Argh, frustrating
I’ve spent the last few days trying to understand the theory of relativity. And by that I mean the theory of general relativity and special relativity — both put forward by Albert Einstein.
I’m sure some of you read in the news about the new spacecraft that was put into orbit in order to look for earth-like planets. That event has spurred a few days of heavy astronomy reading for me. I’ve read about pulsars, black holes, nebula, supernovae (not the PokerStars kind), white dwarfs, red giants, main-sequence stars, Hubble Ultra Deep field, galaxies, local group, dark matter, dark energy, messier objects, Voyager missions, New Horizons, clusters, redshift, etc, etc. The list goes on and on. I think I get the basics behind most of it. Of course it all inevitably led me to Einstein’s theory of relativity.
First, I understand the equivalence principle perfectly well. It simply states that gravity is exactly the same as being accelerated while in outerspace. The example often used to illustrate it is the following:
Let’s say you wake up one day in an elevator and you don’t remember ever getting in so you want to try to figure out where you are. In the process you drop something. It falls to the floor as you would expect it to so you say to yourself “I must be on earth and this elevator must be suspended somewhere”. The thing is — Einstein says you don’t know that. What’s to say you aren’t accelerating in space at the same rate as Earth’s gravity (9.8 meters per second). Einstein drew from this that gravity and acceleration in space are the same thing.
It’s too long for me to explain all of this stuff but the eventual conclusion is that gravity is not a “force” as we believed it to be. It’s actually a curvature in space produced by mass. When we “fall” towards something or “orbit” something we’re actually following the shortest path in space left by the curved space and we’re being accelerated the same as if we were in space. They actually refer to it as “spacetime” (combination of the three spatial dimensions and the fourth temporal dimension — see Lost for examples). And the earth is actually pushing up on us to stop our acceleration. Remember the elevator thing? You can feel your feet on the ground. But if you’re in free fall in, say, orbit then you don’t feel any force. The difference is the earth pushing up on your feet.
Anyway, to get to my point. I’ve found the theory of relativity to be extremely confusing. It’s been very hard for me to understand and I’ve been frustrated by it. I’m still not sure that I really get it. Here’s what confuses me the most:
If gravity is not a force but a curvature in spacetime, what determines the directionality of our acceleration? Einstein says that we’re in an “accelerated reference” while on Earth (I think). What is it about the curvature of spacetime that makes us all go in the same direction (towards earth’s core) no matter what side of the earth we’re on or what time of day it is. I am reading that it’s the “shortest path after spacetime is curved by the large mass objects in our vicinity” but I am confused by that.
Can anyone explain that part? I would great appreciate it.
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I was going to MSN this, but was too slow:
I imagine you’ve heard this before, but the way I was told to understand spacetime is to imagine it’s four dimensional. the way to understand anything four dimensional is to just pretend one of them isn’t there – so you have 3d spacetime as 2d spacetime. You then have heavy objects making dents in the 3rd dimension of what was 2d spacetime, and things moving in 2nd spacetime fall into the dents – in other words, gravity.
Andrew
March 12, 2009
Oh, and it’s hard to understand because it’s counterintuitive. I guess that’s a truism, but our brains haven’t evolved to think about time being relative to the frame of the observer, so we can’t really grasp this stuff properly. I imagine it makes a lot more sense if you look at the maths of it – trying to explain it in dirty imprecise language probably is what causes a lot of the confusion. Not that I have ever tried understanding the math :]
Andrew
March 12, 2009
Have you come across the rubber sheet example?
http://theory.uwinnipeg.ca/users/gabor/black_holes/slide5.html
That is envisioning space as 2 dimensional, but you can extrapolate that to 3-d.
Hope that helps, if you still have questions I might be able to help further.
Jordan
March 12, 2009
The classic example is to think of spacetime as a rubber sheet – when you add a point of high mass, such as a 1kg weight, the sheet is curved by the mass. If you then place a ball on the sheet somewhere fairly close to the weight the ball moves along the curve in the sheet, but regardless of which side of the weight you put the ball on it always moves towards the weight and ends up at the bottom of the curve in the sheet. It’s kind of the same for curves in spacetime.
DougieP
March 12, 2009
Thanks, all of that helped a bunch. I had come across the rubber sheet and it made sense at the time as well because it’s so easy to picture. I am trying to put it all together in my head without such visualizations and it’s proving difficult. But maybe that’s why it took so long for someone to figure it out.
Nat
March 13, 2009