The people behind the greatest leaps in physics - Einstein, Newton, Heisenberg, all had the
uncanny ability to see the fundamentals - see the deepest, underlying facts about the world,
and from simple statements about reality they built up their incredible theories.
Well what if we all had a recipe book for doing exactly this.
Well, one might be just around the corner.
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Pretty much all of physics can be boiled down the following:
Step 1.
describe some aspect of the universe with numbers - like the temperature, pressure,
etc of a gas or the position, velocity, etc. of a particle
Step 2.
Come up with a set of equations that predict how those numbers change over time - e.g.
the laws of thermodynamics or Newton’s laws of motion
Step 3.
Based on some initial state - a starting set of these numbers predict how the system will
evolve at all future times Step 4.
Profit, by building heat engines, airplanes, skyscrapers, and our entire modern world
In short, physics works by applying dynamical laws to some input state in order to predict
an output state.
We consider those laws to be “true” when these predictions match reality.
This mechanistic approach to describing the world has been wildly successful.
In fact it’s hard to imagine another way to do physics.
Except that, in many ways, the mechanistic approach may have reached its limit.
It’s nice to have a set of equations for each separate aspect of the world - but if
these theories are really true then they should ultimately come together into some master
theory - and they do, to an extent.
You can derive all of thermodynamics and Newtonian mechanics and electromagnetism and so on from
two master theories: quantum mechanics and Einstein’s general relativity.
But the master theory that unifies those last two has so far eluded us.
For nearly a century, our greatest minds have been trying to come up with dynamical laws
that describe all of nature - a mechanistic theory of everything.
And they’ve failed.
Some are starting to wonder if we need to rethink how we do physics at the fundamental
level.
One such approach is constructor theory, developed by David Deustch and Chiara Marletto at Oxford
University since 2012.
In the mechanistic approach the fundamentals are the mathematical descriptions of how a
process occurs.
In constructor theory, the fundamentals are simpler - they are binary facts about whether
or not a particular process is possible.
It uses theories like general relativity and quantum mechanics, along with more fundamental
conservation laws, or principles, to rule out impossible output states given an input
state of a system.
The transformations between the input and output states are dubbed tasks, and if a task
is possible, then there exists a system known as a constructor which can perform the task.
Constructor theory is inspired by information theory and the theory of quantum computation.
As David Deutsch says, if a quantum computer can, in principle, simulate any process in
physics, then all of physics can be expressed in terms of the theory of quantum computation.
This hails back to the work of John von Neumann, who came up with the concept of the universal
constructor - basically a generalization of a universal computer - it’s a system that
can perform any computation OR physical task, including creating a copy of itself.
Deutsch realized that this notion could be used as a way to describe how nature works
- we can break up reality in terms of constructors that can cause changes in the world via “tasks”
- transformations that for a given constructor are either possible or impossible.
Ultimately, constructor theory is about something called a counterfactual - which in constructor
theory is a sort of a meta-fact - it’s the fact of whether or not a given task is possible
or impossible for a given constructor.
And, in fact, the counterfactuals are more important than the constructors.
As Marletto puts it, it’s the science of can and can’t, which is also the title of
her pop-sci book on the subject.
The power of constructor theory is that it allows us to explore physics without having
to solve the detailed equations of motion.
On the one hand that allows us to make far more general statements about how a system
can behave.
I’ll come back to an example of that.
But it also potentially allows us to understand aspects of nature where we don’t even know
the dynamical laws.
For example, understanding the union of quantum mechanics and general relativity.
Before we get to how constructor theory is going to explain everything, let’s look
at a simple example to define some of these concepts.
The mechanistic philosophy that dominates physics really started with Isaac Newton,
so it’s appropriate to start with the falling apple that apocryphally inspired a lot of
this.
In Newton’s picture, the apple has a current state, stationary and up in the tree.
We use that state as the input, apply the laws of gravity and motion - and we find the
output state - that the apple fell to the ground.
In the constructor theory view, we ask what tasks are possible and impossible for the
apple given its input state.
Is it possible for the apple to stay where it is, hovering in the air?
It’s not.
The laws of general relativity forbid this task: as a free-falling body the apple must
follow a geodesic through spacetime, which results in it falling towards the Earth.
What about the task of the apple transmuting into gold?
Again, this task is impossible, since it’s ruled out by the laws of quantum mechanics
and the principle of conservation of energy.
In fact, the only possible task available to our apple is the one which results in the
output state that we calculated earlier.
This just serves to give an idea of the perspective
shift in constructor theory.
Let’s look at a case where this is actually useful.
David Deustch gives the example of the perpetual motion machine of the first kind - a device
from which infinite energy can be extracted.
For example, a wheel powered by falling water that also pumps that same water back up to
the top while at the same time driving an electric generator.
We can rule out the possibility of this with a mechanistic explanation, talking about the
torque induced by the generator to slow the wheel, which stops it pumping water fast enough
to maintain the same power.
But that’s not very general.
We’d need a separate mechanistic approach to rule out every different type of the perpetual
motion machine.
Or we could take a shortcut.
The law of conservation of energy says that it’s impossible to create energy from nothing,
and the second law of thermodynamics tells us that it’s impossible for a non-isolated
system to keep running forever.
By applying general rules about what is possible or impossible - by applying counterfactual
statements - we can rule out a much larger space of impossible processes than in the
mechanistic approach.
You’d be justified in thinking that there’s nothing new here.
We already use counterfactuals regularly in physics.
There’s a whole family of rules and laws and theorems that say what can and can’t
be.
We cobble them together into chains of deductive reasoning to carve out our physical laws - they
are the sculpture that’s left after we carve off all the “can’ts” from the marble
block of all possible mathematics.
But there’s something a little ad-hoc about the way these rules are applied.
An aim of constructor theory is to formalise our statements about what is possible and
impossible into a sort of “algebra of possibility”.
At its heart, constructor theory is based on information theory and uses related tools
like set theory in its formalism.
It focuses on what can and can’t be done with information.
This means that constructor theory can be applied even when we don’t know the dynamical
laws of a system - when we don’t have a full mechanistic theory.
For example Chiara Marletto has used constructor theory to describe a scenario for testing
whether gravity is quantum in nature.
And we certainly don’t have a mechanistic theory for quantum gravity.
This approach relies on defining systems of information - called information media - and
how systems of quantum information - or superinformation
media - must differ from regular information
media, which would be purely classical.
For example, for systems of quantum information there’s a particular task that is possible
that is impossible for classical systems.
That task is entanglement between the information elements - the qubits in the quantum case.
The thought experiment goes as follows.
You have two qubits, which could in principle be entangled with each other.
That means their states could be correlated in a way that allows them to have an apparently
non-local effect on each other.
That entanglement has to be initially induced by a local interaction - the qubits must come
into contact.
Or it could be induced by a chain of contact - one qubit to another to another to our final
qubit.
From the definitions of what an information medium is, Marletto argues that this chain
of quantum elements is equivalent to a quantum field.
And she argues that only a "superinformation medium" - aka a quantum field - could mediate
the entanglement of two spatially separated qubits.
Therefore if we could design an experiment that showed that gravity could induce entanglement
between separated qubits, then gravity has quantum properties.
This is cool because it gives us an experimental test of quantum gravity that has absolutely
no dependence on a particular theory of quantum gravity.
It doesn't need the dynamical laws of such a theory, or even of quantum mechanics or
general relativity as they currently stand.
At the very least, it pares down the facts that we need to assume about the mechanistic
theory in order to make the argument - in this case, just the way informational elements
interact, say, by entanglement.
David Deustch has said that constructor theory may be the most fundamental way to describe
reality - in which case the rest of physics can be derived from Constructor Theory once
it’s properly developed.
That’s a lofty claim, but consider how previous great theories emerged.
They came from deductive reasoning - the application
of crystal clear logic - to the most stripped-down
facts about the world.
Einstein’s general theory of relativity came from asking what were the inevitable
implications of simple statements like the equivalence principle and the invariance of
the speed of light.
Werner Heisenberg came up with the first version of quantum mechanics by stripping away all
but the bare facts about the nature of electron
energy levels - including abandoning any pre-existing
dynamical laws.
Deustch has called such efforts “antecedents” of constructor theory, which sounds presumptuous,
but it gets to the spirit of the effort: to formalize the process of applying logical
deduction
from the barest facts - or counterfactuals - of what is possible and what is impossible
within this physical space time.
Before we get to comments, I want to tell you about a new documentary series on PBS Voices,
“American Veteran: Keep It Close.” Each episode tells the story of a U.S. military veteran
and a special object they have from their time in service — a vial of lip gloss, a small stone,
even a microphone — and how these mementos helped keep them grounded through extreme circumstances.
Check it out, link in our description, and let them know that Space Time sent you.
As always, if you've joined us on Patreon, I can't emphasize enough how helpful your support
is in keeping this show going. But today I want to give a huge shoutout to our Big Bang supporter
Ari Paul. Ari, without your support, the task of Space Time would be impossible,
which in the language of constructor theory makes you a counterfactual. We are humbled
and grateful that, as one of the deciders of what is and isn’t possible in this universe,
you’ve decided that the laws of physics should permit the existence of Space Time.
Last time we talked about the latest ideas on the weird world of quantum tunneling.
Let’s see what you had to say.
Jeff page has a great question: Could a particle tunnel through .. nothing. As in could it
quantum teleport even through empty space in Fact do particles even travel at all or do
their wave functions just randomly tunnel every which way so that their apparent path is just
the averaging out of all of this motion. There’s a LOT to unpack here. First on the
question of whether tunneling can happen through empty space. A particle moving in free space does
have a range of possible positions defined by the spread of its position wavefunction, so if
you want to define tunneling as “the particle not being exactly where you thought it would be” then
the answer is sort of, yes. A particle can appear some distance from its most likely position.
But that’s not the technical definition of tunneling. The presence of a barrier changes the
potential energy in that region. If that potential barrier is too high for the particle to cross by
virtue of its own energy, its wavefunction drops away exponentially. Tunneling is explicitly
defined as motion across this exponential decay to the other side of the barrier.
As for whether we can think of all motion as tunneling - well, not by the technical definition.
It’s probably better to think of all motion as … not motion, but rather as the evolution
of the wavefunction until some event causes a choice of position to be made. At that time the
position is chosen from all possible positions, including the low chance of some unexpected jumps.
Farfa asks a related question: can the “travel” during a tunneling event be considered travel at
all. Does it just start existing on the other side of the barrier without crossing the intervening
space. This is a tough one. It’s not clear that the particle itself is ever “inside the barrier”,
but its wavefunction certainly is inside the barrier, and its wavefunction does seem to
take time to traverse the barrier. It’s very, very difficult to define a reasonable concept for time
to measure how long this takes - as we discussed in the episode. But various efforts since the
1980s using various definitions of crossing time have shown that it’s not instantaneous.
In some cases its pretty quick - quicker than light would make the same journey sans barrier.
Dragrath1 says, and I quote Interesting if this does indeed get confirmed to be unable
to violate causality this may be able to greatly strengthen the case for distance being an emergent
consequence of causality. If every particles wavefunction is really spread over all of space
can anything really move at all except in relation to something, say a causal
update propagating through a network?” To that I only have Daniel Jensen’s
comment to quote in reply: “That feel when causality is only highly statistically likely”
These comments are telling me that you lot are really starting to get a sense
of how far our perception of reality is from baseline reality.
For example we could be a simulation. TBatlas says
that the universe saves CPU space by not fully rendering particles that aren't being viewed by
the player. This leads to entities sometimes glitching through walls.
Seriously - Imagine you built a video game and one day you noticed the mobs were tapping on the walls
and measuring framerates. Shush everyone, back to your assigned paths, the devs will notice.