What is quantum field theory?

  • Thread starter Mike2
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ZapperZ said:
Would you call what you have said above as "logical derivation"? I mean, really!
Zz.
Deductive logic can be expressed in terms of AND's and OR's. These are represented by unions and intersection, think Venn diagrams. If reality is logical, then unions and intersections (AND's and OR's) of protions of it must still be part of it. Can you imagine a reality where an intersection of two overlapping regions were not actually a part of reality too? Then accepting that reality is a topology and that we must be able to describe it mathematically if we are to discover or derive mathematical laws of physics, it would seem necessary that reality be some sort of manifold or another.
 
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Mike2 said:
Deductive logic can be expressed in terms of AND's and OR's. These are represented by unions and intersection, think Venn diagrams. If reality is logical, then unions and intersections (AND's and OR's) of protions of it must still be part of it. Can you imagine a reality where an intersection of two overlapping regions were not actually a part of reality too? Then accepting that reality is a topology and that we must be able to describe it mathematically if we are to discover or derive mathematical laws of physics, it would seem necessary that reality be some sort of manifold or another.

But what you did has NOTHING to do with "deriving", as applicable in physics. YOu still could not derive anything via first principles. You even mentioned that you "speculated" the discrete space (which still hasn't been verified), which in itself isn't something "derived" logically. Your explanation, at best, would be categorized as hand-waving.

I'm just a bit amused that when asked to show one clear example on what we know of today in physics that was "derived", you brought up something that hasn't been verified, have not been accepted, and still highly speculative. Do you not see anything strange about this? What happened to all the rest of well-established physics? Can't you find just ONE single example from that huge body of knowledge, rather than having to really dig the very bottom of still-unverified hypothesis barrel?

Zz.
 
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Mike2 said:
I recall, I think it was you, who mentioned that some have proposed something about space not being "connected" at some points or regions, was that concerning mass? Now, as I speculated to the best of my ability, that space may expand so fast that protions do become no longer "connected" to the rest of space (if I remember the term correctly). These regions that are no longer connected to the rest of spacetime would then form a boundary to spacetime, would they not? And you probably know where I would go with that.

As for your comments (thank you), I would think that there does have to be some connected property of spacetime (or other underlying manifold) simply in order to transfer information from one point to another. How can one region "affect" some other region if it is not connected to it, if there is no measure of anything between them? The medium through which one region affects another is broken by a discontinuity. Perhaps they are thinking that if space were compact, though disconnected, that influence is acheived through the boundary between such regions.

Sure people make all sorts of "ansatzes" or guesses. This amounts to assuming, for the sake of argument, one or more premises, and then doing logic (mostly in the form of math) on them. That's what you're doing too. You think this or that is necessary or reasonable and assume it is true and THEN bring in logic. It's a pretty standard technique, but as zapper says, and as for example Feynmann emphasized, the art of imagination in physics is to remain consistent with the enormous body of known stuff that exists.
 
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Originally Posted by Mike2
I recall, I think it was you, who mentioned that some have proposed something about space not being "connected" at some points or regions, was that concerning mass? Now, as I speculated to the best of my ability, that space may expand so fast that protions do become no longer "connected" to the rest of space (if I remember the term correctly). These regions that are no longer connected to the rest of spacetime would then form a boundary to spacetime, would they not? And you probably know where I would go with that.

As for your comments (thank you), I would think that there does have to be some connected property of spacetime (or other underlying manifold) simply in order to transfer information from one point to another. How can one region "affect" some other region if it is not connected to it, if there is no measure of anything between them? The medium through which one region affects another is broken by a discontinuity. Perhaps they are thinking that if space were compact, though disconnected, that influence is acheived through the boundary between such regions.

selfAdjoint said:
Sure people make all sorts of "ansatzes" or guesses. This amounts to assuming, for the sake of argument, one or more premises, and then doing logic (mostly in the form of math) on them. That's what you're doing too. You think this or that is necessary or reasonable and assume it is true and THEN bring in logic. It's a pretty standard technique, but as zapper says, and as for example Feynmann emphasized, the art of imagination in physics is to remain consistent with the enormous body of known stuff that exists.
Thank you. The goal is to be certain of what happened and what is to come so that we know that the basis of our decisions will result as we expect.

However, I would like more comment on the topological questions I mentioned. For example, I'd have to reject out of hand any theory that supposes propagation through absolutely nothing, as in, what, LQG that supposes quantized regions of disconnected spacetime? And you mentioned some theories that that have discrete regions of space(time) put together (connected?) like cubes stacked very close together so that they share a common boundary with its neighbors. Well, it seems to me that such a spacetime could not warp or propagate anything. For as soon as these riggid cubes start moving about, they will create holes where the cubes don't match up anymore. But if the boundary of each side of the cube does change size to allow warping or propagation without creating holes, then I think that would be equivalent to a continuously connected spacetime when the boundaries are an arbitrary construction. Would you agree? Thanks.
 
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LQG has its webs and foams, all connected, and digital physics cells are static. In both cases they are not the phenomenal spacetime which is a "limiting case" of their actions.
 
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selfAdjoint said:
LQG has its webs and foams, all connected, and digital physics cells are static. In both cases they are not the phenomenal spacetime which is a "limiting case" of their actions.
I'm not sure these work with a universe growing out of a singularity. If it does not grow from a singularity, then you have to contend with the illogic of instantaneous existence which by definition defies explaination and thus logic. If the universe did grow from a singularity, then at the differential level, spacetime (at least to begin with) must have a continuous structure in all directions (no webs or foams at this level). I would think think that if spacetime grew from a singularity, then all of spacetime from the beginning must inherit this feature of its roots. Otherwise, I think the change from such a continuous distribution to anything else would imply some very serious topology changes that probably cannot be explained.
 
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Now I wonder if time must be connected and continuous, and space must be connected and continuous, then does this imply some maximum speed that spacetime can expand. For if it cannot expand instantaneously because instantaneous existence defies any reason for its existence and so would defy logic, then does the connectedness of space/time imply some speed limit to the expansion. This would probably be connected to the speed of light as well. Thoughts anyone?
 

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