Relativity: Roll to Disbelieve
Feb. 7th, 2016 12:38 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackI've been trying to get this straight in my mind by asking what the world would look like if relativity wasn't true.
It's probably true that "everywhere in the universe is the same time and everything has speed and position that's the same wherever you measure it from" is simpler and more natural than "the time between two events and the distance between two objects depends how fast you're going". But when you dig into it, it doesn't really hold together.
Lots of explanations try to tell you the details about how the world is different with relativity than if it was all newtonian. I don't understand it well enough to talk about how. But rather than glossing it over, I'd rather tackle head on, why I should think something weird is going on. It's like, explaining calculus without understanding what problems there are that are worth solving, and are hard to solve, but trivial with calculus, just feels like a pointless arbitrary set of rules. But once you get what it's for, you understand it in an equally important way as if you know how to do it.
I think the key question is, how fast does light move? Lots of people know, c, or 300 million m/s, or 1 foot per nanosecond. But relative to whom? When we describe speeds, we normally mean "relative to the Earth's surface", or "to the Sun" for things in the solar system. That's normally obvious, but it's only obvious because it's the same -- you have to pick the right scale, or else you say you can jog at the speed the earth orbits.
What are the possible answers?
1. Like normal objects, light travels at the speed of the object that emitted it, plus c. If you throw a ball on a train, within the train, it travels at the speed of your throw, but relative to the ground, it travels at that speed plus the speed of the train.
2. Like waves, it travels at c relative to a fixed stationary... something. If you drop a big rock into the sea from a fast plane, the waves spread outward at the same speed, however fast the plane is going. If you have a siren on a vehicle, the sound travels at the same speed in the air, however fast the vehicle is going (as you can tell, because if you fast enough you catch up with the sound -- a sonic boom).
3. You measure light as travelling at c, and everyone else measures light travelling at c, even if you're going in different directions at hundreds of thousands of miles per hour. Yes, this is ridiculous, how can different people measure the same thing and get different results? But -- we've measured light in all sorts of ways, and whatever we do we ALWAYS see it going at c, just like maxwell's equations say it should. (Well, slower in atmosphere, but a known amount.) I think if relativity were explained like this, "we measure light going at the same speed everywhere, how come?" it would make more sense than explaining the historical order.
4. Light travels at c relative to the nearest large planet, slowing down or speeding up as it moves from the neighbourhood of one planet to another.
Well, which makes sense? #1 sounds plausible. But we receive the light from stars, and can measure its speed. Stars go VERY fast, so those light beams should be at very different speeds depending what star it came from. But no, they all go at c.
#2 also sounds plausible to start with. But where is this invisible stationary air or water or something? The earth orbits the sun, and the sun orbits the galaxy, etc, etc, at very very high speeds, so we should never be stationary relative to the medium. Which means if you measure the speed of light in the direction of the earth's orbit, and perpendicular to that, you should get very very different answers. But no, the speed is always measured at c.
Alternatively, this medium is always exactly aligned with the Earth specifically. That should sound dodgy. From an orbital mechanics perspective the earth doesn't look at all special. It's hard to disprove this until you get to the fancier experiments in the footnotes, but it should sound like "a bodge", not "the answer".Ironically, of the three wrong explanations, this comes really close -- it works perfectly, it's just that in the real world, it's not just the Earth that has a special "stationary" aether, every point/velocity in the universe does.
What about #4? Again, this should sound dodgy, but is hard to actually disprove. Until relativity was accepted, this was a good theory, that the earth "dragged" the invisible aether with it, so it was always moving at the same speed. I can't remember what disproves this, but it shouldn't sound good. You'd also expect weird effects different to relativity as light moves near other planets and stars. And maybe weird red/blue shift as light moves from one speed of aether to another.
That leaves #3. Which is very counter-intuitive, but actually predicts something very like what we see -- both "at everyday speeds, everything acts like newtonian mechanics" and "but for everyone wherever they are, maxwells equations and the speed of light work exactly the same." It wasn't obvious that those would conflict, but they do, unless you accept relativity.
Footnotes
I can't remember all the relevant experiments. A big one is https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment which measures the speed of light in the direction of the Earth's orbit, and perpendicular to that, and discovers they're the same. It doesn't "measure the speed", by waiting until the light gets from A to B, rather, it sends light down the two paths and then adjusts the path lengths until you get an interference pattern showing they're exactly in sync. Which is when the paths are exactly the same. Every other "measure the speed" is similar.
If there's holes in the above, are there *other* experiments that suggest the universe isn't straight-forwardly Newtonian? Yes, lots, wikipedia has a big list, although not all easy to understand. My favourites are:
* Produce light of a specific frequency (with some crystal that has a very precise frequency response?) Check that's it's re-absorbed by that same crystal. Yes, if the apparatus is horizontal. No, if its vertical. Why does that make a difference? In a non-relativity world, Newtonian gravity and Maxwell's electromagnetism should be completely separate. But relativity says, moving to a different height in a gravitational field will change the energy, and hence frequency, in the light -- which is does.
* The incredibly precise times from GPS satellites needing to be tuned to account for general relativity.
It's probably true that "everywhere in the universe is the same time and everything has speed and position that's the same wherever you measure it from" is simpler and more natural than "the time between two events and the distance between two objects depends how fast you're going". But when you dig into it, it doesn't really hold together.
Lots of explanations try to tell you the details about how the world is different with relativity than if it was all newtonian. I don't understand it well enough to talk about how. But rather than glossing it over, I'd rather tackle head on, why I should think something weird is going on. It's like, explaining calculus without understanding what problems there are that are worth solving, and are hard to solve, but trivial with calculus, just feels like a pointless arbitrary set of rules. But once you get what it's for, you understand it in an equally important way as if you know how to do it.
I think the key question is, how fast does light move? Lots of people know, c, or 300 million m/s, or 1 foot per nanosecond. But relative to whom? When we describe speeds, we normally mean "relative to the Earth's surface", or "to the Sun" for things in the solar system. That's normally obvious, but it's only obvious because it's the same -- you have to pick the right scale, or else you say you can jog at the speed the earth orbits.
What are the possible answers?
1. Like normal objects, light travels at the speed of the object that emitted it, plus c. If you throw a ball on a train, within the train, it travels at the speed of your throw, but relative to the ground, it travels at that speed plus the speed of the train.
2. Like waves, it travels at c relative to a fixed stationary... something. If you drop a big rock into the sea from a fast plane, the waves spread outward at the same speed, however fast the plane is going. If you have a siren on a vehicle, the sound travels at the same speed in the air, however fast the vehicle is going (as you can tell, because if you fast enough you catch up with the sound -- a sonic boom).
3. You measure light as travelling at c, and everyone else measures light travelling at c, even if you're going in different directions at hundreds of thousands of miles per hour. Yes, this is ridiculous, how can different people measure the same thing and get different results? But -- we've measured light in all sorts of ways, and whatever we do we ALWAYS see it going at c, just like maxwell's equations say it should. (Well, slower in atmosphere, but a known amount.) I think if relativity were explained like this, "we measure light going at the same speed everywhere, how come?" it would make more sense than explaining the historical order.
4. Light travels at c relative to the nearest large planet, slowing down or speeding up as it moves from the neighbourhood of one planet to another.
Well, which makes sense? #1 sounds plausible. But we receive the light from stars, and can measure its speed. Stars go VERY fast, so those light beams should be at very different speeds depending what star it came from. But no, they all go at c.
#2 also sounds plausible to start with. But where is this invisible stationary air or water or something? The earth orbits the sun, and the sun orbits the galaxy, etc, etc, at very very high speeds, so we should never be stationary relative to the medium. Which means if you measure the speed of light in the direction of the earth's orbit, and perpendicular to that, you should get very very different answers. But no, the speed is always measured at c.
Alternatively, this medium is always exactly aligned with the Earth specifically. That should sound dodgy. From an orbital mechanics perspective the earth doesn't look at all special. It's hard to disprove this until you get to the fancier experiments in the footnotes, but it should sound like "a bodge", not "the answer".Ironically, of the three wrong explanations, this comes really close -- it works perfectly, it's just that in the real world, it's not just the Earth that has a special "stationary" aether, every point/velocity in the universe does.
What about #4? Again, this should sound dodgy, but is hard to actually disprove. Until relativity was accepted, this was a good theory, that the earth "dragged" the invisible aether with it, so it was always moving at the same speed. I can't remember what disproves this, but it shouldn't sound good. You'd also expect weird effects different to relativity as light moves near other planets and stars. And maybe weird red/blue shift as light moves from one speed of aether to another.
That leaves #3. Which is very counter-intuitive, but actually predicts something very like what we see -- both "at everyday speeds, everything acts like newtonian mechanics" and "but for everyone wherever they are, maxwells equations and the speed of light work exactly the same." It wasn't obvious that those would conflict, but they do, unless you accept relativity.
Footnotes
I can't remember all the relevant experiments. A big one is https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment which measures the speed of light in the direction of the Earth's orbit, and perpendicular to that, and discovers they're the same. It doesn't "measure the speed", by waiting until the light gets from A to B, rather, it sends light down the two paths and then adjusts the path lengths until you get an interference pattern showing they're exactly in sync. Which is when the paths are exactly the same. Every other "measure the speed" is similar.
If there's holes in the above, are there *other* experiments that suggest the universe isn't straight-forwardly Newtonian? Yes, lots, wikipedia has a big list, although not all easy to understand. My favourites are:
* Produce light of a specific frequency (with some crystal that has a very precise frequency response?) Check that's it's re-absorbed by that same crystal. Yes, if the apparatus is horizontal. No, if its vertical. Why does that make a difference? In a non-relativity world, Newtonian gravity and Maxwell's electromagnetism should be completely separate. But relativity says, moving to a different height in a gravitational field will change the energy, and hence frequency, in the light -- which is does.
* The incredibly precise times from GPS satellites needing to be tuned to account for general relativity.