Gravitational Attraction

> [ohlman]: In order for me to travel the finite time between now and tomorrow at this time I am not obligated (unless I am in the dentist chair or a boring class) to *count* the hours between them, nor the minutes, nor the seconds... let alone the micro-seconds, nano-seconds, pico-seconds, etc. and on and on ad infinitum and ad nauseum.

But you are obliged to live through each and every one of these subdivisions.

> [ohlman]: However, in order to get through an *endless* experience (such as a cricket match) I do really and truly have to wait, or read, or sleep, or eat... until the last catch is caught, the last ball hit, etc.

What's the difference with the first example? Other than the subjectivity of the time elapsed?

> [ohlman]: Zeno, with his diverting but experientially useless paradox, ...

The eight (count them) paradoxes of Zeno, and their counterparts for matter, have much to teach us. The effort of resolving them teaches us what is possible and what is not about the nature of space, time, and matter. You can find my description of the paradoxes and their resolution in chapter one of "Dark Matter, Missing Planets and New Comets".

> [ohlman]: ... took something that is factually known (by those of us that accept the real world) as happening... a mile that *is* walked, a book that *is* read, a hot dog that *is* eaten... and made a fun, Alice in Wonderlandish, speculation about finishing each second, each partial page, each molecule eaten... divided... divided again... etc.

Consciousness of each element of time or space is not required. But passing through each and every one is required. The paradox is not the fantasy of an illogical mind. Rather the opposite.

> [ohlman]: If the steps are truly endless, I will never reach the end of them.

The steps are truly infinite in number, and yet you can and will reach the end of them. This is an exact analogy for the infinite series I mentioned. Infinite number of terms, finite sum. You can do a one-to-one correspondence between the series terms and the steps when crossing the street. In both cases, the sum of an infinite series is finite, not infinite.

The paradoxes involved in assuming that space or time or matter have a smallest possible element or division are so severe as to be unresolvable, IMO. Yet concluding that the divisions must then be infinite in number is a profound result about the nature of reality. -|Tom|-

Apparently a lot of people have trouble dealing with the concept of true physical infinity. I don't know why, I find the notion of a finite universe more difficult to understand. What is difficult about imagining the stars and universe extending outward without limit? I have much greater difficulty with someone telling me that no matter what direction I go I will just come back to where I started. And please don't give me that silly ant on the sphere story. The sphere sits within an unbounded Euclidean space. And if the universe is curved in 4-space then there must exist greater extent in that higher space. I think cosmologists should be required to prove what they are claiming as truth and show me the non-inverse square forces that are supposed to exist in their hyperdimensional universe. While they are at it they can show me a jar of dark matter or a photograph of a superstring. And isn't it curious how their theories are always designed with "excuses" for why these things can't be seen or observed? I claim that traffic lights are really operated by Leprechauns that sit inside them.

OOps getting a little off topic here! Tom, a crucial test for particle gravity theories is the measurement of gravitational acceleration between the Earth and Moon before/during/after an eclipse. Maurice Allais many years ago claimed to have measured just such an effect and some time ago a very detailed repetition of his experiment was conducted. However, I have not been able to find anywhere what any of the preliminary results were. Do you know what is going on with the data and if anything can be said on the matter yet?

> [jeremy]: Maurice Allais many years ago claimed to have measured just such an effect and some time ago a very detailed repetition of his experiment was conducted. However, I have not been able to find anywhere what any of the preliminary results were. Do you know what is going on with the data and if anything can be said on the matter yet?

Thanks for your comments. Yes, the Allais effect has been confirmed to high precision. You can read about the latest experimental data at: Phys.Rev.D, v. 62, 041101(R).

Unfortunately for those who would like this to have an exotic explanation, I'm now certain that it has nothing interesting to tell us about gravity. It is way too large and has the wrong sign and form to be a shielding effect. I have examined this and now found a more prosaic explanation that matches the data, quantitatively and qualitatively. That explanation is now in preparation, and (barring unexpected delays) should be published in the June 15 Meta Research Bulletin. -|Tom|-

Dr. Van Flandern writes, (May, 13th, I believe):
To take but one of several such lines of thought, Zeno's paradoxes show that time must be infinitely divisible for motion or change to be possible. But if infinitely divisible, then an infinite number of time components pass by in every nanosecond, just as they do in every trillion years. So it becomes rather irrelevant how long time lasts because it is just a measure of change, and therefore occurs at different effective rates at different scales.

>
In general terms, I would suggest that the use Zeno's paradox to prove cosmological theories or speculations is inconclusive. This is my reasoning: Zeno's paradox says, in simple terms, that "you can't get there from here" because you have to pass over an infinity of points to do so, and so on, as discussed above, and in Dark Matter...It is a "paradox" (apparent contradiction), precicely because we all know that you can get there from here, although the paradox says you can't.

Dr.VF speculates that matter is infinately divisible (because scale is infinate), in which case, the paradox is resolved. But if there is a limit to smallness, as is conventionally supposed, the paradox is not resolved in the same way. In the conventional model of finite smallness, the paradox is resolved simply by stepping over the "infinities of smallness," as we do every day.

Therefore, I would say that you can't rely on Zeno's paradox, any more than you can rely on Occam's razor to prove a point. If logical deductions are made from known facts, they must be valid, as long as the logic is correct. But logical deductions from models or paradoxes which may, or may not be true representations of reality, are not conclusive. The facts must tell. [Neil]

> [neil]: Dr.VF speculates that matter is infinately divisible (because scale is infinate), in which case, the paradox is resolved.

Actually, if you follow the reasoning in "Dark Matter, ...", that is the only logical possibility left. So it is not a "speculation", but a deduction.

> But if there is a limit to smallness, as is conventionally supposed, the paradox is not resolved in the same way.

Zeno's paradoxes (there are eight of them) show an apparent contradiction either way -- if space and time are infinitely divisible, or if there is a smallest possible division. The conventional supposition has no resolution to offer. They simply shrug at the paradox either way, and choose the way they prefer anyway.

> In the conventional model of finite smallness, the paradox is resolved simply by stepping over the "infinities of smallness," as we do every day.

Translation: the paradox is ignored.

> Therefore, I would say that you can't rely on Zeno's paradox, any more than you can rely on Occam's razor to prove a point. If logical deductions are made from known facts, they must be valid, as long as the logic is correct. But logical deductions from models or paradoxes which may, or may not be true representations of reality, are not conclusive. The facts must tell.

I agree with all that, but not with your premise that Zeno's paradoxes are not a true representation of reality. The points they make are of compelling importance to any model that attempts to describe nature. Without a resolution of all the paradoxes (including the extended ones for matter), a model is not viable by my criteria.

And because you bring it up, I know of few instances where ignoring Occam's Razor can yield anything but another form of experimenter bias. Today, we call it "Beysian analysis", but that is just a sophisticated way of saying "Occam's Razor". The model with the fewest degrees of freedom will invariably make better predictions than its competitors. -|Tom|-

This forum seems to be quiet at this time and I have a question. A while back it was said planets radiate more energy than they receive from the sun. Is there any data source for each planet's income/outgo energy budget? I have seen crude estimates of Jupiter radiating about 2.5x it's solar income but that is not data. The Earth does radiate more than it gets from the sun and even this is unknown in the data. This is very important data and NASA should do a better job with its management of this difference in income and outgo. Accounting irregularities are not limited to money matters.