# Thread: INERTIA AND ITS SOURCE

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INERTIA AND ITS SOURCE

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“I heartily beg that what I have here done may be read with forbearance; and that my labors in a subject so difficult may be examined, not so much with the view to censure, as to remedy their defects.” Isaac Newton (Preface of the Principia)
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The following is a condensed paraphrasing of essential ideas in Chapter 8, INERTIA, and Chapter 14, THE SOURCE OF INERTIA, of my book A Journey Beyond the Universe Copyright 2001, Richard J. Hanak. You can read excerpts from my books for free by clicking on the above link. They are also available as inexpensive ebooks at Xlibris
End of commercial. [img]/phpBB/images/smiles/icon_biggrin.gif[/img] Note: the two paragraphs below involving the gamma factor are recent ideas and do not appear in the book.

Hold a weight in your hand with your arm extended and you will be very aware that you are exerting forces in several of your muscles. Those forces you exert are finally applied to the weight and resist the gravitational force between the weight and the Earth. The force you apply to the weight is equal in intensity and opposite in direction to that gravitational force. The situation is in accord with Newton’s third law that requires for every action of exerting a force, a reaction of exerting an equal and oppositely directed force.

Next, quickly withdraw your hand from under the weight. The weight falls. If nothing impeded the motion of the weight it would instantly fall to Earth, contrary to common experience. Therefore, something impedes that motion. As the weight falls, the gravitational force continues to exist between the weight and the Earth, so causing the velocity of the weight to increase as it falls.

We say that the inertia of the weight resists any acceleration that might be forced upon it during the time the weight falls. Despite that resistance, as Galileo would say if he were here, “it moves.” That being the case, perhaps we should think of inertial force as limiting or regulating the acceleration of the weight. The situation is analogous to electrical impedance regulating the flow of current in proportion to the impressed voltage. The inertial impedance of a body regulates its acceleration in proportion to the impressed motivating force. To find out why that is so, let us examine the nature of mass bodies, their inertia, and inertial force.

Not all bodies are electrically charged and externally surrounded by their own electric field; nor are all bodies magnetic and externally surrounded by their own magnetic field. However, all bodies possess mass, are externally surrounded by their own gravitational field, and have the property of inertia.

Newton's first law of motion tells us that an inert body cannot alter its own state of rest or motion and that such changes can only be brought about by an external force. His second law of motion describes the effect an external force has on an inert body; namely, that it causes an acceleration of the body. Laws one and two accurately summarize the meaning of the term inert body and what an external force does to an inert body. Whatever inertia is, we know at least that it is a property shared by all inert bodies.

Although Newton would not hypothesize, especially about the cause of gravitation, others speculated about the cause of inertia. Bishop Berkeley, observing that all motions could be referred to the 'fixed' stars, proposed that those distant stars cause the inertia of local objects. Berkeley reasoned that their great numbers would make up for their great distance. Much later Ernst Mach proposed that all the matter in the universe causes the inertia of local objects. Mach even suggested that if Newton's bucket of water were at rest and the universe were rotated about it, the water would form the same meniscus as when Newton rotated the bucket. It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed. The strongest tidal force imaginable would have emptied the bucket.

If distant bodies caused the inertia of a body, we should expect nearer bodies to cause directional variation in that inertia. Our observation of no such variation suggests that other bodies, near or far, do not cause a body’s inertia. The absence of any observed directional variation of inertia implies that the source of inertia must be uniformly distributed around an inert body. The one thing that every body has, a thing that is uniformly distributed around each body, is its own gravitational field.

The gravitational field, electrostatic field, and the magnetic field produce forces; they are force fields. All force fields store potential energy. Work must be performed to increase the intensity of a force field or to alter is spatial distribution. That work is stored in the field as potential energy. The force field resists increases to its intensity. The greater the intensity of the field, the greater is its opposition to further increases of its intensity. (It may help to think of those properties of a field in terms of an electrostatic capacitor.)

Consider a mass object sufficiently distant from other mass objects and at rest. Its gravitational field is spherically distributed in space with intensity inversely proportional to the square of the distance from the object. The intensity of the gravitational field is greatest at the surface of the object.

If a force from another body acts on that mass object it will begin to move and accelerate. As a consequence of that movement, its gravitational field will also move. However, the whole gravitational field will not move at once. A nearby forward region of the field previously at a lower intensity will now have a higher intensity pushed into it and the change will propagate through the field with a finite velocity. That change is a distortion of the field. But we have noted above that a force field resists increases to its intensity. In the case of a gravitational field, that resistance appears as a force exerted against the body, a force produced by the body’s own gravitational field. That resistance to change in the state of rest or motion is called inertial force. The source of inertia, then, is a body's own gravitational field.

Gravitational force is a manifestation of the static gravitational field of a body interacting with that of another body. Inertial force is a manifestation of the dynamic gravitational field of a body interacting with the body itself. Inertial force is not fictitious. It is a real force with a real source. Inertial force, a gravitational effect, is just as real and just as fundamental as gravitational force. Its behavior is independent of the frame of reference of an observer. It is equal and opposite to the accelerating force as required by Newton's third law. Einstein acknowledged the law equating gravitational mass and inertial mass. We now are aware that the forces by which we know them arise from the same source: gravity. They are not merely equal; they are identical.

The kinetic energy of a body, then, is stored as a distortion of its gravitational field. If such a distortion exists in a gravitational field, its body is moving. If the distortion is increasing the body is accelerating. Thus, the states of rest, unaccelerated motion, or accelerated motion of a body are potentially determinable from its own gravitational field. However, the gravitational field of a body is an attribute of a body, and is inseparable from the body. Therefore, the state of motion or rest of a body, being determined by an aspect of the body itself, and not by its relationship to any other body, is not relative rest or motion; it is absolute rest or motion.

The so-called relativistic increase in mass at high velocities, then, is not really an increase in mass. It is an increase in a body’s inertia as its gravitational field piles up ahead of it. The finite propagation velocity of a gravitational field disturbance limits the velocity of an accelerating body. There can be no such thing as a mass body without a gravitational field. A body cannot escape from its own gravitational field. That is what the Lorentz gamma factor (1-v²/c²)^(-½) is all about.

In that factor, c should now be interpreted as a variable representing the propagation velocity of a gravitational disturbance in space rather than the velocity of light. In my book I show that the propagation velocities of such disturbances decrease with increasing gravitational field strength, that electromagnetic radiation is also a propagating gravitational field disturbance, and that, therefore, the velocity of light cannot be constant.

This new interpretation of the gamma factor affecting inertia is not at all the relativistic increase in mass expressed in a different way. The relativistic increase in mass and increase in inertia concepts differ in at least two fundamental ways. The first is that if a body’s mass increases, its volume, density, or both must change. Increase in inertia requires no such changes. The second is that if a body’s mass increases, its gravitational field strength must increase in all directions. When inertia increases, the gravitational field increases only in the leading direction of the moving body.

Because this is an astronomy venue, I will close by calling to your attention that the information content in the Fraunhofer lines of starlight is independent of relative motions of source or observer. The kinds of atoms that caused those absorption lines are identifiable regardless of the amount of red or blue shift. Without those identifications the Doppler shift of starlight could not even be measured. Those identifications are also independent of red shift causes other than relative motion. Therefore, that information content of radiation is also absolute.
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* Today’s against-the-mainstream has the habit of becoming tomorrow’s mainstream. – Hanak *

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Because this is an astronomy venue, I will close by calling to your attention that the information content in the Fraunhofer lines of starlight is independent of relative motions of source or observer.
I'm not completely clear what you mean by this...

I'm fond of using the very pronounced double emission lines of sodium as a benchmark, simply because even a rank amateur (me!) can recognize them.

If I see them, I know them. "Oh, wow, hot sodium!"

If I see them, and they're red, I know, "Oh, wow, hot sodium that's moving away from me." If see them, and they're blue, I know, "Oh, wow, hot sodium that's moving toward me."

Is that or is that not "information?"

Silas

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My question would be: How would you verify what you've suggested above? What experiments do you propose? Have you undertaken any?

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If a force from another body acts on that mass object it will begin to move and accelerate. As a consequence of that movement, its gravitational field will also move. However, the whole gravitational field will not move at once. A nearby forward region of the field previously at a lower intensity will now have a higher intensity pushed into it and the change will propagate through the field with a finite velocity. That change is a distortion of the field. But we have noted above that a force field resists increases to its intensity. In the case of a gravitational field, that resistance appears as a force exerted against the body, a force produced by the body?s own gravitational field.
from the description above it seems to me that there should be a deacceleration force instead, since it is the objects velocity that is causing the deformed field, and not specifically the increase in velosity.

also, the force field would also have to resist a decrease in field strength also or else the decrease force would counteract the increase force, so therefore you would have a force pulling on the rear as well as a force pushing from the front. Unless you are arguing that it is the narrowing of the field in the front that is causing the restive force, but even then i still do not see a way around the deceration force.

gavitational fields extend on for infinity, so wouldn't you expect a rebound effect. say you turn off the motive force, this information is carred along at a finite speed along the forward vector of the gravity field, so you would expect the inertial force to slack off, in a exponetial way, instead of quitting altogether.

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<font size=-1>[ This Message was edited by: moving_target on 2002-08-18 04:19 ]</font>

5. On 2002-08-17 21:38, Richard J. Hanak wrote:
Much later Ernst Mach proposed that all the matter in the universe causes the inertia of local objects. Mach even suggested that if Newton's bucket of water were at rest and the universe were rotated about it, the water would form the same meniscus as when Newton rotated the bucket. It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed. The strongest tidal force imaginable would have emptied the bucket.
Why is that so surprising? Mach didn't realize it for the same reason that I don't "realize" it: I don't see any reason whatsoever that it should be true.

If distant bodies caused the inertia of a body, we should expect nearer bodies to cause directional variation in that inertia.
"We" don't necessarily expect that. If you look at the theories, and look at the astronomical maps, and do the calculations, it turns out not to be true. Your arguments are based upon your personal fallacies.

6. Guest
<a name="20020819.6:39"> page 20020819.6:39 aka G
On 2002-08-18 14:18, GrapesOfWrath wrote: To: HUb'
.1 As I watched "Gramps" pour coffee straigh up
ito a cup held upside down arms length above..
without spilling 1 drop..{ i thought i should try }
after taking that "CUP forward.. on my way back
I decided to try.. only me instead of coffee
their4 I deliberatly avoided jumping or propelling
and simply limted one leg at a time and seated myself
"inside" of a Gravity Wave pod. and was transported in
a very pleasent and confertable way. from the Wheel house to CIC {maybe 25 feet or more}
POD2 continued there

<font size=-1>[ This Message was edited by: HUb' on 2002-08-22 04:23 ]</font>

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Silas:

Thank you. Yes, the sodium emission D lines, with their characteristic spacing and their carrying most of sodium’s visible light energy, are now admitted to membership in the absolute information club. No relative motion or reference frames of the source or you, the observer, neither linear nor rotational, neither “inertial” nor “non-inertial” would fool you about which atoms emitted those lines. That information is beyond relativity; it is absolute!

overrated:

Thanks for your stimulating questions. So I now must be an experimentalist as well as a theoretician. OK. Here is a possible experiment. Accelerate particle emitting radioactive nuclei with a suitably short half-life to inertialistic velocity (formerly relativistic velocity). At that velocity the particles emitted will predominantly travel in directions other than the travel direction of the nuclei. The emission distribution should approximate a cardioid with the notch facing the travel direction of the nuclei. Under relativity theory I think it should be a circle. It seems like a challenging experiment to design and execute. I might be able to make time available to manage the project if you could obtain the funding. Surely you don’t expect me to do everything myself. [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

Moving_target:
GRAVITY AND LEVITY

Twinkle little star while you may, ‘cause
The gravity monster will get you someday.

I must begin by telling you that I find nothing attractive about Gravity. Aside from the dreadful, ultimate fate it deals to stars, it causes all kinds of harmful accidents to us humans. It even causes people to sag and become less attractive as they get older. Most of my relativist friends are appalled by a black hole curvature of space-time that would rip apart space-time itself. Gravity is worse than just naughty; it is absolutely repulsive.

The words ‘attractive’ [img]/phpBB/images/smiles/icon_smile.gif[/img] and ‘repulsive’ [img]/phpBB/images/smiles/icon_evil.gif[/img] are so emotionally charged that scientists (other than behavioral scientists and psychologists) shouldn’t touch them, not even with a ten-foot pole. We could consider forces to be either tensile or compressive. But those descriptions are engineering and materials sciences oriented. Pushing forces and pulling forces, though suggestive of ideas from childhood, are openly honest, unmistakably descriptive, and well suited to the vocabulary of physics. We will soon be dealing with force in the abstract. Perhaps it is best to begin with the concrete.

Concrete is made of cement, sand, stones and water. A paving contractor I know likes children in the abstract but not in the concrete.[img]/phpBB/images/smiles/icon_lol.gif[/img] On the other hand the Mafia does not like enemies in the abstract. It prefers them in the concrete.[img]/phpBB/images/smiles/icon_lol.gif[/img] Concrete is very successful at resisting compressive forces, but is as weak as a pup when it comes to tensile forces. That is why they sell so much reinforcing rod. Nonetheless, there is a little tensile strength in concrete or they wouldn’t be able to sell garden benches made of it.

There is evidence that gravity is somewhat analogous to concrete. Gravity can generate very strong compressive forces, strong enough to squeeze the life out of any star. In any force field that follows the inverse square rule of field strength, the field is radially symmetric because the field pushes against itself in all directions. The lines of force in the field are closest at the surface of the body that gives rise to the field. They push against the body to keep themselves in the surrounding space. Once in space the lines of force push against each other to achieve the maximum separation between the lines of force. That results in radial symmetry. All that force fields want to do is push, push, push.

If a field pulled against itself in all directions, it would pull itself closer together until it was all on the surface of the body and was no longer a field at all. Therefore, force fields cannot pull; they can only push. Here the analogy to concrete stops. A force field cannot exert the slightest pulling force. The idea of force fields wasn’t thought of until long after Newton’s time; so we can understand his thinking gravity was attractive.

Quantum theory invokes quantum particles in place of fields to produce action at a distance. Quantum particles don’t say, “Come here.” They say, “Here I come!” They can push things in front of them but they cannot pull things behind them. The graviton is the quantum particle of gravity.

There is a position between any two bodies where the gravitational push is the same toward either body. A test particle at that location will move to neither. At that location the field intensities (or graviton fluxes) are equal and oppositely directed. The field intensities are, therefore, vectorially additive and zero at that location. That implies that the gravitational pushing forces between two bodies are weaker than the pushing forces outside them. Consequently, gravity pushes the two bodies towards each other. Newton’s law of universal gravitation is restated to reflect this view in A Journey Beyond The Universe.

Now you can understand why I wrote above that gravity is absolutely repulsive and not at all attractive. The implication of this understanding of gravity for the gravitational source theory of inertia is that the weaker gravitational pushing force of an accelerating body’s own rear field can have no effect on the stronger, opposing, pushing force of its forward gravitational inertial field. (Do not forget the second body that exerts the additional motivating force for the acceleration.)

Force fields, the gravitational field included, are real things. Nothing real can be infinite in any sense. No real rate of change can be infinite. Those ideas are explained more fundamentally in my books.

<font size=-1>[ This Message was edited by: Richard J. Hanak on 2002-08-20 10:32 ]</font>

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it seems to me that you are tring to have it both ways. just now you stated that fields always 'push' outward (regardless if the force is attractive or repellent), but at the beginning you clamed that it is the field that pushes inward and thus causes inertial force.

which is it? if the gravity /field/particle/wave/other/ gets emited outward, how is the information passed inward to the mass?

now, get me straight, i'm not tring to discount the therory about how all fields 'push', i just want to know how you propose that the information is passed inward, the two do not seems compatible

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moving_target: Here is the gravitational theory of inertia and its forces in a nutshell.

1. (Action #1) The gravitational field always pushes inward against its body, so compacting the body.
2. (Reaction #1) The gravitational field also pushes itself outward away from its body, so preventing itself from collapsing and keeping itself extended in space.
3. (Actions & Reactions #2) The gravitational lines of force push each other sideways, producing radial inverse-square intensity distribution.
4. (Action # 3, the force causing acceleration) As long as a body is being accelerated it compresses its own gravitational field in front of itself.
5. (Reaction #3) The compressed field, like a spring compressed even more, presses inward all the more against its body. That incremental inward pressing is inertial force.
6. The compression of the field propagates away from the body with a finite velocity.
7. That finite velocity gives the compressed field time to interact with the body.
8. When the acceleration ceases, the remaining compression of the field propagates away from the body and there is no inertial force against the body.

I hope the above, though compact, is a sufficiently clear explanation of how the forces act.

By the way, the inverse square law of both gravity and light is not a mere geometric coincidence. I mentioned above (in the 15th paragraph of my post) that electromagnetic radiation is a propagating gravitational field disturbance.
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<font size=-1>[ This Message was edited by: Richard J. Hanak on 2002-08-20 20:35 ]</font>

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Hanak, the theory you outline fails to take into account the fact the equivalency of energy, and indeed the fact that light is gravitationally lensed. Explain that with your theory.

Furthermore, your "lines of force" are not physical. What's your mathematical representation? You do not take into account metric formulations from GR, so you have a problem explaining how solutions to Einstein's Field Equations work. There is no equivalence principle in your theory at work.

I'm sorry, it's full of hot air.

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Interesting discussion.
So, here's my theory of inertia. Let's drop a dimension and go to the rubber sheet analogy. A large mass makes a large indentation in the sheet with a smaller body nearby making a small indentation in the "downward" slope of the larger one. As the small body "falls" towards the larger one, its small indentation must propagate through the sheet. The resistance of the sheet to the moving deformation is analogous to the inertia of the small body.
The greater the mass, the larger the indentation, the more resistance to motion.
Bingo. Inertia!

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Senor, you are erroneously conflating two different pheomena, namely laws of gravity and Newton's first law. They are not necessarily connected. If you try to connect the three small scale forces to the one metric large scale force you will end up with problems. This is the current problem haunting modern physicists, in fact. If we try to take the approach you wish to take, we end up failing rather miserably. It seems that we don't quite have it together yet. Someday we might.

Hanak's nonsense, though, is out in left field.

<font size=-1>[ This Message was edited by: JS Princeton on 2002-08-21 02:27 ]</font>

13. Hanak's nonsense, though, is out in left field.
True,but: He will probably sell a lot of books to the gullible without comvincing any of us. [img]/phpBB/images/smiles/icon_frown.gif[/img]

14. Guest
<a name="20020821.6:13"> page 20020821.6:13 aka POD2
On 2002-08-21 07:49, Kaptain K wrote: Too:
POD1
To say My first concern, once underway, was the "DOOR"
as I could see ahead, on my present course:
I would be sliced into 1/2 by the door jam?
i reached for a stearing wheel {but there are no sterring wheels}
(in a Gravity wave Pod) [POD] for short. Soon however
i discovered that a gravity wave POD is both SELF AWARE & enviornmentaly aware
and sencing the door jam {and maybe my angziety} it adjusted itself to the center . By moving LEFT POD2a continued

<font size=-1>[ This Message was edited by: HUb' on 2002-08-22 04:48 ]</font>

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JS Princeton, not so.
Any mass makes a dent in the sheet. To act upon that mass with an external force, ie, to make it move, the wave must still propagate through the sheet. Whether the external force is from the gravitational attraction with another mass or from the stroke of a pool cue. The principle is the same.

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Senor, your analogy seems fine on the qualitative level, but the problem that beguiles physics right now is there is no formal way to put the metric of gravity together with quantum action unless you end up with ridiculously high vacuum energy densities (that are off observationally by factors of 10^60 at best). Your unification idea is one that has been tried often, but as of yet there's no good way to put it together mathematically.

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JS,
What the @#\$% are you talking about. I didn't understand a single word of your reply and cannot even speculate if it was relevant or just a leg-pull.
If you don't know, just say.

18. Guest
<a name="20020821.12"> page 20020821.12 aka POD2a
Much of what i say here 2? must be view in suito?
anyway precieveing the POD indent as it hit the JAM
and sensing {no i do not know HOW humans}
sence Gravit Wave Pods approaching
that "SOME" can do so I have 0 doubt
a ripple effect as the rest of the shell
responded for the collective move "LEFT"
i was very relived [NOT TO BE SLICED IN 1/2]
and continued my journey to 2b

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Senor, for more on problems of Grand Unification and how it implies a connection between small scale (electroweak and strong) and large scale (gravity) forces, please read here. Basically the attempt made to combine metric (that is your rubber sheet) formalism and the so-called "quantum foam" of virtual particles failed miserably at first glance by a staggering 120 orders of magnitude. Today we do a little bit better with supersymmetry (still speculative), but that means we're only down to a discrepancy of 60 orders of magnitude. This implies that quantum forces (that are the result of exchanged particles) and the curvature of space (General Relativity) are not yet reconciliable. Therefore you have a problem ascribing inertial mass as due to the "dimple" in spacetime since any other force other than gravity acting on your mass does not "translate", if you will, into a metric formalism.

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[quote]
On 2002-08-23 18:19, Gsquare wrote:
Richard J. Hanak,

Thanks for finally revealing the conclusion to the novel you were presenting; (that way I don't have to pay for the book!) .... I figured you were going to blame gravity for causing inertia; (God also gets blamed for a lot a' stuff He doesn't do, but that's another story).

Actually there is quite a similarity to what you are saying and what Mach was saying; it's just that Mach attributed inertial effect to distant mass, you are trying to arrange it locally.

I'm all for alternative theories, ...
Nevertheless, there are some problems:

If I'm going to challenge Einstein's assumptions, you should expect I'll certainly challenge yours:

It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed.
I don't believe this has ever been proven either way. SO.. How did you find out??

The strongest tidal force imaginable would have emptied the bucket.
Uh,..I don't believe that inertial effect in Mach's proposal, or otherwise, was ever attributed to tidal forces. Nevertheless, I believe a quick calculation of tidal forces of earth orbiting about the stationary bucket would show negligible effect; [the minimum 'nearness' the earth could get to the bucket would be one earth radius, (~6.6 x 10^6 m.)]

If distant bodies caused the inertia of a body, we should expect nearer bodies to cause directional variation in that inertia.
Not neccesarily. This statement implies you have arbitrarily decided a'priori that the magnitude of inertia is directly proportional to that part of gravitational force that varies at 1/R^2.
**
By the way, it may interest you to know: one Einstein's GR predictions (based on the same expectation from Mach's ideas) was that a body's inertia would increase as massive bodies were brought 'near'. The effect, though, was calculated to be so small as to be immeasureable by typical experiments.

However, this effect was shown later to be untrue by Brans (mid 60's) due to the fact that it would have broken equivilence principle, and his analysis is generally accepted.

Mach thought that inertia depends upon a mutual action of matter, without specifying the nature of the interaction; whereas Einstein specified the nature (and magnitude) of the interaction. You, however, make no mention of the equation you are using ....therefore, any local directional inertial variation or lack thereof is presumptive.

Also, I notice no equation for the local inertial effect that you predict, except to say it is somehow equal to the distortion of grav. potential energy. Without an equation it may be hard to convince even those willing to re-think relativistics.

Inertial force is a manifestation of the dynamic gravitational field of a body interacting with the body itself.
Show me the equation.

The kinetic energy of a body, then, is stored as a distortion of its gravitational field.
Show me the equation!

If the distortion is increasing the body is accelerating. Thus, the states of rest, unaccelerated motion, or accelerated motion of a body are potentially determinable from its own gravitational field.
Great concept, but fill in the blank below.
SHOW ME THE ____________!

The so-called relativistic increase in mass at high velocities, then, is not really an increase in mass. It is an increase in a body’s inertia as its gravitational field piles up ahead of it.
1st of all, lets get on the same page. 'Mass' and 'inertia' in physics are the same quatity,(used interchangeably), its called inertial mass.

G^2

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GrapesOfWrath:]
On 2002-08-17 21:38 I wrote:
It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed. The strongest tidal force imaginable would have emptied the bucket.
On 2002-08-19 14:18 you wrote:
Why is that so surprising? Mach didn’t realize it for the same reason that I don’t “realize” it: I don’t see any reason whatsoever that it should be true.
The ocean tides on Earth are caused by the gravitational effects of the Moon, Sun, and the planets. The Moon, averaging about 230,000 miles between its surface and the surface of the Earth has the strongest effect on the oceans. The Sun, at about 93 million miles, has a lesser tidal effect. The other planets have much smaller effects.

If the moon were at half the distance, 115,000 miles, a place that might otherwise experience a 10-foot tide would experience a 40-foot tide. The moon at 57,500 miles would create a 160-foot tide, and at 28,750 miles a 640-foot tide, at 14,375 miles a 2,560-foot tide. Keep going with the series and by the time the Moon’s surface is 457 miles from Earth’s surface, the tide will be 496 miles high. Not only would the Moon get a bath, but the Moon’s gravitational force would make lots of water leave the Earth and go to the Moon.

The Earth is larger and heavier than the moon. The bucket, being very small and insignificant compared to the Earth, would not have enough gravitational force to keep any of its water. Perhaps you can now understand that if the Earth orbited even a couple of miles away from (let alone right next to) a stationary bucket containing water, the Earth would suck that bucket dry to the last drop.

If Mach meant that only the really far parts of the universe should rotate around the bucket, he should have said so. If you think about that similarly to the Moon-Earth example we just went through, you should find all kinds of disruptive phenomena, including tides, all over again. I still say I’m surprised that a really brilliant physicist like Mach didn’t think of the implications of his impossible-to-do experiment
In reply to my writing: If distant bodies caused the inertia of a body, we should expect nearer bodies to cause directional variation in that inertia.
You wrote: "We" don't necessarily expect that. If you look at the theories, and look at the astronomical maps, and do the calculations, it turns out not to be true. Your arguments are based upon your personal fallacies.
Please let me know which theories, which astronomical maps, and what calculations make it turn out to be false? I am open to all ideas and welcome any constructive criticism and new knowledge. Fallacies are false ideas arising from logical errors in reasoning. In this thread I have presented my ideas and the reasoning supporting those ideas. Have you found logical errors in the reasoning? If so, I would appreciate knowing where, so that I can make corrections.

Did you hear about the California winery whose buildings burned down during the grape harvest? The only space they could quickly rent was a warehouse of the Rath Drapery Company. Now they trample out the vintage where the drapes of Rath are stored. [img]/phpBB/images/smiles/icon_lol.gif[/img]

JS Princeton: On 2002-08-20 20:55 you wrote:
Hanak, the theory you outline fails to take into account the fact the equivalency of energy, and indeed the fact that light is gravitationally lensed. Explain that with your theory.

Furthermore, your "lines of force" are not physical. What's your mathematical representation? You do not take into account metric formulations from GR, so you have a problem explaining how solutions to Einstein's Field Equations work. There is no equivalence principle in your theory at work.

I'm sorry, it's full of hot air.
What I have outlined above is a theory of inertia. It is irrational on your part to expect such a limited theory to take into account phenomena falling outside its scope. The theory presented here is only a portion of a more extensive theory that does indeed account for mass-energy equivalence. That theory presents energy as a gravitational phenomenon. Because gravity is an attribute of mass, there is a more intimate connection between energy and mass in that theory than in relativity theory.

Gravitational lensing fits in easily with my theory of light, though I would prefer to call it gravitational refraction. Refraction is the bending of light that is not travelling perpendicularly to a change of index of refraction in the medium or media through which it travels. The primary cause of that bending is that the velocity of light depends on the index of refraction of the medium in which it travels. That dependency is generally such that the more dense (gm/cc) the medium, the greater the index of refraction and the slower the velocity of light in the medium. Light travels slower in air than in a vacuum, slower in water than in air, slower in glass than in water, and slower still in a metal (infrared in germanium) than in glass.

The denser a light-transmitting medium, the greater is the gravitational field of the atoms in the medium. That field acts on the light travelling through it. As I mentioned above, I have shown that light is a propagating gravitational field disturbance and that such disturbances travel more slowly the stronger the field. If light enters a strong spherical gravitational field, it will be refracted as if by a lens and for the same reason: the change in velocity of the light. The same effect explains any gravitational bending of light.

As for lines of force not being physical, let’s remember that we are trying to model the world about us. In that world we sense or detect things. We also observe effects that things can have on one another. In the case of things that we can only know by their effects, such as the gravitational, electric, and magnetic forces, and light, we hypothesize causes for those effects. Those causes are hypothetical constructs to mediate between the objects causing effects and the objects being affected. We can, for example, hypothesize that there are force fields, that there are quanta, or that there is a space-time manifold to produce action at a distance. All of those hypotheses have proved to be useful in explaining, describing, and predicting effects between bodies.

Sprinkled iron filings and magnet experiments, electrostatic field measurements, or gravitational force vs. height measurements are convincing evidence that force fields have vector properties throughout the fields. And a succession of connected force vectors is, after all, a line of force. The lines of force can be followed from one material body to another. What can be more physical than something that relates one material body to another?

Vector analysis is the preferred mathematical representation for force fields. Embodying Gauss’s theorem, Greeen’s theorem, and Stoke’s theorem, vector analysis can deal with a variety of phenomena including hydrodynamics, heat flow in solids, and, of course, gravitational potential.

As for metric formulations from GR and how solutions to Einstein’s field equations work, it is irrational for you to require an opposing theory to explain features of a theory it opposes.

You claim that there is no equivalence principle at work in my theory. That claim is false because my theory has the Newtonian principle of equivalence at work. That principle of equivalence states that in a gravitational field all objects accelerate at the same rate regardless of their mass or composition.

Einstein’s view was that in a freely falling reference frame, all laws of nongravitational physics, such as electromagnetism, should behave as if gravity were absent. My view is that electromagnetic phenomena are gravitational manifestations, as exemplified, for example, by my explanation of gravitational refraction of light. Accordingly, if a laboratory were freely falling in a strong gravitational field, the velocity of light in it would be less than if the laboratory were freely falling in a weaker gravitational field.

The use of invective cannot strengthen a weak argument or give meaning to one that is meaningless; it is an automatic alarm bell calling attention to the inadequacy of the user’s argument. Only a contrary argument that presents contradictory evidence, points out errors in logic, or calls attention to misrepresentations of fact indicates strength in argument. Though you have my sympathy for your hot summer in Princeton, please don’t blame me.

On 2002-08-21 02:26 Your stated to Senor Molinaro:
Senor, you are erroneously conflating two different pheomena, namely laws of gravity and Newton's first law. They are not necessarily connected.
According to the theory of inertia I presented above, inertia is a gravitational effect and, therefore, those laws are necessarily connected. As for some of the dilemmas of contemporary physics, the gravitational theory I present offers many new avenues for resolving previously intractable problems.

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On 2002-08-23 20:51, Richard J. Hanak wrote:

It is surprising that Mach did not realize that if the Earth rotated around the bucket, let alone the whole universe, no mere meniscus would have been formed. The strongest tidal force imaginable would have emptied the bucket.
The ocean tides on Earth are caused by the gravitational effects of the Moon,....

... by the time the Moon’s surface is 457 miles from Earth’s surface, the tide will be 496 miles high. Not only would the Moon get a bath, but the Moon’s gravitational force would make lots of water leave the Earth and go to the Moon.
Hold it right there R.J.!
The earth radius is FAAAR greater than the bucket! AND the tidal force is proportional to THE RADIUS of the object acted upon. Since the earth's radius is 3.5 x 10^7 times that of a 1/3 meter bucket, the bucket experience 35,000,000 times less tidal force, (all other things being equal). Small radii experience little tidal forces.

Since the tidal force is also proportional to the mass acting on the bucket, even if we replace the mass of the moon with that of the earth (leaving distance the same), then it would only increase the T.F. by a factor of about 81.
Remember those things called equations?

The Earth is larger and heavier than the moon. The bucket, being very small and insignificant compared to the Earth, would not have enough gravitational force to keep any of its water.
Hold on now; you're still not thinking things thru......
The original question was whether an orbiting earth could replicate the spinning water. Obviously if you could get the Earth orbiting at the same rate that the water was formerly spinning in the bucket (say, once per second or so), the water would be unable to leap out in one direction in so short a time before being pulled from the other direction, and the force would circulate quickly around the bucket continuously, keeping the water inside the bucket. (of course, we aren't talking tidal force here, but just plain ol' gravitation).

I'm not saying that this proceedure shows the grav. field to be the source of inertia, but only that it is faulty logic to say the water must exit the bucket. [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

Perhaps you can now understand that if the Earth orbited even a couple of miles away from (let alone right next to) a stationary bucket containing water, the Earth would suck that bucket dry to the last drop.
Not so, as I showed previously; you are forgetting about the orbital rate required to replicate the rotation rate of the spinning water.

I suppose you posted these things without having read my last post but...
Sorry, I just can let these things slide.
G^2

** footnote: Tidal force = 2GMr/d^3 where M is the mass producing the T.F. acting upon a body of radius,r; and d is the distance between the centers of the 2 bodies.
So, even though decreasing the distance increases tidal force by the inverse cube; in our bucket example, the centers would have to get closer than about 10 km. just to approach unity, 1 nt. But the earth's radius is 6300 km., meaning that d can get no smaller than 6300 km. before collision of the surfaces; so the tidal force remains exceedingly small.

<font size=-1>[ This Message was edited by: Gsquare on 2002-08-24 17:23 ]</font>

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On 2002-08-23 20:51, Richard J. Hanak wrote:

Gravitational lensing fits in easily with my theory of light, though I would prefer to call it gravitational refraction....If light enters a strong spherical gravitational field, it will be refracted as if by a lens and for the same reason: the change in velocity of the light. The same effect explains any gravitational bending of light.
No, this is wrong. You are either positing a compositional ether which is a theory that is proven false or saying that gravitational fields are a different media. If the latter is what you are suggesting, you should have a reflection effect for every light beam that crosses a denser gravitational field. Refraction does not take place outside of reflection, you see. If you wish to consider a gravitational field a different medium, then you will necessarily get reflection off that medium. Please explain to me when this phenomenon has EVER been observed. (Hint: Answer begins with an "N" and ends with "ever").

The lines of force can be followed from one material body to another. What can be more physical than something that relates one material body to another?
A physical object that actually exists. Field lines and lines of force are mathematical short cuts to speak about energy differences and potentials. They are not actual objects in the sense AN ELECTRON is an actual object.

As for metric formulations from GR and how solutions to Einstein?s field equations work, it is irrational for you to require an opposing theory to explain features of a theory it opposes.
This is utter baloney. Every theory that has ever supplanted another has explained why the previous theory did a good job almost getting everything right. E.g. Einstein's Theory explains why Newton was nearly right. I expect the same rigor from you. No more, no less.

Einstein?s view was that in a freely falling reference frame, all laws of nongravitational physics, such as electromagnetism, should behave as if gravity were absent. My view is that electromagnetic phenomena are gravitational manifestations, as exemplified, for example, by my explanation of gravitational refraction of light. Accordingly, if a laboratory were freely falling in a strong gravitational field, the velocity of light in it would be less than if the laboratory were freely falling in a weaker gravitational field.
Unfortunately, it wasn't just Einstein's view. Electromagnetic processes are invariant because of Maxwell's equations. They MUST be, or Maxwell's equations are not complete. What are you going to add to maxwell's equations to make the speed of light change? How are you going to alter these fundamental relationships between magnetic and electric fields to allow for light speed to change.

Remember, you cannot appeal to ether, less you deny Michelson and Morley.

Also, you need to explain why every measurement of light speed taken (including bouncing radio waves of Venus) has been consistent.

And you need to explain, if the speed of light DOES change, how a reference frame is forbidden whereby the vacuum solution of Maxwell's Equations are not violated.

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H. When the acceleration ceases, the remaining compression of the field propagates away from the body and there is no inertial force against the body.
if the field compression radiates away, then a non-accelerting object sould not have a deformed gravity field, so how do you define "absolute velosity". if you claim that the deformaty stays then you have to explain why there is not a deceleration force since you stated above that it is the deformation that is the opposing force.

one other thing I just noticed, you claim that there is a maximum propagation for the gravity field and that should be the priciple mesurment instead of the speed of light. the problem for this is that the max propagation should only affect acceleration not speed. and once you stop accelerating the distortion propagates away, along with the extra mass you thought you had stored up in there.

_________________
The universe is not only queerer than we imagine, it is queerer than we can imagine.
J. B. S. Haldane

<font size=-1>[ This Message was edited by: moving_target on 2002-08-24 02:54 ]</font>

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Hanak, have you EVER studied any physics? Basic mechanics? Newtonian dynamics? If so, why is your analysis of ocean tides so ridiculously wrong?

[quote]
On 2002-08-23 20:51, Richard J. Hanak wrote:
The ocean tides on Earth are caused by the gravitational effects of the Moon, Sun, and the planets. The Moon, averaging about 230,000 miles between its surface and the surface of the Earth has the strongest effect on the oceans. The Sun, at about 93 million miles, has a lesser tidal effect. The other planets have much smaller effects.
[quote]

This is fine, but let's evaluate the statement. The earth is a non-inertial frame of reference, so we need to evaluate the acceleration (call it "a") starting at the center of the Earth. Taking into account the Earth's gravity and the moon's gravity, we get the following equation (r being the radius of the Earth, M_e being the mass of the Earth, G being the gravitational constant, M_m being the mass of the moon, e_r being the unit vector in the direction from the surface of the Earth to the center of the earth, e_R being the unit vector in the direction of a line drawn between the Earth's surface and the center of the moon, e_d being the unit vector in the direction of the line connecting the center of the moon to the center of the Earth, R being the distance from the center of the moon to the surface of Earth, and D being the distance from the moon to the center of the Earth):

a=[(G*M_e*e_r)/r^2]-
G*M_m*{(e_R/R^2)-(e_D/D^2)}

The first term which is due to the Earth and the second partis due to the difference bewteen the moon's gravitational pull at the center of the Earth and on the Earth's surface.

We then can evaluate the tida force on a given particle with mass "m" at the Earth's surface which will be simply the second term of the above equation multiplied by "m" (according to Newton's Second Law).

Are you following?

Good, now we ask the question, what is the force along the axis of the tidal bulge at high tide? To do that we use the fact that R^2 is basically (D+r)^2 and combine the two terms that are associated with the two different unit vectors. This means that the F_x force in the direction we're interested in,

F_x = -(G*m*M_m/D^2)*{(1/(1+r/D)^2)-1}

or

F_x = -(G*m*M_m/D^3)[1-2*(r/D)+3(r/D)^2-...-1]

which taking the first term (since r/D is small) to

F_x = +2G*m*M_m*r/D^3

Then we wish to calculate it for the direction at low tide (that's going to be 90 degrees away, the y-axis), and that analysis is much simpler, namely, if you're following me...

F_y= -(G*m*M_m)*{(1/D^2)(r/D)}=-G*m*M_m*r/D^3

so for any point on the Earth's surface you have a linear combination of the vectors...
(let G*m*M_m = N)

F_x=2N*r*cos(theta)/D^3
F_y=-N*r*sin(theta)/D^3

Which will give you the correct heights for the tides. Notice it is a 1/D^3 force. This is true because r/D is small. As you approach Earth r/D is no longer small, so you can't take this approximation, but have to remain in the regime for high tide where

F_x=-(N/D^2)*(1/(1+r/D)^2-1)

the height, then, will be determined by the definition of work, and since we can take any path we choose, we will go the path moving the water from low tide to high tide... or h being the height, g being the acceleartion due to gravity...

h=[Integral[r to 0](F_y*dy)+Integral[0 to r](F_x*dx)]/(g*m)

So you see, Hanak, your analysis of the tides is dead wrong.

If the moon were at half the distance, 115,000 miles, a place that might otherwise experience a 10-foot tide would experience a 40-foot tide. The moon at 57,500 miles would create a 160-foot tide, and at 28,750 miles a 640-foot tide, at 14,375 miles a 2,560-foot tide. Keep going with the series and by the time the Moon’s surface is 457 miles from Earth’s surface, the tide will be 496 miles high. Not only would the Moon get a bath, but the Moon’s gravitational force would make lots of water leave the Earth and go to the Moon.
So you see why this is wrong, right?

The Earth is larger and heavier than the moon. The bucket, being very small and insignificant compared to the Earth, would not have enough gravitational force to keep any of its water. Perhaps you can now understand that if the Earth orbited even a couple of miles away from (let alone right next to) a stationary bucket containing water, the Earth would suck that bucket dry to the last drop.
and the tides have nothing to do with "Earth sucking a bucket dry. Think of it this way: If I hold a bucket of water upsidedown, what happens to the water? It is NOT subject to tidal forces. It is subject to the gravitational acceleration that everything else is subject to.

(Thanks to Marion and Thorton's Classical Dynamics of Particles and Systems for helping me to present the origin of the tides more elegantly than I would have been able to do.)

26. On 2002-08-23 20:51, Richard J. Hanak wrote, addressing me:
If the moon were at half the distance, 115,000 miles, a place that might otherwise experience a 10-foot tide would experience a 40-foot tide.
The lunar tide is not even that high. There are such large tides, but they are the result of coastal configuration, and the size of the tide--if the moon were closer--would not necessarily follow that relationship.

The moon at 57,500 miles would create a 160-foot tide, and at 28,750 miles a 640-foot tide, at 14,375 miles a 2,560-foot tide. Keep going with the series and by the time the Moon’s surface is 457 miles from Earth’s surface, the tide will be 496 miles high. Not only would the Moon get a bath, but the Moon’s gravitational force would make lots of water leave the Earth and go to the Moon.

The Earth is larger and heavier than the moon. The bucket, being very small and insignificant compared to the Earth, would not have enough gravitational force to keep any of its water. Perhaps you can now understand that if the Earth orbited even a couple of miles away from (let alone right next to) a stationary bucket containing water, the Earth would suck that bucket dry to the last drop.
Actually, the Earth would be spinning beneath the bucket, would it not? If the bucket were motionless, but the relationship between the Earth and bucket was the same? So, in Mach's thought experiment, the Earth would not orbit the bucket.

That is a misunderstanding on your part.

If Mach meant that only the really far parts of the universe should rotate around the bucket, he should have said so. If you think about that similarly to the Moon-Earth example we just went through, you should find all kinds of disruptive phenomena, including tides, all over again. I still say I’m surprised that a really brilliant physicist like Mach didn’t think of the implications of his impossible-to-do experiment
As I said before, it wasn't Mach who misunderstood.

27. Guest
<a name="3 MUCUK 3 MOL"> page 3 MUCUK 3 MOL aka 3 MUCUK 3 MOL
On 2002-08-25 20:11, GrapesOfWrath wrote: To: 20:11

On 2002-08-23 20:51, Richard J. Hanak wrote, addressing me:
Years & years ago {on my 8086?} i had a Gravity simulator program
{havent seen it in years} Anyway i did a simulation
of Two Astroids approaching Earth.
1: The Inpactor {smaller} [About Moon size]
2: The Inserter {Larger} [about Mars size]
using two, and carfully adjusting their spacing
so the inpactor(1) collided with Earth
and the inserter(2) passed by just at the
correct moment to insert the Moon into orbit
-------------------------------------------
IT was easy for me to see {um? how Gwandaland ??
became East & West Hemisphere [Um Millions ? NOT Billions ?(years ago)}
================================
ANYWAY2: during some practice runs {at higher resolutions}
I noted [TO MYSELF] that Earth actually does
split into two peices {UM? when lunar Mass =
about 2 to 6 or 10 Lunar Radii from Earth}[hmm?] but it rejells Quickley. Now bback to Delta Temp's

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I apologize to all for my faulty physics of tides and especially for the unnecessary effort it has caused some of you.

Despite my ill-chosen effort to knock Mach, I’m still not happy with his hypothesis that the remotest of objects cause local inertial effects. When Mach suggested that we think of the universe rotating around a stationary bucket, and predicted its effect -
1. He provided not a single equation in support of his idea. None of you complained about that, and neither did Einstein. But many accept the idea nonetheless.
2. He entered the land of fantasy and science fiction. For the purpose of being entertained we willingly go along with a fantasy, temporarily suspend disbelief, and pretend that the unreal is real. But how far should we be expected to stretch our imaginations?

Let’s take Mach literally, that the bucket stayed still and EVERYTHNG else rotated about the former axis of rotation of the bucket. For starters, a bucket-centric universe is a much worse idea by far than the previously discredited geocentric one. Also, somebody would have had to quickly untie the bucket from the rope or the spinning building would twist the rope and bucket, so violating the conditions of the experiment. Next, SOMETHING would have had to hold the bucket unmoving and suspended in space (not an easy job to do.). Surely a grandfather of relativity would not have wanted to glue the bucket to Newton’s absolute space, nor would we.

Then there would be the problems inherent in getting the Earth to rotate about the bucket’s former axis of rotation. The change of rotation axis would have occurred faster than the Atlantic Ocean could have followed it and consequently England would have really been flooded and the bucket, rather than forming a meniscus, would have been filled to the brim (no, not washed away, remember it was being held still). You probably don’t like this any better than the other tide idea.

Now I can hear snickering out there and know that you’re about to pounce on me again and say that everything, Atlantic Ocean included, made the switch all at once. Oh boy! Don’t you realize that such a move would have required instantaneous action at a really big distance and who wants to salute that flag?

Some of you are ready to say that Mach didn’t propose to really do the experiment, and that he was just doing an IF-THEN gedanken experiment. (Is that where Einstein learned to do that?) We all know, of course, that IF wishes were horses then beggars would ride. So, to begin a hypothesis with “If the universe…,” is to begin the wildest kind of hypothesizing and to enter a land where anything goes. Why give any credence to a hypothesis for a source of inertia based on escape into a fantasy requiring us to negate virtually all our knowledge of reality? Especially when that knowledge was won at great cost to many of our scientific pioneers, our intellectual heroes? What greater costs are there than life, limb, or freedom?

I knew in advance that a novel proposal for supplementing Newton’s laws of motion and gravitation would not be welcomed with open arms, especially when some of its consequences go against what relativists hold near and dear. History teaches that the more radical a new proposal, the greater was the difficulty in gaining its acceptance. Ever the optimist, I consider the effort worthwhile.

Gsquare:
I was not presenting the conclusion to the novel, merely the conclusion to ideas on inertia. A novel is a fictitious prose narrative. Surely we don’t want to return to the ‘fictitious vs. real’ thing again. [img]/phpBB/images/smiles/icon_smile.gif[/img] Besides, inertia is just one of several subjects treated in ‘Journey.’

Now I must confess ignorance about gravitational force being parted and that one such part could vary otherwise than approximately 1/R^2, and would welcome enlightenment. I hope you are not trying to resurrect Einstein’s repelling force that only shows up at great distances; that wouldn’t be germane to the subject at hand, i.e., the relationship between a body and its own nearby gravitational field. However, it is not crucial to my theory that the gravitational force responsible for inertia vary as 1/R^2. 1/sqr(R), 1/R, or 1/R^3 would do as well.

Regarding the bodies farther vs. nearer issue, my reasoning is based first on the general expectation that if an effect is produced on a body by a body distant from it, a similar body close to it will also produce the same effect. My second general expectation is that any effect that one body may produce on another will be greater when the bodies are close to each other than when they are far apart (absence making the heart grow fonder excluded). I realize, of course, that expectations and realizations do not always coincide. If either of those expectations cannot be taken as generally valid, I would be glad to learn why.

Had you bought my book, either as paperback or ebook, you would have found that I don’t want to exclude others from potential glory, and am willing to let them be lauded for cloaking my theories in equations. Know that I have found that there are three kinds of people in the world, i.e., those who can do math and those who can’t. These days I am satisfied that the difference between = and = = is second nature to me now. Nonetheless, though facing a steep gradient, I have picked up your gauntlet and hope to return it with one or more equations before too long (famous last words!) or before I reach my allotted time (the proper time for last words), whichever comes first. I think I know the path to take. Thanks for providing the impedance so that all this energy can go somewhere.

JS Princeton: My inability to pierce what seemed like extreme terseness in your initial replies caused me to badly misjudge you. Now I, too, bear the marks of the lion. Please forgive me for any poorly chosen words. Regarding my theory of gravity (of which inertia is only a part), I am trying to show that it does account for the confirmations of relativity theory and at the same time goes a little farther. So for me, it is back to the drawing board! Note that I stop short of quoting General MacArthur.

<font size=-1>[ This Message was edited by: Richard J. Hanak on 2002-08-27 22:58 ]</font>

29. On 2002-08-27 22:57, Richard J. Hanak wrote:
Despite my ill-chosen effort to knock Mach, I’m still not happy with his hypothesis that the remotest of objects cause local inertial effects.
You're not alone, but I personally am happy with it. Giddy even.

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[quote]

Richard:
Well, true about Mach - he only speculated on inertia's source; and even Einstein used imaginary situations often; but shouldn't a valid theory go beyond these constructs?
So I encourage you, and yes, there will be plenty of opposition from entrenched 'relativists' - so what else is new?

Now I must confess ignorance about gravitational force being parted and that one such part could vary otherwise than approximately 1/R^2, and would welcome enlightenment...... Regarding the bodies farther vs. nearer issue, my reasoning is based first on the general expectation that if an effect is produced on a body by a body distant from it, a similar body close to it will also produce the same effect. My second general expectation is that any effect that one body may produce on another will be greater when the bodies are close to each other than when they are far apart..... If either of those expectations cannot be taken as generally valid, I would be glad to learn why
The whole point I was making was that you were trying to show Mach to be invalid by using two fallacious arguments:
1. That tidal force was some how involved; (which I think you now recognize is not), and

2. That if Mach is correct, then nearby masses must of necessity result in anisotropic inertial effect.

Can't you see the assumption you are making in #2 ? You are saying first, that you know the equation that governs how masses interact to originate inertia. (Mach never specified, but only said that there is some interaction that results in inertia).

**Secondly, you are assuming that the small, closely held mass acts to create greater inertial effect than the mass of the entire universe simply because it is closer.

Let me ask you a question: How close would the rest of the universe have to get before the inertial effect of the smaller, closer mass becomes negligible?
You can see why an equation is necessary.

Suppose the inertial effect was proportional not only to 1/R but also to the cube of the mass. Would the cube of the mass of the entire universe offset the greater distance?

Having said that, let be more factually specific:
Gravity is a general term referring to the acceleration of bodies due to the presence of matter. It is not required to have 1/R^2 dependence. Indeed, strictly speaking 1/R^2 relation only holds for spherically symetric masses; oblate spheroids, for ex., add another 1/R^4 term.

In fact, General relativity predicts that gravity also results from acceleration of matter linearly through space - the so called gravitomagnetic gravity field. Also called 'frame dragging' effect.

Also, a rotating acceleration of a massive 'shell' also produces acceleration of mass in the interior; the Lens-Thirring effect.

These gravito-magnetic or frame dragging fields, though typically calculated to be very small, (and I believe show 1/R dependence), can be correlated to inertia since they involve accelerations.

Despite my ill-chosen effort to knock Mach, I’m still not happy with his hypothesis that the remotest of objects cause local inertial effects.
Neither am I, but for quite different reason than the illusory ones you suggest. The main problem in reality has to do with its irreconcilability with the finite speed of light, making it impossible for the mass of the entire universe to
instantaneously 'communicate' inertia upon a locally accelerating object.

However, it is not crucial to my theory that the gravitational force responsible for inertia vary as 1/R^2. 1/sqr(R), 1/R, or 1/R^3 would do as well.
Yes, but it is crucial if you are going to try to invalidate Mach; which is what you were trying to do. But in order to do so you will need to ALSO account for mass density, not just radius.

What I suggest is that you forget Mach and go on with trying to establish the 'local' effect; I think you are on the right track there.

I like the concept that motion modifies the gravitational field. It reminds me of electromagnetic radiation reaction force upon the accelerating electron. Are you familiar? I suggest getting the equations and also go over the historical development which is loaded with difficulties, some which are still not satisfactorily answered to date. You'll get some ideas of how to put quantitative analysis into your situation.

BUT let me warn: Simple non-accelerating motion of a massive object is not likely going to be sufficient to account for inertia. The result would be the same effect of which you accused Mach - anisotropy of gravity on one side of a planet in the direction of motion, an effect never detected, though probably easily detectable from satelitte orbits, etc. Gravity doesn't compress on one side simply due to velocity. Even if we speculate the effect is very small, we still see no such effect even in relativistic orbits, say, of neutron stars etc.

Accelerated motion, analogous to the case of electrons, is necessary if you hope to show any correlation of inertia to the 'local' matter field.

G^2 [img]/phpBB/images/smiles/icon_biggrin.gif[/img]

<font size=-1>[ This Message was edited by: Gsquare on 2002-08-30 00:28 ]</font>

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