Looking for Higher (and bigger) Extra Dimensions

It has been said by many, that gravitational wave astronomy are like a new pair of eyes for humanity; that this technology would enable us to peer far deeper into the depths of the universe and uncover many mysteries. Thanks to LIGO and VIRGO, we’ve already made tons of predictions on previously untestable theories, and many more people are suggesting ways to utilise this new technology in order to detect the number of spatial dimensions that our universe has.

Why do people think that these extra dimensions exist you might ask? Well the thing is, up until now we’ve only witnessed three dimensions of space and one dimension of time. But if our universe had as few as one more dimension of space, then we could easily explain away many questions that plague physicists today, questions like

  • Why is gravity so much weaker than the other forces?
  • What is the nature of dark matter and dark energy?
  • What would a union of quantum mechanics and general relativity look like?

Unlike merging black holes, merging neutron stars collide spectacularly blasting gamma rays through the cosmos. This collision is first observed via gravitational waves and then after a second or it’s observed as a gamma ray burst, followed by a glow across the electromagnetic spectrum. This optical identification gave a completely independent measurement of the distance traveled by the gravitational wave. This alone actually allows us to measure how many dimensions of space the gravitational waves are actually passing through.

Before we talk about hyper-dimensions though, we must talk about gravity in lower, more recognisable dimensions. Imagine light originating from a source spreading out evenly over an expanding spherical shell. As this shell expands, the light rays become more spread out. The intensity of the light drops promotional to the surface area of the sphere, which is proportional to its radius. This is the famous inverse square law.

But what if we instead lived in a universe with two spatial dimensions. Then the same pulse will spread out over an increasing circle, not a sphere and therefore the intensity of the light will drop of as the circumference of the circle increases, so the intensity of the light will be proportional to the inverse of the radius of the circle.

As we can see, the way light or any kind of wave diminishes in intensity depends on the number of dimensions, to be more specific, the intensity of the light is inversely proportional to the number of dimensions of space minus 1.

So in higher dimensions of space light should fade quicker than in lower dimensional space. As I’m sure all of you here would have already guessed, this relation also holds true for the gravitational force. Taking one look at Newton’s universal law of gravitation we can pretty confidently say that in our universe, gravity appears to follow the inverse square law. We can utilise Einstein’s general relativity in those cases where the gravity is extremely strong like close to a black hole, but in general, Einstein’s general relativity describes gravity perfectly while postulating we live in a universe with three spatial dimensions and one temporal.

This is all well and good, but there are a whole lot of things that general relativity does not explain that we can’t ignore. One such observation is gravity’s almost laughable weakness. Even when compared to the weak nuclear force, gravity is ten to the power of 32 times weaker. This mismatch might be due to gravity just being weird, but it could also be due to our ignorance. Those who believe in the latter are looking for a theory of everything, a theory to rule over them all by unifying all the known fundamental forces. This would mean that, gravity must behave like the other forces, that is be much, much, much, much stronger than it is currently at very high temperatures and get weakened in the low energy familiar universe that we currently inhabit.

One way to do that is to have another spatial dimension in the universe. We can drain gravity into another dimension while keeping everything else in the universe restricted to three spatial dimensions thus severely weakening gravity’s power.

A popular idea in string theory is that, whenever you face a problem, just toss in a few dimensions and see if it goes away. Following this mantra, string theorists have come up with a way to have as many as eleven spatial dimensions coiled up and compactified on the tiniest of scales such that at the largest scales the universe still has three spatial dimensions but on a very, very, very small scale it has many, many more. Other smart people figured out a way to reverse this idea, that is instead of compactifying small dimensions we blow them up so that we live in the compactified dimensions. Everything in such a universe, except gravity, would be restricted to the three dimensions of space. If you make your theories just right, you can even get the inverse square law for light and even for gravity at certain scales, on other scales gravity would leak into other dimensions and become weaker.

Compactified extra Dimensions

These extra spatial dimensions can be used to explain not only the absurd weakness of gravity when compared to other forces but also dark energy. Depending on how the theory is configured, our three dimensional observable universe can expand into the extra dimensions, this expansion can be due to what we label as dark energy.

Now how can we use gravitational waves to test such theories?

If gravitational waves can enter into these extra dimensions, then their intensity should fall off by the relation that we discussed previously. So that gives us a simple test. Just observe gravitational waves coming from very far away and see how quickly they reduce in intensity. Depending on how quickly they fall off we can deduce the number of dimensions that it had to travel in to get to us. If the drop in intensity is higher than you expect then you have evidence for extra dimensions.

Remember the colliding neutron stars we talked about at the start? That is extremely helpful because the electromagnetic signals that we got from them can be used to determine the distance to merger completely independent of the gravitational waves.

One more thing, as some of you would’ve realised, in order to measure the drop in the intensity we first need to know what the starting intensity of the gravitational wave was. An amazing property of gravitational waves is that we can find out the initial intensity simply by knowing the mass of the merging objects combined with the distance to the merger.

When LIGO first went online, a group of scientists actually took data from a neutron star merger to see if our universe actually has higher, bigger spatial dimensions.

And so the verdict? Do these extra dimensions actually exist?

We discovered….exactly 0 new spatial dimensions.

This basically rules out the possibility of us living in compactifed dimensions, and the extra dimension theory for dark energy. But don’t lose hope, there still might be some extra compactified dimensions in our three dimensions of space; the only thing that has been ruled out is bigger higher dimensions.