Many Worlds Interpretation may not require worlds to split
And here is what it would look like
I have argued for a while that quantum mechanics can be interpreted correctly if you introduce a 5th dimension. In that case, different quantum outcomes like Schroedinger’s cat being alive and dead simultaneously make sense because the cat is alive at some points in the 5th dimension and dead at other points.
The same goes for anything else: entanglement for example, where two particles appear to exchange information faster than light, need not do anything of the kind if a 5th dimension is introduced because the superluminal exchange of information is an illusion. Each “slice” of that 5th dimension has a perfectly ordinary world in it with ordinary outcomes. It is only because of the interaction between slices that we experience quantum weirdness.
Yet, that interaction is invisible to us.
In my previous post, I swept all that away because I believed that I had calculated a stationary probability distribution across the 5th dimension. That meant that the 5th dimension appeared to disappear. But I had not finished all the calculations so I failed to realize that a stationary probability distribution does not imply a stationary particle.
As an example, I can have particles moving around randomly in an empty room at a fixed pressure and temperature and the probability of finding the room in a particular state at any time is stationary. It does not change with time. Nevertheless, the microscopic state of the room changes all the time.
It turns out that this is true even when things aren’t random.
Let me explain:
Ordinary quantum physics works like this:
At the quantum level, a particle is described by something called a wavefunction. The wavefunction obeys an equation called Schroedinger’s equation. Schroedinger’s equation helps us to calculate the probability of finding the particle in a particular state.
For example, a particle in a very small box, such that quantum effects are measurable, will only be measured in specific, quantized energy levels rather than any energy at all. As the box becomes smaller, the higher energy levels become more likely.
Why should that be so? Why should the box affect the particle?
Well, it’s because the wavefunction fills the whole box and there are non-local effects on the particle, at least that is the standard explanation. The walls of the box affect the particle even if it doesn’t appear to be touching the walls at the point of measurement.
This is the sort of thing that Einstein called “spooky action at a distance”. Why can a wavefunction that fills a whole space suddenly collapse into a tiny particle that fills no space?
My version of quantum physics, however, works like this:
The wavefunction is a complex entity, meaning it is made of real and imaginary parts, but in truth is made up of two real-valued pieces, phase and amplitude, just like any other wave. The phase is proportional to something called the action of the particle while the amplitude describes how the phase moves around in a 5th dimension.
You can think of the phase as being like a potential energy that, when translated into a force field, similar to an electric field, creates a kind of charged fluid for probability. The amplitude describes the magnitude of the charge of that electric field.
Anyway, physicists have long known how to go from Schroedinger’s equation to an equation for the action called the Hamilton-Jacobi equation. Richard Feynman, the great Nobel laureate, made an off-hand remark about it in his paper based on his Ph.D. thesis in 1948 linking the Hamilton-Jacobi, Schroedinger’s equation, and his path integral formulation of quantum theory.
The missing piece was that, if you want to encompass all of quantum physics, you have to add a 5th dimension or you won’t get all the quantum weirdness. You will be stuck with a Hamilton-Jacobi equation that just happens to be the same as your Schroedinger’s equation, but you can’t go further to actual equations of motion.
That is what the 5th dimension gives. It allows you to create equations of motion for motion itself.
At the time I wrote my last post, I had done a lot of this derivation but I hadn’t derived the equations of motion for particle trajectories.
I assumed, wrongly it turned out, that these trajectories would be stationary in the 5th dimension just like the probability distribution. This led me to conclude that I could come up with an interpretation of quantum theory that gets away from the Many Worlds.
Well, the math led me right back to Many Worlds, but not the Many Worlds interpretation that most people are familiar with. Rather, it led me to a Many Worlds Interpretation with no world splitting. In other words, when you measure a quantum particle in a Schroedinger cat state, worlds do not split apart with one result going one way and the other result going the other way as a consequence of measurement. They stay together.
This version of Many Worlds, championed by Lev Vaidman (whom I had the pleasure to meet and interview some years ago for my Aeon piece on Possible Worlds), indicates that our perception of the world as being Single, rather than Many, is an illusion.
This illusion could be because the 5th dimension is like time and we can only perceive one “moment” of it at a time. Although in physics we describe particles using lines called worldlines that trace out the particle’s position over time, we do not ever perceive particles as lines, but only as points. Adding a dimension that has the same characteristic seems reasonable even if we cannot explain it.
Measured outcomes do not appear to become walled off from one another in my equations. They remain connected both in the past and the future. Our perception of a singular past is also an illusion.
When I calculated the particle in the box, I found that the particle’s position behaved like three one-dimensional strings stretched across the 5th dimension. Each string’s displacement represented one of the particle’s position coordinates, so there is an x string, a y string, and a z string. The particle must be somewhere in the box. When it encounters a wall of the box, it is pushed away from it. The walls are impenetrable.
Therefore, the equations are for strings that are vibrating between two walls. When any part encounters a wall, it bounces off elastically (not losing any energy).
What happens when you pluck a string and it is stretched through a box or rod? If the box or rod is very large, nothing much at all happens. If it is small, however, the string vibrates, hits the walls and is propelled backwards. It quickly smacks into the other wall. This would ordinarily have a damping effect on the string but in this ideal case there is no transfer of energy from the string to the walls so the string continues to vibrating, smacking into the walls.
This is a fairly complex problem in mathematics but there are a number of papers that deal with vibrating strings and “straight obstacles” which I am calling “walls”.
As an example, I made this little animation in Mathematica showing a string bouncing against one wall. Two walls would look more or less the same but mirrored. (Also, the string is pinned at either end which may not be true in reality.) I gave the string a flat configuration, corresponding to straight-line particle motion, to make equations easier. The string is the blue line and the wall is the yellow.
