Dimensional Reduction and Mystery Forces

Before we get into the bulk of today’s post, let’s do a super-brief review on the subject of quantum gravity.

As you may be aware, scientists are spending a great deal of time these days searching for a unified theory of everything. In essence, what they are really trying to do is merge two existing theories- quantum theory and relativity. As it stands right now, physicists are able to use quantum theory when studying extremely small things (like elementary particle interactions) and relativity when studying the large (such as planetary movement). Unfortunately, if quantum theory is used to study the large (or relativity to study the small), the equations yield nonsensical infinities. Impossible and inaccurate answers.

It’s obvious that we are missing something.

Now, general relativity is the framework within which we understand gravity, one of the four fundamental forces (along with electromagnetic, strong, and weak). While the other three have been worked into quantum field theory, gravity seems stubbornly resistant to assimilation. So, instead of trying to fold one theory into the other, scientists have instead started searching for a new theory that encompasses and explains all four fundamental forces and the information present in the standard model of particle physics.

Our theory of everything, then, is often referred to as a quantum theory of gravity. It is our attempt to fuse quantum theory and relativity. Multiple theories of quantum gravity exist, the most popular being superstring theory (my personal favorite) and loop quantum gravity.


Superstring theory (along with M-theory) stretches the limits of the imagination when we try to picture the natural world conforming to its predictions. 11+ space/time dimensions? Even if these extra dimensions are curled up on the level of the Planck length (16.163×10^−36 m) in complex manifolds, it seems preposterous to imagine us moving through all these extra dimensions at every moment… and yet being unable to detect them.

Leonard: At least I didn’t have to invent 26 dimensions to get the math to work.
Sheldon: I didn’t invent them. They’re there.
Leonard: Yeah? In what universe?
Sheldon: In all of them, that’s the point!

As mind-boggling as additional dimensions may seem, research in the realm of quantum gravitational theories has found that several of these theories make some very strange predictions about behavior at incredibly small scales (along the lines of the Planck length). They’ve found that particles (and their fields) start to behave as if space was only one-dimensional.

How is this possible?

Down on the level of the Planck length, space-time becomes a frothing, roiling mess known as quantum foam, which we’ve mentioned before. Steven Carlip at the University of California says that this quantum foam may act similarly to space-time close to a singularity. Remember that, according to general relativity, the gravity near a singularity becomes so strong that it actually warps the fabric of space-time. Light is bent so sharply that it can take an infinitely long period of time for it to travel between two nearby points. Because of this, neighboring pieces of space-time become disconnected from each other, allowing them to expand or contract independently.

Carlip is suggesting that at those extremely tiny distances (like the Planck length), light gets bent just like it does near a singularity. Thus, tiny patches of space-time get disconnected, allowing space at different points to expand or contract faster in one dimension than in the others (which also accounts for the choppy surface of quantum foam). As a result, over these very short space-time distances, particle motion can become dominated by the single, grossly expanded dimension of that disconnected portion of space-time. However, if you watch long enough, the particle’s motion will switch between different singular dimensions (as it moves through those isolated chunks of space-time). This means that if you wait long enough or look at larger distance scales, space becomes effectively three-dimensional.

And how did scientists detect this oddity of particle motion?

Well, they were studying the spectral dimension, a parameter which describes how particles or fields gradually move away from a given point (kind of like diffusion). But, to their surprise, they found that this motion happened much more quickly on the level of the Planck length. This speed can be explained if the particles are moving in just one spatial dimension, as the fewer dimensions available, the fewer directions a particle can move and the less time it will take to wander from its original position.

And while this discovery opens up a host of questions (including how quantum foam can focus light so strongly that nearby regions become disconnected from one another), what’s really interesting about all this is that this dimensional reduction pops up in multiple theories of quantum gravity. “Finding that very different approaches have something in common is exciting, as it suggests we may have stumbled upon an underlying property of quantum gravity,” says Leonardo Modesto of the Perimeter Institute for Theoretical Physics in Waterloo, Canada.


All this talk of dimensional movement reminds me of an Anaïs Nin quote:

“We do not grow absolutely, chronologically. We grow sometimes in one dimension, and not in another; unevenly. We grow partially. We are relative. We are mature in one realm, childish in another. The past, present, and future mingle and pull us backward, forward, or fix us in the present. We are made up of layers, cells, constellations.”

That really doesn’t have much to do with what we’re discussing, but I’ve always thought it was a rather lovely quote.


We’ll wrap up today’s post with a short (but tantalizing) bit from NASA.

I don’t know if you are familiar with the Pioneer anomaly, galleons. It refers to two NASA space probes (Pioneer 10 and 11) that have been drifting slightly off-course (toward the sun) for nearly 40 years in a way that defies our knowledge of gravity.

Scientists have eliminated all possible causes- gravity, radiation, equipment problems- and have concluded that, bizarre though it may seem, the craft are being affected by a previously unknown force that’s about 10 billion times weaker than the gravitational force.

That’s right- a brand new fundamental force. Number five.

As to what it is and why we haven’t encountered it before, answers are slow in coming. It appears, though, that we’re about to witness a slew of papers and experiments researching and attempting to verify/disprove this so-called new fundamental force.

Exciting, right?

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