Gravitational Attraction

> [ohlman]: The definition of “infinite time” that I normally use explicitly includes the quality “unfinishable”. The definition I use for “has passed” is linguistically equivalent to “has finished”. Thus they are explicit contradictions (an unfinishable event has finished).

All events finish, but the dimension of time goes on forever. I still see no contradiction here. But then, I'm using "time" with its Meta Model meaning, a measure of change.

> [ohlman]: For an example, the number zero “goes into” the number four an infinite number of times.... as each addition of zero gains us no ground toward the progression toward “four-ness”. Thus to say “I have *finished* transporting four tons of sand by transporting no sand on each trip” is (barring outside agencies) a simply non-sensical statement.

These things are resolved in the standard math of infinities. 4/0 = infinity. However, 0 x infinity is indeterminate. So in your example, you would not take zero sand, but rather an infinitesimal amount of sand on each trip. You have then divided the four into an infinite number of infinitesimal parts, and each trip does make progress toward "four-ness". The statement is rendered "sensical" again.

> [ohlman]: Similary one cannot say, and stay within the bounds of linguistic meaning: “I traveled an infinite amount of distance to arrive at this point” or “This book is infinitely long” (altho I have read books....)

Those concepts are linguistically defined in the field of mathematics, whether possible or not in reality.

> [ohlman]: Thus, using the terms in their normal linguistic sense “an infinite amount of time has passed” is a contradiction in terms.

This really is the stuff of Zeno's paradoxes, about which entire books have been written. (I'm tempted to say "an infinite amount has been written" Instead of re-inventing this particular wheel, I recommend reading up on Zeno and familiarizing with the mathematics of infinities in, e.g., Gamow's work previously cited. These references will provide the "linguistic meaning" you are presently missing. -|Tom|-

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> [ohlman]: For an example, the number zero “goes into” the number four an infinite number of times.... as each addition of zero gains us no ground toward the progression toward “four-ness”. Thus to say “I have *finished* transporting four tons of sand by transporting no sand on each trip” is (barring outside agencies) a simply non-sensical statement.

These things are resolved in the standard math of infinities. 4/0 = infinity. However, 0 x infinity is indeterminate. So in your example, you would not take zero sand, but rather an infinitesimal amount of sand on each trip.


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No. Zero amount of sand. Obviously if I transport any sand at all on each trip then one can contemplate (even if not in my lifetime or yours) my acheiving my goal. However no amount of time, however finitely large, makes ANY progress toward an infite target... thus the appropriate number to reach fourness is zero sand per trip. This is a process which cannot and will not finish (and thus has not finished).

I disagree that this has anything to do with Zenos paradox at all. This is simply straightforward stuff. If the definition of the goal (in this case "the passage of an infinite amount of time") is such that it implies that I can make no progress toward it at all toward it then the appropriate number to measure my progress is zero... zero into four. Filling a small bucket with no sand each trip, and filling an infinitely large bucket with some sand each trip are mathematically equivelant. Each iteration produces no progress toward the goal.

This could be modeled within the physical realm by a man walking attempting to catch a man on a bicycle. If the walking man was going 4 mph and the bike riding man 8 mph then the walking man is making zero progress toward his goal of catching the rider (in point of fact he is receeding, but that is irrelevant). Letting him chase for an infinite amount of time will bring him no closer to victory.

>> [ohlman]: And does this imply that object near to a large gravity source (such as a black hole) are then *heavier* when measured in their relationship with third object??
„« [Tom] You lost me here.

Oops. Sorry to have lost you
You had said
> In the Meta Model, gravity is a force carried by gravitions. Some of these gravitons are absorbed by the bodies they strike. This heats up the bodies. That heat becomes the energy powering their atoms, and is eventually released again in radioactive decay or spontaneous photon emissions. The Earth and the other large planets are known to radiate more heat back into space than they take in from the Sun. This is presumably the excess heat deposited by the gravitons.
>This heat, in the form of lightwaves, joins that radiated by stars and propagates out into the universe. There, it experiences friction from the medium of gravitons, which slowly cause the lightwaves to lose energy and redshift. That is the mechanism of cosmological redshift.
>At the same time the lightwaves are losing energy to the graviton medium, the latter medium is gaining energy lost by the lightwaves. This replaces the energy deposited in bodies such as planets and stars during graviton collisions. So the universe does not run down in this process. If one considers the universe at large, the energy books are balanced.

I understood this to be kind of a chain reaction Gravity(ons) > (are absorbed and create)heat > (which is realed as)photons/lightwaves > (which is absobed by the graviton medium and presumable create more)gravitons. Is this right??

If so, then my comment was that the original gravitons were ordered with respect to their original source (the sun or whatever) but the resulting *new* gravitons would be ordered with respect to their new *hosts* and thus *disordered* with respect to their original source. Thus a form of gravitic entropy.

What I meant by my question about bodies heavier in a field was related to my understanding of the above chain. If my understanding of the above chain is correct, then I would expect that a body *A* if isolated in space from all other bodies, would only attract person *C* to itself with an attraction of, say, 145 pounds on the bathroom scale. However if body *A* were moved into the field of a black hole (and thus receiving more gravitons which produced more heat etc. etc.) would then man then weigh 146 pounds??

> [olhman]: No. Zero amount of sand. Obviously if I transport any sand at all on each trip then one can contemplate (even if not in my lifetime or yours) my acheiving my goal. However no amount of time, however finitely large, makes ANY progress toward an infite target... thus the appropriate number to reach fourness is zero sand per trip. This is a process which cannot and will not finish (and thus has not finished).

You said before this discussion was intriguing. However, it loses some of its luster when reduced to semantics instead of focusing on concepts.

"Infinitesimal" is *not* "finitely large" by its very definition {in-[meaning "not"]-finite-simal). In a sense, it is another form of "zero", but one that recognizes that zero times infinity can be finite.

While you remain unfamiliar with the mathematics of infinities and infinitesimals, we cannot help but to have these semantic differences. I do not know how to make progress beyond what I have done, point you to sources where you can become familiar with these concepts and the rules that govern them. Even if you object, you cannot do so knowledgeably until you familiarize with standard terminology and usage. -|Tom|-

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"Infinitesimal" is *not* "finitely large" by its very definition {in-[meaning "not"]-finite-simal). In a sense, it is another form of "zero", but one that recognizes that zero times infinity can be finite.
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This was just an error on my part. I was contrasting *finitely* large with *infinitley* LARGE... not *infinitely small*.

It is hard, as a linguist, to be faulted for focusing on semantics

This particular thread began, you may recall, when you said you *could not see* where I saw the contradiction in terms. Perhaps I have, perhaps I have not, at least shown where I see such a contradiction.

In general I came to this site because of the fascinating work on the speed of gravity. On doing a web search on the speed of gravity I find almost nothing other than your site that even attempts to answer the question of the speed of gravity.

Given the facts as you have described them, and with purely theoretical measuring devices, is faster-than-light communication possible in your view? (IE the communicator on one planet would waggle some heavy objects about (right, left, left, right, right...) and the person on the other planet measuirng thier location via gravity (right, left...))??

> [ohlman]: I understood this to be kind of a chain reaction Gravity(ons) > (are absorbed and create)heat > (which is realized as)photons/lightwaves > (which is absorbed by the graviton medium and presumable create more) gravitons. Is this right??

Gravitons strike matter. Their mass is absorbed, and their kinetic energy is converted to heat energy in the mass (or kinetic energy of molecules). Matter content, total energy, and even entropy are preserved because, while the absorbed energy increases the heat and internal motions of the absorbing matter (which increases entropy), the absorbed graviton decreases the disorder of the universe by collecting it in one place instead of having it dispersed (which decreases entropy).

Eventually, the heat of the atomic constituents builds up to the point that we have a particle decay or spontaneous photon emission (analogous to a supernove explosion at our scale). That spews absorbed gravitons and an EM wave (like the matter and energy waves from a supernova) back into space. The number of free gravitons in space is restored, but some of their energy is lost to the EM wave. That wave travels through space, losing energy by friction with the graviton medium, until all its ebergy is returned to the gravitons. Again, mass, energy, and entropy are all conserved by this process.

> [ohlman]: If so, then my comment was that the original gravitons were ordered with respect to their original source (the sun or whatever) but the resulting *new* gravitons would be ordered with respect to their new *hosts* and thus *disordered* with respect to their original source. Thus a form of gravitic entropy.

The conservation is moment-by-moment, event-by-event. There is no temporary change in the universe's entropy that is made up later. All actions in a closed system preserve entropy. But "closed system" must now be redefined to include all affected media on all scales.

> [ohlman]: I would expect that a body *A* if isolated in space from all other bodies, would only attract person *C* to itself with an attraction of, say, 145 pounds on the bathroom scale. However if body *A* were moved into the field of a black hole (and thus receiving more gravitons which produced more heat etc. etc.) would then man then weigh 146 pounds??

Your basic idea is correct, but there is a sign difference. Gravitons push from outside masses instead of pulling from inside masses. But masses shadow one another from some gravitons, and this absence of expected gravitons between masses is what pushes them toward one another. So a graviton can also be thought of as a "negative mass" passing between bodies, even though it is really the absence of positive masses between the bodies that would otherwise bombard the bodies from all directions. Such negative masses, of course, would be more abundant near a black hole, and would therefore slightly *decrease* the weight of a man on a scale. -|Tom|-