It took me a long time to develop an intuition for light and electromagnetic wave propagation, and I’m still working on it.
Fundamentally, changes in the EM field propagate always with the speed of light in a vacuum, i.e., c (also known as the speed of causality). Single EM waves propagate with exactly this speed and they do not magically slow down in a medium... they propagate happily at speed c! (FYI EM waves are more complicated like this and involve electric and magnetic fields evolving together).
But since EM radiation interacts with matter and this interaction itself changes the EM field again it results in more EM waves that propagate also at c. Hence, they propagate together and the net result be constructive or deconstructive as well as anything in between. If they have different frequencies, they can also create "interference" patterns or pulse envelopes that seem to propagate slower and even faster than c.
No doubt that the causes and effects are not easy to understand but always thinking in terms of changes in the EM field ALWAYS propagating at c helped me.
changes in the EM field propagate always with the speed of light in a vacuum, i.e., c (also known as the speed of causality)
Speed of causality is a way more intuitive term.
Massless particles travel at the speed of causation in a vacuum. (Usually. Someone else brought up solitons.) Not necessarily in a medium. Trying to work backwards from speed of light to gravity propagating is tortured; understanding that gravity can't cause an effect faster than causality itself is more direct.
In a medium, this can create a "phase kickback" which creates a combined wave that appears to travel slower than the original one. The kickback is just the result of multiple EM changes propagating, i.e. the photons interact with the material, re-emitting photons.
FYI/PSA: If you leave the tracking portion of the youtube link (e.g. after the '?') it is trivial to track back to the youtube account of the person who clicked the 'share' icon. Always best to remove the '?si=...' part before publicly sharing.
I dont think there can be intuition for this. How can one even imagine an electron "flying" through space, there is no measurable thing that travels, we can only see the disturbance of the surrounding space caused by it. But what is the it, does it maybe live in other dimension not accessible to us, or is there no it at all ? I gave up as a layman trying to understand any of this. Sure, there is math and you can somehow make some mental models involving 3d graphics and all, but that is not actually what is going on down there.
Single EM waves propagate with exactly this speed ...
Yes ... and no. Or we should say yes, but not necessarily forward. What about circular? What about ball shaped? What about a vortex? Any valid soliton is a solution and a single wave. Which means this is not just possible in water, but also in the electromagnetic field:
Circular (as in 2d circular in 3d space) propagation in EM waves is like 2 waves in exactly the same location and direction, with opposite rotation along the axis. Which could be extremely useful since they propagate like single waves. In other words, there is a non-circular spectrum ... AND a circular spectrum. So, if we modify all radios we have double the spectrum.
Love this, good point!
It really shows how difficult it is to give an easy explanation that generalizes well...
So, although quite abstract, the fundamental propagation of changes in the EM field at the speed of causality is a good enough approximation?
The issue is many kinds of solutions exist, but aren't common in different fields. On a guitar string, waves are 1d waves in a 1d world. In water everyone knows only standard waves. Which are 1d solitons in a 2d "world". In the electromag field everyone only knows light, which are 2d solitons in a 3d world. Electrons have an axis of rotation that does not point in any spatial or temporal direction.
So everybody thinks these are far more different than they really are.
But the wonder is that water has "light rays", 1d solitons in a 3d world (ie. under water). Dolphins love making them and playing with them. It's possible to make them with your hand in a pool, it's just pretty hard, but with a bit of practice. You need to hold your hand flat above the water, splash down, then retract your hand hard and get out of the way. The faster you retract your hand the further they'll go (but you need time to get out of the way). If you do it right a ring of water bubbles will go into a straight line several meters. Dolphins make them go hundreds of meters, and play with them, seemingly for fun. They aim them at eachother and pass them along (these don't have the same geometric structure as light rays, just the same movement. Except that they trap bubbles and so they "fall upward", especially when they slow down)
Water has "particle-antiparticle soliton pairs". You stick your hand, held flat, 90 degrees to the surface, half submerged, and you move it through the water, parallel to the surface. You do it right, 2 vortices will leave and move through the water. You can see circular shadows move over the bottom of the pool (because of the dimple shape where the vortex meets the surface). These you can probably get to the other side of a quiet pool if you try hard.
According to my math, it should be possible to make a version of this where the vortices rotate around each other. And you should be able to make any even number of vortices (like 4, 6, 8, or 800 for that matter) but I've never done even 2 rotating, nor have I been able to make 4 move together.
Water has 2d solitons in 2d as well, but you can't make just them. If you make 2 waves intersect at exactly 90 degrees, every so often the intersection point will "leave" on it's own. A "hill" on the water will start moving through the water, and you'll swear to God something is moving below the water, but there's nothing there but the wave. But this is almost impossible. You can try in a huge pool (ie. no reflections), and nobody but you in there.
It's weird to think about the properties water has that the electric field does not appear to have. For instance, water has a surface, which reflects solitons. Is there a surface in the electric field somewhere? Would it be a mirror in space, that is not just a perfect reflector of light rays but of matter too?
Comments
It took me a long time to develop an intuition for light and electromagnetic wave propagation, and I’m still working on it.
Fundamentally, changes in the EM field propagate always with the speed of light in a vacuum, i.e., c (also known as the speed of causality). Single EM waves propagate with exactly this speed and they do not magically slow down in a medium... they propagate happily at speed c! (FYI EM waves are more complicated like this and involve electric and magnetic fields evolving together).
But since EM radiation interacts with matter and this interaction itself changes the EM field again it results in more EM waves that propagate also at c. Hence, they propagate together and the net result be constructive or deconstructive as well as anything in between. If they have different frequencies, they can also create "interference" patterns or pulse envelopes that seem to propagate slower and even faster than c.
No doubt that the causes and effects are not easy to understand but always thinking in terms of changes in the EM field ALWAYS propagating at c helped me.
Speed of causality is a way more intuitive term.
Massless particles travel at the speed of causation in a vacuum. (Usually. Someone else brought up solitons.) Not necessarily in a medium. Trying to work backwards from speed of light to gravity propagating is tortured; understanding that gravity can't cause an effect faster than causality itself is more direct.
In a medium, this can create a "phase kickback" which creates a combined wave that appears to travel slower than the original one. The kickback is just the result of multiple EM changes propagating, i.e. the photons interact with the material, re-emitting photons.
3Blue1Brown has a beautiful animation for this phase kickback here: https://youtube.com/shorts/XIW-2ykgVPI?si=PJWiAC2BO7_xP0S6
FYI/PSA: If you leave the tracking portion of the youtube link (e.g. after the '?') it is trivial to track back to the youtube account of the person who clicked the 'share' icon. Always best to remove the '?si=...' part before publicly sharing.
Thanks for the link though, love 3b1b.
Thanks!
I dont think there can be intuition for this. How can one even imagine an electron "flying" through space, there is no measurable thing that travels, we can only see the disturbance of the surrounding space caused by it. But what is the it, does it maybe live in other dimension not accessible to us, or is there no it at all ? I gave up as a layman trying to understand any of this. Sure, there is math and you can somehow make some mental models involving 3d graphics and all, but that is not actually what is going on down there.
Yes ... and no. Or we should say yes, but not necessarily forward. What about circular? What about ball shaped? What about a vortex? Any valid soliton is a solution and a single wave. Which means this is not just possible in water, but also in the electromagnetic field:
https://www.youtube.com/watch?v=909o_kbCdFgll
Circular (as in 2d circular in 3d space) propagation in EM waves is like 2 waves in exactly the same location and direction, with opposite rotation along the axis. Which could be extremely useful since they propagate like single waves. In other words, there is a non-circular spectrum ... AND a circular spectrum. So, if we modify all radios we have double the spectrum.
Love this, good point! It really shows how difficult it is to give an easy explanation that generalizes well... So, although quite abstract, the fundamental propagation of changes in the EM field at the speed of causality is a good enough approximation?
The issue is many kinds of solutions exist, but aren't common in different fields. On a guitar string, waves are 1d waves in a 1d world. In water everyone knows only standard waves. Which are 1d solitons in a 2d "world". In the electromag field everyone only knows light, which are 2d solitons in a 3d world. Electrons have an axis of rotation that does not point in any spatial or temporal direction.
So everybody thinks these are far more different than they really are.
But the wonder is that water has "light rays", 1d solitons in a 3d world (ie. under water). Dolphins love making them and playing with them. It's possible to make them with your hand in a pool, it's just pretty hard, but with a bit of practice. You need to hold your hand flat above the water, splash down, then retract your hand hard and get out of the way. The faster you retract your hand the further they'll go (but you need time to get out of the way). If you do it right a ring of water bubbles will go into a straight line several meters. Dolphins make them go hundreds of meters, and play with them, seemingly for fun. They aim them at eachother and pass them along (these don't have the same geometric structure as light rays, just the same movement. Except that they trap bubbles and so they "fall upward", especially when they slow down)
Water has "particle-antiparticle soliton pairs". You stick your hand, held flat, 90 degrees to the surface, half submerged, and you move it through the water, parallel to the surface. You do it right, 2 vortices will leave and move through the water. You can see circular shadows move over the bottom of the pool (because of the dimple shape where the vortex meets the surface). These you can probably get to the other side of a quiet pool if you try hard.
According to my math, it should be possible to make a version of this where the vortices rotate around each other. And you should be able to make any even number of vortices (like 4, 6, 8, or 800 for that matter) but I've never done even 2 rotating, nor have I been able to make 4 move together.
Water has 2d solitons in 2d as well, but you can't make just them. If you make 2 waves intersect at exactly 90 degrees, every so often the intersection point will "leave" on it's own. A "hill" on the water will start moving through the water, and you'll swear to God something is moving below the water, but there's nothing there but the wave. But this is almost impossible. You can try in a huge pool (ie. no reflections), and nobody but you in there.
It's weird to think about the properties water has that the electric field does not appear to have. For instance, water has a surface, which reflects solitons. Is there a surface in the electric field somewhere? Would it be a mirror in space, that is not just a perfect reflector of light rays but of matter too?