From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
WikiProject Mathematics (Rated B-class, High-priority)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
B Class
High Priority
 Field:  Mathematical physics
One of the 500 most frequently viewed mathematics articles.

Opinion on figure change?[edit]

In figure 3-7, I added little icons illustrating what the observer "sees" in terms of redshift or blueshift. Are these little icons helpful, or do they make the diagram too busy? Prokaryotic Caspase Homolog (talk) 08:21, 28 September 2018 (UTC)

Yes, they are very helpful because they have been stolen from my diagram. I know how to make diagrams clear and simple. However, the icons are too small. Could you please to make it a bit larger? I am going to use your diagram against spacetime concept and relativity in Einstein's incarnation, so that would be fine for my readers to make it easy to understand visually. That will be not a problem to explain them, that observer should move himself and displacement of the source is due to aberration, exactly as in the case of rotation. Could you also please to add the diagram into the section Transverse Doppler Effect in the article Relativistic Doppler effect? It lacks one. Yours most sincerely, Albert Gartinger (talk) 08:49, 28 September 2018 (UTC)

Why do you use such words as "steal"? I told you earlier that that was an aspect of your version of the illustration that I personally thought was rather nice. However, your figure was a JPG figure and did not scale well to different sizes. It looked somewhat "jaggy" to my eyes. You should learn to make SVG images.
I asked about this figure because I do not consider my opinion to be the only opinion, and if the majority indicate that they think that the image is too "busy" and that it should be reverted to the simpler earlier version, then I will do so.
I will have to look at the article Relativistic Doppler effect to see if this diagram fits in with its presentation. I wouldn't want to rewrite the article to accommodate the figure. Rather, I would want any figure I add to enhance what is already there.
Instead of enlarging the icon, I enlarged the entire figure. Does that work? Prokaryotic Caspase Homolog (talk) 09:26, 28 September 2018 (UTC)
Please be sure to check how it looks on mobile devices as well. Around 40% of our viewers are accessing this article on cell phones and tablets. Prokaryotic Caspase Homolog (talk) 09:31, 28 September 2018 (UTC)

I think we can also place a question at which diagram is better, yours or mine. It has hundreds, if not thousands readers. They can also have a look at this polemics. Sadly, I am too busy today and must leave Albert Gartinger (talk) 09:38, 28 September 2018 (UTC) SVG! That's good idea, thank you. I have missed it. Albert Gartinger (talk) 09:45, 28 September 2018 (UTC)

My question is not whether the current Fig. 3-7 is better than Olego_18_09.jpg, but whether the current Fig. 3-7 is better than this earlier version. As I indicated before, Olego_18_09.jpg is unacceptable because it implies that the fundamental distinction between the scenarios discussed in the text is between a moving observer versus a moving source. Rather, the distinction between the scenarios is between the source and receiver being at their geometrically closest approach, versus the receiver seeing the source as being at its closest point. Prokaryotic Caspase Homolog (talk) 15:44, 28 September 2018 (UTC)
Fig. 3-7 does not mesh well with the discussion at Relativistic Doppler effect Prokaryotic Caspase Homolog (talk) 21:06, 28 September 2018 (UTC)
Let me put it to you this way: Suppose observers A and B, moving towards each other in uniform inertial motion along non-intersecting paths, are at their closest approach with respect to each other. The events marking A's and B's points of closest approach are independent of frame. Both A and B are carrying identical monochromatic light sources. A and B both see light from the other's source as being blueshifted relative to his/her own.
  1. If we consider A as being a moving observer, as in Olego-a, then blueshift [added later: "has a significant component"] due to aberration of light. A sees B as apparently not yet having reached the point of closest approach, and A's motion relative to B has a significant longitudinal component.
  2. If we consider A as being a stationary observer, as seemingly depicted in Olego-b, then blueshift [added later: "has a significant component"] due to light-time correction. A receives light from when B had not yet reached the point of closest approach, and B's motion at that time had a significant longitudinal component relative to A.
  3. You could say, "No, no, NO!!! Olego-b is supposed to be depicting the situation where A sees B as being closest to it, when it is actually not! That is why I've drawn the perpendicular image of B as a hollow star, and the displaced image of B as solid and to the right! You're being silly and stupid!!!"
  4. Well, suppose I'm a naive student seeing your figure for the first time. How am I supposed to figure all of that out?
  5. Actually, receiver moving and source stationary versus receiver stationary and source moving have the same effect, although they are analyzed differently, as seen here.
Prokaryotic Caspase Homolog (talk)

Your interpretation of Case 1 is incorrect. If we think in terms of transverse doppler effect, aberration or light time correction cannot have any effect on frequency shift. Only dilation of observer's or source's clock contribute into the frequency shift, if we think in terms of that frame, in which the effect is transverse.

Theoretically, the observer can always know the actual direction to the source, because there is no aberration of forces.

It's hard for me to understand if you are serious. This is an elementary problem! The result of the measuremen depends on how you conduct it, that is, on what you think about your movement. Let's think within the framework of the transverse effect, it means that YOU move in the frame of the source and at the moment of reception the source is at closest approach to you. If you consider yourself moving, then at this moment you keep your head or telescope forward in the direction of movement. The angle of inclination corresponds to the speed that you attributed to youself (the angle of relativistic aberration). The frequency of the source becomes gamma times more blue. You treat this phenomenon as slowing down your own clock, so the clock at rest is ticking faster. It is the same explanation for the both rotational and inertial motion. This is a purely Transverse effect.

I have already written, that this is a question of interpretation. Of course, the same effect can be attributed to the presence of the longitudinal component, should you think that you are at rest. But we are talking about the transverse effect and the chapter is about transverse effect. Albert Gartinger (talk) 12:35, 29 September 2018 (UTC)

It is no wonder that your drawing is so confusing! Anyway, Talk pages are not for general discussion of a subject, but are specifically for discussing matters having to do with improvement of the associated article. Your drawing will not appear in this article. Prokaryotic Caspase Homolog (talk) 12:56, 29 September 2018 (UTC)
I note that I did not quite express myself properly, so I added [added later: "has a significant component"] to my original remarks. If one wants to work things out from the standpoint of the receiver, then whether the receiver considers himself to be moving or stationary, he/she has to take into account a component of longitudinal motion. That makes the analysis more difficult than analysis from the frame of the source. Prokaryotic Caspase Homolog (talk) 13:14, 29 September 2018 (UTC)

───────────────────────── B, as the light source, has a trivially simple view of the system compared with A, considered as the receiver.

  1. B knows, from the conditions of the problem, that A is at its closest point to him.
  2. That means that A has no longitudinal component of motion to complicate the analysis.
  3. A's clocks are time-dilated relative to B.
  4. The light that A receives is therefore blue-shifted by a factor of gamma. End of story.

Prokaryotic Caspase Homolog (talk) 03:46, 30 September 2018 (UTC)

This is exactly what I have pictured on my diagram. This is a purely transverse effect, as it should be. My diagram shows a transverse effect for both cases, frames of the receiver and frame of the source. Your diagram depicts transverse effect in the frame of the receiver and longitudinal in the frame of the receiver. It is not good, to say the least.

The existing in the article explanation in frame B is nowhere suitable. One might think that the change in frequency measured by the spectroscope is due to what B observes. It is very confusing, that the source highlights the receiver by green monochromatic light and in the meantime by violet radiation . It's unclear how an electric light bulb can observe something. It simply shines. Well, and if the source went to sleep?

Everything is simple. Detector's clock slows down, so processes around him run faster, radiation turns violet. Albert Gartinger (talk) 06:28, 30 September 2018 (UTC)

According to the receiver, there is no longitudinal component either, if the receiver considers himself moving. The co-moving with the receiver observer understands, that actually path of the photon is perpendicular to his path. He understands, that displacement of the source is apparent effect, a.k.a aberration of light. Albert Gartinger (talk) 08:01, 30 September 2018 (UTC)

Think about transversely moving mirror. The mirror is a moving observer. A source (laser pointer) in the origin emits green monochromatic light straight up. The light approaches the mirror at relativistic aberration angle. At the reception, when the source crosses Y axis, the light blueshifts, since mirror’s clock runs slower. The mirror reflects the light backward at the same angle as It had once arrived, it travels back into the origin.

Now the mirror turns into is moving source. Since it move in the frame of the laser pointer, its clock dilates, so the light redshifts again and comes back into the origin at the same green color.

There is no even smell of "A is slower than B, B is slower than A" Albert Gartinger (talk) 08:11, 30 September 2018 (UTC)

Another important point about your diagram A. Why did you draw a slanted beam? The ray, as constructed from individual photons, does not undergo aberration. It remains perpendicular in any frame, either "moving" or "stationary". The moving detector crosses the ray and a single light pulse appears coming from the front. But the whole RAY remains at right angle direction of motion of the receiver or the source.

Albert Gartinger (talk) 13:23, 30 September 2018 (UTC)

The beam is drawn slanted because that is the direction from which in which the receiver views the light as coming from. In other words, the arrow is coming from the apparent position of the source.
The scenario where source and receiver are geometrically at their closest approach to each other, as depicted in your Olego-a, is confusing because
  1. You illustrate, correctly, that from the viewpoint of the moving observer, the source appears in an abberated position in the sky.
  2. On the other hand, you illustrate that from the viewpoint of source, its light travels on a direct perpendicular path towards the observer.
  3. You illustrate two different frames in a single scenario. This is confusing.
  4. A consistent illustration from the frame of the would be the "Moving Observer" of this figure.
  5. Analysis of the "Moving Observer" of this figure is more complicated than it should be.
a. It doesn't matter who is considered as being "actually" in motion, the source is time-dilated relative to the observer. This would result in a redshift.
b. On the other hand, since there is a longitudinal component of the observer's motions with respect to the aberrated (apparent) position of the source, the light that the observer receives from this apparent source would be blueshifted.
c. The overall effect (redshift? blueshift?) depends on the relative magnitude of (1) time dilation in the source versus (2) blueshift as the observer approaches the apparent source.
Does it make sense why I consider your Olego-a unsatisfactory? Prokaryotic Caspase Homolog (talk) 14:16, 30 September 2018 (UTC)

Updated Transverse Doppler effect diagram[edit]

Transverse Doppler Effect diagrams in different frames

While I work on animation, I did my best to improve the static picture.

1) I have added “bulbs” with arrows. These arrows demonstrate direction of emission or perception of light pulse. Due to aberration moving source emits “transverse” light pulse backward, moving observer sees transverse light pulse coming from the front,

2) I have added “apparent” positions of the source for all cases.

3) I tried to vividly demonstrate the identity of rotating and inertial observers, the same interpretation of frequency shifts, the same amounts of frequency shift.

Sure, the diagram must be followed by proper explanation in the article.

This analysis is solidly backed by the primary and secondary sources: A. Einstein 1905 article (&7), Kevin S. Brown (Doppler effect at Mathpages) and a number of papers considering Mossbauer rotor experiments, papers and articles on relativistic aberration. Animated will look like that: Observer with laser pointer in the origin emits green light pulse straight up, mirror movies parallel to the x axis, light pulse hits mirror, mirror measures blueshift (blue flash), light pulse comes back to origin (redshifts) and appears to the observer at the same green color.

I believe that diagram makes clear, that:

1) Angle of emission always has corresponding angle of reception; these angles cannot be arbitrary. So, a reference frame is not a private property of observer but mutual. If one is “at rest”, the other will definitely be “moving”.

2) Reciprocal time dilation is two mixed "by force" special cases, when each observer is “at rest” (looks at right angle and one - way speed of light in “his” frame is isotropic). Sure, it is nonsense.

If there is will be no objection, in several days I will replace the diagram.Albert Gartinger (talk) 08:01, 4 October 2018 (UTC)

I object. You continue to illustrate the distinction between scenarios (a) and (b) as between moving observer versus moving source. The distinction rather is between the receiver and source at their closest points to each other, versus the receiver seeing the source as closest. In addition, you continue to mix elements of multiple frames in a single diagram. Prokaryotic Caspase Homolog (talk) 12:56, 4 October 2018 (UTC)
Of course, we are in no hurry. I think your arguments are clear in the text. Before starting any dispute resolutions, could you please clarify exactly which diagram you think is appropriate? That which is now or do you have some kind of improved version? What do you think of the animation scenario that I have proposed?Albert Gartinger (talk) 13:58, 4 October 2018 (UTC)
The principle of relativity dictates that for a given physical scenario, it makes absolutely no difference whether one considers the scenario from the frame of the source or the frame of the receiver. Your diagram misleads the viewer into thinking that choice of frame (moving observer versus moving source) makes a difference in the outcome of otherwise identical physical scenarios. Choice of frame cannot make any such difference. The reason why (a) results in the receiver observing a blueshift, while (b) results in the receiver observing a redshift, is that the physical scenarios are different in the two diagrams. Your illustration is therefore misleading and unacceptable. Prokaryotic Caspase Homolog (talk) 16:45, 4 October 2018 (UTC)
Dear Sir,
You have already expressed several different versions why my diagram “misleads the viewer”. In my opinion, it is your diagram misleads the viewer, so we have some sort of conflict. I am ready to go far, far, far away to defend my diagram. I will be most thankful for reducing our dialogue to discussing exact features of the diagram instead of exchange of philosophical interpretations. Yes, it is clear, that these diagrams describe different physical scenarios (light emitted at closest approach redshifts, light received of closest approach blueshifts), different angles of perception. In regard of the case a - you mentioned yourself that it is “best analyzed from the frame of receiver”, so I feel completely lost and confused. I have already mentioned that I wish to start dispute resolution procedures and to involve as many people as possible inside or outside Wikipedia. If you think, that this diagram is misleading, could you please to provide yours. I haven’t got any answer yet, which diagram according to you is “acceptable“, so will you please:
1) To make clear, whether you wish to leave existing diagram and explanation “as it is” and to reject mine;
2) Should you wish to provide your improved “acceptable” design instead of mine,
3) What is your opinion towards my scenario of dynamic presentation?
Looking forward to your reply, Albert Gartinger (talk) 18:04, 4 October 2018 (UTC)
@Albert Gartinger:
  1. regarding your statement "I am ready to go far, far, far away to defend my diagram": note that without a reliable wp:secondary source in which the diagram appears, together with the text of the article, there is no way that it will be taken on board in Wikipedia. The farther you go—without such a source—the more time you will waste, mostly your time, but as soon as editors see that you are wasting their time, someone will take action to stop you. As you already are on final warning level for talk page abuse, not much is needed to get you blocked.
  2. regarding your statement " involve as many people as possible inside or outside Wikipedia...": be aware of wp:canvassing with people inside Wikipedia, and, lacking internal consensus, new people from outside Wikipedia are likely to be regarded as wp:meat puppets.
- DVdm (talk) 18:56, 4 October 2018 (UTC)
DVdm (talk), thank you very much for you note, I will take it into account. I mentioned reliable wp:secondary source behind my analysis. they may seem unreliable to you, but they may seem reliable to others. I am looking for exact answer from another Wikipedia editor towards design of my diagram to start dispute resolutions Albert Gartinger (talk) 19:08, 4 October 2018 (UTC)
Before you start that, it would be a good idea to have a source that clearly, directly and visually supports the diagram itself. Good luck. - DVdm (talk) 19:18, 4 October 2018 (UTC)
Dear DVdm (talk), thank you very much for your kind words!!! Sadly, my interlocutor only complains that something wrong is with the diagram, but doesn't want to give exact answer exactly what. I don't even understand what exactly scenario is wrong and why and how this scenario should look like. Albert Gartinger (talk) 19:27, 4 October 2018 (UTC)
Your interlocutor is under no obligation to explain anything here. On the contrary, such explanations are off-topic, as you should know by now. The responsibility for providing citations is entirely yours—see wp:BURDEN. - DVdm (talk) 19:33, 4 October 2018 (UTC)

Citations in support of my diagram[edit]

Should someone wishes I to provide quotes, in support of scenario (a) I would like to quote celebrated A. Einstein’s work “On the Electrodynamic of Moving Bodies”, &7, Theory of Doppler Principle and Aberration:

From the equation for it follows that if an observer is moving with velocity relatively to an infinitely distant source of light of frequency , in such a way that the connecting line “source-observer” makes the angle with the velocity of the observer referred to a system of co-ordinates which is at rest relatively to the source of light, the frequency of the light perceived by the observer is given by the equation

Mr. Einstein clearly speaks that "an observer is moving with velocity " and that "with the velocity of the observer referred to a system of co-ordinates which is at rest relatively to the source of light"

That exactly what my diagram case a demonstrates. It is clear, that at the moment when "the connecting line “source-observer” makes the angle with the velocity of the observer" makes angle that formula reduces to:

That exactly what my diagram demonstrates. Sure, I have plenty of sources in support of any other scenario. Albert Gartinger (talk) 20:29, 4 October 2018 (UTC)

I believe that it would be very fair to perpetuate the great teachings of Mr. Einstein in my diagram Albert Gartinger (talk) 20:41, 4 October 2018 (UTC)

Since there doesn't seem to be any means of getting a permalink to the current version of any figure, I am temporarily using a copy of your figure from my drive account. I will switch the link to an permanent archive link on Commons when/if one becomes available.
The question is not whether Albert Einstein understood the theory of relativity. The question is whether your figure as of 7:54, 4 October 2018 provides a clear and understandable interpretation of the scenarios discussed in the text.
Unfortunately, as I have repeatedly pointed out, the figures that you have presented to date are totally baffling because
  1. They mix up elements of multiple frames in a single image
  2. They imply that shifting frames from moving observer to moving source makes all the difference as to whether the observer sees blueshift or redshift.
Consider scenario (a) of your figure.
  • In this one figure, you show the observer as moving in the frame of the source. With a bubble arrow around the source, you show light being emitted from the source perpendicular to the path of the observer. Likewise, with the squiggly green arrow, you show light being emitted from the source perpendicular to the path of the observer.
  • On the other hand, you illustrate the apparent position of the source from the viewpoint of the observer, and you have a bubble arrow pointing to the apparent position of the source.
  • In other words, you have mixed up elements from multiple frames into a single diagram.
  • Your legend indicates that "the arrow indicates direction of the light pulse". In some situations, you use bubble arrows to indicate the direction of the light, in other situations, you use bubble arrows to indicate directions to the light. You are inconsistent in your use of the bubble arrows.
Consider scenario (b) of your figure.
  • You label this scenario as "Moving source" to distinguish it from scenario (a), "Moving observer". As I have indicated above, whether an observer sees the light as blueshifted or redshifted cannot depend on the frame in which the scenario is analyzed. Your figure is therefore totally misleading.
  • You use bubble arrows inconsistently. From the apparent position of the source as seen by the observer, you have a bubble arrow shooting off to the left, heading off to nowhere. From the observer, you have a bubble arrow pointing to the apparent position of the source.
The figures that you have presented to date are all completely unacceptable because of these confusing elements. Until you learn how to present things clearly, you are wasting everybody's time here. Any attempt by you to replace the existing figure in the article with your version will be immediately reverted. Prokaryotic Caspase Homolog (talk) 09:33, 5 October 2018 (UTC)
Dear Prokaryotic Caspase Homolog (talk), thank you very much for your message and your valuable opinion. I will post on your talk page some other secondary sources in regard of the diagram. Surely I do not intend to go into edit wars, I wish to seek consensus. I can recommend you to learn a little bit more about the aberration of light. Light emitted in the frame of the source (Case a) at right angle will approach receiver at oblique angle . Yes, this theory is quite difficult and diagrams my appear confusing, they require some mental efforts indeed. Let's postpone our further talks until dynamic animation is ready. Again, could you please to make it clear, do you wish to leave the current figure with moving sources? Albert Gartinger (talk) 10:47, 5 October 2018 (UTC)
I have offered compromise to my interlocutor on his page - adjust this figure according to his understanding, just to draw two TRANSVERSE effects - in the rest frame of the observer and in the rest frame of the source.Albert Gartinger (talk) 12:05, 5 October 2018 (UTC)

Would this be acceptable to you?[edit]

@Albert Gartinger: I have incorporated various design elements that you favor into a new version of Figure 3-7, while omitting the confusing mixed-frame elements that I have strongly objected to. I have also added an extensive note and supplementary figure to discuss how the ease of analyzing a relativistic scenario often depends on the choice of frame. Figures should have a minimum of wording, since English wording tends to discourage a figure's use in non-English Wikis.

@Albert Gartinger: In your last contribution, you accidentally wrote <math>\sin \alpha = v/c <\math> with an incorrectly oriented slash in the "\math". This resulted in a parsing error that required 15 minutes for me to diagnose and fix. Please be more careful next time.

Figure 3-7. Transverse Doppler effect scenarios

Suppose that a source and a receiver, both approaching each other in uniform inertial motion along non-intersecting lines, are at their closest approach to each other. It would appear that the classical analysis predicts that the receiver detects no Doppler shift. Due to subtleties in the analysis, that expectation is not necessarily true. Nevertheless, when appropriately defined, transverse Doppler shift is a relativistic effect that has no classical analog. The subtleties are these:[1]:541–543

  • Fig. 3-7a. What is the frequency measurement when the receiver is geometrically at its closest approach to the source? This scenario is most easily analyzed from the frame S' of the source.[note 1]
  • Fig. 3-7b. What is the frequency measurement when the receiver sees the source as being closest to it? This scenario is most easily analyzed from the frame S of the receiver.

Two other scenarios are commonly examined in discussions of transverse Doppler shift:

  • Fig. 3-7c. If the receiver is moving in a circle around the source, what frequency does the receiver measure?
  • Fig. 3-7d. If the source is moving in a circle around the receiver, what frequency does the receiver measure?

In scenario (a), the point of closest approach is frame-independent and represents the moment where there is no change in distance versus time (i.e. dr/dt = 0 where r is the distance between receiver and source) and hence no longitudinal Doppler shift. The source observes the receiver as being illuminated by light of frequency f', but also observes the receiver as having a time-dilated clock. In frame S, the receiver is therefore illuminated by blueshifted light of frequency

In scenario (b) the illustration shows the receiver being illuminated by light from when the source was closest to the receiver, even though the source has moved on. Because the source's clocks are time dilated as measured in frame S, and since dr/dt was equal to zero at this point, the light from the source, emitted from this closest point, is redshifted with frequency

Scenarios (c) and (d) can be analyzed by simple time dilation arguments. In (c), the receiver observes light from the source as being blueshifted by a factor of , and in (d), the light is redshifted. The only seeming complication is that the orbiting objects are in accelerated motion. However, if an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation. (The converse, however, is not true.)[1]:541–543 Most reports of transverse Doppler shift refer to the effect as a redshift and analyze the effect in terms of scenarios (b) or (d).[note 2]


  1. ^ The ease of analyzing a relativistic scenario often depends on the frame in which one chooses to perform the analysis. In this linked image, we present alternative views of the transverse Doppler shift scenario where source and receiver are at their closest approach to each other. (left) If we analyze the scenario in the frame of the receiver, we find that the analysis is more complicated than it should be. The apparent position of a celestial object is displaced from its true position (or geometric position) because of the object's motion during the time it takes its light to reach an observer. The source would be time-dilated relative to the receiver, but the redshift implied by this time dilation would be offset by a blueshift due to the longitudinal component of the relative motion between the receiver and the apparent position of the source. (right) It is much easier if, instead, we analyze the scenario from the frame of the source. An observer situated at the source knows, from the problem statement, that the receiver is at its closest point to him. That means that the receiver has no longitudinal component of motion to complicate the analysis. Since the receiver's clocks are time-dilated relative to the source, the light that the receiver receives is therefore blue-shifted by a factor of gamma.
  2. ^ Not all experiments characterize the effect in terms of a redshift. For example, the Kündig experiment was set up to measure transverse blueshift using a Mössbauer source setup at the center of a centrifuge rotor and an absorber at the rim.


  1. ^ a b Morin, David (2008). Introduction to Classical Mechanics: With Problems and Solutions. Cambridge University Press. ISBN 978-0-521-87622-3.

In the future I will try to be more careful writing formulas. As far as I know, you have created many beautiful pictures for Wikipeda readers. They must be very grateful to you for your time and your contributions! Yes, your figure is simple, not too crowded. Very nice, I highly appreciate it! Albert Gartinger (talk) 08:22, 6 October 2018 (UTC)

Thanks! There is a bug in the SVG rendering of the squiggly ray in (c). I do not know if the bug is from the WikiMedia rendering engine, or from Inkscape. I will need to spend time fixing this bug. Prokaryotic Caspase Homolog (talk) 11:15, 6 October 2018 (UTC)
I worked out a solution to the rendering bug, then removed an element that the W3C Validator found objectionable. The image at this link passed W3C validation without any additional changes. Prokaryotic Caspase Homolog (talk) 13:05, 6 October 2018 (UTC)
I replaced the image and text in main article space with the revised version discussed above. Prokaryotic Caspase Homolog (talk) 13:14, 6 October 2018 (UTC)
Additional figure tweaks, adopted more of AG's suggestions. Prokaryotic Caspase Homolog (talk) 01:17, 7 October 2018 (UTC)
Both rendering bugs which exasperated me (misoriented arrowheads and incorrect proportions of rotated bitmap images) are known issue with librsvg, the SVG rendering library used by WikiMedia. Prokaryotic Caspase Homolog (talk) 20:36, 8 October 2018 (UTC)

What is the source of gravitational force in Newton's theory?[edit]

In sect. "sources of spacetime curvature" one reads: "In Newton's theory of gravitation, the only source of gravitational force is mass". This is not true. In Newton's theory mass is absolutely passive (first law of motion). Consequently mass cannot be a source of force. Ed Dellian2003:D2:9703:5982:E5FC:D23:1439:EA1E (talk) 19:22, 7 November 2018 (UTC)

I have never seen a law mentioning absolutely passiveness of mass, but in Newton's law of universal gravitation#Modern form we read (with a pretty reliable source): Every point mass attracts every single other point mass by a force acting along the line intersecting both points. - DVdm (talk) 22:25, 7 November 2018 (UTC)
As well as I ever knew it, Newton didn't try to explain the source, but describe the effect. I believe he was also bothered by the action at a distance not knowing about the mechanism, or possible delay. Gah4 (talk) 22:37, 7 November 2018 (UTC)
The OP may be thinking of Bondi's distinction between three types of mass: (1) active mass which acts as the source of a gravitational field; (2) passive mass which reacts to a gravitational field; and (3) inertial mass which reacts to acceleration. In Newton's theory, active mass must equal passive mass, or the third law of motion would be violated. On the other hand, the equality of passive mass and inertial mass was a mystery that bothered Newton, and which most researchers chose to ignore. Einstein resolved the mystery with his theory of general relativity. The article is very clear on this point. Prokaryotic Caspase Homolog (talk) 22:48, 7 November 2018 (UTC)
I forgot about that one. Reminds me of, what I believe came from Galileo, arguing why heavier masses shouldn't fall faster than lighter ones. If you take two small masses, and tie them together with a thin string, they are now one larger mass. Also reminds me of an undergrad experiment which is supposed to measure gravitational vs. inertial mass, but doesn't. Gah4 (talk) 01:15, 8 November 2018 (UTC)