One of the great challenges of modern science is to unite our thinking about the universe on the largest scale with our notions of how it works on the smallest; in other words to combine relativity and quantum mechanics into a single theory.
The current best effort is a notion called string theory, an idea born of quantum thinking and in which gravity is a byproduct of complexity, a so-called emergent phenomenon.
The trouble with with this process of emergence is that it pays mere lip service to our intuitive ideas about causality: that an affect must be preceded by its cause. At least, that’s how the Nobel prize winning physicist Gerard ‘t Hooft sees things.
To put this right, he has constructed a different model of reality that preserves causality and has some interesting side effects. The fundamental change in his thinking is to accept a new kind of symmetry in the universe.
A symmetry is a property of a system that is left unchanged under a certain transformation. So for example, our laws of physics are derived from the idea that they must remain constant under any change of position or direction in space. It’s a hugely powerful idea.
Now ‘t Hooft says that to preserve the idea of causality in a theory of quantum gravity we need to accept the idea of a symmetry of scale. In other words, teh laws of physcis are the same at every scale. He also introduces an idea called “black hole complementarity” in which an observer inside a black hole sees the universe in a different way to an observer outside a black hole.
The consequences of this thinking are profound. t’ Hooft puts it like this:
“If we add these to our set of symmetry transformations, black holes, space-time singularities, and horizons disappear,”
In exchange, we keep the notion of causality intact.
You can argue the merits of such an exchange but the important question is whether ‘t Hooft’s new universe bears any relation to the one in which we live.
In answer we can say that the existence of black holes is well accepted. Astronomers can see their gravitational effects. And while nobody has directly observed a black hole or the Hawking radiation physicists assume they emit, few doubt that the evidence in favour will mount.
A more serious problem is the notion of scale invariance itself. Here’s a thought experiment for ‘t Hooft. Imagine you were suddenly shrunk or enlarged by some unknown factor inside a closed box, what experiment could you do to determine your new scale?
If the laws of physics were scale invariant, it would be impossible to determine your scale with an experiment.
But suppose you were to measure the position of a ball. Surely, in our universe, the accuracy of your measurement would be a good indication of your scale, since quantum effects would be easily distinguishable from Newtonian ones.
‘t Hooft seems to recognise this limitation admitting that “Newton’s constant G is not scale-invariant at all.”
But that’s a problem of his own making. In answer to the question of how to unite the physics of the very big with the physics of the very small, ‘t Hooft says there is no difference between them.
That may not be as crazy as it sounds. The differences we see could be the result of some other symmetry-breaking process, a kind of illusion. But how does this happen?
He says the answer may come from a better understanding of the way information flows through his universe. “Obviously, this leaves us with the problem of defining what exactly information is, and how it links with the equations of motion, ” he says.
‘t Hooft is not the first to run up against information. When pushed to its limits, every fundamental theory of physics runs foul of our poor understanding of information.
It may be no understatement to say that the biggest breakthrough in physics must come in information theory rather than quantum mechanics or relativity.
Ref: arxiv.org/abs/0909.3426: Quantum Gravity without Space-time Singularities or Horizons
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