Alternative analogies for the curvature of Space-Time

[MigL]

Exactly, stringy.

Space-time 'acts' like its curved.

So GR models it with mathematical curvature of the co-ordinate system..

[StringJunky]

Exactly, stringy.

Space-time 'acts' like its curved.

So GR models it with mathematical curvature of the co-ordinate system..

Right. Thanks.

 

Rather than changing the analogy, people need to understand what they are, learn the limits of them and which area(s) the analogy is describing. People often take them too literally and changing it won't make any difference imo.

[studiot]

That is one of the difficulties. The use of words and definitions which aren't meant to be used for such concepts.

The 'density' of space-time is the density , or spacing if you will, of a co-ordinate system.

It is like taking a sheet of graph paper and changing the spacing of the grid lines.

 

That 'something' is a mathematical concept , and as such, it doesn't need to be anything or live anywhere.

It just needs to be measurable.

 

I really liked and agree with the underlined sentences.

Too many words which already have sound meanings are redefined, causing much confusion, in my opinion.

 

This also applies to 'curvature' when what is meant is 'the curvature tensor'. The curvature tensor reduces, as do many properties such as tangents, to a single choice in 2 dimensions - the scalar radius.

 

There are even models of relativity that introduce a the extra dimension, such as Kaluza's theory.

 

https://www.google.co.uk/search?q=kaluza%27s+theory&rlz=1C1AVNG_enGB673GB673&oq=kaluza%27s+theory&aqs=chrome..69i57.6791j0j8&sourceid=chrome&ie=UTF-8

 

But we do not need curvature at all if we restrict our analysis to the points of the manifold plus some conditions of constraint.

That is the whole message in my surveyor's example.

[Tim88]

 

Tim88

 

on page 6 they give an analogy whereby spacetime is denser around massive bodies.

What do you understand denser to mean?

 

Density (of something) is that something per unit volume.

 

So what is that something, and where does it live?

 

No, I did not write that. And I did not read that article.

 

As it is an analogy, any transparent material can be used in principle - even transparent rubber.

However, an anisotropic crystal would better mimic the math. Did anyone attempt this with for example Ansys or Comsol?

PS I see now that you clarified it later.

With "lensing" is of course meant that the speed of light is affected just as in lenses; I don't know why the authors would want to talk about density, as that surpasses the purpose of such an analogy. One could similarly ask about the elasticity modulus of the rubber band.

[..] Rather than changing the analogy, people need to understand what they are, learn the limits of them and which area(s) the analogy is describing. People often take them too literally and changing it won't make any difference imo.

 

Some analogies are no doubtful more useful in some aspects than others. Apart of that I fully agree, taking them too literally makes them quite useless.

[Mordred]

 

[math]\rho = \mathop {\lim }\limits_{\delta v \to 0} \frac{{\delta m}}{{\delta v}}[/math]

 

 

Since we are saying delta v tends to zero, it makes no sense to talk of compressed space or compressed anything else.

 

You can't compress below zero!

 

I did wonder if the article was referring to what is called tensor density, which is quite a different thing.

 

Perhaps Mordred will enlighten us since that is his field.

 

Finally if spacetime has any sort of 'density' then how can it not be physical?

excellent point. The reason I liked the second analogy over the Rubber sheet is that it immediately introduces freefall due to curvature. Rather than force which the rubber sheet implies.

 

The straight x line showing "no gravity" or rather no potential gradient. This being your Euclidean frame.

When you add curvature you have in the freefall case potential gradient.

 

Now both models do show this but in the last case, the freefall motion acceleration is better shown as a consequence of curvature rather than force.

 

All the required details to calculate the spacetime geodesics via parallel transport can be demonstrated using two parallel gridlines and how parallel transport is lost due to curvature.

 

That model tool is far more flexible than described on the video.

 

A side note using mass density is only one part of the stress tensor "which tells space how to curve" there is also vorticity and flux. For the case of freefall we set those two terms at zero.

 

the x line in the video will be your spacetime geodesic,

 

The best part is the spacetime graph method simply shows geodesic motion without implying a materialistic component "rubber" to spacetime but sticks with the geometry. As far as tensor density you can't have less than zero unless zero is assigned at some arbitary higher value. Particularly on the scalar quantities.

For that matter you require a multi particle system to have a stress tensor. However its simply your SM particles, not spacetime itself. Which the rubber sheet tends to imply through misconceptions.

Edited October 14, 2016 by Mordred