Help with a thought experiment.

[MCarroll]

I was working on a thought experiment to help myself understand the curvature of space when I got stuck on something (I hope) is simple. I realize this might be a basic problem but I was hoping to generate some discussion.

The experiment involves a "universe" two neutrally charged masses of equal weight.

In this universe, the only force acting on either mass is the gravitational attraction and at the beginning of the experiment the objects are at rest relative to each other.

Using Newtons law of Gravity, I expect acceleration to be increasing towards infinity as separation decreases towards zero given that the force of attraction is inversely proportional to the square of separation. On the other hand using special relativity I expect acceleration to approach zero as the (negative) rate of change in separaration approaches the speed of light.

I wanted to explore this further but I am having trouble deriving a non relativistic function for Gravitational Jerk (da/dt) because although I can express time from rest in terns of distance I can't quite figure out distance from rest in terms of time.

Is anyone aware of accessible work on classical Gravitional Jerk?

 

[genneth]

The problem is that Newtonian gravity is incompatible with special relativity. Your answer will depend on what do you take to be the masses (rest/invariant mass, relativistic mass, etc.) and which rest frame do you want to work in. The central problem is that [Newtonian gravity + SR] predicts different things depending on the frame you're in.

 

[MCarroll]

The central problem is that [Newtonian gravity + SR] predicts different things depending on the frame you're in.

Yeah, that is exactly what I want. Essentially I want to compare the results I get being on one object with the results I get at different distances from the collision point on a line perpendicular to the line of motion.

The PROBLEM I have is that I can't plot Jerk against time or find the point where Jerk=0 because I can't resolve classical separation in terms of time before I consider the Lorentz effects on the various terms.

 

[pervect]

I would suggest looking at the GR solution to a simpler problem - the path that a falling particle of negligible mass takes near a large mass, neglecting any gravitational radiation.

This means that the falling particle follows a geodesic path.

You can find some of the equations at http://www.fourmilab.ch/gravitation/orbits/

If you decide to attempt this, you might need a little more help, but this webpage should get you started.

I don't see the point in trying to do Newtonian gravity and SR - the whole purpose Einstein had in developing GR was to develop a theory of gravity that was consistent with special relativity.

 

[MCarroll]

Thanks pervect and genneth for your responses.

Pervect, the link you gave had interesting stuff on it but I am not ready to start thinking about orbits yet. I want to focus on the warp in a one dimensional gravitational system then map the lorentz effects of shifting the frame of reference along a second dimension. I am not saying this is a meaningful thought experiment but it is the one I am after.

my problem is I can't solve for s from:

t = - K * s *$$\sqrt{s_{0}-s}$$

where K, s(o) are constants

because my math ability has very finite limits.

Perhaps it was premature for me to post here in the relativity form. I have simplified the question and reposted in the Classical forum and may also try the math help.

Thanks again for your responses.

 

[kaotak]

That's a cubic equation, which becomes more evident after you square both sides. If you can't find a pretty way to solve it, you can always solve it with a calculator or an online site if you don't have a calculator of that capability. Or, if you really want to, you could use the cubic formula

 

[MCarroll]

thanks,


I got some help with that on a different forum. There turns out to be some good articles on the web.