- #1
Immer Tzaddi
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- TL;DR Summary
- A review of the Lorentz Transformation's derivation has long been a goal. Especially as, it concerns the other quadrants and possible component orientations of the "given" displacement vector.
Recollections of a late Spring semester's lesson describing the derivation of Lorentz's Transformation often solicit many unanswered questions. The textbook used has been secured; however, it is unknown. Whether, that secondary school instructor provided the premises used for the derivation from another textbook or the required reading for the course is unknown. Or if, his given assertion had a "flaw" in them also is uncertain.
What is known is that he provided a standard solution path. Which constructed all of the proof-work among the coordinates of the first quadrant (Q-I). Out of a sense of academic moxie, orneriness, curiosity, or kinesiology; the second quadrant (Q-2) was chosen, personally.
With the northeast quadrant numbered as the primary one (Q-I). And, the cardinality of the quadrants increasing in a clock-wise and not in a counter clock-wise manner. This meant that the displacements along the domain were positive and those along the range were negative. This might seem like the "hand-waving" proof of a "monkeyish" argument. Yet, it seemed that the vector which he presented for the derivation, the one given in the textbook, had positive displacements in both the x- and y-directions. Which was a peculiar constraint for the transformation. Since, it should be a "generalization". The textbook's argument was built solely among the coordinates of the first quadrant.
And although, he might have made a mistake in his description of the given. Along with the fact, the work done in the second quadrant might have had a flaw, such as a dropped or artificially-introduced "sign". The resultant expression was the reciprocal of the traditional Lorentz Transformation.
And, that has left this former student who was quite passionate about physics subconsciously puzzled, for a pair of reasons.
Firstly, a neighbor spied the alternative derivation, reworked it for himself a couple of times, and approached the instructor. Who politely told his pupil that he had been clearly seen and should stop doing what he had been doing for much of the school year. And, it was highly unlikely that his "helper" would successfully make the "transition". He also said that "The Lorentz Transformation has some false quadrants. Which is something that he might encounter and learn more about. If, he pursued physics at the graduate level." Therefore, the associate prefix was chosen for this on-line entry.
Secondly, a few days later, the same instructor was seen reviewing a set of equations on the board. That resembled those used with the Lorentz Transformation. It looked like he was enumerating all of the sixteen "relativistic" possibilities: four different quadrants and positive or negative components describing the displacement vector.
Could someone provide a discrete non-Calculus based description of the Lorentz Transformation and possibly similar references for background reading and review?
Finally, as an educator, outside of the field of physics, who is near the site of his elementary school education. A strange inversion and reversal of directions and orientation when communicating has become glaringly apparent. Primarily because, memories are spatiotemporally located. And, life was vastly different; If not, diametrically-inverted, during those years of elementary school.
The earliest remembered descriptions of the numbering of the quadrants found among coordinate graphs were predicated on the location of the first. Which was in the northeastern corner (Q-I). Then, these progressed "clockwise". Until, they reached the fourth (Q-IV). At some juncture, during passed formal training, these started being numbered in a "counter clockwise" fashion. And, at times, (Q-I), the anchor, has been placed in the northwestern corner of the Cartesian grid. Which makes a "mirror-like", half-rotation of one's perspective and the flow of the quadrant's progression.
Also, the "earliest-description" of the positional numbering system, with its exponents and delimiters and learnt while a fourth grader, described the fractional-portion of a real number as residing on the "left-hand side" of the decimal. With, the weightiest digit on the far "right-hand" side of the value. And, those were the years. When, it was well-understood and communicated that English, as well as, nearly every other Western language was read starting on the right of the page. After which, one's eye scanned leftward. Until, it reached the leftmost part of that line; then, backward, downward, and across the page again. Until, one's eye eventually reached the lower left-hand corner.
Also, that is when it was well-established that any reachable number is finite; based upon the axioms of construction, which undergird our positional numbering system. And, the infinite, by intentional design, is both a unsurpassable and unreachable point on the number line. Because, any new location beyond that old infinity becomes, by the definition the new, and the old one becomes finite.
And, that long-since forgotten lesson resurfaced while working thorough a derivation among other graduate students in later years. One which was pivotal for the development of the theories in that course. As such, it seemed pertinent that a review be made of the fundamentals acquired during earlier years among the core academic subjects.
That is when, the inverted-nature of certain orientations found among diagrams and notations was detected as commonplace. Seemingly, they are the exact opposite of how they were initially introduced. And, it was realized that much had been forgotten concerning cardinal and ordinal numbers plus many other key fundamentals for mathematical learning. Plus, that puzzling, unanswered question concerning Lorentz's Transformation and whether the alternate derivation was truly correct or flawed resurfaced.
So, it seemed rather appropriate that someone who was writing artificially intelligent control routines for synthetic computational units should surely be a master of all of the concepts within the typical primary school and secondary mathematics curriculum. Otherwise, it is highly probable that his work might contain tangible, significant, and problematic reasoning flaws. The very type which might cause the equivalent of a VLSI-aneurism.
If, this question and these comments are not consistent with the policies of this forum. Feel free and remove them.Many Thanks
What is known is that he provided a standard solution path. Which constructed all of the proof-work among the coordinates of the first quadrant (Q-I). Out of a sense of academic moxie, orneriness, curiosity, or kinesiology; the second quadrant (Q-2) was chosen, personally.
With the northeast quadrant numbered as the primary one (Q-I). And, the cardinality of the quadrants increasing in a clock-wise and not in a counter clock-wise manner. This meant that the displacements along the domain were positive and those along the range were negative. This might seem like the "hand-waving" proof of a "monkeyish" argument. Yet, it seemed that the vector which he presented for the derivation, the one given in the textbook, had positive displacements in both the x- and y-directions. Which was a peculiar constraint for the transformation. Since, it should be a "generalization". The textbook's argument was built solely among the coordinates of the first quadrant.
And although, he might have made a mistake in his description of the given. Along with the fact, the work done in the second quadrant might have had a flaw, such as a dropped or artificially-introduced "sign". The resultant expression was the reciprocal of the traditional Lorentz Transformation.
And, that has left this former student who was quite passionate about physics subconsciously puzzled, for a pair of reasons.
Firstly, a neighbor spied the alternative derivation, reworked it for himself a couple of times, and approached the instructor. Who politely told his pupil that he had been clearly seen and should stop doing what he had been doing for much of the school year. And, it was highly unlikely that his "helper" would successfully make the "transition". He also said that "The Lorentz Transformation has some false quadrants. Which is something that he might encounter and learn more about. If, he pursued physics at the graduate level." Therefore, the associate prefix was chosen for this on-line entry.
Secondly, a few days later, the same instructor was seen reviewing a set of equations on the board. That resembled those used with the Lorentz Transformation. It looked like he was enumerating all of the sixteen "relativistic" possibilities: four different quadrants and positive or negative components describing the displacement vector.
Could someone provide a discrete non-Calculus based description of the Lorentz Transformation and possibly similar references for background reading and review?
Finally, as an educator, outside of the field of physics, who is near the site of his elementary school education. A strange inversion and reversal of directions and orientation when communicating has become glaringly apparent. Primarily because, memories are spatiotemporally located. And, life was vastly different; If not, diametrically-inverted, during those years of elementary school.
The earliest remembered descriptions of the numbering of the quadrants found among coordinate graphs were predicated on the location of the first. Which was in the northeastern corner (Q-I). Then, these progressed "clockwise". Until, they reached the fourth (Q-IV). At some juncture, during passed formal training, these started being numbered in a "counter clockwise" fashion. And, at times, (Q-I), the anchor, has been placed in the northwestern corner of the Cartesian grid. Which makes a "mirror-like", half-rotation of one's perspective and the flow of the quadrant's progression.
Also, the "earliest-description" of the positional numbering system, with its exponents and delimiters and learnt while a fourth grader, described the fractional-portion of a real number as residing on the "left-hand side" of the decimal. With, the weightiest digit on the far "right-hand" side of the value. And, those were the years. When, it was well-understood and communicated that English, as well as, nearly every other Western language was read starting on the right of the page. After which, one's eye scanned leftward. Until, it reached the leftmost part of that line; then, backward, downward, and across the page again. Until, one's eye eventually reached the lower left-hand corner.
Also, that is when it was well-established that any reachable number is finite; based upon the axioms of construction, which undergird our positional numbering system. And, the infinite, by intentional design, is both a unsurpassable and unreachable point on the number line. Because, any new location beyond that old infinity becomes, by the definition the new, and the old one becomes finite.
And, that long-since forgotten lesson resurfaced while working thorough a derivation among other graduate students in later years. One which was pivotal for the development of the theories in that course. As such, it seemed pertinent that a review be made of the fundamentals acquired during earlier years among the core academic subjects.
That is when, the inverted-nature of certain orientations found among diagrams and notations was detected as commonplace. Seemingly, they are the exact opposite of how they were initially introduced. And, it was realized that much had been forgotten concerning cardinal and ordinal numbers plus many other key fundamentals for mathematical learning. Plus, that puzzling, unanswered question concerning Lorentz's Transformation and whether the alternate derivation was truly correct or flawed resurfaced.
So, it seemed rather appropriate that someone who was writing artificially intelligent control routines for synthetic computational units should surely be a master of all of the concepts within the typical primary school and secondary mathematics curriculum. Otherwise, it is highly probable that his work might contain tangible, significant, and problematic reasoning flaws. The very type which might cause the equivalent of a VLSI-aneurism.
If, this question and these comments are not consistent with the policies of this forum. Feel free and remove them.Many Thanks
