| Adapted for the Internet from: Why God Doesn't Exist |
- 1.0 The field of Mathematics embodies motion
Unlike any standalone structural concept, the word field embodies motion. A table, a horse and a tree need
not move to be identified as objects. An object is defined exclusively by one attribute: shape. Shape is an
attribute of a static universe. A field, instead, cannot do without its effect on the offending particle. A field is
not a photograph, but a movie. A single frame of the movie of the Sun's gravitational field acting on the Earth
merely shows two celestial objects separated by space. Therefore, one of the most ridiculous notions that the
mathematicians have concocted is that fields can accelerate:
- “ A moving magnetic field generates an electric field, and a moving electric field
generates a magnetic field.” [1]
How can a field move if it is already defined as something in motion. A field is defined as a region where
something 'occurs'. If the region itself now moves, it is not a region. A region is a static concept.
2.0 Field and space are not identical
It could be argued that this last argument reinforces that the gravitational field and space are equivalent. Isn’t
it coincidental that space cannot be conceived without objects either?
Actually, the argument demonstrates the opposite. We need a single object to conceive of space: the one
space momentarily encloses. Fields absolutely require two. This argument debunks Einstein’s idiotic
proposal that field and space (or space-time) are identical.
3.0 A cross-section of the mathematical field is nothing
The word field could also be likened to the word wind. The devil's advocate may argue that the wind can
knock down a barn and that a painter can make three curved strokes with the brush and most anyone will
identify these as the wind. The wind is clearly structural. So how is a field different than the wind?
The word wind is deceiving indeed. The jury gets the misleading impression that the prosecutor is referring
to a physical medium. However, without a priori knowledge of wind all that the extraterrestrial sees on
canvas is three curved lines. Moreover, the three lines stealthily represent motion, a situation that is not
readily discernible. The painter has unwittingly superposed three frames of a film onto a still picture. Wind
is strictly a dynamic concept whereas air is conceptually structural and static. The artist may draw a picture
of air – for example, a shell of gas enveloping the Earth – or color the sky light blue and label this as air in the
painting. Air is a medium because, irrespective of our ability to see it, it can be synthesized in a single frame.
When a tornado blows away the barn, what actually came in contact with the wood was air and ultimately
atoms. Any cross-section of the movie of wind – a single frame of the film – is called air. The wind is just
traveling air.
This argument can also be extended to the word fire. Fire is a process rather than a thing, a movie as
opposed to a photograph. A cross-section or snapshot of fire is called flame. Fire is dynamic whereas
flame is conceptually static. Field is more closely related to fire than it is to flame, but actually neither word
serves as an analogy. Theorists have made field both static and dynamic: a cross-section or a still image
of Jupiter's magnetosphere is also called field. Thus, when astronomers depict the shape of the magnetic
field they use the notion of flame, and when they explain the origin or an interaction of a field they rely on
the notion of fire. The word field is simultaneously an object and a process, a noun and a verb. This
accounts for its explain-it-all power and usefulness to mathematical physicists.
Having discussed external attributes of objects I conclude that a field does not have any properties
associated with the physical world and that its usage as an accelerator of particles is thus misleading.
The next step consists of analyzing the field’s interior and challenging the notion that a field may serve as
a medium that can be traversed by particles. Is a field an ocean? In order to analyze the field in the most
favorable light as a medium I’ll consider two mutually exclusive assumptions: that the field is continuous
and that it is comprised of discrete components. The aim of the instant inquiry is to determine the
composition of the alleged structural field. Specifically, I intend to show that a field can be neither
continuous nor discrete.
4.0 The field of Mathematics is both continuous and made of discrete pieces
A river is conceptualized as a continuous entity but, under the right magnification, we discover that it is
ultimately made of atoms. In fact, no object of the physical world is continuous, so a river actually provides
a test case to show whether a field qualifies as a physical entity. Scientific papers routinely characterize
fields as ‘continuous,’ [2] [3] but these connotations are strictly mathematical and, thus, immaterial to the
present context. Mathematical and physical notions of continuity are notoriously different. A function is
said to be continuous if ‘small changes in the input produce small changes in the output.’ [4] Another
mathematical version refers to the closeness of 'mathematical objects' and yet another to the membership
of an 'element' in a set. [5] These definitions say in so many words that continuity is comprised of many
components. In Physics, the adjective continuous has exactly the opposite meaning. We use it to refer to
a hypothetical physical object that is comprised of a single piece:
- “ In classical mechanics a rigid body is usually considered as a continuous mass
distribution, while in quantum mechanics a rigid body is usually thought of as a
collection of point masses.” [6]
[I believe that this is the closest any mathematician got to breaking the code.]
- If we can distinguish one point from another, there is a medium that stands between them. Therefore, the
mathematical notion of ‘continuous’ is misconceived. It does not result in a hypothetical continuous object
for the purposes of a scientific discussion (i.e., it cannot be used consistently). Pursuant to the definition
of Physics, even the number line of Mathematics is conceptually discontinuous and made of discrete
components. Here we are interested in the structural nature of the field and will therefore use the physical
definition as our standard. Either a field is comprised of discrete components or it is made of a single piece.
There are no other possibilities. We could care less how close a member is located to another or if they are
connected. (The mathematicians have invented and believe in so many stupid arguments that it is absolutely
stunning!).
5.0 The field of Mathematics is simultaneously continuous and traversable
A serious shortcoming of the continuous assumption is that the jury will be deprived of visualizing how a
particle divides what is conceptually made of a single piece. A surface is an external attribute. Therefore,
it is logically inconsistent to suggest that an 'internal' surface comes up against and accelerates a particle
within a continuous field. A continuous field is also at odds with the discreteness proposed by Quantum
Mechanics and with the notion of gradient. A gradient is necessarily made of discrete parts whereas a
continuous entity is conceptually uniform. Hence, from the various behaviors and attributes typically
ascribed to fields, we conclude that prosecutors will run into insurmountable problems if they assume that
a field is physically continuous (i.e., made of a single piece) (Fig. 1).
| 'A' field is not made of particles |
- I can also present the objection in terms of lines of force. If, as is alleged, electric field lines are infinite
and an infinite number of them surround a charge, an electric field permeates the whole of space and is
therefore conceptually synonymous with space.
- “ According to quantum field theory, empty space actually consists of varying
electromagnetic fields.” [10]
This entails, however, that the lines must diverge as we move away from the object's center, more so
when it has been observed that they don't cross. The compulsory question then is: What lies between
them (Fig. 3)?
Fig. 2 The Dirac Sea: space is made of particles |
2.4.2.2 Backdrop
- • A field requires a backdrop to generate a gradient
- The discrete hypothesis also raises questions regarding field gradients. Fields are alleged to
strengthen as we approach an object and to weaken as we drift further away (Fig 3). For example,
when a spaceship approaches the Earth, gravity becomes stronger. What physical interpretation
can the constituents of a field give this ‘strength’ gradient? Do field particles get smaller, larger,
heavier, or colorless? Are the entities that make up field losing their shape, temperature, or mass?
To state that ‘the field is weak’ is really a veiled way of saying that the test particle is changing its
speed. The director is focusing the camera not on the field, but on the affected object. The adjectives
weak and strong should qualify the central character and not the sidekick affected by it. The
mathematicians are saying that because the boxer is trashing you, he is strong. The correct word
is stronger. A boxer is strong or weak on his own, irrespective of you. And it is misleading to
construe this statement in reverse as an affirmation that the field has somehow lost density. Has
the field lost particles? If so, by what process? Therefore, it makes no sense for the prosecutor to
qualify a field as being weak [11] or strong [12] until he has presented the field as a physical object
at the exhibits Phase of the scientific method. The burden shifts to the prosecutor to provide an
unequivocal structural description of the word field before making such claims.
- • If a field is a hole in matter, it is not an object itself
In a related argument we have to answer what remains behind when an accelerator sucks a
component of seething space and brings it into the detectable world (Fig. 2). Recall that the
mathematicians tell you that space and field are equivalent and that they are comprised of particles:
- “ all of the various fundamental fields, such as the electromagnetic field, must be quantized
at each and every point in space… a field in physics may be envisioned as if space were
filled with interconnected vibrating balls” [13]
Therefore, any proposal in favor of discreteness will have to answer what medium serves as backdrop,
more so if these components have independent motion while they comprise the field. Whatever serves
as a backdrop should have a hole in it when the particle is removed.
Magnetic fields would appear to meet this requirement. For example, Jupiter's magnetosphere has been
mapped by the Pioneer and Voyager expeditions. [14] Therefore, it clearly has a shape and a backdrop,
both of which are widely illustrated in books and magazines (Fig. 4). It follows that in order for Jupiter's
magnetic field to produce a cavity within the solar wind (plasma), it too must be physical.
Conceptual problems if field = space |
- I first note that astronomers were able to ‘map’ Jupiter’s magnetosphere after taking a series of
measurements. Mapping is a synonym of function (i.e., a process). Therefore, shape is to photograph
what mapping is to movie.
The mathematician answers that once all the measurement points are in place, the astronomer can
claim to visualize the sculpture.
The trouble now is that the astronomer has not mapped the external shape of a field, but the internal
shape of the solar wind around Jupiter. A doughnut is a physical object. Its hole is not. A hole is a
concept that means ‘absence of matter’. A hole is a relation between two objects. The ‘object’
doughnut can do without the hole. The ‘concepts’ doughnut and hole cannot do without each other.
So far, Jupiter’s magnetosphere is a hole in the solar wind with Jupiter embedded in it. The solar wind
reaches the planet and goes around an invisible barrier. Therefore, mapping a perimeter or surface of
an object due to the inability to see it directly is insufficient evidence to claim that the enclosed region
qualifies as a medium.
Which is the true surface: the solar wind or the magnetosphere?
The interface is a concept that belongs to both. The surface can only belong to one. Jupiter’s
magnetosphere is not a stand-alone object (i.e., it is not a medium) for the purposes of science. There
are several reasons for this. We can only visualize the magnetosphere after the mathematician has
constructed it with many data points. We can also visualize the magnetosphere in the presence of the
solar wind. Without the ‘wind’, the mathematicians can’t tell you where the magnetosphere ends. Their
argument is no different than saying that heat is an object. It is not. Heat is a region of influence of
something that is burning and that we can ‘map’ by finding out where the skin turns to charcoal. Like
heat, the magnetosphere cannot stand alone. It is not a physical object in itself. It has its origin in
something else.
What is undeniable, though, is that there is something physical in the region around Jupiter (i.e., the
magnetosphere) that displaces the solar wind. If as the mathematicians argue, a magnetic field is
made of particles, Jupiter’s protective shell is made of countless discrete particles too. So how
should we distinguish the particles that comprise the ‘infinite’ gravitational field from the ones that
comprise the ‘infinite’ magnetic field? What room is there for magnetic field particles if gravitational
field particles pervade ‘every point in space’? Do the particles that comprise the magnetic field occupy
space, meaning that they occupy the gravitational field? Or do particles of the magnetic field displace
the particles that theorists allege comprise space? If they displace the particles that comprise space,
what ‘space’ do they now occupy?
Nevertheless, a ‘region’ is not synonymous with ‘countless particles’. An ocean is a bunch of particles.
The Pacific Ocean, instead, is a region. Therefore, by its plain definition as a region, the word field is
distinct from a sea of particles.
- • A field cannot generate attraction
Smoke is a medium comprised of particles that originate in the matter undergoing combustion. Once
created, the smoke floats away without permission from the object that gave it origin. These particles
have the power to push a feather away. If a magnetic field is likewise comprised of particles, we can
imagine how these particles push each other away, for example when the positive ends of two
magnets repel each other. A much harder problem is explaining how these particles instantly
produce attraction when we turn one of the magnets 180°? Nevertheless, by what physical
mechanism does a magnet control a bunch of independent particles once it has emitted them? How
does Jupiter compel the blind allegiance of an army of discrete particles of magnetic and gravitational
fields? What is the source of these particles (i.e., of the field)? How can a field incessantly produce
‘energy’ (i.e., particles) without any inputs? Is a magnet a perpetual machine? These are the questions
that the proponents of the word field must answer before telling you their stupid theories. These are the
important questions of Physics and of Science and not fantasies such as time travel and annihilation
that the mathematical idiots discuss ad nauseam in mainstream forums.
• An infinite field has no surface to accelerate a particle
If a field is made of discrete particles, it makes no sense to talk about the field at all. Field is the word
the mathematicians use to refer to the entire ocean of particles. We never say that the Pacific Ocean
accelerates a fish. If anything, a particular undercurrent within the ocean accelerates a fish. Obviously,
the entities responsible for accelerating the intruding particle are the constituents of the field and not
the field as a whole. The only way that the entire ‘field’ can be conceptualized as accelerating a
‘charge’ is if the outer surface of the field comes in contact with the outer surface of the charge. We
can say, for example, that the ocean accelerated a sailboat because the boat is on the surface of the
ocean. So where is the surface of an infinite gravitational field? Where is the surface of an electric
field? The prosecutor should just talk about the sea of particles surrounding an object and proceed
to explain how a group of them accelerate an incoming object. If the field is alleged to be infinite, it
certainly cannot be used as a baseball bat! How are we supposed to conceive of the two surfaces
coming into physical contact if we are denied visualizing the surface of one of them? But, assuming
that a field were a medium (i.e., finite), the prosecutor can at best say that a particle rebounded off the
edge or boundary of the field and not that the field accelerated the particle within itself. And to twist this
around and say that the particle accelerated through the field can only have a cosmetic or political
purpose. The insinuation remains that the particle is traversing an invisible ocean when I have just
shown that a field cannot even be conceptualized as a medium. The word field designates a concept.
Particles cannot go through concepts. The prosecutor can say that the particle accelerates with
respect to its starting point or its destination, but not with respect to or as a result of a concept that
serves as a makeshift medium.
- 7.0 Conclusions
The mathematicians have no rational answers to any of the foregoing questions. These are not trivial
semantic issues, but fatal conceptual objections. As an exhibit, the mathematical field is invalid. What
can be neither continuous nor discrete has no chance of being categorized as an object. In addition, the
arguments reinforce that field and space cannot be synonyms under any circumstance, which is the
mainstream’s position. I now take this one step further and argue that ‘field is unscientific. The anachronistic
term field does not even belong in Physics. It belongs exclusively to the transcendental world of religion.
Anybody who uses the word field to explain a theory should be treated as an idiot and kicked out of science!
Nothing less will do.
Fig. 4 |
| No! Your halo field is not made of particles, Bill. It is made of energy. Now give me back my key chain you little brat. This is the last time I baby-sit you! |
| The assumption that space is comprised of particles carries with it the implication that there is a backdrop A. What should we call the interstitial regions between spherical space particles? B. What delineates and gives shape to each cubic space particle? What remains behind when the accelerator rips particle pairs from the fabric of space-time? |
| A. If gravitational field = space and the gravitational gradient drops as we move away from the Earth, what has changed in the constituents of space? Have they become smaller? Less massive? B. If electric field = space and straight electric field lines diverge farther from the charge, what do we propose to call the ‘space’ between the lines? |
| Mapping of Jupiter's magnetic field |
Fig. 1 |
6.0 A field cannot be comprised of discrete components while retaining the properties ascribed to it
The discrete hypothesis has even greater conceptual obstacles. I summarize them under the subheadings
titled shape, backdrop, interaction, and gradient.
- • A field has no Shape
Dirac was one lost soul who, in order to reconcile his equations with a physical interpretation, invented a
field known as the Dirac Sea. I believe that this sea lies somewhere between the Pacific Ocean and Never-
Never Land:
- “ The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles possessing
negative energy.” [7]
“ Dirac proposed that a 'sea' of negative-energy electrons fills the universe…
Sometimes, however, one of these negative energy particles could be lifted
out of this Dirac sea to become a positive energy particle. But when lifted
out, it would leave behind a hole in the sea which would act exactly like a
positive energy electron with a reversed charge. These he interpreted as the
proton, and called his paper of 1930 A theory of electrons and protons.” [8]
If the field is made of discrete subcomponents as Dirac and others propose, [9] I question what shape
these entities may assume. This question is relevant because it will also present insurmountable
problems. For instance, if the subcomponents of a gravitational field are spherical, the onus is on the
theorist to tell the audience what lies in the interstitial regions between spheres (Fig. 2). Surely not space
because Dirac and Einstein have just finished telling us that space is synonymous with field. In
Mathematical Physics, space and field are one and the same. If, instead, the entities comprising the
field are cubic, what separates one cube from another? What serves as boundary between the cubes?
Obviously, Dirac’s proposal is a non-starter. He can’t begin to tell us about his wonderful theories if his
exhibit is fatally misconstrued.
| Field made of discrete particles versus field made of a single piece (i.e., continuous). |
Module main page: The word field of Mathematical Physics is unscientific
Pages in this module:
- 1. The mathematicians have no idea what a field is
2. The mathematical field is unphysical
3. There is no such thing as 'a' field in Science
4. This page: 'A' field is not made of particles
5. The word field belongs in religion
| Proponents of the 'discrete' field should not even mention the field but limit the discussion to the sub-components that push against the test particle. They are saddled with the burden of showing how these subcomponents interface with and cause the particle to accelerate. Con-versely, proponents of the 'continuous' field must explain how the test particle manages to divide what is conceptually made of a single piece. |
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- Copyright © by Nila Gaede 2008