Physics and Logic.
By David Barwacz
© 2003 David Barwacz
Physicists have been successful in taking the macroscopic things we perceive and molding their properties into mathematical equations in attempts to understand microscopic things. By working in this “backwards” fashion they have generated many good theories, which unfortunately get more and more complex even though common sense might expect things to become simpler.
One could expect that the building blocks of something should not be more complicated then the structure into which they assemble. Try to describe a two by four in terms of the number of bathrooms and windows in a house. If all you could see and knew about were the bathrooms and windows you would have a formidable task. Your description of a two by four would end up being a function of the variables bathrooms and windows. If someone found a flaw in your description (no doubt there would be many) you could patch the formula to account for it, which in most cases would make it even more complex.
In the past, theories have been built with the underlying assumption that space and time, particles and forces etc. exist. The particles have been given many strange properties and space and time have been bent and twisted but the assumptions of the very existence of these always remain.
In this paper I do not assume the existence of space, time, matter or energy.
I will show that simple logic may be behind the constructs of this universe. I will show that actual working theories can be developed using this premise. In fact, some unanswered questions of physics such as baryon asymmetry of the universe, the uncertainty principle and the wave nature of particles, quarks and possibly even gravity can be explained quite simply.
It has long been accepted that there is a connection between the observer and the observable and that the very nature of consciousness may play a role in measurements of physical values. The global consciousness project ( see http://noosphere.princeton.edu/) has logged some surprising results suggesting that consciousness may indeed affect the physical world.
One could write volumes on the “interplay” of consciousness and the physical world and I am sure it has been done. I will not belabor that point but simply state that after much reflection one must conclude that consciousness could very well be all that exists.
If so, then we can start with the assumption that a type or types of logic rather than an assumption of space/time and matter/energy may give some insight into the nature of the “things” we perceive.
That is simple to say, but where does one start? The language of logic doesn’t give many tools. It is a language of 1’s and 0’s, T’s and F’s etc.
After many attempts, I finally found a logical method that seems to work.
I start with the assumption that at least some of the things that we perceive are made of “parts. The ”parts” may be thought of as a defining characteristic but need not actually have any properties. Since we don’t know what the parts are, we may assume that each of them is also made of parts, call them subparts. And again since we don’t know what the subparts are we can only assume that they are made of parts. We can immediately see that this process continues on to infinity.
Consider the situation where the number of parts equals the number of subparts. That is, if we assume something has 4 parts then its parts each have 4 parts and each of those has 4 etc. We also assume that to make a complete observable ‘thing’ we must combine 4 (or whatever number of parts we are looking at) sets of ‘definitions’ of the things. The example below should help clarify what I mean by definition.
Example: Suppose that you could define every color as a combination of 4 other colors.
The minimum thing you could say about color x is that it contains color y, where y is one of the 4 colors that that make up x. But this minimum definition has no meaning unless you have at least a minimum definition of y. If we say y contains z then we have the same dilemma again since we need at least a minimum definition of z. Of course this continues on infinitely, but the result is a minimum definition of the color.
Of course what we are dealing with is just an abstraction and not related to color or any other physical property. In our abstraction we will assume that we can combine 4 of the minimum definitions to define the property.
The next assumption is that the amount by which each component adds to the total definition is equal to it’s percentage of the total. x in the example above would get a weight of 1/4 while y would be assigned a weight of 1/16 and z gets1/64 etc.
Writing this as the equation yields: 
which equals 
Similarly using 3 parts we have: 
which
equals 
And in general 
= 
To produce a complete definition we must combine m sums.
For example using 4 parts, we must combine 4 sums.
As an equation this can be written as: 
= 1
+
And using 3 parts 
= 1
+
And using 2 parts 
= 1
+
What we find is that we produce more than a whole. In the case of 4 parts we made 4/3 of a unit.
Since we can’t be certain that these properties are additive it may be better to just say we have 3 properties of value ½ of something and 4 properties of value 1/3 of something.
By the word property, I mean something we can perceive, observe, measure or conclude exist based on other observations in the world as we know it. It may be a particle, a property of a particle or something entirely different.
We can rewrite the equations in the form - 1 - =0
Doing so gives us what we will call the anti properties. An anti property simply undefines a property. We also assume that anti properties have opposite arithmetic values from their counterparts.
To try to assemble these properties and anti properties into something, I will list them below, separating the properties from the anti properties. The area to the left side of the line we will simply call a view and the right side we will call not view or anti view. I will list the anti properties as positive values with the understanding that they will be negative when viewed from the positive side. Using this convention, a property will switch signs if moved from one side to the other. We also write the 1 as the sum of parts ( they are in bold). We will look at two property sets, made by ¼ and 1/3. We have:
|
view ⅓ ⅓ ⅓ ⅓ ½ ½ ½ |
anti view ⅓ ⅓ ⅓ ⅓ ½ ½
½ |
Now we can try to draw parallels to present day physical theories. It is universally believed that everything is made of particles. Without accepting or denying that belief we shall proceed as if it is true.
Doing so requires that a particle have only one value of any distinguishable property. It wouldn’t make sense to say, for example that a particle has a charge of 1 and a charge of 2/3. It further makes sense to say that any individual particle has one value of any property we can observe. For example, all particles are thought to have spin even if the value is 0.
Using the above reasoning, if we try to make particles out of the table above we have a problem, in that there are too many 1/3s to match the 1/2s. If we combine properties, say 2 of the 1/3s and pair them to one of the 1/2s we can get around this problem. These two 1/3s can now be represented by one property of 2/3s, however should a spare ½ become available we can separate them back into individual 1/3s.
Accepting the fact that we must combine at least some of the properties we can combine them as shown below. I combined the 4 1/3s on the view side to 2 2/3s . I also labled the columns.
|
view A B C
⅔ ⅔ ½ ½ - ½
|
anti view D E F G ⅓ ⅓ ⅓ ⅓ - ½ ½ ½
|
Now, swapping column C with F, and then combining C with E (changing the signs according to convention) we get:
|
view A B F
⅔ ⅔ - ⅓ ½ ½ - ½
|
anti view D E G ⅓ ⅓ ⅓ - ½ ½ ½
|
Any physicist will recognize that the left side looks like the three quarks description of a proton.
At this point we will assume that the ½s are the physical property spin and that the 1/3s and 2/3s are the physical property charge and we will call the original 1/3’s charge proto quarks and the 1/2’s spin proto quarks.
A critic may be tempted to point out that the values we assign to spin and charge are arbitrary. This is true, however the multiples are not. If we gave spin a value of 7.5 we would still determine that it comes in multiples of half integer and integer. This is fundamental to its nature.
The right side looks like a negative particle of charge -1 and spin 1/2. One might be tempted to say it represents an electron, but it may make more sense to make an electron out of 3 charge proto quarks and one spin proto quark. The charge proto quarks in an electron described this way would be indistinguishable.
In this little two particle universe we are limited in what we can build but it nevertheless instructive.
Swapping one of the 2/3s on the left with one of the 1/3s on the right produces two neutral particles. In fact if the right side were an electron, this would explain electron capture and suggest that no positively charged particle can combine with a negatively charged particle without also producing two neutral particles. This would work just as well if the electron was represented by 3 charge proto quarks and one spin proto quark.
Some other interesting observations are listed below.
Charge Neutrality
This theory results in charge neutrality. You cannot produce a positive charged particle without making a negative charged particle of equal value.
Meson creation.
All swapping involves a particle and an anti particle. If the particles making the swap were to combine they would have charge of 0 or 1 and spin of 0 or 1. Could these be Mesons or even force carriers?
Symmetry between matter and anti matter
In this representation what we called a proton was actually 4 parts charge “matter” and 1 part charge “anti matter”. It also contained spin matter and spin anti matter. In a universe built this way there would be perfect symmetry between the amount of matter and anti matter. This is because there is nothing preventing a definition and an anti definition from being part of the same statement.
Leptons may be made of proto quarks.
We can make charge proto quarks indistinguishable (by limiting spin proto quarks). Leptons could be made of proto quarks in this way. Another possibility is that the proto quarks that made up the “1” may be in fact be indistinguishable and therefore could represent leptons..
Force carriers can be made of proto quarks.
Since Leptons could be made of proto quarks so can the force carriers. A photon can be considered a quark anti quark exchange between an electron and a proton for example.
Properties are bound by logic.
The 3 components of any observable property set are a logical set. They are not bound by color forces or any other forces. They simply make up a set of properties that combine to form an observable property.
From here on I will refer to a property element as one of the elements of a property set (i.e. a 2/3 in the 2/3, 2/3, 1/3 set)
When developing this idea we ignored the distinguishable characteristic of the values. Going back to the color example, each of the 1/4s could be distinguished (A,B,C,D). If we take this into account we would have a large number of different quark types. Using some symmetry arguments can limit the amount. For example it might make sense to say if you have an A definition you must have a not A. Or perhaps an A and B require a not A and not B in the anti projection.
The sums can be treated as a group. The operation of multiplying any member by m and subtracting 1 gives a member of the group.
Another interesting fact is that our group operation, can be reapplied an infinite number of times. Proto quarks for example can be split into 4 new proto quarks. It is reasonable to assume that these may have distinguishing properties.
One might be wondering if space/time, mass, energy or any other properties can be generated in this way. Indeed they can as we shall see next.
Assume we take a large number x and apply this reasoning to it. The sum would equal 1/(x-1). Using the generating formula gives x/x-1 properties and x/x-1 anti properties. Matching these properties with our proto quarks and swapping columns as before yields the following diagram:
|
view A B F
⅔ ⅔ - ⅓ ½ ½ - ½
|
anti view D E G ⅓ ⅓ ⅓ - ½ ½ ½
|
The columns have been swapped as before.
Now within one set we can make a number of different sub sets. We could replace the m in the A column with m+1 and the n in the B column with n-1.
The key points are:
1) Any observable
(particle for example) will have an infinite number of properties.
2) If 
represents a property
element in a set and elements are not allowed to equal zero than: -1 <
< 1. For large numbers the maximum value is
very nearly 1 even if elements can equal zero.
These two points at first seem rather troublesome; however we shall see that they result in some surprising physics.
One would expect that as the numbers get larger and larger the properties become harder to distinguish. From the spin/charge results we can assume that it is the denominator that defines the property. As the denominators get larger the properties become less distinguishable. Rather than treating these as separate properties we might assign them all to one property and give that property a large number of values or possible values (in essence creating a continuum).
If we pick a particular property and call it energy-momentum, for example, then we have all the rest to assign to something. Since spin, charge and energy-momentum are taken we might assign them all to space/time or one to space/time and define another physical property to assign the rest to.
This infinite set of properties and the fact that they are very similar as the denominator increases explains the uncertainty principle.
For example;
I ask Stan to retrieve the value of energy-momentum and space- time for an observable. He comes back and gives me an exact value for energy-momentum but says that his space/time measurement could be anything. He just couldn’t narrow it down. This is a perfectly acceptable result and I would tell him he has done a good job.
Now I give Carol the same task with another observable. She returns with an exact value for energy-momentum and an exact value for space-time but says she noticed a property she calls property X that she just couldn’t get a value for at all. This also is a perfectly acceptable result and she has done a good job as well.
Now I ask Jim to retrieve the values of the energy-momentum and space-time for an observable, but I specify exactly what conditions of space-time and energy-momentum I want. He returns the values exactly but says the observable had a lot of other properties. This too is a good result.
We can see that there really isn’t an uncertainty in measurements as long as we can distinguish one property from another.
As I said previously, I have not yet worked out exactly how properties combine. I have however found some interesting results which I will describe next.
Assume we have a property set:
( a b -c)
Multiplying it by 1 seems harmless:
( a b -c) * 1
What is 1 in property set notation? Let’s assume e+f-g =h, then e+f=h-g. Dividing by h-g we have e/h-g + f/h-g = 1. Let’s rewrite this as j + k =1
We now multiple:
( a b -c) * ( j+k)
Now we try to relate this to present day physics.
Everything in physics today assumes orthogonal dimensions (at least locally). In this theory physical dimensions don’t really exist. If we are to draw any parallels to present physical theories we need a mathematical method to create dimensionality.
What makes dimensionality? A mathematical definition might involve the Pythagorean Theorem. We certainly have properties available which we can square, so we can rewrite this as:
( a2 + b2 -c2 ) ( j2 + k2 )
These are not the same values squared; I simply used the same symbols.
Now recognizing that all properties are less than one, and (j)2 + (k)2 =1, we can rewrite it as:
( a2 + b2 -c2 ) ( cos2θ + sin2θ )
Now we rely on the Dirac matrices and replace θ with 
we can rewrite it as (taking the square root):
( 
a + 
b -c) (cos + isin)
Now replace c by - i
and multiple through to yield:
{( a + b) (cos + isin )} = 
(isin + cos)
Calling a + b –c, p + m – E, we have a formula that looks very much like a relativistic quantum mechanics formula for a free particle. We could replace any of the variables with an operator and the right side could just as easily represent space.
Why the Dirac matrices? After developing the basis for this theory it became clear that there had to be way to combine properties to form other properties. It would also be nice if they paralleled dimensional theories. Dirac’s matrices do just that. They take property sets treated dimensionally and combine them to form a property set. That they work is evidence in favor of this property theory. It is also interesting to note that the complex notation required is no surprise. Since properties in no way suggest dimensionality it is simply a mathematical construct.
Another very interesting observation is that the “quantum mechanics” like formula derived here is basically the same as multiplying two relativistic invariants or two property sets.
Of course there are questions to be answered. Two that were most troubling to me are: How does an invariant become a probability like wave? How can values between -1 and 1 account for physical values?
As to the second question, the actual value of time in the above equation would be:
(sin-1k)/E.
For any value of k there are an infinite number of angles (every 2 pi radians).
This is not out of line with present quantum theory where a free particle can be anywhere.
An interesting observation that we shall explore in more detail below is that time and/or space made this way is non linear.
There is yet another way to get an infinite range of values. Consider the formula;
x 2 + y 2 - 1 = 0 eq. 4
Taking the square root, again using the dirac matrices yields;
1x + 2y -c = 0 eq.
5
This equation implies that x and y can take on any values.
But equation 4 could have been written as cos2θ + sin2θ - 1 = 0
And the square root would be 1cosθ + 2sinθ- = 0
There are obviously two different ways to represent the square root using Dirac matrices.
As to the first question, the probability waves of present day quantum theory can be explained as follows.
In the above equation we used one property set and treated each sub set as a function of an angle. In actuality there would be an infinite number of property sets. As we described earlier, if we had no other properties to assign these to, we would have an infinite set of equations to describe all possible space-time values of the particle.
It would be nice to combine them into a single equation.
We first must recognize that all actual observable property values are rational numbers.
Say we have 4 numbers a, b, c and d. The number of rational numbers between b-a relative to the number between d-c is |b-a|/|d-c|. Obviously the number is infinite for either range but the ratio is finite and equal to the value for all numbers. Now the relative number of rational numbers between sinθ and sin(θ+∆ θ) is:
which
is just the cosθ. Using his reasoning it is easy to see that
combining all the equations and dividing by the total possible number of
choices results in the exact same functional form.
How might we get from the quantum formula to classical mechanics? In present theory this is accomplished by a wave packet that somehow gets created and somehow stays together. I’m not sure anyone has ever really liked that explanation. I have developed a somewhat more plausible explanation. It requires the property theory just described but also a slightly different take on relativity theory.
The reasoning is as follows:
Everything in property theory must be in the proper form, (a + b -c) for example. The time we used above is just a number. We must get some real physical time that is in the proper form and hopefully makes sense in terms of our more trusted physical theories.
Below I develop a relativistic time and space set in the proper form.
To help understand this time, we’ll use Einstein’s long train description. His 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. He then went on to show that the time was dilated when one was moving relative to the other by a formula based on the lorentz transform. The nature of the equation didn’t help 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 ticked off seconds only half as fast as the other clock. Each clock had a special measuring scale (ruler) attached to it. The more massive clocks 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 had inches that were only half inches when measured by the ruler on the less massive clock.
All observers were aware of these conditions before the experiment. The observers were able to read gauges that read only the total energy of each clock (the energy due to it’s 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. In some formulations of relativity it is said that the clocks mass doubled. The total energy gauges clearly displayed the clocks total energy relative to the stationary clock. At the velocity where the clocks energy was double its rest energy the stationary observers noticed that the moving clocks time was only ticking at ½ its original speed (1/4 of the stationary clocks rate) and it’s units of measure were only one half their original value (1/4 of the stationary clocks 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 ½ (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 (unit of measure) was simply an inverse ratio of the total energy.
This much simpler explanation of time dilation and length contraction only works if the observer’s clock rates are set according to their respective masses when at rest relative to one another, and an appropriate measuring scale is attached but it does work.
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 is because aging is related to molecular times not the macroscopic total mass time.
One might argue that when one glues an object to another it doesn’t shrink. Again, the size of the object is based on its molecular/atomic size and it’s time on its molecular/atomic time.
We use the total energy time/space representation when we are dealing strictly with macroscopic properties. Take an object orbiting a planet for example. It’s time/space should be the total energy space/time for the purpose of describing its orbit.
It must be noted that when Einstein first developed special relativity these kind of questions were battered around for years and in fact many still are. If we can accept that voids (space/time) can have different measures of space/time than it is not a major leap to accept that certain properties of objects can have different space/time measures.
What is clear is that using the formulas is perfectly good physics. In fact it is much more symmetrical, treating rest energy the same as kinetic energy.
If we lived in a world where everyone had total energy gauges and things moved very fast we might indeed attach a ruler and a clock to each object based on its rest energy. As these things whizzed by at high speeds we could use simple ratios based on our energy gauges to do our calculations.
In this formulization of special relativity, time and space are properties of an object not of an assumed continuum (space/time).
Based on this we can develop the following equation (the speed of light is assumed to be 1).
T
= T
+ T
where;
TE = 1/E, Tm
= 1/m, and
T = v/m where E is the total energy, m is the rest
mass and v is the velocity which as of yet we haven’t developed in this
theory.
TE is the time related to the total energy, Tm is the time related to the rest energy or mass and Tp is the time related to the momentum. It is obvious that Tm is an invariant.
Next we must discuss frequency. It is commonly accepted that
all matter has a frequency associated with it. Since frequency is proportional
to energy we can quickly develop the following equation.
= 
+ 
Which is just a renormalization of 
= 
+ 
Here again it is obvious that the invariants are and
I assume all appropriate constants are equal to one.
What frequency is appropriate in a relativistic quantum formulation?
We will now guess that the frequency appropriate is (due to the momentum
of the particle.)
We will use the invariant time T and 
and apply them to our
“quantum like” formulization above. If we used the invariant s2 – t2 where s2 = x2 +
y2 + z2 in the
above example then what we call space is (cos-1j)/E and time is (sin-1k)/E.
But E is just . ( I haven’t put any constants in
this formulization. If this troubles the reader just assume
planks constant or whatever constant is applicable equals 1.)
Now if this represents a large object, say a baseball then t (time) relative to say an electron is extremely slow. On the order of magnitude of 10 - 30.
It could be expected that the time it takes this baseball to complete a cycle is on the order of trillions of years. In fact over any reasonable period of time the baseball’s angle doesn’t change. It is very small and we can replace the inverse cosj with j. Our true invariant divided by the energy becomes equal to our actual measured values.
The actual measured values of space and time are non linear and as such are approximate when assumed to be true invariants.
To prove the non linearity of measured space time we should look at the value of physical constants from as far back in time as we can. If this theory is correct we should find variations. Since the time angle could be extremely small and virtually linear we might not expect a substantial difference but there should be some detectable changes.
To say this differently, everything is going through quantum cycles. Large things just take extremely long times to do it and because they have barely ticked off any time the angle is small and effectively equal to the measured values.
To say it differently again, quantum mechanics and classical mechanics are basically the same. Large things stay put not because of some magic holding a wave packet together but because they rotate so slowly we never see the effect of it.
An important consequence of this is:
As time increases
space shrinks.
As time increases space shrinks. In fact it eventually shrinks to nothing and then expands as time starts running backwards. The four quadrants all have different combinations of expanding or contracting space and time. For an electron this is happening rapidly. It is no surprise that all we see is a cloud. It is appearing in and out of time and space and as we shall see quite likely going through phases of anti gravity.
Let us analyze two large objects in this “incredible shrinking space”.
I will assume that our property representing energy-momentum multiplied by our property representing space/time yields a property and that this property is a constant.
Start with a simple property ( a + b - c)
Lets expand this using Dieac matrices to yield
(
1p2 + 2m2 -E2) (1S2 - 2T2 -12)
Where S represents space and T represents time.
Taking the square root of the right hand property
(space/time) we get S – T -1 =0 which quickly yields 
S =
- T
Now p2 S2
= a, so
p = - S*k/ S2 where
k is the square root of a.
Substituting mv for p ( even though we have yet to develop the concept of velocity
in this theory) and - T for S and rearranging we get:
m 
= k/ S2
Now substituting
F=
k/ S2 which
is functionally equivalent to
It must be noted that in this crude representation we haven’t yet made two “things” so it doesn’t make sense to expect this formula to have the mass product as a factor of k.
This does nevertheless provide a plausible explanation of gravity.
In property theory space can only represent the distance between the two objects or an object and an observer.
Space is not a continuum.
Gravity would appear to be nothing more than the quantum cycling effects on a large and extremely slow time scale. It would also help explain the observations that the matter in the visible universe is insufficient to slow down the expansion as fast as it appear to be slowing. The non linear terms in the inverse sine are all positive and would result in more apparent gravity..
Anti gravity may even be able to be produced in a laboratory.
What next?
This theory is in a very crude form. Much work needs to be done,
I have not yet developed any precise methods to combine or split properties. Some algorithm is needed.
Perhaps one fixed property will be adequate to expand into all observable properties of an observable. If so then multiple property sets might be possible. If so we can anticipate that such things as virtual particle pair creation and quantum amplitudes might be explainable.
At the very least this theory shows that simple logical reasoning can be used to create properties and values similar to those believed to be the basis of our reality.
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© 2003 David Barwacz
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