I have come across the same 'explanation' multiple times but do not find it satisfactory.
>> This "battle of the infinities" cannot be won by either side, so a compromise is reached in which theory tells us that the fall in potential energy is just twice the kinetic energy, and the electron dances at an average distance that corresponds to the Bohr radius.
This "cannot be won by either side" isn't a good explanation of the problem. By saying "a compromise is reached in which theory tells us ...", the article seems going around the answer instead of actually telling the answer to the question.
Assuming relativity is not invoked and given a finite size of the nucleus, what is actually bringing this situation of compromise? What is pushing the electron (or its probability cloud) outwards to counter-balance?
The opposing effect is the kinetic energy of the electron: as it get squeezed into a smaller area its kinetic energy must go up, assuming energy is constant (a classical system would more or less be the same, think how an elliptical orbit speeds up as it gets closer to the barycenter, but a quantum mechanical system doesn't necessarily have a defined trajectory).
The real sleight of hand in this explanation is it doesn't really explain why the quantum-mechanical electron doesn't radiate energy like the classical electron. That's a bit more subtle, but it's basically due to the fact that the electron is wave-like and confined within the atom (i.e. it does not have enough energy to escape the nucleus). This means that the wave-function has discrete solutions as a series of 'standing waves', which is what causes the quantization in quantum mechanics.
>> The real sleight of hand in this explanation is it doesn't really explain why the quantum-mechanical electron doesn't radiate energy like the classical electron. That's a big more subtle, but it's basically due ...
This subtle part is exactly the piece that I am missing.
So far, we have electron in an orbital. The orbital in itself seems stationary (standing waves), so it may seem nothing is accelerating. I presume that is not it for the answer.
If it is, that still feels like, Oh, I solved Schroginger's equation, and it yields these standing waves for the solution, electron is not really having a certain position and momentum as the wave function hasn't collapsed, and thereby there is no acceleration for the electron to be radiating energy.
Asking a total newbie question. I heard that QM has operators, so momentum also has an operator. Is there one for acceleration? Would it yield a zero?
If so: I see Coulomb's force. Is there another force balancing it? Or is Newton's third law not valid anymore.
The electron's position is smeared out over the entire orbital, so in this sense it's being accelerated in all cartesian directions equally — sure, in spherical coordinates, it's always in the radially inwards direction, but it can't go "in" any further because its own wave function is already there, blocking it.
(Operator specifically: IDK if there is one for acceleration, but this is why electrons can't be pushed in once they're at the final energy level).
>> but it can't go "in" any further because its own wave function is already there, blocking it.
This is good food for thought for me. Though I am still not fully clear. If the above were the setup with classical mechanics and electrostatics, with nuclear charge at the center and electronic charge smeared out, I would use Gauss theorem to find electric field and still find that the smeared charge would feel a net force towards the center and want to move that way.
If you squeeze the wavefunction in space, you spread it out in velocity; the classical analogy would be that beyond a certain point, the more it actually moves inwards, the faster it has to be moving outwards.
The relevant piece here is acceleration. I understand the rest. The problem in classical explanation is acceleration resulting in energy loss to radiations. With QM, we have an explanation without that radiation, but I am not clear how and why that is, as posed in my questions above.
It's not zero in other coordinate systems? Or you are saying it does come out zero in all the systems. If the latter, I would love to read more including the maths. :-)
Coordinate grids are arbitrary, for any system you can always put a different grid on the same physical reality.
It's just intuitively clear with a cartesian system that there's no net acceleration in a way it might not be for spherical coordinates. If you imagine a sphere, attach to all points of that sphere a normal unit vector pointing inwards, then all points on the sphere are "pointing inwards"; but as each point on the sphere has a corresponding point opposite it, where "inwards" means the exact opposite in cartesian coordinates, the sum of all those inward vectors is exactly zero. With spherical coordinates, you have to convince yourself that the vectors really do cancel. But they're the same vectors described differently.
Just to be clear though: these are still all euclidian geometry, just with different gridlines drawn on them. As yet, nobody has fully solved QM for curved spaces.
Will try to find the math that shows acceleration in the cartesian coordinates (and with Euclidian geometry) comes out to be zero. That then hopefully will help me understand how is QM solving the original problem.
The way I see it is that it could only actually collapse if the electron was headed precisely at the nucleus (the nucleus has diameter zero in this simplified model). Even in classical physics, the electron would move on an ellipsis around the nucleus in almost all cases, so the average distance would be non-zero.
Being pointed exactly at the nucleus is not possible in quantum mechanics, because that would require infinite precision, which is precisely what we give up in this model, so the average distance is yet again non-zero.
This explanation is not correct. Here, the electron is again accelerating, will lose energy, and ultimately spiral into the nucleus. This does not require it to be pointing exactly into the nucleus.
Here is a simple explanation: They can't fall in due to Heisenberg's uncertainty. For that, I'd need you to accept as an axiom[1] (unprovable truth) that the following principle is true:
ΔpΔx (uncertainty of momentum times uncertainty of position) is roughly equal (or greater) to some constant, we'll call it H.
Due to this, if one uncertainty grows smaller, the other grows larger.
If the electron is located in the nucleus, its position (Δx) would be much more narrow than if it was around the nucleus. Since the uncertainty of Δx goes down, Δp must go up co compensate. Turns out, this Δp is enough to give it an enough momentum to overcome attractive force.
But then comes a smart observer, and says, but what if an electron managed to lodge itself exactly into the center of a proton. Since Coulomb's law says F= q1q2/r^2, and r is 0[2], that's Infinity! You can't escape infinite charge attractiveness!
To that, you can notice that as r and Δx approaches 0, Δp also approaches infinity, so it will have more chance to escape before that happens. But in some rare cases, it will interact and form a neutron, with some energy being emitted as a neutrino.
[1] It's not an axiom, it's an observation derived from experiments. However, why is the matter behaving like that out of physics wheelhouse. It can tell you a lot about laws, but very little WHY are laws like that. So it might as well be an axiom.
[2] This is, of course, assuming that space is infinitely divisible, which is yet to be confirmed or denied.
I have heard this too and still feel that there's more to this that is critically missed.
>> For that, I'd need you to accept as an axiom (unprovable truth) that the following principle is true: ΔpΔx is roughly equal (or greater) to some constant, we'll call it H.
As far as I know, Heisenberg's principle isn't exactly an axiom. It can largely be derived!
A waveform in time and its Fourier transform have such a relationship, which is entirely mathematical. More confined a time waveform is, more spread out the frequency spectrum is, and vice versa.
Now de Broglie principle linked momentum of a particle to its frequency! That makes the trick. So far, in Newtonian mechanics, momentum just related to position via derivative of position, i.e., velocity. Both were time waveforms.
But with de Broglie principal, momentum (also?) links to frequency domain, while the position remains in time domain. Now the Schrodinger's equation yields the said relation between position and momentum.
What I'll write next fits better in another comment box, so will do that.
How can something be an axiom and at the same time has a mathematical derivation well understood from Quantum Mechanics [1] and are supported by experimental observations ?
The idea of axioms in mathematics is not quite the same as it is with physics.
Physicists don't need the type of mathematical rigor such as the set theory axioms to build up all of mathematics. In fact, by keeping in mind the multitudes of paths from which one part of physics could be related or derived from another part, you are exploring the possibly undiscovered laws in nature.
It will only be relevant to axiomatically define physics (from a set of basic axioms to reach all laws) after we confirmed to have discovered all of physics. That day hasn't come yet - there's no grand unified theory so far, and there's still stuff that we dont know surely.
> How can something be an axiom and at the same time has a mathematical derivation well understood from Quantum Mechanics
See my notes, it's not an axiom, just take it for granted for the explanation to work. You can derive it from experiments like squeezing light, or you can derive it from other things as you mentioned.
It's always possible most of them already have done so :0
Seems to me the positive & negative charges would neutralize, and it would no longer be "matter" as we know it.
Not anti-matter, just not actual matter by any stretch of the imagination.
Which is what most of the universe actually consists of, not actual matter.
Matter itself is extremely rare, few, and far between.
Could be all there is left and can be perceived by those composed of it, are the things that can have a physical nature simply because their electrons haven't collapsed into the nucleii.
I don't like mechanistic explanations of particle physics - they're an attempt to relate what's going on to our macroscopic experience, but they usually fall apart when you look too closely.
I find it much easier to understand the stability of hydrogen by thinking about ground states. If the electron in H could merge with the proton, they'd make a neutron. But a free neutron is not stable and decays in a few minutes back into a proton, electron and an antineutrino.
With very large, proton-rich nuclei, eventually you get to the opposite situation where the ground state is one less proton, one less electron and one more neutron and the atom decays into that state by, you guessed it, an electron "falling into" the nucleus.
Mills has developed a better purely classical atomic model where the electrons are concentric spinning fluid spheres with force balance equivalent to 20k atmospheres pressure. The spinning electrons don't radiate because there is no net charge movement over time. See https://brilliantlightpower.com/theory/
Ah, the forever cry of the crackpots. That's particularly rich complaint given it's a publicly editable resource. The only reason it could be in poor shape and "out of date" is because you yourself left it that way.
If that was a truly workable theory it would have verifiable predictions and compatibility with all prior observation and it would be eagerly explored. Scientists as a whole like to find anomalies and discrepancies; it is what keeps them in business. There is no "conspiracy".
Edits are removed unless they are published in well known journals which is fair enough for scientific results, but you cannot even update the page to state Mills latest engineering improvements or update factual information about the company.
If they have actual engineering improvements this sentence in the Wikipedia article could be easily disproved.
> BLP has announced several times that it was about to deliver commercial products based on Mill's theories but has never delivered any working product.
The main problem is there is so much power the device melts. They have now started using molten gallium electrodes (as of 2016), and now a quartz crystal housing that lets the UV light out and doesn't melt. They are offering hydrinos in a bottle to qualified labs. Stuff goes through a gas chromatograph faster than hydrogen.
> However, an electron, unlike a planet or a satellite, is electrically charged, and it has been known since the mid-19th century that an electric charge that undergoes acceleration (changes velocity and direction) will emit electromagnetic radiation, losing energy in the process.
If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?
To me it seems the rest of the article, i.e. probability density, also means that the electrons undergoe acceleration because their location changes.
> If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?
Yes, they do. But it's only a very very tiny amount.
You're shaking both the positive (nucleus) and negative (electrons) parts of the atoms. The electromagnetic fields outside of the atom almost perfectly cancel out. This means that the acceleration only affects the very small residual field and there is very little radiation at far distances, unless you shake it really really fast.
Another way to look at it is that atoms are in fact already constantly shaking by themselves because of thermal movement. And this does in fact result in them emitting radiation: objects at room temperature will radiate in the infrared spectrum because of this.
The trick is that thermal movements of atoms are very fast compared to moving something by hand. Room temperature infrared radiation frequencies are on the order of tens of terahertz. Compare this to manually shaking an object at (say) 10 times a second. With some hand waving math this is like giving it an equivalent temperature of around 10^-10 kelvin. It will radiate extremely long wave radio waves, but such a tiny amount that it will be completely unmeasurable.
>If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?
The energy they lose by radiating is exactly balanced by the energy they gain from you by accelerating them.
This was quite interesting, and at a level where I found I understood something new without being overwhelmed – I tried looking around the site for more, but the site itself has me confused as to where to start, is this part of a work in progress book? How do I get to the table of contents or start of the book?
ELI5 version, why doesnt an elephant fall into a mouse?
because the elephant wavelength is too long to fit inside the mouse, so it nestles around the mouse at S1 orbit.
so, why doesnt an electron fall into a nucleus?
because the nucleus is too small to encompass an electron wave.
Second law of thermodynamics? The electron and the environment have the same temperature. If it falls, it emits energy warming the environment without consumption of energy. But this is impossible.
For example you can make a very similar system with a positron and an electron https://en.wikipedia.org/wiki/Positronium . It's stable for a while, and it has very similar properties and levels like an Hydrogen atom. So the "second law" should apply too. But it has a mean lifetime of only 0.12 ns (1.2E-10s).
The second law consider also the properties of the materials. For example there are small bags with sodium acetate that are used as hand heaters https://en.wikipedia.org/wiki/Sodium_acetate#Heating_padhttps://www.youtube.com/watch?v=Oj0plwm_NMs You put them in hot water, the content dissolves, and you let them cold to room temperature. When you click the metallic part, they crystallize and release heat.
Another example is connecting a small lamp to a battery. It release light and heat, specially if you can get an old incandescent light bulb.
In the end, that's true for all why questions in physics. In the end, things don't have a reason for how they behave, they just do.
The question of why only makes sense in a framework. Classical EM theory says electrons should fall into the nucleus, but they clearly don't. Asking why they don't is one step towards finding out about quantum mechanics, so it's a really important question to ask.
Yes, at the end of the day, the answer is "because classical EM is wrong and quantum mechanics is right (or at least less wrong)". But there is a lot to learn along the way.
I personally think the mere idea that you can map on abstract functions that have infinities and boundary conditions, on to a representation that extremely precisely models our physical world, is more astonishing than having a low level understanding of the equations. The final image of the probability density summed over the region around the nucleus, really drove that home for me
I have come across the same 'explanation' multiple times but do not find it satisfactory.
>> This "battle of the infinities" cannot be won by either side, so a compromise is reached in which theory tells us that the fall in potential energy is just twice the kinetic energy, and the electron dances at an average distance that corresponds to the Bohr radius.
This "cannot be won by either side" isn't a good explanation of the problem. By saying "a compromise is reached in which theory tells us ...", the article seems going around the answer instead of actually telling the answer to the question.
Assuming relativity is not invoked and given a finite size of the nucleus, what is actually bringing this situation of compromise? What is pushing the electron (or its probability cloud) outwards to counter-balance?
The opposing effect is the kinetic energy of the electron: as it get squeezed into a smaller area its kinetic energy must go up, assuming energy is constant (a classical system would more or less be the same, think how an elliptical orbit speeds up as it gets closer to the barycenter, but a quantum mechanical system doesn't necessarily have a defined trajectory).
The real sleight of hand in this explanation is it doesn't really explain why the quantum-mechanical electron doesn't radiate energy like the classical electron. That's a bit more subtle, but it's basically due to the fact that the electron is wave-like and confined within the atom (i.e. it does not have enough energy to escape the nucleus). This means that the wave-function has discrete solutions as a series of 'standing waves', which is what causes the quantization in quantum mechanics.
>> The real sleight of hand in this explanation is it doesn't really explain why the quantum-mechanical electron doesn't radiate energy like the classical electron. That's a big more subtle, but it's basically due ...
This subtle part is exactly the piece that I am missing.
So far, we have electron in an orbital. The orbital in itself seems stationary (standing waves), so it may seem nothing is accelerating. I presume that is not it for the answer.
If it is, that still feels like, Oh, I solved Schroginger's equation, and it yields these standing waves for the solution, electron is not really having a certain position and momentum as the wave function hasn't collapsed, and thereby there is no acceleration for the electron to be radiating energy.
Asking a total newbie question. I heard that QM has operators, so momentum also has an operator. Is there one for acceleration? Would it yield a zero?
If so: I see Coulomb's force. Is there another force balancing it? Or is Newton's third law not valid anymore.
> Would it yield a zero?
The electron's position is smeared out over the entire orbital, so in this sense it's being accelerated in all cartesian directions equally — sure, in spherical coordinates, it's always in the radially inwards direction, but it can't go "in" any further because its own wave function is already there, blocking it.
(Operator specifically: IDK if there is one for acceleration, but this is why electrons can't be pushed in once they're at the final energy level).
>> but it can't go "in" any further because its own wave function is already there, blocking it.
This is good food for thought for me. Though I am still not fully clear. If the above were the setup with classical mechanics and electrostatics, with nuclear charge at the center and electronic charge smeared out, I would use Gauss theorem to find electric field and still find that the smeared charge would feel a net force towards the center and want to move that way.
If you squeeze the wavefunction in space, you spread it out in velocity; the classical analogy would be that beyond a certain point, the more it actually moves inwards, the faster it has to be moving outwards.
The relevant piece here is acceleration. I understand the rest. The problem in classical explanation is acceleration resulting in energy loss to radiations. With QM, we have an explanation without that radiation, but I am not clear how and why that is, as posed in my questions above.
The net acceleration in cartesian coordinates is zero.
Am genuinely trying to understand.
It's not zero in other coordinate systems? Or you are saying it does come out zero in all the systems. If the latter, I would love to read more including the maths. :-)
Thanks.
Coordinate grids are arbitrary, for any system you can always put a different grid on the same physical reality.
It's just intuitively clear with a cartesian system that there's no net acceleration in a way it might not be for spherical coordinates. If you imagine a sphere, attach to all points of that sphere a normal unit vector pointing inwards, then all points on the sphere are "pointing inwards"; but as each point on the sphere has a corresponding point opposite it, where "inwards" means the exact opposite in cartesian coordinates, the sum of all those inward vectors is exactly zero. With spherical coordinates, you have to convince yourself that the vectors really do cancel. But they're the same vectors described differently.
Just to be clear though: these are still all euclidian geometry, just with different gridlines drawn on them. As yet, nobody has fully solved QM for curved spaces.
I understand. Thanks!
Will try to find the math that shows acceleration in the cartesian coordinates (and with Euclidian geometry) comes out to be zero. That then hopefully will help me understand how is QM solving the original problem.
The way I see it is that it could only actually collapse if the electron was headed precisely at the nucleus (the nucleus has diameter zero in this simplified model). Even in classical physics, the electron would move on an ellipsis around the nucleus in almost all cases, so the average distance would be non-zero.
Being pointed exactly at the nucleus is not possible in quantum mechanics, because that would require infinite precision, which is precisely what we give up in this model, so the average distance is yet again non-zero.
This explanation is not correct. Here, the electron is again accelerating, will lose energy, and ultimately spiral into the nucleus. This does not require it to be pointing exactly into the nucleus.
Oh, I thought you were asking something else. In a spiral motion, the infinities never come into play. Nevermind.
Here is a simple explanation: They can't fall in due to Heisenberg's uncertainty. For that, I'd need you to accept as an axiom[1] (unprovable truth) that the following principle is true: ΔpΔx (uncertainty of momentum times uncertainty of position) is roughly equal (or greater) to some constant, we'll call it H.
Due to this, if one uncertainty grows smaller, the other grows larger.
If the electron is located in the nucleus, its position (Δx) would be much more narrow than if it was around the nucleus. Since the uncertainty of Δx goes down, Δp must go up co compensate. Turns out, this Δp is enough to give it an enough momentum to overcome attractive force.
But then comes a smart observer, and says, but what if an electron managed to lodge itself exactly into the center of a proton. Since Coulomb's law says F= q1q2/r^2, and r is 0[2], that's Infinity! You can't escape infinite charge attractiveness!
To that, you can notice that as r and Δx approaches 0, Δp also approaches infinity, so it will have more chance to escape before that happens. But in some rare cases, it will interact and form a neutron, with some energy being emitted as a neutrino.
[1] It's not an axiom, it's an observation derived from experiments. However, why is the matter behaving like that out of physics wheelhouse. It can tell you a lot about laws, but very little WHY are laws like that. So it might as well be an axiom.
[2] This is, of course, assuming that space is infinitely divisible, which is yet to be confirmed or denied.
I have heard this too and still feel that there's more to this that is critically missed.
>> For that, I'd need you to accept as an axiom (unprovable truth) that the following principle is true: ΔpΔx is roughly equal (or greater) to some constant, we'll call it H.
As far as I know, Heisenberg's principle isn't exactly an axiom. It can largely be derived!
A waveform in time and its Fourier transform have such a relationship, which is entirely mathematical. More confined a time waveform is, more spread out the frequency spectrum is, and vice versa.
Now de Broglie principle linked momentum of a particle to its frequency! That makes the trick. So far, in Newtonian mechanics, momentum just related to position via derivative of position, i.e., velocity. Both were time waveforms.
But with de Broglie principal, momentum (also?) links to frequency domain, while the position remains in time domain. Now the Schrodinger's equation yields the said relation between position and momentum.
What I'll write next fits better in another comment box, so will do that.
(Edit:) Wrote here: https://news.ycombinator.com/item?id=43819506
How can something be an axiom and at the same time has a mathematical derivation well understood from Quantum Mechanics [1] and are supported by experimental observations ?
[1] https://courses.physics.illinois.edu/phys580/fa2013/uncertai...
The idea of axioms in mathematics is not quite the same as it is with physics.
Physicists don't need the type of mathematical rigor such as the set theory axioms to build up all of mathematics. In fact, by keeping in mind the multitudes of paths from which one part of physics could be related or derived from another part, you are exploring the possibly undiscovered laws in nature.
It will only be relevant to axiomatically define physics (from a set of basic axioms to reach all laws) after we confirmed to have discovered all of physics. That day hasn't come yet - there's no grand unified theory so far, and there's still stuff that we dont know surely.
> How can something be an axiom and at the same time has a mathematical derivation well understood from Quantum Mechanics
See my notes, it's not an axiom, just take it for granted for the explanation to work. You can derive it from experiments like squeezing light, or you can derive it from other things as you mentioned.
They do sometimes.
https://en.wikipedia.org/wiki/Electron_capture
>Why do electrons not fall into the nucleus?
It's always possible most of them already have done so :0
Seems to me the positive & negative charges would neutralize, and it would no longer be "matter" as we know it.
Not anti-matter, just not actual matter by any stretch of the imagination.
Which is what most of the universe actually consists of, not actual matter.
Matter itself is extremely rare, few, and far between.
Could be all there is left and can be perceived by those composed of it, are the things that can have a physical nature simply because their electrons haven't collapsed into the nucleii.
Yet.
I don't like mechanistic explanations of particle physics - they're an attempt to relate what's going on to our macroscopic experience, but they usually fall apart when you look too closely.
I find it much easier to understand the stability of hydrogen by thinking about ground states. If the electron in H could merge with the proton, they'd make a neutron. But a free neutron is not stable and decays in a few minutes back into a proton, electron and an antineutrino.
With very large, proton-rich nuclei, eventually you get to the opposite situation where the ground state is one less proton, one less electron and one more neutron and the atom decays into that state by, you guessed it, an electron "falling into" the nucleus.
Mills has developed a better purely classical atomic model where the electrons are concentric spinning fluid spheres with force balance equivalent to 20k atmospheres pressure. The spinning electrons don't radiate because there is no net charge movement over time. See https://brilliantlightpower.com/theory/
For those who don't know Mills and his company: https://en.wikipedia.org/wiki/Brilliant_Light_Power
That wikipedia page has a strong skeptical bias and is seriously out of date.
Sounds like skepticism is warranted.
Ah, the forever cry of the crackpots. That's particularly rich complaint given it's a publicly editable resource. The only reason it could be in poor shape and "out of date" is because you yourself left it that way.
If that was a truly workable theory it would have verifiable predictions and compatibility with all prior observation and it would be eagerly explored. Scientists as a whole like to find anomalies and discrepancies; it is what keeps them in business. There is no "conspiracy".
Edits are removed unless they are published in well known journals which is fair enough for scientific results, but you cannot even update the page to state Mills latest engineering improvements or update factual information about the company.
If they have actual engineering improvements this sentence in the Wikipedia article could be easily disproved.
> BLP has announced several times that it was about to deliver commercial products based on Mill's theories but has never delivered any working product.
The main problem is there is so much power the device melts. They have now started using molten gallium electrodes (as of 2016), and now a quartz crystal housing that lets the UV light out and doesn't melt. They are offering hydrinos in a bottle to qualified labs. Stuff goes through a gas chromatograph faster than hydrogen.
"skeptical bias" is an oxymoron.
A skeptic merely rejects claims without evidence.
Yes and my yoga teacher has an even better theory where the electrons are stopped from falling in by spirits of their time-traveling ancestors.
I want to make a joke about Feynman path integrals and the single electron universe etc., but I can't think of an appropriate yoga pun.
Crank
> However, an electron, unlike a planet or a satellite, is electrically charged, and it has been known since the mid-19th century that an electric charge that undergoes acceleration (changes velocity and direction) will emit electromagnetic radiation, losing energy in the process.
If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?
To me it seems the rest of the article, i.e. probability density, also means that the electrons undergoe acceleration because their location changes.
> If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?
Yes, they do. But it's only a very very tiny amount.
You're shaking both the positive (nucleus) and negative (electrons) parts of the atoms. The electromagnetic fields outside of the atom almost perfectly cancel out. This means that the acceleration only affects the very small residual field and there is very little radiation at far distances, unless you shake it really really fast.
Another way to look at it is that atoms are in fact already constantly shaking by themselves because of thermal movement. And this does in fact result in them emitting radiation: objects at room temperature will radiate in the infrared spectrum because of this.
The trick is that thermal movements of atoms are very fast compared to moving something by hand. Room temperature infrared radiation frequencies are on the order of tens of terahertz. Compare this to manually shaking an object at (say) 10 times a second. With some hand waving math this is like giving it an equivalent temperature of around 10^-10 kelvin. It will radiate extremely long wave radio waves, but such a tiny amount that it will be completely unmeasurable.
>If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?
The energy they lose by radiating is exactly balanced by the energy they gain from you by accelerating them.
How do you know that your shaking action in the scenario isn't the input of the same energy that is emitted?
This was quite interesting, and at a level where I found I understood something new without being overwhelmed – I tried looking around the site for more, but the site itself has me confused as to where to start, is this part of a work in progress book? How do I get to the table of contents or start of the book?
By coincidence I am currently watching this series, which explains this and a lot more:
https://www.thegreatcourses.com/courses/einstein-s-relativit...
It is on Kanopy now, for “free” (local library pays). I think there’s a subatomic-particle specific course as well that is more focused.
ELI5 version, why doesnt an elephant fall into a mouse? because the elephant wavelength is too long to fit inside the mouse, so it nestles around the mouse at S1 orbit.
so, why doesnt an electron fall into a nucleus?
because the nucleus is too small to encompass an electron wave.
Second law of thermodynamics? The electron and the environment have the same temperature. If it falls, it emits energy warming the environment without consumption of energy. But this is impossible.
Good question, but no.
For example you can make a very similar system with a positron and an electron https://en.wikipedia.org/wiki/Positronium . It's stable for a while, and it has very similar properties and levels like an Hydrogen atom. So the "second law" should apply too. But it has a mean lifetime of only 0.12 ns (1.2E-10s).
The second law consider also the properties of the materials. For example there are small bags with sodium acetate that are used as hand heaters https://en.wikipedia.org/wiki/Sodium_acetate#Heating_pad https://www.youtube.com/watch?v=Oj0plwm_NMs You put them in hot water, the content dissolves, and you let them cold to room temperature. When you click the metallic part, they crystallize and release heat.
Another example is connecting a small lamp to a battery. It release light and heat, specially if you can get an old incandescent light bulb.
Single particles do not have a temperature. It's an emergent property of many-particle systems.
you forget the thermal bath
To me the article says: the electron doesn't fall into the nucleus because we found an equation that says it doesn't.
In the end, that's true for all why questions in physics. In the end, things don't have a reason for how they behave, they just do.
The question of why only makes sense in a framework. Classical EM theory says electrons should fall into the nucleus, but they clearly don't. Asking why they don't is one step towards finding out about quantum mechanics, so it's a really important question to ask.
Yes, at the end of the day, the answer is "because classical EM is wrong and quantum mechanics is right (or at least less wrong)". But there is a lot to learn along the way.
Yup. Half of physics is written just like this.
Not sure I understand it any better having read this. but I did find it interesting and thought provoking.
I personally think the mere idea that you can map on abstract functions that have infinities and boundary conditions, on to a representation that extremely precisely models our physical world, is more astonishing than having a low level understanding of the equations. The final image of the probability density summed over the region around the nucleus, really drove that home for me