| Topic: |
Science > Physics |
| User: |
"Etis" |
| Date: |
03 Aug 2006 08:10:35 AM |
| Object: |
"The Limitations of Mathematics in Physics" |
"The Limitations of Mathematics in Physics"
The present philosophy in theoretical physics is to search for
mathematical relationships that predict experimental results that are then
used to verify the validity of the mathematics in defining our physical
Universe, from the microcosmic to the macrocosmic. The philosophy was
expressed succinctly by Dr. Hawking in Scientific American when he stated
that he didn't care about "reality" because he didn't know what "reality"
was, all that he cared about was whether the mathematics correctly predicted
the results of experiment. Unfortunately, requiring that the results of
observation and of mathematics be in agreement is NECESSARY BUT NOT
SUFFICIENT in our study of the Universe around us.
As a research tool, mathematics suffers from two basic limitations:
A:- It is a linear logic process rather than an area logic process.
Any error along the line of logic being used can easily propagate throughout
the remaining logic chain without giving warning of its presence. (A
solution using an area logic process, on the other hand, is similar to the
solution of a crossword or jigsaw puzzle. An error made anywhere in such a
process is revealed by an incongruity somewhere in the solution. As such,
such a logic process is self-correcting because it forces one to go back and
rethink the problem.)
B:- The logic associated with the mathematical treatment of a process
can lead to results in regions of the problem domain where another
constraint is imposed by Nature. To a mathematically trained physicist such
a constraint may well go unrecognized because it is not inherent in the
mathematics. The existence of such a constraint may render the mathematical
conclusions involved useless.
The limitation described in paragraph A is illustrated by the by the
derivation of the Lorentz Transformation for Transverse Force. Unlike the
derivation of the Lorentz Transformation for Parallel Force that provides
the correct result, the derivation of the Lorentz Transformation for
Transverse Force is incorrect. (The derivation of this transformation is
straightforward and is easily accomplished using the conventional Lorentz
Transformations for Mass, Length and Time. The infamous "Right Angle Lever
Paradox" (see figure below) provided a "common sense" warning that an error
had been made in that mathematical derivation. In this thought experiment
shown by the diagram, if forces are applied at the ends of the right angle
lever and the lever is observed not to rotate in both the "moving" and
treference frames, then the moments applied to each arm must be equal in
magnitude and opposite in direction in each of the reference frames.
http://einsteinhoax.com/rf511.gif.
With the conventionally accepted values, the product of the Lorentz
Transformation for Parallel Length and the alleged Transformation for
Parallel Force is not equal to the product of the Lorentz Transformation for
Transverse Length and the alleged Transformation for Parallel Length. This
inequality implies that, if the torques applied to the arms are equal in one
of the reference frames ("moving" or "stationary") they cannot be equal in
the other reference frame ("stationary " or "moving") and the lever would
then rotate in one of the reference frames and not the other. Since the
lever does not seem to know of this equirement, it remains stationary, and
it was necessary to reconcile the dilemma that resulted.
One would think that rational men would accept that an error had been
made in the derivation of the force transformations and search for that
error. Instead, it was assumed that the derivation of the Lorentz
Transformations for the Forces had to be correct, after all they were
derived mathematically. To account for the difficulty, a convoluted
explanation was devised which asserted that the rate of increase of energy
in the transverse lever produced by the parallel force was balanced by the
rate of increase of the angular momentum supplied by the torque difference
between the two directions. The explanation conveniently ignored the fact
that for moments to be applied to the lever by the forces applied to its
ends, equal and opposite forces would result at the hinge pin. As a result,
any energy that is added to the transverse lever arm by the applied parallel
force at its end will be removed at the hinge pin, and the rate of change of
energy in the lever is exactly zero.
What was also ignored was the fact that the angular momentum of the
lever is the product of its moment of inertia and its angular velocity.
Since the lever was observed not to rotate in either reference frames, the
rate of change of the lever's angular momentum is also zero. Properly done,
the mathematical explanation amounts to the statement that 0 = 0. This is
certainly true but is also meaningless. It is frightening that the advanced
academic community could overlook such an error and appear in a large number
of postgraduate level texts. It is even more frightening that individuals
who would embrace such an explanation are in a position to teach our best
and brightest. For a derivation of the correct Lorentz Transformations for
Forces see http://einsteinhoax.com/relcor.htm.
The type of error illustrated by paragraph B occurs in regard to the
idea of "action at a distance" being produced by the exchange of "virtual
particles". Mathematically, such particles are capable of providing both
attractive and repulsive forces. In reality, in the absence of an overlying
substrate for space (e.g.- the classical Aether or Dirac's "Sea of Negative
Energy") with which the "virtual photons" could interchange momentum, the
production by "virtual photons, of attractive forces acting at a distance
would seem to be impossible. But then, if such a substrate exists, why do we
need the concept of "virtual photons"?
Perhaps it would be constructive to illustrate this type of limitation
on the reliability of a purely mathematical treatment by considering the
analysis of a conventional FET transistor circuit, the cascode. This circuit
consists of two FET transistors with the drain of the first one driving the
source of the second one and with the gate of the second biased at a
constant positive voltage. For low frequency signals, the operation of such
an amplifier is completely defined mathematically by a property known as
"transconductance". The electron flow in the collector of the second FET is
the product of the signal voltage applied to the gate of the first FET times
the transconductance of the first FET. The mathematics tells us that a
positive signal will produce a positive flow of electrons at the output and
a negative signal will produce a negative flow of electrons at the output.
What the mathematics doesn't tell us is that the process will not work
unless there was a bias flow of electrons in the amplifier to which the
output signal was added. With the bias current, the amplifier can produce
both positive and negative electron flow signal outputs by adding to or
subtracting from the bias current. Without the bias current, the amplifier
can only produce positive electron flow outputs. The mathematics is
NECESSARY BUT NOT SUFFICIENT to define the process. Similarly, the writer
asserts that the mathematics associated with "virtual photons" is also
NECESSARY BUT NOT SUFFICIENT. A substrate (e.g.- the classical Aether or
Dirac's "Sea of Negative Energy" or one of the several "background energy of
space" concepts) would seem to be necessary for the idea of "virtual
photons" as a force carrier to work, but, if the substrate exists, why is
the concept of "virtual photons" as force carriers required?
Whether "virtual photons" exist can be evaluated by a rather simple
experiment as shown in the diagram below. There is an even simpler means of
evaluating the concept. A recent news item revealed that a loose oxygen
cylinder was captured by the magnetic field of an MIR machine and flew
across the room to crush the skull of a child being examined. If such a
strong magnetic field existed in the room and that field involved "virtual
photons", those photons would be sufficiently numerous to produce an amount
of electromagnetic noise that would be easily measured. I doubt very
seriously if such noise would be found if s search were made.
http://einsteinhoax.com/cf43.gif.
Remember that Dr. Einstein warned "we have not proven that the Aether
doesn't exist, we have merely proven we do not need it (for calculations).
Also remember that it took 25 years of peer pressure to cause Dr. Einstein
to relinquish the idea of "absolute time" (equivalent to believing the
Aether) and accepting the unproven (and rather ludicrous) consensus
viewpoint of space and time as a single entity.
Theoretical physics has taken the easy position that only mathematics
and experiment are required to deal with reality. Unlike every other branch
of science, it is asserted that "mechanism" is irrelevant in physical
theory. Since we live in the "mechanism" represented by our Universe, the
prime goal of any responsible theoretician should be an understanding of the
workings of that "mechanism" with the mathematical and experimental results
used to iteratively improve our understanding of that "mechanization". What
we have today, with the idea of "mechanism" eliminated, is more akin to
group quasi-religious charlatanism (how many Angels can dance on the head of
pin?) practiced by a controlling cadre of self promoting "scientists" than
it is to an organized science.
The source material for this posting may be found in
http://einsteinhoax.com/hoax.htm (1997); http://einsteinhoax.com/gravity.htm
(1987); and http://einsteinhoax.com/relcor.htm (1997). EVERYTHING WHICH WE
ACCEPT AS TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE WE HAVE ACCEPTED AS
TRUE, IT MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND IT MUST BE
MATHEMATICALLY VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS
REQUIREMENT. THE WORLD IS ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM
THOSE IT HAS GRANTED WORLD CLASS STATUS.
All of the Newsposts made by this site may be viewed at the
http://einsteinhoax.com/postinglog.htm.
Please make any response via E-mail as Newsgroups are not monitored on
a regular basis. Objective responses will be treated with the same courtesy
as they are presented. To prevent the wastage of time on both of our parts,
please do not raise objections that are not related to material that you
have read at the Website. This posting is merely a summary.
E-mail:- einsteinhoax@isp.com. If you wish a reply, be sure that your
mail reception is not blocked.
The material at the Website has been posted continuously for over 8
years. In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE
MATERIAL PRESENTED. There have only been hand waving arguments by
individuals who have mindlessly accepted the prevailing wisdom without
questioning it. If anyone provides a significant rebuttal that cannot be
objectively answered, the material at the Website will be withdrawn.
Challenges to date have revealed only the responder's inadequacy with one
exception for which a correction was provided.
.
|
|
| User: "ACE" |
|
| Title: Re: "The Limitations of Mathematics in Physics" |
03 Aug 2006 08:38:36 PM |
|
|
Etis wrote:
"The Limitations of Mathematics in Physics"
The present philosophy in theoretical physics is to search for
mathematical relationships that predict experimental results that are then
used to verify the validity of the mathematics in defining our physical
Universe, from the microcosmic to the macrocosmic. The philosophy was
expressed succinctly by Dr. Hawking in Scientific American when he stated
that he didn't care about "reality" because he didn't know what "reality"
was, all that he cared about was whether the mathematics correctly predicted
the results of experiment. Unfortunately, requiring that the results of
observation and of mathematics be in agreement is NECESSARY BUT NOT
SUFFICIENT in our study of the Universe around us.
As a research tool, mathematics suffers from two basic limitations:
A:- It is a linear logic process rather than an area logic process.
Any error along the line of logic being used can easily propagate throughout
the remaining logic chain without giving warning of its presence. (A
solution using an area logic process, on the other hand, is similar to the
solution of a crossword or jigsaw puzzle. An error made anywhere in such a
process is revealed by an incongruity somewhere in the solution. As such,
such a logic process is self-correcting because it forces one to go back and
rethink the problem.)
B:- The logic associated with the mathematical treatment of a process
can lead to results in regions of the problem domain where another
constraint is imposed by Nature. To a mathematically trained physicist such
a constraint may well go unrecognized because it is not inherent in the
mathematics. The existence of such a constraint may render the mathematical
conclusions involved useless.
The limitation described in paragraph A is illustrated by the by the
derivation of the Lorentz Transformation for Transverse Force. Unlike the
derivation of the Lorentz Transformation for Parallel Force that provides
the correct result, the derivation of the Lorentz Transformation for
Transverse Force is incorrect. (The derivation of this transformation is
straightforward and is easily accomplished using the conventional Lorentz
Transformations for Mass, Length and Time. The infamous "Right Angle Lever
Paradox" (see figure below) provided a "common sense" warning that an error
had been made in that mathematical derivation. In this thought experiment
shown by the diagram, if forces are applied at the ends of the right angle
lever and the lever is observed not to rotate in both the "moving" and
treference frames, then the moments applied to each arm must be equal in
magnitude and opposite in direction in each of the reference frames.
http://einsteinhoax.com/rf511.gif.
With the conventionally accepted values, the product of the Lorentz
Transformation for Parallel Length and the alleged Transformation for
Parallel Force is not equal to the product of the Lorentz Transformation for
Transverse Length and the alleged Transformation for Parallel Length. This
inequality implies that, if the torques applied to the arms are equal in one
of the reference frames ("moving" or "stationary") they cannot be equal in
the other reference frame ("stationary " or "moving") and the lever would
then rotate in one of the reference frames and not the other. Since the
lever does not seem to know of this equirement, it remains stationary, and
it was necessary to reconcile the dilemma that resulted.
One would think that rational men would accept that an error had been
made in the derivation of the force transformations and search for that
error. Instead, it was assumed that the derivation of the Lorentz
Transformations for the Forces had to be correct, after all they were
derived mathematically. To account for the difficulty, a convoluted
explanation was devised which asserted that the rate of increase of energy
in the transverse lever produced by the parallel force was balanced by the
rate of increase of the angular momentum supplied by the torque difference
between the two directions. The explanation conveniently ignored the fact
that for moments to be applied to the lever by the forces applied to its
ends, equal and opposite forces would result at the hinge pin. As a result,
any energy that is added to the transverse lever arm by the applied parallel
force at its end will be removed at the hinge pin, and the rate of change of
energy in the lever is exactly zero.
What was also ignored was the fact that the angular momentum of the
lever is the product of its moment of inertia and its angular velocity.
Since the lever was observed not to rotate in either reference frames, the
rate of change of the lever's angular momentum is also zero. Properly done,
the mathematical explanation amounts to the statement that 0 = 0. This is
certainly true but is also meaningless. It is frightening that the advanced
academic community could overlook such an error and appear in a large number
of postgraduate level texts. It is even more frightening that individuals
who would embrace such an explanation are in a position to teach our best
and brightest. For a derivation of the correct Lorentz Transformations for
Forces see http://einsteinhoax.com/relcor.htm.
The type of error illustrated by paragraph B occurs in regard to the
idea of "action at a distance" being produced by the exchange of "virtual
particles". Mathematically, such particles are capable of providing both
attractive and repulsive forces. In reality, in the absence of an overlying
substrate for space (e.g.- the classical Aether or Dirac's "Sea of Negative
Energy") with which the "virtual photons" could interchange momentum, the
production by "virtual photons, of attractive forces acting at a distance
would seem to be impossible. But then, if such a substrate exists, why do we
need the concept of "virtual photons"?
Perhaps it would be constructive to illustrate this type of limitation
on the reliability of a purely mathematical treatment by considering the
analysis of a conventional FET transistor circuit, the cascode. This circuit
consists of two FET transistors with the drain of the first one driving the
source of the second one and with the gate of the second biased at a
constant positive voltage. For low frequency signals, the operation of such
an amplifier is completely defined mathematically by a property known as
"transconductance". The electron flow in the collector of the second FET is
the product of the signal voltage applied to the gate of the first FET times
the transconductance of the first FET. The mathematics tells us that a
positive signal will produce a positive flow of electrons at the output and
a negative signal will produce a negative flow of electrons at the output.
What the mathematics doesn't tell us is that the process will not work
unless there was a bias flow of electrons in the amplifier to which the
output signal was added. With the bias current, the amplifier can produce
both positive and negative electron flow signal outputs by adding to or
subtracting from the bias current. Without the bias current, the amplifier
can only produce positive electron flow outputs. The mathematics is
NECESSARY BUT NOT SUFFICIENT to define the process. Similarly, the writer
asserts that the mathematics associated with "virtual photons" is also
NECESSARY BUT NOT SUFFICIENT. A substrate (e.g.- the classical Aether or
Dirac's "Sea of Negative Energy" or one of the several "background energy of
space" concepts) would seem to be necessary for the idea of "virtual
photons" as a force carrier to work, but, if the substrate exists, why is
the concept of "virtual photons" as force carriers required?
Whether "virtual photons" exist can be evaluated by a rather simple
experiment as shown in the diagram below. There is an even simpler means of
evaluating the concept. A recent news item revealed that a loose oxygen
cylinder was captured by the magnetic field of an MIR machine and flew
across the room to crush the skull of a child being examined. If such a
strong magnetic field existed in the room and that field involved "virtual
photons", those photons would be sufficiently numerous to produce an amount
of electromagnetic noise that would be easily measured. I doubt very
seriously if such noise would be found if s search were made.
http://einsteinhoax.com/cf43.gif.
Remember that Dr. Einstein warned "we have not proven that the Aether
doesn't exist, we have merely proven we do not need it (for calculations).
Also remember that it took 25 years of peer pressure to cause Dr. Einstein
to relinquish the idea of "absolute time" (equivalent to believing the
Aether) and accepting the unproven (and rather ludicrous) consensus
viewpoint of space and time as a single entity.
Theoretical physics has taken the easy position that only mathematics
and experiment are required to deal with reality. Unlike every other branch
of science, it is asserted that "mechanism" is irrelevant in physical
theory. Since we live in the "mechanism" represented by our Universe, the
prime goal of any responsible theoretician should be an understanding of the
workings of that "mechanism" with the mathematical and experimental results
used to iteratively improve our understanding of that "mechanization". What
we have today, with the idea of "mechanism" eliminated, is more akin to
group quasi-religious charlatanism (how many Angels can dance on the head of
pin?) practiced by a controlling cadre of self promoting "scientists" than
it is to an organized science.
The source material for this posting may be found in
http://einsteinhoax.com/hoax.htm (1997); http://einsteinhoax.com/gravity.htm
(1987); and http://einsteinhoax.com/relcor.htm (1997). EVERYTHING WHICH WE
ACCEPT AS TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE WE HAVE ACCEPTED AS
TRUE, IT MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND IT MUST BE
MATHEMATICALLY VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS
REQUIREMENT. THE WORLD IS ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM
THOSE IT HAS GRANTED WORLD CLASS STATUS.
All of the Newsposts made by this site may be viewed at the
http://einsteinhoax.com/postinglog.htm.
Please make any response via E-mail as Newsgroups are not monitored on
a regular basis. Objective responses will be treated with the same courtesy
as they are presented. To prevent the wastage of time on both of our parts,
please do not raise objections that are not related to material that you
have read at the Website. This posting is merely a summary.
E-mail:- einsteinhoax@isp.com. If you wish a reply, be sure that your
mail reception is not blocked.
The material at the Website has been posted continuously for over 8
years. In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE
MATERIAL PRESENTED. There have only been hand waving arguments by
individuals who have mindlessly accepted the prevailing wisdom without
questioning it. If anyone provides a significant rebuttal that cannot be
objectively answered, the material at the Website will be withdrawn.
Challenges to date have revealed only the responder's inadequacy with one
exception for which a correction was provided.
THE MECHANICS OF
THE UNIVERSE
Copyright 1984-2006 Allen C. Goodrich
No force is necessary to cause orbital motion.
The planets orbit the sun at a special mean orbital
radius L to conserve total energy. The modified
first law of thermodynamics , which states that the
total energy of the universe is a constant, is the
fundamental equation of the universe. The sum
of kinetic and potential energies is a constant.
m (2 pi L)^2 / t^2 + G m(M-m) /L = A CONSTANT.
(if no charges are present)
+ Delta m(2 pi L)^2/T^2 = - Delta Gm(M-m)/L
What's so important about this modified first law of thermodynamics?
Kinetic energy m (2 pi L)^2 / t^2 of a mass m is orbital motion
relative to the rest of the effective universe (M-m) and potential
energy G(M-m) m / L, where L is the mean orbital radius, are nearly
equal at equilibrium, where no energy change occurs and the total
energy is constant. At equilibrium, any change of kinetic energy must
be accompanied by an equal and opposite, sign, change of potential
energy.
The universe has been found to be expanding
at an accelerating rate. The potential energy of the
universe is continually decreasing and the kinetic
energy is continually increasing. Again, to conserve
the total energy relative to the rest of the universe.
This is why the modified first law is so important. The conservation of
total energy must be maintained
relative to the rest of the expanding universe. Kinetic
and potential energies must be computed relative to
the rest of the expanding universe.
This modified first law leads to the conclusion that
the force of gravity and the velocity of light are
misleading illusions.
The definition of Kinetic and Potential Energies
is most important to an understanding that these
energies are relative to the rest of the effective
universe, not just relative to any other mass.
Kinetic energy is mass m times the
square of the velocity relative to the rest of the
effective universe. For example the kinetic energy
of the earth is effectively relative to the sun plus
the rest of the planets of the solar systen.
Potential energy is the product
of the mass m times the mass of the rest of the
effective universe M-m divided by the distance L
between their effective centers of mass.
M is the mass of the entire effective universe.
t is the orbital time for one complete revolution.
G is the gravitational constant.
Once this is clearly understood, the modified
First Law of Thermodynamics becomes the
Fundamental Equatiion of the Universe.
This equation ,then, defines the photon and the
rest of the universe.
The Thomas R. Young two slit defraction pattern,
the complete logic of quantum mechanics, the
true nature of gravitation, the fact that light does
not have a mass or a velocity, all become quite
obvious. This is a simple solution to so many of
the problems that baffled scientists for hundreds
of years.
We remember that Sir Isaac Newton proposed
the force of gravity F_g = k m_1 m_2 / L^2.
Scientists have known that action at a distance
without the transfer of energy was not possible.
A force of gravity would not be possible without
the transfer of energy. The amount of energy
required to cause the so called force of gravity
to make the planets travel in any orbit other than
their equilibrium orbits about the sun would be tremendous and is not
available.
Another explanation is necessary.
Einstein and other scientists have
assuned that masses change the shape of
space time. These explanations have their
problems.
No problems exist if the modified first law
of thermodynamice is used.This is the
fundamental equation of the universe.
One night when I was walking on
Myrtle Beach in the light of the full moon,
the full moon was at its highest point in the
sky, and the beach was very wide.
The lowest tide was present. This is not
what would be expected according to the
gravitational theory. The gravitational theory
states that the tide should be very high.
One can find this explained in most older
dictionaries or encyclopedias. The water
of the ocean is shown bulging on the side of
the earth directly under the full moon.
The tides never occur in this way.
This discrepancy with the law of gravity is
explained by the requirement for the time
required for the water to flow due to the force .
No one has bothered to explain that the
water would have to flow at more than
1000 miles per hour to complete this picture.
This flow would wash all of the continents
away in one day, Here, we have a big problem
with the force of gravity .
The NOAA U.S. Coast and Geodetic Survey
has monitored the tides at many ocean ports for
many years and this data is available.
The Jet Propulsion Laboratory has plotted
the position and phases of the moon with
changes of time. This data is also available.
No one has previously published a correlation
ot these two sets of data. If they had, it would
become very obvious that invariably the lowest
tide occurred when the full moon and new moon
were exactly directly at their highest point in the sky.
It would have been obvious that the lowest tide
also occurred on the opposite side of the earth.
Not at all consistant with the existing
gravitational theory. However, this is predicted
by the modified first law of thermodynamics,
when the kinetic and potential energies are
relative to the rest of the effective universe.
If one calculates the kinetic and potential
energies of the planets and moons,at mean
orbital distance L, one finds that the two are
nearly equal in magnitude.
This is the only mean orbital distance where a
positive change of kinetic energy equals a
negative change of potential energy. In the
expanding universe this is necessary for
equilibriun motion where there is no energy
transfer. A force or transfer of total energy
would be necessary to make the planets travel
at any other mean orbital radius.
Nature obeys the modified first law of
thermodynamics.
The assumption of a force of gravity, with its
energy transfer, action at a distance, is not
necessary to explain orbital motion.
Gravitation is explained by the modified
first law of thermodynamics.
The Thomas R. Young's two slit defraction
pattern is also explained by the modified
first law of thermodynamics if one uses the
charges e in this fundamental equation for
the calculation of kinetic and potential energies.
Delta e_1 (2 pi L)^2 / t^2 = Delta-K e_1 e_2 /
4 pi E_o L.
Where e_2 is the charge of the rest of the
effective universe and . e_1 is the orbital
electron. E_o is the dielectric constant.
Here, the masses would have little effect by
comparison and can be neglected.
The kinetic energy change of the electron
would then be a function of a change of
potential energy relative to the rest of the
effective universe.
The energy of the electron of the atom
on the defraction pattern screen would be
a function of the rest of the effective universe.
The electron would sense the fact that one
or two of the slits was open and the
Thomas R Young defraction pattern is explained.
We now have the basis for a new
quantum mechanics.
Light , that is observed as a change of the
kinetic energy of the electron, which has the
correct energy density (time) , direction and
frequency, relative to the rest of the expanding
universe, is not a particle, but a function of the
potential energy change of the rest of the
effective universe .
The four fundamental forces - strong, weak,
electromagnetic and gravitational - are likewise
illusions that result from Newton's error of
interpretation of the mathematics. A force is not
possible without the transfer of energy. The
graviton is not necessary for equilibrium motion
where no energy transfer takes place.
The modified first law of thermodynamics says
that the total energy of the universe is a constant
in the absence of a force and energy transfer.
Orbital moton is necessary to the conservation of
total energy.
Kinetic and potential energies of masses and
charges are conserved by orbital motion.
.
|
|
|
|
|
Related Articles |
|
|
