The 5th Dimension, More Than Just a Soul Band…

For our creative purposes the universe needs to be more than we see, and as I described in the last post, one of those ways is to propose additional dimensions. So, let’s go into more detail now.

Quickly recapping what we’ve already discussed, a dimension is just a line on a graph. In other words, dimensions are measurements that you want to map with other measures. Then, in mathematical terms, a ‘space’ is just a set of dimensions. So, if I want to map height with milk consumption, I would have a 2-dimensional “space” of height by milk consumed. Of course, that’s not what we are really discussing here. Instead, we are speculating about a 5^th dimension (or more) in addition to the 4 of space-time. But, the height/milk example does illustrate three points: dimensions can be any measurement, there are more than one, and how we define our position in space is the measured position on each dimension. Mathematically, there is a little more when you define measurement as a dimension, such as introducing something called ‘distance’, but that’s all mathematical mumbo-jumbo for us.

Though, this all sounds pretty intuitive to our understanding of space-time, but not so much if we add an additional dimension. Because by proposing a 5^th, we are redefining our position in space-time. Last time we did that, the Theory of Relativity was born, and physics was re-written. In fact, an additional dimension of space-time would not just add to our understanding of physics, it would change it. This is because physics depends on the geometry of space-time and adding dimensions change the geometry.

First off, things would not bump into each other the same way. Since the position of an object is now defined by 5 numbers, a potentially infinite number of objects can be in the same 4 coordinates of space-time. Since, we currently only experience those 4 coordinates, any proposal of a 5th must explain why this is. But the problems get subtler, in that, physical laws would change.

Let’s consider physical laws that follow the inverse square law, like electromagnetism, gravity, and light intensity.

Yes, this is the first time I included equations, so don’t freak out. All you need to see is that all these equations are divided by r² which means the square of the distance. So, in the case of light intensity, if I measure the brightness of a candle from 1 meter away and then again from 2 meters away, it will be ¼ as bright at 2 meters as it was at 1 meter. You would describe this as “light intensity is inversely proportional to the square of the distance”. This is as you would expect because light gets spread out as it travels away from the candle. You can think of each distance as a ball of light getting larger, and at each distance, the brightness of the candle is divided by the surface area of the ball, which is, roughly, a square of the distance.

Now let’s pretend that we live a two-dimensional universe like that described in Flatland. Then the light would spread out in a circle and so would be divided by the circumference of that circle. In other words:

So now our candle is ½ as bright at 2 meters as it is from one meter. Then light intensity is inversely proportional to the distance, not the square of the distance. In fact, if light intensity in Flatland remained inversely proportional to the square of the distance, Flatland physicists would conclude space is made up of 3 dimensions.

Since gravity and electric force also follow the same rule as light intensity, you could suppose that both those force are being spread out as ever-growing balls. That is more than a supposition. That is Quantum Field Theory. And that means not only is the brightness of a candle different, but also does the way stars burn, planets form and, even, chemistry change. Since the geometry of space is different in two dimensions versus three, many other physical laws change our understanding of science. Adding an additional dimension of time would have this consequence.

The same logic applies if we go above three dimensions of space. Thus, with 4 dimensions of space, forces would be inversely proportional to the cube of the distance. But, it’s not, so we know that regardless of how many dimensions our universe has, everything we know of is somehow restricted or “bounded” to four dimensions. In other words, matter and energy could only hold one position in the other dimensions. That’s not unprecedented. All matter and energy are “bounded” to travel in only one direction in time, so why could not the 3 dimensions of space have similar constraints.

In this way, additional dimension act much like what we are calling different planes. Then again, I did warn that my description of universes as dimensions, planes, and spheres was going to be fuzzy and a matter of taste.

But an extra dimension (or plane) is not any use to physicist or us if it does not interact with the objects “bounded” to our four dimensions.  So, when we add more dimensions, the forces of nature get redefined, or a whole new set of forces must be added. The ghost hovering in the bedroom is more than a cranky soul in the 5^th dimension. (Or more accurately a different position in the 5^th dimension than us). The ghost must be part of a new set of physics. In fact, there’s no reason to believe that it’s even in the bedroom (or the ghostly equivalent). It could be just floating in space.

So, there’s a complication with an extra dimension. Whatever does not affect us from the 5^th dimension also does not affect our 5^th-dimensional ghost, including gravity. For our ghost, Earth has no gravity and might as well be empty space. For him to hang around,  a new force must exist to draw him in, or gravity somehow  “leaks” into other dimensions, while still being “bounded” to our three. The latter is not so far fetch. The Physicist Lisa Randell has proposed just that to explain why gravity is so much weaker than the other forces. The idea of gravity from extra dimensions has also been suggested as the source of dark energy (though those theories are far from being the best established).

Then again, rather than being “bounded” the other dimensions could be curled.

So far, I’ve been assuming that the other dimensions are infinite (or practically infinite). But what if they were small loops. Then as light expanded, it would still act as traveling in three dimensions of space, and instead just be fuzzy on a smaller scale. Wait a minute. That’s just like Quantum Mechanics. Coincidence? I think not. Curled dimensions it what String Theory proposes to unify all the forces under a single theory. This means forces can be given a new geometry, and hence new physical laws at small distances. For us to not have detected them already, that distance would have to be shorter than an atom. This is known as the Planck Length.

Given that we need geometry to remain the same for most of physics, you would probably find it easier to think of a dimension as a ‘states’. Again, remember, in the end, a dimension is just a line on a graph. The interaction between objects would mostly be shared by ones with the same state, but those of a different state would have a subdued effect on each other. This is how ‘vibrations’ becomes a synonym for dimensions. Vibrations (or waves) pass through each other unless of the same frequency. However, they do impart some effect on different frequencies, and how much effect depends on how in sync they are. We can then think of the difference between their frequencies as ‘distance’ to further the analogy.

So, what’s our creative take away?

First, extra dimensions rewrite physical laws. Scientists often use this proposal to explain the subtle questions in physics that are not yet understood, but we can use them to introduce different kinds of forces, matter, or energies.

Second, what exists must be “bounded” within these extra dimensions, or the extra dimensions are curled. Here we should provide some description of when and how these new things have influence in our normal world and more importantly when they do not. In other words, when and how they are “bounded”.

If we want to take our extra dimensions seriously, we must spare some thought to what does not exist in those new dimensions as much as what does. The rule of thumb is that if something from another dimension can affect us, we can affect them. That’s really good to know if you ever need to punch a ghost.