The nature of force

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The only way that any two physical entities can interact is by means of contact.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
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.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />I don't think "contact" can be defined at all without reference to both concepts ... field and particle.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="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.

For example, in MM, the gravitational potential field has been shown to be the elysium, composed of elysons. Can you imagine a physical "field" that is not material and tangible, or that somehow avoids being composed of anything?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What is meant by 'contact' in MM?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">A fuller discussion of Zeno's paradoxes in general appears in chapter one of <i>Dark Matter, Missing Planets and New Comets</i>. In that chapter, your question is answered by solving Zeno's extended paradox for matter analogously to the solution for Zeno's motion paradoxes, which involves one-to-one correspondences between physical states and infinite mathematical series (or points in a line segment) having a finite sum. The core of the argument is quoted here:

There is another form of Zeno's Paradox that applies to masses: "If bodies are infinitely divisible, then contact should be impossible." For example, when macroscopic bodies seem to touch, they actually consist of mostly empty space at the atomic level; so it must be their atoms which actually touch. But atoms are themselves composed of smaller particles and mostly empty space, so it must be these smaller constituents which actually touch. But if matter is infinitely divisible, this argument can be prolonged indefinitely, and nothing can ever actually touch.

One might use this argument to conclude that there is a smallest possible unit of matter or substance. Imagine such a "unit particle." It must be utterly uncomposed. It therefore cannot be broken or divided, nor even deformed by spin or collision -- since these are properties of bodies composed of yet smaller particles. What then are we to assume will happen when two such unit particles collide? What density will the unit particle have? Indeed, will there be anything inside it at all? (It would seem that the substance in its interior could never contribute in any way to anything in the universe outside the particle, since it can never interact with it.) What would the unit particle's "surface" be like? Could it be hollow inside? With what thickness of shell? Would two colliding unit particles have to stick, since they can't rebound elastically? If they rebounded, with what resultant velocity? What about the slightest of grazing collisions? Would the unit particles be spherical in shape? Why would they have finite space dimensions, yet infinite dimension in time? Or do they come into and go out of existence constantly? Where and when would they appear and disappear?

It should be apparent from these considerations that postulating a "minimum possible unit of substance" is no more logically palatable than a "minimum possible unit of space or time." Substance must be infinitely divisible, as must space and time; or else the paradoxes quickly lead to unresolvable logical dilemmas. But how then can matter ever experience "contact," if everything which might experience contact is itself composed of smaller substances? The resolution of this paradox would seem to be analogous to that for space-time. If the substance of bodies always gets denser (more substance per unit volume) at smaller and smaller scales, then in the limit as dimensions approach zero, density approaches infinity and substances approaching each other must make "contact." (That is, at infinite density, they cannot be "transparent" to other substance). In the real universe, the density of matter greatly increases as scale decreases. Hence the ratio of mass to volume in electrons is enormously greater (about 10^10 g/cc) than the same ratio for matter in ordinary human experience (of order 1 g/cc), which in turn is enormously greater than the ratio for the entire visible universe (10^-31 g/cc). [Since this density difference of 41 orders of magnitude occurs over a scale difference of 42 orders of magnitude, it would seem a reasonable speculation that the mean density of substance is inversely proportional to scale for all ranges of scales. If it were otherwise, substance would have to fundamentally change in character at extremely large or extremely small scales.] "Contact" is therefore possible for infinitely divisible matter, as long as the smaller and smaller particles continue to increase in density with sufficient rapidity, without limit.

Ultimately, this is just another one-to-one correspondence between powers of 10 for a density ratio and decimals between 0 and 1. But I appreciate that it is very difficult for the intuition to grasp this concept. Consider the approach of one minute particle of substance to another. As the outer surfaces approach, the lesser particles (call them "second-level" particles) of which each is composed begin to approach each other. After the original particles traverse only a very small distance, the third-level particles of which the second-level particles are composed begin to approach each other. After an even more minute traverse of distance, and after an ever smaller lapse of time, the fourth-level particles begin to interact.

Although this continues without limit, as we have already seen, the process takes place in a finite time and a finite distance. The penetration of each level of particle into its counterparts in the approaching particle continues until the density of matter in the approaching particle is too great for it to penetrate deeper. Then the smaller particles at the next level penetrate until the density becomes too great for them to make further progress, and so on. By one-to-one correspondence with terms in our infinite series with a finite sum, we see that the depth of penetration has a finite limit and requires a finite time, after which the original particles react with resistance to the intrusion of new substance into their ranks just exactly as if there had been a collision!

By analogy with the proposed resolution of Zeno's paradoxes for space and time, the paradox for mass is resolved, apparently necessarily, by the conclusion that substance must be infinitely divisible and that it must approach infinite density as size decreases toward zero dimensions. This conclusion is reached by reasoning alone; it is reinforced by the observation that matter does in fact increase rapidly in density as scale becomes smaller over a range of more than 40 orders of magnitude in the observable universe. -|Tom|-

For a collision of two particles you need a force acting between them because otherwise their momentum could not change (F=dp/dt) and you would thus by definition not have a collision.
As indicated earlier, there is therefore no point trying to rationalize a fundamental force (e.g. gravity) away as a matter of principle and substitute it by a macroscopic force caused by collisions with some hypothetic particles, because for the latter you would need again an interaction force to have the desired effect.
Of course if there would be evidence that the Gravitational or Coulomb Law in its present form lead to contradictions with experiments, then this might justify doubts if these are really fundamental forces, but then you would have to come up with a new fundamental force instead (unless you can explain it it in terms of other already known fundamental forces, which for Gravity for instance looks more than unlikely).

---

www.physicsmyths.org.uk
www.plasmaphysics.org.uk

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br />For a collision of two particles you need a force acting between them because otherwise their momentum could not change (F=dp/dt) and you would thus by definition not have a collision.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">By definition? What definition of "collision" are you using?

Consider two bare equal-sized particles in isolated space. By "bare", I mean particles that have no fields. If their momentum vectors are colinear but unequal, then the two must eventually either collide of occupy the same space at the same time. Please describe your view of the physical encounter between two field-less particles as described.

If two field-less particles do collide and elastically deform, that collisional deformation creates a force that did not pre-exist, and the new force changes the momentum. Your description seems to put the effect (force or change of momentum) before the cause (collision and concomitant deformation).

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">if there would be evidence that the Gravitational or Coulomb Law in its present form lead to contradictions with experiments, then this might justify doubts if these are really fundamental forces, but then you would have to come up with a new fundamental force instead.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I submit that the only fundamental thing common to all forces is contact collisions. I have yet to hear a physical description of another way in which two material, tangible entities can affect one another, much less how a non-material or non-tangible entity could affect anything. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="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.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
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.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />Surely, there must be some sort of "field" in MM if only the reference frame itself.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">As I mentioned, the gravitational potential field is the elysium (light-carrying medium), composed of elysons. It is like an extended atmosphere of bodies, growing denser near mass because of gravity. Although only gravitons are responsible for gravitational force, elysium by itself is responsible for light-bending, radar time delay, and gravitational redshift through the mechanism of refraction in the elysium medium.

This is in every sense a "field" as used in relativity, but a plainly material, tangible field ultimately as composed of particles as anything else that has physical existence. There is no magic allowed in real physics.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I assume a flat Euclidean 3D field for MM, correct?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That depends on definitions. MM's elysium does change density near mass, which makes light bend in an identical way to the so-called "curvature of space". But because space itself in MM is merely a set of orthogonal axes used for measuring lengths, space is indeed flat and Euclidean. But space is not a field, nor vice versa.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">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?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">In MM, all space and time and scale intervals are finite. Nothing physical can reach an infinite distance, or an eternal time, or an infinite or infinitesimal scale. So mathematical point "particles" cannot exist in reality in MM. We can merely speak of them as concepts, in which case its collision probability would indeed be zero. But that is irrelevant for your purposes because it does not apply to anything real.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">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.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is incorrect. The same argument was used by Zeno to prove that motion is impossible because (to paraphrase a more sophisticated argument) if nothing is moving at any one instant of time, it cannot ever move because there is no "between" for instants of time. Likewise, you can never reach the other side of the street or the end of a line segment because there are an infinite number of mathematical intervals or points remaining in both.

But the solution (developed in chapter one of my book) to all these parallel paradoxes lies in mathematical limits and one-to-one correspondences. We know that the infinite series 1/2 + 1/4 + 1/8 + ... has the finite sum 1.0 exactly. So each of the preceding examples of infinite series, including the "contact" example, can have finite sums also. And "contact" is therefore possible for infinitely divisible matter. (See the referenced chapter for the details.)

In short, every scale, however large or small, looks exactly like our scale, consisting of many seemingly "solid" bodies immersed in mostly empty space. The fact that both the solid and the empty parts are infinitely composed does nothing to alter the practicalities. Collisions occur whenever matter encounters matter of comparable scale, but not when the scales are too different. -|Tom|-