Bill S

I didn’t intend giving the impression |I thought the “big bang” caused the inflation; rather, I saw it as a result. Is it better to consider the image of a sphere rolling down a slope as a visual representation of a symmetry break? Vilenkin talks of a situation in which a false vacuum exists at every point in space. This is represented by a sphere resting in a valley that is at a higher level than the true vacuum. Would that equate to your pencil balanced on its point?

Images of this landscape are inhabited by scalar fields; represented by spheres. These spheres appear to have energy levels that reflect the energy level of their positions in relation to the height they occupy on the landscape. A scalar field that is at, or near, the top of a hill will equate to a false vacuum state. If/when a sphere rolls down to a lower energy level its energy dissipates as a “big bang”, and results in the formation of a new universe.

I’ve just read Alex Vilenkin’s “Many Worlds in One”. There were several references which gave me this impression. Possibly “eternal” would have been a better word. Infinite extent (in space) seems to be optional, but infinite extent into past and future appear to be an essential feature of “eternal” inflation. Given this eternally existing vacuum; my next impression is that the variations in vacuum energy can be visualised as a “landscape” in which higher energy conditions are represented by hills and lower by valleys. The lowest of these valleys would be the “true vacuum”, and the hills and slopes represent “false vacuum” states, which are unstable.

I’m trying to grasp, in a non-technical way, the ideas underlying the theory of eternal inflation. If I post some of my thoughts, I would really welcome comments/criticism as I go. In order to have a situation in which this eternal inflation can operate, we must have an infinite vacuum, with a measurable vacuum energy. Quantum mechanics provides us with this, because it forbids us from having the classical vacuum, which can be identified as absolutely nothing. Absolute nothing provides absolute information about its state, and the uncertainty principle does not give us that luxury. There has to be the possibility that the vacuum is something. In fact, to the best of our knowledge, the vacuum is, on the scale of the Planck’s length, a very active and energetic place.

OK, that’s a better way of describing it. I was trying to clarify in my own mind the relationship between thermal equilibrium, restricted degrees of freedom and low/high entropy, and to relate that to the Big Bang.

Popular science literature often raises questions about a “boundary condition” at the Big Bang, which necessitated a low entropy scenario. In the FLRW model the Universe in its first instant is miniscule (a single quantum, as Lemaître described it). This “Primordial Atom” contained all the matter and energy of the Universe, which completely filled the tiny space it occupied. In that first “quantum” matter/energy occupied all the available space; there was no room for “manoeuvre”; entropy could not have started evolving until more space became available (?). What does it mean to equate this to a low entropy boundary condition? Surely, in that first instant, entropy was at the maximum possible for the conditions, albeit for only the briefest instant.

The OP arose from Anathaswamy’s article in New Scientist, 07.08.2010, which I found when throwing out some back numbers. The article contained a ref. to Physical Review D, vol 79; which took to material that was beyond me, and seemed not relevant to my problem. The following is an extract from the article: “Something has to give in this tussle between general relativity and quantum mechanics, and the smart money says that it's relativity that will be the loser. So Horava began looking for ways to tweak Einstein's equations. He found inspiration in an unlikely place: the physics of condensed matter, including the material of the moment- pencil lead. Pull apart the soft, grey graphite and you have a flimsy sheet of carbon atoms just one atom thick, called graphene, whose electrons ping around the surface like balls in a pinball machine. Because they are very small particles, their motion can be described using quantum mechanics; and because they are moving at only a small fraction of the speed of light there is no need to take relativistic effects into account. But cool this graphene down to near absolute zero and something extraordinary happens: the electrons speed up dramatically. Now relativistic theories are needed to describe them correctly. it was this change that sparked Horava's imagination. One of the central ideas of relativity is that space-time must have a property called Lorentz symmetry: to keep the speed of light constant for all observers, no matter how fast they move, time slows and distances contract to exactly the same degree. What struck Horava about graphene is that Lorentz symmetry isn't always apparent in it. Could the same thing be true of our universe, he wondered. What we see around us today is a cool cosmos, where space and time appear linked by Lorentz symmetry- a fact that experiments have established to astounding precision. But things were very different in the earliest moments. What if the symmetry that is apparent today is not fundamental to nature, but something that emerged as the universe cooled from the big bang fireball, just as it emerges in graphene when it is cooled?” Having read it again, I think I was wrong first time, and Horava is actually saying that Lorentz symmetry isn't always apparent in the graphene until it is cooled, when it becomes apparent. He then compares this to the Universe, and speculates that Lorentz symmetry might have appeared as the Universe cooled. Could I have solved my own problem?

Thanks for the info, folks. Sluggish response on my part does not equate to lack of interest, just lack of time. Just need to do some follow up, now.

I’v I've been looking for “hitch-hiker” level information about Horava gravity. Most of what I have found is way beyond my maths, but I’m wondering about the reasoning of this point from Anathaswamy. (NS. 07.08.10.). “Investigating the properties of graphene was a significant factor in the development of Horava’s ideas.”…..”An odd feature of this material is that its electrons move about on its surface”. their movements are described using QM, and, “…because their motion is at only a small fraction of the speed of light, relativistic effects can be ignored”. When it is cooled to temperatures close to 0K. “… the motions of its electrons speed up to the extent that relativistic effects become important. Lorenz symmetry is now required”…. “Horava noticed that Lorenz symmetry was not always apparent in the motions of these electrons. He wondered if this could be applied to the Universe. If what we observe is a cooled Universe, in which Lorenz symmetry is a well established feature, could it be that this was not the case in the earlier, hotter, stages? In other words, might Lorenz symmetry not be fundamental? Could it be something that emerged as the Universe cooled?” I run into a problem here. What he seems to be saying is: Lorenz symmetry applies to the motion of the electrons at higher temperatures, but may be absent at very low temperatures. In transferring this idea to the Universe, he seems to be saying that Lorenz symmetry applies, rigidly, to the (cooled) Universe, but might not have applied when the Universe was hotter. Have I misinterpreted this?

I get that part. Perhaps I’m trying to understand something that comes into the “shut up, and calculate” area of QM, but the bit that bugs me is the idea that if it is a single photon that takes both paths, its manifestation on each path can be different, and “it” can do different things on different paths.

This was, more or less, the point I had reached, but doubts crept in when I read Michael Brooks’ explanation: “To visualise what is going on, think of a photon entering the interferometer and taking one path while a ghostly copy of itself goes down the other. In Elitzur and Vadman’s thought experiment, half the time there is a photon-triggered bomb blocking one path” ……. “Only the real photon can trigger the bomb, so if it is the ghostly copy that gets blocked by the bomb, there is no explosion – and nor is there an interference pattern at the other end. I appreciate that this is an analogy, and that as such, nit-picking its details is not very helpful, but it does seem to say there is a basic difference between the “entities” that follow each path. How can this be, if “they” are the same photon?

Hi Siskos. I’ve not read "The Invention of Science", but have just followed your Vatican links. I found it interesting, as I had not met these ideas before, but the interest is, probably, historical, rather than scientific. Obviously, it sparks a particular interest for you. Perhaps you could say a bit more about that|?

So far, so good. If a single photon is sent through, and a photon is a quantum, how can it be “split”? My guess is it is linked to the fact that the “photon” travels as a wave, but explanations talk of a photon being split. I thought a quantum was as small as one could go.

My thinking was that each detector detected light from only one path, so how/where would the recombination happen?

So, nothing to observe any interference pattern after recombination?