“Great spirits have always encountered violent opposition from mediocre minds.” –Albert Einstein
It may be hard to believe, seeing as how it’s been our leading theory of gravity for nearly a century now, but Einstein’s General Relativity is possibly the most frequently challenged scientific idea of all-time. Of course, it’s emerged victorious from each and every one of those challenges, making a slew of unintuitive predictions that have been spectacularly confirmed each time they’ve been tested.
This includes the bending of distant starlight by the predicted amount by gravitationally strong objects such as the Sun, as is only visible during a total solar eclipse (as shown above), and goes well-beyond to gravitational lensing (of both the strong and weak varieties) of extremely distant galaxies by intervening sources of mass.
There are plenty of other tests that have succeeded, ranging from test of the gravitational time delay of light to the decay of binary pulsar systems to the Lense-Thirring effect (relativistic Frame-Dragging) and more.
But perhaps the test you’re most familiar with comes every single time you use your GPS device.
Without relativity, the errors in a GPS signal, even if you calibrated it daily, would accumulate to give you an incorrect position of 10 kilometers after just 24 hours! In order to compensate and make our GPS devices work properly, we need an understanding of two things:
- Special relativistic time dilation, or the fact that objects moving more quickly experience the passage of time differently, and
- General relativistic gravitational redshift, or the fact that light red-or-blueshifts its frequency dependent on the relative gravitational field of the observer and the emitter.
Gravitational redshift is a little bit counterintuitive to most: a photon (or light-wave) that has to climb out of a gravitational field loses energy and becomes longer-wavelength, or lower in energy, while one that plummets into a gravitational field gains energy and becomes shorter-wavelength, or higher energy.
But it’s not going to be counterintuitive to you any longer, because you’re going to follow one of the simplest thought experiments (that I first heard described in a talk by Mark Trodden) that tells you exactly why gravitational redshifts-and-blueshifts must be real.
If you begin at rest, high up in a gravitational field, you have plenty of gravitational potential energy, but no kinetic energy. And if you let that object free-fall, it gains energy, meaning that it’s more energetic at the bottom.
In other words, an object at rest that’s in a shallower gravitational potential well has the same amount of energy as an object with some kinetic energy that’s deeper in a gravitational potential well. The three objects below — effects exaggerated for clarity — all have the same amount of total energy, and that’s just classical, basic mechanics.
But now, instead of a single particle, imagine we had two particles: an electron (which is a form of matter) and a positron (an anti-electron, a form of antimatter). When electrons and positrons collide at rest, they produce two photons that are exactly equal in energy to the rest mass (via E=mc2) of the electron/positron.
Consider these three facts, now:
- If I had an electron/positron annihilate from rest high up in a gravitational field, they would make two photons of a very specific energy at the point where they annihilated, high in that field.
- If I had an electron/positron annihilate from low down in a gravitational field, they would make two photons of that same energy at the point where they annihilated, low down in that field.
- If I had an electron/positron at rest high up in a gravitational field and I released them, letting them fall, they would gain energy, turning that gravitational potential energy into kinetic energy as they fell.
Agreed? So tell me, when that electron/positron pair that I released reaches that lower point in that gravitational field, where they have kinetic energy, and now they find each other and annihilate, what is the energy of the photons that they produce?
It’s going to be greater than in case two, because you have the rest-mass energy of the electron-positron, plus the gravitational potential energy that must be turned into kinetic energy of the photons, which means we have bluer (higher-frequency, higher-energy) light the deeper we are in the gravitational field!
It also means that if we produce light of a certain energy deep in the gravitational field, it’s going to gravitationally redshift — and lose energy — as it climbs out of that field!
If light didn’t change its frequency in a gravitational field, it’d be possible to build a perpetual motion machine simply by having electrons/positrons annihilate deep in a gravitational field, building a mirror to reflect those photons upwards and out of the gravitational potential well, re-form them into electrons and positrons again (which you could do if and only if they didn’t lose energy as they climbed out of the gravitational field), and then let them fall back to Earth, gaining kinetic energy which you used to turn your turbine/produce power.
And you know what I think of schemes like that.
So the next time someone questions relativity, ask them about the gravitational redshift; there’s no wriggling your way out of what science tells us is true about the natural world!