# Redshift Of Light Due To The Curvature Of Spacetime In A Closed Universe

Relativity

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### #1 A-wal

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Posted 22 November 2015 - 06:09 PM

Carried on from the other topic.

What doesn't happen to the orientation of light as it moves across a curved four dimensional surface:

What does happen:

Why time dilation stretches the wavelength of light as it moves across a curved four dimensional surface in the same way that relative velocity changes the orientation of objects:

Edited by A-wal, 22 November 2015 - 08:01 PM.

### #2 xyz

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Posted 22 November 2015 - 06:58 PM

Redshift Of Light Due To The Curvature Of Spacetime In A Closed Universe

Two points in red.

1.  Space has no known medium/aether, so what exactly do you think is curving of space itself?

2.  A closed Universe?   A suggestion of a firmament type Universe, a boundary , an edge, I suggest this is an observation limitation and the inability to travel to the ''edge'' to see what is beyond it.

History of a suggested sky firmament were debunked when we entered space.

Edited by xyz, 22 November 2015 - 07:00 PM.

### #3 A-wal

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Posted 22 November 2015 - 07:42 PM

Redshift Of Light Due To The Curvature Of Spacetime In A Closed Universe

Two points in red.

1.  Space has no known medium/aether, so what exactly do you think is curving of space itself?

Spacetime, not space. You need to understand general relativity if you want to fully grasp curved spacetime. The curvature of spacetime generally refers to the length contraction and time dilation experienced by an object that travels through a gravitational field, as in objects following straight paths through curved spacetime. It can also be used to describe the path of an accelerating object in flat spacetime. There's an equivalence there that I believe goes deeper than is described by general relativity which describes an object traveling on a straight path through curved spacetime as physically distinct and different from an object following a curved path through flat spacetime.

2.  A closed Universe?   A suggestion of a firmament type Universe, a boundary , an edge, I suggest this is an observation limitation and the inability to travel to the ''edge'' to see what is beyond it.

History of a suggested sky firmament were debunked when we entered space.

As I already explained to you many times and at great length in the other topic, a closed and finite universe no more has an edge than an open and infinite one!

This topic is about what would be observed if the universe were a particular one (closed) of the already established geometries, with the exception that I'm using the same geometry for time (a circle) and the three spatial dimensions. If you want to discuss the nature of curved spacetime and/or its possible global geometries further please open a new topic.

Edited by A-wal, 22 November 2015 - 07:51 PM.

### #4 xyz

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Posted 23 November 2015 - 09:42 AM

an object following a curved path through flat spacetime.

with the exception that I'm using the same geometry for time (a circle) and the three spatial dimensions.

I do not think you grasp the understanding of relativity. There is no curvature of space-time that is a virtual representation, the curving and time dilation is between masses made by the masses, and time is not a circle, time is dependent to individual mass and the individual mass's relative  motion to a gravitational body. And you cant say enclosed with out it meaning enclosed and finite.

### #5 A-wal

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Posted 23 November 2015 - 10:39 AM

I told you to open up another topic!

You're the one who doesn't grasp relativity. Curved spacetime in general relativity is not a virtual representation! It's a literal one and it's perfectly valid. Again you're claiming that gravitation is needed for time dilation. Again you're forgetting that length contraction happens whenever time dilation occurs. I am using a closed finite model and again, it has no edges!

Don't post in this topic again!

### #6 xyz

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Posted 23 November 2015 - 04:51 PM

I told you to open up another topic!

You're the one who doesn't grasp relativity. Curved spacetime in general relativity is not a virtual representation! It's a literal one and it's perfectly valid. Again you're claiming that gravitation is needed for time dilation. Again you're forgetting that length contraction happens whenever time dilation occurs. I am using a closed finite model and again, it has no edges!

Don't post in this topic again!

Hum , Hum, clears throat!  Excuse me? You have posted a post for discussion in a science discussion forum, then in a narcissist  manner command me to not to post in this thread with relative comments.

If you do not want comments from members and opinions on your idea do not post. You are rather rude.

### #7 A-wal

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Posted 23 November 2015 - 06:42 PM

Hum , Hum, clears throat!  Excuse me? You have posted a post for discussion in a science discussion forum, then in a narcissist  manner command me to not to post in this thread with relative comments.

Because you don't listen! I explained the difference between a flat and curved global model for the universe over and over yet you just raised the exact same BS objections that you did before. How can you refute something that you don't understand? How can you discuss this model when you don't even understand the established models that this one is based on?

If you do not want comments from members and opinions on your idea do not post. You are rather rude.

If you want to discuss this model then I fully and wholeheartedly and without reservation welcome any input that you might wish to bring to the discussion. If you want to continue to refute the accepted models that this idea is based on then kindly sod off! It belongs in another thread. Please don't post again in this one.

### #8 xyz

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Posted 23 November 2015 - 07:03 PM

If you want to discuss this model then I fully and wholeheartedly and without reservation welcome any input that you might wish to bring to the discussion. If you want to continue to refute the accepted models that this idea is based on then kindly sod off! It belongs in another thread. Please don't post again in this one.

Ok, I will discuss your model , you respectively in your first post say  light moving across a 4 dimensional surface, then you go on to use space time contradicting you first own post, Minkowski space-time is independent of matter yet you have incorporated time dependent to your  XYZ dimensional surface and called it a 4 dimensional surface?

### #9 A-wal

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Posted 23 November 2015 - 07:17 PM

Ok, I will discuss your model , you respectively in your first post say  light moving across a 4 dimensional surface, then you go on to use space time contradicting you first own post, Minkowski space-time is independent of matter yet you have incorporated time dependent to your  XYZ dimensional surface and called it a 4 dimensional surface?

Huh? Spacetime is four dimensional. Three dimensions of space, one dimension of time. Yes it's a four dimensional surface and no, I didn't contradict myself. Minkowski spacetime is flat. It's used to describe special relativity. Special relativity describes time dilation and length contraction as effects of the path of objects without different relative velocities using flat spacetime, not the straight paths in curved spacetime used to describe gravitation in general relativity.

### #10 xyz

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Posted 24 November 2015 - 07:34 AM

Huh? Spacetime is four dimensional. Three dimensions of space, one dimension of time. Yes it's a four dimensional surface and no, I didn't contradict myself. Minkowski spacetime is flat. It's used to describe special relativity. Special relativity describes time dilation and length contraction as effects of the path of objects without different relative velocities using flat spacetime, not the straight paths in curved spacetime used to describe gravitation in general relativity.

I think you must be missing the point , spacetime is independent of 3d objects, you are defining a surface as 4d stating time is dependent to the surface and not independent like space-time. Unless this surface you are trying to describe is a virtual representation of something?   Are you trying to describe a black hole in N-dimensional space?

### #11 A-wal

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Posted 24 November 2015 - 12:57 PM

I think you must be missing the point , spacetime is independent of 3d objects, you are defining a surface as 4d stating time is dependent to the surface and not independent like space-time.

That makes no sense! Space in the standard closed finite model creates an unbounded three dimensional sphere. Spacetime in the model I'm using creates an unbounded four dimension sphere (hypersphere).

Unless this surface you are trying to describe is a virtual representation of something?   Are you trying to describe a black hole in N-dimensional space?

The dimensions are at right angles to each other so exactly a quarter of the way around the sphere from the perspective of any observer can be thought of as an event horizon and the combined mass of anything beyond that point as a singularity.

Edited by A-wal, 24 November 2015 - 01:00 PM.

### #12 A-wal

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Posted 24 November 2015 - 01:01 PM

Ah, sketches! Sketches are good, thank you A-wal.

I understand now your idea about curved light paths causing redshift. I think the idea is wrong, though, due to a critical, fundimental misunderstanding of what electromagnetic waves are.

Electromagnetic waves can be thought of as a graph of the force that would be exerted on a stationary charged particle (the electric field) and force (a vector, that is a quantity with a direction) that would be exerted on a moving charged particle (the electric field). The direction of these potential force vectors is always perpendicular to the direction the wave travels. If they were not, Maxwell’s equations and quantum electrodynamics, which a huge amount amount of experimental and practical testing have shown to be correct, would be incorrect. We simply never see a charged particle behave in contradiction to Maxwell’s laws or QED theory.

So the “this doesn’t happen” sketch is correct, while the “what does happen” on is not.

If you want to avoid classical or quantum theory, you can show this empirically by observing that light that follows a curved path due to gravitational lensing doesn’t exhibit redshift.

I'll admit I'm doing a bit of reverse engineering here. Starting with the assumption that the universe is spherical in four dimensions because it's so neat and tidy and working backwards from that assumption. I know that's not regarded as the best way to do science but I bet that's the way at least 90% of new insights were achieved and in fairness, physicists are guilty of doing this all the time. So much so that they're unwilling to entertain any possibility that doesn't fit their assumptions.

Having said that, I do still think the curved light paths cause redshift idea has merit. I'm not that fluent on the exact process of how light interacts through an electric field but I don't think your description of the way electromagnetic waves interact with charged particles is a literal model of the orientation of light waves. Also I'm not entirely convinced that there is sufficient evidence to claim that gravitational lensing has ever been detected. I don't know how reliable this is but I've heard it said on numerous occasions and from multiple source that the super massive black hole at the centre of the galaxy doesn't cause any lensing and that the sun doesn't either outside of its atmosphere, meaning that the observed lensing would be caused by refraction rather than the curvature of spacetime.

I'm not convinced either way because I don't know the data well enough but it would help my model a lot if gravitational lensing does occure. Assuming it does, does it provide evidence that the path of light has no effect on its wavelength? I don't believe it does because from what I understand, the path of light is curved by a tiny amount in the observed lensing but it creates more of an effect the further away it's observed from, as it would if the path of light has been altered, in the same way a tiny change in direction of a space ship would cause it to move progressively further off course the further/longer it goes without a course correction. This would make any redshift from observed gravitational lensing negligible.

I'm a bit confused about how redshift can even be used to infer that an object is receding faster than the speed of light. Redshift should increase with relative velocity in exactly the same way that dime dilation and length contraction increase. If an object were somehow able to move away from us at the speed of light (BS!) the light from it should be infinitely redshifted. When an object approaches the event horizon of a black hole, the redshift approaches infinity. In flat space time the four dimensions are at right angles to each other. As curvature increases, the angles between the dimensions decrease and at the event horizon they'd have decreased to zero (time and space actually switch over past the event horizon). So general relativity's description of an object approaching an event horizon describes redshift increasing as a result of curved spacetime. That's exactly what I'm describing and if you think general relativity gives an accurate description of this then you must also conclude that light traveling around the surface of a sphere would redshifted in exactly the same way!

### #13 A-wal

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Posted 24 November 2015 - 02:11 PM

From wikipedia:

"In astrophysics, gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that is in a gravitational field is reduced in frequency, or redshifted, when observed in a region of a weaker gravitational field. This is a direct result of gravitational time dilation - as one moves away from a source of gravitational field, the rate at which time passes is increased relative to the case when one is near the source. As frequency is inverse of time (specifically, time required for completing one wave oscillation), frequency of the electromagnetic radiation is reduced in an area of a lower gravitational field (i.e., a higher gravitational potential). There is a corresponding reduction in energy when electromagnetic radiation is red-shifted, as given by Planck's relation, due to the electromagnetic radiation propagating in opposition to the gravitational gradient. There also exists a corresponding blueshift when electromagnetic radiation propagates from an area of a weaker gravitational field to an area of a stronger gravitational field.

If applied to optical wavelengths, this manifests itself as a change in the colour of visible light as the wavelength of the light is increased toward the red part of the light spectrum. Since frequency and wavelength are inversely proportional, this is equivalent to saying that the frequency of the light is reduced towards the red part of the light spectrum, giving this phenomenon the name redshift."

So redshift approaches infinity as an object approaches an event horizon. The dimensions are at 90 angles to each other in flat spacetime and approach zero degrees at an event horizon. So in a closed universe redshift increases with distance in a non-linear fashion and approaches infinity as objects approach the quarter way round mark from the perspective of any observer.

As objects approach an event horizon their velocity approaches the speed of light relative to any distant observers. If an object were able to cross an event horizon it would be moving faster than the speed of light relative to any distant observers and no amount of acceleration, gravitational or otherwise can ever do that, which is one of the many reasons why no object can ever reach a black hole. The Schwarzschild coordinates show this. If you want to see it from the free-fallers perspective you need to use the Rindler coordinates and you'll see that the Rindler horizon approaches the falling object in exactly the same way that the event horizon does from the opposite direction and neither can actually reach the object because both horizons approach a falling object as their acceleration increases at exactly the same rate as constantly accelerating objects approach speed of light as their velocity increases as described by special relativity. There's equivalences everywhere. I digress.

So even if the observed redshift was caused by objects moving away from each other they wouldn't be moving faster than the speed of light anyway because that would mean infinite redshift and no object can move at the speed of light relative to any other. It's ridiculous to claim there's a difference between objects moving and expanding/contracting space just is it's ridiculous to claim that there's a difference between following a curved path in flat spacetime and following a straight path in curved spacetime.

Let's see you find genuine fault with that!

### #14 CraigD

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Posted 24 November 2015 - 02:59 PM

I'll admit I'm doing a bit of reverse engineering here. Starting with the assumption that the universe is spherical in four dimensions because it's so neat and tidy and working backwards from that assumption. I know that's not regarded as the best way to do science but I bet that's the way at least 90% of new insights were achieved and in fairness, physicists are guilty of doing this all the time. So much so that they're unwilling to entertain any possibility that doesn't fit their assumptions.

I think that starting with a collection of assumptions – let’s use the more usual scientific term hypotheses – and working backwards to attempt to explain them with mathematically rigorously, experimentally falsifiable theories is the best way to do science, and is how physicists and other hard scientists usually work. In my albeit limited experience, the best educated and most brilliant people have the wildest and most unorthodox hypotheses, while people with poor science educations have ideas they believe to be wild and unorthodox, but which are dull, obvious, and of little value to people with a modicum of science education and experience. A big part of the “science for everyone” mission that Hypography was made to pursue is to help people like me, and I hope many of our passive readers and active posters, reach and maintain that modicum in an informal and fun forum.

Having said that, I do still think the curved light paths cause redshift idea has merit. I'm not that fluent on the exact process of how light interacts through an electric field but I don't think your description of the way electromagnetic waves interact with charged particles is a literal model of the orientation of light waves.

The key point I’m trying to make is that electromagnetic waves are not like water surface waves or traveling waves in a taunt string, which are shapes of recognizable objects like the surface of bodies of water and strings, but changing fields of potential force. There is nothing but these fields – the electric and magnetic – to be “oriented” with regards to the direction the wave travels (or “propogates”) – not multiple photons, vibrations in a luminescent aether, higher-dimensional objects, etc.

EM waves have been intensely studied for over 150 years, with no statistical deviation in large samples from the behavior defined by Maxwell's equations. For 50 years, the predictions of QED have been tested with the best human and automation observed experiments the world scientific community could perform, with no deviation for even single photons from the statistics this theory provides.

In short, it appears that Maxwell was right in the classical approximation, and Tomonaga, Schwinger and Feynman were right exactly. There’s nothing in these theories that allow the wavelength of many or a single photon to be changed by twisting its associated waves to have an orientation other than orthogonal to its propagation direction.

Also I'm not entirely convinced that there is sufficient evidence to claim that gravitational lensing has ever been detected. I don't know how reliable this is but I've heard it said on numerous occasions and from multiple source that the super massive black hole at the centre of the galaxy doesn't cause any lensing and that the sun doesn't either outside of its atmosphere, meaning that the observed lensing would be caused by refraction rather than the curvature of spacetime.

I think most of the scientifically literate world was convinced that gravitational lensing had been demonstrated by Eddington’s observation of the Haydes cluster during the 29 May 1919 solar eclipse at Principe island – and, more importantly to most, matched the new predictions of General Relativity rather than 200 year old predictions of Newtonian gravity, which predicts half the deflection angle of GR. I found this 2011 blog post a pretty good account of Eddington’s famous observation, and learned that it’s depicted in a 2008 movie starring David Tennant of Dr Who fame as Eddington. I plan to watch it, and hope a generation of few of Whovians have and will learn some science history from it.

Among professional astronomers, gravitational lensing is not only in the subject of the search for gravitational lensing events like crosses and rings, of which a several thousand have been cataloged, but a factor used to improve the angular precision of everyday observational data by accounting for the effect of the Sun’s gravity. I was introduced to this when I interned in observatory in high school, even though the telescopes at my observatory lacked to resolution to be much impacted by it. Present day space telescopes as so sensitive they must account for it – see this Phys.org article for more.

There’s also been interest in using the Sun as gigantic light gathering device, but since its optical focus is 542 AU away, such a project isn’t feasible given present day spaceflight technology. ([wki]Voyager 1[/wki] is only about 133 AU away, at a speed of about 3.60 AU/year, so won’t reach this distance until the mid 22nd Century)

I'm not convinced either way because I don't know the data well enough but it would help my model a lot if gravitational lensing does occure. Assuming it does, does it provide evidence that the path of light has no effect on its wavelength? I don't believe it does because from what I understand, the path of light is curved by a tiny amount in the observed lensing but it creates more of an effect the further away it's observed from, as it would if the path of light has been altered, in the same way a tiny change in direction of a space ship would cause it to move progressively further off course the further/longer it goes without a course correction. This would make any redshift from observed gravitational lensing negligible.

Angle of deflection is given by $\theta = \frac{4GM}{rc^2}$
Though the maximum angle of deflection for Sun (M=1.98855 x 1030 kg, is small, about 0.0000084 (0.00049 degrees), the maximum angle for a black hole of any mass (r = rs) is 2 (about 116 degrees).

My best google-fu failed to find anything from a pro more detailed than mentions like

“The effect is typically pretty small (less than 1% for most images, though the effect can be huge for images in just the right place), so you need to average over hundreds of images to make a good map, but fortunately there are lots and lots of galaxies out there.”

(from this Ask a Physicist io9 column) and some unspecific mentions in papers addressing more fundamental physics. So, while I’m fairly sure there’s data showing that images stars gravitational deflected by angles up to and greater than 90 degrees don’t show any anomalous spectral shift, I’m admitting reference search defeat. You’ll need to either do it yourself, or get ask a pro or enlist the aid of a more talented amateur than me.

I'm a bit confused about how redshift can even be used to infer that an object is receding faster than the speed of light.

Me too. I’ve seen good semi-classical explanations, but can’t remember them well enough to give one off the top of my head, and given that this post is already overlong, will get back to it later.

### #15 A-wal

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Posted 24 November 2015 - 06:58 PM

What to call this model? The actual theory of relativity? The correct theory of relativity? The total theory of relativity? I think I prefer the what you get if it's done properly theory of relativity, proper relativity for short. That has a double meaning as well because the model describes a difference from general relativity in the observer dependent measurements of proper time and space.

From the wikipedia article I quoted in my last post:

"In astrophysics, gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that is in a gravitational field is reduced in frequency, or redshifted, when observed in a region of a weaker gravitational field. 'THIS IS A DIRECT RESULT OF GRAVITATIONAL TIME DILATION' - as one moves away from a source of gravitational field, the rate at which time passes is increased relative to the case when one is near the source."

That can't be right. It's a direct result of time dilation AND length contraction. If one has an effect then the other has to. If they cancelled each other out there'd be nothing to observe so they must be cumulative.

I think that starting with a collection of assumptions – let’s use the more usual scientific term hypotheses – and working backwards to attempt to explain them with mathematically rigorously, experimentally falsifiable theories is the best way to do science, and is how physicists and other hard scientists usually work.

It just doesn't feel right to start with the overall model and then trying to back engineer it into less fundamental models. I firmly believe that there's no real difference between time and space. There's only an apparent difference due to the way we perceive it. We have a three and a half dimensional view of the universe, we can only see in one direction of time. At every point in our lives we remember only what came before and that's all that's need to create the illusion of a moving time line. If you think there's something special about the present moment, just remember that you have that same sense of nowness at every moment of your life.

I have actually managed to make it meet with the idea that gravitational acceleration is no different from conventional acceleration rather than general relativity's postulate that gravitational free-fall is equivalent to an inertial object rather than an accelerating one, with one exception. I'd would be so much better if curved and flat spacetime were perfectly equivalent all the way up to the global universal scale, meaning they'd be no distinction between distant objects being redshifted because they're moving away from each other and being redshifted because the observer is looking at them from across curved spacetime. Maybe there kind of isn't.

If every object in a closed universe is moving away from every other object the net result is that relatively they stay the exact same distance from each other rather than the sphere expanding because the size of the event horizon of the sphere is the sphere's circumference and is determined by the mass of the singularity, which is determined by the combined mass of everything on the other side of the sphere, so the size of the sphere is determined purely by the amount of mass that it contains. Hmm, not sure whether this paragraph makes sense or not. I think it does.

There's no actual singularities in this model, in the sense that it's like chasing a rainbow. If you were to accelerate towards one then you would be moving into time dilated and length contracted spacetime relative to your previous perspective and the singularity would reduce in mass as the matter it's comprised of appears to spread out. This applies to the global spherical spacetime model as well as any smaller apparent singularities that it contains. This makes a lot more sense.

I read that the four dimensional closed finite universe was actually considered early on but rejected on the grounds that it leads to the paradox of an observer in principle being able to re-experience the same moments in time. Big mistake! There's no paradox because there's no way to get any information through a singularity, so there's no way that an observer could remember. It's not as if the moment is repeating because time doesn't move, it's just our perception of it that makes it seem progressive. In reality it exists all at once just like space, so it's the same moment in question and not a repeat of it. If you think you could get round the problem of getting information through a singularity by using an intermediate step along the way, that's the equivalent of saying that object B is moving away from object A at over half the speed of light and object C is moving away from object B at over half the speed of light so object C is moving away from object A faster than the speed of light. It doesn't work like that. At any point in time there's an apparent singularity if you look across time in the same way as there is if you look across space so it can never cause a paradox. My brain hurts.

The key point I’m trying to make is that electromagnetic waves are not like water surface waves or traveling waves in a taunt string, which are shapes of recognizable objects like the surface of bodies of water and strings, but changing fields of potential force. There is nothing but these fields – the electric and magnetic – to be “oriented” with regards to the direction the wave travels (or “propogates”) – not multiple photons, vibrations in a luminescent aether, higher-dimensional objects, etc.

EM waves have been intensely studied for over 150 years, with no statistical deviation in large samples from the behavior defined by Maxwell's equations. For 50 years, the predictions of QED have been tested with the best human and automation observed experiments the world scientific community could perform, with no deviation for even single photons from the statistics this theory provides.

In short, it appears that Maxwell was right in the classical approximation, and Tomonaga, Schwinger and Feynman were right exactly. There’s nothing in these theories that allow the wavelength of many or a single photon to be changed by twisting its associated waves to have an orientation other than orthogonal to its propagation direction.

I don't know the models of light well enough and my sketches were probably an over simplification, but the important thing is that observing an object that's time dilated and length contracted relative to the observer causes the light from it to be redshifted. That's all that matters.

I think most of the scientifically literate world was convinced that gravitational lensing had been demonstrated by Eddington’s observation of the Haydes cluster during the 29 May 1919 solar eclipse at Principe island – and, more importantly to most, matched the new predictions of General Relativity rather than 200 year old predictions of Newtonian gravity, which predicts half the deflection angle of GR. I found this 2011 blog post a pretty good account of Eddington’s famous observation, and learned that it’s depicted in a 2008 movie starring David Tennant of Dr Who fame as Eddington. I plan to watch it, and hope a generation of few of Whovians have and will learn some science history from it.

Best Doctor ever! He never should have left. I've heard that the margin for error in that experiment was actually greater than predicted change of position of the light, making it useless, and that it was retested more accurately later and was found to roughly match the predictions of GR but only when the light interacted with the sun's atmosphere.

Among professional astronomers, gravitational lensing is not only in the subject of the search for gravitational lensing events like crosses and rings, of which a several thousand have been cataloged, but a factor used to improve the angular precision of everyday observational data by accounting for the effect of the Sun’s gravity. I was introduced to this when I interned in observatory in high school, even though the telescopes at my observatory lacked to resolution to be much impacted by it. Present day space telescopes as so sensitive they must account for it – see this Phys.org article for more.

If it really is true that there's no observed lensing at the centre of the milky way it completely kills it. If there's any instance of mass not affecting the path of light then it never does and all observed lensing has some other cause.

"The design of modern lensing tools frequently used by astrophysicists to estimate the gravitational lensing effects on light rays have been found to seriously ignore important fundamental principles in optics and gravitation. Convincing observational evidence at the site of Sagittarius A* at the galactic center appears to confirms this finding. It is revealed with convincing observational evidence that the theory pertaining to the lensing of light rays at the vicinity of a "point-like" gravitating mass is flawed and that an incorrect understanding of the lensing of light rays still prevails. The events at the site of Sagittarius A* clearly show a lack of evidence for gravitational lensing. This event has already been published in a renowned refereed journal. The article is reference as: "Time resolved images from the center of the Galaxy appear to counter General Relativity", Dowdye, Jr., E.H., Astronomische Nachrichten, Volume 328, Issue 2, Date: February 2007, Pages: 186-191. "

Angle of deflection is given by $\theta = \frac{4GM}{rc^2}$
Though the maximum angle of deflection for Sun (M=1.98855 x 1030 kg, is small, about 0.0000084 (0.00049 degrees), the maximum angle for a black hole of any mass (r = rs) is 2 (about 116 degrees).

My best google-fu failed to find anything from a pro more detailed than mentions like

“The effect is typically pretty small (less than 1% for most images, though the effect can be huge for images in just the right place), so you need to average over hundreds of images to make a good map, but fortunately there are lots and lots of galaxies out there.”

(from this Ask a Physicist io9 column) and some unspecific mentions in papers addressing more fundamental physics. So, while I’m fairly sure there’s data showing that images stars gravitational deflected by angles up to and greater than 90 degrees don’t show any anomalous spectral shift, I’m admitting reference search defeat. You’ll need to either do it yourself, or get ask a pro or enlist the aid of a more talented amateur than me.

How can light be redshifted by traveling across a curved path sometimes, like light originating from an area of spacetime with greater curvature such as close to a black hole but not at other times, like gravitational lensing? What's the difference?

Me too. I’ve seen good semi-classical explanations, but can’t remember them well enough to give one off the top of my head, and given that this post is already overlong, will get back to it later.

I appreciate the input.

Edited by A-wal, 25 November 2015 - 09:13 PM.

### #16 xyz

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Posted 25 November 2015 - 03:48 PM

How can light be redshifted by traveling across a curved path sometimes,

I appreciate the input.

Light can't , the observers angle is shifted.

### #17 CraigD

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Posted 25 November 2015 - 04:09 PM

How can light be redshifted by traveling across a curved path sometimes, like light originating from an area of spacetime with greater curvature such as close to a black hole but not at other times, like gravitational lensing? What's the difference?

The difference is that, for gravitational redshift to occur, light must travel from a place with lower gravitational potential to a place with greater. The redshift depends only on the difference in gravitational potential at the source and receiver, not that of other places through which the light travels, nor whether its path is deflected by gravitational lensing or other means.

Your question suggest to me, A-wal, that you’re confusing the curvature of spacetime, which is a property of points on a 3 spacelike + 1 timelike dimensional manifold, with the curvature of a path in 3 dimensional space, of which an example is the path of light deflected by gravitational lensing. These are very different things.

What to call this model? The actual theory of relativity?

I uncertain to what you’re referring, A-wal, but I wouldn’t call a model a theory, because they’re very different things.

A scientific model is a way of calculating some measurable feature of physical reality that’s hard or practically impossible to calculate exactly using approaches. For example, there’s no know exact way of calculating in general the position of 3 or more bodies with nonzero mass using Newton’s theory of universal gravity, but it’s easy to calculate them approximately using a model in which you calculate the force on each body, apply it as constant (or changing linearly) for some duration to calculate the bodies’ velocities, then apply the velocities to calculate their position (for example, with my GRAVSIM4 program, which we’ve used for various simple orbital mechanics discussions).

Scientific theories provide ideas that can be used to write models, and models can be used to solve practical problems, but theories and models are different kinds of things.

Newtonian mechanics and Relativity are theories that describes exactly the positions of bodies for a given instance under the influence of gravity and arbitrary well-defined forces, as measured from any reference frame with any possible velocity. They are not models making it easier to calculate these positions, nor are they ad-hoc adjusted to better agree with observations of actual reality.

Newtonian mechanics has been show to not agree with observations, but in most case not so badly that it does not remain a very useful theory. Relativity has not been show to disagree with observations, provided that those observations are of large bodies.

"The design of modern lensing tools frequently used by astrophysicists to estimate the gravitational lensing effects on light rays have been found to seriously ignore important fundamental principles in optics and gravitation. ... This event has already been published in a renowned refereed journal. The article is reference as: "Time resolved images from the center of the Galaxy appear to counter General Relativity", Dowdye, Jr., E.H., Astronomische Nachrichten, Volume 328, Issue 2, Date: February 2007, Pages: 186-191. "

I’m suspicious of Dowdye’s paper, because I suspect he’s a crank with a religious agenda. Here’s what lead me to this suspicion: Comments from Dowdye and reviewers rejecting his article submission to scitizen.com; Dowdye’s website, “Extinction Shift Principle”; Dowde’s scienceinthebible.net “about the author” page.