As far as TV shows are concerned, I’m a big fan of The Big Bang Theory. I’ve always thought nerds were cool, but the show only popularized that opinion – at least in some circles that wouldn’t have accepted, to use lingo from the show, the paradigm. My only problem with the show is the character I really like, Dr. Sheldon Cooper, is a string theorist and a character I find annoying, Leslie Winkle, is an LQG-adherent (Loop Quantum Gravity).

I haven’t received any formal training in particle physics. I believe that understanding the natural philosophy of the universe can happen to perfection just by a lot of reasoned thought with a compatible dose of theories and a few formulae.

On that note: I’m an advocate of LQG, and I’m going to spend the rest of this post on detailing why that is and how it works. Or, if you like, I’m going to try and explain what the squiggles on Sheldon’s and Leonard’s boards mean and what the squiggles on Leslie’s board could mean.

The story must begin the way all histories of physical theories do: with Isaac Newton. In describing the fundamental laws of classical mechanics, Newton needed a frame reference, a fixed entity with reference to which objects could accelerate. Without a frame of reference, we’d never be able to understand how an apple falls from a tree, for example. We know it did because we see it against an unmoving background. Thinking as he was in much more stripped-down terms, Newton conceived of a background space against which all things could be measured.

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– Sir Isaac Newton

In the 19th century, there was a breakthrough by Michael Faraday and James Clerk Maxwell. Working with electricity, Faraday imagined that two charges interacted via a mediating electric field. He established that the field lines started and ended with charges, and in a space where there were no charges, the field lines bent around and formed loops. These field lines were called Faraday lines. Maxwell then transcribed Faraday’s hypothesis onto paper and birthed the Maxwellian equations, which described the behaviour of electromagnetic fields in much the same way.

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– The image shows a point source generating a field. Notice how the field lines are all parts of closed loops.

And then, there was Albert Einstein, whose principle contribution was the idea that gravity is not just a force but an inherent attribute of space-time itself. However, when attempting to work this into his general theory of relativity, he realized that gravitational force also had to be mediated by a field like electricity and magnetism were. This meant that a gravitational field had to exist with loops, lines and everything else.

Einstein also stumbled across one other astounding realization. All those years ago, when Newton had conceptualized a background space to serve as a frame of reference, he’d described acceleration in terms of a gravitational force – a discovery he’s the most known for. Einstein found, however, that this Newtonian background space was nothing other than gravitational field itself. Because the field permeated through space-time and gave mass to objects that interacted with the field, it became a frame of reference.

These “stumblings” gave rise to two important conclusions.

  1. Loops didn’t exist in a background space (as was previously thought) but on another layer of loops. And those loops? On yet another layer of loops. And those loops? You get the idea.
  2. Because there was a gravitational field that mediated gravity, low-frequency excitations of the field had to manifest as some particle. Just as the low-frequency manifestation of an electric field are electrons and of an electromagnetic field are photons, the excitations of a gravitational field are called gravitons. (Note: these have nothing to do with the Higgs boson)

This lack of a background space was disturbing to many physicists. At this point, some decided to ignore this outcome of general relativity and proceeded as if there was background space – a region that didn’t have any underlying loops. In fact, these theorists went on to postulate that the gravitational field was the resultant when a background space and a quantum field acted together. These are today known as the string theorists.

String_theory

– xkcd comic #171

The other faction decided to take into account this lack of background space and set about trying to formulate a background-independent theory of the nature of the universe. These are the LQG-advocates. According to them, the universe offers no background space naturally but they are created when the Faraday lines of the gravitational fields are quantum-excited.

Let me explain.

The gravitational field exists on another layer of loops (we don’t know what they are). Because the point sources that created the gravitational field quickly decayed long ago, the lines are large closed loops. The gravitational field permeates throughout the space-time continuum, and therefore there are infinitely many such loops.

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– One of the decay signatures of a Higgs boson is a tau lepton-antilepton pair, shown above. Tau leptons are extremely hard to detect because they decay too quickly. However, other signatures include quark-antiquark pairs and electron/muon lepton-antilepton pairs, which are relative more long-lived.

When one of these loops is excited to some energy, physical space is created. It is important to understand that the loops are not in that space but that they are the space. Earlier, there was a conundrum: if there are two loops that are separated by a really small distance, then each loop will represent one degree of freedom for the universe, i.e. one avenue of change.

Since there are infinitely many such loops, the universe has to have infinite degrees of freedom. But that is not the case. That was dissolved after physicists realised that all the loops were a part of the same field, and no space could have separated the loops because the loops were space.

Lqg

– In LQG, the point where two loops intersect is called a node. The region that corresponds to a node is called a cell, the section of a loop joining two nodes is called a link, and the surface of a cell that a link passes through is called a… well, a surface.

So, that is the story of the universe – according to some. The string theorists believe that long, one-dimensional strings exist in a background space, and their vibrations manifest as particles that make up the universe.

I chose to be on the LQG side of things because I see no reason to disregard Einstein’s conclusion that there is no background space. Also, string theory has turned up no testable hypotheses because it claims the strings exist at the Planck scale (one-hundred-billion-trillion-trillionth of a metre) whereas the mathematics of LQG has been able to explain the formation of black holes (I’ll save that for another post, another day).

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– While string theory claims that the universe exists as strings at the Planck scale, LQG claims that at such scales, the granular cells that the space-time continuum is made of should show up. But such claims are yet untested.

In conclusion: when Leonard says he prefers his universe stringy, not loopy, all this is what he means. However, I can sympathise with Leslie when she leaves in a huff after Leonard wants to “let the kids decide” which hypothesis to choose.

2 comments

  1. Einstein didn’t conclude there was no background space. Space-time, a theory he developed, is the background space and is interchangeable with the concept of Aether that was thrown of of science years before.

    Like

  2. Einstein didn’t conclude there was no background space. Space-time, a theory he developed, is the background space and is interchangeable with the concept of Aether that was thrown of of science years before.

    Like

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