A Universe of 10 Dimensions

When someone mentions “different dimensions,” we tend to think of things like parallel universes – alternate realities that exist parallel to our own, but where things work or happened differently. However, the reality of dimensions and how they play a role in the ordering of our Universe is really quite different from this popular characterization.

To break it down, dimensions are simply the different facets of what we perceive to be reality. We are immediately aware of the three dimensions that surround us on a daily basis – those that define the length, width, and depth of all objects in our universes (the x, y, and z axes, respectively).

Beyond these three visible dimensions, scientists believe that there may be many more. In fact, the theoretical framework of Superstring Theory posits that the universe exists in ten different dimensions. These different aspects are what govern the universe, the fundamental forces of nature, and all the elementary particles contained within.

The first dimension, as already noted, is that which gives it length (aka. the x-axis). A good description of a one-dimensional object is a straight line, which exists only in terms of length and has no other discernible qualities. Add to it a second dimension, the y-axis (or height), and you get an object that becomes a 2-dimensional shape (like a square).

The third dimension involves depth (the z-axis), and gives all objects a sense of area and a cross-section. The perfect example of this is a cube, which exists in three dimensions and has a length, width, depth, and hence volume. Beyond these three lie the seven dimensions which are not immediately apparent to us, but which can be still be perceived as having a direct effect on the universe and reality as we know it.

The timeline of the universe, beginning with the Big Bang. Credit: NASA
The timeline of the universe, beginning with the Big Bang. According to String Theory, this is just one of many possible worlds. Credit: NASA

Scientists believe that the fourth dimension is time, which governs the properties of all known matter at any given point. Along with the three other dimensions, knowing an objects position in time is essential to plotting its position in the universe. The other dimensions are where the deeper possibilities come into play, and explaining their interaction with the others is where things get particularly tricky for physicists.

According to Superstring Theory, the fifth and sixth dimensions are where the notion of possible worlds arises. If we could see on through to the fifth dimension, we would see a world slightly different from our own that would give us a means of measuring the similarity and differences between our world and other possible ones.

In the sixth, we would see a plane of possible worlds, where we could compare and position all the possible universes that start with the same initial conditions as this one (i.e. the Big Bang). In theory, if you could master the fifth and sixth dimension, you could travel back in time or go to different futures.

In the seventh dimension, you have access to the possible worlds that start with different initial conditions. Whereas in the fifth and sixth, the initial conditions were the same and subsequent actions were different, here, everything is different from the very beginning of time. The eighth dimension again gives us a plane of such possible universe histories, each of which begins with different initial conditions and branches out infinitely (hence why they are called infinities).

In the ninth dimension, we can compare all the possible universe histories, starting with all the different possible laws of physics and initial conditions. In the tenth and final dimension, we arrive at the point in which everything possible and imaginable is covered. Beyond this, nothing can be imagined by us lowly mortals, which makes it the natural limitation of what we can conceive in terms of dimensions.

String space - superstring theory lives in 10 dimensions, which means that six of the dimensions have to be "compactified" in order to explain why we can only perceive four. The best way to do this is to use a complicated 6D geometry called a Calabi-Yau manifold, in which all the intrinsic properties of elementary particles are hidden. Credit: A Hanson. String space - superstring theory lives in 10 dimensions, which means that six of the dimensions have to be "compactified" in order to explain why we can only perceive four. The best way to do this is to use a complicated 6D geometry called a Calabi-Yau manifold, in which all the intrinsic properties of elementary particles are hidden. Credit: A Hanson.
The existence of extra dimensions is explained using the Calabi-Yau manifold, in which all the intrinsic properties of elementary particles are hidden. Credit: A Hanson.

The existence of these additional six dimensions which we cannot perceive is necessary for String Theory in order for their to be consistency in nature. The fact that we can perceive only four dimensions of space can be explained by one of two mechanisms: either the extra dimensions are compactified on a very small scale, or else our world may live on a 3-dimensional submanifold corresponding to a brane, on which all known particles besides gravity would be restricted (aka. brane theory).

If the extra dimensions are compactified, then the extra six dimensions must be in the form of a Calabi–Yau manifold (shown above). While imperceptible as far as our senses are concerned, they would have governed the formation of the universe from the very beginning. Hence why scientists believe that peering back through time, using telescopes to spot light from the early universe (i.e. billions of years ago), they might be able to see how the existence of these additional dimensions could have influenced the evolution of the cosmos.

Much like other candidates for a grand unifying theory – aka the Theory of Everything (TOE) – the belief that the universe is made up of ten dimensions (or more, depending on which model of string theory you use) is an attempt to reconcile the standard model of particle physics with the existence of gravity. In short, it is an attempt to explain how all known forces within our universe interact, and how other possible universes themselves might work.

For additional information, here’s an article on Universe Today about parallel universes, and another on a parallel universe scientists thought they found that doesn’t actually exist.

There are also some other great resources online. There is a great video that explains the ten dimensions in detail. You can also look at the PBS web site for the TV show Elegant universe. It has a great page on the ten dimensions.

You can also listen to Astronomy Cast. You might find episode 137 The Large Scale Structure of the Universe pretty interesting.

Source: PBS

 

Why Our Universe is Not a Hologram

Editor’s note: This article was originally published by Brian Koberlein on G+, and it is republished here with the author’s permission.

There’s a web post from the Nature website going around entitled “Simulations back up theory that Universe is a hologram.” It’s an interesting concept, but suffice it to say, the universe is not a hologram, certainly not in the way people think of holograms. So what is this “holographic universe” thing?

It all has to do with string theory. Although there currently isn’t any experimental evidence to support string theory, and some evidence pointing against it, it still garners a great deal of attention because of its perceived theoretical potential. One of the theoretical challenges of string theory is that it requires all these higher dimensions, which makes it difficult to work with.

In 1993, Gerard t’Hooft proposed what is now known as the holographic principle, which argued that the information contained within a region of space can be determined by the information at the surface that contains it. Mathematically, the space can be represented as a hologram of the surface that contains it.

That idea is not as wild as it sounds. For example, suppose there is a road 10 miles long, and its is “contained” by a start line and a finish line. Suppose the speed limit on this road is 60 mph, and I want to determine if a car has been speeding. One way I could do this is to watch a car the whole length of the road, measuring its speed the whole time. But another way is to simply measure when a car crosses the start line and finish line. At a speed of 60 mph, a car travels a mile a minute, so if the time between start and finish is less than 10 minutes, I know the car was speeding.

A visualization of strings. Image credit: R. Dijkgraaf.
A visualization of strings. Image credit: R. Dijkgraaf.

The holographic principle applies that idea to string theory. Just as its much easier to measure the start and finish times than constantly measure the speed of the car, it is much easier to do physics on the surface hologram than it is to do physics in the whole volume. The idea really took off when Juan Martín Maldacena derived what is known as the AdS/CFT correspondence (an arxiv version of his paper is here ), which uses the holographic principle to connect the strings of particle physics string theory with the geometry of general relativity.

While Maldacena made a compelling argument, it was a conjecture, not a formal proof. So there has been a lot of theoretical work trying to find such a proof. Now, two papers have come out (here and here) demonstrating that the conjecture works for a particular theoretical case. Of course the situation they examined was for a hypothetical universe, not a universe like ours. So this new work is really a mathematical test that proves the AdS/CFT correspondence for a particular situation.

From this you get a headline implying that we live in a hologram. On twitter, Ethan Siegel proposed a more sensible headline: “Important idea of string theory shown not to be mathematically inconsistent in one particular way”.

Of course that would probably get less attention.

A Capella String Theory: Bohemian Gravity (Video)

There’s not much to say except you MUST watch this. Incredible.

Here is Tim Blais’ master’s thesis: A New Quantization Condition for Parity-Violating Three-Dimensional Gravity.

Words to the song below:

A Capella Science – Bohemian Gravity!

Is string theory right?
Is it just fantasy?
Caught in the landscape,
Out of touch with reality
Compactified
On S5 or T*S3

Space is a pure void
Why should it be stringy?
Because it’s quantum not classical
Nonrenormalizable
Any way you quantize
You’ll encounter infinity
You see

Quanta
Must interact
Via paths we understand
Using Feynman diagrams
Often, they will just rebound
But now and then they go another way
A quantum
Loooooop
Infinities will make you cry
Unless you can renormalize your model
Of baryons, fermions
And all other states of matter

Curved space:
The graviton
Can be thought of as a field
But these infinities are real
In a many-body
Loop diagram
Our results diverge no matter what we do…
A Quantum Soup (any way you quantize)
Kiss your fields goodbye
Guess Einstein’s theory wasn’t complete at all!

I see extended 1-D objects with no mass
What’s their use? What’s their use? Can they give us quark plasma?
What to minimize?
What functional describes this
String?
Nambu-Goto! (Nambu-Goto)
Nambu-Goto! (Nambu-Goto)
How to quantize I don’t know
Polyakov!
I’m just a worldsheet, please minimize me
He’s just a worldsheet from a string theory
Reperametrized by a Weyl symmetry!

Fermi, Bose, open, closed, orientable?
Vibrations
Modes! They become particles (particles!)
Vibrations
They become particles (particles!)
Vibrations
They become particles (particles!)
Become particles (particles!)
Become particles (many many many many particle…)
Modes modes modes modes modes modes modes!
Oh mamma mia mamma mia,
Such a sea of particles!
A tachyon, with a dilaton and gravity-vity-VITY

(rock out!)

Now we need ten dimensions and I’ll tell you why
(anomaly cancellation!)
So to get down to 4D we compactify!
Oh, Kahler!
(Kahler manifold)
Manifolds must be Kahler!
(Complex Reimannian symplectic form)
If we wanna preserve
Any of our super-symmetry

(Superstrings of type I, IIa and IIb)
(Heterotic O and Heterotic E)
(All are one through S and T duality)
(Thank you Ed Witten for that superstring revolution and your new M-theory!)

(Maldecena!)
(Super-Yang-Mills!)
(Type IIB String!)
Dual! Dual!
(In the AdS/CFT)
(Holography!)

Molecules and atoms
Light and energy
Time and space and matter
All from one united
Theory

Any way you quantize…

Lyrics and arrangement by Tim Blais and A Capella Science
Original music by Queen

Scientists Say They Can Now Test String Theory


The idea of the “Theory of Everything” is enticing – that we could somehow explain all that is. String theory has been proposed since the 1960’s as a way to reconcile quantum mechanics and general relativity into such an explanation. However, the biggest criticism of String Theory is that it isn’t testable. But now, a research team led by scientists from the Imperial College London unexpectedly discovered that that string theory also seems to predict the behavior of entangled quantum particles. As this prediction can be tested in the laboratory, the researchers say they can now test string theory.

“If experiments prove that our predictions about quantum entanglement are correct, this will demonstrate that string theory ‘works’ to predict the behavior of entangled quantum systems,” said Professor Mike Duff, lead author of the study.

String theory was originally developed to describe the fundamental particles and forces that make up our universe, and has a been a favorite contender among physicists to allow us to reconcile what we know about the incredibly small from particle physics with our understanding of the very large from our studies of cosmology. Using the theory to predict how entangled quantum particles behave provides the first opportunity to test string theory by experiment.

But – at least for now – the scientists won’t be able to confirm that String Theory is actually the way to explain all that is, just if it actually works.

“This will not be proof that string theory is the right ‘theory of everything’ that is being sought by cosmologists and particle physicists,” said Duff. “However, it will be very important to theoreticians because it will demonstrate whether or not string theory works, even if its application is in an unexpected and unrelated area of physics.”

String theory is a theory of gravity, an extension of General Relativity, and the classical interpretation of strings and branes is that they are quantum mechanical vibrating, extended charged black holes.The theory hypothesizes that the electrons and quarks within an atom are not 0-dimensional objects, but 1-dimensional strings. These strings can move and vibrate, giving the observed particles their flavor, charge, mass and spin. The strings make closed loops unless they encounter surfaces, called D-branes, where they can open up into 1-dimensional lines. The endpoints of the string cannot break off the D-brane, but they can slide around on it.

Duff said he was sitting in a conference in Tasmania where a colleague was presenting the mathematical formulae that describe quantum entanglement when he realized something. “I suddenly recognized his formulae as similar to some I had developed a few years earlier while using string theory to describe black holes. When I returned to the UK I checked my notebooks and confirmed that the maths from these very different areas was indeed identical.”

Duff and his colleagues realized that the mathematical description of the pattern of entanglement between three qubits resembles the mathematical description, in string theory, of a particular class of black holes. Thus, by combining their knowledge of two of the strangest phenomena in the universe, black holes and quantum entanglement, they realized they could use string theory to produce a prediction that could be tested. Using the string theory mathematics that describes black holes, they predicted the pattern of entanglement that will occur when four qubits are entangled with one another. (The answer to this problem has not been calculated before.) Although it is technically difficult to do, the pattern of entanglement between four entangled qubits could be measured in the laboratory and the accuracy of this prediction tested.

The discovery that string theory seems to make predictions about quantum entanglement is completely unexpected, but because quantum entanglement can be measured in the lab, it does mean that there is way – finally – researchers can test predictions based on string theory.

But, Duff said, there is no obvious connection to explain why a theory that is being developed to describe the fundamental workings of our universe is useful for predicting the behavior of entangled quantum systems. “This may be telling us something very deep about the world we live in, or it may be no more than a quirky coincidence”, said Duff. “Either way, it’s useful.”

Source: Imperial College London

Method to Test String Theory Proposed

What is the universe made of? While general relativity does a good job providing insights into the Big Bang and the evolution of stars, galaxies and black holes, the theory doesn’t help much when it gets down to the small stuff. There are several theories about the basic, fundamental building blocks of all that exists. Some quantum physicists propose string theory as a theory of “everything,” that at the elemental heart of all matter lie tiny one-dimensional filaments called strings. Unfortunately, however, according to the theory, strings should be about a millionth of a billionth of a billionth of a billionth of a centimeter in length. Strings are way too small to see with current particle physics technology, so string theorists will have to come up with more clever methods to test the theory than just looking for the strings.

Well, one cosmologist has an idea. And it’s a really big idea.

Benjamin Wandelt, a professor of physics and astronomy at the University of Illinois says that ancient light from the beginnings of our universe was absorbed by neutral hydrogen atoms. By studying these atoms, certain predictions of string theory could be tested. Making the measurements, however, would require a gigantic array of radio telescopes to be built on Earth, in space or on the moon. And it would be really gigantic: Wandelt proposes an array of radio telescopes with a collective area of more than 1,000 square kilometers. Such an array could be built using current technology, Wandelt said, but would be prohibitively expensive.

So for now, both string theory and this method of testing are purely hypothetical.

According to Wandelt, what this huge array would be looking for are absorption features in the 21-centimeter spectrum of neutral hydrogen atoms.

“High-redshift, 21-centimeter observations provide a rare observational window in which to test string theory, constrain its parameters and show whether or not it makes sense to embed a type of inflation — called brane inflation– into string theory,” said Wandelt. “If we embed brane inflation into string theory, a network of cosmic strings is predicted to form. We can test this prediction by looking for the impact this cosmic string network would have on the density of neutral hydrogen in the universe.”

About 400,000 years after the Big Bang, the universe consisted of a thick shell of neutral hydrogen atoms (each composed of a single proton orbited by a single electron) illuminated by what became known as the cosmic microwave background.

Because neutral hydrogen atoms readily absorb electromagnetic radiation with a wavelength of 21 centimeters, the cosmic microwave background carries a signature of density perturbations in the hydrogen shell, which should be observable today, Wandelt said.

Cosmic strings are filaments of infinite length. Wandelt compared their composition to the boundaries of ice crystals in frozen water.

When water in a bowl begins to freeze, ice crystals will grow at different points in the bowl, with random orientations. When the ice crystals meet, they usually will not be aligned to one another. The boundary between two such misaligned crystals is called a discontinuity or a defect.

Cosmic strings are defects in space. String theory predicts that a network of strings were produced in the early universe, but this has not been detected so far. Cosmic strings produce fluctuations in the gas density through which they move, a signature of which Wandelt says will be imprinted on the 21-centimeter radiation.

Like the cosmic microwave background, the cosmological 21-centimeter radiation has been stretched as the universe has expanded. Today, this relic radiation has a wavelength closer to 21 meters, putting it in the long-wavelength radio portion of the electromagnetic spectrum.

If such an enormous array were eventually constructed, measurements of perturbations in the density of neutral hydrogen atoms could also reveal the value of string tension, a fundamental parameter in string theory, Wandelt said. “And that would tell us about the energy scale at which quantum gravity begins to become important.”

But questions remain about the validity of this experiment. Also, could the array somehow be “shrunk” to search only a small area of the 21-centimeter radiation? Or possibily, could an instrument similar to WMAP (Wilkinson Microwave Anisotropy Probe) be constructed to look at the entire sky for this radiation?

Wandelt and graduate student Rishi Khatri describe their proposed test in a paper accepted for publication in the journal Physical Review Letters, and the paper is not yet available for public review.

Original News Source: University of Illinois Press Release