Two of the triumphs of the early 20th century
were the development of Einstein’s theory
of relativity and the theory of quantum mechanics.
Einstein’s theory came in two categories.
One was his special theory of relativity,
which mostly dealt with objects traveling
at constant velocity, and the second was his
theory of general relativity, with objects
whose velocity is changing.
And, yes, for the purists, that delineation
is not perfect.
But it works pretty well.
If you take his second formulation and follow
it down the rabbit hole, you go from changing
velocities, to accelerations, and eventually
gravity.
Ultimately, Einstein’s theory of general
relativity is a sophisticated theory of gravity,
which has taught us that what we experience
as gravity is really the bending of space
and time.
Pretty weird stuff, to be sure.
But it’s been proven time and again, with
detailed predictions about the orbit of Mercury
and the recent observation of gravitational
waves.
There is no credible doubt in the scientific
community about general relativity.
It’s a good representation of reality.
The problem comes when Einstein’s ideas
meet quantum mechanics.
Now there’s no issue with special relativity.
Special relativity and quantum mechanics merge
just fine.
The result is quantum electrodynamics, quantum
chromodynamics and quantum field theories
in general.
I made perhaps a dozen videos on those subjects.
However, when general relativity- which is
to say Einstein’s theory of gravity- meets
quantum mechanics, the result is very different.
The two theories simply can’t coexist.
You get infinities and conceptual difficulties
everywhere.
And, even though some of the very smartest
minds of the last century have worked on this,
it’s still a problem.
We don’t know how to merge quantum mechanics
and gravity.
Now I made an earlier video about just why
scientists think that a quantum theory of
gravity should exist and it’s probably worth
your time to take a look at it.
But in this video, I’m not going to repeat
those reasons.
Instead, I’m going to just talk about an
idea as how one might merge quantum mechanics
and gravity.
The name of this particular idea is called
loop quantum gravity, or LQG.
Essentially, what it does is try to use what
mathematicians call discrete mathematics.
An example is simple counting and it is this
type of math on which quantum mechanics is
based.
This approach could avoid all the nasty and
troubling infinities that have perplexed mathematicians.
Loop quantum gravity then imposed two core
principles of general relativity.
The first is what is called background independence.
This means that it doesn’t require that
space exists prior to writing down the theory.
To give an analogy, if you're writing on a
piece of paper, you can assume the paper is
there and then you write on it.
Further, you can assume the paper has a certain
shape.
It’s flat.
The assumption of flat and unchanging space
is very common for most physics theories.
But in loop quantum gravity, you make no assumptions
on the nature of space.
To continue our metaphor, it's as if the equations
can exist independently of the paper, and,
even more interesting, they can bend and change
just like general relativity.
The second core principle has the very cool
name of diffeomorphism invariance.
The phrase is definitely a winner that you
can drop at your next cocktail party.
Diffeomorphism invariance simply means that
what’s going on at a point in space depends
only on that point and not where it is located
in space, nor what's happening at other spots
in space.
So, if you combine those two core ideas and
don’t require that the mathematics be continuous,
you can then explore the equations to find
out if they force you to conclude that space
and time is continuous or quantized and it
turns out that- drum roll please- both space
and time are quantized.
One of the core consequences of that conclusion
is that loop quantum gravity implies that
there is a smallest length, which is 10 to
the -35 meters, a smallest area, which is
10 to the -70 square meters and a smallest
volume, which is 10 to the -105 cubic meters.
Further, there is a smallest time, which is
10 to the -43 seconds.
So that’s a very strong implication.
It says that it's literally impossible to
have a smaller volume than 10 to the -105
cubic meters.
It’s kind of like looking at a beach closer
and closer, until you're resolving individual
grains of sand.
But, in loop quantum gravity, it’s impossible
to go smaller than a grain of sand, which
is our metaphor for a grain of space.
Similarly, this implies that there is no shorter
duration than a quantum of time.
It’s like a digital stopwatch, which counts
out the seconds, one after the other, but
there's nothing in between- except this time,
it goes 10 to the -43 seconds, then 2 times
10 to the -43 seconds, 3 times 10 to the -43
seconds and so on.
That’s really the core consequence of loop
quantum gravity- the smallest bit of space
and time.
Now there's been a bunch of mathematics and
ways to draw this out, involving terms like
spin networks and spin foam, but those take
some time to dig into and they don’t really
help your understanding all that much.
So, I won’t go into them here.
I’ll put a link in the description if you
want to read more.
Now one of the interesting questions is how
do you get from the quantum of space and time
to Einstein’s theory of general relativity?
It’s because when you add mass and energy,
you can distort the shape of the little volumes.
Now that seems like it wouldn’t make sense
because I said that there were quanta of lengths,
areas, and volumes, but you need to remember
that you are bending space and time and that
has the property that you can distort the
local definition of space in such a way that
the volumes are unchanged.
So these ideas of quantum spacetime are all
good and all, but are they real?
I mean, is there any way that we can test
them?
Well, we can’t get at them with our current
particle accelerators.
They simply aren’t powerful enough.
But it turns out that there is at least one
way to test the theory.
It turns out that if you take the idea of
quantized space and time and apply it to the
passage of light, there is hope.
Loop quantum gravity implies that different
colors of light travel through spacetime at
slightly different speeds.
High energy light- that is to say shorter
wavelength light- travels more quickly through
quantized spacetime than longer wavelength
light.
Now the differences are ginormously small
and aren’t accessible except through a cute
idea.
If you let light travel for very long distances
across the known universe, maybe you’d see
a difference.
There are a few examples of sources of light
that are bright enough to be seen across the
visible universe, and one of them is called
a gamma ray burst, which are the brightest
explosions in the history of the universe,
second only to the Big Bang itself.
They allow us to look at different color light
that has travelled for a very long time.
There are multiple instruments looking for
these, but one of the most powerful is called
the Fermi Large Area Telescope.
By the way, even though the Fermi telescope
and my own Fermilab share a name, they aren’t
related in any way, except for a respect for
Enrico Fermi.
When astronomers looked at distant gamma ray
bursts and analyzed the arrival time of light
of different wavelengths, it appears that
light of all wavelengths travel at exactly
the same speed.
So this could be a problem for loop quantum
gravity, or it could just mean that this particular
prediction isn’t universal.
We just don’t know.
But we’ll keep working on it because- either
way- the idea of a smallest bit of space and
time is simply a very cool idea.
Okay- that was fun.
Do I believe in loop quantum gravity?
No, of course not.
There’s no confirming data.
But it’s a fascinating idea and I am very
interested in finding ways to test it.
If loop quantum gravity is real, I’m sure
we’ll figure it out and, even if it’s
not, the journey will be fascinating.
Learning about this stuff is a great way to
stretch your mind, because, of course, physics
is everything.
