We know that the universe has four dimensions, but why only four? Why not five?
String theorists claim that the universe has many dimensions: 10, 11, or 26, but that all but the four are curled up so small that we can’t detect them.
That’s not what I’m talking about here. I’m talking about a real 5th dimension, one that is as big and uncurled as the other four.
The idea that the universe might have a fifth dimension came hot on the heels of the realization that the universe had four dimensions. In 1919, only four years after Einstein published his theory of General Relativity, a scientist named Kaluza proposed the idea and sent his paper to none other than Albert Einstein who loved it. The reason why he loved it, I’ll get to later, but the point was that Kaluza had to explain why the fifth dimension could exist while being invisible.
After all, if you and I agree to meet anywhere in the universe, all I need to give you are three numbers (like latitude, longitude, and altitude) and a time. I don’t have to locate our meeting somewhere in the fifth dimension. I don’t have to say, yeah, meet me at fifth and elm, in the fourth floor lobby, at 3 pm Tuesday and by the way, make sure you are in the 9th underworld.
Kaluza’s explanation for why we couldn’t see the fifth dimension was an assumption he made called cylindricity. The idea is simple: we can’t see that fifth dimension because everything is exactly the same in the fifth dimension. It’s like a rectangular loaf of bread. If all you want is a slice, it doesn’t matter where you slice it. It’s always the same.
Everyone thought this wasn’t a sensible idea, which is why a scientist named Klein later came along and said, no, the dimension isn’t the same, it’s just curled up very small. Later, string theorists would run with what is now called Kaluza-Klein theory and describe their theory of everything.
But, suppose Kaluza was right? Suppose the universe does have a fifth dimension where everything is kind of the same? But what if it’s not exactly the same?
This is the idea I explored in my paper:
Quantization of fields by averaging classical evolution equations
This paper extends the formalism for quantizing field theories via a microcanonical quantum field theory and Hamilton's…
The paper simply presents, mathematically, why a fifth dimension makes sense in a quantum theory.
What follows are some of the implications of the fifth dimension.
The basic idea is that the universe has a fifth dimension, but we can’t ordinarily detect the dimension, not because everything is exactly the same, but because, when we make measurements of anything, we only perceive either an average or random value.
If this is true, it would mean that rather than being random, quantum mechanics is simply the result of classical motion in a largely invisible dimension.
Let’s look at an analogy: imagine a sealed box of gas. The box of gas is in equilibrium, so its state does not change with time. When we put a barometer or a thermometer into the box, it always reads the same value, e.g., 1 atmosphere and 20 degrees Celsius. Nevertheless, all the individual gas molecules in the box are in constant motion. So it is changing in time, but we cannot perceive that change because we are so large we can only measure the averages which never change.
It is the same in quantum mechanics. Our universe changes not only in time but in this fifth dimension.
Unlike time where entropy is always increasing, in the fifth dimension, entropy, a measure of disorder or information, is essentially constant. This constant entropy is what makes motion in that dimension invisible. I can illustrate this with the following:
A thought experiment:
Suppose we want to build a clock that can measure change in the fifth dimension. This clock never changes in time. Rather it is designed to change only in this other dimension, which I will call the quantum dimension.
All clocks work based on some process of work being done, i.e., potential energy converting to kinetic, such as a falling rock or water, a turning planet, an unwinding spring, or a decaying radioactive atom. It seems as though we could, likewise, determine change in the quantum dimension by some similar transformation.
In my paper, I introduce something analogous to kinetic energy in that dimension (based on work by Callaway), and it is a necessary component to make the whole thing work for quantum physics. Thus, we can set up a clock based on some quantum field that we prepare and are ready to measure based on its change in this form of kinetic energy.
Now, clocks rely on one other principle and that is increasing entropy. This is a more subtle issue, but, in order to record the passage of time, we have to know the time at at least two points, a point in the past, and the present. In order to do that the clock has to do useful work which requires some kind of energy flow and an increase in entropy. (This is called a flow of free energy.) This provides the directionality of the clock that distinguishes the past from the present. Without it all moments are essentially equally each others past and future.
This is where the clock actually doesn’t work for the quantum dimension. You would be as equally likely to take a tick away as add one at any given point and so the number of ticks you would end up with would be random and, on average, zero.
Another way to think of the fifth dimension is that it behaves like time because we are moving through it (unlike space where we have freedom to move about through accelerations), but it has no arrow, unlike time. The arrow of time is what allows us to perceive it at all. No arrow. No past. No future. There really is only now.
One way out of this might be to look at our flow in the quantum dimension and time together and create a hybrid clock that does change in time. Could we then distinguish change in the quantum dimension versus time? Perhaps so.
Brownian motion is a good analogy.
The only way we are aware of this dimension for now is in quantum measurements which perceive the individual fluctuations that are always occurring in that dimension. These are not averages but measurements of randomness.
This is sort of like observing Brownian motion, the vibrations of tiny objects in gases and liquids. Brownian motion is normally invisible to us except when we look at very small objects under a microscope. Then it becomes visible through the vibrations of, say, pollen that is constantly bombarded by molecules of liquid around it.
Thus, by observing the behavior of quantum effects like individual particles of light or electrons, we can be aware of this dimension, but we cannot directly perceive our flow through it.
You can make a sort of clock from Brownian motion. Simply set a piece of pollen down at a point and record where you put it. Then over time it will follow what is called a random walk. On average, it will travel a distance proportional to the square root of the time elapsed. While the liquid is in equilibrium, you are not and so you can observe this and record it. Could we do the same in quantum mechanics? Perhaps.
Seen through the lens of a fifth dimension, quantum physics is no longer mysterious or weird. All the strange effects of quantum physics like its ability to be multiple things and then suddenly be one thing when observed (quantum measurement interpretation) and its nonlocal nature can all be explained as classical motion through a fifth dimension.
Kaluza, therefore, may have been right all along but wrong in that he didn’t associate his discovery with quantum physics. Rather, his theory is the classical limit of the quantum version of the theory.
More reasons to love Kaluza sans Klein.
There are more good reasons to love Kaluza’s idea because, if you combine a fifth dimension with Einstein’s general relativity theory of space and time, you get a theory in which general relativity in five dimensions equals general relativity in four dimension and electromagnetism, meaning that it says that electromagnetism is gravity in the fifth dimension. You also get a scalar field (a field that is just one number at each point) that you can choose what to do with. Kaluza just assumed it was constant.
If you make a strict cylindricity assumption as Kaluza did, you get exactly those two forces, but, if you relax it a bit, you can also show that matter itself is just spacetime curvature variations in the fifth dimension. This means that there is no actual matter, only spacetime geometry.
Paul Wesson was a major force behind this idea until his death. (He also suggested that the other dimension/scalar field was responsible for mass.) The basic idea is that we don’t need matter if we assume a fifth dimension. We only need Einstein’s theory in a vacuum. (This theory does not explain a lot of quantum phenomena like gauge forces so it is incomplete.)
Wesson’s approach was strictly classical, while mine is a fully quantum theory (albeit not a theory of everything). Thus, it explains the fifth dimension as not only responsible for electromagnetism and matter but also quantum physics and all the weird phenomena that we observe in that theory.
How can we be sure?
Whether the fifth dimension is real or not depends on whether we can depart from standard theory when we observe it. One difference, for example, might be in observing processes that behaves differently depending on whether they are flowing in a dimension or actually behaving randomly. This idea is called ergodicity.
Ergodicity is a fancy term for the equivalence of averaging a physical process over time versus averaging over its configuration space, space of all possible arrangements of, say, a set of molecules in a box of gas. A box of molecules is said to be ergodic because in an infinite amount of time every possible configuration will be reached.
If a system has configurations that cannot be reached, even in an infinite amount of time, we say that it is non-ergodic. If quantum theory is a flow in a fifth dimension, then any non-ergodic quantum systems would differ from standard quantum theory because standard quantum theory is based on averaging over a configuration space.
Another possibility is that even if all matter and forces are ergodic, some may not have what is called a thermodynamic limit, that is, their standard quantum theory simply does not exist. This may be the case with gravity. In that case, a theory of gravity as flow in a fifth dimension may exist while its standard quantum theory doesn’t. Stephen Hawking ran into this problem in his theory on black hole thermodynamics. The thermodynamic limit of black holes does not exist in standard statistical theory, but it does exist as a flow in time.
In any case, if we are moving through a fifth dimension but are not aware of it that does not necessarily mean that we cannot affect our motion through it. Einstein showed, for example, that we could change our motion in time by accelerating or moving near to strongly gravitating objects like neutron stars or black holes. We may not be able to do a U-turn in time, but we can affect it somewhat. This fifth dimension may be similar, in which case, discovering it and learning how to manipulate it could open a wide range of scientific and engineering possibilities that four dimensions simply does not offer.
Overduin, James Martin, and Paul S. Wesson. “Kaluza-klein gravity.” Physics Reports 283.5–6 (1997): 303–378.
Wesson, Paul S. Space-time-matter: modern Kaluza-Klein theory. World Scientific, 1999.
Hawking, Stephen W., and Don N. Page. “Thermodynamics of black holes in anti-de Sitter space.” Communications in Mathematical Physics 87.4 (1983): 577–588.