Physics progresses by breaking our intuitions, but we are now at a point where further progress
may require us to do away with the most intuitive and seemingly fundamental concepts of all—space
and time themselves.
Physics
came into its modern form as a description of how objects move through space and time.
They are the stage on which physics plays out.
But that stage begins to fall apart on the tiniest scales and the largest energies, and
physics falls apart with it.
Many believe that the only way to make physics whole again is to break what may be our most
powerful intuition yet.
In our minds, space and time seem pretty fundamental,
but that primacy may not extend beyond our
minds.
In many of the new theories that are pushing the edge of physics, spacetime at its elementary
level is not what we think it is.
We’re going to explore the “realness” of space and time over a few upcoming episodes.
We’ll ask: Do our minds hold a faithful representation of something real out there,
and if not, why do we think about space and time the way we do?
And if space and time aren’t fundamental, what is?
What do space and time emerge from?
But today we’re taking the first step by exploring how the notion of absolute space
and time in physics came about in the first place, and how that notion is beginning to
fall apart.
We have this sense of space as an extended emptiness - a volume waiting to be filled
with matter - a regular, continuous, mappable … space, in which everything that exists
is embedded.
Meanwhile time is the continuous rolling of future into past through the present, all
governed by the same unstoppable clock.
But this idea of space and time as having an existence “out there”, independent
of its contents, became cemented in popular intuition relatively recently, at the same
time that they became cemented in physics.
However humans have been arguing over the reality or the fundamentalness of the dimensions
for millenia.
We can summarise the two main conceptions of spacetime as either relational— space
as a network of positional relationships of objects —or absolute—a real entity that
exists independently of objects, and rather, contains the objects.
The latter seems to have emerged only relatively recently.
Let’s start with the ancients.
They certainly thought a lot about space—after all, they had maps and they invented geometry.
But the geometries of Euclid and Pythagorus and others didn’t need the notion of space
as an absolute entity—they were relational.
For example, a triangle is defined by the relative lengths of its sides and its internal
angles.
You don’t need a coordinate grid to define a triangle—which is good, because the ancient
Greeks didn’t have one.
Sure, their maps had longitude and latitude, but they didn’t have our own mathematical
habit of gridding up empty space with x, y, and z axes.
As such, they didn’t tend to think of empty space as having its own independent existence.
The idea of the coordinate grid came much, much later.
Perhaps you’ve heard of the Cartesian coordinate system.
X, y, and z axes, each at 90 degrees to the others and gridded up so that any point in
space can be defined with three numbers - the value of the closest grid-mark on each of
the axes.
This idea feels pretty intuitive to many of us, but it wasn’t commonly used until after
1637, when the French mathematician and philosopher
Rene Descartes made it cool.
With the coordinate system, it became possible to represent abstract numerical concepts in
spatial terms—for example, by graphing an algebraic function.
But it also gave us a tool for describing
arbitrarily large and imaginary physical spaces—and
this application would soon revolutionise all of physics.
Regarding the actual nature of space, Descartes was firmly in the camp of philosophers like
Plato, who didn’t believe in empty space.
Descartes said that space is only real as far as it defines the extension of objects
and matter.
But the invention of the first true mathematical coordinate system opened the door for a very,
very different conception of space.
And that new conception was almost entirely due to Isaac Newton.
He gave us a set of equations that could, apparently, completely describe the motion
of objects and how those motions change through the forces of their interactions.
Newtonian mechanics is built on Descartes’ coordinates, and assume a universal clock.
Those mehcanics proved wildly successful— revolutionary, really.
So much so that many, including Newton, began to see the foundational building blocks of
the mechanics—the coordinate of space and time—as in some way physically real.
Newton himself insisted that space is absolute; it exists completely independently of any
objects within it.
The empty volume implied by the Cartesian grid is a thing in itself.
And according to Newton time is also absolute.
From Aristotle to Descartes, “time” was mostly understood as a counting of events.
But In Newton’s view, there’s a single universal clock that keeps the same time for
all observers--time passes “by itself ”, even in the absence of any change.
Newton also believed that there was an absolute notion of stillness.
Like, a master frame of reference whose x, y, and z axes are unmoving, and if your position
was fixed relative to those axes then you were truly still.
This is contrary to the ideas of Galileo a century prior, who showed us that velocity
is relative—the speed you measure for another traveller depends on your own speed.
The laws of physics are the same in any non-accelerating,
or inertial frame, and so all such frames
are equal.
While Newton accepted the mathematical consequences
of Galilean relativity, he thought the difficulty we had
in defining a preferred inertial frame was a limitation of the human mind, not of the
universe.
The success of Newtonian mechanics elevated the notion of the realness of space and time
in everyone’s minds.
But there was one prominent naysayer.
Newton had a nemesis.
Or maybe it was Newton who was the nemesis to this guy.
Ok, he shared a mutually nemetical relationship
with the German mathematician Gottfried Wilhelm Leibniz.
Their most famous rivalry was over the discovery
of calculus, which they figured out independently—with
Leibniz probably getting to it first.
Newton however accused him of plagiarism, and being by far the most powerful scientist of his
day, secured the credit for himself.
But another point of contention between these two was on the nature of space and time.
Leibniz did not accept Newton’s assertion that these dimensions were in some sense real
and independent of anything in them.
Instead, he thought that both space and time were relational.
What does that even mean?
Well, it means that objects exist, but they don’t live in a 3- or any other dimensional
space.
Rather, what we think of spatial separation is a quality of the objects themselves—or
rather of the connection between them.
Exactly why Leibnitz thought this and rejected Newton is a whole thing, that we don’t
have time to get into right now.
Instead, let me try to give you a sense of what it could mean for space to be encoded
in objects or in their relationships, rather than existing independently to those objects.
Let’s start by imagining only one dimension of space, represented as a line.
This is a Newtonian space, where every point represents an absolute position in a 1-D universe.
We can put some particles in the universe.
The position of each in space is defined by - well, its position in space—whatever grid
mark it’s next to if we add a coordinate system.
The particles might have intrinsic or internal properties—say, mass, electric charge, etc.,
but their position isn’t a quantity that’s intrinsic to the particle.
In Leibniz’s view there is no space, so we get rid of the line.
The particles still exist, but they aren’t anywhere.
They’re sort of just bundles of properties with no size or location.
Space doesn’t exist so maybe we should place these particles on top of each other, but
then again if location is meaningless we might as well separate them so we can see them.
Let’s add a new property to each particle that we’ll call X.
X is what we call a degree of freedom—something about the particle that can take on different
values, and it can change.
Other degrees of freedom could be energy and phase and spin and so on.
X behaves in a particular way.
For example, it can change freely.
If it’s changing, then it keeps changing at the same rate and in the same direction.
Now these particles have no idea about each
other's existence, except in a special circumstance.
For example, If two particles have values of X that are close to each other then those X values influence
each other, changing the rate at which the dials turn.
Maybe they want to try to be more similar, or maybe they try to be more different.
If we were to represent these X values with position on a number line - an x-axis - then
the behaviour of the particles looks just like particles moving around in space and
attracting or repelling each other only when they’re close together.
We can’t tell the difference between particles moving in space versus space-like behaviour
emerging from a degree of freedom within the particles.
This thought experiment isn’t explicitly
what Leibniz described, nor is it how things should
really be to explain a universe like our own.
For one thing, we need 3 spatial dimensions, not one.
X, Y, & Z would all have to be close to each other for particles to interact.
Also, Leibnitz thought that position was encoded in the relationship between particles,
not in the objects themselves.
He gave his elementary particles names - monads - which among other things had rudimentary
Comments
Post a Comment