Adapted for the Internet from:

Why God Doesn't Exist

    Relativists propose three different and irreconcilable ‘physical interpretations’ for gravity:

    a.   The field:

    “ The gravitational field at any point in space is by definition the ratio of the gravitational force
       acting on any object located at this point in space, to the mass of this object.” [1]

    b.   The well:

    “ In physics, and specifically with respect to the Theory of General Relativity, a gravity well
       is a distortion in space-time caused by a massive body such as a planet or star, or any other
       object which has mass.” [2]

    “ Space-time of General Relativity is supple and can be visualized as a rubber sheet, bent by
       massive bodies. The Sun for example, being heavy, bends spacetime enormously. Planets
       like Earth move in this curved geometry.” [3]

    c.   The wave:

    “ Gravitational waves emanate from the sun and change the shape of space around it.” [4]

    Therefore, unless you want to spend the rest of your life knocking down strawmen, you have to demand that
    relativists clarify which of these is their true-blue version of gravity and hold them to it (Fig. 1).

    The mathematicians may argue that I am misrepresenting and making a mockery of their beloved theory.
    These versions are one and the same and it is I who just doesn’t seem to understand what relativity is about.
    In their view, GR ‘predicts’ waves, fields, and wells without detriment to the others. That’s why we have the
    $600 million Gravity Probe B project investigating the well and field versions and the $400 million LIGO project
    investigating the wave. The way relativists see it, the field that surrounds the Sun is the famous well, and
    waves are the undulations traveling through this medium. So what is it that I don’t understand?

    Perhaps the real problem is that the mathematicians have not defined their terms rigorously enough and this
    enables them to escape through loopholes during the feedback segment of their presentation. Is there no
    difference between the object ‘well’ and the concept ‘field’? Are these words synonyms? And how do we
    reconcile dynamic waves with a static well that is already there, stretched from Sun to Earth?

    The problem is that the mathematicians incorporate these three irreconcilable mechanisms into a single
    hypothesis in order to cover all the bases. This enables a mathematician to respond to criticism of one point
    by invoking attributes of another. If you argue that the concept field has no physical way of attracting a
    particle, the mathematician points to the well and describes how a marble spirals into a funnel [5] [6] or rolls
    down a hill. [7] If you say that the well is a static object, the mathematician tells you that gravity is comprised
    of dynamic waves. (pp. 29-30) [8] And if you say that a wave must necessarily travel from the Sun to the Earth,
    the mathematician explains that a field exists permanently around our star. [9] Thus, they appear to be
    consistent when in reality they end up chasing their tails around. What the mathematicians are doing, in
    effect, is amending their assumptions retroactively.

    So let’s distinguish clearly between these versions, show that they are irreconcilable, and compel the
    mathematicians to choose. The field version proposes that there is a magical substance (i.e., a ‘field’) that
    envelopes a celestial object all around (Fig. 1 D). In contrast, a well covers only the bottom half of a celestial
    object (Fig. 1 C). The Sun weighs the canvas down in one direction to produce a well (e.g., ‘downwards’). A
    gravitational ‘field’ also differs from a ‘rubber sheet’ in that it cannot be illustrated all by itself in the absence of
    the source and the target objects. A field is an abstract mathematical concept whereas a well (as used in
    relativity) is presented as a physical object.  It is irrational to propose that a concept such as a field has the
    ability to affect particles or planets. Anyone using the word field to explain gravity is not offering a physical
    interpretation. We cannot make a movie of a field because a field neither stands alone nor has shape.

    The wave is not a valid hypothesis in and of itself especially if it is proposed as the undulation of nothing, but
    here relativists are insinuating that these waves consist of ripples in space-time. They are proposing that the
    physical object that is waving is the gravity well itself. If we assume that space-time is a physical object, like
    we do in the well scenario, then the wave explanation can still be regarded to be in the running.

    A non-starter with waves, however, is that they are undetectable. Caltech and MIT run the gargantuan project
    known as LIGO. It consists of two intersecting and interfering lasers which would presumably distort if
    perchance a gravity wave should pass by and tickle the detector. One wonders how the mathematicians plan
    to catch these waves when Quantum Mechanics has as one of its principles that photons, gravitons, and
    other ‘entities’ travel as waves and are detected as particles. As soon as the people at the LIGO control center
    attempt to touch a gravity wave it instantly morphs into a particle. So assuming that the mathematicians are
    successful, what will this expensive experiment prove? Will it prove that a gravity ‘wave’ is made of particles
    called gravitons and confirm the mechanics’ version of gravity over relativity? Do gravity waves travel directly
    (i.e., rectilinearly) from the center of the Moon to the center of the Earth as Newton insinuated (force) or do
    they travel along the curved gradient of the Earth’s well (i.e. to the South Pole) (Fig. 1 A vs. 1 C)?

    A well is clearly amenable to illustration and this is the reason GR was heralded as a ‘physical interpretation’,
    something that was missing until then. In contrast, Newton made absolutely clear that he had no hypothesis
    to back his ‘force’ theory, and this certainly did not help his theory when it competed against relativity for the
    hearts and minds of the mathematicians. But this, again, reinforces that the novel physical interpretation is
    what attracted the experts of the guild to relativity and not a petty difference in numerical results as often
    stated.

    However, a well is as different from a wave as it is from a field. A well is static whereas a wave is dynamic. A
    well is a photograph. A wave is a movie. A well is already formed and does not have to travel from here to
    there. By its mere presence in space, the Sun weighs down the canvas, creates a dimple, and the Earth is
    compelled to roll around like a tiny marble spiralling down a funnel. The Earth could roll around this roulette
    without the well changing its shape. In such case, if gravity is simply the curvature of space, the effect of the
    Sun’s presence on our planet is instantaneous. Indeed, GR’s equations predict so much in what the
    mathematicians call the low velocity/weak field scenario:

    “ at low speeds and weak gravitational fields, general and special relativity reduce to
       Newtonian physics, i.e. everyday experience.” [10]

    “ The weak stationary field limit of general relativity reproduces Newtonian gravity with
       instantanous action at a distance”  [11]

    What meaning would a gravity wave traveling at c have in the context of instantaneous action?

    If, on the other hand, the motion of the Earth depends on waves coming from the Sun and these waves travel
    at a ‘finite’ speed, the wave model can never be instantaneous as required by the well. A wave is said to travel
    the 150 million km from the Sun to the Earth in 8 minutes. If these ripples are traveling along the curved walls
    of the well, the distance has to be greater than if the same wave travels directly along an axis connecting the
    centers of the Sun and Earth. Hence, relativists have to decide whether their gravitational waves travel
    rectilinearly from the center of the Sun to the center of the Earth (force) or curvilinearly along the wall of the
    Sun's well (i.e., the ‘field’ potential version). Nevertheless, these arguments show that the wave and the well
    are two irreconcilable models for gravity. By blending them, relativists have borrowed the best from the static
    and the dynamic worlds in order to protect their beloved theory from every possible angle.

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    Last modified 02/22/08


        Copyright © by Nila Gaede 2008

Fig.  1   The three irreconcilable relativistic physical interpretations of gravity

Relativists discovered the
true mechanism of gravity:
the well, the field, and the wave.
A. Newton’s force law (straight vector): The equation
requires instantaneous action. The problem with this
model is that instantaneity cannot be simulated with
one-way waves or QM particles (i.e., gravitons). By
definition we cannot depict motion in a still image.

B. GR gravitational waves: must necessarily travel at
slower-than-instantaneous speeds as required by the
definition of motion. However, if gravity traveled at the
speed of light, this would cause distortions in the orbits
of the planets. Be aware, however, that there are two
versions of the wave. One wave travels ‘straight’ from
the Sun to the Earth (B). This is the ‘force’ version of
wave. The other wave is a ripple that propagates along
the wall of the well (C). This is the ‘potential’ or ‘field’
version of wave. This distinction will become relevant
when we discuss the speed of gravity.
C. GR gravity well (curved space): A gradient such as the Sun’s gravity well is alleged to be is
conceptually and by definition a static depression. It is permanently stretched across two objects. In
contrast, a wave has to travel from here to there. Therefore, the well model is a static version whereas
the wave model is dynamic. The well is also irreconcilable with the field version. A celestial object
may only push the canvas in a single direction. Relativists would like you to believe that in 4-D the
Sun pushes radially. This is absolutely ridiculous. Just ask them to show you a motion picture of
their proposal to see if the orbits of Mercury or Earth would make sense then. The only way the well
analogy works is in 3-D.

D. GR amorphous field: Unlike a well, a field envelopes a celestial object all around. Unlike the wave, a
field doesn’t travel away from the object. A field permanently surrounds it. However, the word ‘field’
does not represent a physical entity. There is no such thing’ as a ‘field’ in Physics. A field is a concept
and thus cannot be comprised of particles. A field is formally defined as a ‘region of space’. A region is
defined as a ‘portion of space’ and space is defined as a ‘field’. This set of definitions is circular.

    In conclusion, the mathematicians have to choose. They can’t have it every which way but lose. If LIGO
    (waves) is right, Gravity Probe B (well) is wrong. The only reason relativists talk interchangeably about fields,
    wells, and waves is to incorporate favorable static and dynamic aspects of each of these dissimilar concepts
    into their theory.

    How did the mathematical physicists end up in such a conceptual mess? Was it some bad moonshine they
    drank?

    We discover that the most critical factor underlying the question of gravity is the speed at which it acts.