Welcome to NRICH.

 
Discussion of Gravity
By Yatir Halevi on Saturday, March 09, 2002 - 05:49 pm:

I know that gravity can be thought of either as bending of space-time around matter, or as a force.
Lets say that only the first one is true. If that is the case, I can understand why the course of a body moving in constant velocity near the matter will bend, But why does a body not moving at all, that is near the matter, falls into it?
It like taking a trumpet putting it in space, and putting a marble on its edge, there is no reason for the marble to fall in!

Thanks,
Yatir

By Dan Goodman on Saturday, March 09, 2002 - 06:14 pm:

I'm not sure how good a picture this is physically, but I always think of a big rubber sheet. A planet is like a heavy rock placed on the rubber sheet, it makes a sort of depression in the rubber sheet. A particle placed near the planet will fall towards the rock if placed somewhere near it because it is on an inclined surface.

By William Astle on Saturday, March 09, 2002 - 06:31 pm:

Also, I don't think there is quite the difference between the two situations as there appears to be. After all a in orbit is moving by virtue of the 'gravity' in much the same way as one falling inwards.

By Yatir Halevi on Saturday, March 09, 2002 - 07:59 pm:

The problem with what you both said is that it relys on the fact that they BOTH exists. I say, that lets think of gravity as only a curvature in space-time.
With that picture in mind, there is no reason for a body to fally in (there in no force pulling it in)


Yatir

By William Astle on Saturday, March 09, 2002 - 08:22 pm:

I understand what you are saying but I'm afraid I don't now enough physics to give an answer.

My point is that there is no reason for the orbiting body to start to move around the edge of the 'trumpet' either in the trumpet in space model. Perhaps only the trumpet/rubber sheet on earth model works or perhaps its something to do with the fact that space and time are not independent. I guess someone knows...

By Julian Pulman on Saturday, March 09, 2002 - 10:07 pm:

I think the problem comes when you use gravity to explain the "bending-space-time" model of gravity - the rubber sheet thing. It's like assuming a result is true to prove the result.

By Yatir Halevi on Monday, March 11, 2002 - 07:37 pm:

What I'm saying is that matter bends space-time, and we interpert it as a force that is acting on a body neard the curvature.
My question is: What makes a body move in-wards into the curvature, if it's initial velocity is 0 (relative to the matter)...?

Yatir

By Philip Ellison on Monday, March 11, 2002 - 08:15 pm:

Erm, can't give a very good answer I'm afraid, but I use a version of the "path of least resistance" idea... this explains why a body will orbit another, and the space-time curvature could also be thought of as a pressure or concentration gradient... with objects moving towards the area of least pressure/"concentration". I don't know whether this helps or not... and I'm even less sure about its accuracy as a physical model. I think the main problem lies in how we perceive space-time: the "rubber-sheet" analogy is not only limited to 2 dimensions but, as Julian pointed out, relies on the "force" of gravity to make sense (though, actually, gravity's not a force.. it's a field that produces an acceleration... meaning that the "force" idea isn't very self-explanatory either!...perhaps someone with a decent understanding of physics could use this to explain it better) Anyone?

By Yatir Halevi on Monday, March 11, 2002 - 08:26 pm:

I know that Arun has knowledge in physics. So if he or anyone else would care to enlight us...


Yatir

By Graeme Mcrae on Monday, March 11, 2002 - 11:45 pm:

A good website, which explains both special and general relativity, is http://www.physics.purdue.edu/~hinson/ftl/html/FTL_intro.html .

From my reading of this website, I can offer the following suggestion to explain the apparent force of gravity in a four-dimensional curved space-time continuum.

A point object that appears, from a 3-dimensional view, to be at rest in a field of gravity, can be interpreted as a straight line in curved 4-dimensional space-time. This straight line is almost parallel to the "time" dimension, but as space is curved, the straight line veers closer to the source of the gravity field (e.g. the planet, or star, or whatever) in both directions; or, to put it another way, the source of the gravity field veers closer to the straight line in 4-space as you travel in either direction along the line.

All objects in "free fall" trace straight lines in 4-space. That applies to a satellite in Earth orbit as it does to a bullet fired from a gun (neglecting air resistance) as it does to a football which appears to make a parabola in 3-space (again, neglecting air resistance). In all of these examples, the objects trace straight paths in 4-space which are all nearly parallel to the "time" axis, and the slight curvature of space caused by gravity is enough to cause apparent curvature from our limited perspective.

By Arun Iyer on Tuesday, March 12, 2002 - 04:42 am:

i would give directions to a site which gives a very short and handsome descriptions on theory of relativity..
Theory of general and special relativity

It should clear your doubts....if it doesn't then post back and i will try my best to explain...

love arun

By Yatir Halevi on Tuesday, March 12, 2002 - 12:43 pm:

Arun, It doesn't seam that short!

Anyway, let me rephrase my question:
(Graeme, maybe you answered it already, if so, then I didn't understand).

What would make a body fall (when released from some height) to the earth, if we explain gravity as a curvature in space-time, but not as a force.


Yatir

By Graeme Mcrae on Tuesday, March 12, 2002 - 04:13 pm:

Yatir,

In a word, the thing that makes the body appear to fall in our 3-dimensional world is momentum -- the tendency for an object in motion (or still) to stay that way. In a four-dimensional world, where one of the dimensions is time, and the universe is curved, momentum is the tendency of objects in free fall to trace straight lines.

Since the universe is curved by gravity, the straight lines might appear parallel for part of their length. (We 3D beings perceive this as objects that remain at rest with respect to one another for a period of time.) As one travels along the lines (which we perceive as time moving forward) we observe the lines, which never deviate from straight, intersect (which we perceive as the objects touching one another).

The reason straight lines can appear parallel and then intersect (perhaps a finite number of times greater than one) is that the universe is curved.

The "momentum" explanation of the apparent behavior of objects in free fall puts the "force" of gravity on the same footing as the centrifugal force on a person inside a car going around a curve. This force on the person feels real enough (it forces the person against the door in a real way) but it isn't a "real" force, because what is acting on the person is nothing more than his tendency to go in a straight line (i.e. momentum). In the same way, the force of gravity, which is holding me against my chair as I type this message, is a fictitious force, when viewed in terms of general relativity, because it arises from the fact that the chair is preventing my body from tracing a straight line in space-time.

By Arun Iyer on Wednesday, March 13, 2002 - 06:19 pm:

Yatir,
the site gives a short intro to the "entire theory of relativity!!!!"Also there is a section in the site which explains the gravity part....

personally,i think,Graeme has given some very good illustrations.....which along with the theory given in the site should help you out!!!

love arun

By Yatir Halevi on Wednesday, March 13, 2002 - 08:50 pm:

I do understand it better though it hard to grasp, since I can not see it infront of me. What you are saying is because there is curvature the body must move, according to some inertial force???


Yatir

By Arun Iyer on Friday, March 15, 2002 - 04:42 am:

Yatir,
i think you are getting confused at some places..

i will try and explain this gravity problem to the best of my abilities...

Albert Einstein once said that "I was in the patent office at Bern when all of a sudden a thought occured to me:'if a person falls freely,he will not feel his own weight.'I was startled.This simple thought made a deep impression on me.It impelled me towards a theory of gravitation."..This is actually how he began forming his general theory of relativity...

We know that newton explained that gravity is due to force between masses....Einstein explains that gravity is due to curvature of shape that is caused by masses..

Picturing how space can have curvature is difficult.An analogy might help.....Suppose that from the orbit we watch a race in which two boats begin on the equator with a separation of say 30 km...and head due south..To the sailors the boats travel along flat parallel paths.However with time the boats draw together until near the south pole they touch....(Here's a not so good diagram to illustrate the race)
boatrace
The sailors in the boat can explain why they come near to each other in terms of forces acting on them.However,we can see that the boats draw together i.e come near to each other simply because of the curvature of earth's surface....We can see this because we are viewing the race from "outside" the surface of earth....

Now consider this diag..
apples
Two horizontally separated apples are dropped from the same height above earth.Although the apples may appear to travel along parallel paths,they actually move towards each other because they both fall towards earth's center.We can interpret the motion of apples in terms of gravitational force on the apples from earth..We can also interpret the motion in terms of curvature of space near earth,due to the presence of earth's mass...This idea is depicted in this diag...
curvature

Now the major question is which is correct
should we see gravity as force between masses
or
should we see it as curvature of space caused by mass
or
should we see it as a phenomenon caused by some particle called as graviton,as conjectured in some modern physical theories...
This question still remains unanswered...

love arun