A 5th Dimension May Explain The Quantum Interpretation Paradox

Combining the best of many worlds and consistent histories, the 5th dimension may resolve a 100 year old debate.

The Many Worlds Interpretation (MWI) of quantum mechanics has been a subject of fierce debate in the physics community with some coming down on one side or the other with the vehemence of a religious zealot.

The MWI, briefly, says that every time we make some observation of the outcome of a quantum wavefunction containing a superposition of states that are contradictory, the universe splits into multiple, mutually exclusive universes, each with a different outcome.

A quantum wavefunction is simply the state of any piece of matter, a particle like an electron or photon (particle of light). This includes the matter than makes up everything from lab equipment to people.

The key difference between a quantum wavefunction and a classical state of motion is that a wavefunction can contain many different, contradictory observations. For example, a particle can be in two places at once, going in two directions at once, or be in a spin up and spin down state (since particles almost all spin like tops) at once.

How we measure the outcome can also influence what we measure as well. If we put a detector in one spot, we detect one thing but if we put it in another we detect something else. It may determine whether universes split or stay together for us.

The classic experiment that shows that quantum wavefunctions really do carry with them contradictory realities is the double slit experiment. Dr. Quantum explains this experiment in this video:

It tells us that “particles” behave like both particles and waves. The MWI says that, no, particles really are just particles but copies of the same particle exist in many, many different universes or worlds. As long as nobody makes a measurement of those particles, our conscious minds (and experimental apparati) span those universes and so we observe how the many universes interact with one another. This gives the appearance of the particle as a wave. It is the many copies of the particle in the different universes interacting like many molecules of water.

As soon as we observe the particle, however, we become integrated with one particular universe and so that universe must split off (for us) from other universes. Because of the complicated interactions between the particle, the experimental apparatus, the observer, and the world, the wavefunction decoheres such that the particle can no longer interact with its other copies. It is no longer pure. The universes are separated completely.

Like many theories that try to resolve the quantum interpretation problem, MWI suggests that something fundamental happens to reality when we observe a quantum state. If you think that is problematic, you are not alone.

So far, there is zero evidence that MWI is true and so, like many scientists, I have argued that in the absence of scientific evidence we should take a philosophical perspective and ask whether MWI is the best idea we can come up with.

Like most philosophical questions, that is up for debate, but there are certainly many compelling alternatives from hidden variable theories to superselection to consistent histories.

A New Interpretation of Quantum Mechanics

In this article, I am throwing my hat into the ring, so to speak, and suggesting an alternative quantum interpretation. My explanation rests on the following premises:

1. The universe has an additional dimension, meaning that it is five dimensional.
2. All quantum fields (including us) move (or flow) in that fifth dimension obeying 5D classical equations of motion.
3. At each point in that fifth dimension the universe in all time and space only takes on one classical configuration.
4. The 5th dimension is in statistical equilibrium (meaning entropy is constant) with a “temperature” such that it explains quantum uncertainty (this is a temperature of Planck’s reduced constant).

By classical, I mean quantum fields obey the principle of least action just like classical Newtonian physics.

Since we are only at one position within the 5th dimension at any given time (even though we don’t know where because it is invisible), the universe only ever has one definite, classical state. Because of the uncertainty, in that dimension, however, we can only predict in terms of probabilities.

It works sort of like this. Imagine you emit a particle and it has a wavefunction that has two states in superposition. These can be called up and down or 1 and 0, it doesn’t really matter. Now, within the wavefunction, each exists with probability 1/2. This does not mean that the wavefunction has 50% probability of being up and 50% of being down. In fact, the wavefunction is half up and half down, but when we go to measure it is one or the other with 50% probability.

The way to interpret this in the 5 dimensional theory is that the particle is up half and down half as it flows in the 5th dimension. This is true of many classical statistical systems like gases. The difference between ordinary statistical physics and the quantum case, however, is that in ordinary physics the randomness occurs in time. Here it occurs in a different dimension altogether, not time. I call this the quantum dimension.

When we go to measure the particle’s state, what we measure is determined by where we and the particle are in the quantum dimension. This does not necessarily change with time, i.e., we cannot necessarily wait a little bit and have the outcome change. Because the quantum dimension is perpendicular to time, we have no control over our motion in it at all and, most importantly, no way of measuring where we are in that dimension.

This is because, unlike with time, there is no arrow in the 5th dimension since it has constant entropy. There is no clock that measures our motion in that direction alone.

If you take an example such as the double slit experiment, you can see that each point along the quantum dimension corresponds to a different complete path between the emitter and detector. The path is called a world line and in the quantum dimension traces out a kind of sheet (world sheet) that forms a complete whole with each path influencing every other path continuously.

This is very much like in the MWI, however, there is no splitting of universes here. What happens is that when the measurement is made, the sheet ceases past a certain point in time because the measurement apparatus has disrupted it (decohered it).

Wherever we are in the 5th dimension is the history that we end up in. So it is more like a consistent histories interpretation but the particular history we get is determined by that flow in the quantum dimension, so, unlike consistent histories, there is nothing random about it. It is entirely deterministic. The only uncertainty is our own about where we are in the 5th dimension.

As in consistent histories, reality doesn’t change when we make a measurement. It goes on being reality as before but two parts of it: us and the particle we measured, now have interacted.

The 5th dimension is compatible with all quantum predictions

One of the nice things about this interpretation is that it is mathematically consistent with quantum theory, including relativistic quantum field theory, provided that you accept a couple of statistical assumptions. To get technical, these are ergodicity and the equivalence of microcanonical and canonical ensembles. These are the same assumptions that underlie much of equilibrium statistical mechanics for gases, liquids, and so on. I’ve shown how this can be done in a recent peer reviewed journal paper. The results of this paper are for scalar fields but can be extended to others using 5-D theories such as Kaluza-Klein’s as well as old fashioned molecular dynamics.

In all our predictions, the 5th dimension is just averaged out the same way that statistical equilibrium physics averages out the time dimension, yet it is precisely that hidden piece of information, where we are in the quantum dimension, that determines which outcome of all the expected outcomes of experiments is actually measured, and “superposition” can be seen as just a statistical description of a world sheet.

The implications for quantum physics are that rather than being mysterious, interpreting quantum theory is very much the same as interpreting classical statistical theories, but with one additional dimension. In classical statistical theories, we know that, say, a box of particles has only one state at a time, but we describe it as if it has all possible states. If we were to go and look at an individual particle, however, we would only ever get one of those outcomes. Adding a dimension, you get the same result, but you also get weird effects like non-locality.

Non-local effects (spooky action at a distance), of course, are explained in a 5-D theory as the evolution of particle world lines (which are nonlocal structures) in the quantum dimension. A particle isn’t just a point. It is a filament in spacetime.

These filaments can be extended to four dimensional fields of particles as well, which allows for particle creation and annihilation as in particle accelerators. That’s what I did in my paper, but I will mainly address the one dimensional filament case here.

As we flow in the 5th dimension, the entire history of each particle can change, moving randomly between different states as in retrocausal theories where future influences past and vice versa.

This is especially true when we haven’t measured anything yet. Once we have measured a particle, it is no longer free to flip through random histories and retrocausality is strongly curtailed.

The 5th dimension resolves the EPR Paradox

If you look at a classic thought experiment in this area, the Einstein-Podolsky-Rosen or EPR paradox experiment, you can see how the 5-D theory resolves it.

In this experiment, for which I will use David Bohm’s more simple version, you have an electron-positron pair emitted from some source like a particle accelerator.

I send the electron to Alice and the positron to Bob.

Alice now measures the electron’s spin along the z-axis (electrons of course can spin in any axis, x, y, or z). She can measured +z or -z (spin up or spin down). Now, if she measures +z, we know that, if Bob measures the positron’s spin along the z axis, he will get the opposite, -z. If she gets -z, he will get +z. Thus, her measurement confirms what he will measure before he measures it.

If, however, Alice measures her electron’s z axis and Bob then measures another axis, x, for example, he will get +x or -x with 50% probability each.

It therefore seems like the measurement Alice made must be transmitted from Alice to Bob. You cannot assume that Bob’s particle had the opposite spin all along because he only gets that measurement when he measures along the z axis and a random outcome otherwise. Yet the electron can only have one direction of spin.

Let’s see how the 5-D theory solves this problem.

In this theory, each particle’s complete path from emitter to detector is a world line and evolves in the 5th dimension as a world sheet. This world sheet contains all possible measureable outcomes including all possible spin state configurations.

When Alice makes her measurement, the electron interacts with her apparatus such that its state at that point in quantum time and ordinary time is measured. The point in quantum time determines which particle history is measured (this is why this approach resembles consistent histories).

Because Alice’s apparatus has selected out that history for the particle by interacting with the electron, that same history must be reflected by Bob’s positron. This is because the electron and positron’s shared state evolves in the 5th dimension like a single field and measurements affect the pair of worldlines as if they were one.

Once Alice makes a measurement, the evolution of that shared field in the quantum dimension is altered and that evolution is propagated over all time and space where the field resides.

The Best of Many Worlds

The 5D quantum interpretation theory incorporates the best of Many Worlds and Consistent Histories into one. It lacks the many copies of us of MWI as well as the constant splitting of universes and the alteration of reality upon measurement. It also lacks the randomness of consistent histories. It does not invoke additional fields like Bohmian mechanics, only an additional dimension, and it handles particle creation and annihilation naturally, without randomness. In this way, it seems like the best of many different interpretations, a consistent, single universe theory in which nonlocal behavior is reflected through interacting world lines evolving in a 5th dimension.

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