Finding the God Equation

Could a 1-inch equation describe all of physics?
26 May 2021
Presented by Ben McAllister, Adam Murphy
Production by Adam Murphy, Ben McAllister.


An artistic image of travelling through space, with stars passing by surrounded by wisps of bright colours, and a bright star in the centre


This month on Naked Astronomy, we're seeking the answer to Life, the Universe and Everything. We're looking at the "God Equation", an equation that could describe everything we know in physics. What would it look like, and what would it mean? Adam Murphy and Ben McAllister were joined by physicist Michio Kaku, author of the God Equation, to discuss how this kind of equation would come about, and the kind of science that might be needed to explain it...

Ben - So physics as a discipline is doing pretty well, we've explained a lot of things about the universe, but there is one very big problem at the heart of a lot of physics that we just don't have an answer to yet.

Adam - How do you unite the tiniest physics, quantum mechanics, with the biggest physics general relativity?

Ben - Let's back up a minute. There are, as far as we know, four fundamental interactions that describe everything that happens in the universe. They're called the strong interaction, the weak interaction, electromagnetism and gravity. Those first three, we understand through what's called quantum mechanics, which is the theory of physics that describes things on very, very small length scales. For example, quantum mechanics tells us that photons, which are particles of light, are the tiniest particles involved in electromagnetism. And they mediate that interaction throughout the universe,

Adam - Strong and weak interactions have their own little particles that carry them along, also defined in the quantum picture of the universe. But gravity is described through a different theory, namely Einstein's theory of relativity, which looks at the big scale. And things get a little hinky when you try to combine the two.

Ben - A theory, which would be able to combine these two radically different length scales and describe all of the interactions in the universe is often called a theory of everything. Now, when asking what a theory of everything might be, remember, we don't have one yet, it's probably worth asking why we need one in the first place. Why do we need a grand unified theory if an adequate disparate theory might do?

Michio - Well. First of all, all of biology, all the life we see around us can eventually be reduced to chemistry. And chemistry in turn can be reduced to the laws of physics. And physics in turn, can be reduced down to relativity. That is the theory of the big bang and black holes. And also the quantum theory, the theory of the atom, which gives us transistors, lasers, and the internet. The whole ball of wax is to unify these two theories into a single theory. The God equation, an equation, perhaps no more than one inch long that will allow us to quote, "read the mind of God." Einstein spent the last 30 years of his life chasing after this grand unified theory. And we think that we are making breakthroughs in terms of achieving this one inch equation.

Ben - Figuring out this equation would be a massive breakthrough in physics. We’re talking instant Nobel Prize sort of thing. It’s the kind of thing people can, and have, spent their lives reaching for. A lot of people think that something like this is just so far out of our grasp, and is wishful thinking.

Adam - The thing is though it wouldn't be unheard of in physics. There's already something like this called the Schrodinger equation.

Ben - And the Schrodinger equation doesn't quite describe everything, but with just this one small equation, you can derive a huge amount of what we know about quantum mechanics.

Adam - And most of what we know about electromagnetism comes from just a few equations: Maxwell's equations. So we know we can write down very powerful things in just a few lines. So what would a theory of everything then look like?

Michio - Well, you know, I get a lot of emails from people that say "I got it. I got the theory of everything," and they'd make their proposal. So what is the criteria? If you're listening to this program and you want to win a Nobel prize in physics, and you want to go down as the next Einstein, what do you have to do? Well, the unified theory has to have three ingredients, just three. One: It has to contain Einstein's theory, which is about an inch long. General relativity is about an inch long. Then you have to include the standard model, this horrible theory of subatomic particles. That's about, maybe 10 lines of a sheet of paper. So on a sheet of paper, you can write down Einstein's theory, the standard model. And if it's finite, which is the third criteria, that's it. If you can create a finite amalgamation and finite mixture of Einstein's theory, plus the standard model, that's it, that's it. You will go down as the next Einstein. Your name would be mentioned by your great, great, great grandchildren as the great pioneer. That's all it takes, but you see the greatest minds in science have tried to meld these two theories together and have failed until recently.

Ben - If you had this theory, this one inch equation, you could begin to understand the universe at its most granular level. You could start to understand how everything comes together at a very, very fundamental scale.

Adam - Many scientists are asking then what physics needs to be applied to this situation, or even created out of whole cloth that could lead to a theory of everything and answer the question: What is the universe made of?

Michio - Pythagoras, the great geometer, thought it was music. A lyre string has harmonics, notes that you could categorise using mathematics, the mathematics of octaves and melodies and thirds and fifths. He thought that was the paradigm for the universe. Well, it never went anywhere. However, 2000 years later, we think that maybe Pythagoras was onto something. Today, we have something called string theory. In which case, music is the language of the universe, the language of subatomic particles, language of everything we see around you. And to be frank, that's what I do for a living. I'm one of the early pioneers in string theory, and we say maybe it's music, the language of the universe. So subatomic particles would be nothing but vibrations on a very, very tiny string. And then physics would be the harmonies of the string. Chemistry would be the melodies you can play on interacting strings. The universe would be a symphony of strings. And then the mind of God, the mind of God that Einstein chased after for so many decades would be cosmic music resonating through hyperspace. That would be the mind of God.

Ben - String theory then is one candidate or idea for explaining the entire universe on very small scales and therefore, a candidate to give us a theory of everything.

Adam - It is however, quite a complex beast, not helped by dozens of different pop culture explanations built on top of it. Essentially, it says that all the things we know in the universe are actually made of little tiny strings and the things we perceive as particles are different vibrations in these strings. Just as different vibrations of a violin string might give you an A or a D, different vibrations of these little universal strings would appear to us as a proton or a neutron.

Ben - It strives to explain gravity as an aspect of these strings, because just as one mode of vibration on a string could be a photon, which is you'll remember the particle that mediates the electromagnetic interaction, a different vibration might give you the particle that mediates the gravitational force. So you could sort of link these two very disparate length scale theories together. You could link these large-scale gravity theories with little quantum ones, as both aspects of the same fundamental strings.

Adam - Still with us? We know, it's weird. And while string theory might be pretty new and seem incredibly complex. According to Michio, the groundwork has been laid a lot earlier than you might think.

Michio - Well, it all began with Aristotle. Aristotle thought that, wind, earth, fire, water, four ingredients is what the universe is made up of. Democrates on the other hand said, no, no, no, no. It's not that, it's atoms. "A" in Greek means cannot "tom" means cut. So, atom means that which you cannot cut, that is indestructible atoms. And then as I mentioned Pythagoras comes along: "I can use mathematics. Mathematics to describe the notes on a vibrating string." And he went to a blacksmith shop and he saw the blacksmith pounding a piece of metal, the longer the metal, the lower the sound, the lower the note. And he said, "aha, length corresponds to frequency." And so he developed a whole theory of mathematics of harmonics and music, which we still use today, by the way, then the Roman empire fell apart. And for a thousand years, uh, science went into darkness until the coming of chemistry, with Mendeleev beginning to create order among the elements of the world. And then finally, by smashing these atoms, we then get a picture of what atoms look like, electrons circulating around protons and neutrons, but where do they come from? Every time you smash a proton, you come up with hundreds of subatomic particles. J Robert Oppenheimer, the father of the atomic bomb once said in frustration, the Nobel prize in physics should go to the physicist who does not discover a new particle this year. Well, how do we make sense of all these things? You know, many things have been proposed. Niels Bohr gave a talk at Columbia university in New York where I am right now. And he listened to a talk by Professor Pauli, his version of the unified field theory and Niels Bohr was shaking his head and said, "no, no, no, no, that can't be right." So finally, Niels Bohr, the founder of the quantum theory stood up and said, "Mr. Pauli, we in the back are convinced that your theory is crazy, but what divides us in the back is whether or not your theory is crazy enough." In other words, all the easy things have been tried. All the easy theories have been shown to be wrong, wrong, wrong. The only theory which has survived to create the God equation is string theory.

Adam - So if you're thinking that all this stuff sounds completely crazy, at least you're in good company

Ben -  And it gets a bit stranger. As we said earlier, according to string theory, everything is made up of tiny strings. And through the vibration of these strings, you get all the particles that we know around us. But these strings are tiny. Much, much smaller than the smallest subatomic particles we know of today. So how can we test it? Is there any way to see these strings?

Michio - Well, you know, people often ask the question, can we see atoms? Can we see atoms? And the answer is, well, not quite. You see, what do you mean by seeing. By seeing, you mean visible light, visible light. Visible light has a wavelength. The wavelength of visible light is larger than an atom. So you have to go to x-rays. With x-rays, you can then quote "see" atoms individually. So there are indirect ways in which you can quote "see" atoms. String theory is somewhat similar. String theory vibrates on a tiny, tiny scale called the Planck length. The Planck length is 10 to the minus 33 centimetres. It's really small. As a consequence, you cannot see it with visible light. Visible light is simply too big. Even with gamma rays, you cannot see strings. So in other words, strings is the ultimate basis of reality itself. Therefore, how do you see it? You cannot see it with light. Light is of course a by-product of the size of our retina. Okay. It's a by-product of biology. So you cannot see strings. Sorry about that.

Adam - String theory is hardly a sure thing. It may be promising, but we're still lacking the hard experimental evidence. And while it might be the most well-known, it's not the only theory working to do what string theory is. There's theories like loop quantum gravity, which works to reconcile quantum mechanics and general relativity without needing to be a theory of everything.

Ben - And then they all suffer from the same problem. Whilst the maths that described the theory checks out, everyone's carried their ones, and it's all been double and triple checked. The theories haven't been tested yet. And unfortunately, just because something works out really nicely mathematically, that doesn't make it correct physics. There's a lot of really elegant ways you can write down mathematical theories that just turn out not to be how the universe works.

Adam - So when you're trying to prove string theory, what are you looking for?

Michio - So we're looking for deviations. And that's where string theory and other theories come into play. There's got to be a higher theory. A theory beyond the standard model. And that's why, in some sense, that's why we built this $10 billion machine. This is the most expensive machine of particle physics ever created. And it was created to prove the correctness of the standard model and then to go beyond the standard model, and what lies beyond the standard model. We hope, string theory. There are other experiments that can prove the correctness of string theory, or point in that direction. Gravity wave detectors have now been built on the Earth. The Nobel prize was given to physicists who helped to build it. We're going to put them in outer space. Outer space. Space- based gravity detectors that are about 3 million miles across. Think of a triangle where each vertex of the triangle is a satellite shooting laser beams, over 3 million miles, to the next satellite. The slightest vibration from the Big Bang, the slightest vibration from the instant of creation, would be recorded by Lisa: Laser Interferometer Space Antenna. And this could give us baby pictures of the infant universe. Baby pictures or the infant universe, a trillionth of a second after creation itself. And maybe, just maybe we'll have baby pictures of the infant universe emerging from the womb. And maybe, just maybe, an umbilical cord, maybe we'll detect an umbilical cord connecting our infant universe to a parent universe. This is called inflation theory. It fits all the data, and inflation theory of course is compatible with string theory. So it means that we might be able to detect the presence of parallel universes, which of course is predicted by string theory. Our universe may not be the only game in town. If you have radiation after the instant of creation, you can then test it against string theory predictions, and string theory of course, goes before the Big Bang. It's a finite theory. It goes before the Big Bang and you can then surmise which of the post Big Bang radiations are compatible with the pre Big Bang radiation. You connect the dots in that way, you can actually begin to determine what the pre Big Bang universe might have been like. And we have theories about this called inflation. Inflation, of course, fits all the data so far. It is the leading theory of the Big Bang, but it doesn't tell you why it banged. Doesn't tell you what banged. It doesn't say anything about the bang itself. It just describes the bang, after the incident of creation. That's where string theory comes in. String theory then takes inflation and takes you to the pre Big Bang universe.

Adam - For string theory to be the winner, we're looking for things that based on what we know, don't make sense, that don't quite fit physics as we understand it. But that could be perfectly explained by string theory. Every time we see something like that, a little deviation from what is predicted by our current understanding, it would strengthen string theory.

Ben - And of course there aren't any discoveries that actively discount string theory, though. There is another thing that's probably required for string theory to work. And that's an idea called supersymmetry, which suggests that every particle has its own super superpartner. Electrons would have selectrons. Top quarks would have stop quarks.

Adam - Adams would have their super partners. Bens

Ben - Sure. Yeah, but all that aside Michio says he already sees symmetry like this in a lot of places in our universe.

Michio - To a physicist beauty is symmetry. And what is symmetry? Symmetry is such that if you have an equation or an object like a sphere and rotate it, you shuffle it around, it remains the same. Why is the kaleidoscope so beautiful? Because if you rotate it, you see that there's a symmetry, that it remains the same. That's why a snowflake. That's why a sphere. They are symmetrical and beautiful. Now what about equations? The same thing with equations. You might take Einstein's equations of space and time and rotate it. Rotate time into space and space into time. Bingo, the equations remained the same. That's why Einstein's theory is based on symmetry. What is the symmetry? Four dimensional rotations in Lorentz space. Now let's take a look at the quark model. The quark model, which is a model for the inside of the proton, has three quirks. If you rotate three quark among themselves, the equations remain the same. It's symmetrical under something called SU(3). Now you mentioned electromagnetism, which has a symmetry called U(1), and the weak force has a symmetry SU(2). So if you combine them, U(1) cross SU(2) cross SU(3), bingo, what do you get? The standard model of particle physics, which fits all the data. In fact, it is frustrating because we see no deviation from the standard model. So why is the standard model the standard model? Because there is a symmetry. The symmetry that you wrote particles into and the equations remained the same. Now just two weeks ago, it hit the papers, we found a slight deviation in the standard model. People are jumping on this because people are saying, "Aha. Now we're getting a glimpse, a glimpse of the post Large Hadron Collider era. We're getting a glimpse into a new law of physics." Hopefully what'll come out of that blip there, in the newspaper, is supersymmetry, a new symmetry beyond the symmetry of the standard model. Again, the standard model has a symmetry, U(1) cross SU(2) cross SU(3), the theory of rotating quarks, and light into each other, but there could be a new symmetry out there. We think that supersymmetry could be the ultimate symmetry of the universe. What does it rotate? It rotates the entire universe into itself. It is the biggest symmetry known to physics. It encapsulates every single subatomic particle into one equation, the God equation. So why is the GOD equation so beautiful and compact, because it has a symmetry, a symmetry that resonates with the human mind. And this is what we consider beautiful.

Ben - Supersymmetry then, according to string theory could also lead to this grand unified theory, but it's still a race to see which of the various candidate theories turns out to be the right one.

Adam - Why is string theory the thing that caught on then, why is it the big one? Why is it the one we've heard everywhere in so many different movies and TV shows?

Michio - Well, yes, if you take a look at The Big Bang Theory on television. Sheldon, the great theoretical physicist on that program works on string theory. And in some sense, if you don't work on string theory, you're missing the bandwagon. There is a bandwagon, for good or bad. There is a bad wagon. And if you don't work on it, in some sense you're missing the boat because so many of the brightest minds in physics are jumping on this theory. Now why? Well, a cynic would say it's because it's the only game in town.

Adam - Of course, these days it does have to share the stage with competing theories, but it's the one that got in on the ground floor, if you will, and it's the one that got into people's heads.

Ben - It's certainly a compelling idea. And it definitely captured Michio's imagination.

Michio - Well, personally, my parents were Buddhists, and in Buddhism, there's only Nirvana, there was no beginning of the universe. However, as a child, I was raised as a Presbyterian, where the Judeo-Christian theory is that there was an origin to the universe. So I've had two contradictory points of view in my head, either the universe had a beginning or it didn't, there's no ifs, ands or buts about this one or the other. But you see, the multiverse idea allows you to combine these two pictures together. Our universe had a beginning, our universe did have a big bang that set everything into motion, but you see, what does it expand into? Children ask that question. If the universe is expanding, what does it expand into, if this theory is correct? Then the quote, "mind of God '' is 11 dimensional hyperspace, that our bubble expands into a larger dimension, 11 dimensional hyperspace. And so we can now combine it with Buddhism. What is Nirvana? Nirvana, this timelessness into which the universe expands is 11 dimensional hyperspace. And that's what I work on professionally.


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