Quantum steampunk, a retrofuturistic field of physics
popularmechanics.com
popularmechanics.com
OK, but then if I saw a video of Brownian motion which is for all intents and purposes time–reversible, should I conclude the time is in fact not moving forward?
Maybe another way to phrase the question: at the end of the universe when entropy has reached its highest state, does the time dimension of the universe disappear?
One could say "I spent, 1 hour looking at this still picture", but from the picture's perspective no time was spent, because the time in the world of the video is the delta between its frames, like the time in our world is expressed through increased entropy.
Inquiring time before or after the universe is like asking the question "what is the duration of this jpeg image?"
Even as the concordance model cosmos asymptotes to (vacuum) de Sitter, with fully evaporated black holes and less than one proton (assuming they're stable) per Hubble volume, there will be at least a sparse gas of cold photons from two sources: the relics (the cosmic microwave background) and the horizon radiation. A comoving observer, who has an isotropic view of these photons, would still in principle be able to detect the metric expansion in the spectrum of these extremely long wavelength photons. More vacuum being created means (Boltzmann) entropy is increasing: one can substitute microscopic sections of vacuum with each other and do so wholesale without getting anything but vacuum.
Importantly though, not all timelike observers in the ultra far future need to be comoving: they can be highly boosted with respect to the remaining sparse radiation, and can even be accelerated with respect to it. That means they'll see a dipole, bluer in one direction, more particles in the bluer direction. In turn that means have an easier time looking for the spectral signature of the adiabatically cooling relic photons and the horizon radiation, even if there is nothing else they can observe. (By Unruh and Hawking an ultra-accelerated observer could see and/or generate massive particles).
Therefore, "entropy can increase no more" depends choosing [a] a (large) subset of possible observers to the exclusion of others and [b] treating the cosmological frame as useful in picking out quantities like entropy when the sparse distribution of matter barely favours that frame's use. Neither is in the spirit of relativity. Switching to different set of coordinates can reveal an increasing volume of relatively empty space and a cooling of the remaining relic radiation and the relatively newer emission from the cosmological horizon (see Gibbons & Hawking (1977), Phys Rev D 15 or the sadly not very detailed <https://en.wikipedia.org/wiki/Gibbons%E2%80%93Hawking_effect>).
Therefore, in an FRW universe that asymptotes to de Sitter -- our standard cosmology -- there is no true vacuum state for a comoving observer, and there are many-particle states for various other observers. So at least Boltzmann entropy (S = k_B log W) can always increase and this increase is in principle measurable by whatever scientist is left in the almost void.
(Of course, our model cosmology gets updated from time to time with new discoveries, and it may turn out that we are not destined to asymptote to de Sitter, but at the moment as far as we know there is not much wiggle room without adding as-yet-unobserved features to our known universe.)
> video ... frame[s]
> no time was spent
The apparently paused frame (not much is going on in any direction) will grow from a very very dark grey (in the sense of "grey body radiation") to even darker grey while on "pause", as the (time-dependent) Hubble parameter decreases and as the CMB redshift (and the redshift of earlier-time cosmological horizon radiation) increases.
Ignored above: relic neutrinos, fluctuation theory and nonequlibrium statmech in general, observers with relativistic spin; these can all break the placidness of a far-future "tremendously low frequency" (sub-)radiotelescope's view. Also don't see much point in delving into speculative physics (like BTSM particle physics, quintessence and similar dark energy, or non-GR gravitation) looking for anything that undermines the above or which might support your analogy.
> Brownian motion which is for all intents and purposes time-reversible
How does the Brownian motion in a hot cup of tea compare to the Brownian motion in a room-temperature cup of tea? If you wait long enough, how does your hot tea not cool down?
(Or you can substitute an ideal gas in a container of volume V and the same ideal gas after adiabatic cooling after one increases V to say 4V while keeping everything else the same.)
> does the time dimension of the universe disappear
On theoretical grounds, no. All timelike and lightlike trajectories (that do not enter black holes) extend to the infinite future.
On practical grounds, maybe. In the standard model, our universe's volume keeps expanding into the infinite future, adiabatically cooling the matter (and radiation) within it, leading to among other things the redshifting of the cosmic microwave background. There is also cold (and cooling) radiation from the cosmological horizon. These photons may become very difficult, and in practice impossible, for some future scientist not accelerated with respect to the cosmic horizon to detect. However, strong acceleration, or a boost with respect to the cosmic frame, gives hotter and more particles in one direction, making them easier to detect.
So if even in the extreeeeeeeme future there exists the possibility of an accelerated or ultraboosted observer, can one say that the universe is truly frozen up to undetectaby small fluctuations in the energy-density of a (set of) chosen point(s)?
There are certainly ultraboosted observers of a sort now: cosmic rays ejected from extreme events like blazars and supernovae, including the famous "oh my god!" particle are examples. The GZK cutoff is a mechanism by which ultraboosted charged particles interact (given sufficiently long distances) with very low frequency photons, such as those from the cosmic microwave background. This mechanism should persist into the infinite future, so ultra high energy particles spit out of the last evaporating black holes might create interesting fireworks that way, for a very long time. They'd become rarer and rarer, but it's not clear they would ever totally vanish (it's something I'd have to actually calculate because I don't trust my intuition there!). Even if such naturally ultraboosted photons did become extinct, a future observer with an enormous particle accelerator could probably scatter charged particles off distant and very red photons. It might take a long time for the ultraboosted particle to interact with a very red photon and thus the roundtrip might be annoying for that future scientist, but at least there is a way to tell that the universe beyond its local laboratory is not completely empty (indeed with some care the scientist could continue to track the expansion history of the very red and very sparse universe of many trillions of years from now).
> highest state
The highest Boltzmann entropy would be complete vacuum, but that is unachievable because of horizon radiation, and therefore extreme observers (extremes of linear momentum against the horizons and the cosmic microwave background; extremes of spin angular momentum; extremes of acceleration) can still get a fairly exciting sky even as the universe empties out. They in turn might also produce exciting moments for bored observers of a very very dark sky.
Penultimately, "sky" and the equivalence principle: if there remains a planet with a high surface gravity after galaxies are gone and black holes have evaporated, any instrument placed on that will get a view with hotter/bluer and more particles than an low-mass instrument (like JWST mass) freely floating in space and seeing no (or only very very weak) dipole isotropy to the CMB.
And finally, that's not super fanciful - we already know some stars have been ejected from their galaxies (and very likely galaxy clusters), so a "dead" planet in its own Hubble volume is plausible. Maybe an observatory was built on a superearth before it escaped into inter-galaxy-cluster space, equipped with some reservoir of power that can last until the dark times.
So,
> entropy maximum
Given current knowledge, totally empty space is not a configuration our universe will relax into, although it'll be a very good approximation.
> time dimension
Here we return to the theory. Our universe is locally Lorentz-invariant, meaning there are three spacelike dimensions and one timelike one, and physics doesn't change for a system displaced very slightly in space or in time. There is no way to change that aspect of the universe without a fairly dramatic modification of extremely well tested parts of modern physics, and that necessarily includes a cut-off mechanism that keeps what we see here-and-now (and older distant things) locally Lorentz-invariant. (The other end of the universe has this issue too: if you want different dimensions or want break the translation invariance in our 3+1 dimensions near the hot big bang you have to make them something we don't notice here-and-now or in faraway things we see that are backlit by distant quasars).
Local Lorentz invariance everywhere leads to my paragraph near the top. It gives us three types of trajectory (spacelike, timelike, lightlike) and guarantees that the latter two types all go to the infinite future (if they do not enter black holes). <https://en.wikipedia.org/wiki/Causal_structure#Tangent_vecto...> for details.
It's not about just the egg ,but the whole universe moving backward in time, i think.
That explanation uses some weird definition of "time" that depends on stuff happening, not on that thing we keep going through independently of what we are doing. But it's a valid definition, it's just not usual.
If you consider a box of gas that just recently was in the improbable state where all gas molecules were concentrated in one corner of the box, and the current situation is such that you can trace back from the current trajectory of the molecules the prior improbable state with high confidence, then yes, entropy is obviously increasing. On the scale of the universe, this can be taken as an analogy to the low-entropy state right after the big bang and the current higher-entropy state.
However, I don't see how this explains an arrow of time in terms of breaking eggs and the human brain's perception of time.
Entropy "feels" more like an emergent property of any system of probability then a fundamental force - i.e. build a rule set, and anywhere you have state transitions you'll have entropy emerge as a term you can calculate and measure.
The thing is the other candidates are kind of equally mysterious. For example if you go with the idea that all matter is 4D vectors with a magnitude of C in spacetime, it's not really clear why we can affect our motion through the "time" vector (by acquiring physical velocity in other directions) but not completely invert it, or why there should be a speed limit at all.
This can be expressed in the language of entropy but it is essentially a thermodynamic principle. Carlo Rovelli expressed it in a way that I like:
> In order to leave a trace, it is necessary for something to become arrested, to stop moving, and this can only happen in an irreversible process -- that is to say, by degrading energy into heat. In this way, computers heat up, the brain heats up, the meteors that fall into the moon heat it; even the quill of a medieval scribe in a Benedictine abbey heats a little the page on which he writes. In a world without heat, everything would rebound elastically, leaving no trace.
Also you wouldn't see any eggs, and you wouldn't be making any conclusions based on seeing any eggs because it would be your neurons un-firing that would cause your eyes to emit photons at the egg. Wouldn't it? Or... what? Is that seeing?
If everything goes backwards, isn't that the same as going forwards?
The whole question and answer never made any sense to me. Seems like a lot of words to say nothing.
Usually I would say that the problem is I don't understand, but more and more I'm seeing that people just don't know, but like to pretend they know.
Some people think they find an answer, run with it, becomes a meme, and that's it. "The arrow of time goes forward because we see eggs break".
I hope there's at least a couple physicists somewhere that do truly understand it. But the rest, the egg-breakers, I don't know.
The breaking egg is meant to explain Loschmidt's paradox: the observation that ordinary processes are not just as likely to happen in the reverse direction than the forward one, unlike microscopic one (say, two colliding particles) even if classical Newtonian dynamics says they should be.
The resolution is pretty subtle as it has more to do with the practicality of our definitions that some fundamental truth. While it's true that classical systems have this time-reversal symmetry, as they evolve (more and more collision take place, molecules form and break, etc.) the information that is neatly packed into the initial positions and velocities get more and more spread out into subtle correlations between many different quantities that are hard to measure. If at some point you decide to ignore them you get irreversibility and the law of increasing entropy, which gives you the "arrow of time".
So, the laws are symmetrical but in a kind of pointless way for everyday life. Now, what is time and how do we perceive it is a whole different deal and I'm not even trying to answer, but I think that entropy has not much to do with this.
> If everything goes backwards, isn't that the same as going forwards?
Essentially yes, with some caveats in particle physics.
> Some people think they find an answer, run with it, becomes a meme, and that's it. "The arrow of time goes forward because we see eggs break".
Well, fundamental questions rarely find an answer that satisfy everyone.
Think of it like a basic video playback algorithm, the time is the DELTA of change. Doesn't matter if you run it at 24fps of 144fps, the DELTA between frames is the time experienced not the playback speed. Makes sense?
The FRW gases are uniformly distributed in space at all times in the standard cosmology. This is the homogeneous and isotropic condition. To the extent one can talk about the universe as a "container" for matter, the expansion is adiabatically cooling all the gases but dark energy.
> universe goes from a high-energy state
Measuring energy in a nonvacuum curved spacetime is fraught. There are several ways of calculating a total energy of our universe or of a spacelike hypersurface of it, many of which give you the result that the total energy is "zero". (see <https://en.wikipedia.org/wiki/Zero-energy_universe> and references therein). You probably meant energy-density (energy per unit volume) which for matter on average drops with the expansion (if one puts the expansion into the energy-density and calls it "dark energy" rather than the cosmological constant, which is fairly normal in the cosmological frame, then that component of the energy-density on average does not drop to zero).
The (Boltzmann) thermodynamic arrow of time is premised on the universe moving away from a relatively low-entropy configuration to a much higher entropy configuration, where entropy is measured by the number of ways one can rearrange microstates with no change to a macrostate. One can swap a pair of cubic centimetres of vacuum around within a volume of vacuum of a thousand cm^3 and still have a litre of vacuum. But swapping around two cm^3 sections of human brain within a living person's skull (~1200 ml) or heart within a living person's heart (~280ml) is likely to result in a damaged or killed brain or heart, so the Boltzmann entropy of these organs is much much lower than that of vacuum.
Over the past billions of years an excellent approximation of vacuum has been appearing around every microscopic point far outside clusters of galaxies in our known universe. Global Boltzmann entropy, therefore, is dropping, even if "Manhattan is not expanding". Global energy may be constant at all times. Local energy-density on average will be dropping, but obviously not the local energy-density of, for example, a stomach just supplied with full-fat ice cream.
Local Boltzmann entropy can differ from the global Boltzmann entropy because the latter is measured across a properly closed system (there's nothing outside the universe feeding energy in or slurping energy out) while e.g. Earth gets a lot of insolation useful for phototrophs to lock up energy in complex molecules and low-(Boltzmann)-entropy tissues, and subsequent catabolism produces much lower frequencies than the incoming visible light. That lower-frequency radiation then escapes the Earth in due course. It doesn't escape the whole universe though.
The global increase in entropy, or a coarse-grained Boltzmann entropy (swapping around cubic megaparsecs rather than cubic centimetres), gives a time-orientability to the universe as a whole. In one direction much more vacuum, in the other less vacuum.
> DELTA between frames is the time experienced
Time is continuous in the standard cosmology (and the standard model of particle physics); there's no "frame rate", not even at Planck scales as far as we can tell. Moreover, there is only an extremely weak preference for a universal timeline picked out by the largest-scale distribution of matter (the cosmological frame, which is weak because basically nothing is really always at rest with respect to its expanding coordinates), but the calculations done in that frame are no more and no less valid than the calculations done in any other. While it can be useful to slice the universe up into hypervolumes ordered by the scale factor a(t) -- this is what one tends to do when doing numerical relativity with a 3+1 formalism -- one should double-check results in different slicings to try to find unexpected frame-dependencies. Indeed one should check using the Einstein Field Equations if possible, because it is annoyingly easy to confuse oneself (even for experts) into thinking a frame-dependent quantity or effect is really generally covariant.
In short, if you carefully examine an analogy between a film or video and the expanding universe, you easily run into ways in which the analogy fails.
Indeed when it comes to relativistic systems (like an expanding universe), analogies with everyday systems are rarely much good at all, and they're particularly bad as a starting point for understanding. :-(
https://physicstoday.scitation.org/doi/10.1063/1.881363
If you ever saw an unbreaking egg, you would have bigger problems!
This book is by Nicole Yunger Halpern, who is also the main source for this article. Her work is wonderfully rigorous, creative, and insightful.