Wikipedia:Reference desk/Archives/Science/2022 October 22

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October 22

Boltzmann constant & Black body

In the entropy of black body radiation, Planck involves the product "kT". It is in Joules, so it is energy, but the energy of what? — Preceding unsigned comment added by Malypaet (talk • contribs) 04:37, 22 October 2022 (UTC)

kT is a Boltzmann factor which is the adjustable parameter for the probability distribution. The shape of the distribution as a function of frequency is determined by the temperature of the radiating object. In order to express the distribution as a function of frequency, the units in the exponent ${\textstyle {\frac {h\nu }{k_{b}T}}}$ need to cancel. You can think of ${\textstyle {\frac {h}{k_{b}}}}$ as a proportionality constant from frequency to inverse temperature, or vice versa. PianoDan (talk) 07:26, 22 October 2022 (UTC)

kT is the energy characteristic of the temperature T. In a blackbody radiation field, the average photon has an energy of kT. More generally, in a random system (a radiation field, a bunch of molecules in a gas, a bunch of magnetic dipoles flipping around, a bunch of stars in a globular cluster, whatever) of temperature T, kT/2 is the energy stored on average in each degree of freedom (see equipartition theorem), for as far as quantum physics allows those energies be be freely chosen. PiusImpavidus (talk) 10:41, 22 October 2022 (UTC)

Power vs energy

I interpret power as a flow of energy. So I add a time dimension to the energy. Are there other interpretations and if so which ones? — Preceding unsigned comment added by Malypaet (talk • contribs) 05:49, 22 October 2022 (UTC)

Not in physics, no. For other meanings of the word generally, see power. PianoDan (talk) 07:28, 22 October 2022 (UTC)

In some cases the interpretation may be helpful to one's intuitive understanding, but in other cases not so much. The concept of flow implies a direction. Power can be used for the speed in which one form of energy is transformed into another form. When powerfully braking a spinning flywheel, the flywheel may become hot. Kinetic energy is transformed into heat. Both are located in the flywheel; there is no direction of transfer in a physical sense.  --Lambiam 08:13, 22 October 2022 (UTC)

In physics, power is the flow of energy. You have to interpret "flow" quite generally. It's not only a flow in space, but could also be a flow in type, for example from kinetic energy to thermal energy. PiusImpavidus (talk) 10:50, 22 October 2022 (UTC)

Thanks, I find in wiki " energy transfert or conversion", also in the example of a hydroelectric plant, we have at the entrance a winding river with a flow of water molecules which each carry a quanta of energy and at the exit electrons which each carry a quanta of energy in all the directions of a region. A flow of water molecules, a flow of electrons, therefore globally a flow of energy. Malypaet (talk) 21:33, 22 October 2022 (UTC)

You seem to be conflating a number of different forms of energy that have nothing to do with each other. PianoDan (talk) 16:50, 23 October 2022 (UTC)

Power as a flow of energetic discrete elements

As energy is always attached to an object or group of objects for which it may vary continuously (kinetic energy), if power is considered as a flow of energy, it may be deduced that power may in addition to vary continuously, be also discrete? If not, how can I correct my analysis? — Preceding unsigned comment added by Malypaet (talk • contribs) 06:09, 22 October 2022 (UTC)

Gravitational waves carry energy. This energy may be transported by gravitons, but their existence is thus far entirely hypothetical, so I don't think it is necessarily true this energy is attached to "an object or group of objects" (are gravitons "objects"?) or transported by "energetic discrete elements". Even if a flow is one of discrete objects, say the output of marbles produced by a marble factory, when the rate of production is geared up to meet rising demand from 10,000 marbles per hour to 11,500 marbles per hour, the "flow" of marbles will not go up in identifiable discrete jumps. So the suggested deduction is a non sequitur.  --Lambiam 08:36, 22 October 2022 (UTC)

Two sections up I mentioned that energy can be attached to a degree of freedom. Is that an object? Or is it really attached to the object that has that degree of freedom? Or all those objects together? If we have a wave in the ocean, is the energy attached to the continuous water, or to a bunch of water molecules, or to some quasiparticle (a kind of phonon) we invent for the purpose? With the wave-particle duality we can do that.

As for continuous versus discrete, if something varies discretely in 10²⁵ steps, isn't it easier to consider it continuously? PiusImpavidus (talk) 11:05, 22 October 2022 (UTC)

The raw data from X-ray telescopes such as Chandra look pretty much like what the OP describes: lists of detector events (let's simply say each corresponds to a photon) with energy and arrival time. The energy deposited in the detector, E(t), is a step function. The power can mathematically be defined as the derivative, ${\frac {dE}{dt}}$, which is then a sequence of Delta peaks, infinitely sharp and infinitely high. While mathematically possible, this description is useless for any practical purpose. In practice, power (strictly speaking flux, but let's skip over that) is measured by integrating (summing the energy deposited) over a finite time and then dividing by that time. Power is a useful quantity in the many-particle or continuum case, not for single particles. --Wrongfilter (talk) 11:30, 22 October 2022 (UTC)

Electromagnetic energy propagates in energy packets (quanta) called photons. The energy of a photon depends on the wavelength and frequency but that raised questions recently about where comes or goes the difference in energy due to to a Doppler shift. Let us consider that electromagnetic energy is emitted from a galaxy light-years distant either by a natural process, or if you like the conjecture, by an alien radio transmitter operator. The emission is a wave whose (reciprocally related) wavelength and frequency can be known at the emitting location. I think it is not possible to transmit defined photons (energy packets) like a machine gun which is constructed to shoot bullets of any defined mass, velocity and kinetic energy. Photons are massless and have only one constant velocity in space. The alien cannot predict where, when or by whom his photon will be detected; in particular no one knows what the relative velocities of transmitter and receiver shall be. That relative velocity dictates what Doppler shift the detected photon will experience: three human observers riding on different moving platforms could see the same photon as red-shifted, non-shifted or blue-shifted depending who observes it. But the energy quantum carried by the photon depends on its detected frequency (colour and wavelength). I conclude that em energy can be emitted only as waves and that its quantization as photon particles happens only when it is detected, and that the energy per photon is not definable until the actual detection. Philvoids (talk) 23:12, 22 October 2022 (UTC)

If you have a single atom in an exited state, it will emit a single photon when it decays to its ground state. So you can definitely emit a single photon (or would you say that you can't have a single atom either?). But the energy of this photon indeed depends on the observer. If the alien emits a 1 s beam of light of 600 nm wavelength with 1 J of energy and I travel towards the alien when receiving that beam, I will detect the same number of photons, I will detect a wavelength shorter than 600 nm, a duration shorter than 1 s and an energy larger than 1 J, so I heat up more than the alien would have expected. But it all works out. The beam of light carries momentum, so my velocity changes as I receive the beam. In my own frame of reference, I accelerate from rest to a low backwards velocity, so I gain a very small bit of kinetic energy. In the alien's frame of reference, I was speeding towards him at a very high speed and slowed down a little bit, releasing kinetic energy. So I heat up a bit more. PiusImpavidus (talk) 09:29, 23 October 2022 (UTC)

I both allow the alien to be female and let her emit a single photon (that in her frame of reference has momentum 1.104345 x 10^-27 joule seconds per meter). She may even transmit a beam of them that extends throughout 299 792 458 meters towards you. For this she may use a focused transmit antenna/orange laser device. During transmission she must stabilise her device against a recoil whose magnitude is calculable in her own frame of reference assuming her antenna is impedance matched (VSWR=1, no reflection) to free space. She may not expect you to rush into her beam but doing so has three impacts: her equipment that might have Lidar capability detects the photon(s) that you must reflect (unless you are exceptionally stealthy) and by their blue-shift it finds your speed of approach, and you do indeed experience a deceleration. That spot of orange light that you chase seems to Doppler-shift towards the sodium yellow D₁ line (see Fraunhofer lines). Your deceleration and heating depend on your own initial speed of approach, your Reflectance and Heat capacity i.e. things she could not have planned for long ago. I don't think anyone since Tesla (?) has seriously claimed that wireless power transmission can be lossless. Philvoids (talk) 19:54, 23 October 2022 (UTC)

Product of time vs division of time

I know the meaning of the units m/s, j/s, kg/s, etc... It is a question of quantifying a unit by a unit of the time that passes. But what is the meaning if I use m*s, j*s, kg*s, etc...? What is the meaning of a product by unit of time ? Malypaet (talk) 22:07, 22 October 2022 (UTC)

Any time you multiply a quantity with units of meters by a quantity with units of seconds, you'll get a quantity with units of meter-seconds. The meaning would depend on the meaning of the quantities you're multiplying.

I can't think of any "typical" example, but you could come up with something contrived. For example, suppose you have a wide river of uniform depth and speed, and you want to know how much water passes a given interval perpendicular to the river in a given time. That would be proportional to the product of the length of the interval and the time, which would be measured in m·s. Maybe someone else will be able to come up with something less contrived. --Trovatore (talk) 22:38, 22 October 2022 (UTC)

I asked about this before. One might say that a 3 billion year old diamond with only 1 gram of matter is more time-massive than a quadrillion gram iceberg that's 1 minute old. Sagittarian Milky Way (talk) 23:11, 22 October 2022 (UTC)

If I understand correctly, this notion cannot be part of the domain of physics (reality), but rather of the domain of mathematics, where one can lay any foundations of a new set and then evaluated in this set to pose and solve problems. Malypaet (talk) 04:22, 23 October 2022 (UTC)

"All observations are theory-laden." I agree that these examples are not extremely "natural" concepts, but I'm not sure in what way they're "less physical" than other physical quantities. If you have a way of making this precise, it could be interesting. (As an aside, I also consider jerk to be a "less natural" quantity than acceleration, but I haven't been able to make precise what I mean, so I would be genuinely interested in considerations along these lines.) --Trovatore (talk) 20:19, 23 October 2022 (UTC)

Typical example would be impulse, F.t, which is equal to the change in momentum. (I vaguely remember that is how Newton stated F=m.a) . But you are right it is rare to see t in the numerator. Greglocock (talk) 06:33, 23 October 2022 (UTC)

If something acts on something for a while, the effect may well be proportional to how hard it is acting and for how long it is acting. A typical example would indeed be a force acting over a time, giving a change in momentum, or a pressure acting over some time on a highly viscous fluid, giving the resulting deformation. Energy times time, also known as action, is a common one too, but is more theoretical. We don't see action, but it helps to find the equations of motion of a system. Planck's constant and angular momentum also have the dimension of action, showing us how to quantise the latter. PiusImpavidus (talk) 09:54, 23 October 2022 (UTC)

@Malypaet: First of all please notice that a 'product of units' notion is secondary to a 'product of quantities'. For example velocity (assume a uniform motion of a small body) is a ratio of distance travelled and time we consider. For the same body and the same motion we can apply different units, thus getting the velocity in miles per hour, meters per second, astronomical units per year, and so on. So, there's nothing special in multipying or dividing by 'seconds' here, it's actually just a result of quantifying a specific quantity (time) in some chosen unit (second). The underlying, and the actual question here, is what it means some quantity is directly proportional, or inversely proportional, to time.

To see it, just take any correlation with the direct proportionality to time, and inverse it.

Let's take the example above: the distance covered in a motion is a product of velocity and time: s=vt. If we assume some constant velocity of an object, and ask how the distance covered depends on time; then the answer is 'the distance travelled is proportional to a time of movement', which is concisely expressed by the equation. We can, however, assume a constant path to be travelled and ask for a velocity needed to complete the path in any given time. Then we get 'velocity needed to travel the given distance is inversely proportional to a time required', v=s/t.

Similarly, an electric charge q (measured in coulombs, C) transmitted through a conductor in time t (in seconds, s) by a current I (amperes, A) is q=It, and a current I that transports a charge q in time t is I=q/t. This results in units' equivalence A=C/s or C=As, which are the same equations above for unit quantities: 1C=1A·1s or 1A=1C/1s.

The same way power is energy or heat transmitted or work done, divided by time and, coversely, energy/work is power times time: P=E/t, E=Pt, hence the unit's equivalence watt=joule/s, joule=watt·s.

Same applies to any physical process in which some quantity is proportional to time. --CiaPan (talk) 15:34, 23 October 2022 (UTC)

But in all tour lasts examples, as for joule=watt*s and all, you multiply a quantity that is time dependent to remove time and get it's value.

I challenge you to provide me with an opposite example like "joules*s", "C*1s" or "s*t". These relations are not commutative, contrary to what you present to us. Malypaet (talk) 21:18, 23 October 2022 (UTC)

And of course, joules, coulombs and distances are not dependent on time, which is why we add quantities like watts, amperes and speed to them. Malypaet (talk) 21:21, 23 October 2022 (UTC)

In quantities belonging to SI base units, energy is mass times area divided by time squared. Power is mass times area divided by time cubed. Both of them have time in their dimension, but that doesn't make either of them explicitly time-dependent. Neither are they area-dependent. Electric current is expressed in a base unit, electric charge is electric current multiplied by time. A coulomb is defined as an ampère-second, an ampère isn't defined as a coulomb per second. So there you get one. Of course, the selection of base units is arbitrary. Instead of using base units for time, length, mass and electric current, we could have used them for energy, momentum, angular momentum and electric charge. Then, power is energy squared divided by angular momentum and current is charge times energy divided by angular momentum. It's just that we already had established base units for length, mass and time before we started doing proper science and current is easier to deal with experimentally than charge. And guess what, to define the base units, we defined some constants of nature: charge, action or angular momentum, frequency and speed. PiusImpavidus (talk) 09:26, 24 October 2022 (UTC)