The nature of force

Make the effort - you'll be glad you did.

You are welcome,
LB

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

I see, but we can take different "densities" for such groups, even though the groups themselves are infinitely divisible. Thus, a particle at some scale has a particular group density with repsect to another particle at comparable scales.

There cannot be a particle that has a size as a closed interval. It must always be the case that its size can only be taken as a limit, so that contact is attributed to "overlap" of the boundaries. Thus,

No contact: (a,b)(c,d) where b&lt;c


Contact: (a,b)(c,d) where c&lt;b.

I just take that all forms and object are open sets, not closed sets...

So, if you touch an object with your hand, you will "visit" a neighborhood of the thing you are touching and vice versa.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I see, but we can take different "densities" for such groups ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
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:
<font size="4">1)</font id="size4"> 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.
<font size="4">2)</font id="size4"> 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.

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PS ... Mr. Burford evinces no understanding of the issue whatsoever.

I have been away for a week. Please excuse any lapses if I repeat questions already asked and answered.

<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 />It is true that not all so called 'collisions' are associated with force fields in the classical sense (e.g. excitation of atomic radiative transitions by electron impact or electron-proton recombination), but this means that in these cases the momentum change can not possibly result in any recoil force.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Your sentence did not make sense to me. “Force” is defined as the time rate of change of momentum. So there could not exist a momentum change without a force acting. Likewise, the non-relativistic definition of “momentum” is the product of mass and velocity. If that changes as the result of a collision, how is that not a “recoil” by definition?

To be able to follow your thoughts, I will need clear definitions. Let’s focus on why solar radiation pressure, which results from the collision of photons with bodies orbiting the Sun and is a major player these days in astronomy, is not a counterexample to your notion that all forces or recoils from collisions require a field to be present. Photons have no fields.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">the observed macroscopic force is only consistent with the assumption of an interaction between particles through static force fields. At what level this happens may be an open question, but at some level you certainly have to assume it this way.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I have no need of that assumption, and the assumption seems to defy experimental physics and logic as well.

In any case, what exactly is the physical nature of a “force field” if it is not itself composed of physical bodies on a smaller scale that can interact by collision? Ultimately, how can anything affect anything else without something colliding? You seem to have answered this difficult question with “by means of force fields”, then left the concept undefined.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Only if the bee hits the obstacle can there be a resulting force (and this force is then due to the electrostatic interaction of the corresponding atoms).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">In your view, can neutron stars (with no electrostatic interactions at the atomic level) collide, or not?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"> Neutrons may not possess an electrostatic field but can be assigned a strong interaction field (and of course also a gravitational field as they have mass). Particles without any field could not interact with any matter at all and would hence be unobservable.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Let’s ignore the neutron’s gravitational field because we both agree that it is negligible and not a factor in the collision. Then your answer boils down to this “interaction field”, yet another undefined concept. But since it is not gravitational, electrostatic, or strong or weak nuclear, haven’t you just proposed a new fundamental force of nature to save your hypothesis and avoid the clear implication that not all collisions can be explained by fields? -|Tom|-

<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 />If [Tom's MIs, elysons and such] go as the real numbers ... then ... an MM particle can possess the required finite cross-section ... but ... so does all of space which in MM is filled. Hence, it is "solid"? ... and no movement is possible.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This claim is logically fallacious. In MM, every scale “looks” visually like our own scale, with some apparently solid objects at that scale (composed of smaller entities) and lots of apparently empty space between them. If apparently empty space dominates filled space at every scale, then motion remains possible because there is plenty of “room” at every scale that can be occupied.

Yet nothing about this picture is contrary to MM’s conclusion that every point of space exists only because it is occupied at some much smaller scale. Obviously, the densities at each point of space are a function of scale. They might be low at our scale, high at the scale of gravitons, low again at some smaller scale, then high again at smaller scales, etc. And at each scale, changes of density remain possible. But a change of density is a form of movement.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">an exact description of "collide" is necessary<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That is where Zeno’s paradox comes in. To cross a street, one must traverse an infinite number of space points in a finite time. But every line segment is an infinite number of points in a finite space. So a one-to-one correspondence is clearly possible. In particular, we can create a correspondence between “half-the-remaining-distance” intervals crossing a street and the infinite series 1/2 + 1/4 + 1/8 + 1/16 + … = 1.

The same is true in scale. If two physical objects are dense enough that filled space exceeds empty space, then they can “collide” (appear to make contact) even though infinitely composed. To collide, it suffices that density keeps increasing at smaller and smaller scales to infinitesimal. At each scale step we can define a parameter log (1/rho), where rho is the density at that scale. Then after an infinite number of finite density steps, the sum of all the parameter values is a finite number, just as the sum of our infinite series above is a finite number. So in the limit, it is just as if the body were solid (infinite density), when in fact that never occurs in physical space.

We can also think of this “collision” matter geometrically. If a large number of comets are shot toward the vicinity of the Sun from a common starting point, gravity will cause the comets to round the Sun and return toward their starting direction. Moreover, the collective effect of all the comets will tug on the Sun and start it moving away from the comet source. So the net result is a “bounce back” for the comets and a “push” on the Sun even if no comet ever makes real contact with the Sun. From a larger scale where one could not see the details of the comets rounding the Sun, it would appear that each collided with the Sun. And the result is the same as if that had happened.

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 super-small entities create the appearance that they did collide. And so on, through an infinite range of scales.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">This is where MM theory fails in my view. It cannot adequately define what a collision is ... as in "What is colliding with what?"<hr height="1" noshade id="quote"></blockquote id="quote"></font id="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.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">That's one reason why the concept of "field" remains in physics. It's not going away.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">”Field” does nothing whatever to answer the essential point because fields have no means to interact (other than mathematically, or by magic) except by collision with their constituents. And if fields no not have constituents, then how can they carry momentum or interact with material, tangible bodies? Are fields material and tangible, or magical? I see “fields” as no solution whatever, but as the logical equivalent of “God made it that way”, which is not an explanation of the physics.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">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.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You seem to deny the mathematics of infinities. In this case, you deny that infinity plus infinity equals infinity.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">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.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Given the relevant parameter as log (1/rho), we have an infinite number of finite quantities, in perfect analogy to the Zeno solution. -|Tom|-

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

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">You seem to deny the mathematics of infinities. In this case, you deny that infinity plus infinity equals infinity.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
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?