So here’s the big problem.

Right now, physicists have a detailed mathematical model for how the fundamental forces in nature work: electromagnetism, and the strong and weak nuclear forces. Added to this is a detailed list of the fundamental particles in nature like the electron, the quarks, photons, neutrinos and others. Called the Standard Model, it has been extensively verified and found to be an amazingly accurate way to describe nearly everything we see in the physical world. It explains why some particles have mass and others do not. It describes exactly how forces are generated by particles and transmitted across space. Experimenters at the CERN Large Hadron Collider are literally pulling out their hair to find errors or deficiencies in the Standard Model that go against the calculated predictions, but have been unable to turn up anything yet. They call this the search for New Physics.

Along side this accurate model for the physical forces and particles in our universe, we have general relativity and its description of gravitational fields and spacetime. GR provides no explanation for how this field is generated by matter and energy. It also provides no description for the quantum structure of matter and forces in the Standard Model. GR and the Standard Model speak two very different languages, and describe two very different physical arenas. For decades, physicists have tried to find a way to bring these two great theories together, and the results have been promising but untestable. This description of gravitational fields that involves the same principles as the Standard Model has come to be called Quantum Gravity.

The many ideas that have been proposed for Quantum Gravity are all deeply mathematical, and only touch upon our experimental world very lightly. You may have tried to read books on this subject written by the practitioners, but like me you will have become frustrated by the math and language this community has developed over the years to describe what they have discovered.

The problem faced by Quantum Gravity is that gravitational fields only seem to display their quantum features at the so-called Planck Scale of 10^-33 centimeters and 10^-43 seconds. I cant write this blog using scientific notation, so I am using the shorthand that 10^3 means 1000 and 10^8 means 100 million. Similarly, 10^-3 means 0.001 and so on. Anyway, the Planck scale also corresponds to an energy of 10^19 GeV or 10 billion billion GeV, which is an energy 1000 trillion times higher than current particle accelerators can reach.

There is no known technology that can reach the scales where these effects can be measured in order to test these theories. Even the concept of measurement itself breaks down! This happens because the very particles (photons) you try to use to study physics at the Planck scale carry so much energy they turn into quantum black holes and are unable to tell you what they saw or detected!

One approach to QG is called Loop Quantum Gravity. Like relativity, it assumes that the gravitational field is all there is, and that space and time become grainy or ‘quantized’ near the Planck Scale. The space and time we know and can experience in-the-large is formed from individual pieces that come together in huge numbers to form the appearance of a nearly-continuous and smooth gravitational field.

The problem is that you cannot visualize what is going on at this scale because it is represented in the mathematics, not by nuggets of space and time, but by more abstract mathematical objects called loops and spin networks. The artist rendition above is just that.

So here, as for Feynman Diagrams, we have a mathematical picture that represents a process, but the picture is symbolic and not photographic. The biggest problem, however, is that although it is a quantum theory for gravity that works, Loop Quantum Gravity does not include any of the Standard Model particles. It represents a quantum theory for a gravitational field (a universe of space and time) with no matter in it!

**In other words, it describes the cake but not the frosting.**

The second approach is string theory. This theory assumes there is already some kind of background space and time through which another mathematical construct called a string, moves. Strings that form closed loops can vibrate, and each pattern of vibrations represents a different type of fundamental particle. To make string theory work, the strings have to exist in 10 dimensions, and most of these are wrapped up into closed balls of geometry called Calabi-Yau spaces. Each of these spaces has its own geometry within which the strings vibrate. This means there can be millions of different ‘solutions’ to the string theory equations: each a separate universe with its own specific type of Calabi-Yau subspace that leads to a specific set of fundamental particles and forces. The problem is that string theory violates general relativity by requiring a background space!

**In other words, it describes the frosting but not the cake!**

One solution proposed by physicist Lee Smolin is that Loop Quantum Gravity is the foundation for creating the strings in string theory. If you looked at one of these strings at high magnification, its macaroni-like surface would turn into a bunch of loops knitted together, perhaps like a Medieval chainmail suit of armor. The problem is that Loop Quantum Gravity does not require a gravitational field with more than four dimensions ( 3 of space and one of time) while strings require ten or even eleven. Something is still not right, and right now, no one really knows how to fix this. Lacking actual hard data, we don’t even know if either of these theories is closer to reality!

**What this hybrid solution tries to do is find aspects of the cake that can be re-interpreted as particles in the frosting!**

This work is still going on, but there are a few things that have been learned along the way about the nature of space itself. At our scale, it looks like a continuous gravitational field criss-crossed by the worldlines of atoms, stars and galaxies. This is how it looks even at the atomic scale, because now you get to add-in the worldlines of innumerable ‘virtual particles’ that make up the various forces in the Standard Model. But as we zoom down to the Planck Scale, space and spacetime stop being smooth like a piece of paper, and start to break up into something else, which we think reveals the grainy nature of gravity as a field composed of innumerable gravitons buzzing about.

But what these fragmentary elements of space and time ‘look’ like is impossible to say. All we have are mathematical tools to describe them, and like our attempts at describing the electron, they lead to a world of pure abstraction that cannot be directly observed.

**If you want to learn a bit more about the nature of space, consider reading my short booklet ‘Exploring Quantum Space‘ available at amazon.com. It describes the amazing history of our learning about space from ancient Greek ‘common sense’ ideas, to the highlights of mind-numbing modern quantum theory.**

*Check back here on Thursday, December 22 for the last blog in this series!*

It seems to me that any astrophysist who retains his/her sanity while exploring these questions is doing pretty well. Quantum mechanics alone is a thorough test of mental stability.

Hi Gloria! I have always found it so amazing that we share the world with something like quantum mechanics, that none of us really understands although we can make fantastically accurate calculations with it. It is far better than science fiction! Even astrophysicists have a hard time wrapping their minds around it so don’t feel too bad. It’s like anything else in life, the more hours you elect to spend with it the better you get at understanding it. It’s like any other skill that is difficult to master! The only thing is that this kind of physics is not one that you ‘get’ after a few hundred hours, but is a life-time challenge!

An interesting question is, is there any evidence that gravity should be quantised? As an example of what I mean, I am very happy with quantum electrodynamics (at least, given someone else is doing the calculations) because when I look at something like electron spin resonance, superficially the g factor might be 2, but in fact it is something like 2.0023. It is only a small discrepancy, but QED requires it, so that makes me happy that QED is at least a valid theory so far. But there is no effect I know of with gravity that requires quantisation – or is there?

Hi Ian! To my knowledge, there is no indisputable evidence for gravity (e.g spacetime) quantization through observational means. There was some interest in the results from gamma-ray bursts that seemed to show the higher-energy photons arriving at a different time than the lower-energy ones, consistent with some kind of spacetime graininess amplified over the several billion light years of travel, but those results are not apparently without some controversy. I’ll write about this fascinating story at a later time. There are many theoretical demonstrations that something like spacetime quantization is needed, but that is not the same as evidence. For instance, even in QED you have to assume electrons are point particles to insure that their structure is relativistically invariant, but that leads you to the so-called Infinity Problem that can only be cured by the mathematical technique called renormalization where you define the observed electron mass as the difference between the infinite bare mass and the infinite field mass/energy. Spacetime quantization also comes up in studies of quantum black holes and what happens to information as it passes through the horizon. For example, the information in the volume of a black hole is encoded on its 2-d horizon surface, but this surface is finite, so therefore the volume has to be divided into a finite number of information nuggets, which means the interior spacetime is quantized at the Planck scale. Again, all of the ‘proofs’ of gravity (spacetime) quantization I have ever heard about are not based on observable concepts, but theoretical necessity and ‘beauty’. Still, it would be very cool indeed if spacetime were quantized because I think the theoretical ideas are amazing and simply too good to be just logical fantasy!! I do recall a famous quote from Richard Feynman who developed modern QED. He said, and I paraphrase, ‘Maybe the reason we haven’t been able to unify gravity with the other forces is because gravity is not a quantum field afterall!’

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