Happy 100th Birthday, General Relativity!

Wayne,

This year is the 100th anniversary of Einstein’s theory of general relativity. This amazing and beautiful theory is our best thinking about gravitation and about the universe at the largest scales. In 100 years it has passed every experimental and observational test, yet physicists believe that it should be replaced!

What is the problem? General relativity is not a quantum theory, and physicists believe that all fundamental theories should be quantum theories. What would that mean? One thing it would mean is that space-time would be quantized. It, and they, that is, space and time, would have smallest pieces. It’s hard to picture but the physicists who think about such things tend to picture foam, or a magnified picture of a sponge.

How small is the smallest unit of space? The Planck length is:

\ell_\mathrm{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616\;199 (97) \times 10^{-35}\ \mathrm{m}

How small is the smallest unit of time? It’s the length of time for light to move a Planck length:

t_\mathrm{P} \equiv \sqrt{\frac{\hbar G}{c^5}}\approx 5.39106 (32) \times 10^{-44}\ \mathrm{s}.

Roughly speaking, these dimensions are 20 orders of magnitude smaller than anything physicists can detect in the world’s most powerful accelerators. Physicists believe that distances and times might come into play at the center of black holes or that they might have been important in the earliest and tiniest aspects of the Big Bang, or earlier in the era of inflation.Thus, we are hard-pressed for experimental data to guide theorists as to how to quantize gravitation. When we do, in addition to the chunkiness of space-time, there will be a particle, known as the graviton, which will be massless, travel at c, and have spin 2. Or so it seems to us today.

Both Einstein’s 1905 theory of special relativity and general relativity could have better names,as Einstein also thought, in light of modern ideas about nature. They ought to be called theories of invariance.While special relativity tells us that observers will see space and time differently depending upon their relative motion at constant velocities, it tells us that the distance between events specified in space-time will be invariant. Everyone will agree, for example, as to which event comes before another, but they will disagree as to the time and distance between those events. General relativity extends this invariance to observers who may be accelerating with respect to one another. Einstein would say that the laws of physics must be the same for various observers. Impose this symmetry upon our observations of space-time, and gravitation emerges.

These days, physics at its deepest levels, we’d say nature at its deepest levels, has to do with symmetry. What things remain the same as other things change. Our great conservation laws, energy, linear momentum, and angular momentum, arise from the fact that (under appropriate conditions) when we do an experiment, or where we do it, or how we arrange in angle our equipment makes no difference to the outcome of the experiment.In quantum theory, there are other symmetries, apparent in the equations, but without simple mental pictures, that also lead to conservation laws.

Physicists try this in both directions. If we observe a conservation law, say the conservation of electric charge, then we will seek to form our theories with a suitable symmetry. If we observe a symmetry in our equations, then we will look for a conservation law in nature. In this way, we can learn things about equations that we don’t know yet.The Higgs boson, and the Higgs mechanism, which made the news recently are predictions based upon some of these abstract symmetries.In addition, we observe that some symmetries hold in certain circumstances, but not in others. Symmetries may be broken. As when a pen balanced on its tip is symmetric in direction, but not after it has fallen flat. Or as when a spherical chamber full of steam is symmetric, but not after it has condensed into liquid, or frozen into ice.

Physicists believe that at the earliest moments in the universe, all of the forces were, somehow, symmetric, and that as the universe expanded and cooled, one after another, then forces separated themselves. In today’s universe, the strong, weak, electromagnetic, and gravitational force appear very different.

Bernard

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