Could Dark Matter Possibly Be . . .

The cosmos at our fingertips.
Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Sat Nov 15, 2008 5:54 pm

Speed of Light - a question for Chris or anyone -

If light travels in straight lines only, as Chris you have said, why then do even writers like David N. Schramm and Michael Riordan in their 'Shadows of Creation' published 1991 speak repeatedly of light being "bent" by gravitational lensing .. and include diagrams showing light bending?
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Methods for estimating the age of the universe

Post by astrolabe » Sat Nov 15, 2008 6:18 pm

Hello Sputnick,

Thank you for clarifying. Looked it up myself an found it in the "Physics" issue from Dec. 2005. I wish you could find a way to argue your other comments as well:
Sputnick wrote:
Nereid wrote: When may readers expect to see the first post presenting support for your inflammatory remarks? A post which, I hope, will outline the scope of that support, summarise the nature of that support and key arguments, and make a firm commitment to providing references to peer-reviewed papers published in relevant journals as the primary sources of your case.
When I'm good and ready! Which may be awhile, as the 'good' position remains elusive, and the 'ready' position would require considerable education which I do not have the means to attain. I hope, Nereid, I detect a little humour in your question?
Then please get off the soapbox.
"Everything matters.....So may the facts be with you"-astrolabe

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Sat Nov 15, 2008 6:33 pm

Hello Sputnick,

Your last point:
Sputnick wrote:Speed of Light - a question for Chris or anyone -

If light travels in straight lines only, as Chris you have said, why then do even writers like David N. Schramm and Michael Riordan in their 'Shadows of Creation' published 1991 speak repeatedly of light being "bent" by gravitational lensing .. and include diagrams showing light bending?
should say to you yourself that the argument is is for it's own sake. You've learned much as have I about astronomy and this Forum has been Great and patient with me as well as yourself. You say you have (had?) an IQ of 170? Then use it to put the pieces that you have learned together. For instance, light doesn't bend- space curves. You're getting a little lazy here, I think
"Everything matters.....So may the facts be with you"-astrolabe

User avatar
Chris Peterson
Abominable Snowman
Posts: 18045
Joined: Wed Jan 31, 2007 11:13 pm
Location: Guffey, Colorado, USA

Re: Could Dark Matter Possibly Be . . .

Post by Chris Peterson » Sat Nov 15, 2008 6:34 pm

Sputnick wrote:If light travels in straight lines only, as Chris you have said, why then do even writers like David N. Schramm and Michael Riordan in their 'Shadows of Creation' published 1991 speak repeatedly of light being "bent" by gravitational lensing .. and include diagrams showing light bending?
I explained that before. It is a shorthand for describing the apparent path of light as we see it in 3D space. These writers are using imagery and analogy to try and make a difficult subject (GR) accessible to their non-scientific audience.

Light always travels in a straight path called a geodesic (you can use the Internet to read up on these; an interesting subject). Another way of saying this is that light always takes the shortest distance between two points (called a line in Euclidean space, but light doesn't travel through Euclidean space, it travels through spacetime). It has been rigorously observed that the apparent bending of light around strong gravitational fields is the result of a distortion of space, not a 3D bending of the rays. The latter case would produce a slightly different effect than what is actually seen.
Chris

*****************************************
Chris L Peterson
Cloudbait Observatory
https://www.cloudbait.com

User avatar
BMAONE23
Commentator Model 1.23
Posts: 4076
Joined: Wed Feb 23, 2005 6:55 pm
Location: California

Re: Could Dark Matter Possibly Be . . .

Post by BMAONE23 » Sun Nov 16, 2008 2:24 am

Chris,
Couldn't the fact of Gravitational Lensing and the "Einstein Cross" be considered evidence of bending light? Wouldn't physics dictate that for a single point source to appear as several separate sources after passing through a large gravity well, the light's path would need to have been bent (in the case of the Einstein Cross) in four separate directions?

First paragraph from Wiki on Gravitational Lensing

"A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is "bent" around a massive object (such as a cluster of galaxies) between the source object and the observer. The process is known as gravitational lensing, and is one of the predictions of Albert Einstein's general theory of relativity."

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Sun Nov 16, 2008 2:37 am

Hello BMAONE23,

I know you addressed your question to Chris so I hope you don't think it rude of me to wade in. The quote from Wikipedia does place the word (bent) in quotation marks which, to me is a heads up on what the word represents.
"Everything matters.....So may the facts be with you"-astrolabe

User avatar
Chris Peterson
Abominable Snowman
Posts: 18045
Joined: Wed Jan 31, 2007 11:13 pm
Location: Guffey, Colorado, USA

Re: Could Dark Matter Possibly Be . . .

Post by Chris Peterson » Sun Nov 16, 2008 2:40 am

BMAONE23 wrote:Chris,
Couldn't the fact of Gravitational Lensing and the "Einstein Cross" be considered evidence of bending light? Wouldn't physics dictate that for a single point source to appear as several separate sources after passing through a large gravity well, the light's path would need to have been bent (in the case of the Einstein Cross) in four separate directions?

First paragraph from Wiki on Gravitational Lensing...
Ah, but notice how careful they were in that article to put the quotes around "bent". They did that because the word is an analogy, but not a perfect description of what happens.

We observe an apparent change in direction when light passes near a large mass. We see it in gravitational lensing, we see it here in our own solar system when a planet occults a star. So how to explain that? An obvious hypothesis would be that the gravity pulls the light inwards, just like we'd see if shooting billiard balls near a large mass (an effect I have to compensate for, in fact, when I analyze meteor orbits). That might be called the Newtonian hypothesis. Another hypothesis, call it the GR version, would suggest that we aren't seeing photons deflected by the gravitational field, but light following a geodesic through curved space. What is interesting is that these two hypotheses result in slightly different predictions of the "deflection". Thousands of observations have demonstrated that the GR hypothesis accurately predicts what we see, and the Newtonian does not. So, in true scientific fashion, the Newtonian theory (in this context) loses support, the GR theory gains support. A person viewing this rationally concludes that, while either could be wrong, the Newtonian is more likely to be wrong than the GR. And most people would consider the extremely accurate prediction of GR to be a rather strong argument that the theory is, in fact, very good.
Chris

*****************************************
Chris L Peterson
Cloudbait Observatory
https://www.cloudbait.com

User avatar
BMAONE23
Commentator Model 1.23
Posts: 4076
Joined: Wed Feb 23, 2005 6:55 pm
Location: California

Re: Could Dark Matter Possibly Be . . .

Post by BMAONE23 » Sun Nov 16, 2008 2:41 am

Astro, I don't mind your chiming in as you always have some relavent wisdom to interject.

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Sun Nov 16, 2008 3:19 am

Hello BNAONE23,

Gosh :oops:
"Everything matters.....So may the facts be with you"-astrolabe

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Sun Nov 16, 2008 9:10 pm

Hello All,

Has anyone actually read the about the 700 Galaxy cluster slide? I did. Cosmological sensationalism at it's best! :roll:
"Everything matters.....So may the facts be with you"-astrolabe

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Mon Nov 17, 2008 4:38 pm

astrolabe wrote:Hello Sputnick,

Your last point:
Sputnick wrote:Speed of Light - a question for Chris or anyone -

If light travels in straight lines only, as Chris you have said, why then do even writers like David N. Schramm and Michael Riordan in their 'Shadows of Creation' published 1991 speak repeatedly of light being "bent" by gravitational lensing .. and include diagrams showing light bending?
should say to you yourself that the argument is is for it's own sake. You've learned much as have I about astronomy and this Forum has been Great and patient with me as well as yourself. You say you have (had?) an IQ of 170? Then use it to put the pieces that you have learned together. For instance, light doesn't bend- space curves. You're getting a little lazy here, I think
Hi Astro - I simply fail to see why Shcramm and Riordan, if they want to share with others what they know, and that seems to be the intention of their book, why they would not explain that 'light does not bend space bends.' It would take only those many words. Perhaps they aren't convinced that light doesn't bend.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Mon Nov 17, 2008 4:48 pm

Chris Peterson wrote:
BMAONE23 wrote:Chris,
Couldn't the fact of Gravitational Lensing and the "Einstein Cross" be considered evidence of bending light? Wouldn't physics dictate that for a single point source to appear as several separate sources after passing through a large gravity well, the light's path would need to have been bent (in the case of the Einstein Cross) in four separate directions?

First paragraph from Wiki on Gravitational Lensing...
Ah, but notice how careful they were in that article to put the quotes around "bent". They did that because the word is an analogy, but not a perfect description of what happens.

We observe an apparent change in direction when light passes near a large mass. We see it in gravitational lensing, we see it here in our own solar system when a planet occults a star. So how to explain that? An obvious hypothesis would be that the gravity pulls the light inwards, just like we'd see if shooting billiard balls near a large mass (an effect I have to compensate for, in fact, when I analyze meteor orbits). That might be called the Newtonian hypothesis. Another hypothesis, call it the GR version, would suggest that we aren't seeing photons deflected by the gravitational field, but light following a geodesic through curved space. What is interesting is that these two hypotheses result in slightly different predictions of the "deflection". Thousands of observations have demonstrated that the GR hypothesis accurately predicts what we see, and the Newtonian does not. So, in true scientific fashion, the Newtonian theory (in this context) loses support, the GR theory gains support. A person viewing this rationally concludes that, while either could be wrong, the Newtonian is more likely to be wrong than the GR. And most people would consider the extremely accurate prediction of GR to be a rather strong argument that the theory is, in fact, very good.
Well said, Chris, far better than your 'light doesn't bend, space bends'. I will have far greater respect for your opinions when I see them presented not as plain fact, but as theory, adding to that word 'stronly supported' if you like. Also, a few days ago you made the statement to me that Kant's philosophysing of island universes (galaxies) did not spring from philosolphy, but from astronomical observations. I left my notes at home, but I've done a lot of reading the the past week and was reminded that direct observations of other galaxies were not made until the last century .. the 1900s. Kant, I think I recall but I may be wrong .. perhaps it was the 1800s, did his philosphyzing in the 1700s.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Mon Nov 17, 2008 4:49 pm

Hello Sputnick,

Sounds like it. I don't buy it though.
"Everything matters.....So may the facts be with you"-astrolabe

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Mon Nov 17, 2008 4:56 pm

astrolabe wrote:Hello Sputnick,

Sounds like it. I don't buy it though.
Sounds like what? You don't buy what? I have no idea what you're saying.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

User avatar
bystander
Apathetic Retiree
Posts: 21570
Joined: Mon Aug 28, 2006 2:06 pm
Location: Oklahoma

Re: Could Dark Matter Possibly Be . . .

Post by bystander » Mon Nov 17, 2008 5:08 pm

astrolabe wrote:Hello All,

Has anyone actually read the about the 700 Galaxy cluster slide? I did. Cosmological sensationalism at it's best! :roll:
Image
xkcd.com - A WebComic - Dark Flow

Galaxies on the Move
Science News Magazine
October 25th, 2008
Vol.174 #9 (p. 12)

Scientists detect a mysterious flow of galactic clusters

A newly discovered “dark flow” appears to carry clusters of galaxies toward a point in the southern sky, a new study suggests.

Cosmic 'Dark Flow' Detected Across Billions Of Light Years
ScienceDaily (Sep. 24, 2008)

Using data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP), scientists have identified an unexpected motion in distant galaxy clusters. The cause, they suggest, is the gravitational attraction of matter that lies beyond the observable universe.

Scientists Detect Cosmic 'Dark Flow' Across Billions of Light Years
NASA News Release 08-83: Sept. 23, 2008
Goddard Space Flight Center

Asterisk Café: Big Bang or Big Flush?

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Mon Nov 17, 2008 5:09 pm

Hello Sputnick,
Sputnick wrote:
Chris Peterson wrote:
BMAONE23 wrote:Chris,
Couldn't the fact of Gravitational Lensing and the "Einstein Cross" be considered evidence of bending light? Wouldn't physics dictate that for a single point source to appear as several separate sources after passing through a large gravity well, the light's path would need to have been bent (in the case of the Einstein Cross) in four separate directions?

First paragraph from Wiki on Gravitational Lensing...
Ah, but notice how careful they were in that article to put the quotes around "bent". They did that because the word is an analogy, but not a perfect description of what happens.

We observe an apparent change in direction when light passes near a large mass. We see it in gravitational lensing, we see it here in our own solar system when a planet occults a star. So how to explain that? An obvious hypothesis would be that the gravity pulls the light inwards, just like we'd see if shooting billiard balls near a large mass (an effect I have to compensate for, in fact, when I analyze meteor orbits). That might be called the Newtonian hypothesis. Another hypothesis, call it the GR version, would suggest that we aren't seeing photons deflected by the gravitational field, but light following a geodesic through curved space. What is interesting is that these two hypotheses result in slightly different predictions of the "deflection". Thousands of observations have demonstrated that the GR hypothesis accurately predicts what we see, and the Newtonian does not. So, in true scientific fashion, the Newtonian theory (in this context) loses support, the GR theory gains support. A person viewing this rationally concludes that, while either could be wrong, the Newtonian is more likely to be wrong than the GR. And most people would consider the extremely accurate prediction of GR to be a rather strong argument that the theory is, in fact, very good.
Well said, Chris, far better than your 'light doesn't bend, space bends'. I will have far greater respect for your opinions when I see them presented not as plain fact, but as theory, adding to that word 'stronly supported' if you like. Also, a few days ago you made the statement to me that Kant's philosophysing of island universes (galaxies) did not spring from philosolphy, but from astronomical observations. I left my notes at home, but I've done a lot of reading the the past week and was reminded that direct observations of other galaxies were not made until the last century .. the 1900s. Kant, I think I recall but I may be wrong .. perhaps it was the 1800s, did his philosphyzing in the 1700s.
Why. Schramm and Riordan's article of course! Unless it's out of context, sounds like they're saying the same thing as light going through a space curvature by utilizing a different interpretation of the phenom.
"Everything matters.....So may the facts be with you"-astrolabe

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Mon Nov 17, 2008 11:57 pm

=Sputnick. Well said, Chris, far better than your 'light doesn't bend, space bends'. I will have far greater respect for your opinions when I see them presented not as plain fact, but as theory, adding to that word 'stronly supported' if you like. Also, a few days ago you made the statement to me that Kant's philosophysing of island universes (galaxies) did not spring from philosolphy, but from astronomical observations. I left my notes at home, but I've done a lot of reading the the past week and was reminded that direct observations of other galaxies were not made until the last century .. the 1900s. Kant, I think I recall but I may be wrong .. perhaps it was the 1800s, did his philosphyzing in the 1700s.
=?Why. Schramm and Riordan's article of course! Unless it's out of context, sounds like they're saying the same thing as light going through a space curvature by utilizing a different interpretation of the phenom.
Language is important as research. If space is bent and light travels in a straight line, which is possible, why do Schramm and Riordan not use that language instead of saying light is bent? I have discovered two schools of thought, one saying light is bent by gravity, the other saying space is bent -- so to say "light only travels in a straight line" might not be true. Saying it could travel either way, or even in bent and straight lines, leaves science open to exploration rather than closing it in a 'fact' which may be false.
Last edited by Sputnick on Tue Nov 18, 2008 12:12 am, edited 1 time in total.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

apodman
Teapot Fancier (MIA)
Posts: 1171
Joined: Wed Aug 15, 2007 6:48 pm
Location: 39°N 77°W

Re: Could Dark Matter Possibly Be . . .

Post by apodman » Tue Nov 18, 2008 12:01 am

Sputnick wrote:I have discovered two schools of thought
You have inferred two schools of thought.

"Light doesn't bend" is a phrase that applies with respect to the geodesic. If you set your frame of reference in a regular orthogonal grid covering space and not affected by mass (a model that mathematics can be happy with, though it doesn't do much for physics), the phrase "light bends" is perfectly acceptable; in fact, the phrase "the way light bends is that space curves" is good too. The trouble with all that in the real universe is that, once you've introduced the curvature of space as the explanation, describing the bending of light in addition to that would be redundant, as it implies a curving away from the geodesic which is not the case. The geodesic is curved in the imaginary regular orthogonal mathematical grid we started with, but it is a straight line (in the sense of the shortest distance between two points) in the real physical space with mass present.
Last edited by apodman on Tue Nov 18, 2008 12:18 am, edited 1 time in total.

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Tue Nov 18, 2008 12:05 am

Perhaps Dark Matter anti-matter particles are too small and too weak to affect us? Or perhaps they do effect us .. causing mutation as well as cosmic rays. Seeing how every particle known to science seems to have an anti-particle it is only natural to assume Dark Matter has anti-Dark Matter.

Perhaps Dark Matter is anti-gravity, acting the opposite of gravity, and not infusing galaxies, but merely surrounding them .. 'pushing' down on the galaxy and hindering the natural tendency of centrifugal force.

In the picture of the galaxy which is perhaps giving birth to the smaller gravity, the straight arm seems to have escaped the theoretical Dark Matter of the large galaxy, whereas the arm nearest the large galaxy is obviously bent by something.

If redshift shows the small galaxy 2008 November 15: Arp 273 (sorry I can't seem to remember how to include the url although I did it earlier today) is moving away from the large galaxy, and that it is escaping the large galaxy's DM, that could mean galaxies acquire Dark Matter as they move by sweeping up DM so to speak, perhaps clearing 'lanes' free of Dark Matter. This would be the opposite of 'rivers' of DM.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Tue Nov 18, 2008 12:15 am

Chris Peterson wrote: First paragraph from Wiki on Gravitational Lensing...
Ah, but notice how careful they were in that article to put the quotes around "bent". They did that because the word is an analogy, but not a perfect description of what happens.[/quote]

In Riordin & Schramm's book there were no quotation marks around the word bent, the word appearing a few times in that context.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

User avatar
bystander
Apathetic Retiree
Posts: 21570
Joined: Mon Aug 28, 2006 2:06 pm
Location: Oklahoma

Re: Could Dark Matter Possibly Be . . .

Post by bystander » Tue Nov 18, 2008 1:19 am

Perhaps an analogy will help. Great circles routes provide the shortest distance between any two points on the surface of a sphere. When projected onto a 2d map, they appear curved, or "bent". But in 3d, on the surface of the sphere, they are analogous to a straight line in 2d.

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Tue Nov 18, 2008 3:03 am

Hello Sputnick,

Go to the http heading at the top of the page. Click on it, then right click. Choose "copy". Go to your selected location (Post a reply, for instance), right click again and choose paste.
"Everything matters.....So may the facts be with you"-astrolabe

astrolabe
Science Officer
Posts: 499
Joined: Wed Feb 13, 2008 1:53 am
Location: Old Orchard Beach, Maine

Re: Could Dark Matter Possibly Be . . .

Post by astrolabe » Tue Nov 18, 2008 3:25 am

Hello All,

A subject like this is always a coaster ride. I've been waiting for the right moment to send this along and while this may not be IT, I guess it's as good a time as any. If anyone gors to this website make sure to read every word carefully- no glossing over. It almost made me want to stop asking any more questions in this Forum or any other. Almost!

http://hyperphysics.phy-astr.gsu.edu/Hb ... ck.html#c2
"Everything matters.....So may the facts be with you"-astrolabe

Sputnick
Science Officer
Posts: 458
Joined: Thu Apr 10, 2008 7:18 pm
AKA: Sputnick
Location: Peterborough, Ontario, Canada

Re: Could Dark Matter Possibly Be . . .

Post by Sputnick » Tue Nov 18, 2008 5:43 pm

bystander wrote:Perhaps an analogy will help. Great circles routes provide the shortest distance between any two points on the surface of a sphere. When projected onto a 2d map, they appear curved, or "bent". But in 3d, on the surface of the sphere, they are analogous to a straight line in 2d.
I can't see how the analogy applies to gravitational lensing. If you put two points far apart on the sphere, and then put a galaxy in between, a line connecting the two points if it is to avoid going through the galaxy will have to take an actual bend around the galaxy .. so it will be bending in two ways.

Of course I know you know what I am about to say, but actually the shortest distance between two points on a sphere might be through the sphere.
If man were made to fly he wouldn't need alcohol .. lots and lots and lots of alcohol to get through the furors while maintaining the fervors.

User avatar
bystander
Apathetic Retiree
Posts: 21570
Joined: Mon Aug 28, 2006 2:06 pm
Location: Oklahoma

Re: Could Dark Matter Possibly Be . . .

Post by bystander » Tue Nov 18, 2008 8:29 pm

Sputnick wrote:I can't see how the analogy applies to gravitational lensing. If you put two points far apart on the sphere, and then put a galaxy in between, a line connecting the two points if it is to avoid going through the galaxy will have to take an actual bend around the galaxy .. so it will be bending in two ways.
Light (EM) travels through spacetime (4d). A geodesic is the shortest distance through spacetime. Light follows the geodesic. Massive objects cause space (3d) to warp (gravity), the more massive, the greater the warp. As light follows the geodesic, as it passes a massive object,the projection of that 4d geodesic in 3d space will appear to bend.
Sputnick wrote:Of course I know you know what I am about to say, but actually the shortest distance between two points on a sphere might be through the sphere.
Ah, but that wouldn't be on the surface of the sphere.