What if light were influenced by gravity?

[Antonio dela Vinci]

How would the world be if light didn't travel in a straight line? I was wondering how it would affect life.

 

[Orodruin]

Light is influenced by gravitation.

 

[Ibix]

How would the world be if light didn't travel in a straight line? I was wondering how it would affect life.

Light doesn't generally travel in a straight line. Look up refraction (mirages are a particularly interesting case), diffraction (and Huygens' principle more generally) and gravitational lensing.

 

[SiennaTheGr8]

Light doesn't generally travel in a straight line. Look up refraction (mirages are a particularly interesting case), diffraction (and Huygens' principle more generally) and gravitational lensing.

Hm. Does that depend on what one means by "light" and "in a straight line"?

For refraction: should a polarization wave traveling through a medium at $\beta < 1$ be called "light"? And if so, should it be regarded as the "same" light as the incoming/outgoing electromagnetic wave? My rudimentary and likely flawed understanding of the extinction theorem is that we can think of the incoming EM wave as continuing to propagate through the medium at $\beta = 1$ in a straight line but undergoing destructive interference so that it's effectively "canceled," leaving only a polarization wave traveling through the medium at $\beta < 1$ at an angle to the incoming light.

For gravitational lensing: isn't the notion of traveling in a straight line inherently ambiguous in GR?—i.e., straight in space vs. straight in spacetime, as reckoned in which coordinate system, locally vs globally, etc.

Semantics, perhaps.

 

[Antonio dela Vinci]

I might have made it ambiguous but what I meant was that light affected by gravity in the same way that solids are.

 

[Ibix]

I might have made it ambiguous but what I meant was that light affected by gravity in the same way that solids are.

It is affected the same way. There are differences in available trajectories due to the fact that light moves at a speed massive objects cannot reach, but the underlying effect is the same.

In what way do you think light is affected differently from massive objects?

 

[Ibix]

For refraction: should a polarization wave traveling through a medium at $\beta < 1$ be called "light"?

Good point. But at least in the case of a mirage (and most optical applications, I think) this is a negligible effect. And, if memory serves, if you convert the evanescent wave back to a normal wave you typically get an offset in the output beam position similar to normal refraction, so I think the point stands.

For gravitational lensing: isn't the notion of traveling in a straight line inherently ambiguous in GR?

Yes, the "path through space" of a light beam depends on what you are calling "space". But I think you'd be hard pushed to find a choice of spacelike foliation that yields a straight line path - I'm not sure one can even really define a straight line path in this case.

The path light follows through spacetime is a geodesic, yes, and this is a generalisation of the notion of "straight line" to a curved space. But it's not a straight line - geodesics can cross more than once, for example.

 

[Orodruin]

But I think you'd be hard pushed to find a choice of spacelike foliation that yields a straight line path - I'm not sure one can even really define a straight line path in this case.

If you find a foliation such that space is self-similar at every time (such as a RW spacetime), you could do this by looking at geodesics on the simultaneities. In a general dynamic spacetime I imagine it would be more of a hassle ...

 

[Grinkle]

How would the world be if light didn't travel in a straight line?

Light does travel in what passes for a straight line in curved space time.

If light were to leave a visible trail in its wake you would see what looks to you to be a curved trail where the light passes mass - the more mass and the closer the light comes to the mass the more curve you would see. This path traced out is the shortest distance through spacetime that anything could take - the 'straight line' through spacetime. You can't see any fabric or surface that is spacetime, so its hard to picture. If I take a beach ball, draw two dots on it, and connect those dots with a line, the line looks curved but you can see immediately that its the shortest distance along the surface of the beach ball that connects those two points. If the beach ball were invisible, a statement that the curved line is shortest distance between those points on the curved surface I call a beach ball would be similarly hard to picture, but it would still be true, given the appropriate definition of the beach ball surface.

 

[Antonio dela Vinci]

It is affected the same way. There are differences in available trajectories due to the fact that light moves at a speed massive objects cannot reach, but the underlying effect is the same.

In what way do you think light is affected differently from massive objects?

You could shine your flashlight into a wall and see that the light still hits the wall without bending significantly towards the ground unlike when you throw a ball to the same wall and see it hit the wall (given you apply enough force) and fall back to the ground.

 

[Antonio dela Vinci]

Light does travel in what passes for a straight line in curved space time.

If light were to leave a visible trail in its wake you would see what looks to you to be a curved trail where the light passes mass - the more mass and the closer the light comes to the mass the more curve you would see. This path traced out is the shortest distance through spacetime that anything could take - the 'straight line' through spacetime. You can't see any fabric or surface that is spacetime, so its hard to picture. If I take a beach ball, draw two dots on it, and connect those dots with a line, the line looks curved but you can see immediately that its the shortest distance along the surface of the beach ball that connects those two points. If the beach ball were invisible, a statement that the curved line is shortest distance between those points on the curved surface I call a beach ball would be similarly hard to picture, but it would still be true, given the appropriate definition of the beach ball surface.

Does the beach ball represent the Earth with its curved surface and the line between the two dots represent the light from one point to another? Does this mean that as for us observers in the plane, light appears to travel in a straight line but if we look at it from the perspective of the surface of the earth, we see a curvature in the path of light?

 

[PeroK]

You could shine your flashlight into a wall and see that the light still hits the wall without bending significantly towards the ground unlike when you throw a ball to the same wall and see it hit the wall (given you apply enough force) and fall back to the ground.

If you throw a ball, it moves in an obvious curve. If you fire a high-speed bullet, then it moves in a curved, but close to a straight line, over a short distance. If you shine a beam of light, it also moves in a curve, but so close to a straight line as to be almost undetectable.

One of the first experimental confirmations of General Relativity was to measure the deviation of light as it passed the Sun during a total eclipse. You could search the Internet For That.

Also, where gravity becomes very strong, the curvature of a beam of light becomes move significant. And, in fact, it is possible to have light move in a circular orbit around a black hole - although the orbit is unstable.

Search for "photon sphere".

And, if You are interested, you could also search for "gravitational lensing".

 

[Ibix]

You could shine your flashlight into a wall and see that the light still hits the wall without bending significantly towards the ground unlike when you throw a ball to the same wall and see it hit the wall (given you apply enough force) and fall back to the ground.

If you throw a ball gently it falls a long way before it reaches the wall. If you throw a ball fast it fall less because it has less time to fall. If you use a gun you will barely notice the fall of the bullet at short range, because the bullet has even less time to fall. Light is the fastest thing there is, so it has the least time to fall - but it does fall, as I have told you three times now. You need a really long distance to see it, that's all.

Look up gravitational lensing. See also the later posts in this thread where I posted some graphs of light paths curving near a black hole: https://www.physicsforums.com/threads/null-geodesics-in-schwarzschild-spacetime.895174/

 

[Grinkle]

Does the beach ball represent the Earth with its curved surface and the line between the two dots represent the light from one point to another? Does this mean that as for us observers in the plane, light appears to travel in a straight line but if we look at it from the perspective of the surface of the earth, we see a curvature in the path of light?

The beach ball surface is an example of a curved geometry that is easy to visualize. 4 dimensional space time as far as I know is impossible for a human to visualize but it is the geometry through which light (and everything else) travels, and it is not flat. But I now think my post is a red herring for you - I suggest you follow the advice @PeroK gave in post 12 and @Ibix in post 13 and just clarify for yourself that light can definitely be observed to travel a curved path due to gravity.

 

[Ibix]

If you find a foliation such that space is self-similar at every time (such as a RW spacetime), you could do this by looking at geodesics on the simultaneities.

You mean - find a definition of space picked out by some symmetry, find the geodesics of the space at each time, and show that the geodesics of each space map on to the geodesics of any other using said symmetry? Doesn't this still have the issue that the 3-space geodesics may cross multiple times?

 

[Orodruin]

You mean - find a definition of space picked out by some symmetry, find the geodesics of the space at each time, and show that the geodesics of each space map on to the geodesics of any other using said symmetry? Doesn't this still have the issue that the 3-space geodesics may cross multiple times?

Yes, the parallel axiom does not generally hold. You may have a different geometry than Euclidean.

 

[Sorcerer]

You mean - find a definition of space picked out by some symmetry, find the geodesics of the space at each time, and show that the geodesics of each space map on to the geodesics of any other using said symmetry? Doesn't this still have the issue that the 3-space geodesics may cross multiple times?

Yes, the parallel axiom does not generally hold. You may have a different geometry than Euclidean.

I love how in this forum you can be learning one thing and then two advisors or mentors will come in and add something totally unexpected that offers an additional facet of the proverbial diamond being examined in the thread. Further enrichment and detail.

 

[Sorcerer]

Does the beach ball represent the Earth with its curved surface and the line between the two dots represent the light from one point to another? Does this mean that as for us observers in the plane, light appears to travel in a straight line but if we look at it from the perspective of the surface of the earth, we see a curvature in the path of light?

I think the beach ball was just an analogy trying to point out that on a curved surface a geodesic is the closest thing to a line. Don't take it too much beyond that. But you'll notice that if you look at a very tiny piece of the curved line drawn on the beach ball, it will look straight (just like on Earth, locally it looks flat for the most part). Like with this MS paint I did, where I just copied portions of the circle and zoomed in (colored squares to help see):

So gravity curves light, but I doubt we'd notice it locally, unless we look in the distance and see how huge bodies curve light.
We do in fact see it on the large scale. It's how gravitational lensing happens. This wikipedia article has a bunch of animations that show what happens.

https://en.wikipedia.org/wiki/Gravitational_lens

 

[Mister T]

You could shine your flashlight into a wall and see that the light still hits the wall without bending significantly towards the ground unlike when you throw a ball to the same wall and see it hit the wall (given you apply enough force) and fall back to the ground.

But that's true of any two objects moving at different speeds.

 

[Dr_Zinj]

A straight line is a mathematical concept. Doesn't actually exist in our universe if you take into account all influences on a moving object, be it a rock or a photon.

 

[FactChecker]

A straight line is a mathematical concept. Doesn't actually exist in our universe if you take into account all influences on a moving object, be it a rock or a photon.

I disagree. A geodesic (essentially a path with no turning) is a good mathematical expression of an unaccelerated path in space-time. That definitely has a physical meaning, which is why light follows those paths.
PS. I hope that I have not butchered things in my statement, but I am confident that physics experts can make it rigorous.

 

[Grinkle]

I hope that I have not butchered things in my statement, but I am confident that physics experts can make it rigorous.

HAHA! I want to make that my signature! :-)

 

[Ibix]

I disagree. A geodesic (essentially a path with no turning) is a good mathematical expression of an unaccelerated path in space-time. That definitely has a physical meaning, which is why light follows those paths.

I think it depends whether you regard a geodesic as a straight line. Certainly straight lines are geodesics (of flat spaces), but I'm not sure the other way around. Geodesics have some of the sense of straight line, in that it's what you get if you follow your nose in the absense of forces. But, on the other hand, they can do things like cross more than once, and even meet themselves. So I'd be inclined to say they aren't straight lines. @Orodruin may disagree, given his #8 in this thread.

I hope that I have not butchered things in my statement, but I am confident that physics experts can make it rigorous.

I feel like this all the time...

 

[Orodruin]

I think it depends whether you regard a geodesic as a straight line. Certainly straight lines are geodesics (of flat spaces), but I'm not sure the other way around. Geodesics have some of the sense of straight line, in that it's what you get if you follow your nose in the absense of forces. But, on the other hand, they can do things like cross more than once, and even meet themselves. So I'd be inclined to say they aren't straight lines. @Orodruin may disagree, given his #8 in this thread.

A geodesic is the only reasonable definition of what it means for a curve to be ”straight”. Given a curved manifold, you have a choice between using this definition or not talking about straight lines at all.

Straight lines not crossing more than once is just a result of the parallel postulate that is necessary to define Euclidean geometry. You can let go of this postulate and still have reasonable maximally symmetric geometries. I do not see this as an argument not to call geodesics in hyperbolic spaces straight.

In fact, the other four axioms explicitly refer to straight lines.

 

[Ibix]

or not talking about straight lines at all.

That would be my choice. Unless there's an enormous professional consensus that "geodesic" and "straight line" are interchangeable terms. And even then I'd be wary of using it "in public", because of the potential confusion when geodesics do cross multiple times.

I do see your point, and there's certainly no candidate for "straight line" in GR other than geodesics. I just think there's potential for confusion if you use "straight line" that way.

 

[FactChecker]

I can see the objection to using the term "straight line" in a curved space. If we stick with the term "geodesic", we may have all we need functionally and have no argument about terminology.

The thing I will always have trouble visualizing is how the accelerated path which a stone falling to the ground follows is really a geodesic in space-time.

 

[Orodruin]

If it was good enough for Euclid, it is good enough for me.

 

[Nugatory]

The thing I will always have trouble visualizing is how the accelerated path which a stone falling to the ground follows is really a geodesic in space-time.

The problem is that it is almost impossible to get the picture of a stationary Earth and moving stone out of your mind. So try to leave the surface of the Earth out of the picture... you and the stone are free-falling side by side through a dense fog, and the stone is the only thing you can see.

 

[PeroK]

The thing I will always have trouble visualizing is how the accelerated path which a stone falling to the ground follows is really a geodesic in space-time.

Now that one really is a straight line!

 

[Grinkle]

Now that one really is a straight line!

Not if I'm watching from the Space Station.

 

[FactChecker]

Now that one really is a straight line!

Well, yes. Poor example. I should have used the example of a ball thrown horizontally. But even falling straight down (in the Earth-centered-Earth-fixed coordinate system) is not straight in a non-rotating inertial coordinate system, so it is an example of something.

 

[Mister T]

A straight line is a mathematical concept.

Okay. But so are all curved lines.

Doesn't actually exist in our universe if you take into account all influences on a moving object,

What is your point? That objects don't move in straight lines or curved lines, either? No, I doubt it. I think the issue is that the mathematical concept is a model, and the motion of the object is the thing being modeled. Of course the former is an approximation of the latter.