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his is and exchange from Tom Van Flandern's site (metaresearch.org betweem June 27 and July 6, 2004) concerning our differences of opinion about the nature of a collision between two particles of any sort. I see no hope of any resolution here. It serves to show how difficult it is to come to any sort of agreement about fundamentals. This, to me, is the best you can do on the internet ... keep discussing the issue until each party understands the others opinion. You still don't find agreement but at least you're disagreeing about the correct ideas ;o)

EBTX:
What is meant by 'contact' in MM? Since all particles are made up of constituents ad infinitum ... no particle has a "pure" geometric surface to deform in which we might see the analog of a rubber ball hitting a brick wall. The logic of contact is "geometric deformation" (however small) yet MM seems to sidestep this by infinite regress, i.e. no particle' constituent actually touches any other particle's constituents. We could say that the pure, geometrical arrangement of constituents is deformed ... but ... this is exactly what the standard model says about the rubber ball. So without actual, purely geometric contact deformation of the surface of a pure sphere, all that can be left is "field".

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.

TVF quote:
Please try to give me a physically sensible description of "field" that does not involve constituents. When discussing fundamentals, it is important to avoid all "fuzzy think", including mathematical concepts that have no physical counterparts.

EBTX:
Surely, there must be some sort of "field" in MM if only the reference frame itself. I assume a flat Euclidean 3D field for MM, correct? It is non-physical (from the particle standpoint) but is entirely "physical" if you wish to list the constituents of physics because it is necessary to order events. And ... there are alternative possibilities such as a polar type reference frame or other more exotic types which must be excluded logically ... unless one asserts that Euclidean-flat is the default frame in 3 space. However, if you define -physical- as "only that mediated by particles" you can of course get rid of the concept of "field" by fiat. But that would be neither logical nor scientific.

Let me ask a question for MM basics.

Given a hypothetical, moving, point-particle, 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 point-particle, 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 point-particle 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 re-introduces the rejected concept of "field" at the most fundamental logical level possible.

EBTX:
"Zeno" is about an infinite number of finites summing to a finite. I don't see that here. Since no particle's constituents in MM can sum to a finite cross-section required for any understandable collision sans "field". As I understand it, MM rejects the "point particle" as unphysical ... and also rejects a finite geometrical sphere (a "ball-particle") for any number of sound reasons [though this type could conceivably sum to a finite cross-section in the Zeno manner since each sphere has a finite cross-section].

What then is a particle to be composed of ... ?? If it is not composed of either finite little balls of various sizes or point-particles ... 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 non-physical as well.

When two MM particles collide ... in terms of constituents, exactly what is hitting what?

Another person's quote in the same thread while TVF was absent:
Now, perhaps there is no such thing as empty space. The universe is filled with particles of arbitrary size ...

EBTX:
According to Tom, particles have size but the sum of all their constituents presents no cross-section to hit because particles in MM have no intrinsic geometric properties except "position", i.e. they have no shape or size as individuals ... only as groups. For instance, if you shoot a BB (pun ;o) at a swarm of flies, you have a chance of hitting one because each fly takes up a finite cross-section. But if each fly has the cross-section of a "point", then ... it doesn't matter if there are an infinite number of flies ... you can't hit them with a BB which has also been reduced to a "point" or swarm of points. Something must provide a valid embodiment of "size". MM does not do this.

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.

EBTX:
I suggested as much also. And that would be OK. However, I don't know what the collision of "densities" would mean. This concept has no meaning (qua "collision") independent of constituents. If a collision between two particles is to occur ... the particles must offer a cross-section to be hit ... or, to hit with ... or both.

There are only two ways to accomplish this:
1) The constituents have finite size (e.g. little balls) ... and ... there could be an infinite number of them on ever smaller scales summing to a finite cross-section as Tom's theory implies.
2) The constituents have "fields" which serve to present a cross-section. A "field" would be like a little ball too, but with no defined "edge", i.e. an asymtotic attenuation in "field density" originating at a source where "density" might be defined as the standard of distance and direction in the surrounding space so that "hit" means a redirection or diminution/increase of velocity. I suspect that whatever it is that is implied in MM is, at length, the same as the concept "field" and that the differences will, at length, end up being only semantic. Tom has erred in stating that the problem is similar to those in Zeno's paradox. Zeno's paradox consists of an infinite number of finites summing to a finite. The collision problem in MM is, on face value, about an infinite number of infinitely small quantities summing to a finite which is on logically unsustainable ground.

EBTX:
So, there is no "contact" in MM ... hmmm. If no contact ... how is momentum transferred? Are you saying that it can be "apparently" transferred? I don't see where you can go without "real" contact unless it is into the realm of fields (as logical primaries).

EBTX:
I mean that if more "room" is to be got on the number line, another advance in mathematics must be made similar to the discovery that there are infinitely more irrational numbers than integers. Do you accept Cantor's diagonal proof in regard to these infinite sets?

EBTX:
I think I now understand completely your point of view, though I disagree with it at the deepest level. You've chased the problem down an infinite hole and decreed a solution which is identical the concept of "field". The only difference I can see is that "field" is considered a logical primary and no one frets over its lack of "parts".

EBTX:
I couldn't agree more about current models having no connection to actual human experience. But I don't see the field concept as divorced from experience ... at least it wasn't in Faraday's experience. In the case of neutral bodies the concept of collision is obviously paramount but when looking at the less common charged (or magnetic) body experience there is no obvious collision element. So Faraday invented the field concept.

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 3-space. 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 P-branes all over the place. We would then be putting "experiential pieces" into a bag labeled "P-brane" 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 open-ended than yours. I can't in principle add anything more either. ;o)