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# How the universe could possibly have more dimensions

String theory is a purported theory of everything that physicists hope will one day explain … everything.

All the forces, all the particles, all the constants, all the things under a single theoretical roof, where everything that we see is the result of tiny, vibrating strings. Theorists have been working on the idea since the 1960s, and one of the first things they realized is that for the theory to work, there have to be more dimensions than the four we're used to.

But that idea isn't as crazy as it sounds.

## Dimensional disaster

In string theory, little loops of vibrating stringiness (in the theory, they are the fundamental object of reality) manifest as the different particles (electrons, quarks, neutrinos, etc.) and as the force-carriers of nature (photons, gluons, gravitons, etc.). The way they do this is through their vibrations. Each string is so tiny that it appears to us as nothing more than a point-like particle, but each string can vibrate with different modes, the same way you can get different notes out of a guitar string.

Each vibration mode is thought to relate to a different kind of particle. So all the strings vibrating one way look like electrons, all the strings vibrating another way look like photons, and so on. What we see as particle collisions are, in the string theory view, a bunch of strings merging together and splitting apart.

But for the math to work, there have to be more than four dimensions in our universe. This is because our usual space-time doesn't give the strings enough "room" to vibrate in all the ways they need to in order to fully express themselves as all the varieties of particles in the world. They're just too constrained.

In other words, the strings don't just wiggle, they wiggle hyperdimensionally.

Current versions of string theory require 10 dimensions total, while an even more hypothetical über-string theory known as M-theory requires 11. But when we look around the universe, we only ever see the usual three spatial dimensions plus the dimension of time. We're pretty sure that if the universe had more than four dimensions, we would've noticed by now.

How can the string theory's requirement for extra dimensions possibly be reconciled with our everyday experiences in the universe?

## Curled up and compact

Thankfully, string theorists were able to point to a historical antecedent for this seemingly radical notion.

Back in 1919, shortly after Albert Einstein published his theory of general relativity, the mathematician and physicist Theodor Kaluza was playing around with the equations, just for fun. And he found something especially interesting when he added a fifth dimension to the equations — nothing happened. The equations of relativity don't really care about the number of dimensions; it's something you have to add in to make the theory applicable to our universe.

But then Kaluza added a special twist to that fifth dimension, making it wrap around itself in what he called the "cylinder condition." This requirement made something new pop out: Kaluza recovered the usual equations of general relativity in the usual four dimensions, plus a new equation that replicated the expressions of electromagnetism.

It looked like adding dimensions could potentially unify physics.

In retrospect, this was a bit of a red herring.

Still, a couple of decades later another physicist, Oskar Klein, tried to give Kaluza's idea an interpretation in terms of quantum mechanics. He found that if this fifth dimension existed and was responsible in some way for electromagnetism, that dimension had to be scrunched down, wrapping back around itself (just like in  Kaluza’s original idea), but way smaller, down to a bare 10^-35 meters.

## The many manifolds of string theory

If an extra dimension (or dimensions) is really that small, we wouldn't have noticed by now. It's so small that we couldn't possibly hope to directly probe it with our high-energy experiments. And if those dimensions are wrapped up on themselves, then every time you move around in four-dimensional space, you're really circumnavigating those extra dimensions billions upon billions of times.

And those are the dimensions where the strings of string theory live.

With further mathematical insight, it was found that the extra six spatial dimensions needed in string theory have to be wrapped up in a particular set of configurations, known as Calabi-Yao manifolds after two prominent physicists. But there isn't one unique manifold that's allowed by sting theory.

There's around 10^200,000.

It turns out that when you need six dimensions to curl up on themselves, and give them almost any possible way to do it, it … adds up.

That's a lot of different ways to wrap those extra dimensions in on themselves. And each possible configuration will affect the ways the strings inside them vibrate. Since the ways that strings vibrate determine how they behave up here in the macroscopic world, each choice of manifold leads to a distinct universe with its own set of physics.

So only one manifold can give rise to the world as we experience it. But which one?

Unfortunately, string theory can't give us an answer, at least not yet. The trouble is that string theory isn't done — we only have various approximation methods that we hope get close to the real thing, but right now we have no idea how right we are. So we have no mathematical technology for following the chain, from specific manifold to specific string vibration to the physics of the universe.

The response from string theorists is something called the Landscape, a multiverse of all possible universes predicted by the various manifolds, with our universe as just one point among many.

And that's where string theory sits today, somewhere on the Landscape.

Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute, host of Ask a Spaceman and Space Radio, and author of Your Place in the Universe.

Learn more by listening to the episode "Is string theory worth it? (Part 3: Dimension is destiny)" on the Ask A Spaceman podcast, available on iTunes and on the Web at http://www.askaspaceman.com. Thanks to John C., Zachary H., @edit_room, Matthew Y., Christopher L., Krizna W., Sayan P., Neha S., Zachary H., Joyce S., Mauricio M., @shrenicshah, Panos T., Dhruv R., Maria A., Ter B., oiSnowy, Evan T., Dan M., Jon T., @twblanchard, Aurie, Christopher M., @unplugged_wire, Giacomo S., Gully F. for the questions that led to this piece! Ask your own question on Twitter using #AskASpaceman or by following Paul @PaulMattSutter and facebook.com/PaulMattSutter.

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• punktyras
sting theory→string theory
• rod
String theory is a purported theory of everything that physicists hope will one day explain … everything.

How the universe could possibly have more dimensions : Read more

Quite a report and interesting 2:46 video from Paul Sutter. The report made some interesting comments.

"With further mathematical insight, it was found that the extra six spatial dimensions needed in string theory have to be wrapped up in a particular set of configurations, known as Calabi-Yao manifolds after two prominent physicists. But there isn't one unique manifold that's allowed by sting theory. There's around 10^200,000. It turns out that when you need six dimensions to curl up on themselves, and give them almost any possible way to do it, it … adds up. That's a lot of different ways to wrap those extra dimensions in on themselves. And each possible configuration will affect the ways the strings inside them vibrate. Since the ways that strings vibrate determine how they behave up here in the macroscopic world, each choice of manifold leads to a distinct universe with its own set of physics. So only one manifold can give rise to the world as we experience it. But which one? Unfortunately, string theory can't give us an answer, at least not yet. The trouble is that string theory isn't done — we only have various approximation methods that we hope get close to the real thing, but right now we have no idea how right we are. So we have no mathematical technology for following the chain, from specific manifold to specific string vibration to the physics of the universe. The response from string theorists is something called the Landscape, a multiverse of all possible universes predicted by the various manifolds, with our universe as just one point among many. And that's where string theory sits today, somewhere on the Landscape."

The math of string theory leads to a *multiverse*. I have other reports in cosmology that shows the multiverse contains 1E+500 or more different universes and now I see 1E+200,000 Calabi-Yao manifolds in the report. The video indicated problems continue with quantum gravity used in quantum mechanics called loop quantum gravity with gravitons. Apparently each universe that evolves in string theory can have its own unique set of physicals laws or likely no natural laws operating.

In astronomy I enjoy using my telescopes to observer Jupiter and the Galilean moons. Well predicted events take place at Jupiter like Io eclipses and transits. In the heliocentric solar system, Kepler's laws (elliptical orbits), Newton gravity, laws of motion, predict those events accurately and are verifiable using telescopes. It seems someone in a multiverse could live in a geocentric solar system then, but verifying this looks difficult :). Presently, astronomical observations showing the multiverse is true like the debate between geocentric astronomy vs. heliocentric astronomy where the geocentric teachers were falsified, is a work in progress.

So here is my bottom line. The heliocentric solar system is more verifiable than the multiverse with 1E+500 or more different universes and now I read about 1E+200,000 Calabi-Yao manifolds. Very interesting math and physics developed to explain the origin of our universe. The model(s) seem to have a long way to go before they meet the science testing standards used in the geocentric vs. heliocentric debate in astronomy. I enjoyed this report because I can see more details then past reports I read about string theory. I am of the school in science - publish the report showing warts and all :)
• William Pennat
Riddle me this. The extra dimensions of string theory are themselves supposed to be very very small. But this means those dimensions also have a size relative to the three ordinary spatial dimensions. Not sure that makes a lot of sense, given the definition of "dimension". Time is a dimension and time does not have any "spatial size". That's what dimension means, a fundamental way of measuring some aspect of existence. But if that measurement itself has a spatial measurement, how fundamental is that. The other problem with string theory is that it strikes me as basically unverifiable. (Not to say that it violates Occam's razor big time.) Plus there doesn't seem to have been a whole lot of progress in this area in the last couple of decades. A lot of highly ingenious mathematical thinking has obviously gone into the whole theory and I think this is a lot of its attraction.
• LijeBaley
Einstein's General Relativity made specific, testable (these days) predictions. And so far General Relativity has proven correct every time. None of the new theories can or have been confirmed through experimentation or observation. It's all math at this point, speculation. I don't even know the data being used to justify a theory to explain it. I understand the goal is to unify General Relativity with Quantum Mechanics in a grand theory of everything but the Quantum side has not progressed vey much at all so far.
• jayh
Considering that the Universe as we know it represents only one living entity, there are probably many billions of other Universes that are unknown to us. Of course our Universe is in contact with them just like we are in contact with other people. We are each a "universe" unto ourselves.
• Anonymous010
So there are parts to this that I don't agree with.

First, the statement that we would've noticed extra dimensions by now if they existed. I'm not sure that's true - after all, the ancient Greeks thought the same thing about stellar parallax (they thought that they'd have seen it if it was there, so the Earth had to be the center of the universe). We see the universe in a very specific way because we have a subjective view of space and time. We can't even visualize how to put a fourth axis on a standard Cartesian grid, so how would we even know what we are looking for when it comes to extra dimensions, and how could we be sure we'd recognize it if we saw it?

Second, the bit about the extra dimensions being very small seems like an unnecessary extra complication. Why would these extra dimensions be so tiny while x,y,z and t are not? Yes, the math works out if you do this, but that could just as easily be a red herring. Physical evidence is very much needed.
• Bigrob215275
Scientists can ONLY explain 4-6% of this unique Universe and then they want to suggest 11 dimensions and or multiple universes. Their atheistic religion is looking like a Hale-Bopp justification of foolishness. The problem is because they are scientists, everybody, bows in obeisance to their presumed intelligence and supposed reason and logic. They are NOT gods and in fact, most scientists and the science they support are found to need correction by future scientists.
• C. R. MacCluer
We already live in more than three spatial dimensions. General Relativity takes place in a locally three-dimensional differential manifold that is observed to have more than three actual spatial dimensions, as verified by the precession of Mercury, GPS errors, or the famous observations during eclipses. It is very misleading to assert, as the author does at the outset, that we know only four dimensions --- that view belongs to the warm up exercise of special relativity. Space is curved near mass.
• Truthseeker007
Considering that the Universe as we know it represents only one living entity, there are probably many billions of other Universes that are unknown to us. Of course our Universe is in contact with them just like we are in contact with other people. We are each a "universe" unto ourselves.

As Above so Below. The ancients knew this long before these University driven scientist are trying to figure it out. I find it interesting that only science is finding out now what the Ancients new long long ago and taught in the mystery schools.
• Truthseeker007
On a guitar are 12 frets. 12 dimensions of how the strings can be played. On the 12th fret it starts over just on higher octaves working up to 22-24 frets. So I would think guitar string theory isn't much different then well string theory.lol! So it would be my estimate that their are 12 dimensions. Especially since in most ancient writings 12 is an important number. We are in the 3rd dimension at the moment.