Schwarzschild Diameter of One Quantum of Energy

[Ontophobe]

I've never heard or seen it stated this way before, so I'm asking this question just to check my intuition and to see if my understanding is correct: The Planck distance IS the Planck distance PRECISELY BECAUSE its the Schwarzschild Radius (or diameter, I suppose) of a single quantum of energy. Is this true?

 

[mfb]

There is no "single quantum of energy" with a fixed energy.
The Planck distance is the smallest length scale where our known physics could make sense. Beyond that, both gravity and quantum mechanics are relevant and it is unclear how to combine them there.
It is also the Schwarzschild radius of a possible black hole with one Planck mass, which is the energy needed to probe such small distances. Everything up to small prefactors like 2 or pi that don't matter here.

 

[Heinera]

A good starting point: https://en.m.wikipedia.org/wiki/Planck_units

 

[Ontophobe]

There is no "single quantum of energy" with a fixed energy.
The Planck distance is the smallest length scale where our known physics could make sense. Beyond that, both gravity and quantum mechanics are relevant and it is unclear how to combine them there.
It is also the Schwarzschild radius of a possible black hole with one Planck mass, which is the energy needed to probe such small distances. Everything up to small prefactors like 2 or pi that don't matter here.

So the Planck distance is the Schwarzschild Radius of the Planck mass, but the Planck mass isn't "equal to" a "quantum of energy," largely because there's no such thing as a "single quantum of energy." Can you say a little more to dispel this common misconception about what it actually means to talk about "quanta" of energy?

 

[mfb]

So the Planck distance is the Schwarzschild Radius of the Planck mass, but the Planck mass isn't "equal to" a "quantum of energy," largely because there's no such thing as a "single quantum of energy."

Right.

Can you say a little more to dispel this common misconception about what it actually means to talk about "quanta" of energy?

Take a hydrogen atom in the ground state, for example. It can absorb photons with an energy of 10.205 eV, 12.094 eV, 12.756 eV and various other energies, and all photons with at least 13.6 eV, but it cannot absorb a photon with an energy of 11.000 eV or 12.092 eV.
In the same way, an excited atom just has a few options for possible photon emissions. Everything in between is not possible. The allowed energy values correspond to the energy differences of the possible states of the atom.

Helium has the same features, but the energies here are completely different. A hydrogen molecule made out of two hydrogen atoms again has a completely different energy spectrum, and so on.

 

[Ontophobe]

Okay, if you'll indulge me, I'd like to try to spell out what little I think I know about black body radiation and absorption. If you might correct me wherever I stray from truth I'd be much obliged :)

Since 0 degrees Kelvin is unattainable, the coldest black body we can sensibly talk about would be some fraction of a degree above absolute zero. If we're talking about a chunk of matter; i.e., a cluster of particles, then it would be a cluster of neutrons. The fact that these neutrons are not at absolute zero doesn't just imply logically that they're vibrating ever so slightly, or "oscillating" I should say, it literally means it, semantically. But these oscillations don't make waves because neutrons don't cast EM fields into space. If the neutrons' vibrations were to speed up, they reach a speed at which some of them (but not all of them) would collapse into protons and electrons. At this rate of oscillation (still very close to absolute zero) the oscillations produce waves, because at this rate of oscillation EM fields are produced, because, again, at this rate of oscillation some neutrons become protons and elections and protons and electrons cast EM fields into space. And so it seems as if there can never be any such thing as a perfectly still EM field, because the necessary conditions for the field's creation and perpetuated existence are the very oscillations which cause the waves in it. In order for a dropped pebble to makes ripples on the surface of a pond, the pond must already be there. But we're talking about a pond that owes its existence to the oscillations of the pebble; a pond that can never be still. In contrast, a gravitational field is a pond that is about as still as the EM pond is turbulent. We have yet to even detect a wave in the gravity pond, but it's not forbidden by the laws of physics in the same way that a perfectly still EM pond is forbidden - that's where the dichotomous symmetry breaks down - it's at least theoretically possible to generate a gravitational wave.

Back to oscillating particles. Only two things can cause a particle to oscillate: collisions with other particles and the absorption of a photon; i.e., the absorption of an EM wave. So particles emit EM waves and they absorb them. Oscillations cause wave-emission, but wave-emission causes oscillations to decelerate, while wave-absorption causes oscillations to accelerate. This is where it breaks down for me. If we were talking about atoms and molecules and not just protons, neutrons and electrons individually, then I'd say that, because electrons can only take certain orbits around atomic nuclei, token-atoms and any atom-type, as well as token-molecules of any molecule-type, can only absorb certain wavelengths of EM waves. That is to say, if there's no electron in a given orbit around a nucleus, then that atom will not absorb EM waves whose frequency corresponds to that empty orbit. Electrons do the absorbing, not the orbits, but it just so happens that electrons are always in certain discrete orbits. So we have orbits, and for each orbit, there's a frequency of EM-waves that resonates with it, and causes the electron at that orbit to take the next higher orbit. And the taking of this higher orbit causes the atom or molecule as a whole to oscillate faster?

So energy doesn't come in discrete units. Atoms and molecules can only emit and/or absorb energy in discrete units, but this is a feature of atoms and molecules, not an intrinsic feature of the energy that they emit and absorb?

I've given myself a headache. Maybe I've given you one, too. If so, I'm sorry

 

[mfb]

Since 0 degrees Kelvin is unattainable, the coldest black body we can sensibly talk about would be some fraction of a degree above absolute zero.

Bose-Einstein condensates, if you ignore particles long belonging to the condensate, are at absolute zero.

If we're talking about a chunk of matter; i.e., a cluster of particles, then it would be a cluster of neutrons.

Why neutrons?

The fact that these neutrons are not at absolute zero doesn't just imply logically that they're vibrating ever so slightly, or "oscillating" I should say, it literally means it, semantically.

This is philosophy.

But these oscillations don't make waves because neutrons don't cast EM fields into space.

Electric charge has nothing to do with this.

At this rate of oscillation (still very close to absolute zero) the oscillations produce waves, because at this rate of oscillation EM fields are produced, because, again, at this rate of oscillation some neutrons become protons and elections and protons and electrons cast EM fields into space. And so it seems as if there can never be any such thing as a perfectly still EM field, because the necessary conditions for the field's creation and perpetuated existence are the very oscillations which cause the waves in it. In order for a dropped pebble to makes ripples on the surface of a pond, the pond must already be there. But we're talking about a pond that owes its existence to the oscillations of the pebble; a pond that can never be still. In contrast, a gravitational field is a pond that is about as still as the EM pond is turbulent. We have yet to even detect a wave in the gravity pond, but it's not forbidden by the laws of physics in the same way that a perfectly still EM pond is forbidden - that's where the dichotomous symmetry breaks down - it's at least theoretically possible to generate a gravitational wave.

That does not make sense at all. And I don't think making up stuff like this helps if you want to learn physics.

Back to oscillating particles. Only two things can cause a particle to oscillate: collisions with other particles and the absorption of a photon; i.e., the absorption of an EM wave.

Depends on what exactly you can "oscillate", but it is wrong in all reasonable cases. Also, you can describe some particle collisions with the exchange of photons...

Electrons do the absorbing, not the orbits

No, the whole atom does it.

So energy doesn't come in discrete units. Atoms and molecules can only emit and/or absorb energy in discrete units, but this is a feature of atoms and molecules, not an intrinsic feature of the energy that they emit and absorb?

Right.

Forget the whole "oscillation" thing. I don't know what you imagine there, but it certainly does not help.

 

[Ontophobe]

You asked why neutrons. I was told that at temperatures within a few degrees of absolute zero, matter becomes a sludge of pure neutrons. Somewhere around 3 degrees Kelvin, neutrons collapse into protons and neutrons. An astronomy teacher told us that once

So if all matter reduces to neutrons near zero kelvin, and if neutrons don't emit an EM field, then their minute oscillations don't "jiggle the field" the way oscillating protons and electrons "jiggle their EM fields," because there's no field yet to jiggle. By jiggle the field I just mean "cause ripples in it." If protons and electrons don't "show up" until after a certain temperature has been attained (i.e., until after a certain rate of oscillation has been achieved), then such EM fields are "born jiggling." There's therefore no such thing as a perfectly still, ripple-less, wave-less EM field. If I'm wrong, and I don't doubt that I am, please tell me where I've gone wrong in my reasoning. And as for making stuff up, I agree that it doesn't aid the learning of physics, but I'm not sure I was making anything up.

Okay the oscillation thing is a dead end. I guess I remember being told that waves in EM fields are caused by the oscillations or vibrations of charged particles, like a piece of cork bobbing in a pool of water. I was imaging a vibrating particle jiggling a field; a field that's sort of tethered to it, such that it "waves the field" the way one might wave a flag.

Just emailed that astronomy teacher the same rant I just posted here and he says my analysis is spot on, even the part you said didn't make sense, so now I'm confused. He's a physicist by trade and an astronomy teacher on the side, so you both seem really qualified. I'm not sure what to think. If I'm wrong I want to know it, and if you think I'm incorrect, please tell me where I veered off course so I can make the correction. And thanks for your help :)

What's the difference between a particle with one temperature and a particle with another temperature if it's not the rate at which they're vibrating? I need to replace this idea of oscillation with something else but I don't know what

 

[mfb]

Please use the edit function if you want to add something to your post. I merged the posts.

You asked why neutrons. I was told that at temperatures within a few degrees of absolute zero, matter becomes a sludge of pure neutrons. Somewhere around 3 degrees Kelvin, neutrons collapse into protons and neutrons.

It does not. This is just nonsense. Protons and electrons combine to neutrons in the formation of a neutron star, but this is an incredibly hot object.

the way oscillating protons and electrons "jiggle their EM fields," [...]By jiggle the field I just mean "cause ripples in it."

They do not, unless they get accelerated by some interaction.

If protons and electrons don't "show up" until after a certain temperature has been attained (i.e., until after a certain rate of oscillation has been achieved), then such EM fields are "born jiggling."

Even if the condition would be true (it is not), this would not make sense.

There's therefore no such thing as a perfectly still, ripple-less, wave-less EM field.

That depends on your favorite interpretation of quantum mechanics.

What's the difference between a particle with one temperature and a particle with another temperature if it's not the rate at which they're vibrating?

Particles do not have a temperature. Temperature is a macroscopic quantity of a system with many particles, and it is related (but not the same) to the unordered energy (kinetic and potential) in this system.
Particles can have different kinetic energies, then their difference is their different kinetic energy.

 

[f95toli]

You asked why neutrons. I was told that at temperatures within a few degrees of absolute zero, matter becomes a sludge of pure neutrons. Somewhere around 3 degrees Kelvin, neutrons collapse into protons and neutrons. An astronomy teacher told us that once

This is -as has been stated above- just plain wrong. Nothing in particular happens to the actual structure of matter when you cool something down to low temperatures: there is obviously less thermal energy available (which is why we cool things in the first place) but this is irrelevant at the sub-atomic scale.
Note that there plenty (hundreds) of labs around the world with the equipment to cool samples down to millikelvin temperatures, and with a bit of effort we can cool even large (kg of copper) things down to microkelvlin temperatures. Hence. 3K is not even a very low temperature by modern standards (you can easily get down below 2K by just pumping on a volume of liquid helium, this was first done about a 100 years ago).
In fact, all the superconducting magnets in the LHC are cooled below 3K and they are still fine