Oh! So you’re saying the spectrum of the acoustic noise at a given temperature will be the spectrum of black body radiation! Yes, I could definitely believe that. That is high-frequency indeed.
Sort of. Blackbody radiation is electromagnetic in nature, however under some ideal assumptions you can assume that the molecules emitting that radiation are also vibrating at roughly the same spectrum. ‘vibrating’, though, can mean a lot of different things; this is related to the microscopic properties of the substance and its degrees of freedom. In an ideal gas, it’s taken to mean the particle collision frequency spread (but not necessarily the frequency of particle collisions). If you consider heat to be composed of a disordered collection of phonons, then you could definitely say that this is ‘sound’, but it’s probably neater to draw a distinction between thermal phonons (high-entropy, low free energy) and acoustic phonons.
The reasoning behind blackbody electromagnetic radiation applies equally well to thermal vibrations in solids and gases. Meaning the spectral limits derived from a quantum consideration of the quantization of electromagnetic radiation (into photons) applies equally well to the quantum considerations of vibrational radiation (into phonons).
“Thermal” photons are indistinguishable individually from photons from other sources. The thing that makes a thing thermal is the distribution and prevalence of photons in time and frequency, those from a thermal source follow a well understood set of statistics, while photons from other sources clearly deviate from that. So a photon arising from a cell phone tower’s radio transmitter reacts similarly with a cell phone’s radio receiver as a photon at a similar frequency arising from thermal emission from the air. Physics can’t distinguish between these two photons which is why it is a major effort in building radio communications to get enough signal-sourced photons compared to the thermal-sourced photons so that the signal-sourced photons dominate, and therefore the signal can be accurately derived from their detection.
Similarly with phonons. Vibrations because something is hot are indistinguishable from vibrations from a vocal cord. It is the statistical distribution of the vibrations in time and frequency that defines a thermal set of vibrations. And again, to hear what someone is saying, it is important to get enough phonons from their vocal cords into your ears compared to the phonons from other sources in order to accurately enough derive the intended information.
Thermal noise or other white noise, and a symphony, have the same kind of phonons and both can be heard by the same kinds of ears. They carry different kinds of information (they sound different) because of their different time and frequency statistics.
Black-body radiation is electromagnetic radiation, so I’m a bit confused how that’s connected with acoustic noise. As to molecule collisions, I’m not sure vibrations at sufficiently high frequency can be called “acoustic” at all.
As to molecule collisions, I’m not sure vibrations at sufficiently high frequency can be called “acoustic” at all.
Your reasoning here carries useful information. For example, when you are dealing with vibrations whose frequency is so high that the wavelength of the vibration is less than the average spacing between molecules in a gas, or in a solid lattice, then a lot of what you calculate about the detection and interactions with lower frequency vibrations no longer applies.
However, the same limitations apply to electromagnetic radiation. For example we think of vacuum or empty space as transparent to EM radiation, and it is as long as the EM frequency is low enough frequency. But high enough frequency EM radiation, empty space is opaque to it! For example, at high enough frequencies, a single photon has enough energy to create a positron-electron pair in free space. Photons at that frequency don’t travel very far before they are destroyed by such a spontaneous generation of particles.
So in principle, EM radiation and acoustic vibrations are the same in this respect: as long as you are considering frequencies “low enough” that they don’t rip apart the medium in which the wave exists, they behave in the ways we usually think of for sound and light. But above those frequencies, they rip apart the media they are traveling through, even if that medium is so-called empty space.
For example, at high enough frequencies, a single photon has enough energy to create a positron-electron pair in free space. Photons at that frequency don’t travel very far before they are destroyed by such a spontaneous generation of particles.
So what kind of energies are we talking about here, and what distances?
Photons with over 1 Million electron volts of energy can create a positron-electron pair, but only when near another massive particle (like the nucleus of an atom). The other massive particle is moved in the interaction but is otherwise not-necessarily changed. https://en.wikipedia.org/wiki/Pair_production. This process has been demonstrated experimentally. The mean free path of the energetic photon near an atomic nucleus is something down on the atomic scale, the experiment I read about used a piece of gold foil and generated lots of positron-electron pairs.
A single photon in otherwise empty space cannot create a pair of particles I was wrong when stating that. However, space with nothing but two photons in it can create matter. Two photons each with a bit over 511 million electron volts of energy can collide and result in the creation of a positron and an electron. https://en.wikipedia.org/wiki/Two-photon_physics Alternatively a single 80 Tera Electron Volt photon can collide with a very low energy photon to create an electron-positron pair. This effect actually makes our existing universe opaque to photons above 80 TeV because our universe is filled with approximately 0.0003 eV photons known as the Cosmic Microwave Background radiation. This background radiation is left-over radiation from the big bang which by now has cooled down to about 3 Kelvin in temperature. I don’t know any of the actual mean-free-paths associated with this, just that they are much shorter than interstellar distances.
https://en.wikipedia.org/wiki/Wien%27s_displacement_law
Oh! So you’re saying the spectrum of the acoustic noise at a given temperature will be the spectrum of black body radiation! Yes, I could definitely believe that. That is high-frequency indeed.
Sort of. Blackbody radiation is electromagnetic in nature, however under some ideal assumptions you can assume that the molecules emitting that radiation are also vibrating at roughly the same spectrum. ‘vibrating’, though, can mean a lot of different things; this is related to the microscopic properties of the substance and its degrees of freedom. In an ideal gas, it’s taken to mean the particle collision frequency spread (but not necessarily the frequency of particle collisions). If you consider heat to be composed of a disordered collection of phonons, then you could definitely say that this is ‘sound’, but it’s probably neater to draw a distinction between thermal phonons (high-entropy, low free energy) and acoustic phonons.
The reasoning behind blackbody electromagnetic radiation applies equally well to thermal vibrations in solids and gases. Meaning the spectral limits derived from a quantum consideration of the quantization of electromagnetic radiation (into photons) applies equally well to the quantum considerations of vibrational radiation (into phonons).
“Thermal” photons are indistinguishable individually from photons from other sources. The thing that makes a thing thermal is the distribution and prevalence of photons in time and frequency, those from a thermal source follow a well understood set of statistics, while photons from other sources clearly deviate from that. So a photon arising from a cell phone tower’s radio transmitter reacts similarly with a cell phone’s radio receiver as a photon at a similar frequency arising from thermal emission from the air. Physics can’t distinguish between these two photons which is why it is a major effort in building radio communications to get enough signal-sourced photons compared to the thermal-sourced photons so that the signal-sourced photons dominate, and therefore the signal can be accurately derived from their detection.
Similarly with phonons. Vibrations because something is hot are indistinguishable from vibrations from a vocal cord. It is the statistical distribution of the vibrations in time and frequency that defines a thermal set of vibrations. And again, to hear what someone is saying, it is important to get enough phonons from their vocal cords into your ears compared to the phonons from other sources in order to accurately enough derive the intended information.
Thermal noise or other white noise, and a symphony, have the same kind of phonons and both can be heard by the same kinds of ears. They carry different kinds of information (they sound different) because of their different time and frequency statistics.
Black-body radiation is electromagnetic radiation, so I’m a bit confused how that’s connected with acoustic noise. As to molecule collisions, I’m not sure vibrations at sufficiently high frequency can be called “acoustic” at all.
Your reasoning here carries useful information. For example, when you are dealing with vibrations whose frequency is so high that the wavelength of the vibration is less than the average spacing between molecules in a gas, or in a solid lattice, then a lot of what you calculate about the detection and interactions with lower frequency vibrations no longer applies.
However, the same limitations apply to electromagnetic radiation. For example we think of vacuum or empty space as transparent to EM radiation, and it is as long as the EM frequency is low enough frequency. But high enough frequency EM radiation, empty space is opaque to it! For example, at high enough frequencies, a single photon has enough energy to create a positron-electron pair in free space. Photons at that frequency don’t travel very far before they are destroyed by such a spontaneous generation of particles.
So in principle, EM radiation and acoustic vibrations are the same in this respect: as long as you are considering frequencies “low enough” that they don’t rip apart the medium in which the wave exists, they behave in the ways we usually think of for sound and light. But above those frequencies, they rip apart the media they are traveling through, even if that medium is so-called empty space.
So what kind of energies are we talking about here, and what distances?
Photons with over 1 Million electron volts of energy can create a positron-electron pair, but only when near another massive particle (like the nucleus of an atom). The other massive particle is moved in the interaction but is otherwise not-necessarily changed. https://en.wikipedia.org/wiki/Pair_production. This process has been demonstrated experimentally. The mean free path of the energetic photon near an atomic nucleus is something down on the atomic scale, the experiment I read about used a piece of gold foil and generated lots of positron-electron pairs.
A single photon in otherwise empty space cannot create a pair of particles I was wrong when stating that. However, space with nothing but two photons in it can create matter. Two photons each with a bit over 511 million electron volts of energy can collide and result in the creation of a positron and an electron. https://en.wikipedia.org/wiki/Two-photon_physics Alternatively a single 80 Tera Electron Volt photon can collide with a very low energy photon to create an electron-positron pair. This effect actually makes our existing universe opaque to photons above 80 TeV because our universe is filled with approximately 0.0003 eV photons known as the Cosmic Microwave Background radiation. This background radiation is left-over radiation from the big bang which by now has cooled down to about 3 Kelvin in temperature. I don’t know any of the actual mean-free-paths associated with this, just that they are much shorter than interstellar distances.