The nature of force

Hmmm. Remember, focus on the physics.

Math is a useful tool. But this is about the physics. If you have an idea about what some math might mean physically, but putting the idea into words describes a universe different from the one we see when we look, then reject that idea and try another one.

Consider the form known as a "monitor" (like the one you are looking at right now).

It has a specific amount of mass. It is finite.

The monitor fills a specific volume of space.

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And yet, if you look closely you see that it comprises several parts. A case, a display device, some electronic circuit boards, etc.

The total finite mass of the monitor is subdivided.

The monitor "fills" a particular volume, and yet that same volume also contains the various parts of the monitor. Hmmm.

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And if you look closely at any of those parts you see that each of them comprises still more parts. Plastic panels of various shapes, knobs, switches and logo stickers. Or resistors, capacitors and wires.

The total finite mass of the monitor is subdivided some more.

The parts of the monitor "fill" particular volumes of space, and yet those same volumes also contain the various parts of the parts of the monitor.

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And a closer examination of any of these smaller parts reveals that they comprise yet smaller parts. And so on and so on. But the mass is still the same.

Pretty soon we are finding atoms and molecules as we look closer still.

Then protons and electrons.

The total finite mass of the monitor is subdivided some more.

And the volume of space filled by the monitor, and its parts, etc, is also filled with these particles.

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Look closer. Quarks.

The total finite mass of the monitor is subdivided some more.

And the volume of space filled by the monitor, and its parts, etc, is also filled with these additional particles.

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Look closer. Elysons, then gravitons (speculating now, of course), then ...

And guess what? The total finite mass of the monitor is subdivided yet some more. And even some more.

But somewhere down there we are going to find forms that resemble galaxies (more or less). And they will be made of forms that resemble stars (more or less - don't take these things too literally). And those stars are likely to have forms orbiting them that resemble planets.

Perhaps these orbiting things will look EXACTLY like planets, and have living creatures on them just like Earth. Perhaps not.

These "planets" will be made of "dirt" and "rock" and "water". And these living creatures will be made of "protoplasm". And all of it will in turn be made of "atoms", which will in turn be made of "quarks", and so on.

And would you look at that! There is one of those "creatures" on one of those "planets". It is looking at a "computer monitor". And thinking "The mass of this 'monitor' is known. It is finite. But the 'monitor' is made of parts, and those parts are made of parts. The mass is subdivided. And even though those subdivisions go on forever, the mass is unchanged, finite."

This other "monitor" fills a specific volume of space ...

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IT'S TURTLES ALL THE WAY DOWN, boys and girls.

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And the total mass of the monitor in front of you is still the total mass of the monitor in front of you.

Unchanged, and very finite.

But infinitely subdivided.



Say bye-bye to Zeno for me,
LB

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Now, perhaps there is no such thing as empty space. The universe is filled with particles of arbitrary size ...<hr height="1" noshade id="quote"></blockquote id="quote"></font 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. 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.

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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] " ... a set of numbers which is infinitely more numerous than the set of all real numbers."

Imagine a line through zero on the number line, perpendicular to the number line.

Imagine another line through one on the number line, perpendicular to the number line and parallel to the line through zero.

Imagine some more lines through each of the points on the number line between zero and one, all parallel to the first two lines.

Pick one and call it Number Line 2.

Pick another and call it Number Line 3.

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And so on. Is that enough? NO???

OK, Imagine a similar set of lines just like the first except that they are not perpendicular to the number line, but cross it at angle a1 instead.

Call these Number Line a1-2, a1-3, etc.

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And so on. Is that enough? (HINT - there are an infinite number of values for angle a1)

NO???

OK, choose any one of the lines imagined so far, call it a Number Line, and repeat the process for the interval from 42.002945000 to 42.002946000.

And/or some other interval.

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Take off your math blinders. This is physics we are talking about.

Infinity is really very cool, if you will just take the time to understand it.

In the physical sense. Understanding it in the math sense is a necessary first step, but doesn't get you to real understanding.