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In the classical theory of gravity, which is based on real space-time, there are only two possible ways the universe can behave: either it has existed for an infinite time, or else it had a beginning at a singularity at some finite time in the past. In the quantum theory of gravity, on the other hand, a third possibility arises. Because one is using Euclidean space-times, in which the time direction is on the same footing as directions in space, it is possible for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge. Space-time would be like the surface of the earth, only with two more dimensions. The surface of the earth is finite in extent but it doesn’t have a boundary or edge: if you sail off into the sunset, you don’t fall off the edge or run into a singularity.
If Euclidean space-time stretches back to infinite imaginary time, or else starts at a singularity in imaginary time, we have the same problem as in the classical theory of specifying the initial state of the universe: God may know how the universe began, but we cannot give any particular reason for thinking it began one way rather than another. On the other hand, the quantum theory of gravity has opened up a new possibility, in which there would be no boundary to space-time and so there would be no need to specify the behavior at the boundary. There would be no singularities at which the laws of science broke down, and no edge of space-time at which one would have to appeal to God or some new law to set the boundary conditions for space-time. One could say: “The boundary condition of the universe is that it has no boundary.” The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed, It would just be.
I’d like to emphasize that this idea that time and space should be finite “without boundary” is just a proposal: it cannot be deduced from some other principle. Like any other scientific theory, it may initially be put forward for aesthetic or metaphysical reasons, but the real test is whether it makes predictions that agree with observation. This, how-ever, is difficult to determine in the case of quantum gravity, for two reasons. First, we are not yet sure exactly which theory successfully combines general relativity and quantum mechanics, though we know quite a lot about the form such a theory must have. Second, any model that described the whole universe in detail would be much too complicated mathematically for us to be able to calculate exact predictions. One therefore has to make simplifying assumptions and approximations – and even then, the problem of extracting predictions remains a formidable one.
Under the no boundary proposal one learns that the chance of the universe being found to be following most of the possible histories is negligible, but there is a particular family of histories that are much more probable than the others. These histories may be pictured as being like the surface of the earth, with the distance from the North Pole representing imaginary time and the size of a circle of constant distance from the North Pole representing the spatial size of the universe. The universe starts at the North Pole as a single point. As one moves south, the circles of latitude at constant distance from the North Pole get bigger, corresponding to the universe expanding with imaginary time. The universe would reach a maximum size at the equator and would contract with increasing imaginary time to a single point at the South Pole. Even though the universe would have zero size at the North and South Poles, these points would not be singularities, any more than the North and South Poles on earth are singular. The laws of science will hold at them, just as they do at the North and South Poles on earth.
The history of the universe in real-time, however, would look very different. At about ten or twenty thousand million years ago, it would have a minimum size, which was equal to the maximum radius of the history in imaginary time. At later real times, the universe would expand like the chaotic inflationary model proposed by Linde (but one would not now have to assume that the universe was created in the right sort of state). The universe would expand to a very large size and eventually it would collapse again into what looks like a singularity in real time. Thus, in a sense, we are all still doomed, even if we keep away from black holes. Only if we could picture the universe in terms of imaginary time would there be no singularities.
If the universe really is in such a quantum state, there would be no singularities in the history of the universe in imaginary time. It might seem therefore, that my more recent work had completely undone the results of my earlier work on singularities. But the real importance of the singularity theorems was that they showed that the gravitational field must become so strong that quantum gravitational effects could not be ignored. This in turn led to the idea that the universe could be finite in imaginary time but without boundaries or singularities. The poor astronaut who falls into a black hole will still come to a sticky end; only if he lived in imaginary time would he encounter no singularities.
This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations. In real time, the universe has a beginning and end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just an idea that we invent to help us describe what we think the universe is like. But a scientific theory is just a mathematical model we make to describe our observations: it exists only in our minds. So it is meaningless to ask: which is real, "real" or "imaginary" time? It is simply a matter of which is the more useful description.
The proposed no boundary condition leads to the prediction that it is extremely probable that the present rate of expansion of the universe is almost the same in each direction. This is consistent with the observations of the microwave background radiation, which show that it has almost the exact same intensity in any direction. If the universe were expanding faster in some directions than in others, the intensity of the radiation in those directions would be reduced by an additional red shift.
Further predictions of the no boundary condition are currently being worked out. A particularly interesting problem is the size of the small departures from uniform density in the early universe that caused the formation first of the galaxies, then of the stars, and finally of us. The uncertainty principle implies that the early universe cannot have been completely uniform because there must have been some uncertainties or fluctuations in the positions and velocities of the particles. Using the no boundary condition, we find that the universe must have started off with just the minimum possible nonuniformity allowed by the uncertainty principle. During this period, the initial nonuniformities would have been amplified until they were big enough to explain the origin of the structures we observe around us. In an expanding universe in which the density of matter varied slightly from place to place, gravity would have caused the denser regions to slow down their expansion and start contracting. This would lead to the formation of galaxies, stars, and eventually even insignificant creatures like ourselves. Thus all the complicated structures that we see in the universe might be explained by the no boundary condition for the universe together with the uncertainty principle of quantum mechanics.
The idea that space and time may form a closed surface without boundary also has profound implications for the role of God in the affairs of the universe. With the success of scientific theories in describing events, most people have come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the universe to break these laws. However, the laws do not tell us what the universe should have looked like when it started - it would still be up to God to wind up the clockwork and choose how to start it off. So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have no beginning nor end: it would simply be. What place then, for a creator?
TA1LGUNN3R wrote:I hate when theoretical physicists give shitty analogies and turn the study of motion into a philosophical masturbation where they compete on who can spew out the most complex sounding history of the universe.
The surface of the earth doesn't have a "boundary" because it's so many atoms clustered together. You don't fall off the edge because the attraction between your mass of atoms and that of the earth prevent such a fate. End of story.
"The uncertainty principle implies that the early universe cannot have been completely uniform because there must have been some uncertainties or fluctuations in the positions and velocities of the particles."
The Heisenberg uncertainty principle? That's a limitation of our ability to infer knowledge of complementary properties. Just because we can't determine both position and momentum of an electron around its orbital doesn't mean it doesn't have them at any instant in time. How does that imply non uniformity of the proto universe? They seem unrelated.
TA1LGUNN3R wrote:why how dare you
Anyway, he's banned, I'll do my best to fill his shoes.
Bernie Sanders wrote:TA1LGUNN3R wrote:why how dare you
Anyway, he's banned, I'll do my best to fill his shoes.
Thank God! This site needs at least 1 full time troll with a troll waiting in the shadows to immediately replace a troll being banned.
patches70 wrote:Stephen Hawking was a terrible role model, he didn't stand for anything. But, it's a sad day to see him gone. His wife, Siri, is devastated I'm sure. Interesting thing about Hawking, he belted out a lot of great one liners. One liners was his secret passion though he wasn't very good at stand up. He once went on a blind date and came back with a broken leg. I can't believe the lady had the nerve to stand him up.
I shouldn't be so hard on the fellow, after all he can't stand up for himself. He was an entrepreneur, founded meals on wheels. Does anyone know, when he died did they take him to a funeral home or to PC world? He had recently fallen in love. When asked why he loved this new woman so much he replied "because she pushes all the right buttons". Maybe he's not really dead, his update just failed. He was a lucky guy, when he went out and got wasted and came home his wife never said anything because she couldn't tell if he was wasted or not! I always got hit with rolling pin, I envy the guy. His favorite song was by the Beach Boys- "I get around". Seriously!
I bet his wife feels really guilty right about now. She forgot to pay the electric bill.
He once scolded some children, told them to not spend so much time on the computer. He then apologized to them, obviously. Hawking was a lot of things, but a hypocrite, not so much.
Anyway, it's been great having Hawking around, to remind the rest of us of how good we got it. Now he's just gotta figure out how he's going to climb that Stairway to Heaven. He's a genius, he'll figure it out. Oh, scratch that, he thought Heaven is a fairy tale so I guess it's either black oblivion for him or, even worse, Hell. Either way, he will be missed. God Speed Stephen Hawking.
HitRed wrote:Read the book. Enjoyed it. Toys R Us had a bigger impact in my life though.
RIP, 1957-2017: Geoffrey
HitRed wrote:Read the book. Enjoyed it. Toys R Us had a bigger impact in my life though.
RIP, 1957-2017: Geoffrey
tzor wrote:Hawking was brilliant; much like Einstein. But brilliance isn't always enough. Much like Einstein failing to understand beyond relativity and into quantum mechanics, so too did Hawking have his own lines which he dared not cross. A lot of his work may in key areas already be obsolete as scientists try to grapple with even more complex theories about the nature of space and time.
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