Dark matter and 5D physics

The Beginning

This is my inaugural letter on Substack. Everything I’ve published before have been republished from my Medium publication, The Infinite Universe. My medium articles are just that, articles. They are written as if for a magazine, for a wide audience. I hope for these substack letters to be a bit more intimate and free flowing. I don’t plan to necessarily stay on topic. Right now, I plan to send one out every Friday. Here goes.

I’m looking at how dark matter may be connected to 5D physics right now. The progress has been very slow. Theoretical physics research is a process of following up one dead end after another. What gets published is the one that worked, all the wrong stuff gets thrown in the trash. This probably creates the wrong impression that if you are failing, you are a failure. And that really depends on your attitude.

If your attitude is that your idea must be correct and your arguments must be perfect, then you are failing even if you don’t know it. I have had people approach me saying that they have “solved” quantum gravity for example or that they have already done the work that I say I’m doing. Discounting that most don’t have the math skills to back up their claims, that just shows they don’t understand the problem.

There are actually several solutions to quantum gravity. They work great. We just don’t know if they are right because most of them involve predictions that we can’t test. Quadratic gravity is a good example. Quadratic gravity works in 4D for the same reason that normal gravity works in 2D. (And cubic gravity would work in 6D and so on.) It is invariant to changes in scale. Yes, it is unstable in some cases but not all.

Most physicists don’t want a theory that just works though. They want something interesting. That’s why so many people piled onto string theory. It’s interesting.

If you approach the problem with humility, you are succeeding even if you don’t solve it.

I have had to learn this the hard way.

I’m not sure any physcist succeeded by trying to come up with a theory of everything. There are quite a few outstanding problems in physics that require a more concentrated approach. Let Nature guide you, not human desires.

I had the idea for a 5D theory about 14 years ago. Unfortunately, I knew almost nothing about general relativity at the time. My training was in statistical mechanics and quantum theory. I knew far more about lattice gauge theory. I was steeped in quantum field theory and Kenneth Wilson’s ideas, so that led me down the wrong path.

Eventually, I made my way through all the important books: Wald, MTW, and Will, not to mention countless review articles.

I’m going to lay out how I think dark matter works in 5D here by using an analogy. I have written this up mathematically elsewhere, but I assume most of you aren’t up to date on differential geometry. (If you want to be, please read Needham’s Visual Differential Geometry and Forms.)

Suppose we observe some 2D beings. We will call them the Flattians. These beings live in the x-y plane in some coordinate system, for example, such as on lines of lattitude on a planet. Their time points towards the North pole so that their future is North and their past is South.

These beings are unaware of our time. They are only aware of their own time, North-South. Yet, as they propagate North, they also move in time.

They are unaware of time because they are made of gas spread evenly over the planet. They don’t change in time because everything on their planet is in thermal equilibrium. They do change from South to North, so they are of course aware of that change.

The Flattians experience non-uniform acceleration in all directions across their planet. Acceleration is something that happens in time, however, so they see this as a gravitational force acting on them.

They also propagate North at non-uniform velocities (that also change) so that some parts are moving faster than others. They are unaware of this too because their clocks are only designed to measure based on changes in themselves from South to North and not anything more objective like rock features. In fact, their planet is all gas, and they are the gas.

This non-uniform movement North is another fictitious force (called a shift because they shift North each moment in time from their perspective).

When you combine these fictitious forces together, you get forces that look like gravity. Since the Flattians know that gravity comes from matter, they assume that there must be “dark” matter somewhere on their planet.

In certain form, these fictitious forces can even look like a modification of Newton’s gravitational theory. This very specialized form leads to Milgrom’s MOdified Newtonian Dynamics or MOND.

All of this is made possible by a cardinal principle of General Relativity, Einstein’s Equivalence Principle, but it is a little different than how Einstein envisioned it. Einstein saw the equivalence principle as the equating of a uniform acceleraing motion to a gravitational force. You can’t tell the difference between gravity and acceleration in other words. In this case, we are talking about non-uniform acceleration creating a fictitious gravitational field. Non-uniform fields can create any gravitational field you want, not just in a particular direction. And that looks like dark matter.

The Flattian planet is our universe and the Flattians represent the reference frame that we measure things in given that we are unaware of the 5th dimension. This is my theory of dark matter.

There is an enormous amount of math that goes along with this, so don’t take this as being a whole theory. If anything, it is an after-the-fact interpretation of the math. Most of the work is trying to present a theory that agrees with observation (including now not only galaxies but gravitational waves and cosmology) which is the difference between an idea and a theory.