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October 24 - November 3, 2019
Nobody really gets it. It’s one of the biggest puzzles of cosmology where the organization comes from, and in what way the Big Bang really represents organization in any case.’ ‘Maybe there was something more organized before the Big Bang? That might do it.’
‘People have actually tried suggesting things like that for some while. There are theories in which our presently expanding universe had a previous collapsing phase which “bounced” to become our Big Bang. And there are other theories where little bits of a previous phase of the universe collapsed into things we call black holes, and these bits “bounced”, to become the seeds of lots and lots of new expanding universes, and there are others where new universes sprang out of things called “false vacuums”…’
What the Second Law indeed states, roughly speaking, is that things are getting more ‘random’ all the time. So if we set up a particular situation, and then let the dynamics evolve it into the future, the system will evolve into a more random-looking state as time progresses.
Entropy is clearly an extremely useful physical concept, but I do not see why it need be assigned a truly fundamental and objective role in physics. Indeed, it seems reasonable to me that the usefulness of the physical notion of entropy has its origin largely in the fact that, for systems that we tend to encounter in the actual universe, it turns out that the normal measures of ‘macroscopic’ quantities give rise to coarse-graining volumes that do in fact differ from one another by stupendously large factors.
In fact we can understand this seeming past-teleology of behaviour if we simply suppose that the very origin of our universe was represented in phase space by a coarse-graining region of quite exceptional tininess, so that the initial state of the universe was one of particularly small entropy.
Provided that there is no corresponding low-entropy ultimate state of the universe, or some such, providing us with a teleological demand that the universe’s evolution curve has to terminate in some other extraordinarily tiny ‘future’ region in , then our reasoning for the increase of entropy in the future time-direction seems to be perfectly acceptable. It is the initial low-entropy constraint, demanding that the evolution curve originate within the extraordinarily tiny region that gives us a theoretical basis for the Second Law that we actually experience in our universe.
it has occasionally been argued that the existence of a Second Law holds no mystery, for our experience of the passage of time is dependent upon an increasing entropy as part of what constitutes our conscious feeling of the passage of time; so whatever time-direction we believe to be the ‘future’ must be that in which entropy increases.
Thus, so the argument goes, our psychological experiences of the passage of time would always be such that the Second Law holds true, irrespective of the physical direction of the progression of entropy.
This early spatial uniformity represents the universe’s extraordinarily low initial entropy.
The structure of life on this planet would run rapidly down were it not for a powerful low-entropy source, upon which almost all life on Earth depends, namely the Sun.
Thus, there are many more photons carrying the same energy away from Earth than there are that carry it in from the Sun. See Fig. 2.9. More photons imply more degrees of freedom and therefore a larger phase-space volume. Accordingly, Boltzmann’s S=klogV, (see §1.3) tells us that energy coming in from the Sun carries a considerably lower entropy than that returning to space.
So what the Sun does for us is not simply to supply us with energy, but to provide this energy in a low-entropy form, so that we (via the green plants) can keep our entropy down, this coming about because the Sun is a hot spot in an otherwise dark sky. Had the entire sky been of the same temperature as that of the Sun, then its energy would have been of no use whatever to life on Earth.
Einstein was less than enthusiastic about the idea. But later he realized the crucial importance of Minkowski’s geometric notion of space-time. Indeed, it formed an essential ingredient of his own generalization of Minkowski’s proposal to provide the curved space-time basis of his general theory of relativity.
the points of this 4-space are frequently referred to as events, since any such point has a temporal as well as a spatial specification.
Thus, in Minkowski’s 4-geometry, we are not now to think of the space-time as being simply built out of a succession of 3-surfaces, each representing what we think of as ‘space’ at various different times (Fig. 2.10). For that interpretation, each of these 3-surfaces would describe a family of events all of which would be taken to be simultaneous with one another.
What Minkowski’s space-time achieves is to provide an objective geometry, that is not dependent on some arbitrary observer’s view of the world, and which does not have to change when one observer is replaced by another. In a certain sense, what Minkowski did was to take the ‘relativity’ out of special relativity theory, and to present us with an absolute picture of spatio-temporal activity.
This illustrates the key fact about the metric of space-time, namely that it is really something that has much more directly to do with the measurement of time rather than distance. Instead of providing a length measurement for curves, it directly provides us with a time measurement.
It is important for the physical basis of general relativity theory that extremely precise clocks actually exist in Nature, at a fundamental level, since the whole theory depends upon a naturally defined metric g.[2.32] In fact, this time measure is something quite central to physics, for there is a clear sense in which any individual (stable) massive particle plays a role as a virtually perfect clock. If m is the particle’s mass (assumed to be constant), then we find that it has a rest energy[2.33] E given by Einstein’s famous formula E=mc2, which is fundamental to relativity theory. The
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The presence of such space-time singularities has presented physicists with a fundamental conundrum, often viewed as the converse problem to that of the Big-Bang origin to the universe. Whereas the Big Bang is seen as the beginning of time, the singularities in black holes present themselves as representing the end of time—at least as far as the fate of that material that has, at some stage, fallen into the hole is concerned. In this sense, we may regard the problem presented by black-hole singularities to be the time-reverse of that presented by the Big Bang.
