A Unification Theory
By David Barwacz
http://members.triton.net/daveb
In this paper I will develop a simple theory based almost entirely on existing physics. I do not make many assumptions although the assumptions may seem a bit radical at first. The result will clearly show a link between relativistic classical mechanics and relativistic quantum mechanics. It will explain spin as well as the Hubble formula, and give the form of Newton’s Law of Gravity.
I will start by developing some concepts based on special relativity as it is today. These concepts will help substantiate the proposals I will make.
I will then propose that every object cycles through space and time and that the cycle time is inversely proportional to the total energy. For small objects like electrons this cycling is very rapid and makes an intuitive jump to quantum mechanics easy.
For large objects I will show that the cycle time is very small. For these small times it will be clear that a linear time can be developed that is proportional to the cyclic time.
I will then show that the Lorentz transformations can be derived by simple geometry from the cyclic space/time using the linear time and the assumption of fixed (non-changing) space.
Conceptual development
In this section I will use existing accepted physics with
modifications. I do this to give some rationality to the assumptions I will
make later. Some of the formulas developed here will be used later in this
paper.
When attempting to explain relativity, Einstein often used high speed trains.
The passengers were all given a clock and the clocks all clicked off time at the same rate when they were at rest relative to each other. Einstein then went on to show that the time was dilated when one was moving relative to the other. The formula for the dilation, as we all know, is based on the Lorentz transform. The somewhat complex nature of the equation didn’t help people understand what was happening.
Let’s redo his explanation in a different but equally correct way.
Assume that the experiment was done with two clocks. One of the clocks was twice as massive as the other. The more massive clock was pre set to tick off ‘seconds’ only half as fast as the other clock. Each clock had a special measuring scale (ruler) attached to it. The more massive clock’s unit of measure was only half that of the other clock. In other words, if inches were used on the less massive clock then the more massive clock had inches that were only measured as half inches by the ruler on the less massive clock.
All observers were aware of these conditions before the experiment and had no pre conceived notions about time.
We tend to believe
that time is a property of the space associated with it. This however is an
assumption and is not a provable fact. How can you know that the time of one
object is in fact the same as another object? We have always believed that time
and space was independent of the objects that occupy it. There is no way to
prove this and therefore, having no prior pre conceived notions of time, we
will assume our observers have an open
mind.
The observers were able to read gauges that read the total energy of each clock (the energy due to its rest mass plus the energy due to any relative motion).
The more massive clock was put on the train and accelerated to a velocity such that his total energy (that due to its mass and its momentum) was doubled. Its ruler was aligned in the direction of motion. In some formulations of relativity, it is said that the clock’s mass doubled. The total energy gauges clearly displayed the clock’s total energy relative to the stationary clock. At the velocity where the clock’s energy was double its rest energy, the stationary observers noticed that the moving clock’s time was only ticking at ˝ its original speed (1/4 of the stationary clock’s rate) and its units of measure were only one half their original value (1/4 of the stationary clock’s unit of measure).
It was then accelerated to a velocity where its total energy was again doubled (4 times the mass when at rest) and sure enough the clock slowed by another ˝ (now it was only 1/8 the rate of the stationary clock) and its unit of measure shrunk again to only 1/8 that of the stationary clock.
The observers concluded that time (the rate of time) was simply an inverse ratio of total energy and that the space was simply an inverse ratio of the total energy.
Clearly, this conclusion can only be reached if the clocks are preset to run at a rate that is inversely proportional to their energy.
Our clocks are all set to run at the same rate. However, if we lived in a high speed world, where near light speeds were common, we might indeed find it more convenient to set time rates proportional to total energy. It would make many calculations much easier.
In this paper I assume that there is in fact a natural time for every object and it is in fact inversely proportional to total energy.
The result, as I shall show, unifies many ideas in physics.
Initial attempts to
explain this concept have been met with intense objection. I will simply remind
the reader that strange ideas are not foreign to physics. Ideas like 20
dimensions; time running backwards, wave particle duality etc. have been and
are accepted.
We can use the following equations to convert from one object’s time to another.
where
are the rates of time for 
To get the actual time for objects relative to a common reference object we can use the following formula:
where
is the time for 
when 
=0, and 
is some reference
energy. 
is
a constant with the appropriate conversion units. We shall see that this
constant may very well relate Planks constant to the gravitational constant.
It makes sense to have all clocks at zero when viewed from
the reference object, so we will assume equals zero for the
examples that follow.
Similarly we can develop the following Space conversion formula:
Again we can assume that
is equal to zero by aligning all our measuring devices such that
the zero point is aligned when viewed by the reference object.
This explanation of time dilation and length contraction only works if the observer’s clock rates are set according to their respective masses (rest energies) when at rest relative to one another, and an appropriate measuring scale is attached; but it does work.
It must be noted that time and space, as represented in this manner, are properties of the object and not properties of some assumed void.
Of course, one can easily get the conventional space/time relativistic formulas by simply assuming that every imaginary coordinate system contains an object with the same rest energy, basically attaching space and time to a coordinate system rather than an object.
The reader might have a number of questions at this point regarding using this space/time representation.
One might argue for example, that an overweight person does not age slower than a thin person. This can be easily explained. Aging is related to molecular times not the macroscopic total mass time. The overweight person simply has more molecules.
If the two were put into orbit around the earth we could use
the macroscopic (inverse total energy) time and space. In fact we shall see
that using this representation (with a little physics) produces
What is clear is that using this method is perfectly good physics. In fact, it is much more symmetrical; treating all forms of energy the same.
Next I develop the concept of a three component time invariant. Again, this will not in any way contradict special relativity.
We start with the well known equation 
Inverting and squaring we get we get 
Rearranging gives 
And finally using inverse energy (multiplying by the
appropriate constants) as time we get: 
It is clear that 
is invariant.
Propositions
In this section I will propose a few new concepts.
Proposal 1
The following
equation is invariant over all time for any inertial object.
where 
and 
are the total energy space and time of an object and K is a
constant. K does not change with time.
This equation is clearly cyclic in both space and time.
We can convert the cyclic equation to the standard form that
is invariant in form under a Lorentz transformation.
Rewriting this universal invariant using our 3 component time formula gives
This can be rearranged to read:
where 
The above equation looks like the conventional relativistic
formula which is invariant in form from observer to observer, but the 
is not
invariant over time. It also has a spatial component that is nearly constant
which is what is assumed in the present formulation of special relativity. It
basically is a representation that is “pseudo” linear in space and time.
From these equations we can infer that for small low energy objects
( large) we must use the universal invariant which is cyclic
in space and time.
For large objects with high velocity we can use the conventional equation and also infer that space is inversely proportional to time.
For large objects with little or no velocity we can eliminate
from the conventional
formula and get 
which is what we
expect.
We shall see that gravity is the result of using the universal invariant on large objects with low kinetic energy.
All of the above
considerations assumed linear space and time. We shall now diverge substantially
from that, but show that it is a very precise approximation under a wide
variety of conditions.
Proposal 2
I now propose that every
observable object cycles repeatedly in space and time and that the frequency of
this natural cycling is inversely proportional to it total energy
Stated differently: Given that the proportionality constant is equal then, if one object completes a cycle in one second of its time then every other object completes one cycle in one second of its time.
We wish to find a reference energy such that any object
completes a cycle in one second of it’s time for equal to 1.
To do so we will assume that the Ry
cycles (in our case
seconds), as viewed from the reference object, in the time the reference object
completes one cycle (1 sec). I will use the cgs
system of units. The exact value isn’t important for explaining many physical phenomenons,
but it should at least be in a range that makes sense. I will assume for now that
is just a unit conversion constant.
.
I left the 
in so we can work just
with masses in grams.
A mass on the order of 
grams then cycles in one second.
In this theory, quantum mechanics “merges” with classical mechanics simple because things cycle slower as they get larger.
It is instructive to show the cycle times for a number of different masses. Again, we are assuming non relativistic velocities.
|
Mass (grams) |
Object |
Cycle time sec/sec0 |
Time to complete one of our seconds |
|
1 |
reference |
|
10,569 years |
|
|
baseball |
|
1.5 million years |
|
|
earth |
|
|
The values listed above would be the cycle times in free space. Setting a baseball on a shelf would no doubt stabilize it even more.
The diagram below illustrates the rotation of a large object and an electron.
We can now define our cycle frequency and the time component.
1) Cycle frequency can be written mathematically as:
Where 
is our clock time. The x simply refers to the object and E its total
energy.
2) Measurable time or real time. This is the time component of the space time line. It is sinusoidal in nature. It can be expressed mathematically as:
For small
angles it is clear that 
which brings us back
to the original formula.
A summary is in order at this time.
1) I used special relativity to develop the concept of inverse energy time. This was just instructive and meant to make the concept of energy related time more palatable to the reader.
2) I proposed that every inertial object cycles in space time and proposed a simple cyclic formula.
3) I proposed that the cycle time (frequency) is inversely proportional to total energy.
From the assumptions, we can see that for large objects the measurable time becomes linear and is itself inversely proportional to time.
An interesting result of what we have discussed can now be derived:
Assuming that has a base value 
that is the same for
every object then it is clear that 
If we choose a
reference space and a fixed unit of distance 
in it, we can write.
which
is a constant.
This says that there is an intrinsic angular momentum that is the same for everything.
This explains intrinsic spin. Every fundamental particle that has spin will have the exact same value of angular momentum.
To develop an inertial reference frame we first must recognize that the frequency developed above is relative to our reference time. If we want to find the linear velocity of an object we multiply its angular frequency by the distance of the object from its center of rotation in a reference space. To relate the linear velocity of one object to another we must multiple each by the distance in its own space that correspond to the same distance in the reference space. Mathematically this is shown below.
Where 
is the distance in the
objects space that corresponds to a fixed distance in our reference space.
Now converting to the reference space we get:
But 
is inversely
proportional to and hence we can
conclude that any object at this point in the reference space will have the same
linear velocity.
We can then define a base angular frequency for the inertial reference frame:
If the distance from the center of rotation is very large relative to the distance between the objects, there would be imperceptible relative motion between any objects. In cyclic space this then is an inertial reference frame.
It is instructive at this time to show just how stable large things are and get a feel for why the non linearity has eluded us. To do so we must understand that it is not the non linearity in time that we might perceive but the non linearity in time ratios. If time got non linear for everything simultaneously, there would be no reference time by which to measure it.
We start by writing the time equation in the following form.
where 
We can now evaluate the time ratios for objects of the same
rest mass and same value of , but one with kinetic energy as well.
The following table represents an energy ratio of 1.01. In terms of velocity, the moving object would be traveling at about 14 % the speed of light.
|
|
|
|
1 to 10,000 |
.9900990099021453 |
|
100,000 |
.9900990099010016 |
|
1,000,000 |
.9900990099021453 |
|
|
.9900990100116517 |
|
|
.9900990214536779 |
|
|
.990100165972603 |
|
|
.9902148153870884 |
The following example will help understand the table.
Assume the objects were 1 gram at rest. When 
equals
, there is about a 1 ppm deviation
from linearity. We can calculate the
time in seconds that has transpired. The time that has passed for an observer
at rest is just .003 seconds. Traveling at 14 % the speed of light the gram is
now about 126,000 meters away. Clearly we have no instruments to accurately
measure a one ppm deviation in time for something
moving at 14 % the speed of light 126,000 meters away. Another interesting fact
is that the time rate of the moving object increases as it gets further
away. This would manifest itself as a
decrease in the Doppler shift of any signals sent from the moving object. We
would conclude that the object is slowing down.
The above observation
has been made. All distant space probes appear to be slowing down. Nasa has not been able to explain
this with any conventional physics.
See http://news.bbc.co.uk/1/hi/sci/tech/1332368.stm
I must note that, if we define a cyclic inertial reference frame, then the one gram objects could be replaced with objects of any mass and the above example would apply equally.
The above observation
has been made. All distant space probes appear to be slowing down. see http://news.bbc.co.uk/1/hi/sci/tech/1332368.stm
Let one of our objects travel along with the pioneer 10
space craft. It’s velocity is 12.24 km/sec or 
. In terms of energy ratio this is 1.000000008323. It has
traveled for about 20 years. We can find from the above equation that the
velocity will appear to be slowed by about 37cm/sec. A constant force applied
opposite the direction of travel would have to be 
. If you assume, as NASA does that the force is directed
toward the sun, then you must increase it by a factor of the 
where 
and 
is the average angle
that the craft has been traveling relative to a line between it and the center
of the sun. If we assume that this has been traveling away at 
then we must adjust
our acceleration by 1.414. This gives a net acceleration of 
. The value published by NASA is 
. NASA has not been
able to explain this slow down. It is clearly a
manifestation of the cyclic nature of space time.
Now that we have a feel for the extremely slow time rates of large objects (things smaller than a microgram fit this category), we can substantiate our original assumptions and also show that the Lorentz transform is completely compatible with this cyclic space and in fact can be derived from it using the assumptions we make in present physics.
Now that we have a feel for the extremely slow time rates of large objects (things smaller than a microgram fit this category), we can substantiate our original assumptions and also show that the Lorentz transform is completely compatible with this cyclic space and in fact can be derived from it using the assumptions we make in present physics.
Assume we have two fairly large objects (baseballs) and that they have exactly the same rest energy. One has some kinetic energy as well, and therefore is moving relative to the other. Their positions correspond when their clocks are started. The situation is illustrated in the diagram below. We label the one assumed to be at rest E0 and the other E1.
The true space time picture is depicted to the right. However, in physics today we do not assume space changes and hence we shall first find a representation that is consistent with special relativity.
Because E1 has more energy it rotates slower and therefore lags E0. The angle is very small after a short time (remember that a short time may be thousands of years). Even the diagram above exaggerates the angle over any period of time in which we may do an experiment. The actual times are shown and because of the small angle we can treat them as inversely proportional to time (we replace the sin with the angle)
The two diagrams below show the assumed orthogonal space time diagram and the actual space time diagram with the times shown so as to make space constant. The small angle is exaggerated even more in order to visualize the situation and show that the Lorentz transformation is simply the result of assuming a constant space with situations where time is very small.
Space time assuming constant space
We use k/E0 and k/E1 as the times. I must note that these times are not the true time. The actual times are T0 and T1. What is important is that the ratio of these times is the same as the ratio of the actual times. What also is clear is that these hyperbolic times have no meaning in of themselves; there must be at least two objects before they can even be defined. It is therefore no surprise that the theory they are based on is called relativity.
K is simply the reference energy times the reference time times any scaling constant that may be needed. In this example we assume that it is the same for both objects. It factors out of the equations we are about to develop and therefore its value is not important.
Everything we have done in physics up until now has assumed that space is constant for an object at rest. In reality, the above space for both objects has shrunk over the period of the measurement.
If we assume that it has not changed for E0, then what we call space is S’ and remains S’. However it has rotated. The time that has actually occurred on any clock moving along with E0 will have advanced by k/E0. Both objects were at the same point in space when their clocks were at 0. From E0’s standpoint it hasn’t moved in space but is has advanced in time. It was at point E1 when the clock was at 0 so its time is just its distance from E1 It can be represented by the line connecting the two points. The length of this line is ck/E0. Note that E1 is no longer at that point from E0 point of view. E1’s space time line is now a combination of space and time as viewed form E0.
The true time that has occurred on any identical clock moving along with E1 has advanced by k/E1. To find the spatial distance that exists between the objects at the end point of the observation, we drop a perpendicular from E1 to a space time line that intersects the point E0. I will show in a later addendum to this paper that this line is always at a slightly smaller angle to the time line k/E0 then its actual space time line. We are basically finding the component of E1’s space time line that is “space” on our assumed space line of E0.
The following equation is obvious from the diagram.
Now multiple and divide the left side by 
to yield:
Converting the 
in the numerator to time (
) and noting that the 
is just the
velocity squared as viewed form E0 we finally get:
eq. 5.0 which
can be rearranged to yield:
but
E0 is just the rest mass and E1 is the total energy of the object.
Inverting and taking the square root yields;
Another way to express eq. 5,0 is as follows
or 
eq. 5.1
Two things are clear from eq.5.1
1) 
This tells us that,
at least in this limiting case, nothing can exceed c in speed
2) Any thing with zero rest energy and non zero total energy will necessarily have a velocity of c
We can easily develop time dilation and length contraction form eq. 5.1
We know that 
and hence we can
quickly arrive at:
or in the more
familiar form 
Referring to the diagram below we
can find some additional relationships. 
For clarity, the above diagram refers to the previous times
without the delta symbol. It is clear from the diagram that 
It is also clear that 
And 
It is obvious that
But 
Therefore 
which can be written as :
Substituting into eq. 5.3 we get the complete form of the Lorentz time transformation:
where 
was replaced with x.
It is obvious that 
Using eq. 5.1 we get the standard length contraction formula:
It is clear that the Lorentz transform is simply a result of our obsession with treating space as constant and the fact that real time is very slow for large objects.
One might ask why an object with E1 rest mass would not be seen speeding away a high velocity? The reason is that this is a cyclic inertial reference frame. The base frequency of each object is a function of its rest energy in this frame. Additional energy will appear as motion, or more appropriately a change in the angular velocity.
Next we will look at an object that has a spin or angular velocity within the cyclic inertial reference frame.
Cycling object in cyclic inertial reference frame
In the above diagram, an amount of energy has been added to an object in a cyclic inertial reference frame but rather than causing a “linear” motion it manifest itself as a cycling.
Obviously there is no true linear motion only near linear motion hence the quotes around the word linear.
Let 
represent the base frequency of the reference frame, 
the base energy of the
object and 
the total energy of
the object.
If the object were traveling in a “linear” fashion, the angular frequency would be:
from
which we can conclude that:
Now 
must be the frequency of the object in the cyclic inertial
reference frame which we shall call 
and 
is the kinetic energy
of the object in the reference frame which we shall call 
Therefore:
However the object is no longer rotating as a part of the cyclic frame but is rotating on it’s own within the frame. We therefore must convert back to its own space using the formula:
times
is a constant
The reader might, in fact should have noticed that there were certainly other ways to interpret the above diagram. It may seem that the space for E0 and E1 should be swapped. If they were, they would be orthogonal to their respective times. This is correct and perhaps perfectly valid physics, but not consistent with our present understanding of physics. I explain below.
Einstein was quick to dispel conceptions about constant space and time and simultaneity but he was rigid in his belief that there is symmetry to the laws of physics. He believed that the laws must be the same in any inertial coordinate system. To that end, he inferred that the velocity of one inertial frame with respect to another must be the same regardless of which system the velocity was measured from. In our above diagram then we wish the velocity of E0 to be the same as that of E1 as viewed from the other. This would not be the case if we swapped the space values.
In physics we develop sets of assumptions and then create methods and devices to measure properties and if the measurements match our assumptions we believe we may have a working theory. If we further demand that the same assumptions must hold in a moving reference frame, we take our devices and measure the same phenomenon in the moving system and if the measurements match we conclude that our assumptions are valid.
The above diagram clearly illustrates this symmetry between the reference frames of E0 and E1. The same relative magnitudes hold and the angles are all the same provided we assign the appropriate space and time values to each object. Since we cannot go to the corner hardware store and buy a square to actually see if our space and time are truly perpendicular we simply assume they are.
Stated differently, nature simply cooperates with certain assumptions provided we use consistent methods and remain within the boundaries in which the assumptions work.
We will now look briefly at the concept of simultaneity. The only ways we can have two events simultaneous is either to have them be at the same spot in space time or lie on an axis that is all space. The choice of which space time line is all space is totally arbitrary, but there can only be one such true space time line. The diagram below illustrates the situation.
We choose to put A and B on the horizontal axis thereby making the events simultaneous in the space time line on which they lie. The same events when viewed from any other true space time line will not be simultaneous. This may seem arbitrary. Indeed it is. Einstein referred to simultaneity neither as a supposition nor a hypothesis but as a stipulation. Although it is a stipulation we cannot infer that any two events can be stipulated to occur at the same time. For example the points A and C above can not be put on a line that has no time component because the line that connects them does not intersect the origin and/or is not perpendicular to the zero time line.
In the above example, where we developed the Lorentz time
conversion formula, the space line we used that was perpendicular to 
could never have
simultaneous events occur at different points in space.
We can then distinguish two types of coordinate systems:
1) Proper coordinate systems, In a proper coordinate system the space time line intersects the origin. It can be stipulated as all space and therefore can have events that are simultaneous.
2) Non proper coordinate systems. These system’s space and or time lines do not intersect the origin. In such a coordinate system events may or may not be able to be stipulated as simultaneous.
The above rationalization should not be troubling but in fact refreshing. Take the example of two people sitting across the room from one another. Each has a flashlight. One flashes his first then the other flashes his 20 minutes later. It would be very troubling if somehow these two events could be simultaneous. Clearly they do not lie in a proper coordinate system and therefore we never have to worry about this absurd event happening.
The reader may be tempted to suggest at this time that if space is in fact changing for everything, then would we not see some effects of this change? Indeed we do see the effects as I shall now show. The most obvious effect is gravity.
The following discussion is a formulation of Gravity. The material has been made into a separate paper. The reader is advised to return to the home page and click on the link to the paper on Gravity.
We will assume we have two large objects and that their times both read 0 at the same time, which is the start of the observation, in an observer’s reference space. We will assume that our cyclic system is very large, (the Milky Way galaxy for example) and our objects are the earth and moon.
Under these constraints we can conclude that 
and 
both scale, when
scaled to a reference space, to essentially the same value which we shall call
. We will later discuss what happens when they can’t be
considered to scale to the same value.
We write the following equations for both.
Object 1 Object
2
eq. 4.0 
eq. 4.1
eq. 4.2 
eq. 4.3
Now we take the square root of each equation using the Dirac matrices.
eq.
4.4 
eq 4.5
eq 4.6 
eq. 4.7
P and S are vectors but we can simplify them to one dimension. Since we only have two objects we make one axis lie on the line connecting the objects. We assume that they at rest relative to our observer at time 0, so we need only concern ourselves with one component of P which also will lie on the same axis. S is simply the distance between them in their respected spaces.
Now we multiply equation 4.4 by equation 4.7. If we assume that the total energy for both objects remains constant over the length of any measurement, then this is no different than saying 2 x 2 = 4.
The result of the multiplication is:
These are massive objects and 
remains small over the time of our observation. From
our previous discussion, this could literally be millions of years. is
essentially 
We will eliminate the term 
as it is very small compared to 
.
This leaves 
.
We can evaluate the change in P to get:
Now from equation 4.7
We can now “vaporize” the matrices by squaring and then taking the square root to get;
but
This leaves us with:
where we are using 
Now we convert everything to our common reference frame
using the following relations. Remember that simple becomes by the restrictions we
set.
. The reference energy for space and time are
distinguished since they may be different.
and 
Substituting yields
dividing
by 
and substituting
We get 
In the above discussion I arbitrarily used but I could have used 
and got the opposite
force. Could there be anti-gravity?
No need for dark
matter
It is also clear that the gravitational “constant” as
developed here is not a constant but is proportional to , the total space time distance from the origin of the
rotating system. It is common knowledge that the amount of known mass in any
galaxy is not sufficient to hold it together using
Next I will show that the cyclic nature of the universal invariant is responsible for the Hubble equation regarding the apparent expansion of the universe.
The universal invariant clearly describes a circle. Space
and Time can be considered to be the 
and 
where 
is an angle relative
to some axis for small angles.
It would appear that for large galaxies, the increase in
this angle from the “beginning” to the present hasn’t been too large (about 
).
The “linear” space time we perceive is the tangent to a sine wave.
This is illustrated below.
Space and time are about 4 degrees different now then when
we look far back in time. Since the angle is small, the tangent of it is very
nearly equal to the angle. From relativity we know that the tangent of the
angle is equal to 
and we expect a near
linear relationship between the apparent velocity of things and their distance
from us. This is exactly what is perceived.
I must note that this isn’t a true velocity. In fact, things may very well be moving towards us.
Another interesting consequence is the appearance of black
holes at the center of galaxies. Clearly large objects near the center would
have to have small values of space (rotated near 
). A rotation of this amount virtually shrinks space down to
nothing and would appear as a dark region. Beyond the “event horizon” we would
expect an entire region of space time where negative space is growing and time
is running backwards. In fact for each quadrant there is an expanding/shrinking
space with time moving either forward or backward.
I will now show that for small objects using the universal invariant we can infer relativistic quantum mechanics. It is obvious that small objects must be represented by cyclic functions if our measurement resolution time is not small enough.
Consider the equations
We can normalize it to
where
we simply divided by .
We can multiply anything by 1 so we write:
(
) (
)
Now we can write 
and 
, since the universal invariant traces out a circle.
() (
)
we can take the square root again using the Dirac matrices to yield:
(
)
For simplicity I have treated S as a single variable.
What is clear is that replacing with and replacing any one
of the variables on the left side with 
yield a similar
equation with 
equal to the sum of
other two variables.
I do not intend in this paper to develop a quantum like theory using the universal invariant but rather to point out that it seems a rather natural outcome of this theory for small objects.
One thing is clear: Small objects such as electrons complete life cycles. They go backwards and forward in “linear”space and time depending on the quadrant they are in.
If they were to exit at a different time than they started their previous cycle, there would be two of them. It is clear that they must remain in some stable cycles. Any additional motion apart from their natural cycle must be related in frequency in such a way that they start out at the same point in space and time as the previous cycle.
If an electron were confined to an orbit around a proton for example, then it is clear that its orbital angular momentum must be related to its intrinsic angular momentum.
The success of Borh’s assumption was the result of requiring the electron to come back to the same point in space and time.
It also appears that they can cheat by borrowing energy. For example, one can get out of phase by producing a positive and negative pair where the positive one replaces it in the proper cycle.
We can think of additional motion as cycles on top of or perpendicular to the space time circle. Whatever the case the waves must be standing waves.
If a mathematician were asked to find all possible cyclic paths that resulted in an electron being in the same place and time each cycle and he were given the mathematical constraints and knew that the results could be represented by sinusoidal functions, he would set up a differential equation based on the constraints to find all possible paths.
Space and time are coupled. The common method of finding solutions to quantum equations is separation of variables. It is clear that the phase relationship between space and time is lost by doing so.
A new time variable must be introduced and the question of
just what time variable is the linear one we perceive must be asked. If it is
in fact the t of that is, in fact, perceived as linear then the time we use in
relativity and everything we just did are not linear. We would expect than that
universal constants might be changing over time.
It would appear that a relationship between Planks constant and the gravitational constant exist.
Clearly there is a lot of exciting work ahead with this theory.
Please email me with comments and questions.
I posted a web site with answers to frequently asked
questions. http://members.triton.net/daveb/
http://members.triton.net/daveb