Another dimension may explain time and quantum mechanics
The problem of how to interpret quantum mechanics has been baffling physicists for 100 years. How do you understand the phenomenon where a particle or anything for that matter can be in two states at once? This is the so-called Schroedinger’s cat paradox in which a cat is both dead and alive until you look. Likewise, a quantum particle can be in two or more places at once, seemingly, creating the famous double slit experiment in which a particle appears to interfere with itself.
Weirder still, particles can become entangled, sharing a state even when they are separated by light years so that when one is looked at, it affects the other one’s state.
The traditional interpretation of this, championed by Heisenberg (and erroneously attributed to Niels Bohr), was a phenomenon called wavefunction collapse, in which looking at a quantum particle causes its state to collapse into one. This is called the Copenhagen interpretation of quantum physics.
Contemporary physicists who care about such notions love to knock down Copenhagen, which is little more than a strawman argument (an argument deliberately constructed to be easy to knock down like a straw man). Copenhagen is made stronger by modifying the equations of quantum mechanics, of course, using, for example, something called dynamic reduction equations which deliberately model the collapse. Nevertheless, there are many, many interpretations of quantum physics beyond wavefunction collapse, all with their own adherents.
One that has caught the attention of the public is the Many Worlds Interpretation (MWI) which says that people as well as quantum particles exist in multiple contradictory states and these states are divided into “worlds” so they can’t perceive one another. The mechanism for such as division is not well understood at all for it seems it would require some kind of special physics at the size of the universe to cause worlds to divide at every quantum observation.
Nevertheless, one can model MWI in a 5D general relativity (a model of the curved universe with an extra dimension added to the usual three space and one time) with ease. Each world gets its own slice of the 5th dimension and these interact sometimes and other times they don’t (as when worlds split). Instead of point particles following paths as in ordinary, classical physics you have lines, like a front line of soldiers advancing over a field, of many copies of the same point particle. These copies follow many different paths, sometimes bumping into each other, and sometimes avoiding each other completely.
If a classical path is a 1D curve in 4D spacetime, the quantum analog is a 2D surface within a 5D spacetime. One dimension of the surface is time, t, and the other dimension is the 5th dimension representing worlds or, as Richard Feynman liked to call them, histories, h. Thus you have a time dimension along which particles move from past to future, and a history dimension which represents the different possible realities the particle can take on.
This would be true for human beings as well. If you imagine a person’s center of mass, say, as a point, then that point would occupy a 2D surface, as long as the separate realities were coherent with one another. Thus, your life, rather than a line from your birth to death, is a sheet containing myriad little quantum variations of your life that normally are inconsequential. When something happens that causes a contradiction, that surface that is your life splits apart into two surfaces, like a sheet of fabric torn in the middle. They decohere and go their separate ways.
For example, a cosmic particle in a superposition of states strikes a DNA strand in an egg that causes a woman to have a red hair baby in one world and a brown haired one in the other. The sheet of her life splits, never to reform, and copies of her continue on. This is essentially the MWI point of view.
Another perspective appears if you turn the sheet on its side and look at a particle or life evolving in histories rather than time. You then get a dynamic histories interpretation of quantum mechanics. In this interpretation, histories are like long strands of events (called world lines) and they evolve and change in the 5th dimension so that the past is ever changing. Thus, history changes. For example, the world where the woman has a red haired baby suddenly evolves into a world where she has a brown haired one and she is never the wiser because history, the past, has literally changed.
The dynamic histories model, as I have so far presented it, is, in reality, equivalent to the MWI interpretation because in a 5D, Einsteinean universe, everything depends on your point of view. If you move forward in time, you get MWI. If you move in the 5th dimension, you get dynamic histories. It is all part of a single, crystal reality. For general relativity, time is just another dimension. It has no intrinsic nature inherently different from space.
I say dynamic histories as I have presented it because I have not dealt with the problem of the flow of time. Indeed, the problem of the present moment looms large over all of physics, an unanswered question, and to not address it in any theory of history is surely falling short.
Indeed, we know a lot in physics about what time is but almost nothing about the present moment, how it comes to be, why it appears to change, are we changing or just moving through time?
It is clear, from experience, that, while time is a dimension, it also has an intrinsic reality that is far more than a dimension.
Because time flows, change is possible.
Einstein would have time as a railroad, with the engine of the universe driving us to some unknown destination, completely outside our own control. Yet, experience seems to suggest time is a flow of the universe in which we participate.
In a 4D universe governed by Einstein’s and Schroedinger’s equations for gravity and quantum mechanics both ideas cannot be correct. Yet seemingly they are. Time is a road and a flow.
This suggests that perhaps we are conflating two dimensions here, one that represents time and another that represents the present moment.
Imagine the present moment as a wavefront (like that of a huge explosion) an expansion of time itself, but, if time is expanding, it must be expanding into something else. If we attribute that something else as a 5th dimension, it is not merely a dimension but also a marker of the present moment. That is, we in the present live on the expanding three dimensional surface of the present of a four dimensional surface of history in a five dimensional universe.
With this interpretation the equivalence between MWI and dynamic histories suddenly breaks.
To see why, imagine now that, instead of particles sweeping out a 2D sheet of time and worlds, each “world” represents a different present moment. Particles flow from moment to moment and world to world riding the expansion of the temporal wavefront. As the present moment changes, history underlying the present can also change randomly as each present moment represents a different world with a different history.
In this interpretation, each world has a past but no future. They all abruptly stop at the present moment and the universe moves on to the next world. Thus, MWI breaks down. We only ever inhabit one world at a time. Dynamic histories makes more sense in this interpretation as well because history is indeed changing from moment to moment.
All of this, of course, can be made rigorously equivalent to quantum theory. Indeed, stochastically evolving histories of particles is one of many computational methods for solving quantum equations (called the stochastic or Langevin/Fokker-Planck approach and championed by a Bell Labs scientist named John Klauder in the early ‘80’s).
Since we can’t see the future, there is no reason to suppose that one exists for each particle history. I propose that, in fact, none exists for any particle history and that the future is constantly being written out of the present as time itself expands into the 5th dimension.
What this means for us is that, unlike in MWI, each of us has a unique self that moves along the wavefront of the present moment. While our past may not be precisely fixed as it appears to be in classical physics, we do not experience a splitting of worlds. Rather, each world represents a moment in time.
Andersen, Timothy D. “A Dynamic Histories Interpretation of Quantum Theory.” arXiv preprint arXiv:2009.04244 (2020).
Klauder, John R. “Stochastic quantization.” Recent developments in high-energy physics. Springer, Vienna, 1983. 251–281.