How does classical fail in here

[atom888]

if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus.

Can someone give more details how this happens?

 

[peter0302]

A moving charge such as an electron emits electromagnetic radiation as it undergoes acceleration. If the electron were orbiting the nucleus like a planet, the centrifugual force would thus cause such radiation. The energy has to come from somewhere, i.e., the potential energy - distance - between the electron and the nucleus, causing the electron to spiral toward the nucleus continually until it collided.

Does that make sense?

 

[atom888]

A moving charge such as an electron emits electromagnetic radiation as it undergoes acceleration.

Does that make sense?

by this do you mean it emits some kind of wave silimar to radio, gama, micro, light... if undergoes acceleration? If that is the case, then : This is a centipital force we're talking about (hence require no energy for this kind acceleration), therefore, it shouldn't emit anything and thus not violation energy conservation.

 

[peter0302]

An object orbiting clasically is always undergoing acceleration in some dimension.

 

[malawi_glenn]

atom888, charges that is accelerated radiates EM - this energy must come from somewhere. If the atom was a classical orbiatal system, them it must, as peter0302 be more and more bound and eventually enter the nucleus.

This thing happens in circular accelerator, one looses some of the energy of the electron, and that has to be supplied by some devices (called RF cativities). The energy is lost by EM-radiation, which is called synchrotron radiation Here you can read more about this:

http://en.wikipedia.org/wiki/Synchrotron_radiation
http://uw.physics.wisc.edu/~himpsel/synrad.html
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/synchrotron.html

Here is something about circular accelerators:

http://nobelprize.org/educational_games/physics/accelerators/light-1.html
http://en.wikipedia.org/wiki/Particle_accelerator

So this is a true classical analogy of the planet-orbit-atom picture. So sorry atom888... the planet-orbit-atom picture is still invalid :-)

If you want very good overview reading material with lots of pictures of accelerators, send me a personal message and I'll send it to you,

 

[atom888]

atom888, charges that is accelerated radiates EM - this energy must come from somewhere. If the atom was a classical orbiatal system, them it must, as peter0302 be more and more bound and eventually enter the nucleus.

This thing happens in circular accelerator, one looses some of the energy of the electron, and that has to be supplied by some devices (called RF cativities). The energy is lost by EM-radiation, which is called synchrotron radiation Here you can read more about this:

http://en.wikipedia.org/wiki/Synchrotron_radiation
http://uw.physics.wisc.edu/~himpsel/synrad.html
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/synchrotron.html

Here is something about circular accelerators:

http://nobelprize.org/educational_games/physics/accelerators/light-1.html
http://en.wikipedia.org/wiki/Particle_accelerator

So this is a true classical analogy of the planet-orbit-atom picture. So sorry atom888... the planet-orbit-atom picture is still invalid :-)

If you want very good overview reading material with lots of pictures of accelerators, send me a personal message and I'll send it to you,

Thx glenn. It's not that I refuse to buy it. It is just that I need something solid evident like radiation lost in the accelerator dual to CENTRIPETAL accerlation. I'm trying to do a fast paste on physics so the best way is to ask and read about it simultaneously. I'll look up your reference. Thx again.

 

[malawi_glenn]

All electric charges radiates EM when acceleratred, understanding the proof for that requires the very highest undergraduate courses in electrodynamics.

Also in a book of classical electrodynamics (c.f Jackson, wiley) you can find how to derive the forumulas for how much the electron looses energy per turn for a given energy and a given radius.

So perhaps this 'solid' evidence will wait until you are ready for heavy physics ;-)

But the most fundamental is that acceleration = $$\frac{d^2\vec{r}}{dt^2}$$, where $$\vec{r}$$ is the position vector. You should go back to the textbook where centripetal acceleration was derived.

 

[peter0302]

atom888, is your question why centripetal movement means acceleration? Look at it this way. An object in orbit is constantly being pulled the central object. Its own inertia in the orthogonal direction, however, balances out the attractive force, resulting in a circular or elliptical orbit. But if you take _any_ arbitrary direction as an axis, the object's velocity in that direction is never constant; hence, it's always undergoing acceleration in some direction.

 

[atom888]

atom888, is your question why centripetal movement means acceleration? Look at it this way. An object in orbit is constantly being pulled the central object. Its own inertia in the orthogonal direction, however, balances out the attractive force, resulting in a circular or elliptical orbit. But if you take _any_ arbitrary direction as an axis, the object's velocity in that direction is never constant; hence, it's always undergoing acceleration in some direction.

I know acceleration occur in circular motion. My point is in linear accerlation, it require energy. In circular accerlation, it doesn't require energy.

Glenn, I have read over your sources. It's disappointing that synchro radiation go in tamdem with a magnetic field. It still not proving my point. :(

 

[peter0302]

Well, that's true, an ideal circular orbit does not require energy, if an orbiting object were to do any work with its angular momentum, it would lose some energy and start to spiral towar the object it's orbiting. It's just a property of charged objects that they emit photons when they accelerate; that energy has to come from somewhere.

 

[atom888]

Well, that's true, an ideal circular orbit does not require energy, if an orbiting object were to do any work with its angular momentum, it would lose some energy and start to spiral towar the object it's orbiting. It's just a property of charged objects that they emit photons when they accelerate; that energy has to come from somewhere.

I can't agree with you any less. If it is a property of charged object the energy would have come from somewhere and thus it will spiral to the nucleus.

My only concern left now is the question "is it a property of a charge object?" Right now so far I got:

1 accelerating charge in linear + 0 magnetic field = radiation (makes sense)
2 accelerating charge in linear + magneticfield = radiation (sure)
3 accererating charge in circular + magneticfield = radiation
4 accelerating charge in circular + 0 magnetic field = ?

It's not so easy to make electron move in circular without a magnetic field, there for it's hard to determine the answer to 4

 

[peter0302]

What part do you not agree with?

 

[DavidWhitbeck]

atom888-- Coulomb's Law is mathematically the same as Newton's Law of Gravitation (inverse squared law). Newton's Law predicts closed orbits, so then should Coulomb's Law.

Consider then an electron orbiting a proton. The direction of the electric force exerted by the proton on the electron is always directed inwards towards the proton. But the position of the electron is continuously changing in time, and thus the direction between them.

That means that the electric force the electron experiences is continuously changing in time.

A changing electric field induces a magnetic field.

So do you still think that there is no magnetic field?

 

[atom888]

atom888-- Coulomb's Law is mathematically the same as Newton's Law of Gravitation (inverse squared law). Newton's Law predicts closed orbits, so then should Coulomb's Law.

Consider then an electron orbiting a proton. The direction of the electric force exerted by the proton on the electron is always directed inwards towards the proton. But the position of the electron is continuously changing in time, and thus the direction between them.

That means that the electric force the electron experiences is continuously changing in time.

A changing electric field induces a magnetic field.

So do you still think that there is no magnetic field?

If you put it that way I have to agree. A changing electric field cause a magnetic field while a changing gravitational field cause jack. That probably is the reason.

 

[malawi_glenn]

I know acceleration occur in circular motion. My point is in linear accerlation, it require energy. In circular accerlation, it doesn't require energy.

Glenn, I have read over your sources. It's disappointing that synchro radiation go in tamdem with a magnetic field. It still not proving my point. :(

You must add energy in order get the electrons moving(linear/tangential motion), and that you do by having RF cavites that make sure that the electron always see a positve charge in front of him, and a negative charge behind him. Then in order go get a circular path, you apply a magnetic field and now the electron obeys the lorentz force law: [tex] \vec{F} = e(\vec{E} + \vec{v}+\vec{B}). Now you increase the E, more and more, and that makes you either increase the |B| or the radius of the circular path. BUT since the electron will

And what do you mean: "its not proving my point"?

If you want the real, heavy stuff, go to Jackson: https://www.amazon.com/dp/047130932X/?tag=pfamazon01-20
It is page 661 in the second edition of this book.

 

[monish]

atom888-- Coulomb's Law is mathematically the same as Newton's Law of Gravitation (inverse squared law). Newton's Law predicts closed orbits, so then should Coulomb's Law.

Consider then an electron orbiting a proton. The direction of the electric force exerted by the proton on the electron is always directed inwards towards the proton. But the position of the electron is continuously changing in time, and thus the direction between them.

That means that the electric force the electron experiences is continuously changing in time.

A changing electric field induces a magnetic field.

So do you still think that there is no magnetic field?

Your argument is a little unfair. The only electric field that's changing in time is the one created by the electron itself. It's hard to see how this creates a magnetic field that then acts back on the same electron. Atom888 was making a pretty good point: it's hard to see where the energy comes from to create radiation when all the forces are perpendicular to the direction of motion. That's why I call your answer a bit unfair: I don't think it deals with this essential point.

The fact of the matter is that it's really hard to understand why an accelerating charge should radiate energy in any situation, with or without magnetic fields present, parallel or perpendicular to the direction of the field. I don't believe this phenomenon is usually derived at the undergraduate level and I'm not aware of a really good explanation of why it happens.

 

[reilly]

It'd been well known for more-or-less than a century that an accelerating charge necessarily radiates, and hence creates an energy loss mechanism. You want to look up the Leonard-Weichart potentials, the basis of all classical radiation physics, from radar to accelerators. The quantum version, gives an entirely different picture in practice, but is based on the same Green's functions as in classical physics. There are no mysteries here: both classical and radiation theories work extraordinarily well. Do a Google, you will find thousands of listing for the L-W potentials.



The energy? Simply the kinetic energy of the charge in an orbital situation.
Regards,
Reilly Atkinson

 

[DavidWhitbeck]

Your argument is a little unfair. The only electric field that's changing in time is the one created by the electron itself.

You seem to be assuming that the proton is stationary, it's not. Newton's 3rd Law applies here. No self-force needed. The motion of the proton is not much, but it doesn't have to be, it just has to be non-zero.

But the force doesn't point where the proton is, it points where it was (and vica versa), retarded by time delay (relativity to the rescue!) and so the force is not centripetal, but has a tangential component as a consequence, which is why it can lose energy.

Your post was insightful, and I thought more about it, and I hope that's right.

 

[monish]

You seem to be assuming that the proton is stationary, it's not. Newton's 3rd Law applies here. No self-force needed. The motion of the proton is not much, but it doesn't have to be, it just has to be non-zero.

But the force doesn't point where the proton is, it points where it was (and vica versa), retarded by time delay (relativity to the rescue!) and so the force is not centripetal, but has a tangential component as a consequence, which is why it can lose energy.

Your post was insightful, and I thought more about it, and I hope that's right.

I'm going to have to oppose your argument. I don't think it is right to invoke the motion of the proton to justify the radiation. If it was an essential part of the mechanism, I would then expect the radiation to go to zero as the proton's mass became infinite. I'm quite sure this isn't the case. Or alternately, consider a charged moon circling a neutral earth. Would this system fail to radiate? I don't think so, but your model seems to suggest it would.

But more to the point, I don't think anyone has dealt with atom888's question: why does the planetary atom radiate? I don't have a great deal of sympathy for his distinction between centrifugal vs linear acceleration: to me, the planetary atom viewed from a distance at an oblique angle looks exactly like the harmonic oscillator...if one of them radiates, so should the other. But if someone asked me to explain why an oscillating "charge-on-a-spring" system radiates, I'd be hard pressed to give him a good answer. If someone has any helpful insight on this question, I wish they'd post it.

 

[DavidWhitbeck]

I would then expect the radiation to go to zero as the proton's mass became infinite.

You are confusing gravitational force and electric force. The force depends on the charge not the mass.

 

[monish]

You are confusing gravitational force and electric force. The force depends on the charge not the mass.

That wasn't my point. You suggested that we could understand the radiation of the planetary atom by taking into account the motion of the proton; in fact, you seemed to say that this was an essential part of the mechanism. I disagreed with your argument on the grounds that the radiative power of the system should then be dependent on how much the proton moves. That's why I suggested the earth-moon system with a charged moon: in this case, there is no pair of mutually-interacting charges, just a single charged body in a rotating orbit. Yet we both believe it must still radiate, even though the only field present is the self-created field.

 

[ironhill]

The argument relying on a moving proton is invalid, for one thing you can use the reduced mass and forget about it completely.

Where does the energy come from? Potential energy due to the proton in the middle depends on 1/r, so does kinetic energy (equate centripetal force and coulomb repulsion). The total energy is proportional to 1/r and is negative. If the electron gets closer to the proton its potential gets more negatve and some light is emitted with positive energy to conserve energy. So energy 'comes from' the change in potential as the electron changes position.

Of course that's absolute garbage and you should use Maxwell's equations. Though maybe it helps.

 

[atom888]

Well, my argument is entirely on the case of perfect circle path. Some planet have eliptical path so... the electron would have radiate/obsorb/radiate... which doesn't really make sense. However, Neils Bohr suggested that our assumption is alright, only if it does in quantize. ah...so there we have it.

 

[ironhill]

Well, my argument is entirely on the case of perfect circle path. Some planet have eliptical path so... the electron would have radiate/obsorb/radiate... which doesn't really make sense. However, Neils Bohr suggested that our assumption is alright, only if it does in quantize. ah...so there we have it.

Acceleration means changing velocity, a particle going in a circle has velocity that is changing (direction). Accelerating particles radiate. If you want to know why you really have to do the math, you can't prove anything arguing qualitatvely.

It is a fact that accelerating particles radiate, antennas work. The whole point is that classical theory doesn't work for atoms.

 

[DavidWhitbeck]

Monish, I get you. I badly screwed up, I need to review this, it's been too long.

 

[jimgraber]

gravity also causes radsiation and inspiral

If you put it that way I have to agree. A changing electric field cause a magnetic field while a changing gravitational field cause jack. That probably is the reason.

Actually, atom888, the no-inspiral solution only exists in the Newtonian approximation to the laws of gravity. If you move on to general relativity, you also get an effective gravito-magnetic field, gravitational radiation, and eventual inspiral. (Google LIGO for an attempt to measure this). But this effect is very weak and happens exceedly slowly, except close to black holes and neutron stars.
Best,
Jim Graber