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Main Question or Discussion Point
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.How would the world be if light didn't travel in a straight line? I was wondering how it would affect life.
Hm. Does that depend on what one means by "light" and "in a straight line"?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.
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.I might have made it ambiguous but what I meant was that light affected by gravity in the same way that solids are.
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 refraction: should a polarization wave traveling through a medium at ##\beta < 1## be called "light"?
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.For gravitational lensing: isn't the notion of traveling in a straight line inherently ambiguous in GR?
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 ...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.
Light does travel in what passes for a straight line in curved space time.How would the world be if light didn't travel in a straight line?
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.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?
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?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.
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.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.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.
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.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?
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?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.
Yes, the parallel axiom does not generally hold. You may have a different geometry than Euclidean.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?
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?
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.Yes, the parallel axiom does not generally hold. You may have a different geometry than Euclidean.
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):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?
But that's true of any two objects moving at different speeds.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.
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.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.
HAHA!!!! I want to make that my signature! :-)I hope that I have not butchered things in my statement, but I am confident that physics experts can make it rigorous.
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 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 feel like this all the time...I hope that I have not butchered things in my statement, but I am confident that physics experts can make it rigorous.
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.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.
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.or not talking about straight lines at all.