Philip Mannheim: The Story of Conformal Gravity

**Philip Mannheim** (0:00)
The missing mass that we've defined as the dark matter problem isn't missing. It's the rest of the visible universe, and it's been hiding in plain sight. It's been there all along.

**Curt Jaimungal** (0:10)
Is the graviton then composite or fundamental?

**Philip Mannheim** (0:13)
It's neither. It doesn't exist.

**Curt Jaimungal** (0:15)
Man, talk about fighting words.

**Philip Mannheim** (0:18)
Nature will keep you honest.

**Curt Jaimungal** (0:19)
This is the legendary Professor Philip Mannheim, and today I'm excited to bring you his first ever podcast. He's been working on a theory which solves dark matter and quantum gravity simultaneously for literally decades.

**Philip Mannheim** (0:32)
You start out with the standard theory.
It doesn't work for galaxies, so you invent dark matter. It doesn't work for cosmology, you invent dark energy. It doesn't work for quantum theory, so you invent string theory. I haven't done that. I've just taken the theory and I've solved it.

**Curt Jaimungal** (0:46)
On this channel, I, Curt Jaimungal, interview researchers regarding their theories of reality with rigor and technical depth. Today, what the professor argues is that we've been wrong about dark matter. We also have no big bang in the universe, according to his theory. Add further speculations on what collapses the wave function is a particle that we don't see.

**Philip Mannheim** (1:05)
It's one of the most startling discoveries in human history. I can't describe it any other way.

**Curt Jaimungal** (1:10)
Welcome to the story of conformal gravity. Professor, what precisely is Einstein's theory of gravity?

**Philip Mannheim** (1:19)
Well, I have to give you a somewhat extensive answer to that.
Einstein, in the early 20th century, developed what's called the special theory of relativity, and he was dealing with a problem. The problem was, there was Newton's laws of motion, and there were the Maxwell equations of electromagnetism, and they had different symmetries. What Einstein realized was, there had to be a universal symmetry, which we now call Lorentz invariance, which meant modifying Newton's law. And you can see this very simply. If you take Newton's law, it just says, you apply a force, you get an acceleration. Keep on applying the force, the acceleration will get bigger and bigger and bigger, and eventually you'll be able to go faster than the speed of light.
And so something had to change, if you were not going to be able to go faster than the speed of light. So what he did was, he came up with special relativity, and in a sense, this just generalized Galileo's objective, and Newton's first law of motion, that there's no force felt for uniform velocity, and Einstein made it for uniform covariant velocity. And so he finishes up with the theory in which observers can move with arbitrary speeds, but uniformly up to the speed of light, and the physics must be the same.
Now, missing from that were two things. One was, the observer is not required to only go at uniform velocity. The observer is allowed to accelerate. And there was another theory of Newton's, called Newton's law of gravity, which did not obey the relativity principle. So he had two problems that he had to solve. And it turns out that the solution to those two problems are different. Even though we usually look at Einstein gravity as a package, and that the first issue was, well, suppose you take Newton's second law of motion, the force is equal to mass times acceleration, and you rotate the system. Then you generate a new term. And Mach was very concerned about that new term. And he said, well, maybe it's fixed by an interaction with the distant stars. But what was really happening was that Newton's law of motion, as just written by Newton, and it starts out force is equal to mass times acceleration, but then is generalized to special relativity, still was not invariant under an arbitrary change in the coordinates. So if the observer chose to rotate, the physics should not change, but the equation changed. And Einstein found a way of writing down a more general form of Newton's second law of motion so that it would not change when the observer changed his speed or rotated. And that one is what we call the geodesic. And let me write it, state it down. m d2 x lambda d tau squared, that's the generalization to special relativity of Newton's law of motion, plus gamma lambda mu nu dx mu d tau dx mu d tau equal to zero, where gamma lambda mu nu is the first derivative of the metric. It's called the connection. And that equation is a general coordinate vector. And so if you make a transformation, that equation will transform and will remain zero.