- #1
daandezwart
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Hi all!
I'm a first year physics student and I've got some questions I'm hoping someone is able to enlighten me on.
Since I'm only in my first year and I haven't had a full course on GR, I'm most likely to have made some errors, so please point out the flaws in my reasoning and gaps in my knowledge :)
A few days ago I was traveling by train to the university. When it pulled out of the station, I began thinking about its acceleration.
Consider an isolated particle in the following situations:
a) constant velocity in a straight line
b) constant acceleration in a straight line
Let's say, for simplicity, they're both in the x-direction. Then, when you look at their x-t diagrams you'll notice that (a) is a straight line and (b) is curved. So my conclusion from those diagrams is that acceleration could be described as a "deviation from a straight line in space time" or "change of direction in space time". I'm not entirely satisfied with either definition (as I'll get to in a moment), but I'm unsure how else to call it.
Then I started thinking about what I know concerning GR. As I understand it, matter causes space time to curve and what we perceive as acceleration is actually following a straight line on a curved space (here is where I feel my previous definitions start to break down..).
Next thought experiment. Say there's a sufficiently isolated star with a certain mass M which curves space time in a certain way. If I were to fly at it in my, well, spaceship with constant velocity, it'd be experiencing an acceleration towards the star when I near it. If I were to counteract the acceleration (I want to pass the star, not hit it), I'd have to accelerate in the opposite direction and thus take a different path through space time. In this case, to stay on course, acceleration would mean I'm (to rephrase my previous defintion) "changing from a 'predetermined' path through space time".
Although I feel this should be enough to ask my question, I'd like to include a more general approach. As I understand it, from a given mass configuration, we're able to define the gravitational potential. Drawing a V-x diagram of such a potential, we'd be able to draw an x-t diagram displaying the path of a particle when it should enter such a potential. I've tried to draw several x-t diagrams resulting from V-x diagrams and all the x-t diagram seems to follow a similar pattern to the 'ordinary accelerating' particle diagram I mentioned earlier. Therefore, I might as well conjure up a gravitational potential resulting in the exact acceleration pattern of the particle as if it were accelerating towards a particular mass. I'm sure in the context of GR something similar is possible, am I right?
There seems to be a connection between 'ordinary acceleration' and 'gravitational acceleration' (obviously, since there's no reason to have two types of acceleration). But, gravitational acceleration is the result of the curving of space time, does that mean the converse is also true? And, if so, how does it work? As I recall an increase in the velocity of a particle means an increase in the energy of that particle and therefore the particle itself has an influence on the curving of space time, but it just doesn't feel 'enough' and I certainly lack the appropriate knowledge to calculate it (for some reason I'm inclined to think curving space time requires a lot of effort <grin>).
So, when the train pulls out of the station, does it actually curve space time? And, getting back to my previous definition, does it then follow that 'changing direction in space time' causes the actual curving? And this is where it gets seriously strange. I've tried to imagine that principle and it seems to lead to bizarre situations and questions, so I'm inclined to say 'no'. But then again, doesn't that mean we'd have to have two types of acceleration? Surely, a particle doesn't need to know the cause of its acceleration to be able to accelerate...
There's obviously something wrong with my line of reasoning. Could someone please point it out and clarify?
Thanks in advance!
Daan
I'm a first year physics student and I've got some questions I'm hoping someone is able to enlighten me on.
Since I'm only in my first year and I haven't had a full course on GR, I'm most likely to have made some errors, so please point out the flaws in my reasoning and gaps in my knowledge :)
A few days ago I was traveling by train to the university. When it pulled out of the station, I began thinking about its acceleration.
Consider an isolated particle in the following situations:
a) constant velocity in a straight line
b) constant acceleration in a straight line
Let's say, for simplicity, they're both in the x-direction. Then, when you look at their x-t diagrams you'll notice that (a) is a straight line and (b) is curved. So my conclusion from those diagrams is that acceleration could be described as a "deviation from a straight line in space time" or "change of direction in space time". I'm not entirely satisfied with either definition (as I'll get to in a moment), but I'm unsure how else to call it.
Then I started thinking about what I know concerning GR. As I understand it, matter causes space time to curve and what we perceive as acceleration is actually following a straight line on a curved space (here is where I feel my previous definitions start to break down..).
Next thought experiment. Say there's a sufficiently isolated star with a certain mass M which curves space time in a certain way. If I were to fly at it in my, well, spaceship with constant velocity, it'd be experiencing an acceleration towards the star when I near it. If I were to counteract the acceleration (I want to pass the star, not hit it), I'd have to accelerate in the opposite direction and thus take a different path through space time. In this case, to stay on course, acceleration would mean I'm (to rephrase my previous defintion) "changing from a 'predetermined' path through space time".
Although I feel this should be enough to ask my question, I'd like to include a more general approach. As I understand it, from a given mass configuration, we're able to define the gravitational potential. Drawing a V-x diagram of such a potential, we'd be able to draw an x-t diagram displaying the path of a particle when it should enter such a potential. I've tried to draw several x-t diagrams resulting from V-x diagrams and all the x-t diagram seems to follow a similar pattern to the 'ordinary accelerating' particle diagram I mentioned earlier. Therefore, I might as well conjure up a gravitational potential resulting in the exact acceleration pattern of the particle as if it were accelerating towards a particular mass. I'm sure in the context of GR something similar is possible, am I right?
There seems to be a connection between 'ordinary acceleration' and 'gravitational acceleration' (obviously, since there's no reason to have two types of acceleration). But, gravitational acceleration is the result of the curving of space time, does that mean the converse is also true? And, if so, how does it work? As I recall an increase in the velocity of a particle means an increase in the energy of that particle and therefore the particle itself has an influence on the curving of space time, but it just doesn't feel 'enough' and I certainly lack the appropriate knowledge to calculate it (for some reason I'm inclined to think curving space time requires a lot of effort <grin>).
So, when the train pulls out of the station, does it actually curve space time? And, getting back to my previous definition, does it then follow that 'changing direction in space time' causes the actual curving? And this is where it gets seriously strange. I've tried to imagine that principle and it seems to lead to bizarre situations and questions, so I'm inclined to say 'no'. But then again, doesn't that mean we'd have to have two types of acceleration? Surely, a particle doesn't need to know the cause of its acceleration to be able to accelerate...
There's obviously something wrong with my line of reasoning. Could someone please point it out and clarify?
Thanks in advance!
Daan