It
appears that matter is a substance like wood. Momentum refers to the amount of
motion there is, such as, in a moving log. Kinetic Energy is the work done in
stopping the moving log.
When
two billiard balls collide, their motion changes, and work is done in changing
that motion. But, according to the conservation laws, the net change in motion
is zero, and the net work done is zero also. If the motion of a ball has
increased, the motion of the other ball has decreased. If one ball did work on
the other then the other ball did work back on the first one.
We
started out with some substance in a closed system, and that substance has
remained the same in spite of the interactions within that system. That is the
case with our universe.
Here the word “substance” means that which is substantial and undergoes changes, but the total motion and energy remain the same.
.
The Innate Force
The
primary characteristic of substance is that it is substantial enough to be
detected. It is possible to detect substance because it interacts with our
sense channels and with other instruments of detection. In that interaction
there is change in motion and energy. We all have experienced that we cannot
push something which does not put any resistance. We cannot change its motion
or energy. In other words, we cannot detect it.
Therefore,
the core of substance is the resistance it puts to force. A substance always
reacts to force by returning force. If there is no force in any shape or form,
there is no substance, motion or energy. More fundamental to motion and energy
is the concept of force. It is this force that defines the substance. This innate
force in matter was defined as INERTIA by Newton.
At the core of substance is an innate force.
.
Is Light Substance?
Nobody
questions matter being substance. When we stub our toe by dropping a brick on
it, we know that brick has substance. Is light a substance? We can detect light
by our eyes and with other instruments. There is change in motion and energy.
Underlying that change there is force. Light has innate force.
But
if light is substance, it is very different from matter. It obeys laws of
nature which are very different from the laws that matter obeys. Still light
has innate force. We may not call it inertia because that word is used for
matter. We may simply refer to it as “innate force” of light.
Light has innate force; therefore, light is a substance.
.
Past Views of Light
Newton
extended the corpuscular theory of light. He viewed light to be made up of
particles. Obviously, particles are particles of some substance. We may say
that Newton implied light to be substance but he didn’t associate inertia
(innate force) with it.
Einstein
also viewed light to be made up of particles, which he called light quanta. He implied
these particles to be packets of energy that had discrete existence in space.
These particles carried enough momentum to expel electrons from the surface of
certain metals. The prerequisite of energy is substance. We may say that
Einstein implied light to be a substance and associated innate force with it.
.
Summary
Light has momentum and energy. It must have resistance when it is pushed because its speed is finite. If light had no resistance its speed would be infinite. Therefore, light must be a substance with a very small amount of innate force or “inertia”. The current physics does not look at light that way. That is a big misunderstanding.
We may say that there are two types of substances: atomic and non-atomic. Matter is an atomic substance. Light is a non-atomic substance Both are detected by their innate force or inertia.
This paper presents Appendix 3 from the book RELATIVITY: THE
SPECIAL AND GENERAL THEORY by A. EINSTEIN. The contents are from the original
publication of this book by Henry Holt and Company, New York (1920).
The paragraphs of the original material (in black) are accompanied
by brief comments (in color) based on the present understanding. Feedback
on these comments is appreciated.
The heading below is linked to the original materials.
A scientific theory is the view evolved from a continuous
assimilation of observations of the physical universe into the mental matrix. The
initial stages of a scientific theory are constructed out of a process of
arrangement from a large number of single observations. Guided by empirical
data, the investigator intuitively develops a system of thought, which, in
general, is built up logically from a small number of fundamental assumptions,
the so-called axioms.
But there may be several theories corresponding to the same
complex data. These theories may differ from one another to a considerable
extent, while agreeing on deductions that are capable of being tested. General
theory of relativity differs fundamentally from Newtonian mechanics, but there
have been only a few testable deductions that are different.
Newton’s theory gives an angle of 360° for the period (from
perihelion to perihelion). General relativity, however, provides a slightly
different result. The result from general relativity is confirmed by actual
observations for the motion of the perihelion of mercury.
Light rays bend near the sun due to its gravity, such that a
star behind the sun can be seen at a somewhat greater distance from the centre
of the sun than corresponds to its real position. This phenomenon of the change
in the angle of light was confirmed quite accurately by experimental evidence.
The completely objective
observer is the universe. In other words, the universe provides the absolute
reference system K0 that is absolutely at rest. We measure the
motion of all the parts of the universe against the backdrop of the universe.
Einstein’s rotating disc
is the whirlpool model. As one moves away from the center of the disc the
linear velocity increases and inertia decreases. In other words, both time and
space expand. The inertia provides the gravitational potential.
This paper presents Appendix 2 from the book RELATIVITY: THE
SPECIAL AND GENERAL THEORY by A. EINSTEIN. The contents are from the original
publication of this book by Henry Holt and Company, New York (1920).
The paragraphs of the original material (in black) are accompanied
by brief comments (in color) based on the present understanding. Feedback
on these comments is appreciated.
The heading below is linked to the original materials.
The math of Minkowski’s World is based on the following consideration:
The fourth dimension is generally interpreted as the dimension
of time. But from the earlier comments it appears that it should be interpreted
as the dimension of the DURATION of substance. This is the dimension of inertia.
The first three dimensions are generally interpreted as the
dimensions of space. But it now appears that they should be interpreted as the
dimensions of the EXTENTS of substance. These are the dimensions of the substance
as quanta, which are taken as an abstract point for matter.
We may say that x, y, and z are the dimensions of what we have
been considering as a dimensionless point in space for matter.
This paper presents Part III, Chapter 3 from the
book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The
contents are from the original publication of this book by Henry Holt and
Company, New York (1920).
The paragraphs of the original material (in black) are accompanied
by brief comments (in color) based on the present understanding. Feedback
on these comments is appreciated.
The heading below is linked to the original materials.
According to the general theory of
relativity, the geometrical properties of space are not independent, but they
are determined by matter. Thus we can draw conclusions about the geometrical
structure of the universe only if we base our considerations on the state of
the matter as being something that is known. We know from experience that, for
a suitably chosen co-ordinate system, the velocities of the stars are small as
compared with the velocity of transmission of light. We can thus as a rough
approximation arrive at a conclusion as to the nature of the universe as a
whole, if we treat the matter as being at rest.
Matter is a substance of
infinite inertia. It occurs at the upper end of the dimension of inertia. The geometrical
properties of space are not only dependent on matter, but also determined by
the inertia of substance. This is because space is the extent of substance. As
the inertia of the substance increases, its velocity decreases. This appears as
a “whirlpool” of substance. At the center of the “whirlpool” we have
substance as solid matter. Because of the “whirlpool” phenomenon, the matter at
the center spins about an axis.
This whirlpool is elliptical
that is almost flat as visible in the shape of a galaxy. The same whirlpool model
applies to the solar system. It is very likely that this model applies also to
the atom and to the whole universe too.
We already know from our previous
discussion that the behaviour of measuring-rods and clocks is influenced by
gravitational fields, i.e. by the distribution of matter. This in itself is
sufficient to exclude the possibility of the exact validity of Euclidean
geometry in our universe. But it is conceivable that our universe differs only
slightly from a Euclidean one, and this notion seems all the more probable,
since calculations show that the metrics of surrounding space is influenced
only to an exceedingly small extent by masses even of the magnitude of our sun.
We might imagine that, as regards geometry, our universe behaves analogously to
a surface which is irregularly curved in its individual parts, but which
nowhere departs appreciably from a plane: something like the rippled surface of
a lake. Such a universe might fittingly be called a quasi-Euclidean universe.
As regards its space it would be infinite. But calculation shows that in a
quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be
inhabited by matter everywhere; it would present to us that unsatisfactory
picture which we portrayed in Section
XXX.
Einstein is operating on the model of matter and void. He is considering the dimension of inertia only indirectly. It is true that inertia takes a big jump at the interface between “void” and matter. It increases very slowly in the “void” domain, and again quite slowly in the material domain.
If we are to have in the universe an
average density of matter which differs from zero, however small may be that
difference, then the universe cannot be quasi-Euclidean. On the contrary, the
results of calculation indicate that if matter be distributed uniformly, the
universe would necessarily be spherical (or elliptical). Since in reality the
detailed distribution of matter is not uniform, the real universe will deviate
in individual parts from the spherical, i.e. the universe will be
quasi-spherical. But it will be necessarily finite. In fact, the theory
supplies us with a simple connection1 between the space-expanse of
the universe and the average density of matter in it.
Each atom is an elliptical whirlpool at the center of which the nucleus exists. That means a solid body is made if an infinite number of atomic whirlpools. But that solid body itself forms the center of a much larger whirlpool. This same model then scales up to solar and star systems, the galaxies, and finally the universe. The universe shall exist much farther outwards than its relatively solid core.
.
FINAL COMMENTS
The final comments are pretty much the comments above.
This paper presents Part III, Chapter 2 from the
book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The
contents are from the original publication of this book by Henry Holt and
Company, New York (1920).
The paragraphs of the original material (in black) are accompanied
by brief comments (in color) based on the present understanding. Feedback
on these comments is appreciated.
The heading below is linked to the original materials.
But speculations on the structure of the universe also move in quite another direction. The development of non-Euclidean geometry led to the recognition of the fact, that we can cast doubt on the infiniteness of our space without coming into conflict with the laws of thought or with experience (Riemann, Helmholtz). These questions have already been treated in detail and with unsurpassable lucidity by Helmholtz and Poincaré, whereas I can only touch on them briefly here.
The development of non-Euclidean geometry led
to the recognition of the fact, that we can cast doubt on the infiniteness of our space without coming into conflict with the laws of thought
or with experience.
In the first place, we imagine an
existence in two-dimensional space. Flat beings with flat implements, and in
particular flat rigid measuring-rods, are free to move in a plane. For them nothing exists outside
of this plane: that which they observe to happen to themselves and to their
flat “things” is the all-inclusive reality of their plane. In particular, the
constructions of plane Euclidean geometry can be carried out by means of the
rods, e.g. the lattice construction, considered in Section XXIV. In contrast to ours, the universe of
these beings is two-dimensional; but, like ours, it extends to infinity. In
their universe there is room for an infinite number of identical squares made up
of rods, i.e. its volume (surface) is infinite. If these beings say their
universe is “plane,” there is sense in the statement, because they mean that
they can perform the constructions of plane Euclidean geometry with their rods.
In this connection the individual rods always represent the same distance,
independently of their position.
Let’s consider the reality of flat beings existing in
two-dimensional space. What they observe to happen to themselves and to their
flat “things” in their plane is their reality. To them their space will extend
to infinity. It will be consistent with Euclidian geometry.
Let us consider now a second
two-dimensional existence, but this time on a spherical surface instead of on a
plane. The flat beings with their measuring-rods and other objects fit exactly
on this surface and they are unable to leave it. Their whole universe of
observation extends exclusively over the surface of the sphere. Are these
beings able to regard the geometry of their universe as being plane geometry
and their rods withal as the realisation of “distance”? They cannot do this.
For if they attempt to realise a straight line, they will obtain a curve, which
we “three-dimensional beings” designate as a great circle, i.e. a
self-contained line of definite finite length, which can be measured up by
means of a measuring-rod. Similarly, this universe has a finite area, that can
be compared with the area of a square constructed with rods. The great charm
resulting from this consideration lies in the recognition of the fact that the universe of these beings is finite and
yet has no limits.
But if that two-dimensional existence is on a spherical surface
instead of on a plane, then their geometry is no longer consistent with the
Euclidean geometry. Their straight line will be a curve. Their universe will
have a finite area. The universe of these beings is finite and yet has no limits.
But the spherical-surface beings do not need to go on a world-tour in order to perceive that they are not living in a Euclidean universe. They can convince themselves of this on every part of their “world,” provided they do not use too small a piece of it. Starting from a point, they draw “straight lines” (arcs of circles as judged in three-dimensional space) of equal length in all directions. They will call the line joining the free ends of these lines a “circle.” For a plane surface, the ratio of the circumference of a circle to its diameter, both lengths being measured with the same rod, is, according to Euclidean geometry of the plane, equal to a constant value, which is independent of the diameter of the circle. On their spherical surface our flat beings would find for this ratio the value
i.e. a smaller value than π,
the difference being the more considerable, the greater is the radius of the
circle in comparison with the radius R of the “world-sphere.” By means of
this relation the spherical beings can determine the radius of their universe
(“world”), even when only a relatively small part of their world-sphere is
available for their measurements. But if this part is very small indeed, they
will no longer be able to demonstrate that they are on a spherical “world” and
not on a Euclidean plane, for a small part of a spherical surface differs only
slightly from a piece of a plane of the same size.
These spherical-surface beings may not know that they are living
on a spherical surface; but if they draw large enough circles, they will find
the ratio of the circumference to its diameter is not constant. It becomes
smaller as the radius increases. Thus, they can discover that they are not
living in a Euclidean universe, and that their universe is finite.
Thus if the spherical-surface beings
are living on a planet of which the solar system occupies only a negligibly
small part of the spherical universe, they have no means of determining whether
they are living in a finite or in an infinite universe, because the “piece of
universe” to which they have access is in both cases practically plane, or
Euclidean. It follows directly from this discussion, that for our sphere-beings
the circumference of a circle first increases with the radius until the
“circumference of the universe” is reached, and that it thenceforward gradually
decreases to zero for still further increasing values of the radius. During
this process the area of the circle continues to increase more and more, until
finally it becomes equal to the total area of the whole “world-sphere.”
It may be difficult for them to discover this if they have
access to only a very small part of their universe.
Perhaps the reader will wonder why we
have placed our “beings” on a sphere rather than on another closed surface. But
this choice has its justification in the fact that, of all closed surfaces, the
sphere is unique in possessing the property that all points on it are
equivalent. I admit that the ratio of the circumference c of a circle to its
radius r depends on r, but for a given value of r
it is the same for all points of the “world-sphere”; in other words, the
“world-sphere” is a “surface of constant curvature.”
In this example, we assume the “world-sphere” to be a “surface
of constant curvature because this makes all points equivalent.
To this two-dimensional
sphere-universe there is a three-dimensional analogy, namely, the
three-dimensional spherical space which was discovered by Riemann. Its points
are likewise all equivalent. It possesses a finite volume, which is determined
by its “radius” (2π2R3). Is it possible to imagine a
spherical space? To imagine a space means nothing else than that we imagine an
epitome of our “space” experience, i.e. of experience that we can have in the movement
of “rigid” bodies. In this sense we can imagine a spherical space.
Riemann discovered a three-dimensional analogy of a spherical
space. That means an object moving in a straight line in any direction will
ultimately reach its starting point.
Suppose we draw lines or stretch
strings in all directions from a point, and mark off from each of these the
distance r with a measuring-rod. All the free end-points of these
lengths lie on a spherical surface. We can specially measure up the area (F)
of this surface by means of a square made up of measuring-rods. If the universe
is Euclidean, then F = 4πr2; if it is spherical, then F is
always less than 4πr2. With increasing values of r, F increases from zero up
to a maximum value which is determined by the “world-radius,” but for still
further increasing values of r, the area gradually diminishes to
zero. At first, the straight lines which radiate from the starting point
diverge farther and farther from one another, but later they approach each
other, and finally they run together again at a “counter-point” to the starting
point. Under such conditions they have traversed the whole spherical space. It
is easily seen that the three-dimensional spherical space is quite analogous to
the two-dimensional spherical surface. It is finite (i.e. of finite volume),
and has no bounds.
It is easily seen that the three-dimensional spherical space is
quite analogous to the two-dimensional spherical surface. It is finite (i.e. of finite volume), and has
no bounds.
It may be mentioned that there is yet
another kind of curved space: “elliptical space.” It can be regarded as a
curved space in which the two “counter-points” are identical (indistinguishable
from each other). An elliptical universe can thus be considered to some extent
as a curved universe possessing central symmetry.
We can have the curved space to be “elliptical” in form too. This shall look like a galaxy.
It follows from what has been said,
that closed spaces without limits are conceivable. From amongst these, the
spherical space (and the elliptical) excels in its simplicity, since all points
on it are equivalent. As a result of this discussion, a most interesting
question arises for astronomers and physicists, and that is whether the
universe in which we live is infinite, or whether it is finite in the manner of
the spherical universe. Our experience is far from being sufficient to enable
us to answer this question. But the general theory of relativity permits of our
answering it with a moderate degree of certainty, and in this connection the
difficulty mentioned in Section XXX finds its solution.
Thus, close spaces without limits are conceivable. From amongst
these, the spherical space (and the elliptical) excels in its simplicity, since
all points on it are equivalent.
.
FINAL COMMENTS
We as three-dimensional beings live in a material universe. We find it hard to imagine the fourth dimension of inertia in which the substance of variable durations has existence. This fourth dimension is not some abstract “time”. It is a dimension that accounts for variable duration characteristic (inertia) of substance.
The fourth dimension is INERTIA and not some abstract notion of
TIME.
