General Discussion > Aspect Relativism
Horace,
I don't think that I do treat them independently. The duality (two "directions") of both numbers and physical magnitudes is the property of more than or less than. In number systems, negative numbers are considered less than positive numbers. However, increasing the value of a negative number makes it more negative, while increasing the value of a positive number makes it more positive, Thus, increase is possible in two "directions," negative and positive.
It is the same in the case of space|time physical magnitudes, A given value of space|time progression can be more than or less than another value, in two "directions," positive or negative.
However, space cannot have a value independent of time and vice versa, just as the denominator of a rational number has no meaning without a corresponding numerator and vice versa. The expansion/contraction of the space aspect of a unit of space|time progression is an expansion/contraction of space, in all space directions, relative to a given point of space, over time. Likewise, the expansion/contraction of the time aspect of a unit of time|space progression is an expansion/contraction of time, in all time directions, relative to a given point of time, over space.
Nevertheless, since time does not have direction in space, and space does not have direction in time, the progression of the space aspect over time is the motion of space expansion/contraction, while the progression of the time aspect over space is the motion of time expansion/contraction.
These two, reciprocal, aspects of the progression are indistinguishable from the persepective of locations in their respective domains; In other words, what we call space from the less than unit perspective, behaves as time from the more than unit perspective, and vice-versa.
Regards,
Doug
I don't think that I do treat them independently. The duality (two "directions") of both numbers and physical magnitudes is the property of more than or less than. In number systems, negative numbers are considered less than positive numbers. However, increasing the value of a negative number makes it more negative, while increasing the value of a positive number makes it more positive, Thus, increase is possible in two "directions," negative and positive.
It is the same in the case of space|time physical magnitudes, A given value of space|time progression can be more than or less than another value, in two "directions," positive or negative.
However, space cannot have a value independent of time and vice versa, just as the denominator of a rational number has no meaning without a corresponding numerator and vice versa. The expansion/contraction of the space aspect of a unit of space|time progression is an expansion/contraction of space, in all space directions, relative to a given point of space, over time. Likewise, the expansion/contraction of the time aspect of a unit of time|space progression is an expansion/contraction of time, in all time directions, relative to a given point of time, over space.
Nevertheless, since time does not have direction in space, and space does not have direction in time, the progression of the space aspect over time is the motion of space expansion/contraction, while the progression of the time aspect over space is the motion of time expansion/contraction.
These two, reciprocal, aspects of the progression are indistinguishable from the persepective of locations in their respective domains; In other words, what we call space from the less than unit perspective, behaves as time from the more than unit perspective, and vice-versa.
Regards,
Doug
April 25, 2007 |
Doug
Doug
How do you determine the "direction" of eg. space, alone ? Huh?
What is this negative, decreasing quantity? Relative to what?
I say it is relative only to a SECOND unit of motion that constitutes an observer.
It makes no sense do define "direction" of one aspect within a single unit of motion. A unit of motion cannot observe itself !
What is the negative shrinking spatial volume, with time "direction" disregarded? Whatever happended to the reciprocal principle "less time is equivalent to more space"?
Shrinking time volume is equivalent to growing space volume, and vice versa.
I claim that the "directions" you're musing about can be defined only between at least two units of motion.
What is this negative, decreasing quantity? Relative to what?
I say it is relative only to a SECOND unit of motion that constitutes an observer.
It makes no sense do define "direction" of one aspect within a single unit of motion. A unit of motion cannot observe itself !
What is the negative shrinking spatial volume, with time "direction" disregarded? Whatever happended to the reciprocal principle "less time is equivalent to more space"?
Shrinking time volume is equivalent to growing space volume, and vice versa.
I claim that the "directions" you're musing about can be defined only between at least two units of motion.
April 26, 2007 |
Horace
Horace
Horace,
Very good questions! Let me try to answer. First, we must understand that the "direction" of scalar (M4) motion is not the direction of vector (M2) motion, which, as you point out, must be motion relative to another entity. The "direction" of scalar (M4) motion is a less than, greater than "direction." That's why it always appears in quotes. The quotes are meant to distinguish this "direction" from the direction expressed by angle.
Unlike the infinite number of values that angles defining direction can take, there are only two values that "direction" can take. We can arbitrarily designate these two "directions" as positive and negative "directions." In the quantitatively interpreted concept of numbers, the positive "direction" is the opposite of the negative "direction," relative to a given number, representing quantity; that is, given two quantities, one greater than the other, there is always another quantity greater than them both.
However, in the operational interpretation of number, the concept of number is not expressed as a standalone quantity, but rather it is expressed as a relation between two quantities. Thus, the relationship between the two quantities can take only one of two values:
1) Equal, or
2) Unequal
If the relationship between the two quantities is unequal, then it can be unequal in one of two "directions," less than equal, or greater than equal, and which is which is a completely arbitrary designation, because of the perfect symmetry of nothing; that is, an equal relationship between two quantities is perfectly symmetrical. There is zero difference between them.
Now, if we have an operationally defined value that is less than equal, and one that is greater than equal, there is a "distance" between them of some number x. In the case of the minimum imbalance, 1, the "distance" between these two "directions" is 2. We can express this distance in quantitatively interpreted numbers, as three integers:
-1, 0, 1
Hence, just as we can say that -1 is a single number in the negative "direction," we can say the same thing about it's corresponding operationally interpreted number: it is a single, unequal, relationship on the negative side of the equal condition, as shown below:
1/2, 1/1, 2/1
If the above three numbers were quantitatively interpreted rational numbers, they would be equal to
.5, 1, 2.
However, the operational interpretation makes them equal to
-1, 0, 1,
because the rational number is interpreted as possible displacements (differences) between two quantitites.
When we turn to considering numbers as physical magnitudes, we have to have some explanation as to what the numbers represent. In the RST, the explanation is contained in the fundamental postulates of the system: numbers must represent magnitudes of motion, because it's a system of nothing but motion.
The difference between numbers and magnitudes of motion is that motion defines a change of quantities, not static quantities. Thus, the first operationally defined number, 1/1, is employed to represent a one to one change of space and time units in the RST. We can write this symbolically as
ds/dt = 1/1,
where ds is the change rate of space and dt is the change rate of time. Numerically, we can define any operationally interpreted number as a combination (sum) of numbers
(1+n)/(1+m),
but to do this physically we have to have a physical principle upon which to base a change in the change rate. In the RST, this physical principle is called "direction" reversal. In "direction" reversal, the change rate of the denominator, or the change rate of the numerator is altered by a series of "direction" reversals in the reciprocal aspect of the unit of motion.
The best way to understand this is to imagine the denominator and numerator of the initial motion in terms of two, electronic, counters, incrementing at precisely the same rate. If at a certain count, one, or the other of the two counters, decrements its count, instead of incrementing it, and then continues to increment/decrement its count between two values from that point on, while the reciprocal counter continues to increment its count normally, the relative rate of increase between the two counters will be altered, from 1|1, to 1|2, or 2|1, depending upon which counter begins alternately reversing its counting "direction" (We substitute the pipe symbol "|" for the division symbol "/" to distinguish the operational from the quantitative interpretation of the rational number.)
In other words, the continuous "direction" reversals in one of the two counters, reduces the change rate of increase by half in that counter, relative to the unaltered counter, changing, or imbalancing, the previously balanced rate, at that location.
To physically interpret this change from increase to decrease, or vice versa, at every count, in the numbers of the altered counter, we have to envision a physical increase from a point x to a unit volume at point x + 1. The subsequent decrease would then be from volume x + 1, to point x.
If the reversing counter is the numerator counter, which corresponds to the space counter in the equation of motion in the material sector, then the reciprocal counter, the time counter, simply increases at each count. If the reversing counter is the denominator, which corresponds to the time counter in the equation of motion in the material sector, then the reciprocal counter, the space counter, simply increases at each count.
In the research of the LRC, these two possibilities correspond to the space unit-displaced ratio (SUDR) and the time unit-displaced ratio (TUDR), and, as you point out, the "shrinking time volume is equivalent to the [expanding] space volume, and vice versa."
Hope this clarifies it better for you.
Regards,
Doug
Very good questions! Let me try to answer. First, we must understand that the "direction" of scalar (M4) motion is not the direction of vector (M2) motion, which, as you point out, must be motion relative to another entity. The "direction" of scalar (M4) motion is a less than, greater than "direction." That's why it always appears in quotes. The quotes are meant to distinguish this "direction" from the direction expressed by angle.
Unlike the infinite number of values that angles defining direction can take, there are only two values that "direction" can take. We can arbitrarily designate these two "directions" as positive and negative "directions." In the quantitatively interpreted concept of numbers, the positive "direction" is the opposite of the negative "direction," relative to a given number, representing quantity; that is, given two quantities, one greater than the other, there is always another quantity greater than them both.
However, in the operational interpretation of number, the concept of number is not expressed as a standalone quantity, but rather it is expressed as a relation between two quantities. Thus, the relationship between the two quantities can take only one of two values:
1) Equal, or
2) Unequal
If the relationship between the two quantities is unequal, then it can be unequal in one of two "directions," less than equal, or greater than equal, and which is which is a completely arbitrary designation, because of the perfect symmetry of nothing; that is, an equal relationship between two quantities is perfectly symmetrical. There is zero difference between them.
Now, if we have an operationally defined value that is less than equal, and one that is greater than equal, there is a "distance" between them of some number x. In the case of the minimum imbalance, 1, the "distance" between these two "directions" is 2. We can express this distance in quantitatively interpreted numbers, as three integers:
-1, 0, 1
Hence, just as we can say that -1 is a single number in the negative "direction," we can say the same thing about it's corresponding operationally interpreted number: it is a single, unequal, relationship on the negative side of the equal condition, as shown below:
1/2, 1/1, 2/1
If the above three numbers were quantitatively interpreted rational numbers, they would be equal to
.5, 1, 2.
However, the operational interpretation makes them equal to
-1, 0, 1,
because the rational number is interpreted as possible displacements (differences) between two quantitites.
When we turn to considering numbers as physical magnitudes, we have to have some explanation as to what the numbers represent. In the RST, the explanation is contained in the fundamental postulates of the system: numbers must represent magnitudes of motion, because it's a system of nothing but motion.
The difference between numbers and magnitudes of motion is that motion defines a change of quantities, not static quantities. Thus, the first operationally defined number, 1/1, is employed to represent a one to one change of space and time units in the RST. We can write this symbolically as
ds/dt = 1/1,
where ds is the change rate of space and dt is the change rate of time. Numerically, we can define any operationally interpreted number as a combination (sum) of numbers
(1+n)/(1+m),
but to do this physically we have to have a physical principle upon which to base a change in the change rate. In the RST, this physical principle is called "direction" reversal. In "direction" reversal, the change rate of the denominator, or the change rate of the numerator is altered by a series of "direction" reversals in the reciprocal aspect of the unit of motion.
The best way to understand this is to imagine the denominator and numerator of the initial motion in terms of two, electronic, counters, incrementing at precisely the same rate. If at a certain count, one, or the other of the two counters, decrements its count, instead of incrementing it, and then continues to increment/decrement its count between two values from that point on, while the reciprocal counter continues to increment its count normally, the relative rate of increase between the two counters will be altered, from 1|1, to 1|2, or 2|1, depending upon which counter begins alternately reversing its counting "direction" (We substitute the pipe symbol "|" for the division symbol "/" to distinguish the operational from the quantitative interpretation of the rational number.)
In other words, the continuous "direction" reversals in one of the two counters, reduces the change rate of increase by half in that counter, relative to the unaltered counter, changing, or imbalancing, the previously balanced rate, at that location.
To physically interpret this change from increase to decrease, or vice versa, at every count, in the numbers of the altered counter, we have to envision a physical increase from a point x to a unit volume at point x + 1. The subsequent decrease would then be from volume x + 1, to point x.
If the reversing counter is the numerator counter, which corresponds to the space counter in the equation of motion in the material sector, then the reciprocal counter, the time counter, simply increases at each count. If the reversing counter is the denominator, which corresponds to the time counter in the equation of motion in the material sector, then the reciprocal counter, the space counter, simply increases at each count.
In the research of the LRC, these two possibilities correspond to the space unit-displaced ratio (SUDR) and the time unit-displaced ratio (TUDR), and, as you point out, the "shrinking time volume is equivalent to the [expanding] space volume, and vice versa."
Hope this clarifies it better for you.
Regards,
Doug
April 27, 2007 |
Doug
Doug
Doug,
And how do you propose to distinguish in|in from out|out without resorting to an "observing unit" ?
see:
http://forum.rs2theory.com/fileattachments/inout_210.gif
...INward and OUTward are directionless words, devoid of vectorial angle connotations.
And how do you propose to distinguish in|in from out|out without resorting to an "observing unit" ?
see:
http://forum.rs2theory.com/fileattachments/inout_210.gif
...INward and OUTward are directionless words, devoid of vectorial angle connotations.
April 28, 2007 |
Horace
Horace
Horace,
I'm not sure that I understand your question. Abstractly, the outward "direction" is the "direction" of increasing quantity, increasing numbers, while the inward "direction" is the "direction" of decreasing quantity, decreasing numbers. With regards to units of space|time progression, this translates to increasing, or decreasing space|time.
However, since time never decreases in the material sector, and space never decreases in the cosmic sector, one of the two conditions, depicted in your graphics, is not possible; that is, it's not possible for both aspects of an instance of space|time progression to decrease simultaneously. One aspect is always continuously increasing, while its reciprocal aspect alternately increases and decreases.
Hence, in the case where the progression of one aspect, or the other, is alternating, one-half of the cycle is a unit increase of space|time while the other half is a decrease of space, or time, but never both.
This indicates that a phase difference between units of the same type is possible, creating something like "up" and "down" spin, I think, where two quantum states are possible, relative to each other. In other words, various SUDRs (or various TUDRs) can be either in phase, or out of phase.
Doug
I'm not sure that I understand your question. Abstractly, the outward "direction" is the "direction" of increasing quantity, increasing numbers, while the inward "direction" is the "direction" of decreasing quantity, decreasing numbers. With regards to units of space|time progression, this translates to increasing, or decreasing space|time.
However, since time never decreases in the material sector, and space never decreases in the cosmic sector, one of the two conditions, depicted in your graphics, is not possible; that is, it's not possible for both aspects of an instance of space|time progression to decrease simultaneously. One aspect is always continuously increasing, while its reciprocal aspect alternately increases and decreases.
Hence, in the case where the progression of one aspect, or the other, is alternating, one-half of the cycle is a unit increase of space|time while the other half is a decrease of space, or time, but never both.
This indicates that a phase difference between units of the same type is possible, creating something like "up" and "down" spin, I think, where two quantum states are possible, relative to each other. In other words, various SUDRs (or various TUDRs) can be either in phase, or out of phase.
Doug
April 29, 2007 |
Doug
Doug
Doug,
I think you are not understanding my question because you haven't thought along those lines. I would dare to venture that this issue is the proverbial white patch on your map of understanding.
I strongly disagree with such statements as "time never decreases in the material sector".
Take the low and high frequency photons, or electrons and positrons.
In these phenomena, I bet the cosmic-Doug also claims that "his" time never decreases", but his time is YOUR space, and you know very well that your space "decreases", just like he knows that his space "decreases", but wait ... his space is your time, thus you cannot be both correct!
I won't explain more now as not to confuse you, but think about it seriously and keep an open mind. I think this is the piece you are missing...
I think you are not understanding my question because you haven't thought along those lines. I would dare to venture that this issue is the proverbial white patch on your map of understanding.
I strongly disagree with such statements as "time never decreases in the material sector".
Take the low and high frequency photons, or electrons and positrons.
In these phenomena, I bet the cosmic-Doug also claims that "his" time never decreases", but his time is YOUR space, and you know very well that your space "decreases", just like he knows that his space "decreases", but wait ... his space is your time, thus you cannot be both correct!
I won't explain more now as not to confuse you, but think about it seriously and keep an open mind. I think this is the piece you are missing...
April 29, 2007 |
Horace
Horace
Horace,
I have thought about this for months and, you are right, it is confusing. One has to be really careful to avoid speculation and ad hoc inventions.
Presently, I'm taking the approach that, in the case of a discrete instance of space|time motion, two, reciprocal, physical perspectives are possible, one above and one below unity. In one of these, the reversing aspect of the instance appears as an expanding/contracting sphere, while its reciprocal appears as a true scalar (point) at the center of the sphere.
Meantime, the same instance, from the reciprocal perspective, is the inverse of this; that is, what was the point becomes the sphere, and what was the sphere becomes the point.
Mathematically, this is consistent with the four linear spaces of the 2^3 = 8 octonion, which, when combined together, form the 2x2x2 Larson cube. The first space is the point (2^0 = 1); the second space is the line (2^1 = 2); the third space is the plane (2^2 = 4), and the fourth space is the volume (2^3 = 8).
Of course, the fourth space also contains the first, second, and third spaces - it's an all in one space, so-to-speak, and as soon as we remember that the number 2 is actually 2/1, we recognize that its inverse, 1/2, has the same exact, but inverse, spaces.
Hence, (1/2)^0 = 1/1, (1/2)^1 = 1/2, (1/2)^2 = 1/4, and (1/2)^3 = 1/8, which, consequently, is the exact inverse of Larson's cube, or Larson's cube turned inside out, if you will.
When we make the numbers deltas of space or time, or physical magnitudes, then the magnitudes correspond to the numbers. This is very good news.
Doug
I have thought about this for months and, you are right, it is confusing. One has to be really careful to avoid speculation and ad hoc inventions.
Presently, I'm taking the approach that, in the case of a discrete instance of space|time motion, two, reciprocal, physical perspectives are possible, one above and one below unity. In one of these, the reversing aspect of the instance appears as an expanding/contracting sphere, while its reciprocal appears as a true scalar (point) at the center of the sphere.
Meantime, the same instance, from the reciprocal perspective, is the inverse of this; that is, what was the point becomes the sphere, and what was the sphere becomes the point.
Mathematically, this is consistent with the four linear spaces of the 2^3 = 8 octonion, which, when combined together, form the 2x2x2 Larson cube. The first space is the point (2^0 = 1); the second space is the line (2^1 = 2); the third space is the plane (2^2 = 4), and the fourth space is the volume (2^3 = 8).
Of course, the fourth space also contains the first, second, and third spaces - it's an all in one space, so-to-speak, and as soon as we remember that the number 2 is actually 2/1, we recognize that its inverse, 1/2, has the same exact, but inverse, spaces.
Hence, (1/2)^0 = 1/1, (1/2)^1 = 1/2, (1/2)^2 = 1/4, and (1/2)^3 = 1/8, which, consequently, is the exact inverse of Larson's cube, or Larson's cube turned inside out, if you will.
When we make the numbers deltas of space or time, or physical magnitudes, then the magnitudes correspond to the numbers. This is very good news.
Doug
April 29, 2007 |
Doug
Doug
How about you think why the high frequency photons appear the same as the low frequency photons (besides the frequency - of course).
Specifically, why it makes no difference whether the "direction" reversals happen in space or time.
If you get stuck, consider why the temporal reversals can give the illusion of spatial reversals, if we make the assumption of uniformly expanding time. (less time is more space, and vice versa, one at the expense of the other, bla bla bla...)
Specifically, why it makes no difference whether the "direction" reversals happen in space or time.
If you get stuck, consider why the temporal reversals can give the illusion of spatial reversals, if we make the assumption of uniformly expanding time. (less time is more space, and vice versa, one at the expense of the other, bla bla bla...)
May 2, 2007 |
Horace
Horace
Horace,
If you look at the photon S|T unit, it's all green, or balanced in both space and time reversals (same number of SUDRs and TUDRs). This means, then, that the frequency must be a matter of total speed-displacement. The more displacement, the lower the frequency. However, this also means an upper limit (minimum displacement) exists. I don't know what observation indicates about that.
Doug
If you look at the photon S|T unit, it's all green, or balanced in both space and time reversals (same number of SUDRs and TUDRs). This means, then, that the frequency must be a matter of total speed-displacement. The more displacement, the lower the frequency. However, this also means an upper limit (minimum displacement) exists. I don't know what observation indicates about that.
Doug
May 2, 2007 |
Doug
Doug
It seems that way as long as you consider SUDR and TUDR collectively without considering them individually.
May 5, 2007 |
Horace
Horace
Maybe there are ONLY localized (pointlike) time scalar reversals, which have the effect of contracting the normal scalar expansion of space. If we are going to propose that space is physically "real", how can you simply smash it inward again, except by a time reversal? This time-oscillating, contracting/expanding space unit would still be carried outward at c, but it would also pulsate as it goes.
Just a thought. I'm really worried about how to create a LINEARLY vibrating photon.
Just a thought. I'm really worried about how to create a LINEARLY vibrating photon.
May 8, 2007 |
Dave
Dave
Hi Dave,
The SUDR becomes a stationary unit of oscillating space, expanding time, while the TUDR becomes a stationary unit of oscillating time, expanding space. Combining the two together, then, the S|T combo becomes an expanding unit of oscillating space|time.
As for a linearly, vibrating, photon, I'm not sure what you mean.
The SUDR becomes a stationary unit of oscillating space, expanding time, while the TUDR becomes a stationary unit of oscillating time, expanding space. Combining the two together, then, the S|T combo becomes an expanding unit of oscillating space|time.
As for a linearly, vibrating, photon, I'm not sure what you mean.
May 9, 2007 |
Doug
Doug
In your musings, the "direction" of space is independent of the "direction" of time. Why ?
According to Aspect Relativism - no property of space can be considered without relating it to the property of time. In other words: no property of space (or time) stands alone. There is no "background"...
Horace