- #1
OneEye
A little parable. Sorry about the length, but I welcome responses and speculations based on this little gedanken.
Dr. Aphos is a brilliant and innovative theoretical physicist. He is also blind. This is not a particularly noteworthy fact where Dr. Aphos is concerned, since he is a resident of a universe parallel to ours, identical in every respect, with this one exception: No creature on the whole of the parallel Earth is endowed with the faculty of sight. All are blind; all use sound, smell, hearing, and touch to navigate. As a consequence of this, neither Dr. Aphos nor any creature in his world has ever traveled faster than a slow walk. The dangers are too great.
The level of scientific advancement of Dr. Aphos’ world is approximately equal to that which pertained in our Earth in the late Victorian era, with the obvious exception that nothing is known of light and its effects. Some primitive work has been done to catalog the diurnal warming effects (though the existence of the sun is, of course, unknown), but the field of solar and astronomical theory is for obvious reasons primitive and insubstantial. No serious scientist attempts to investigate diurnal warming and cooling; it is only the subject of speculation for crackpots and amateurs.
However, Dr. Aphos is famous for advancing two ideas: First, the good doctor has successfully shown that the Earth is a finite, measurable mass, and has successfully estimated its weight within 1% of the correct value. This he did by extrapolating the principles of gravity which had been investigated and categorized some centuries before his time. Further, Dr. Aphos has advanced the idea that the Earth moves, but has done so on purely philosophical grounds, believing that it is unnecessarily anthropocentric to think otherwise.
In order to prove this view out, Dr. Aphos constructs an experiment: Drawing on the newly-recognized wave properties of sound, Dr. Aphos arranges a table which contains a flute (blown by a rotary bellows) and an arrangement of baffles, dampers, and reflectors. The tone emitted by the flute is thus directed along two courses, of the same length but at right angles to each other, and then rejoined in one meeting place. (Physics students will recognize in this apparatus a sonic duplication of our own Michelson-Morley experiment.)
Dr. Aphos reasons that, if the Earth is indeed moving, its motion will be detectable via a difference in the speed of sound on different axes relative to the motion of the earth. This variation in the speed of sound will result in wave interference between the two, differently-routed, sound signals. Implicit in this experiment is the idea that the Earth moves through the medium of sound.
Imagine Dr. Aphos’s surprise, then, when his experiment produces no interference at the nexus of the recombined tones! Dr. Aphos repeatedly rechecks his results, moving his apparatus in a variety of ways, reorienting it, moving it to the top of a tower, then to the third basement of a great house, inside a cave and into a public square, and in every kind of weather. Dr. Aphos even tries orienting his table vertically, and inverting it! But all to no avail, since the speed of sound measures constant in every direction.
Needless to say, this result proved quite a setback for Dr. Aphos. He could see only one conclusion: The earth, indeed, was not moving relative to the medium of sound. He was crestfallen. It was at this point that Dr. Aphos did what, in retrospect, was probably unethical, was certainly regrettable, and turned out to be unnecessary: Dr. Aphos buried his experiment and the results. Literally. The table, flute, bellows, dampers, and reflectors all went into a hole in the garden, and Dr. Aphos hid his results from his peers. For two decades, Dr. Aphos kept his secret, contenting himself with such trivial research as he later came to call “conjuring tricks.” But his secret gnawed at him – and he gnawed at it.
Eventually, Dr. Aphos came to a new realization regarding his experiment: The results only proved that the Earth was static if one assumed that sound traveled through a medium. If one dispensed with the concept of this “ether”, then it only made sense that sound would travel at the same velocity in every direction, even if the Earth were moving.
Dr. Aphos then began constructing a new physics based on this concept: That the speed of sound (c) would be measured to be the same to all observers. This led Dr. Aphos to some startling conclusions.
To begin with, the concept of distance must be relative. Specifically, when two observers are moving relative to each other, they would each perceive the others’ distances as contracted. Also, the concept of time must be relative: When two observers are moving relative to each other, they would perceive each other as experiencing a dilation of time. Based on the constancy of c, Dr. Aphos derived mathematical relationships for time dilation and distance contraction in the form of the following formulas:
Physics students will immediately recognize our Lorentz Transformations. And the physics student will also recognize the process of deriving these equations – from the fact of an unaltering c – from their physics classes. Those who are unfamiliar with this process of reasoning are commended to Dr. Einstein’s care in his book, Relativity: The Special and General Theory (Crown Publishers, Inc.; New York), especially Appendix I. The chief difference between our Lorentz transform and the Aphos equations, however, is that c is the velocity of light in our equations, but the velocity of sound in Dr. Aphos’s.
Dr. Aphos’s theory of the motion of the Earth is thus rescued by disposing of the “ether” theory of sound wave propagation and by adopting a new theory of special relativity which results in the velocity of sound being identical to all observers at any speed. Most astonishing of all is Dr. Aphos’s direct conclusion that “the velocity c plays the part of an unattainable limiting velocity.” This shocking conclusion is sure to be one of extraordinary controversy – especially since the velocity c is, here, the speed of sound, not that of light.
What are we to make of this? Although the physical laws are identical in Aphos’s universe to those of ours, we have here a peculiarity: Dr. Aphos correctly believes that the Earth moves, but incorrectly jettisoned the idea of an etheric medium for sound propagation. However, he did so on the grounds of correct observations. Finally, Dr. Aphos uses his observation of the apparent constancy of the velocity of sound to derive a set of equations which, though agreeable in form to ours, are certainly wrong in one constant, and in their practical conclusions. A false cosmology plus correct observations and correct theoretical practice leads to the wrong conclusion – but one which appears cogent, and which appears to accord well with other observations.
So, what reflections might this little parable cause us to make on the theories which we, in our universe, hold? Can we use this thought exercise to reflect on our own theoretical construct? If so, how? Something to think about…
Dr. Aphos Discovers the Theory of Relativity
Dr. Aphos is a brilliant and innovative theoretical physicist. He is also blind. This is not a particularly noteworthy fact where Dr. Aphos is concerned, since he is a resident of a universe parallel to ours, identical in every respect, with this one exception: No creature on the whole of the parallel Earth is endowed with the faculty of sight. All are blind; all use sound, smell, hearing, and touch to navigate. As a consequence of this, neither Dr. Aphos nor any creature in his world has ever traveled faster than a slow walk. The dangers are too great.
The level of scientific advancement of Dr. Aphos’ world is approximately equal to that which pertained in our Earth in the late Victorian era, with the obvious exception that nothing is known of light and its effects. Some primitive work has been done to catalog the diurnal warming effects (though the existence of the sun is, of course, unknown), but the field of solar and astronomical theory is for obvious reasons primitive and insubstantial. No serious scientist attempts to investigate diurnal warming and cooling; it is only the subject of speculation for crackpots and amateurs.
However, Dr. Aphos is famous for advancing two ideas: First, the good doctor has successfully shown that the Earth is a finite, measurable mass, and has successfully estimated its weight within 1% of the correct value. This he did by extrapolating the principles of gravity which had been investigated and categorized some centuries before his time. Further, Dr. Aphos has advanced the idea that the Earth moves, but has done so on purely philosophical grounds, believing that it is unnecessarily anthropocentric to think otherwise.
In order to prove this view out, Dr. Aphos constructs an experiment: Drawing on the newly-recognized wave properties of sound, Dr. Aphos arranges a table which contains a flute (blown by a rotary bellows) and an arrangement of baffles, dampers, and reflectors. The tone emitted by the flute is thus directed along two courses, of the same length but at right angles to each other, and then rejoined in one meeting place. (Physics students will recognize in this apparatus a sonic duplication of our own Michelson-Morley experiment.)
Dr. Aphos reasons that, if the Earth is indeed moving, its motion will be detectable via a difference in the speed of sound on different axes relative to the motion of the earth. This variation in the speed of sound will result in wave interference between the two, differently-routed, sound signals. Implicit in this experiment is the idea that the Earth moves through the medium of sound.
Imagine Dr. Aphos’s surprise, then, when his experiment produces no interference at the nexus of the recombined tones! Dr. Aphos repeatedly rechecks his results, moving his apparatus in a variety of ways, reorienting it, moving it to the top of a tower, then to the third basement of a great house, inside a cave and into a public square, and in every kind of weather. Dr. Aphos even tries orienting his table vertically, and inverting it! But all to no avail, since the speed of sound measures constant in every direction.
Needless to say, this result proved quite a setback for Dr. Aphos. He could see only one conclusion: The earth, indeed, was not moving relative to the medium of sound. He was crestfallen. It was at this point that Dr. Aphos did what, in retrospect, was probably unethical, was certainly regrettable, and turned out to be unnecessary: Dr. Aphos buried his experiment and the results. Literally. The table, flute, bellows, dampers, and reflectors all went into a hole in the garden, and Dr. Aphos hid his results from his peers. For two decades, Dr. Aphos kept his secret, contenting himself with such trivial research as he later came to call “conjuring tricks.” But his secret gnawed at him – and he gnawed at it.
Eventually, Dr. Aphos came to a new realization regarding his experiment: The results only proved that the Earth was static if one assumed that sound traveled through a medium. If one dispensed with the concept of this “ether”, then it only made sense that sound would travel at the same velocity in every direction, even if the Earth were moving.
Dr. Aphos then began constructing a new physics based on this concept: That the speed of sound (c) would be measured to be the same to all observers. This led Dr. Aphos to some startling conclusions.
To begin with, the concept of distance must be relative. Specifically, when two observers are moving relative to each other, they would each perceive the others’ distances as contracted. Also, the concept of time must be relative: When two observers are moving relative to each other, they would perceive each other as experiencing a dilation of time. Based on the constancy of c, Dr. Aphos derived mathematical relationships for time dilation and distance contraction in the form of the following formulas:
[tex]{ x^\prime = { { x - vt } \over { \sqrt { 1 - { v^2 \over c^2 } } } } } \quad { t^\prime = { { t - { v \over c^2 }x } \over { \sqrt { 1 - { v^2 \over c^2 } } } } } [/tex]
Physics students will immediately recognize our Lorentz Transformations. And the physics student will also recognize the process of deriving these equations – from the fact of an unaltering c – from their physics classes. Those who are unfamiliar with this process of reasoning are commended to Dr. Einstein’s care in his book, Relativity: The Special and General Theory (Crown Publishers, Inc.; New York), especially Appendix I. The chief difference between our Lorentz transform and the Aphos equations, however, is that c is the velocity of light in our equations, but the velocity of sound in Dr. Aphos’s.
Dr. Aphos’s theory of the motion of the Earth is thus rescued by disposing of the “ether” theory of sound wave propagation and by adopting a new theory of special relativity which results in the velocity of sound being identical to all observers at any speed. Most astonishing of all is Dr. Aphos’s direct conclusion that “the velocity c plays the part of an unattainable limiting velocity.” This shocking conclusion is sure to be one of extraordinary controversy – especially since the velocity c is, here, the speed of sound, not that of light.
What are we to make of this? Although the physical laws are identical in Aphos’s universe to those of ours, we have here a peculiarity: Dr. Aphos correctly believes that the Earth moves, but incorrectly jettisoned the idea of an etheric medium for sound propagation. However, he did so on the grounds of correct observations. Finally, Dr. Aphos uses his observation of the apparent constancy of the velocity of sound to derive a set of equations which, though agreeable in form to ours, are certainly wrong in one constant, and in their practical conclusions. A false cosmology plus correct observations and correct theoretical practice leads to the wrong conclusion – but one which appears cogent, and which appears to accord well with other observations.
So, what reflections might this little parable cause us to make on the theories which we, in our universe, hold? Can we use this thought exercise to reflect on our own theoretical construct? If so, how? Something to think about…
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