam that small dimension.
They can even wind around it,
perhaps multiple times in either direction,
before forming a closed loop.
The number of times a string winds around this compactified dimension
is called its winding number. The energy of such a string depends on the winding number
times the radius of the compactified dimension. That makes sense, it basically gives the length of the string.
These strings are vibrating with standing waves like guitar strings, and their energy also depends on the frequency of that vibration.
That frequency depends on the density of wave cycles on the string.
That's just the number of wave cycles around each coil, or the mode number
divided by the radius. So, there are two ways to get a high-energy string: have a large winding number along with a large radius
that gives you a long string, or have a large mode number with a small radius and that gives you a high frequency vibration.
It turns out that mathematically, these two are completely equivalent.
At least, they give exactly the same physics, either winding number times radius, or mode number divided by radius can be used to define the momentum of a particle produced by this string.
So you can construct a theory in which momentum increases with the size of the compact dimension, or where momentum decreases with that size and both give the same results.
It sounds weird but this may just have saved string theory. I just described a type of duality, in this case t-duality, short for target space duality.
In a duality two apparently contradictory way of describing the mechanics of the universe can lead to exactly the same results.
The appearance of dualities tells us that we probably can't take our geometric interpretations of the math as seriously as we'd like to.
T-dualities prove that some of these different versions of string theory are actually different expressions of the same theory.
The other main type of duality in string theory is s-duality, strong-weak duality.
In this case it's a duality between strongly versus weakly interacting strings. This seems even more contradictory, but it's incredibly powerful.
We will glimpse the mechanics and the implications of s-duality, as we look deeper into m-theory and holography in the future.
S-duality provided the final linchpin that demonstrated that the five different types of string theory were all manifestations of the same theory.
The guy who ultimately brought it together was Ed Witten.
At a string conference in '95, Witten showed that the disparate string theories were all just different perspectives, different limits or special cases of a single overarching theory.
This was m-theory, where M stands for really what have you want it to: membrane, magic, mother theory.
According to Witten is to be decided when the full nature of the theory is understood. We'll come back to M-theory in real detail,
but the important thing here is that it adds a single extra dimension, to connect all of the five super string theory types via s-duality.
So whereas the original superstring theories were ten dimensional with six compactified, M-theory is 11D, with seven hidden dimensions.
Wait, didn't the movie seven come out in '95 also?
Whoa
Well, that all sounds a bit arbitrary. Your theory not working? Just add an extra dimension.
Actually, the realization that superstring theory could be 11 dimensional was a revolution. It sparked the second superstring revolution.
See, in parallel to the development of super string theory, other physicists have been working on super gravity.
For independent reasons that we don't have time to get into,
11 is also the magic number for super gravity dimensions. Super gravity should be the low energy,
large-scale limit to super string theory. So it was incredibly exciting that string theory appeared to have an
11 dimensional version, M-theory, to correspond to everyone's favorite 11 D super gravity.
This convergence of the superstring theories with each other and with super gravity
restored the sense of beauty to string theory. It appeared to be on the track to rightness once again, so
So where did things go wrong?
Well, in a sense they were never really right. This M-theory thing, it's still not well-defined.
It's not solvable using perturbation theory, which doesn't leave much room to explore its implications.
In all superstring theories the extra spatial dimensions are wrapped, not in simple loops, but in complicated geometries
called Calabi-Yau manifolds.
The behavior of strings in these hyper dimensional surfaces is only understood in idealized cases.
For example, sections of these manifolds that can be approximated as simple tubes, like in Kaluza-Klein line theory.
But more worrying, there are countless possible geometries,
countless Calabi-Yau manifolds, to choose from. The standard number given is 10 to the power of 500 different topologies,
the actual number is a lot higher. This is the string landscape. Each geometry for the compactified dimensions implies a different set of porperties
for vibrating strings, and so a different family of particles and different laws of physics to go with them.
It seems an impossible task to find which one corresponds to our universe, if any do.
This is the impasse.
In principle the standard model lives somewhere in the string landscape,
but without knowing the geometry of the extra dimensions, this can't be verified
nor can we make testable predictions beyond the standard model.
Well there is supersymmetry.
Essentially all string theories require supersymmetry in order to work.
Physicists at the Large Hadron Collider had expected to find supersymmetric particles by now.
They haven't.
There's a hint from cosmic rays, we talked about it earlier.
But string theories are still rightly concerned. Their elegant theory which was converging so beautifully has stalled.
Will they follow in the example of Hermann Weyl and choose beauty over truth?
One last word on Weyl.
His idea of explaining electromagnetism by adding his gauge symmetry to general relativity was wrong,
but it inspired the entire field of gauge theory upon which much of our understanding of the quantum world depends.
It also gave us the sought after quantum electromagnetism in the end, just with a slightly different symmetry.
So perhaps string theorists should also stick to their guns.
As wrong or incomplete as current string theory may be,
it may also be the inevitable early step as we seek an even more beautiful and ultimately more right understanding of space-time.
learning the physics required to understand string theory is tough
thankfully there are online tools that can help
like brilliance a
problem-solving website that teaches you to tackle difficult topics and think like a scientist by breaking up complexities into
Understandable pieces and instead of just passively listening to lectures you get to master concepts by solving interesting and challenging problems?
So whether you want to learn about special relativity in quantum physics or brush up on your complex algebra and differential equations
you can learn more at brilliant org slash space-time
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now last week we peered into the looking-glass and saw how a universe that's spatially reflected in a mirror
has fundamentally different laws of physics to our own you had your own
Reflections on the subject. socks with sandals points out that parity inversion isn't the only thing reflected in a true mirror universe
And that's right. In a perfect reflection of our universe, not only are spatial coordinates flipped,
charges are also reversed and in fact time is reversed too.
Only when you reverse parity charges and time do you get a universe that behaves like, ours
one full of mirror reflected antimatter traveling backwards in time
Well so the cpt theorem tells us and we'll get back to that real soon
and yes if matter from that Mirror Universe broke through and came into contact with ours it wouldn't be pretty
infinity years bad luck
William wonders whether the helix of the DNA molecule would be reverse in a mirror universe
well I think the answer is both yes and I don't know
Depending on how you think about it William is referring to the fact that DNA always wins in a particular direction
it's chiral and always has the same chirality
we define DNA to be right-handed
So if you look at DNA in a mirror its left-handed but is its chirality
determined by something fundamental about our universe if DNA forms on another planet is it always
right-handed would a parity reflected universe always have left-handed DNA now that's not so obvious
Right-handed DNA is built entirely of right-handed amino acids but those are in equal abundance to
left-handed amino acids in nature so why only right-handed DNA
and it's likely because the first are in a precursor to DNA just by chance happen to form from right-handed amino acids
these could replicate but only using other right-handed amino acids after that
right-handed replicators were the only game in town
At least for the earth so have you accused us of filming that episode in a mirror universe
apparently balls were spinning clockwise when I said counter clockwise left became right and vice-versa on multiple occasions
Some of you even heard Yee and Lang instead of Li and yang come on people if I was in a mirror universe
I'd have a beard be evil and be like Australian or something
Anyway, as chiral-chauvinist as it seems, I guess you have a right to complain about daintiness.
Or as James Drusco puts it: "it's my parity and i'll cry if I want to."