Why do electromagnetic waves have the magnetic and electric field intensities in the same phase?
$begingroup$
My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the changing magnetic field generates the electric field and the changing electric field generates the magnetic field, so according to my opinion if the accelerating electron generates a sine electric field change, then its magnetic field should be a cosine function because $frac{d(sin x)}{dx}=cos x$.
electromagnetic-radiation
edited 14 hours ago
David Z♦
63.5k23136252
asked 20 hours ago
Bálint TataiBálint Tatai
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$
add a comment |
$begingroup$
My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the changing magnetic field generates the electric field and the changing electric field generates the magnetic field, so according to my opinion if the accelerating electron generates a sine electric field change, then its magnetic field should be a cosine function because $frac{d(sin x)}{dx}=cos x$.
electromagnetic-radiation
edited 14 hours ago
David Z♦
63.5k23136252
asked 20 hours ago
Bálint TataiBálint Tatai
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
"changing magnetic field generates the electric field and the changing electric field generates the magnetic field" - I think this is misleading. Maxwell's equations aren't statements of cause and effect. Although we talk about one field changing inducing another, they happen at the same time. An increasing magnetic field doesn't really cause a curl to exist in the electric field, they are physically the same - an increasing magnetic field cannot exist without the curl in the electric field.
$endgroup$
– andars
13 hours ago
$begingroup$
It's worth stating clearly that the in-phase nature of the waves is true in the far field (i.e. when the waves are examined much farther from the source than the size of the source), but that this is not the case in the near field (i.e. when you are close to the source).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
Note that for standing waves E and B are out of phase.
$endgroup$
– my2cts
11 hours ago
$begingroup$
@my2cts, i do not believe you meant what you wrote, just think of an open ended (or short circuited) transmission line.
$endgroup$
– hyportnex
3 hours ago
add a comment |
$begingroup$
My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the changing magnetic field generates the electric field and the changing electric field generates the magnetic field, so according to my opinion if the accelerating electron generates a sine electric field change, then its magnetic field should be a cosine function because $frac{d(sin x)}{dx}=cos x$.
electromagnetic-radiation
edited 14 hours ago
David Z♦
63.5k23136252
asked 20 hours ago
Bálint TataiBálint Tatai
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the changing magnetic field generates the electric field and the changing electric field generates the magnetic field, so according to my opinion if the accelerating electron generates a sine electric field change, then its magnetic field should be a cosine function because $frac{d(sin x)}{dx}=cos x$.
electromagnetic-radiation
electromagnetic-radiation
edited 14 hours ago
David Z♦
63.5k23136252
asked 20 hours ago
Bálint TataiBálint Tatai
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 14 hours ago
David Z♦
63.5k23136252
asked 20 hours ago
Bálint TataiBálint Tatai
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 14 hours ago
David Z♦
63.5k23136252
edited 14 hours ago
David Z♦
63.5k23136252
edited 14 hours ago
David Z♦
63.5k23136252
63.5k23136252
asked 20 hours ago
Bálint TataiBálint Tatai
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 20 hours ago
Bálint TataiBálint Tatai
541
asked 20 hours ago
Bálint TataiBálint Tatai
541
541
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Bálint Tatai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
"changing magnetic field generates the electric field and the changing electric field generates the magnetic field" - I think this is misleading. Maxwell's equations aren't statements of cause and effect. Although we talk about one field changing inducing another, they happen at the same time. An increasing magnetic field doesn't really cause a curl to exist in the electric field, they are physically the same - an increasing magnetic field cannot exist without the curl in the electric field.
$endgroup$
– andars
13 hours ago
$begingroup$
It's worth stating clearly that the in-phase nature of the waves is true in the far field (i.e. when the waves are examined much farther from the source than the size of the source), but that this is not the case in the near field (i.e. when you are close to the source).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
Note that for standing waves E and B are out of phase.
$endgroup$
– my2cts
11 hours ago
$begingroup$
@my2cts, i do not believe you meant what you wrote, just think of an open ended (or short circuited) transmission line.
$endgroup$
– hyportnex
3 hours ago
add a comment |
1
$begingroup$
"changing magnetic field generates the electric field and the changing electric field generates the magnetic field" - I think this is misleading. Maxwell's equations aren't statements of cause and effect. Although we talk about one field changing inducing another, they happen at the same time. An increasing magnetic field doesn't really cause a curl to exist in the electric field, they are physically the same - an increasing magnetic field cannot exist without the curl in the electric field.
$endgroup$
– andars
13 hours ago
$begingroup$
It's worth stating clearly that the in-phase nature of the waves is true in the far field (i.e. when the waves are examined much farther from the source than the size of the source), but that this is not the case in the near field (i.e. when you are close to the source).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
Note that for standing waves E and B are out of phase.
$endgroup$
– my2cts
11 hours ago
$begingroup$
@my2cts, i do not believe you meant what you wrote, just think of an open ended (or short circuited) transmission line.
$endgroup$
– hyportnex
3 hours ago
1
1
$begingroup$
"changing magnetic field generates the electric field and the changing electric field generates the magnetic field" - I think this is misleading. Maxwell's equations aren't statements of cause and effect. Although we talk about one field changing inducing another, they happen at the same time. An increasing magnetic field doesn't really cause a curl to exist in the electric field, they are physically the same - an increasing magnetic field cannot exist without the curl in the electric field.
$endgroup$
– andars
13 hours ago
$begingroup$
"changing magnetic field generates the electric field and the changing electric field generates the magnetic field" - I think this is misleading. Maxwell's equations aren't statements of cause and effect. Although we talk about one field changing inducing another, they happen at the same time. An increasing magnetic field doesn't really cause a curl to exist in the electric field, they are physically the same - an increasing magnetic field cannot exist without the curl in the electric field.
$endgroup$
– andars
13 hours ago
$begingroup$
It's worth stating clearly that the in-phase nature of the waves is true in the far field (i.e. when the waves are examined much farther from the source than the size of the source), but that this is not the case in the near field (i.e. when you are close to the source).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
It's worth stating clearly that the in-phase nature of the waves is true in the far field (i.e. when the waves are examined much farther from the source than the size of the source), but that this is not the case in the near field (i.e. when you are close to the source).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
Note that for standing waves E and B are out of phase.
$endgroup$
– my2cts
11 hours ago
$begingroup$
Note that for standing waves E and B are out of phase.
$endgroup$
– my2cts
11 hours ago
$begingroup$
@my2cts, i do not believe you meant what you wrote, just think of an open ended (or short circuited) transmission line.
$endgroup$
– hyportnex
3 hours ago
$begingroup$
@my2cts, i do not believe you meant what you wrote, just think of an open ended (or short circuited) transmission line.
$endgroup$
– hyportnex
3 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The Maxwell equations that relate electric and magnetic fields to each other read (in vacuum, in SI units) as
begin{align}
nabla times mathbf E & = -frac{partialmathbf B}{partial t} \
nabla times mathbf B & = frac{1}{c^2} frac{partialmathbf E}{partial t},
end{align}
where the notation $nabla times{cdot}$ is a spatial derivative (the curl). This means that both sides have derivatives, and if you're applying them to a function like $cos(kx-omega t)$, then they will both change the cosine into a sine. This is what locks the phase of both waves to equal values.
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
$endgroup$
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
add a comment |
$begingroup$
This is one of those 'why' questions that physics can or cannot answer, depending on what you want from answer to 'why'.
If equations are a satisfactory explanation, then the Maxwells Equation in Emilios answer are a complete answer.
Unfortunately, not far beneath the surface of that answer is 'why do Maxwells Equations' fit reality?' or 'why do fields behave the way they do so that we can derive Maxwells Equations?'. Wigner along with many other physicists was similarly troubled by such questions.
It doesn't get any more intuitive if you go down further to QED to try to explain the classical behaviour.
At the lowest level, the answer is 'that's the way Nature behaves'.
answered 11 hours ago
Neil_UKNeil_UK
1425
$endgroup$
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The Maxwell equations that relate electric and magnetic fields to each other read (in vacuum, in SI units) as
begin{align}
nabla times mathbf E & = -frac{partialmathbf B}{partial t} \
nabla times mathbf B & = frac{1}{c^2} frac{partialmathbf E}{partial t},
end{align}
where the notation $nabla times{cdot}$ is a spatial derivative (the curl). This means that both sides have derivatives, and if you're applying them to a function like $cos(kx-omega t)$, then they will both change the cosine into a sine. This is what locks the phase of both waves to equal values.
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
$endgroup$
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
add a comment |
$begingroup$
The Maxwell equations that relate electric and magnetic fields to each other read (in vacuum, in SI units) as
begin{align}
nabla times mathbf E & = -frac{partialmathbf B}{partial t} \
nabla times mathbf B & = frac{1}{c^2} frac{partialmathbf E}{partial t},
end{align}
where the notation $nabla times{cdot}$ is a spatial derivative (the curl). This means that both sides have derivatives, and if you're applying them to a function like $cos(kx-omega t)$, then they will both change the cosine into a sine. This is what locks the phase of both waves to equal values.
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
$endgroup$
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
add a comment |
$begingroup$
The Maxwell equations that relate electric and magnetic fields to each other read (in vacuum, in SI units) as
begin{align}
nabla times mathbf E & = -frac{partialmathbf B}{partial t} \
nabla times mathbf B & = frac{1}{c^2} frac{partialmathbf E}{partial t},
end{align}
where the notation $nabla times{cdot}$ is a spatial derivative (the curl). This means that both sides have derivatives, and if you're applying them to a function like $cos(kx-omega t)$, then they will both change the cosine into a sine. This is what locks the phase of both waves to equal values.
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
$endgroup$
The Maxwell equations that relate electric and magnetic fields to each other read (in vacuum, in SI units) as
begin{align}
nabla times mathbf E & = -frac{partialmathbf B}{partial t} \
nabla times mathbf B & = frac{1}{c^2} frac{partialmathbf E}{partial t},
end{align}
where the notation $nabla times{cdot}$ is a spatial derivative (the curl). This means that both sides have derivatives, and if you're applying them to a function like $cos(kx-omega t)$, then they will both change the cosine into a sine. This is what locks the phase of both waves to equal values.
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
answered 20 hours ago
Emilio PisantyEmilio Pisanty
83.6k22203419
83.6k22203419
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
add a comment |
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
Just to comment with my comment on the questions, this explanation works nicely if spatial arrangement of the fields is uniform enough (as in a plane wave, which is to say in he far-field), but misses important details if the wave has a no-planar structure (as in the near-field).
$endgroup$
– dmckee♦
12 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
$begingroup$
@dmckee Oh, absolutely. And indeed if you don't have a plane wave (which can mean that you have anything from a near-field to something as sophisticated as the superposition of two plane waves) then the fields are not required to be (strictly) orthogonal to each other or to the propagation direction. Hence the "if..." in this answer.
$endgroup$
– Emilio Pisanty
11 hours ago
add a comment |
$begingroup$
This is one of those 'why' questions that physics can or cannot answer, depending on what you want from answer to 'why'.
If equations are a satisfactory explanation, then the Maxwells Equation in Emilios answer are a complete answer.
Unfortunately, not far beneath the surface of that answer is 'why do Maxwells Equations' fit reality?' or 'why do fields behave the way they do so that we can derive Maxwells Equations?'. Wigner along with many other physicists was similarly troubled by such questions.
It doesn't get any more intuitive if you go down further to QED to try to explain the classical behaviour.
At the lowest level, the answer is 'that's the way Nature behaves'.
answered 11 hours ago
Neil_UKNeil_UK
1425
$endgroup$
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
add a comment |
$begingroup$
This is one of those 'why' questions that physics can or cannot answer, depending on what you want from answer to 'why'.
If equations are a satisfactory explanation, then the Maxwells Equation in Emilios answer are a complete answer.
Unfortunately, not far beneath the surface of that answer is 'why do Maxwells Equations' fit reality?' or 'why do fields behave the way they do so that we can derive Maxwells Equations?'. Wigner along with many other physicists was similarly troubled by such questions.
It doesn't get any more intuitive if you go down further to QED to try to explain the classical behaviour.
At the lowest level, the answer is 'that's the way Nature behaves'.
answered 11 hours ago
Neil_UKNeil_UK
1425
$endgroup$
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
add a comment |
$begingroup$
This is one of those 'why' questions that physics can or cannot answer, depending on what you want from answer to 'why'.
If equations are a satisfactory explanation, then the Maxwells Equation in Emilios answer are a complete answer.
Unfortunately, not far beneath the surface of that answer is 'why do Maxwells Equations' fit reality?' or 'why do fields behave the way they do so that we can derive Maxwells Equations?'. Wigner along with many other physicists was similarly troubled by such questions.
It doesn't get any more intuitive if you go down further to QED to try to explain the classical behaviour.
At the lowest level, the answer is 'that's the way Nature behaves'.
answered 11 hours ago
Neil_UKNeil_UK
1425
$endgroup$
This is one of those 'why' questions that physics can or cannot answer, depending on what you want from answer to 'why'.
If equations are a satisfactory explanation, then the Maxwells Equation in Emilios answer are a complete answer.
Unfortunately, not far beneath the surface of that answer is 'why do Maxwells Equations' fit reality?' or 'why do fields behave the way they do so that we can derive Maxwells Equations?'. Wigner along with many other physicists was similarly troubled by such questions.
It doesn't get any more intuitive if you go down further to QED to try to explain the classical behaviour.
At the lowest level, the answer is 'that's the way Nature behaves'.
answered 11 hours ago
Neil_UKNeil_UK
1425
edited 9 hours ago
answered 11 hours ago
Neil_UKNeil_UK
1425
answered 11 hours ago
Neil_UKNeil_UK
1425
answered 11 hours ago
Neil_UKNeil_UK
1425
1425
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
add a comment |
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
Lower level physical theories can describe why, but I don't think any where put forth outside if either theories because at the time of Maxwell the atom hadn't yet been proven or shown necessary. Gravitation and any field theories had this problem. I think in general everyone supposed the mechanisms describing these fields, happen on scales far to small, and for all they knew possibly fundamental to reality. Then quantum came along and were all taught to not try and describe these mechanisms. Simply by the words of Feynman that it is impossible to understand.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
And here we are today, no further really have we progressed it seems. Further it is maybe just as interesting to ask why nobody considers this? Perhaps for the pure sport of it alone, why nobody has framed wiled hypothesis as to the mechanisms underlying fields?
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
But from an abstract math perspective, chaos, infinitely complicated systems i guess are more interesting. Maybe they all know and don't say, that we need to be able to handle insanely complex, large systems and discover abstract principles which emerge at large scales, to get ahead of the curve.
$endgroup$
– marshal craft
10 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
$begingroup$
This refusal of even an attempt of a deeper understanding is unsatisfying. A mathematical formula, such as given by Emilio, is nothing but an insight cast into a strict notational form. Only by understanding the formula and the insight it communicates do we obtain a true mental grasp of a matter which allows us to mentally proceed on our own.
$endgroup$
– Peter A. Schneider
4 hours ago
add a comment |
Bálint Tatai is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
"changing magnetic field generates the electric field and the changing electric field generates the magnetic field" - I think this is misleading. Maxwell's equations aren't statements of cause and effect. Although we talk about one field changing inducing another, they happen at the same time. An increasing magnetic field doesn't really cause a curl to exist in the electric field, they are physically the same - an increasing magnetic field cannot exist without the curl in the electric field.
$endgroup$
– andars
13 hours ago
$begingroup$
It's worth stating clearly that the in-phase nature of the waves is true in the far field (i.e. when the waves are examined much farther from the source than the size of the source), but that this is not the case in the near field (i.e. when you are close to the source).
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– dmckee♦
12 hours ago
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Note that for standing waves E and B are out of phase.
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– my2cts
11 hours ago
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@my2cts, i do not believe you meant what you wrote, just think of an open ended (or short circuited) transmission line.
$endgroup$
– hyportnex
3 hours ago