In my previous post I talked about the existence of higher, hidden dimensions other than the three dimensions of space we experience, the concept of the sci-fi novel flatland, and a little bit about their structures.You can read that post here. Now the question is, if there are indeed so many dimensions, why did only three of them expanded into our familiar space, while the rest remained curled into fascinating small sizes?
This is a really interesting, thought-provoking question. I remember last year, before my first year finals, our group (all of us pursuing physics) was staying back at one of the friend’s house, and that night we were on the terrace, and using an astronomy app to look at the stars. As the time passed, we started taking about stuff, theories, and suddenly we came on the topic of dimensions. We were talking about why is it that ours is a 3-D world, and not some other dimensional world. One of my friends said this interesting thing, that what if there is a ‘God’ who is in the 4-D, and is viewing us like the story of flatland I mentioned in my last article, and we are not able to see him. I tried to counter him at that moment, that it isn’t possible, the other dimensions did not expand, or that what if he himself has a ‘God’ in 5-D, that would make him a normal being of 4-D. These were all crude answers, but the thought was very insightful. At that moment I did not know the reason why ours is a 3-D world, and so when I got back home I read a few articles, studies and researches on this topic, and I think I can explain the reason now to my friends.
The universe was very dense before big bang, but just after big bang happened a few seconds later, out of all the higher dimensions only three expanded, and become our known, familiar world. This confused scientists a lot. But now, the might have an answer. Careful calculations show that at dimensions higher than 3, say 4 or 5 or 10, the electrostatic and gravitational orbits become unstable. Unlike in 3-D world, where classical mechanics doesn’t allow atomic orbits but quantum mechanics provides a solution, in higher dimensions of space, both the theories show that atoms will be unstable, and hence cannot form. Since atoms will be unstable, no elements like hydrogen, helium or lithium would be formed, which means no stars, no galaxies and hence no universe. Calculations also show that not only does gravitational orbits get unstable in higher dimensions, but in lower dimensions(like the 2-D flatland) gravity would be non-existent itself. But be careful, this does not mean higher dimensions do not exist, it just shows why they did not expand and why ours is not a 4-D world.
Another result comes from thermodynamics. A measure of useful work is the Helmholtz Work Function A. Here A = U + TS, where U is the Internal Energy of the body, T is the temperature, and S is the entropy(or disorder) in the system. Calculations shows that the Helmholtz work function shows a maximum (or stability) when the number of dimensions is 3. So when inflation occurred(big-bang), all the dimensions in fact did expand, but as soon as three of them expanded, the function A reached a maximum(most amount of obtainable work), and all other dimensions suddenly stopped to expand, and the three dimensions which already expanded, expanded much much faster within seconds, at speeds higher than the speed of light. This does not violate relativity, because the speed limit applies to objects in the space-time fabric, not the space-time fabric itself.These three space dimensions along with the time dimension, makes up our 4-D space-time.
More information is to be known on how the inflation of these dimensions happened, the mechanisms involved, and more is to be known on the stability of higher dimensions, but as of now, they don’t seem a possibility because of unstable atoms, and forces. Though it is completely possible many Universes inflated, some of them had expanded in other three dimensions than ours, and hence cannot be interacted with, some inflated in the same three dimensions as ours, and a more advanced civilization might find a way to interact with them. I will write on multiple universe theories some time in the near future. Till then be thankful ours is a 3-D space, so that atoms could be formed, and as a consequence we could exist to know ourselves, and our universe, and hence be thankful indeed. For those of you, who are interested in the studies, I have provided links to the papers. Happy Reading!
-The Cosmogasmic Person
Links To Papers: