To Hernik:
You wrote, among other things: "I have a question about the OP Perimeter lecture of Smolin
http://pirsa.org/13020146/ from approx 44.00: Here Smolin concludes that Spacetime emerges from the equations.
This part is strange to me. Maybe just because I can't read the equations. :-) But also because It seems to me that space logically was there from the start when the concept of an event is introduced. I fail to understand how an event can take place if not in a space of some kind..."
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i too was struck by Smolin's claim that he sees space-time emerging from the his Knopf algebra. Perhaps all i can do is commiserate with you, but i do have a take on your question.
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Of course he is not declaring that he discovered a physical space, he's talking about finding mathematical descriptions of space in the math.
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Briefly, any sequentiality can been seen as space-like in one dimension. Any series of two pronged forks in the world path of a particle can be seen as 2-dimensional, to the extent that the decision trees for the particles described can be viewed as covering or at least spreading across a plane. To me, this two-dimensionality looks fractal in detail but since fractals can have fractional dimensionality i suppose you could correctly say that his simple tree diagrams approach 2 dimensionality.
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So, given the simple rules for his decision tree diagrams, he begins with a 1-D space-like sequence of events and then connects daughter events such that, as generations are produced, the history of the process takes on a 2-D structure. 2 dimensions is space. If i remember correctly, he said there were some problems extending this notion to 3-D, but since the advent of the holographic principle, he may not consider this to be a fatal flaw. After all, if 3-D is the illusion, 2 dimensions should be enough.
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You also voice concern regarding what you see as an a priori assumption of space for the momentum to inhabit. Have you considered that space is an unneeded construct? What science can measure is fields, more accurately it measures fields on fields. When a physicist predicts all the places a particle might go by tunneling or otherwise, he is describing predictions given fields. "Space" may be a superfluous concept. So for the purposes of these few paragraphs i define space as the places defined by fields where energy can go.
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Smolin's biggest contribution to cosmology may be his theory that from the inside, black holes are new universes similar to ours but possessing a mass not necessarily equal to the imploding mass of the hole as seen from outside the black hole. Mass/energy is not conserved in General Relativity. Lagranges constrain the mass energy, but once the energy goes past the event horizon, the constraints are lost or at least mooshed around. The geometry of the black hole is cut off from the rest of the universe in a non-trivial way. Thus the new universe can have more mass than the stuff that fell in.
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Presumably these new universes expand. Stuff collapsing into the hole initiates the expansion of space perceived from within the hole. So which came first? The stuff, or the space?
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My read, and this is personal, is that the potential for energy to move IS space. Space emerges from the movement of mass/energy. Space is any place a thing could go. But particles determine where they can go according to the rules of fields in their environment. Since gravity, and anti-gravity in the form of dark matter are features of space, i would say that energy over time creates space, gravity, and dark energy.
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Whether the celebritous Dr. Smolin agrees completely with me, i don't know. But we are surely of the same ilk.
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What i think that Smolin hasn't voiced, is that the expansion of space is due to the presence of mass/energy over time. Over time, there are more and more possible places where a particle can be. That IS the expansion of space.
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Your fellow enthusiast,
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