4 ms·

Well, the egg is just an example. The actual definition is that the universe goes from a high-energy state to an equilibrium of distributed energy (like a gas s

Well, the egg is just an example. The actual definition is that the universe goes from a high-energy state to an equilibrium of distributed energy (like a gas spreads to take up its container space). This tendency for entropy to ever increase marks the arrow of time. 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?

raattgift 4y ago
> like a gas spreads to take up its container space 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 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. :-(

raattgift 4y ago

> like a gas spreads to take up its container space 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 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. :-(