The New Thermodynamic Understanding of Clocks
quantamagazine.org
quantamagazine.org
There sort of is though. No fundamental force is time dependent per se. Here is a simple recipe:
1. Introduce a "clock system" to your experiment, whose job it is to be in state |t> at time t. Notice that the eigenstates of the clock system are the same as the quantum fourier transform. The clock Hamiltonian is thus easy to construct.
2. Change any time dependent term in the Hamiltonian into an interaction term between the original system and the clock system. In other words, rewrite H(t)|x> as H|t>|x>.
3. Solve as a time independent Hamiltonian.
4. Time is now an observable |t>. Oddly, it is now entangled with position states |x>.
To make an analogy, instead of having a time dependent force you can imagine your experiment is being conducted on a train moving at constant speed, and the time dependent part is encoded in the curves of the track. Technically the particles of the experiment apply a reaction force on the clock system, but assuming your commuter train is several tons heavier than your subatomic particles this is irrelevant (except of course to get theoretical perfection one requires infinite mass). The entanglement aspect is just another way of saying that if you observe the 3:15 to Yuma at the station, this is highly correlated with observing the time 3:15 on the clock system.
The rest of the article is interesting.
The article describes a clock as a “flow meter for entropy”. That is, that a clock is anything that measures the rate at which entropy is increasing in a system.
The other major idea is that the more energy introduced into the clock, and the more entropy produced, the more accurate the clock.
You may be interested in "Time Orientability" [0]
But the very first clocks don't rely on this at least not as a principle mechanism. Sundials, early astronomical observatories such as Stonehenge, or simply observing transits and occlusions, don't involve an entropic process. Rather, they track the regular and sustained rotational or orbital movement of the Earth, Moon, and planets. They track the passage of periods of time, but that tracking itself doesn't necessitate entropic flow.
(The light that's necessary to observe the movements, of course, does. But that would be part of any time-based observation, and isn't fundamental to the regular movement itself being measured.)
Thought experiment: imagine a box through which 0 information passes; no light, heat, radio waves nothing. There’s a clock in the box. Does the clocks progress reflect the progress of time outside the box?
No, because time is based on causality and in space that’s propagated largely by massless particles.
Light does play a role in illuminating the system, rendering it observable. It's a signalling component. But again, that's exogenous to the system itself. (See discussion of Maxwell's Daemon and the resolution of that paradox for the role of light in that specific thermodynamic process.)
But, and this is key: ANY clock needs some way of passing information on to the observer. From TFA, that might be light, or sound, or chemical potential (received as the smell of rotting garbage). But that is a common element, part of the signalling mechanism, but not of the timekeeping mechanism itself.
For an astronomical clock, in most cases, the regular rotational or orbital motion is the timekeeping mechanism. The signalling mechanism is entirely separate.
E.g., in the Earth-Moon system, timekeeping is noted by both the daily rotation of the Earth, and the monthly orbit of the Moon. The kinetic energy of both those regular motions is not driven in any sense, nor is it measuring a decay.[2]
The signalling comes from an exogenous light source (the Sun) which illuminates both bodies. But the Sun isn't powering the timekeeping mechanism in question. And is equally significant in providing the light necessary for you to read a wristwatch or wall clock (of a non-illuminated variety).
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Notes:
1. I'm going to leave discussion of just what gravity is and/or how it's manifested out of this discussion. Veritassium tackled this recently though: https://youtube.com/watch?v=XRr1kaXKBsU
2. Yes, there's tidal friction. That's removing energy from the system, and is measurable with sufficiently precise clocks and over time. But that's also incidental and secondary to the motions in quesiton. We could use far more remote bodies (e.g., the Earth and another planet) in which mutual tidal forces are minimal, to eliminate this consideration. Or presume tidally-locked bodies in which orbital / rotational kinetic energy and angular momentum are constant.
The clock here isn't the sundial but the movement of Earth (the sundial or the astronomy observatory is effectively a measurement device). If you see the movement of Earth as a whole, it's clear it's losing energy to heat, like all clocks.
Something else that can be said is that clocks are computing devices; and computers are thermal machines too.
That is: as the Earth rotates or orbits, is it going through some cyclical energy potential flux of any significant magnitude?
I'd maintain that it's not.
The rotation of an astronomical body, or its orbit, is reversible in ways that thermodynamic events are not. If you were to observe a single body spinning in space, or two bodies orbiting one another, you could not tell from a simple observation of the movement whether you were seeing the motion played forward or backward.
(With sufficient numbers of bodies, or a sufficiently long period of time, this would eventually be disernable. But not at a macro level.)
For other thermodynamic clocks, this seems in general not to be true. Not only does a clock measure time and do so using a thermodynamic gradient, but we can tell which way is forward in time by casually observing the clock itself. Weights fall, springs unwind, batteries discharge, chemicals dissipage or entropise, etc., etc.
That is, an orbit is unlike falling sand, a discharging electric cell, an excited atom, or an unwinding spring. It's not even a periodic exchange of potential for kinetic energy as with a pendulum.
Solar emissions are not integrally central to the clock. That source of entropy can be eliminated.
Tidal losses are not integrally central to the clock, that source of entropy can be eliminated.
What are we left with?
That is the point.
As the Earth rotates, its molten core gets continually mixed (as it doesn't rotate at the same rate as the crust[0]) and this generates heat. Likewise, the atmosphere doesn't rotate at the same speed as the crust, and this generates heat too. And, well, since perfectly rigid bodies can't exist[1], rotating bodies will always release heat, even those who are solid [2]. On the interaction of many bodies, tidal forces generate heat too, again because the bodies aren't rigid.
Those are all dissipative forces. I think it's not possible to have an orbital system composed of purely reversible processes. In this case, any orbital system counts as a clock in the sense of the article.
[0] https://en.wikipedia.org/wiki/Inner_core_super-rotation
[1] due to relativity, https://physics.stackexchange.com/a/201499
[2] actually.. I'm not so sure. I was searching a bit and https://phys.libretexts.org/Bookshelves/Classical_Mechanics/... says the non-rigid body eventually settles into rotating around its principal axis of rotation, which makes it not have any internal stresses, and thus not release heat. I think Earth revolves around its principal axis of rotation though (it had billions of years to settle).
At this point I'm trying to read about orbital mechanics of non-rigid bodies, like this https://impa.br/wp-content/uploads/2017/04/30CBM_03.pdf - the only thing I can gather is that indeed there are dissipative forces even in solids.
Valid point, and a possible out.
Your other suggestions could be eliminated with the tidally-locked black darf / dead planet thought experiment. Here you'd have bodies about as inert as we can conceive of bodies being, keeping a regular time.
Consider what would happen if we used the earth's rotation as a clock, but without generating entropy. We would have a system which would go back to its original state every day, each rotation. This means there would be no way to discern how many days have passed, as the system would be in the same configuration as it was at the beginning of the rotation.
In order to encode how many days have passed, you need to increase the system's information, and by doing so you increase its entropy. The same problem applies to a pendulum clock: you can't have a pendulum clock as anything but an entropy-generating device, or else it will keep going back to its initial state without any changes, not measuring any passage of time at all.
In the pendulum clock, the mainspring provides the entropy flow that allows it to time-keep and register the passing of time on the indicator. In the sundial, the flow of light from the sun into the sundial and into our eyes provides the flow. The light flow gets interrupted by the gnomon, casting a shadow (an irreversible process). In order to register that this has happened, you look at the sundial and take note of the time (another irreversible process). You can replace yourself with light-sensitive paper, which gets etched by the light (yet again another irreversible process).
The other sources of entropy (like tidal friction, as well as atmospheric friction and friction between the layers inside the Earth) are irrelevant for the sundial's working, but could possibly be used to create timekeeping devices themselves.
I'd say the main difference between the Sundial and the Pendulum clock's working is that in the pendulum clock, the energy to keep the pendulum oscillating and to register the passage of time are both provided by the same source (the mainspring), while for the Sundial there are two different sources of energy: sunlight provides the energy to register the passage of time, while the Earth's inertia is the only source of energy that keeps it rotating.
We could make the two systems more similar by changing the pendulum clock so it's only a pendulum, creating a separate indicator consisting of a light shining onto a pendulum and a sheet of photosensitive paper slowly moving down and receiving the pendulum's shadow, registering the passage of time onto the paper without using the pendulum's energy for that.
That's precisely what bodies in angular rotation or orbits do.
"One day looks pretty much like another."
For a sundial, the (apparent) movement of the shadow provides the marker of time throughout the day. It (mostly) doesn't indicate the passage of time greater than a day (not strictly true: see the annalema). But within any 24 hour period, you've got a timekeeping piece in which entropy plays no role in the measurement of the passage of time itself, but only as a signalling mechanism (casting a shadow).
In order to complete the clocked-ness, you either need a second repeating phenomenon (e.g., Earth's rotation vs. Moon's orbit, Earth's rotation vs. Earth's orbit). In which case with an external recording mechanisms the passage of time can be noted.
But the fundamental timekeeping mechaism, the phenomenon which is regularly occurring with time occurs without discernable entropic decay, once set in motion.
The rotation or orbit is the escapement here. It's functioning without an entropic drive.
Pointing out that an entropic flow might be used independently of a sundial does not explain how it relates to the sundial.
You don't need a second repeating phenomenon, just as you don't need a second pendulum in the pendulum clock. The pendulum might repeat its motion at a short interval, but is able to measure intervals longer than its period.
If you have a sundial that works without increasing entropy, it doesn't work as a clock. Just as a perpetual motion pendulum alone wouldn't work as a clock. Using other orbits doesn't change that. You need the entropic flow to register the passage of time. In the case of the sundial, it can be done by recording its cycles.
A sundial on a rotating planet isn't able to measure time within its cycle without increasing entropy any more than a pendulum is able to measure time within its period without increasing entropy. They're not able to do that. A Sundial without light and a recording device isn't a clock, just as a lone pendulum with no energy losses and no recording device isn't a clock.
also note that if there's no sun (no energy), time keeping functionality is severely limited.
Sundials and astronomical observations are not principle mechanisms of clocks.. they are a window of observation into the clock system of moving planetary bodies. Those planetary bodies indeed follow the thermodynamic principles outlined.
Imagine you had a rotating disc occluding a light source with a thin slot cut in the disc such that every rotation at one small interval the light source is visible. Rotate it using, say, a coiled spring, and you have a clock, revealing a pulse of light with a constant frequency. This is easy enough to fit into the mold of a thermodynamic clock as proposed in the article.
Now, we can think of earth orbiting the sun similarly to our disc rotating in front of the light source…. Every time earth rotates on its axis, half is exposed to the light and half is not…. Quite a wide ‘slot’ cut into our planetary ‘disc’, not useful for much more than knowing what day it is.
All a sundial does is narrow that ‘slot’ to make a more accurate observation of our planetary clock’s state.
Same goes for observing other planets / stars etc. While these planetary motions appear to be ‘regular and sustained’ on our timescales, they are still subject to the same thermodynamic principles as all other matter, and reach lower entropy over time, until the heat death of the universe :(
Someone posted about two bodies orbiting each other, and not know time forward from backward.. again, you can’t ignore physics, those orbits will measurably and irreversibly decay over time until the bodies collide.. just not on timescales that would effect our species using them as clocks!
How is the nuclear fusion happening in the Sun and other stars producing rays of light not an entropic process?
As I've suggested elsewhere in the thread: imagine a black dwarf and dead planet in orbit.
Clock or no clock?
Entropic or not entropic?
Because without fusion we would not observe them.
That's a common element to any observation-based system.
Or, put another way: if a dead planet orbits a black dwarf whilst tidally locked in an utterly dark Universe, does time exist?
Is the observer necessary?
- I'm familiar with Eddington's "arrow of time" and the concept's fascinated me since I first encountered it listening to a lecture by Stephen Hawking, and reading his own A Brief History of Time. (The lecture was effectively a chapter from the book.)
- The question of whether or not all clocks are entropic has bothered me ever since.
- It's relatively recent delvings into origins of technology, and recognising that astronomy was in large part the science of time, as well as the fact that most of our historical measures of time were based on astronomical phenomena (the day, month, and year, as well as multiples and subdivisions --- reliance on nonastronomical standards is a modern departure largely undertaken for accuracy but not basis).
- In the Seven Liberal Arts, the trivium concerns data input/output and processing (grammer: parsing input, logic: processing, rhetoric: output), whilst the quadrivum is quantitative: arithmatic is quantity, geometry is quantity in space, music is quantity in time, and astronomy is quantity in space and time. That adds an additional dimension to astronomy, but again, the role of ancient astronomers in timekeeping, prophecy, and navigation remains significant.
Reducing my argument above to its essence, I like the formulation I arrived at in one subthread here, a variant on the "if a tree falls in a forest" conundrum:
If a dead planet orbits a black dwarf whilst tidally locked in an utterly dark Universe, does time exist?
Is the observer necessary?
Incidentally, I've been thinking about a time travel game along those lines: if you ever return to a save point but the game is at a previous configuration, this counts as a time travel (which can be, like.. a multiverse travel if time branched out.. which amounts to the same thing), just like if you selected a time travel in the UI.. two game states can't be in a different time if they are identical.
Of course if the mechanic is just this, then this is just a regular save/load state with infinite save lots. Which is a funny observation. Then I need to add other mechanics on top, like carrying things from a timeline to another, which is where the physical analogy would break up.
The many-worlds quantum interpretation says that, likewise, when we go to the _future_ we also have multiple timelines, and nature somehow just pick one arbitrarily, and this becomes "our" timeline. Then to reverse time, perhaps it's sufficient to employ the same mechanism, but in reverse. (Perhaps there's already beings that live backwards in time, it's just that "their" timeline works that way. Like the movie Tenet). Or even, perhaps each time the timeline splits in the future direction due to quantum phenomena, it also equally splits when going in the past, in the exact same way.
(Well I'm trying to recover some symmetry here, but not sure if it works)
A clock by definition is something that produces a regular series of pulses. In other words its signal is sparse in the frequency domain.
To keep it sparse, you constrain it by its geometry (if it’s electrically driven then you contain the fields in a narrow region of space). If it’s mechanical you constrain its physical dimensions etc. And finally you filter out thermal noise by lowering the entropy of the system. This is where standard thermodynamics enters into the picture…to cool the clock (say) you have to increase the entropy of the universe. The “lab conditions” under which you operate the clock though, are a low entropy zone.
But the nature of pure oscillations has no dependence on entropy—quite the reverse, the clock itself operates in a low entropy environment. In other words you can predict exactly what frequency state it’s in. Proof of this is the fact that you can print the frequency on the outside of the box in permanent paint.
Astronomical bodies float in space and they are already in a sparse environment as far as gravity is concerned. There are 7 major planets besides earth and the sun has most of the mass of the solar system. The spaces between the planets are relatively debris free. The asteroid belt is quasi-uniform. So they move kind of regularly. Where they couple energy between planets that can be predicted using Newtons laws. What makes it a clock is the empty space between the planets. If the solar system was full of dust with storms etc then the motion of the planets would be subject to “weather” like conditions and nobody would treat it like a clock (just as we don’t keep time by the arrival of the rain).
We’re spoiled on earth by the presence of this regular motion on the skies above that is independent of all that is happening in earth. So that’s where our notion of a “fixed” absolute clock comes from.
What does this mean for atomic clocks? In the lab we try to reproduce these space like conditions (by keeping air currents, external stimuli out) and think that vibrating atoms are telling us something absolute about nature. It’s perhaps better to say that they are relatively more stable than our living environments and independent of whatever we are trying to measure. But is there some master clock in the universe that these atoms are tapping into and recording for us? No. There’s no such thing. They are just drums that beat to their own tune which happens to be defined by their dimensions and the local properties of space around them. The fact that all atoms of the same type under the same conditions are all the same size makes atomic clocks possible.
Logically, both time and gravity are essentially inferred substrates to how we observe space and mass/energy.
Regarding the explanation in the article about how they're using thermodynamic entropy and information entropy together as a defining gauge for clocks at all scales, I would wonder if time relates to mass and gravity the way width relates to height, in that one is conceptually "perpendicular" to the other, and what it might mean for time to be perpendicular to gravity (if they weren't just the same thing).
Last I read, there wasn't a full quantum theory of gravity that is consistent with experimental observations of macro gravity via relativity because of quantum "weirdness," because at that quantum scale there is almost no physical "time" effect other than entropy that we use as a reference.
What we call quantum weirdness could literally just be the lack of time effects preventing things from happening all at once, and it's absent because gravity at that scale is effectively absent.
No gravity, no time (quantum weirdness). Less gravity from being far from a well, faster time (aging effects). Total singluarity gravity, stretched time over its horizon (black hole time). When you never see them together, I'm just saying it starts to looks suspicious.
I only mention it because I was literally just on a crazy bit that started with the joke where someone said, "faster than light travel is impossible," and ever the optimist I said, "helicopters, also impossible," which is funny to anyone who knows about helicopters. It turned into whether instead of super massive objects distorting space, there could be lower energy pulses and oscillations with effects like a resonant frequency, where instead of causing big distortions, could cause whorls and ripples of equivalent "space-turbulence" around them - not unlike the conceptual effect of helicopter blades, but using EM, and likely from an element or crystaline structure that facilitated an amplification feedback loop. You could detect the distortions because they would become "cold," as the space around them "spread." If gravity and time were the same thing, you could create a wave in space using turbulence and travel the substrate (time/gravity) directly. Faster than light travel is impossible only in space, where in a time/gravity substrate it's moot.
Totally sci-fi speculation, but as a result I have since put a sticker on my eurorack synth that says, "danger: time machine"
But seriously, how much confidence do we have that time and gravity are NOT the same thing?
Well gravity is the curvature of spacetime. So maybe not time exactly.
It seemed like the question that needed to be answered was does the inherit randomness of a clock tell us anything about spacetime itself? Or is it just telling use how well we can measure it?