in TVF's MM Model
TVF quote: The only way that any two physical entities can interact is by means of contact.
EBTX:
And ... if a pure, geometrical sphere did exist it would introduces the concept of quanta which in turn tends to rule out scale infinities. I don't think "contact" can be defined at all without reference to both concepts ... field and particle.
EBTX:
Let me ask a question for MM basics. Given a hypothetical, moving, pointparticle, what is the probability that it would collide with another particle of any type in the MM model ... over any finite range? I will define collision as a deflection of the path of the pointparticle, coincident with any MM particle being in about the same location so as to be suspect as the causal reason for the deflection. I would guess that your answer must be "0" in your model. For if particles in MM are aggragates of aggragates ad infinitum, an infinite number of smaller particles must be in any finite space. And ... this infinite number must exist in a one to one correspondence with the integers. Then ... because the set of real numbers is infinitely greater than the set of all integers ... you are yet left with a relative inifinte amount of "unassigned" empty space through which the hypothetical pointparticle might pass without collision. Or, if space is completely filled (particles in MM correspond one to one with the real numbers) ... it must be that no unassigned space exists and the above probability is "1". But in this case, I don't see that movement would be logically possible at all. Is this a correct assessment? Now, if it is the case that the probability is "0", then no MM particle can collide with another directly because none of its constituents can do so. So we are than left to conclude that the "arrangement" of the constituents is deformed and this is taken for collision. In this manner: Suppose that some finite number of constituents are arranged on the surface of a sphere. Then, a collision would be constituted by the deformation of that sphere shape into, say, an oblate spheroid which then rebounds back to its original sphere shape. But this reintroduces the rejected concept of "field" at the most fundamental logical level possible.
TVF quote: The same argument was used by Zeno ...
EBTX:
What then is a particle to be composed of ... ?? If it is not composed of either finite little balls of various sizes or pointparticles ... what's left? Are we speaking here of collisions between "densities"? That could sum to a finite ... but that begs the question "How does a density collide with another density?". This seems to be nonphysical as well. When two MM particles collide ... in terms of constituents, exactly what is hitting what?
EBTX:
That's one reason why the concept of "field" remains in physics. It's not going away. As far as squeezing the points in a line of "real numbers" down so as to allow extra room for some empty space ... The real numbers filling the line constituents a mathematical definition and is not subject to squeezing. To get some more "room" out of a line, you must discover another class of numbers ... specifically a set of numbers which is infinitely more numerous than the set of all real numbers.
Another person's quote in the same thread while TVF was absent: I see, but we can take different "densities" for such groups ...
EBTX:
There are only two ways to accomplish this:
TVF quote: By the preceding argument and the analogy with Zeno’s paradox, no real contact is needed as long as apparent contact is the mathematical limit of the infinite series involved.
EBTX:
TVF quote: You seem to deny the mathematics of infinities. In this case, you deny that infinity plus infinity equals infinity.
EBTX:
TVF quote: Of course, this assumes that gravitons can collide with comets and accelerate them. But by extension, gravitons do not need to actually collide with matter ingredients in comets to create the appearance that they did, provided that some supersmall entities create the appearance that they did collide. And so on, through an infinite range of scales
EBTX:
TVF quote: And that is a pity. Models that depend on axioms suspended from clouds (with no possible logical basis) such as "fields" without parts are very unsatisfying to a physicist because they invoke magic in that assumption. But such assumptions lacking in a physical basis are now so common in mathematics that few people even raise an eyebrow anymore.
EBTX:
There was nothing else to do ... and ... more importantly, no reason to postulate something unseen to fulfill a collision requirement. It is not that the field cannot, in principle, be reduced to particles as MM suggests ... it's that it is logically unnecessary to do so ... unless ... one can detect (directly and unambiguously) the particles of which it is composed. Until then, all the particles which compose the "field" can be tied up in a bag and ... I should just examine the bag itself as the primary existential element. I see the field concept as being composed of only a few parameters. These are properties which denote ... distance, direction and a tension analog as in twists or compression/stretching ... all of which have experiential analogs in the real world (like a block of rubber). A field, in my view, can have no attribute without a clear physical analog. For instance, there can be no Higgs field which exists solely to assign mass to particles. My question would then be ... How ?? in terms of motion, expansion/contraction, rotation, etc. Thus, there are only a few conceivable things that can happen in 3space. An object can move relative to another object laterally or toward/away. It might rotate on an axis (with some complications). It might expand or contract like a balloon (again with some complications). It might disappear and reappear elsewhere (not necessarily observed, just conceivable). If we add a field concept we also have the above mentioned properties.
Beyond that, there is nothing else that can happen in our universe ... unless we go to "floating abstractions" of which there are an infinite number. We need only make up a word to identify the phenomenon then we have phlogiston and Pbranes all over the place. We would then be putting "experiential pieces" into a bag labeled "Pbrane" and accepting that as an existential primary which I reject. Our difference is that you have only particles in your model. I have fields as well but they are limited to experiential properties. I say that you do not have enough stuff to build the observed universe. You say that I have too much. But my view is no more openended than yours. I can't in principle add anything more either. ;o)
