In particle physics we try to understand reality by looking for smaller and smaller building blocks.
But what if that has been the wrong philosophy all along?
The year is 1925 and the young Werner Heisenberg is striving to understand the mechanics of
the newly-discovered electron orbitals of hydrogen.
His approach is strange and radical - rather than trying to map the detailed inner workings
of the invisible atomic structure - the traditional reductionist approach - he sought a model
that ignored the fundamentally unobservable internal mechanics.
His mathematical description should depend only on observable quantities - in this case,
the mysterious frequencies of light produced as electrons jump between orbitals.
This philosophy led to a series of seemingly miraculous mathematical insights, with the
final result being the birth of modern quantum theory and first complete formulation of quantum
mechanics - matrix mechanics.
Other representations of quantum mechanics soon followed - for example, the wave mechanics
driven by the Schrodinger equation and Paul Dirac’s notation representing evolution in a space of
quantum states.
These became better known than matrix mechanics, but the underlying philosophy of the Heisenberg
representation was not forgotten.
In fact the great Neils Bohr passionately advocated it, insisting that matters are the
observables - the measurable start and end points of an experiment.
According to this philosophy, the unobservable details that happen in between are not only
irrelevant, it may be meaningless to even talk about those details as real, physical events.
Despite its importance in the foundation of quantum mechanics, and being championed by
Bohr and Heisenberg, most physicists over the following decades did not subscribe to
this philosophy - at least not in practice.
They remained reductionists, and the quest continued for a detailed, mechanical description
of the hidden inner workings of atoms and of the universe.
This search for the underlying clockwork of reality led to quantum field theory, in which
all particles are described by vibrations in elementary fields that fill the universe,
and all interactions are calculated by adding up the exchanges of infinite number of virtual
particles.
But one ignores the wisdom of Heisenberg and Bohr at great peril.
Early quantum theory was plagued by problems - for example, how do you compute
infinite interactions?
And how do you avoid the infinite interaction strengths produced by some of those infinite
sums?
Some clever hacks - perturbation theory and renormalization - worked in many cases to
tame the infinities and yielded the incredibly accurate predictions of quantum electrodynamics,
which describes the interactions of the electromagnetic field.
But problems returned when we started to peer into the atomic nucleus.
At the beginning of the 1960s the atom was understood as fuzzy, quantum electron orbits
surrounding a nucleus of protons and neutrons.
Those nuclear particles were originally thought to be elementary - to have no internal structure,
just like the electron.
But new experiments were revealing that they seemed to have some real size - as though
they were made of yet-smaller particles.
These were scattering experiments - particles were shot into atomic nuclei, and the internal
structure was probed by the way those or other particles emerged.
Such experiments revealed that the forces binding these sub-nuclear particles together
must be so strong that space and time should break down at those scales, and our even best
field theory hacks seemed to fail.
And so a number of physicists turned back to Heisenberg’s old idea.
What if it was possible to understand a scattering experiment - like those used to probe the atomic
nucleus - not by modeling all the cogs and wheels of the field theory of the internal
nucleus, but rather by understanding the observables only.
In this case the observables were the particles that entered and left the nucleus in a scattering
experiment.
In fact, Heisenberg himself was way ahead of the game.
He’d already laid the groundwork in the early 40s with his work on something called
the scattering matrix, or S-matrix.
The S-matrix is a map of the probabilities of all possible outgoing particles, or out-states,
for a given set colliding particles - in-states.
The idea was invented by John Archibald Wheeler in the late 30s as a convenient way to express
the possible results of a quantum interaction.
In fact, it's still a very important tool in quantum mechanics today.
But Heisenberg took it in a very different direction.
In standard use, the S-matrix can be calculated if you understand the forces in the interaction
region - for example, in the nucleus of an atom.
But what if you don’t know those internal interaction forces?
Heisenberg sought a way to ignore that internal structure and, rather, treat the S-matrix
itself as fundamental.
The S-matrix was to become the physics of the interaction, rather than an emergent property
of more fundamental, internal physics.
Heisenberg’s made some progress in the 40s, but the approach came into its own 20 years
later when the atomic nucleus refused to give up its mysteries.
Through the 60s and 70s Geoffrey Chew and others took Heisenberg’s work on the S-matrix
and his anti-reductionist philosophy and developed S-matrix theory.
At the time, nuclear scattering experiments were producing a startling variety of different particles.
For example, many different mesons were discovered, which we now know to be composed of two elementary
quarks.
But at the time, prior to the discovery of quarks, no point-like, elementary nuclear
particles were known.
Rather than searching for smaller and smaller particles, Chew and collaborators promoted
a “nuclear democracy”, in which no nuclear particle is more elementary than any other.
They attempted to build scattering matrices with no elementary particles at all, and with
no details of nuclear structure.
But how is this even possible?
Remember, that quantum field theory fastidiously adds together a complete set of virtual interactions
that contribute to the real interaction.
S-matrix theory sought to avoid this, and instead tries to model a scattering experiment
- to build an S-matrix - by applying some general consistency conditions and then looking
for the only scattering results consistent with those conditions.
These conditions include things like conservation of energy and momentum, the behavior of quantum
properties like spin, and the assumption of a family of particles that can be involved
in the interaction.
But in order to avoid those sums of Feynman diagrams, S-matrix theory also relies on symmetries
between those virtual interactions.
In particular something called crossing symmetry.
An example of this is the fact that antimatter can be treated as matter traveling backwards
in time - that folds together large sets of Feynman diagram and helps us ignore the actual
causal structure within the interaction region.
And here’s another example of crossing symmetry.
Imagine two particles scattering off each other.
Two go in, and two go out - the out particles could be the different to the in particles,
or they could be the same just with different momenta.
There are two broad ways this can happen as follows: 1) the ingoing particles exchange a virtual
particle which deflects or transforms them into the outgoing particles - this is called
the S-channel; or 2) the particles annihilate each other, briefly forming a virtual particle,
which then creates the two outgoing particles - that’s the T-channel.
In regular quantum field theory you’d need to add up all the different versions of both
these two channels separately.
Before quarks and their interactions were properly understood, doing that sum seemed
impossible in the case of strong force interactions.
But in 1968, italian physicist Gabriele Veneziano figured out a hack.
It had been postulated that the S-channel and the T-channel should lead to identical
scattering amplitudes.
That fact enabled Veneziano to ignore the fiddly details of the separate channels and
derive a scattering matrix, which in turn allowed him to explain the peculiar relationship
between the mass and the spin of mesons.
The S-matrix approach to solving problems in quantum mechanics based on these global
consistency conditions and taking advantage of symmetries is also called a bootstrap model
- from expression “pull yourself up by the bootstraps” - the idea of raising yourself
up without concrete starting point to push off of.
So S-matrix theory looked extremely promising … until it didn’t.
It presented severe challenges on par with those plaguing quantum field theory - and,
as it happened, physicists solved the QFT challenges first.
Breakthroughs in our understanding of the behavior of quarks and gluons revealed that
the strong nuclear force does not actually approach infinite strength as was once feared,
and so a full quantum field theoretic description of the strong nuclear force was possible after
all.
The result is quantum chromodynamics - our modern description of sub-nuclear physics.
QCD deserves its own episode, so I’ll skip the details for now.
But the results was that S-matrix theory was sidelined, and quantum field theory reigns
supreme to this day as our reductionist description of the subatomic world.
So do we really now have a perfect mechanical description of the smallest scales of reality?
Well, not so fast.
Standard QCD employs sums over large numbers of intermediate virtual states.
And as we discussed in our episode on virtual particles, the physical-ness of these states
are questionable at best.
Quantum field theories like QCD surely gives us insights into the nature of the fundamental
workings of the universe.
Given their astounding predictive success, S-matrix theory now seems less fundamental
- it seems like an emergent set of relationships - what we call an “effective” theory - but
it turns out that it has led to deep insights that even quantum field theories could
not reach.
So I said that S-matrix theory got sidelined - that’s not exactly true.
Remember that clever little bit of work by Gabriele Veneziano?
It turned out that the Veneziano amplitude for meson scattering represents something
rather more profound that just predicting the results a scattering experiment.
Other physicists quickly realised that it was telling us that mesons could be described
by a very particular type physical system: a vibrating string.
And so string theory was born - at first as a description of strong nuclear force interactions
before quantum chromodynamics took over - but then as a theory of quantum gravity.
So our leading, and perhaps only current contender for a theory of everything was first derived
as a bootstrap model, an S-matrix theory.
Oh another example of bootstrapping a scattering experiment without understanding the internal
physics, Steven Hawking's derivation of Hawking Radiation.
And physicists are bringing the S-matrix back.
Here’s an especially awesome example.
We think that the largest structures in the universe today - galaxies and galaxy clusters -
as collapsed from quantum fluctuations in the extremely early universe.
Those fluctuations sometimes caused by individual particles.
Princeton’s Nima Arkani-Hamed and collaborators have performed what they call a cosmological
bootstrap to understand the nature of those early subatomic scale interactions based only
on current observations - which in this case is the distribution of gigantic galaxies on the sky.
That’s a cool result, but Arkani-Hamed’s work on something called the amplituhedron
has hinted that the S-matrix approach can be taken much, much further.
The amplituhedron takes Heisenberg’s old philosophy to the extreme - “only consider
the observables”- the amplituhedron doesn’t just eliminate the fiddly mechanics of quantum
field theory, it removes the very concepts of space and time.
These only emerge later as a consequence of spaceless, timeless particle scattering.
But all of these new efforts deserve their own episodes, then we’ll see how a simple
insight by a young scientist back in 1925 allowed us to pull ourselves up by our bootstraps
towards a better understanding of the quantum weirdness of space time.
Before we jump your questions, I just want to mention that the best and fastest way to
get smart people answering your questions is to join the Space Time discord channel.
It's hopping with lively conversations about everything space, physics, or things that
spacey physicsy people are into.
The discord is open to anyone who joins us on Patreon, even at the lowest $2 a month
tier.
OK, so previously we talked about a compelling new idea for how black holes might merge - perhaps
they're captured and then brought together in the searing hot accretion disks of quasars.
Persona non grata asks whether migration traps are like Lagrange points.
Not really - in fact we covered Lagrange points last week.
Migration traps are different.
If you place any massive body in an accretion disk it will both tug on and be tugged by
the surrounding gas.
In some places it gives up angular momentum - it's orbital energy - to the gas, causing
it to migrate inwards, while in other places it steals angular momentum, migrating outwards.
And between these inward and outward migration regions are places where no angular momentum
is exchanged. And, well, the black hole is trapped.
Adam Wulg asks whether gas surrounding a pair of merging black holes might significantly
affect the gravitational wave signature.
Well, the answer is that those waves would be affected - but not by much.
Gas causes the black holes to merge faster, so that should increase the frequency of the
those waves and to a lesser extend the actual shape of the waves.
But the fact is, almost all gas is going to be ejected from the near region of these merging
black holes before they actually collide, and LIGO only sees the merger in the last
second, so the effect would be weak.
LIGO is unlikely to have the sensitivity to distinguish a gassy from a non-gassy merger
for any individual merger.
It may be easier with neutron star mergers, which we see a LIGO signal up to a minute
before the merger.
"Q" suggests that it's oxymoronic to say that “All you need is a little quasar" to catch
black holes. Suggesting that there's no such thing as a little quasar.
Well actually, that's not quite true.
Active galactic nuclei come in many sizes - quasar is the name we use for the largest
and most powerful, where you can actually see the accretion disk.
Full-blown quasars our powered by supermassive black holes a few tens of millions to 10 billion
times the mass of the sun - and the small end of that range is indeed a "little" compared
to the insane top end.
And below the quasar range we have weaker active nuclei.
Those "little" accretion disks are still very capable of capturing even smaller black holes - and may
in fact be better at it because densities can be higher in the centers of small
galaxies where those weaker active nuclei are found.
But you should take all of this with a grain of salt; as rjw elsinga notes:
there are a lot of holes in this theory