MATT O'DOWD: Between them, general relativity and quantum mechanics seem to describe all of observable reality.

And yet, they can't be simultaneously true.

They must be united in a deeper, yet undiscovered, theory.

After a century of work by the greatest minds in all of physics, why does this union still elude us?

[MUSIC PLAYING] The first few decades of the 20th century was a time of miracles for physics.

First, Einstein's relativity utterly changed the way we think about space, time, motion, and gravity.

Then the quantum revolution of the '20s and '30s overturned all of our intuitions about the subatomic world.

Together, general relativity and quantum mechanics have allowed us to explain nearly every fundamental phenomenon observed.

And they've predicted many unexpected phenomena that have since been verified.

And yet these two theories contradict each other in fundamental ways.

In the century since that golden era of physics, we've been trying to reconcile the two without success.

But today, on "Space Time," I'm going to begin our discussion of the great quest for this union, the quest for a theory of quantum gravity and for a theory of everything.

This is a big topic.

So in this episode, I want to give you the motivation.

What exactly are the conflicts between general relativity, or GR, and quantum mechanics?

I'll save the solutions for future episodes.

Let's start with summaries.

General relativity, GR, is Einstein's great theory of gravity.

In it, the presence of mass and energy warp the fabric of space and time.

And the motion of objects is, thereby, altered.

This results in the effect we perceive as gravity.

General relativity incorporates the earlier special relativity, which describes how our perceptions of space and time also depend on motion.

Unlike the earlier ideas of Isaac Newton, in which space and time are treated as separate and universal, special and general relativity blend them together into a combined and mutable space-time.

Where general relativity describes the universe of the large and the massive, quantum mechanics talks about the subatomic world.

It describes particles as waves of infinite possibility whose observed properties are intrinsically uncertain.

Our experience of the universe appears to be plucked from this landscape of possibilities in strange, but mathematically predictable, ways.

That math started with the Schrodinger equation, which tracks these probability waves through space and time.

But the Schrodinger equation treats space and time as fundamentally separate in the old-fashioned Newtonian way.

So clearly, there's a problem.

We already talked about how Paul Dirac fixed part of the problem with a relativistic wave equation for the electron.

Nowadays, modern quantum field theories fully incorporate the melding of space and time predicted by special relativity.

And yet they still don't directly incorporate the warping of space and time predicted by general relativity.

This causes issues-- some mild and fixable, others catastrophic.

Starting with the mild, we have the black hole information paradox.

We've gone on about that at length.

The black holes of pure general relativity swallow information in a way that can remove it completely from the universe, especially when those black holes evaporate via Hawking radiation.

That's a big conflict with quantum theory right there, which tells us that quantum information should never be destroyed.

But that same Hawking radiation offers part of the solution to the information paradox.

Following the work of Hawking, Jacob Bekenstein, and Gerard 't Hooft and others, it has become clear that information swallowed by black holes can be radiated back out into the universe via their Hawking radiation.

In a sense, both the source and the solution to the information paradox came from the discover of Hawking radiation.

Hawking, actually, derived the latter by finding a way to unite general relativity and-- in quantum field theory.

But that union was approximate and incomplete.

Really, it was a brilliant hack.

And you can check our previous episode for the gory details.

In fact, it's very possible to shoehorn the curved geometry of general relativity into the way quantum field theory deals with space and time.

But that approach completely fails when you have strong gravitational effects on the smaller scales of space and time, like the central singularity of the black hole or at the instant of the Big Bang.

For that, you need a true quantum theory of gravity.

But even thinking about the structure of curved space on the smaller scales leads to craziness and catastrophic conflicts.

I want to talk about these in two ways-- first, very conceptually, then a bit more technically.

Let's start by thinking about what it means to define a location in a gravitational field with perfect precision or, in other words, what it means to talk about very, very tiny chunks in the fabric of space.

In order to measure a location in space-- say, the location of a particle-- you need to interact with it.

You would typically do that by bouncing a photon or other particle off the object.

The more precisely you want to measure position, the higher the energy of that interaction.

That's why we use electron microscopes or X-rays or even gamma rays to take images of extremely small things.

So let's say we shoot a particle with a beam from a particle accelerator to measure its location with extreme precision.

The Heisenberg uncertainty principle tells us the minimum energy of our beam for a given precision.

It turns out that to measure a position to an accuracy better than a Planck length around 10 to the power of negative 35 of a meter, the amount of energy you would need to put into that region of space would make a tiny black hole with an event horizon one Planck length in diameter.

Try to measure more precisely, and you need more energy.

That means you make an even larger black hole.

So general relativity plus Heisenberg say it's impossible to measure a length smaller than the Planck length.

Steady viewers will remember that the uncertainty principle talks about the trade-off between position and momentum.

But large momentum also means large energy.

The uncertainty principle also defines the precision trade-off between time and energy.

So this same argument can be used to suggest a fragmentation of time.

Try to measure any time period shorter than 10 to the power of negative 43 seconds, the Planck time, and boom-- black hole.

For those of you who already watched our episode on the Heisenberg uncertainty principle, here's another way to think about this.

We know that for a particle to have a highly defined location, its position wave function needs to be constructed from a wide range of momentum wave functions that include extremely high frequencies or extremely high momenta, i.e., the more certain its position, the less certain its momentum.

And so large momenta are possible.

So position can be defined to within a Planck length.

And then momentum becomes extremely uncertain and includes the possibility of ridiculously high values.

That means ridiculously high kinetic energies.

Particles whose positions are defined within a Planck length can spontaneously become black holes.

Of course, those black holes don't really happen.

Rather, they're an absurdity that tells us that something is missing in our description of either quantum theory or general relativity, or both, at the smaller scales.

Let's look at the real conflict.

Standard quantum theories treat the fabric of space-time as the underlying arena on which all the weird quantum stuff happens.

Given that sensible underlying structure, it's relatively routine to apply quantum principles, or quantize, most of the forces of nature.

For example, classical electromagnetism becomes quantum electrodynamics when you quantize the electron field and the electromagnetic field.

But in the resulting math, the new quantum fields still lie on top of a smooth, continuous grid of space and time.

So what if you want to quantize gravity?

The gravitational field doesn't lie on top of space-time.

It is space-time.

To quantize gravity, you have to quantize space-time itself.

That leaves no clean coordinate system on which to ground your theory.

This sounds annoying.

In fact, it's a disaster.

It leads to several problems.

But I'll focus on the one that wrongly predicts these crazy fluctuations on the Planck scale.

In general relativity, the presence of mass or energy warps the gravitational field.

There can be no exceptions.

Any energy must cause space-time curvature.

If not, you could build perpetual motion machines, for example, using the Casimir effect.

In quantum gravity, gravity itself becomes an excitation in our quantized space-time.

The energy of those excitations should themselves precipitate more space-time curvature, represented as further excitations.

In other words, gravity should produce more gravity, ad infinitum.

This type of self-interaction or self-energy is seen in other quantum field theories and is hard to deal with, even there.

For example, in quantum electrodynamics, the electron has a self-interaction due to its electric charge messing with the surrounding electromagnetic field.

In QED, the mess is fixed with something called perturbation theory.

It's a scheme to calculate a complex interaction, like the buzzing electromagnetic field around an electron, with a series of corrections to a simple, well-understood interaction, which might be the electron in a quiet electromagnetic field.

We talk about this more in our episode on the g factor.

So perturbation theory is applied throughout quantum field theories of the standard model.

And it works because, one, these corrections are small and/or, two, even in the case where the corrections appear large or even infinite, they can be constrained.

They can be brought back to reality by actual physical measurements of a few simple numbers in a process called renormalization.

For example, measurement of the mass and charge of an electron renormalizes quantum electrodynamics to allow incredibly precise calculation of the electron's self-energy.

None of this works when you try to quantize general relativity.

When you have strong gravitational effects on the quantum scale, the self-energy corrections blow up to infinity.

But unlike other quantum field theories, there are no simple measurements you can do to renormalize those corrections.

In fact, you would need infinite measurements to do so.

We say that a quantized space-time of general relativity is non-renormalizable.

The non-renormalizability of quantized general relativity is connected to the idea that precisely localized particles produce black holes.

Space and time simply cannot behave in the familiar way below the Planck scale.

And so the simplest approach to quantizing gravity and space-time must be wrong.

Generations of physicists, starting with Einstein himself, spent their lives trying to fix this to unite quantum mechanics and general relativity.

They are still trying.

Even though we still lack an accepted resolution, the struggle has not been without progress.

There are two main approaches.

One is that you search for a way to quantize general relativity in a way that avoids the infinities and non-renormalizability.

The leading example of this is loop quantum gravity, or you just assume that GR and, indeed, the mutable fabric of space-time itself are emergent phenomena from a quantum theory deeper than our currently accepted theories.

That's exactly what string theory seeks to do.

In upcoming episodes, we'll explore these and other ingenious approaches to crack the greatest problem in modern physics,