The rubber sheet analogy

[geordief]

I  have read a good few people complain that  the rubber sheet or trampoline analogy is a bad one.

Or rather perhaps what they say is that it is taken too literally and that it is not well enough described as simply an analogy and so, like all analogies breaks down at certain points.

I want to ask at what points this analogy is actually accurate.

For example ,if we actually drew grid lines on the rubber sheet and placed a metal object in the centre how accurately would the distorted parallelograms depict the  spacetime graph lines that are actually used to  model  spacetime in the vicinity of massive or energetic object?

Is there anything in fact about the analogy that is really accurate rather than broadly representational?

 

I may have asked this before(or someone else may have) :Who came up with this analogy? Not Minkowski was it?

Or perhaps Einstein in need of a little populist outreach?

[MigL]

It is only half accurate.
It shows bending in 2 out of 4 dimensions.

[Eise]

I think it is very inaccurate. Relativity describes gravity as the curving of spacetime, the rubber sheet only shows spacial dimensions (and neither one represents time).

This video shows it much better, I think. Closer to what GR is really saying, and still understandable:

 

(I think I posted it already a few times, but maybe you did not see it yet?).

[Strange]

One problem is: what pulls the sheet down:

 

[Silvestru]

1 hour ago, Strange said:

One problem is: what pulls the sheet down:

Actually scary question for the scientifically uninitiated.

Spoiler

 

[StringJunky]

It's good for showing how the path of a moving object is influenced by a larger object but I generally visualise it pictorially  as a density-gradient, distributed around objects; higher density equals stronger gravity or more curved space time. I can visualise that in 3D.

Edited October 30, 2017 by StringJunky

[Strange]

1 hour ago, Silvestru said:

Actually scary question for the scientifically uninitiated.

  Reveal hidden contents

 

This is also relevant to another problem with the analogy: it implies that there needs to be another dimension for the sheet to curve into. Whereas, the curvature of space-time is intrinsic - it doesn't need to be embedded in a higher dimensional space.

[geordief]

I am wondering what aspects can be said to be  correct with the analogy.If the whole thing is put into a detailed computer simulation could it actually be used to make any accurate predictions?

What would happen if one attempted to model the Solar System for example.? How soon the playout deviate noticeably  from the  reality ?(assuming the simulation was  entirely faithful to the required proportions and velocities of all the bodies involved)

 

Aside from that it is clearly a fantastic pedagogic device (might also make a good virtual reality game along  the lines of  fairground dodgems )

 

If the trampoline was made of spandex would the ratios of the adjacent sides of the stretched  parallelograms correspond to any actual space/time ratios that would actually occur? (in the basic analogy)

4 hours ago, Eise said:

I think it is very inaccurate. Relativity describes gravity as the curving of spacetime, the rubber sheet only shows spacial dimensions (and neither one represents time).

This video shows it much better, I think. Closer to what GR is really saying, and still understandable:

 

(I think I posted it already a few times, but maybe you did not see it yet?).

Yes I have seen that . It seems closer to how I have understood curvature but I have not learned the inner mechanisms involved  as the maths is beyond me.  Perhaps eventually I will understand them (a very long term project)

[J.C.MacSwell]

5 hours ago, Strange said:

One problem is: what pulls the sheet down:

 

 

Very clever young man...very clever!

But it's rubber sheets and weights all the way down!

[MigL]

I think the analogy works well to demonstrate how a test mass moves in the presence of a gravitational field based on curvature.
Two dimensional curvature only, not four dimensional, but what do you expect from a model ?

So it's unrealistic in some aspects, but so is every other model, no matter how elaborate.
Are you going to throw away the mathematical model based on GR, because it predicts unrealistic singularities ?
Or because it predicts infinite strengths at close separation, because of self-coupling ?
Heck, Quantum Mechanics/Field theory requires a whole new paradigm as to how we view reality; Should we say that model is flawed ?

If you don't ask unrealistic questions from a model, you don't get unrealistic answers.

[beecee]

1 hour ago, MigL said:

I think the analogy works well to demonstrate how a test mass moves in the presence of a gravitational field based on curvature.
Two dimensional curvature only, not four dimensional, but what do you expect from a model ?

So it's unrealistic in some aspects, but so is every other model, no matter how elaborate.
Are you going to throw away the mathematical model based on GR, because it predicts unrealistic singularities ?
Or because it predicts infinite strengths at close separation, because of self-coupling ?
Heck, Quantum Mechanics/Field theory requires a whole new paradigm as to how we view reality; Should we say that model is flawed ?

If you don't ask unrealistic questions from a model, you don't get unrealistic answers.

Totally agree! All analogies are limited, but also most are very helpfull ways in describing an otherwise difficult situation or scenario, to a non scientific person. If that person then has more then just a passing interest in the subject, he will make more inquiries, and ultimately when asking more complicated questions, will realize that analogies are limited.

IMO one of the most helpful analogies is the river/waterfall model of a BH by Professor Hamilton...see  https://arxiv.org/pdf/gr-qc/0411060.pdf

Analogies certainly got me interested and off the bottom rung of the ladder so to speak!  

[Stclaim]

It works as an analagy only and really only in 2 dimensions. However because planetary bodies rotate about an axis then the plane of the tea police cab he considered as perpendicular to the axial rotation.

[geordief]

2 hours ago, Stclaim said:

It works as an analagy only and really only in 2 dimensions. However because planetary bodies rotate about an axis then the plane of the tea police cab he considered as perpendicular to the axial rotation.

What ,like this ?   

or maybe   https://i.pinimg.com/originals/c0/92/b8/c092b8fa1a046287a0a733ebf9438619.jpg   ?

[Stclaim]

Where did that come from? 

Tea police cab????

It should read.  Trampoline!!!!!

 

[Mordred]

gotta love auto edits lmao

[Phi for All]

1 hour ago, Stclaim said:

Where did that come from? 

Tea police cab????

It should read.  Trampoline!!!!!

!

Moderator Note

Don't drink and jump. Just sayin'.