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The image seems to be an illustration of curved spacetime, and/or gravity potential, but why is the surface highest at a certain distance from the central mass? Does that make any sense? - Patrick (talk) 11:34, 28 April 2015 (UTC)[reply]

I replaced it, see also de:Diskussion:Beschleunigung/Archiv#Gravitationspotential: "not suitable to illustrate curved spacetime". - Patrick (talk) 07:56, 18 May 2015 (UTC)[reply]

Hi, Patrick – I've been a little busy and just noticed this change of image. The distortion is explained in the caption found in the Gravity article. It's true that the actual gravitational distortion is best depicted by a rectilinear grid such as the one in the image you used to replace this one; however, that distortion in this image is explained as the artist's conception of the x,y,z coordinate system that would be imposed on the curved spacetime, and not the actual curvature of space. Also keep in mind that these renditions are 2D representations of a 3D concept (nobody's figured out how to better represent such a complex 3D concept on a 2D medium). Yet another reason to favor this image is the fact that it also depicts Gravity Probe B within. So if you were looking for an opinion regarding the keeping of this image in this template, now you have it. In my opinion this image is far superior. – Paine 01:28, 24 May 2015 (UTC)[reply]

Changing from a polar to a rectilinear grid was not the point. My question is: why is the surface highest at a certain distance from the central mass (with the radial curves having an inflection point further out)? Does it have a physical meaning or did the artist draw this just arbitrarily because he thought it looked nice? Is it related to the rotation of the Earth?

The caption, including "which would be rectilinear in a flat spacetime" does not seem to make much sense. Both in a curved and in a flat 2D space one can use polar spacial coordinates.

As I think that old discussion shows, these analogy drawings are not the perfect way to illustrate such a complex physical three-dimensional (actually 4D when relativistic spacetime is also considered) concept. In this respect the drawing you used is equally imperfect as this drawing that you replaced. Over the years since that old discussion, nobody has been able to put into words a better caption for this image than you see above. Tell me, Patrick, how would you rephrase the caption to make the analogy more clear? Remember that what we see in both images is but one plane of an infinite number of planes of x,y,z,t coordinates, so for each x there are x=1, x=2, x=3 → x=∞ ("infinity" in case that last symbol does not appear correctly). This of course also goes for the y, z and time coordinates as well. This is not an easy thing to picture in one's mind, let alone to depict it on a two-dimensional medium. So again, the question would be: How would you rephrase the caption on this image, or even compose a caption for the image you used to replace this image? Since both images are equally imperfect to depict the concept they are attempting to show, then other aspects must be used to decide between them. So again, my choice is this image, which should be restored to this template as soon as possible. – Paine 17:44, 24 May 2015 (UTC)[reply]

More reasons to restore the status quo image are that it has been in this sidebar since the template was first created in 2012, and that a similar template, {{General relativity sidebar}}, already has the image that replaced the original image at its top. Both sidebars are sometimes used in the same article, so it may confuse readers to see the exact same image in different sidebar templates. – Paine 18:34, 25 May 2015 (UTC)[reply]

I agree that it is difficult to illustrate. May be a picture causes more confusion than clarity and can better be left out. However, in File:GPB circling earth.jpg the fact that the surface is highest at a certain distance from the central mass (with the radial curves having an inflection point further out) causes unnecessary extra confusion, so I do not agree that the pictures are equally imperfect. Therefore, in the case we want an illustration, I prefer File:Spacetime curvature.png. - Patrick (talk) 10:29, 27 May 2015 (UTC)[reply]