Space Time fabric graphic is misleading

[megacal]

This has been bothering me for some time, and would like to get a physicist's view of it.
If my understanding or contention is in error, please correct me (gently). I only have under grad
physics from 1970, and was a microbiologist, though am interested in quantum physics, cosmology.

My contention is, all the graphic representations of gravity wells, and space time as a flexible fabric are very misleading, and incorrect.

The distortion of space time must extend in ALL dimensions, xyzt, about the distorting mass, from a proton to a black hole. The "depth" of the well is really the extent of the gravitational field, and is infinite in all directions,
though is so weak that it cannot be measured at some point.

We effect Andromeda and vice versa. The whole universe is connected by gravity.

Is that correct?

Thanks in advance.

 

[Ibix]

It leads to a lot of misunderstandings, yes. Unfortunately it isn't possible to draw the kind of manifolds that general relativity uses accurately. You can produce useful maps of highly symmetrical cases, but their interpretation is not necessarily intuitive.

Usually what is being plotted in the "rubber sheet" model is Flamm's hyperboloid, which is a representation of what you might reasonably call "two dimensions of space at a given time" around a gravitating mass. Unfortunately it's not that relevant to why gravity works around Earth (it's a second order effect at best). What you really need is one dimension of time and one of space. And that's difficult to draw and doesn't have the intuitive curved-surface-makes-paths-curve interpretation.

So, yeah. See https://xkcd.com/895/

 

[FactChecker]

My contention is, all the graphic representations of gravity wells, and space time as a flexible fabric are very misleading, and incorrect.

That is probably correct although "all" is a very strong word. I have never seen a graphical representation like that which was anything more than a crude hint at the reality. But it is a very useful crude hint.

The distortion of space time must extend in ALL dimensions, xyzt, about the distorting mass, from a proton to a black hole. The "depth" of the well is really the extent of the gravitational field, and is infinite in all directions,
though is so weak that it cannot be measured at some point.

We effect Andromeda and vice versa. The whole universe is connected by gravity.

Is that correct?

Yes. But for any practical purpose (or even impractical) our solar system does not influence Andromeda. Andromeda is 2.5 million light-years away. I am not expert enough to know if the Milky Way has any influence that far away.

 

[phinds]

My contention is, all the graphic representations of gravity wells, and space time as a flexible fabric are very misleading, and incorrect.

All analogies are incorrect at some level else they would not be analogies they would be actual descriptions, BUT ... they are often reasonable attempts to convey, TO LAYMEN, in layman's language something that could only be faithfully conveyed in a way that would make their eyes glaze over (thus the cartoon that ibix pointed to). See for example the link in my signature.

 

[megacal]

Thanks all, especially for the cartoon link...very clever & humorous.

"...they are often reasonable attempts to convey, TO LAYMEN, in layman's language something that could only be faithfully conveyed in a way that would make their eyes glaze over" -phinds

Yes, I felt my eyeballs rolling up into my head as I got a short way into Sean Carroll's "A No-Nonsense Introduction to General Relativity".

I wonder what Newton would say about it. Amazing things to ponder about & wonder at.

Thank you for all your helpful replies.