JonF
The rubber sheet analogy is an analogy. But it is my understanding that the equivalence of acceleration and gravity is not an analogy. They are two ways of looking at the same thing. If the “box” is small enough that you cannot detect tidal forces or notice the convergence of plumb bobs, there would be no way to distinguish gravity and acceleration. Two things that cannot be distinguished are identical. paintsvillecom
My guess (as to where one would weigh the most) is on one of the poles. Is this the answer? Seems a little obvious… What did the class and teacher say?
Back on topic…What makes gravity work? GR supposes it to be curvature of space-time. QM supposes forces to be mediated by particles.
Virtually yours,
DrMatrix
These words are mine and they are true - Chief Meninock
Don’t think so. The elevation of the south pole reaches up around a mile (I think) above sea level, removing you just a tad from the rest of the big ball of earth.
I suppose I may have phrased the question slightly wrong when I wrote it. As it is, it would be at sea level, as we were reading Newton at the time and pretty much just dealing with the earth as a sphere. In the class, our discussion led several to speculate the answer was the center of the earth (which is where I erred in phrasing the question, since that would be “in” and not “on”), under the mistaken assumption that the since gravity is weaker the higher up you go, it must be stronger the further down you go, and the center of the earth is as down as you can get. The teacher also bought into this. But actually, at the center of the earth, one should be weightless, since you would be “pulled” more or less equally from all sides.
Absolutely true. However, the illustration of that equivalence by equating the Earth’s gravitational field “force” to the “force” felt in a spaceship at constant acceleration is either an analogy or an incorrect application, depending on how you look at it. The Earth’s gravitation field “force” is radially oriented and varies with distance from the Earth, and the “force field” in a spaceship under constant acceleration exhibits neither of those characteristics.
GR admits the possibility of a gravitational “field” that has exactly the same characteristics as the “force field” in a spaceship under constant acceleration (without specifying how such a field might be generated in the real universe [grin]). GR says that there is no experiment that you can perform to detect the difference between a spaceship under constant acceleration and a gravitational field that generates “forces” that are always parallel to each other and whose magnitude does not depend on position.
As to the OP question, damned if I know. As someone else said, if you know then reserve your seat to Stockholm. First class.
I can at least address one of the questions in the OP:
Yes, it takes energy to move things. Whenever anything moves, start by assuming that energy is supplied to move it, and then start looking for the source.
For example, drop something. It starts in your hand with potential energy because of its distance from the center of mass of the Earth. When you let go, the Earth’s gravity accelerates it towards the center of mass of the Earth, and some of the potential energy is converted to kinetic energy (energy of motion). When it hits the floor, that kinetic energy is cconverted to heat, and it sits there with a little less potential energy (because it’s a little closer to the center of mass of the Earth).
Momentum is conserved when you drop something, too. Actually the object falls toward the Earth and the Earth falls towards the object. The momentum of the object and the momentum of the Earth are always equal in magnitude but opposite in sign, so they add up to zero.
True, as long as you define “shortest path” and “go straight” appropriately. Drawing a line or curve connecting the start and end points in three-dimensional space is incorrect.
Objects move under the influence of a gravitational “field” so that the elapsed “proper time” is maximum. The “proper time” is the time measured by a clock carried on the moving object. Note that acceleration/gravity speeds up clocks, while velocity slows down clocks. So the object would “like to” move at high speed so its clock would run real slow, but the acceleration required to get up to high speed and the deceleration required to stop at the end point speed up the clock. There’s only one path and acceleration/decelration choice that maximizes the proper time.
Well, according to logic (unless of course, you’re talking about actual LAND) wouldn’t it be the Marianas (sp?) Trench?
Well, either you’re closing your eyes to a situation you do not wish to acknowledge or you are not aware of the power of the presence of a pool table in your community. Ya’ got trouble my friends! -
Prof. Harold Hill
Gary Conservatory
Gold Medal Class
'05
JoeyBlades
Yes, I really believe that. Is a sufficiently small (infinitesimal) region, what is acceleration in one frame of reference is gravity in another frame of reference. Inertial mass and gravitational mass cannot be distinguished because they are two ways of looking at the same thing - mass. Likewise, acceleration and gravity cannot be distinguished because they are two ways of looking at the same thing - the curvature of space-time.
Virtually yours,
DrMatrix
These words are mine and they are true - Chief Meninock