The nature of force

As I see things the proton is more dense than the moon but the moon is less dense than the Earth. That has nothing to do with my question however but I hope it does at least answer the question you are asking. The question I am asking might be clearer to you if you read the post by TVF above.

It has everything to do with your question.

You are making too fine a distinction. Relative to a proton, Earth and Moon are the same size and they are also the same density.

For scale changes of less than a few orders of magnitude there may very well be variations in the relationship between size and density that are "locally inverted". You offered a good one, another is a marble and a balloon.

Actually that example should be the other way around. A nerf ball and a bowling ball, for instance. The smaller nerf ball is less dense than the larger bowling ball. But only by small amounts. Relative to a proton both are the same density and same size.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The same argument was used by Zeno ...<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
"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?

<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>
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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].

<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

You have to concede that a "point particle" does have various obscurities. For if you take the function f(x)=arctan(x), then it is seen that the real line, for points x in (-inf,inf), maps into the interval (pi/2,-pi/2). Now, the real line looks "solid" to me on paper, having "no gaps", yet it is possible to place all points of the real line next to each other in an arbitrary small interval (epsilon, -epsilon). Hence, an infinite "solid" horizon of seemingly touching points fits into an arbitrary interval in a one-to-one manner.

Returning to physics, the above problem can be explained by arguing that point particles are actually composed of other particles with (infinitesimal) space in between. Their size is not "fixed" but can be described by a limiting procedure only, such as the infinite sum that Tom tries to impart.

Does this seem to be a fair assessment?