Curvature of Spacetime

[geordief]

I am posting in this subforum * because I do not know if this is actually the accepted theory (or one of them) and if I am just a slow learner.....

 

This is my question.:

 

Does mass and energy curve spacetime because spacetime , firstly is just a mathematical model with lines along parallel to the 4 axes that meet at all the points {x,y,z,t} that are the set of all possible events?

 

In the real world (not the model) there are areas of mass/energy where "events" cannot take place because the "spot is taken" .

 

As a result ,for the model to be accurate we have to make a "detour" ** around these particular areas when we draw the lines parallel to 4 axes and this is the

"curvature of spacetime" (in the model)

 

 

* let's hope I was right to post here.

** A bit like the way the running water a stream goes around a rock which is poking out above the surface.

Edited April 7, 2016 by geordief

[studiot]

OK I will start the ball rolling.

 

First the word abscissa refers to plots of specific points on 2D planar graph paper. It is the coordinate relative one of the two sets of gridlines, by convention the horizontal gridlines on the graph paper.

The other coordinates are called ordinates. By convention these are relative to the vertical gridlines on the graph paper.

 

Now for the 'curvature' of spacetime.

 

This depends upon your point of view.

 

Here is an analogy, due to John Baez, a noted californian physicist.

 

 

Two men stand at the equator and look directly at each other.

They both mark off a right angle from the equator towards the North and start walking, both keeping straight on due North.

That is as far as each can tell they are each walking in a straight line and they check this by checking the perpendicularity as they cross each parallel of latitude.

As they approach the pole they realise that they are coming closer and closer together, although both are walking along a gridline perpendicular to their startline.

 

So what is happening?

 

Explanation 1) There is a mutual attraction, a sort of personal gravitational force drawing them together.

 

Explanation 2) They are somehow not wallking in a straight line but a curved one.

 

Now this example is not yet into spacetime, it is simply 3D space.

But it is sufficient to explain quite a few things.

 

The men are confined to a 2D world, the surface of the Earth.

We call this a manifold.

The manifold is simply all the places (points) accessible or available to the men.

 

From the point of view of an outsider the surface (manifold) is curved in 3D so the gridlines of longitude converge.

Further they are not straight but curved.

So the outsider goes for explanation 2

 

From the point of view of the men, who cannot (let us say for the purpose of this exercise) see 3D, they cannot see this curvature

So the men feel justified in going for explanation 1.

 

There we have two explanations, a curved manifold or gravity in our model.

 

But there is a further twist.

 

The men have a choice.

 

They could carry on with their coordinate system of lines of latitude and longitude, completely within the manifold.

Or they could postulate the existence of curvature in a third dimension and draw up an X, Y, Z coordinate system.

Then their paths become space curves (arc of circles) and they could call them geodesics.

 

Projecting this forward to 4D spacetime we can do the same thing.

Edited April 7, 2016 by studiot

[geordief]

OK I will start the ball rolling.

 

First the word abscissa refers to plots of specific points on 2D planar graph paper. It is th

The other coordinates are called ordinates. By convention these are relative to the vertical gridlines on the graph paper.e coordinate relative one of the two sets of gridlines, by convention the horizontal gridlines on the graph paper.

 

Thanks(a little learning is a dangerous thing )

 

I have edited my post and hopefully that error has been ironed out- and the post is a little clearer as a result.

 

To address the rest of your post ,I don't think you have addressed my question directly (perhaps because it was badly formed )

 

I am prepared to accept that I am in error but I was hoping that the error could perhaps be shown up more closely.

 

As for the points you raised about the two men walking towards the N.Pole from the equator are they supposed to be idealised 2 dimensional creatures ?-because it seems to me that they must know that they exist in 3 (if not 4 dimensions) if they want to tie their shoelaces and brush their hair

Edited April 7, 2016 by geordief