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Science Forum Index » Physics - Electromagnetic Forum » Photon radiation from accelerating electrons?
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| Steersman |
 Posted: Wed Dec 13, 2006 2:06 pm |
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Guest
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It is commonly claimed that an electromagnetic model of the atom won't
work because electrons radiate energy under acceleration and would
therefore spiral into the nucleus. The general idea is that when an
electron is accelerated it radiates energy, increasing its inertia, and
hence increasing the work done during acceleration in order to provide
the extra energy for the released photic energy. As an aside, the
radiated energy is some power of acceleration, so this effect is only
seen at high accelerations.
The problem I have with this is that if you reverse the operation, and
decelerate an electron into your rest frame, the electron does not
differentiate between acceleration and deceleration, the latter being
simply acceleration in another direction. So during deceleration the
electron radiates, the inertia is increased, and so the work recovered
during deceleration is increased. Straight away you have violated the
conservation of energy since you get both the extra inertia and the
radiation. According to this theory, you could generate power by simply
bouncing an electron to and fro.
So as far as I can see, an electron cannot radiate under acceleration.
The escape of any energy (such as photons) from the system appears to
lead directly to violation of conservation.
There are a couple of related issues...
1. Bremsstrahlung - or braking radiation, seen in X-Ray sets, was once
thought to be due to this, but is now believed to be the result of fast
electrons interacting withn the fields inside atoms.
2. Maxwell's equations - are sometimes claimed to prove that electrons
radiate under acceleration, but they do not deal with moving
electrostatic fields with an inertial rest frame, merely changing
electric and magnetic fields with no rest frame.
3. The loss in energy as an electron spirals in a magnet is attributed
to this, but I have never seen the mathematical proofs, and it might
simply be driving a magnetic spin wave (a sort of propagating
precessing wave) along the surface of the magnetic poles.
Anyone got a proof of radiative loss under acceleration, that still
works under deceleration? |
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| Dave |
| Posted: Wed Dec 13, 2006 7:03 pm |
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of course decelerating electrons radiate. electrons moving in an antenna
under control of a sinusoidal current spend half their time accelerating and
half decelerating... but they radiate the whole sine wave.
the obvious answer is that electrons don't 'orbit' the nucleus in nice
little circles like you saw in models in elementary school.
"Steersman" <mwnsinger@yahoo.co.uk> wrote in message
news:1166033214.629347.18760@l12g2000cwl.googlegroups.com...
Quote: It is commonly claimed that an electromagnetic model of the atom won't
work because electrons radiate energy under acceleration and would
therefore spiral into the nucleus. The general idea is that when an
electron is accelerated it radiates energy, increasing its inertia, and
hence increasing the work done during acceleration in order to provide
the extra energy for the released photic energy. As an aside, the
radiated energy is some power of acceleration, so this effect is only
seen at high accelerations.
The problem I have with this is that if you reverse the operation, and
decelerate an electron into your rest frame, the electron does not
differentiate between acceleration and deceleration, the latter being
simply acceleration in another direction. So during deceleration the
electron radiates, the inertia is increased, and so the work recovered
during deceleration is increased. Straight away you have violated the
conservation of energy since you get both the extra inertia and the
radiation. According to this theory, you could generate power by simply
bouncing an electron to and fro.
So as far as I can see, an electron cannot radiate under acceleration.
The escape of any energy (such as photons) from the system appears to
lead directly to violation of conservation.
There are a couple of related issues...
1. Bremsstrahlung - or braking radiation, seen in X-Ray sets, was once
thought to be due to this, but is now believed to be the result of fast
electrons interacting withn the fields inside atoms.
2. Maxwell's equations - are sometimes claimed to prove that electrons
radiate under acceleration, but they do not deal with moving
electrostatic fields with an inertial rest frame, merely changing
electric and magnetic fields with no rest frame.
3. The loss in energy as an electron spirals in a magnet is attributed
to this, but I have never seen the mathematical proofs, and it might
simply be driving a magnetic spin wave (a sort of propagating
precessing wave) along the surface of the magnetic poles.
Anyone got a proof of radiative loss under acceleration, that still
works under deceleration?
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| dishington |
| Posted: Thu Dec 14, 2006 3:04 am |
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| Steersman |
| Posted: Thu Dec 14, 2006 12:31 pm |
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Antenna do not radiate because the electrons are accelerating. As the
electrons sweep up the antenna they induce a magnetic field; for a
vertical antenna this field will be horizontal. While the electrons are
near-stationary at the end of the anttenna the induced magnetic field
drops to zero, while the electric field between the ends of the antenna
reaches its maximum; in a vertical antenna this field will be vertical.
These orthogonal changing and alternating elecric and magnetic fields
generate Maxwellian radiation.
If antenna depended on electron acceleration, since according to the
theory any radiation is a power of the acceleration of the electrons,
there would not be any noticable radiation until the drive voltage to
the antenna reached several million volts.
Nor does the electron path affect the problem. Whatever the path, in a
relativistic universe where there is no special frame of reference, if
energy is lost from the system and the path may be traverse in the
opposite direction, there appears to be a violation of conservation.
Dave wrote:
Quote: of course decelerating electrons radiate. electrons moving in an antenna
under control of a sinusoidal current spend half their time accelerating and
half decelerating... but they radiate the whole sine wave.
the obvious answer is that electrons don't 'orbit' the nucleus in nice
little circles like you saw in models in elementary school.
"Steersman" <mwnsinger@yahoo.co.uk> wrote in message
news:1166033214.629347.18760@l12g2000cwl.googlegroups.com...
It is commonly claimed that an electromagnetic model of the atom won't
work because electrons radiate energy under acceleration and would
therefore spiral into the nucleus. The general idea is that when an
electron is accelerated it radiates energy, increasing its inertia, and
hence increasing the work done during acceleration in order to provide
the extra energy for the released photic energy. As an aside, the
radiated energy is some power of acceleration, so this effect is only
seen at high accelerations.
The problem I have with this is that if you reverse the operation, and
decelerate an electron into your rest frame, the electron does not
differentiate between acceleration and deceleration, the latter being
simply acceleration in another direction. So during deceleration the
electron radiates, the inertia is increased, and so the work recovered
during deceleration is increased. Straight away you have violated the
conservation of energy since you get both the extra inertia and the
radiation. According to this theory, you could generate power by simply
bouncing an electron to and fro.
So as far as I can see, an electron cannot radiate under acceleration.
The escape of any energy (such as photons) from the system appears to
lead directly to violation of conservation.
There are a couple of related issues...
1. Bremsstrahlung - or braking radiation, seen in X-Ray sets, was once
thought to be due to this, but is now believed to be the result of fast
electrons interacting withn the fields inside atoms.
2. Maxwell's equations - are sometimes claimed to prove that electrons
radiate under acceleration, but they do not deal with moving
electrostatic fields with an inertial rest frame, merely changing
electric and magnetic fields with no rest frame.
3. The loss in energy as an electron spirals in a magnet is attributed
to this, but I have never seen the mathematical proofs, and it might
simply be driving a magnetic spin wave (a sort of propagating
precessing wave) along the surface of the magnetic poles.
Anyone got a proof of radiative loss under acceleration, that still
works under deceleration?
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| Tom Roberts |
| Posted: Fri Dec 15, 2006 11:52 am |
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Steersman wrote:
Quote: It is commonly claimed that an electromagnetic model of the atom won't
work because electrons radiate energy under acceleration and would
therefore spiral into the nucleus. The general idea is that when an
electron is accelerated it radiates energy, increasing its inertia, and
hence increasing the work done during acceleration in order to provide
the extra energy for the released photic energy. As an aside, the
radiated energy is some power of acceleration, so this effect is only
seen at high accelerations.
Hmmm. For energy and momentum conservation to hold, it must occur for
any acceleration; it's just larger for larger accelerations.
Quote: The problem I have with this is that if you reverse the operation, and
decelerate an electron into your rest frame, the electron does not
differentiate between acceleration and deceleration, the latter being
simply acceleration in another direction. So during deceleration the
electron radiates, the inertia is increased, and so the work recovered
during deceleration is increased. Straight away you have violated the
conservation of energy since you get both the extra inertia and the
radiation. According to this theory, you could generate power by simply
bouncing an electron to and fro.
When you wave your hands, conservation laws hold only to the accuracy
with which you are waving.
Do a real computation, and you'll find energy is indeed conserved.
Note your notion of "extra inertia" seems singularly ill defined to me,
and for simple interpretations of it you got it backwards -- in
decelerating to your frame the electron will have LESS "inertia", not
more (interpreting "inertia" as momentum, or perhaps as "relativistic
mass").
The "inertia" of a charge can be considered to be larger than that of an
equal-mass neutral object in the following sense: if one pulls on them
with equal force, the charge will accelerate less because of the force
due to radiation reaction. But in physics the term "inertia" is rather
nebulous and poorly defined -- there is no quantity in the equations to
which it refers. For instance, in this case certainly the mass of the
two objects remains the same.
The phrase "inertial motion" _IS_ well defined. But beware:
in the context of GR it means something different than in the
context of SR and Newtonian mechanics (the GR meaning can be
applied to them, but not vice-versa).
Quote: So as far as I can see, an electron cannot radiate under acceleration.
The escape of any energy (such as photons) from the system appears to
lead directly to violation of conservation.
No. radiation is required in order to maintain conservation of energy
AND momentum.
Quote: Anyone got a proof of radiative loss under acceleration, that still
works under deceleration?
Look it up in Jackson.
The $.02 version is that for a moving charge observed from a distance L
in an inertial frame, the E field is pointed at the location of charge
right now (i.e. not where it was a time L/c ago). In essence the
velocity-dependent part of the field equation "extrapolates" the
position of the charge along an inertial path. A deviation of the charge
from that inertial path results in radiation, because at a time L/c
after the deviation the E field must suddenly change to point to the NEW
"extrapolation". Any deviation does this, including deceleration.
This is, of course, a classical explanation. A discussion using QED and
photons is quite a bit more complicated....
Tom Roberts |
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| Tom Roberts |
| Posted: Fri Dec 15, 2006 12:05 pm |
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Steersman wrote:
Quote: Antenna do not radiate because the electrons are accelerating.
Hmmm. Your description is seriously lacking.
Quote: As the
electrons sweep up the antenna they induce a magnetic field; [...]
Electrons do not "sweep up the antenna" -- for metals at room
temperature the electron drift velocity is on the order of centimeters
per second, and for frequencies of kilo- or mega-Hertz they obviously
cannot move very far at all. Rather, this is a collective phenomenon,
and the sinusoidal E field in the wire/antenna pushes the electrons
around a few microns. The reason this results in macroscopic amounts of
energy being radiated is that there are a lot of them -- Avogadro's
number is enormous.
Ultimately the radiation is indeed due to all those many electrons being
accelerated by very small amounts.
Tom Roberts |
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| Steersman |
| Posted: Fri Dec 15, 2006 2:08 pm |
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Tom Roberts wrote:
Quote: Electrons do not "sweep up the antenna" -- for metals at room
temperature the electron drift velocity is on the order of centimeters
per second, and for frequencies of kilo- or mega-Hertz they obviously
- true, I was attempting to simplify the explanation. It is indeed the
net current flowing along the dipole that generates the Maxwellian
magnetic field during the current phases, and the voltage across the
dipole ends that generates the electric field 90 degrees later in the
cycle when the voltage is at its peak and the current is zero.
Quote: Ultimately the radiation is indeed due to all those many electrons being
accelerated by very small amounts.
Sorry, no. The electrons obviously have to accelerate linearily
dependent on drive voltage (with the obvious caveat you mentioned)
since they are moving up and down the dipole. This makes electron
acceleration proportional to the square root of antenna power. The
equations I have seen state that radiation energy is dependent on the
third power of acceleration (and is significant only at extremely high
energies) which implies that the output power would be proportional to
the sixth power of drive voltage. This is not the case. The magnetic
field energy is proportional to the square of the field strength and
hence to the square of the current. The electric field energy is
proportional to the square of the electric field strength, and hence to
the square of the voltage. Simple Faraday electromagnetics is
sufficient to explain the operation of an antenna. |
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| Steersman |
| Posted: Fri Dec 15, 2006 2:29 pm |
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Tom Roberts wrote:
Quote: When you wave your hands, conservation laws hold only to the accuracy
with which you are waving.
Surely conservation laws hold absolutely?
Quote: Note your notion of "extra inertia" seems singularly ill defined to me,
Sorry if I was unclear. In the theory I have read, work is required to
both accelerate the electron, and to generate the photic radiation.
This work appears as an increased inertia for both effects, forcing the
driving mechanism to input more work during acceleration. Specifically,
the extra energy for the radiation presents as an increased inertia. I
am using the term inertia in its original concept of "resistance to
acceleration", rather than relating it to "inertial mass".
Quote: and for simple interpretations of it you got it backwards -- in
decelerating to your frame the electron will have LESS "inertia", not
more (interpreting "inertia" as momentum, or perhaps as "relativistic
mass").
I'm not clear on your input here, I'm afraid. In a relativistic
universe with no special frame of reference, the electron can not
differentiate deceleration into my frame from acceleration from
another, so will still radiate, and still present an increased inertia,
thus violating conservation.
Quote: The $.02 version is that for a moving charge observed from a distance L
in an inertial frame, the E field is pointed at the location of charge
right now (i.e. not where it was a time L/c ago). In essence the
velocity-dependent part of the field equation "extrapolates" the
position of the charge along an inertial path. A deviation of the charge
from that inertial path results in radiation, because at a time L/c
after the deviation the E field must suddenly change to point to the NEW
"extrapolation". Any deviation does this, including deceleration.
That deceleration issue is exactly the problem. |
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| Steersman |
| Posted: Fri Dec 15, 2006 2:54 pm |
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| Neil Bates |
| Posted: Sun Dec 24, 2006 8:47 pm |
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"Steersman" <mwnsinger@yahoo.co.uk> wrote in message
news:1166033214.629347.18760@l12g2000cwl.googlegroups.com...
Quote: It is commonly claimed that an electromagnetic model of the atom won't
work because electrons radiate energy under acceleration and would
therefore spiral into the nucleus. The general idea is that when an
electron is accelerated it radiates energy, increasing its inertia, and
hence increasing the work done during acceleration in order to provide
the extra energy for the released photic energy. As an aside, the
radiated energy is some power of acceleration, so this effect is only
seen at high accelerations.
The problem I have with this is that if you reverse the operation, and
decelerate an electron into your rest frame, the electron does not
differentiate between acceleration and deceleration, the latter being
simply acceleration in another direction. So during deceleration the
electron radiates, the inertia is increased, and so the work recovered
during deceleration is increased. Straight away you have violated the
conservation of energy since you get both the extra inertia and the
radiation. According to this theory, you could generate power by simply
bouncing an electron to and fro.
....
Much of your problem with this is due to not appreciating the role of the
"self-force" in radiation. Acceleration and deceleration act only on the
effective mass, regardless of how much of that is "electromagnetic in
origin." The radiative field of course does not distinguish between relative
acceration and deceleration. However, the force f_rad hat makes work
necessary to compensate for the radiation actually depends on changes in
acceleration: f_rad = 2kq^2(da/dt)/3c^3. That will slow down the electron
during say simple harmonic motion (play with the derivatives of A = A_0 (sin
omega t), and see the f_rad opposing the velocity.)
See what you think of this: "The paradox of the extra momentum exerted on a
wiggler by a photon-emitting atom", below this question.
Well, this got stuck in my outbox for awhile...Merry Christmas or what you
please.... |
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