Fraser Cain: So, this week we are going to be coming back and doing part two of an episode we started back at episode nine. Back at episode nine, we covered Einstein’s theory of special relativity, but that’s only half the relativity picture. The great scientist made an even more profound impact on physics with his theory of general relativity, replacing Newton with a better model for gravity.

 

Why don’t we give a quick synopsis of special relativity for listeners, in case they don’t want to hurry back and listen to episode nine again.

Dr. Pamela Gay: Special relativity basically covers things like the famous e=mc^2 equation, which has appeared everywhere from The Simpsons to just about every other TV and cartoon thing out there, anywhere.

 

From there it went on to work on trying to figure out what people/observers travelling at different speeds perceive relative to one another. We end up with neat effects like time dilation, mass getting bigger as you move faster… end up with just a lot of really weird, neat thought experiments that we went into a lot of in detail in show nine.

 

One thing that didn’t come out of special relativity is how does gravity play into all of this. In general, everything discussed in special relativity is just sort of dealing with, “so, you’re moving. Let’s discuss the motion.” It doesn’t get into the details of the force of gravity and how it causes things to accelerate. Einstein worked to try and figure out how to bring in gravity, and it took him a few years. In 1916 he came out with his generalized theory of relativity that introduced in gravity.

Fraser: All right, so what are the basics of this theory?

Pamela: Prior to Einstein, people had viewed gravity as just a force: the larger mass something has, the more it’s going to pull on other things with that mass. After Einstein, our way of looking at it had changed a little bit. It’s best summarised perhaps by John Wheeler, who said that Einstein’s geometric theory of gravity can be summarised as space-time tells matter how to move, but matter tells space-time how to curve.

 

What this means is instead of seeing matter as something that’s exerting some sort of invisible, magical force, he instead was able to conceptualise the universe in four dimensions and see mass as a way of bending the shape of space, such that when I’m falling to the Earth, it’s not that there’s some force pulling on me, but rather the geometry has me going downhill into gravity.

Fraser: That’s that picture you always see of a ball suspended on some sheet of rubber, and there’s some grid on the rubber and the heavier the ball is, the ball is kind of pushed down into that sheet of rubber and so if you have some object orbiting the ball, you can see how it would be trying to follow a straight line but it’s actually going on a curved line because the heavier object is actually warping the space-time around it.

Pamela: A satellite is basically nothing more than a ball bearing rolling around the inside of a curved bowl. It’s just a different way of visualising space and time that Einstein was somehow able to come up with. Every experiment we’ve ever done has come out showing that Einstein was completely right with everything that he came up with.

Fraser: so where, then, do Newton’s calculations for the universe and Einstein’s’ calculations for the universe diverge, with Einstein being more correct?

Pamela: As you get to higher velocities, as you get to larger masses, the two of them begin to diverge. When you start bringing in energy, one thing that Newton’s theory of gravity doesn’t take into account is that energy has mass. This means that a laser is able to exert some sort of a gravitational pull the same way a stream of ball bearings would be able to exert a gravitational pull. Neither is going to pull very hard, but that pull is still there.

 

Where it starts to come more into mattering is, say you take an electron. It’s a little tiny bit of mass. As you accelerate it so it’s moving faster and faster and faster, velocity is just another form of energy. We have the kinetic energy equation (0.5mv^2) for non-relativistic cases. When you start looking at a high-speed electron, its mass noticeably changes as you make it go faster.

Fraser: I guess Newton didn’t know of electrons, but it’s at these higher speeds, these high-mass and energies where Einstein’s calculations come in. That’s amazing.

Pamela: basically anytime the numbers start to get too large to work with in your head, then you start worrying.

Fraser: Right. Okay, so what were some of the predictions made by Einstein? How were people able to prove that his calculations were correct?

Pamela: There’s a lot of different ways. For instance, gravitational redshift is something he predicted. This basically says that as light tries to leave a high-mass source, it’s getting pulled on by that mass so it’s colour is going to end up changing. We discovered this by looking at the white dwarf Sirius B experimentally in astrophysics (other people have done laboratory experiments).

 

Sirius B is a white dwarf orbiting the brightest star in our northern hemisphere sky, Sirius. As this little white dwarf gives off light, the light trying to escape from its surface ends up getting shifted to the red. Similarly, here on Earth there’s slight differences between what we on the surface of the planet and what a satellite ends up observing in terms of colour. As the light comes toward the surface of the Earth, it slowly gets shifted in wavelength toward the blue as it comes toward the surface of our planet. All these different little shifts add up.

 

Now, because our planet is fairly low mass and it has a fairly large radius, these differences aren’t ones we’re ever going to notice, but when we start looking at high-mass objects with small radii, there the gravitational pull at the surface is so strong that we can actually see the colour change by the equivalent of over 80km/s in the light trying to escape from the star.

Fraser: so the light is pulled back as it’s trying to get away from the star, and then sped up. I guess my question is how can it be changing the speed of light? Isn’t the speed of light just the speed of light?

Pamela: It’s not so much changing the speed of light as much as it’s changing the colour of light. This is where we refer to it as redshifted.

Fraser: Oh, so it’s stretching out the wavelengths.

Pamela: Yeah.

Fraser: Right, okay. So the light is staying the same speed, but the amount of energy that’s hitting us at any mom