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EM Wave propagation
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There are lots of posts about EM wave model of photons, but I haven;t read one that covers the more specific question I am focusing on here.
Here How does energy transfer between B and E in an EM standing wave? david was concerned about the presence of a zero $E$ & $B$ field point in the wave, close, but that is not my concern.
An electromagnetic waves is propagated by the oscillations of the electric and magnetic fields. A changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field. An electromagnetic wave is self propagating and does not need a medium to travel through.
But I can't overcome the idea that in order to achieve propagation an $dot E$ or $dot B$ in one place must be capable of inducing a $dot B$ or $dot E$ in a different place.
How do we understand a change in position to occur?
In Maxwells Vacuum Equations (such as
$nabla times E = -dot B$
) does not curl E result in a vector located in the same place as E, suggesting that it is only at that point a B field may be induced.
The rest of the post is just a list of dead ends I considered.
2) If a $dot E$ resulted in a distant $dot B$ (or vice versa), energy would need to be carried between the locations. I suppose this might be by a propagating EM wave. However I am trying to understand a propagating EM wave in the first place, and it is difficult (although not impossible) to work with a recursive or circular explaination.
3) if constant speed is assumed one can easily turn a time dependent wave equation to a (space) spatially dependent one. However, what I'm looking for is a mechanism from which to derrive or at least justify propagation, and the assumption of any speed essentially skips over that step.
4) Matter waves, such as on a string exhibit a clear coupling in the form of tension along the string. Although as they are a fundamentally different kind of wave looking for something very similar to that may be flawed. Is there some conceptual aspect of field waves I've managed to miss or forget, I wonder?
5) Maybe I got it backwards, and photon propagation is the evidence of E to B induction over a distance/ I haven't got very far with that line of reasoning
6) Special relativity "explains" magnetic fields as the relativistic effect of charge motion. I always felt this was one of the greatest insights, so I started to wonder if there is any way to make use of it to develop an argument for motion of energy in an E field. Must be googling the wrong keywords though.
7) Another approach is to imagine that $dot E$ is equivalent to the motion of a charge, and then try to think about the B-field that moving charge would induce. However E fields being present omnidirectionally around the charge seems to make this impossible.
electromagnetism visible-light electromagnetic-radiation photons maxwell-equations
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
asked Sep 7 at 1:40
JMLCarter
3,8791822
add a comment |Â
up vote
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down vote
favorite
There are lots of posts about EM wave model of photons, but I haven;t read one that covers the more specific question I am focusing on here.
Here How does energy transfer between B and E in an EM standing wave? david was concerned about the presence of a zero $E$ & $B$ field point in the wave, close, but that is not my concern.
An electromagnetic waves is propagated by the oscillations of the electric and magnetic fields. A changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field. An electromagnetic wave is self propagating and does not need a medium to travel through.
But I can't overcome the idea that in order to achieve propagation an $dot E$ or $dot B$ in one place must be capable of inducing a $dot B$ or $dot E$ in a different place.
How do we understand a change in position to occur?
In Maxwells Vacuum Equations (such as
$nabla times E = -dot B$
) does not curl E result in a vector located in the same place as E, suggesting that it is only at that point a B field may be induced.
The rest of the post is just a list of dead ends I considered.
2) If a $dot E$ resulted in a distant $dot B$ (or vice versa), energy would need to be carried between the locations. I suppose this might be by a propagating EM wave. However I am trying to understand a propagating EM wave in the first place, and it is difficult (although not impossible) to work with a recursive or circular explaination.
3) if constant speed is assumed one can easily turn a time dependent wave equation to a (space) spatially dependent one. However, what I'm looking for is a mechanism from which to derrive or at least justify propagation, and the assumption of any speed essentially skips over that step.
4) Matter waves, such as on a string exhibit a clear coupling in the form of tension along the string. Although as they are a fundamentally different kind of wave looking for something very similar to that may be flawed. Is there some conceptual aspect of field waves I've managed to miss or forget, I wonder?
5) Maybe I got it backwards, and photon propagation is the evidence of E to B induction over a distance/ I haven't got very far with that line of reasoning
6) Special relativity "explains" magnetic fields as the relativistic effect of charge motion. I always felt this was one of the greatest insights, so I started to wonder if there is any way to make use of it to develop an argument for motion of energy in an E field. Must be googling the wrong keywords though.
7) Another approach is to imagine that $dot E$ is equivalent to the motion of a charge, and then try to think about the B-field that moving charge would induce. However E fields being present omnidirectionally around the charge seems to make this impossible.
electromagnetism visible-light electromagnetic-radiation photons maxwell-equations
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
asked Sep 7 at 1:40
JMLCarter
3,8791822
1
I know on S.E. it's blasphemous to seriously consider photons as real particles that propagate the energy of light. Sure everyone says duality but they don't mean it. A so called EM wave can easily be derived mathematically and physically based on individual photons. EM waves and fields can't even begin to be explained without incorporating many coherent photons. Photons will explain what your looking for, especially the propagation part.
– Bill Alsept
Sep 7 at 6:10
@Bill no one serious ever objects to using the photon picture in places where it makes sense, nor to claims that phenomena can be described in the photon picture. What I object to is any kind of absolutist suggested that photons is either (a) the only way or (b) always the better way to address problems in E&M.
– dmckee♦
Sep 8 at 17:17
@dmckee I appreciate you at least discussing it. What you are objecting to, is exactly what I am objecting to. 90% of The books or comments (probably You too) always claim that interference can only be caused by a wave and that particles cannot explain this. I object to that and it can be proven otherwise. The status quo is very biased on this subject when it comes to photons. They claim duality but they don’t really visualize it.
– Bill Alsept
Sep 8 at 18:34
90% of books claim that classical particles can not explain interference which is exactly true. Photons are not classical particles. Photons are also not the complete quantum picture, as the represent unlocalized Fock states of the field with well defined momentum. That expansion is the correct one for asymptomatic states (i.e. the far field), but is not fully general. And you have repeatedly claimed that situation perfectly described by classical E&M have to be treated in terms of photons, which is simply not the case.
– dmckee♦
Sep 8 at 19:16
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
There are lots of posts about EM wave model of photons, but I haven;t read one that covers the more specific question I am focusing on here.
Here How does energy transfer between B and E in an EM standing wave? david was concerned about the presence of a zero $E$ & $B$ field point in the wave, close, but that is not my concern.
An electromagnetic waves is propagated by the oscillations of the electric and magnetic fields. A changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field. An electromagnetic wave is self propagating and does not need a medium to travel through.
But I can't overcome the idea that in order to achieve propagation an $dot E$ or $dot B$ in one place must be capable of inducing a $dot B$ or $dot E$ in a different place.
How do we understand a change in position to occur?
In Maxwells Vacuum Equations (such as
$nabla times E = -dot B$
) does not curl E result in a vector located in the same place as E, suggesting that it is only at that point a B field may be induced.
The rest of the post is just a list of dead ends I considered.
2) If a $dot E$ resulted in a distant $dot B$ (or vice versa), energy would need to be carried between the locations. I suppose this might be by a propagating EM wave. However I am trying to understand a propagating EM wave in the first place, and it is difficult (although not impossible) to work with a recursive or circular explaination.
3) if constant speed is assumed one can easily turn a time dependent wave equation to a (space) spatially dependent one. However, what I'm looking for is a mechanism from which to derrive or at least justify propagation, and the assumption of any speed essentially skips over that step.
4) Matter waves, such as on a string exhibit a clear coupling in the form of tension along the string. Although as they are a fundamentally different kind of wave looking for something very similar to that may be flawed. Is there some conceptual aspect of field waves I've managed to miss or forget, I wonder?
5) Maybe I got it backwards, and photon propagation is the evidence of E to B induction over a distance/ I haven't got very far with that line of reasoning
6) Special relativity "explains" magnetic fields as the relativistic effect of charge motion. I always felt this was one of the greatest insights, so I started to wonder if there is any way to make use of it to develop an argument for motion of energy in an E field. Must be googling the wrong keywords though.
7) Another approach is to imagine that $dot E$ is equivalent to the motion of a charge, and then try to think about the B-field that moving charge would induce. However E fields being present omnidirectionally around the charge seems to make this impossible.
electromagnetism visible-light electromagnetic-radiation photons maxwell-equations
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
asked Sep 7 at 1:40
JMLCarter
3,8791822
There are lots of posts about EM wave model of photons, but I haven;t read one that covers the more specific question I am focusing on here.
Here How does energy transfer between B and E in an EM standing wave? david was concerned about the presence of a zero $E$ & $B$ field point in the wave, close, but that is not my concern.
An electromagnetic waves is propagated by the oscillations of the electric and magnetic fields. A changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field. An electromagnetic wave is self propagating and does not need a medium to travel through.
But I can't overcome the idea that in order to achieve propagation an $dot E$ or $dot B$ in one place must be capable of inducing a $dot B$ or $dot E$ in a different place.
How do we understand a change in position to occur?
In Maxwells Vacuum Equations (such as
$nabla times E = -dot B$
) does not curl E result in a vector located in the same place as E, suggesting that it is only at that point a B field may be induced.
The rest of the post is just a list of dead ends I considered.
2) If a $dot E$ resulted in a distant $dot B$ (or vice versa), energy would need to be carried between the locations. I suppose this might be by a propagating EM wave. However I am trying to understand a propagating EM wave in the first place, and it is difficult (although not impossible) to work with a recursive or circular explaination.
3) if constant speed is assumed one can easily turn a time dependent wave equation to a (space) spatially dependent one. However, what I'm looking for is a mechanism from which to derrive or at least justify propagation, and the assumption of any speed essentially skips over that step.
4) Matter waves, such as on a string exhibit a clear coupling in the form of tension along the string. Although as they are a fundamentally different kind of wave looking for something very similar to that may be flawed. Is there some conceptual aspect of field waves I've managed to miss or forget, I wonder?
5) Maybe I got it backwards, and photon propagation is the evidence of E to B induction over a distance/ I haven't got very far with that line of reasoning
6) Special relativity "explains" magnetic fields as the relativistic effect of charge motion. I always felt this was one of the greatest insights, so I started to wonder if there is any way to make use of it to develop an argument for motion of energy in an E field. Must be googling the wrong keywords though.
7) Another approach is to imagine that $dot E$ is equivalent to the motion of a charge, and then try to think about the B-field that moving charge would induce. However E fields being present omnidirectionally around the charge seems to make this impossible.
electromagnetism visible-light electromagnetic-radiation photons maxwell-equations
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
asked Sep 7 at 1:40
JMLCarter
3,8791822
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
edited Sep 7 at 7:53
Qmechanic♦
96.7k121631022
96.7k121631022
asked Sep 7 at 1:40
JMLCarter
3,8791822
asked Sep 7 at 1:40
JMLCarter
3,8791822
asked Sep 7 at 1:40
JMLCarter
3,8791822
3,8791822
1
I know on S.E. it's blasphemous to seriously consider photons as real particles that propagate the energy of light. Sure everyone says duality but they don't mean it. A so called EM wave can easily be derived mathematically and physically based on individual photons. EM waves and fields can't even begin to be explained without incorporating many coherent photons. Photons will explain what your looking for, especially the propagation part.
– Bill Alsept
Sep 7 at 6:10
@Bill no one serious ever objects to using the photon picture in places where it makes sense, nor to claims that phenomena can be described in the photon picture. What I object to is any kind of absolutist suggested that photons is either (a) the only way or (b) always the better way to address problems in E&M.
– dmckee♦
Sep 8 at 17:17
@dmckee I appreciate you at least discussing it. What you are objecting to, is exactly what I am objecting to. 90% of The books or comments (probably You too) always claim that interference can only be caused by a wave and that particles cannot explain this. I object to that and it can be proven otherwise. The status quo is very biased on this subject when it comes to photons. They claim duality but they don’t really visualize it.
– Bill Alsept
Sep 8 at 18:34
90% of books claim that classical particles can not explain interference which is exactly true. Photons are not classical particles. Photons are also not the complete quantum picture, as the represent unlocalized Fock states of the field with well defined momentum. That expansion is the correct one for asymptomatic states (i.e. the far field), but is not fully general. And you have repeatedly claimed that situation perfectly described by classical E&M have to be treated in terms of photons, which is simply not the case.
– dmckee♦
Sep 8 at 19:16
add a comment |Â
1
I know on S.E. it's blasphemous to seriously consider photons as real particles that propagate the energy of light. Sure everyone says duality but they don't mean it. A so called EM wave can easily be derived mathematically and physically based on individual photons. EM waves and fields can't even begin to be explained without incorporating many coherent photons. Photons will explain what your looking for, especially the propagation part.
– Bill Alsept
Sep 7 at 6:10
@Bill no one serious ever objects to using the photon picture in places where it makes sense, nor to claims that phenomena can be described in the photon picture. What I object to is any kind of absolutist suggested that photons is either (a) the only way or (b) always the better way to address problems in E&M.
– dmckee♦
Sep 8 at 17:17
@dmckee I appreciate you at least discussing it. What you are objecting to, is exactly what I am objecting to. 90% of The books or comments (probably You too) always claim that interference can only be caused by a wave and that particles cannot explain this. I object to that and it can be proven otherwise. The status quo is very biased on this subject when it comes to photons. They claim duality but they don’t really visualize it.
– Bill Alsept
Sep 8 at 18:34
90% of books claim that classical particles can not explain interference which is exactly true. Photons are not classical particles. Photons are also not the complete quantum picture, as the represent unlocalized Fock states of the field with well defined momentum. That expansion is the correct one for asymptomatic states (i.e. the far field), but is not fully general. And you have repeatedly claimed that situation perfectly described by classical E&M have to be treated in terms of photons, which is simply not the case.
– dmckee♦
Sep 8 at 19:16
1
1
I know on S.E. it's blasphemous to seriously consider photons as real particles that propagate the energy of light. Sure everyone says duality but they don't mean it. A so called EM wave can easily be derived mathematically and physically based on individual photons. EM waves and fields can't even begin to be explained without incorporating many coherent photons. Photons will explain what your looking for, especially the propagation part.
– Bill Alsept
Sep 7 at 6:10
I know on S.E. it's blasphemous to seriously consider photons as real particles that propagate the energy of light. Sure everyone says duality but they don't mean it. A so called EM wave can easily be derived mathematically and physically based on individual photons. EM waves and fields can't even begin to be explained without incorporating many coherent photons. Photons will explain what your looking for, especially the propagation part.
– Bill Alsept
Sep 7 at 6:10
@Bill no one serious ever objects to using the photon picture in places where it makes sense, nor to claims that phenomena can be described in the photon picture. What I object to is any kind of absolutist suggested that photons is either (a) the only way or (b) always the better way to address problems in E&M.
– dmckee♦
Sep 8 at 17:17
@Bill no one serious ever objects to using the photon picture in places where it makes sense, nor to claims that phenomena can be described in the photon picture. What I object to is any kind of absolutist suggested that photons is either (a) the only way or (b) always the better way to address problems in E&M.
– dmckee♦
Sep 8 at 17:17
@dmckee I appreciate you at least discussing it. What you are objecting to, is exactly what I am objecting to. 90% of The books or comments (probably You too) always claim that interference can only be caused by a wave and that particles cannot explain this. I object to that and it can be proven otherwise. The status quo is very biased on this subject when it comes to photons. They claim duality but they don’t really visualize it.
– Bill Alsept
Sep 8 at 18:34
@dmckee I appreciate you at least discussing it. What you are objecting to, is exactly what I am objecting to. 90% of The books or comments (probably You too) always claim that interference can only be caused by a wave and that particles cannot explain this. I object to that and it can be proven otherwise. The status quo is very biased on this subject when it comes to photons. They claim duality but they don’t really visualize it.
– Bill Alsept
Sep 8 at 18:34
90% of books claim that classical particles can not explain interference which is exactly true. Photons are not classical particles. Photons are also not the complete quantum picture, as the represent unlocalized Fock states of the field with well defined momentum. That expansion is the correct one for asymptomatic states (i.e. the far field), but is not fully general. And you have repeatedly claimed that situation perfectly described by classical E&M have to be treated in terms of photons, which is simply not the case.
– dmckee♦
Sep 8 at 19:16
90% of books claim that classical particles can not explain interference which is exactly true. Photons are not classical particles. Photons are also not the complete quantum picture, as the represent unlocalized Fock states of the field with well defined momentum. That expansion is the correct one for asymptomatic states (i.e. the far field), but is not fully general. And you have repeatedly claimed that situation perfectly described by classical E&M have to be treated in terms of photons, which is simply not the case.
– dmckee♦
Sep 8 at 19:16
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3 Answers
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7
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This answer is general, but too long for a comment.
When modeling physical behavior with mathematical functions one has to be clear:
Are we talking : a) mathematics creates reality or b)mathematics models reality.
a) is the platonic view and b) the realist view.
Under a) the predictive power of mathematics leads to questions as the ones above and they are answered by the other answers
Under b) one is not surprised by the underlying quantum mechanical level, that is modeled with a quantized maxwell equation, which eventually builds up the classical electrodynamics equations, as both depend on the same mathematics with different application. How the classical light description emerges from a confluence of probabilistic photons in quantum field theory is outlined here
Imo it is the realist view that physicists should have, using mathematics as a tool of modeling new data and asking questions of the theories that fit them. That is how science has progressed since the time of Newton.
A rough analogy for the classical electromagnetic wave:
If one maps a dry river bed mathematically, the shape of the water flow when it rains can be predicted immediately, long before the water reaches the bends. In a similar sense, Maxwell's equations map space time, and given the initial conditions (light beam) the "flow" is beautifully predictable.
answered Sep 7 at 3:52
anna v
151k7143431
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
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6
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You are (roughly speaking) correct that “in order to achieve propagation an E˙ or B˙ in one place must be capable of inducing a B˙ or E˙ in a different placeâ€Â. This can be seen directly in Maxwell’s equations.
Faradays law says $nabla times E = -dot B$. Note that the curl is a spatial derivative, and the dot is a time derivative. So a B field changing in time gives an E field changing in space. This introduces coupled changes over time and space.
Similarly with Ampere’s law.
answered Sep 7 at 2:06
Dale
60718
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3
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Looking at matter waves on a string: As long as the oscillations aren't too big, we get the wave equation for $f(x, t)$:
$$
fracpartial^2 fpartial t^2 = c^2fracpartial^2 fpartial x^2
$$
Your question applies to this equation just as well as it does to the equations of electricity and magnetism. Don't both the terms in this equation apply just to a single point? How can disturbances propagate through space without violating locality?
The key is to go back to the definition of a partial derivative:
$$
fracpartial f(x, t)partial x = lim_h to 0 fracf(x+h, t) - f(x,t)h
$$
Now this next bit is going to get a little hand-wavey, since that's the nature of this question. This partial derivative doesn't just care about $f$ at the point $(x,t)$. It also cares about the value of $f$ in a tiny, ever-shrinking neighborhood right around $x$. Similarly, the derivative $fracpartial^2 fpartial x^2$ cares about an arbitrarily small, but not point-like, neighborhood around $x$.
Suppose that we stop the shrinking of these neighborhoods at some point, so they have size $epsilon$. Then instead of behaving like a string, our model behaves like a bunch of point masses connected by springs of length $epsilon$. However, as $epsilon$ goes to 0, this behavior approximates that of a truly continuous string.
So the short version of this answer is that having spatial derivatives in your PDE is what allows things happening in one point in space to affect other points in space. This has something to do with derivatives existing in a strange twilight zone where, on one hand they are local, but on the other they care about change over spatial distance.
And spatial derivatives appear in Maxwell's equations in the terms $nablacdot E$, $nablacdot B$, $nablatimes E$, and $nablatimes B$, so it shouldn't be too much of a mystery that light travels through space.
answered Sep 7 at 2:52
Ricky Tensor
59616
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
This answer is general, but too long for a comment.
When modeling physical behavior with mathematical functions one has to be clear:
Are we talking : a) mathematics creates reality or b)mathematics models reality.
a) is the platonic view and b) the realist view.
Under a) the predictive power of mathematics leads to questions as the ones above and they are answered by the other answers
Under b) one is not surprised by the underlying quantum mechanical level, that is modeled with a quantized maxwell equation, which eventually builds up the classical electrodynamics equations, as both depend on the same mathematics with different application. How the classical light description emerges from a confluence of probabilistic photons in quantum field theory is outlined here
Imo it is the realist view that physicists should have, using mathematics as a tool of modeling new data and asking questions of the theories that fit them. That is how science has progressed since the time of Newton.
A rough analogy for the classical electromagnetic wave:
If one maps a dry river bed mathematically, the shape of the water flow when it rains can be predicted immediately, long before the water reaches the bends. In a similar sense, Maxwell's equations map space time, and given the initial conditions (light beam) the "flow" is beautifully predictable.
answered Sep 7 at 3:52
anna v
151k7143431
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
add a comment |Â
up vote
7
down vote
This answer is general, but too long for a comment.
When modeling physical behavior with mathematical functions one has to be clear:
Are we talking : a) mathematics creates reality or b)mathematics models reality.
a) is the platonic view and b) the realist view.
Under a) the predictive power of mathematics leads to questions as the ones above and they are answered by the other answers
Under b) one is not surprised by the underlying quantum mechanical level, that is modeled with a quantized maxwell equation, which eventually builds up the classical electrodynamics equations, as both depend on the same mathematics with different application. How the classical light description emerges from a confluence of probabilistic photons in quantum field theory is outlined here
Imo it is the realist view that physicists should have, using mathematics as a tool of modeling new data and asking questions of the theories that fit them. That is how science has progressed since the time of Newton.
A rough analogy for the classical electromagnetic wave:
If one maps a dry river bed mathematically, the shape of the water flow when it rains can be predicted immediately, long before the water reaches the bends. In a similar sense, Maxwell's equations map space time, and given the initial conditions (light beam) the "flow" is beautifully predictable.
answered Sep 7 at 3:52
anna v
151k7143431
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
add a comment |Â
up vote
7
down vote
up vote
7
down vote
This answer is general, but too long for a comment.
When modeling physical behavior with mathematical functions one has to be clear:
Are we talking : a) mathematics creates reality or b)mathematics models reality.
a) is the platonic view and b) the realist view.
Under a) the predictive power of mathematics leads to questions as the ones above and they are answered by the other answers
Under b) one is not surprised by the underlying quantum mechanical level, that is modeled with a quantized maxwell equation, which eventually builds up the classical electrodynamics equations, as both depend on the same mathematics with different application. How the classical light description emerges from a confluence of probabilistic photons in quantum field theory is outlined here
Imo it is the realist view that physicists should have, using mathematics as a tool of modeling new data and asking questions of the theories that fit them. That is how science has progressed since the time of Newton.
A rough analogy for the classical electromagnetic wave:
If one maps a dry river bed mathematically, the shape of the water flow when it rains can be predicted immediately, long before the water reaches the bends. In a similar sense, Maxwell's equations map space time, and given the initial conditions (light beam) the "flow" is beautifully predictable.
answered Sep 7 at 3:52
anna v
151k7143431
This answer is general, but too long for a comment.
When modeling physical behavior with mathematical functions one has to be clear:
Are we talking : a) mathematics creates reality or b)mathematics models reality.
a) is the platonic view and b) the realist view.
Under a) the predictive power of mathematics leads to questions as the ones above and they are answered by the other answers
Under b) one is not surprised by the underlying quantum mechanical level, that is modeled with a quantized maxwell equation, which eventually builds up the classical electrodynamics equations, as both depend on the same mathematics with different application. How the classical light description emerges from a confluence of probabilistic photons in quantum field theory is outlined here
Imo it is the realist view that physicists should have, using mathematics as a tool of modeling new data and asking questions of the theories that fit them. That is how science has progressed since the time of Newton.
A rough analogy for the classical electromagnetic wave:
If one maps a dry river bed mathematically, the shape of the water flow when it rains can be predicted immediately, long before the water reaches the bends. In a similar sense, Maxwell's equations map space time, and given the initial conditions (light beam) the "flow" is beautifully predictable.
answered Sep 7 at 3:52
anna v
151k7143431
answered Sep 7 at 3:52
anna v
151k7143431
answered Sep 7 at 3:52
anna v
151k7143431
answered Sep 7 at 3:52
anna v
151k7143431
151k7143431
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
add a comment |Â
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
regarding your last paragraph, would it be correct to say, we can replace "flow" with "the propagation of photons through space"?
– undefined
Sep 7 at 7:22
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
@undefined it s a qualitative analogy, so it depends how far you take it.
– anna v
Sep 7 at 7:29
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
I know, I meant it for my understanding of it
– undefined
Sep 7 at 8:22
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
"a) mathematics creates reality or b)mathematics models reality" - Well said.
– safesphere
Sep 7 at 16:07
add a comment |Â
up vote
6
down vote
You are (roughly speaking) correct that “in order to achieve propagation an E˙ or B˙ in one place must be capable of inducing a B˙ or E˙ in a different placeâ€Â. This can be seen directly in Maxwell’s equations.
Faradays law says $nabla times E = -dot B$. Note that the curl is a spatial derivative, and the dot is a time derivative. So a B field changing in time gives an E field changing in space. This introduces coupled changes over time and space.
Similarly with Ampere’s law.
answered Sep 7 at 2:06
Dale
60718
add a comment |Â
up vote
6
down vote
You are (roughly speaking) correct that “in order to achieve propagation an E˙ or B˙ in one place must be capable of inducing a B˙ or E˙ in a different placeâ€Â. This can be seen directly in Maxwell’s equations.
Faradays law says $nabla times E = -dot B$. Note that the curl is a spatial derivative, and the dot is a time derivative. So a B field changing in time gives an E field changing in space. This introduces coupled changes over time and space.
Similarly with Ampere’s law.
answered Sep 7 at 2:06
Dale
60718
add a comment |Â
up vote
6
down vote
up vote
6
down vote
You are (roughly speaking) correct that “in order to achieve propagation an E˙ or B˙ in one place must be capable of inducing a B˙ or E˙ in a different placeâ€Â. This can be seen directly in Maxwell’s equations.
Faradays law says $nabla times E = -dot B$. Note that the curl is a spatial derivative, and the dot is a time derivative. So a B field changing in time gives an E field changing in space. This introduces coupled changes over time and space.
Similarly with Ampere’s law.
answered Sep 7 at 2:06
Dale
60718
You are (roughly speaking) correct that “in order to achieve propagation an E˙ or B˙ in one place must be capable of inducing a B˙ or E˙ in a different placeâ€Â. This can be seen directly in Maxwell’s equations.
Faradays law says $nabla times E = -dot B$. Note that the curl is a spatial derivative, and the dot is a time derivative. So a B field changing in time gives an E field changing in space. This introduces coupled changes over time and space.
Similarly with Ampere’s law.
answered Sep 7 at 2:06
Dale
60718
answered Sep 7 at 2:06
Dale
60718
answered Sep 7 at 2:06
Dale
60718
answered Sep 7 at 2:06
Dale
60718
60718
add a comment |Â
add a comment |Â
up vote
3
down vote
Looking at matter waves on a string: As long as the oscillations aren't too big, we get the wave equation for $f(x, t)$:
$$
fracpartial^2 fpartial t^2 = c^2fracpartial^2 fpartial x^2
$$
Your question applies to this equation just as well as it does to the equations of electricity and magnetism. Don't both the terms in this equation apply just to a single point? How can disturbances propagate through space without violating locality?
The key is to go back to the definition of a partial derivative:
$$
fracpartial f(x, t)partial x = lim_h to 0 fracf(x+h, t) - f(x,t)h
$$
Now this next bit is going to get a little hand-wavey, since that's the nature of this question. This partial derivative doesn't just care about $f$ at the point $(x,t)$. It also cares about the value of $f$ in a tiny, ever-shrinking neighborhood right around $x$. Similarly, the derivative $fracpartial^2 fpartial x^2$ cares about an arbitrarily small, but not point-like, neighborhood around $x$.
Suppose that we stop the shrinking of these neighborhoods at some point, so they have size $epsilon$. Then instead of behaving like a string, our model behaves like a bunch of point masses connected by springs of length $epsilon$. However, as $epsilon$ goes to 0, this behavior approximates that of a truly continuous string.
So the short version of this answer is that having spatial derivatives in your PDE is what allows things happening in one point in space to affect other points in space. This has something to do with derivatives existing in a strange twilight zone where, on one hand they are local, but on the other they care about change over spatial distance.
And spatial derivatives appear in Maxwell's equations in the terms $nablacdot E$, $nablacdot B$, $nablatimes E$, and $nablatimes B$, so it shouldn't be too much of a mystery that light travels through space.
answered Sep 7 at 2:52
Ricky Tensor
59616
add a comment |Â
up vote
3
down vote
Looking at matter waves on a string: As long as the oscillations aren't too big, we get the wave equation for $f(x, t)$:
$$
fracpartial^2 fpartial t^2 = c^2fracpartial^2 fpartial x^2
$$
Your question applies to this equation just as well as it does to the equations of electricity and magnetism. Don't both the terms in this equation apply just to a single point? How can disturbances propagate through space without violating locality?
The key is to go back to the definition of a partial derivative:
$$
fracpartial f(x, t)partial x = lim_h to 0 fracf(x+h, t) - f(x,t)h
$$
Now this next bit is going to get a little hand-wavey, since that's the nature of this question. This partial derivative doesn't just care about $f$ at the point $(x,t)$. It also cares about the value of $f$ in a tiny, ever-shrinking neighborhood right around $x$. Similarly, the derivative $fracpartial^2 fpartial x^2$ cares about an arbitrarily small, but not point-like, neighborhood around $x$.
Suppose that we stop the shrinking of these neighborhoods at some point, so they have size $epsilon$. Then instead of behaving like a string, our model behaves like a bunch of point masses connected by springs of length $epsilon$. However, as $epsilon$ goes to 0, this behavior approximates that of a truly continuous string.
So the short version of this answer is that having spatial derivatives in your PDE is what allows things happening in one point in space to affect other points in space. This has something to do with derivatives existing in a strange twilight zone where, on one hand they are local, but on the other they care about change over spatial distance.
And spatial derivatives appear in Maxwell's equations in the terms $nablacdot E$, $nablacdot B$, $nablatimes E$, and $nablatimes B$, so it shouldn't be too much of a mystery that light travels through space.
answered Sep 7 at 2:52
Ricky Tensor
59616
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Looking at matter waves on a string: As long as the oscillations aren't too big, we get the wave equation for $f(x, t)$:
$$
fracpartial^2 fpartial t^2 = c^2fracpartial^2 fpartial x^2
$$
Your question applies to this equation just as well as it does to the equations of electricity and magnetism. Don't both the terms in this equation apply just to a single point? How can disturbances propagate through space without violating locality?
The key is to go back to the definition of a partial derivative:
$$
fracpartial f(x, t)partial x = lim_h to 0 fracf(x+h, t) - f(x,t)h
$$
Now this next bit is going to get a little hand-wavey, since that's the nature of this question. This partial derivative doesn't just care about $f$ at the point $(x,t)$. It also cares about the value of $f$ in a tiny, ever-shrinking neighborhood right around $x$. Similarly, the derivative $fracpartial^2 fpartial x^2$ cares about an arbitrarily small, but not point-like, neighborhood around $x$.
Suppose that we stop the shrinking of these neighborhoods at some point, so they have size $epsilon$. Then instead of behaving like a string, our model behaves like a bunch of point masses connected by springs of length $epsilon$. However, as $epsilon$ goes to 0, this behavior approximates that of a truly continuous string.
So the short version of this answer is that having spatial derivatives in your PDE is what allows things happening in one point in space to affect other points in space. This has something to do with derivatives existing in a strange twilight zone where, on one hand they are local, but on the other they care about change over spatial distance.
And spatial derivatives appear in Maxwell's equations in the terms $nablacdot E$, $nablacdot B$, $nablatimes E$, and $nablatimes B$, so it shouldn't be too much of a mystery that light travels through space.
answered Sep 7 at 2:52
Ricky Tensor
59616
Looking at matter waves on a string: As long as the oscillations aren't too big, we get the wave equation for $f(x, t)$:
$$
fracpartial^2 fpartial t^2 = c^2fracpartial^2 fpartial x^2
$$
Your question applies to this equation just as well as it does to the equations of electricity and magnetism. Don't both the terms in this equation apply just to a single point? How can disturbances propagate through space without violating locality?
The key is to go back to the definition of a partial derivative:
$$
fracpartial f(x, t)partial x = lim_h to 0 fracf(x+h, t) - f(x,t)h
$$
Now this next bit is going to get a little hand-wavey, since that's the nature of this question. This partial derivative doesn't just care about $f$ at the point $(x,t)$. It also cares about the value of $f$ in a tiny, ever-shrinking neighborhood right around $x$. Similarly, the derivative $fracpartial^2 fpartial x^2$ cares about an arbitrarily small, but not point-like, neighborhood around $x$.
Suppose that we stop the shrinking of these neighborhoods at some point, so they have size $epsilon$. Then instead of behaving like a string, our model behaves like a bunch of point masses connected by springs of length $epsilon$. However, as $epsilon$ goes to 0, this behavior approximates that of a truly continuous string.
So the short version of this answer is that having spatial derivatives in your PDE is what allows things happening in one point in space to affect other points in space. This has something to do with derivatives existing in a strange twilight zone where, on one hand they are local, but on the other they care about change over spatial distance.
And spatial derivatives appear in Maxwell's equations in the terms $nablacdot E$, $nablacdot B$, $nablatimes E$, and $nablatimes B$, so it shouldn't be too much of a mystery that light travels through space.
answered Sep 7 at 2:52
Ricky Tensor
59616
answered Sep 7 at 2:52
Ricky Tensor
59616
answered Sep 7 at 2:52
Ricky Tensor
59616
answered Sep 7 at 2:52
Ricky Tensor
59616
59616
add a comment |Â
add a comment |Â
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1
I know on S.E. it's blasphemous to seriously consider photons as real particles that propagate the energy of light. Sure everyone says duality but they don't mean it. A so called EM wave can easily be derived mathematically and physically based on individual photons. EM waves and fields can't even begin to be explained without incorporating many coherent photons. Photons will explain what your looking for, especially the propagation part.
– Bill Alsept
Sep 7 at 6:10
@Bill no one serious ever objects to using the photon picture in places where it makes sense, nor to claims that phenomena can be described in the photon picture. What I object to is any kind of absolutist suggested that photons is either (a) the only way or (b) always the better way to address problems in E&M.
– dmckee♦
Sep 8 at 17:17
@dmckee I appreciate you at least discussing it. What you are objecting to, is exactly what I am objecting to. 90% of The books or comments (probably You too) always claim that interference can only be caused by a wave and that particles cannot explain this. I object to that and it can be proven otherwise. The status quo is very biased on this subject when it comes to photons. They claim duality but they don’t really visualize it.
– Bill Alsept
Sep 8 at 18:34
90% of books claim that classical particles can not explain interference which is exactly true. Photons are not classical particles. Photons are also not the complete quantum picture, as the represent unlocalized Fock states of the field with well defined momentum. That expansion is the correct one for asymptomatic states (i.e. the far field), but is not fully general. And you have repeatedly claimed that situation perfectly described by classical E&M have to be treated in terms of photons, which is simply not the case.
– dmckee♦
Sep 8 at 19:16