Dr. Aphos and the Theory of Relativity: A Parable of Perception and Physics

[OneEye]

A little parable. Sorry about the length, but I welcome responses and speculations based on this little gedanken.

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:

$${ x^\prime = { { x - vt } \over { \sqrt { 1 - { v^2 \over c^2 } } } } } \quad { t^\prime = { { t - { v \over c^2 }x } \over { \sqrt { 1 - { v^2 \over c^2 } } } } }$$​

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…

 

[turin]

I appologize, I did not read the entire parable. A few things that did strike me as odd:

How could this blind society have the same technology as ours did a century ago? Our society has clearly developed with an intimate correlation to our visual faculty, and to pose a parallel society that has made all of the same, or even analogous advancements over several millennia without such a faculty I find just a tad far-fetched. For one, it would be quite phenomenal to be able to conduct many of the scientific efforts required. For another, I doubt that the need for many of our societies technologies would even occur to this society in the first place.

I don't believe that such a regular periodic phenomenon as a diurnal warming cycle would be condemned as crackpottery. It would be obvious to everyone with the faculty for sensation of temperature. Something of this level of profundity that is so ubiquitously undeniable could hardly be considered mere speculation.

How has the doctor shown the finite mass of the earth? How can sense be made of the concept of the weight of the Earth without reference to other celestial bodies (the concept of there existence being completely inaccessable to this society)? The principles of gravity, if they are to be cast in any recognizable form to our society, also require the observation of the celestial bodies. Otherwise, there would only be this virtually constant g-field that we all used in freshman physics to arrive at our parabolic trajectories (or, in more advanced courses, the logarithmic assymptotes).

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.

This is why I stopped reading. I have nothing against a philosophical basis; in fact, I prefer it. But to cast this as a parallel philosophical breakthrough to that of Einstein is absurd. Where are Maxwell's equations to scoff at the earlier mechanics of Newton? Philosophically, why should there be anything through which the Earth moves? I don't have a very good idea what would be my scientific phenomenology if I were blind. In fact, I read about an blind astrophysicist that has made tremendous contributions to his field, so I can't rule out the feasability. But, for the entire society to be based on senses other than sight is too large a gap to allow such an analogous consideration, IMHO.

 

[OneEye]

turin,

Sorry that the apparatus of the parable threw you off so badly. Of course, a world populated by sightless creatures would be completely unlike ours, since, as you say, sight is fundamentally integral to the mechanisms of our biosphere. But, the parable required that the effects of sound be considered in a solitary fashion, and that no creature be able to travel at a significant fraction of the speed of sound - and this seemed an expedient way to serve those ends. Further, when reading any parable, one must accept some poesy and allow some artistic liberty - not getting caught up in the economies of the parabolic milieu, but rather focusing on the author's essential concerns. I admit to more than a little irony in constructing the parable thus, with the intention of demanding a "suspension of disbelief" on the part of the reader. Apparently, this did not work well for you - and for this, I tender my apologies.

I was developing quite a sense of astonishment: My little tale languished for almost a week - over eighty reads - and despite its sharply controversial nature, still no replies. I was obliged to speculate as to why this might be. Was the parable so tiresome that no-one read it through? Was my communication so foggy that no-one could fathom it? Was my point so plebian as to be unworthy of comment? In any case, I supposed that there must be some defect in the story, else I should have expected some sort of discussion. It seems that you would opt for the first explanation (though I have had some favorable offline reviews from others,) but I worried about the length to begin with. So, perhaps this is the explanation for the now-only-almost-complete silence regarding my little story: A gedanken of this length strains the medium, and so might be better shopped in a different agora.

By the way, the "discovery" of Aphos was not that the Earth moved in space, but rather a conception of relativity which we would claim to be "wrong", but which is derived in an almost identical manner to the theory of special relativity - hence an examination of the theoretical and observational grounds for our own theory.

Also, one could come to a good estimate of the Earth's mass by a simple comparison between $F=ma$ and $F=mg$ - though the calculation of G would require some scrupuluous work. One begins by assuming that the earth, which is made of matter, is the cause of the gravitic attraction which the terrestrial observer experiences, continues by deciding that the mass of the Earth is finite, and then constructs a series of relatively simple, Newtonian experiments which pit various accelerational forces (EMF, chemical propulsion) against gravity to determine the magnitude of the Earth's mass. That, I had already thought through.

I wish that you had made it through the rest of the story, since I think that it raises some important considerations. The fact that Dr. Aphos got the wrong answer despite following a course of reasoning which we consider completely valid is, I think, tremendously provocative. However, as your response implies, perhaps this is not the right venue for such considerations.

In any case, thank you for taking the time to reply. I was starting to get a complex!

 

[turin]

... the parable required that the effects of sound be considered in a solitary fashion, and that no creature be able to travel at a significant fraction of the speed of sound - and this seemed an expedient way to serve those ends.

Well, this premise would require quite a suspension of disbelief on my part at the very least. What would you consider a significant fraction of the speed of sound. I would suggest that an interferometry would be able to distinguish any discrepancies on the order of a % of a % of the speed of sound. Why couldn't an experiment be conducted in uniform motion wrt the air? I think certain things would be obvious from a scientific standpoint, such as the definitiveness of motion wrt the air, induced eddy currents, the lack of sound propogation in a vacuum, and such.

I was developing quite a sense of astonishment: My little tale languished for almost a week - over eighty reads - and despite its sharply controversial nature, still no replies.

I appologize. Apparently I decided to take leave from the forums for a while at the same time that you posted, so I wasn't doing my part.

Was the parable so tiresome that no-one read it through?

I would suspect.

Was my communication so foggy that no-one could fathom it?

I doubt it. Your posts have always been relatively clear, IMO.

Was my point so plebian as to be unworthy of comment?

Absolutely not. But, it seems to me that you have attempted a similar point on occasion, and perhaps this is beginning to agitate some of the patrons.

In any case, I supposed that there must be some defect in the story, else I should have expected some sort of discussion.

I would say there is a defect. There is no analog to Maxwell's equations (and the associated experimentally demonstrated phenomena), which are essential to the theoretical/philosophical development/motivation of SR.

... the "discovery" of Aphos was not that the Earth moved in space, but rather a conception of relativity which we would claim to be "wrong", but which is derived in an almost identical manner to the theory of special relativity - hence an examination of the theoretical and observational grounds for our own theory.

There was nothing wrong with the experimental results of Aphos' experiment. I must have missed his/her explicit conclusion. There was some talk of a burial and whatnot, but I didn't quite follow the scientific ramification. I still am not at all in agreement with the philosophical basis for the Earth to be moving through anything. From my interpretation of the parable, the Earth is the universe to the people as far as they can tell. It would be analogous to us saying that the entire universe moves, but that wouldn't make any sense to me. If that's your point, then maybe you could develop it further.

One begins by assuming that the earth, ... is the cause of the gravitic attraction which the terrestrial observer experiences, continues by deciding that the mass of the Earth is finite, ...

Why would one make either of these two assumptions. They are not reasonable IMO. I see no reason to attribute the acceleration of gravity to the existence of the universe in a nontrivial way. For these people, the existence of the Earth is unavoidable, and they have no observations (through any of their senses, directly or indirectly) to apply to a situation that excludes the existence of the Earth (i.e. the universe). For all they know, the acceleration is exactly a fundamental field that exists by virtue of existence itself, and their model of reality is not simplified nor empowered by attributing it to the existence of the earth.

The fact that Dr. Aphos got the wrong answer despite following a course of reasoning which we consider completely valid is, I think, tremendously provocative.

Why is it provocative? What wrong answer did he/she get? Scientists have periodically encountered such a situation in our sighted society throughout history (of science). That is exactly what separates science and philosophy. Pure reasoning can conceive of things that do not actually exist, or, at least, things that are contrary to experimental evidence. Oh, and just so that we understand each other on this point, I do not consider the reasoning completely valid.

 

[Eyesaw]

OneEye titled his essay a "parable" for a reason, turin- means you should
read it carefully- or better yet, finish reading it before you reply. How do
you explain that if you substituted c for the speed of sound in the Lorentz
Transformations, you get a different time dilation and length contraction factor,
for the same relative velocity between inertial frames than when the speed of
light was used? OneEye provided a fabulous argument against a physical
interpretation of the time dilation/length contraction factors in the Lorentz
Transformations.

 

[turin]

OneEye titled his essay a "parable" for a reason, turin- means you should
read it carefully-

How do you know what the title of the "essay" was supposed to mean? Are you confriming my suspicions? If someone is going to call some "essay" a parable, I actually infer that I should take it with a grain of salt. Since when does calling something a parable elevate it to a level of scrutiny?

- or better yet, finish reading it before you reply.

Well, I was not aware of this qualification. I thought that OneEye would have appreciated my response:

... I welcome responses and speculations ...

, together with the fact that no one else had seemed to bother. Did you, Eyesaw, not have one single comment in the entire week that this essay was posted without reply? Why, only now that I have responded, do you chose to retort? Come to think of it, I don't recall you having ever responded to anything that OneEye has written, yet I have seen you respond in a few of OneEye's threads (to other posters).

How do
you explain that if you substituted c for the speed of sound in the Lorentz
Transformations, you get a different time dilation and length contraction factor,
for the same relative velocity between inertial frames than when the speed of
light was used?

You know, I have never really given any serious consideration to substituting c for the speed of sound. So, I never thought that I had to explain such a thing. Perhaps that makes me a poor scientist.

The only similarity that I consider between light and sound is the mathematical formulation of both phenomena as waves. Beyond that, I do not attach any physical significance, and I do not consider the similarity to be significant. They are even, mathematically, completely different kinds of waves (i.e. longitudinal vs. transverse). Why not suggest a gratuitous relativistic analogy between light and waves in the ocean (which are at least transverse)? Wave nature itself is not what led to SR. I can point out that the reasoning is flawed without reading through the entire "essay," which, might I add IMO, is a credit to OneEye's organisation and clarity.

OneEye provided a fabulous argument against a physical
interpretation of the time dilation/length contraction factors in the Lorentz
Transformations.

I do not deny the fabulousness. What I adduced from OneEye's parable was a flaw in the line of reasoning that ignores the crucial behavior indicated by Maxwell's equations.

 

[Janus]

Just a few problems that I see:

Obviously they should be aware that sound travels at different velocities through different substances, and that the more rigid the object, the higher the velocity. So it would be odd to conclude that the speed of sound through air would be the ultimate speed limit, when you already have evidence that sound itself travels at greater speeds than that at times.

They also would likely have done the bell jar experiment where you pump the air out of a container containing a sound creating device. So they should also be aware that air provides a medium for sound transmission and that the lack of it prevents the propagation of sound.

You say that he gets a null result is any weather. But this would not be the case in a high wind if the device is not enclosed. (And why would it be? They already know that air provides a medium, and they would want to test sound's response to moving air.

Thus your Dr. Aphos would only expect to get a non null reading if the Earth moved with respect to the air surrounding it, but that would create a measurable wind that could be felt.

Thus he must conclude that the Earth carries its air( the sound medium) with it.

He also has no evidence that the air extends much beyond the surface of the Earth. ( in fact, barometric readings would show that the air thins with altitude.) He doesn't detect any sounds that originated from points far removed from Earth. (And no way to detect the sound equivalent of stellar aberration.)

Thus he has no reason to postulate an all prevading medium of sound that fills space and that the Earth moves in respect to.

The upshot is that there is no way that he would ever come up with the equivalent of the Lorentz transformations while experimenting with sound, as you suggest.

 

[Eyesaw]

Just a few problems that I see:

Obviously they should be aware that sound travels at different velocities through different substances, and that the more rigid the object, the higher the velocity. So it would be odd to conclude that the speed of sound through air would be the ultimate speed limit, when you already have evidence that sound itself travels at greater speeds than that at times.

They also would likely have done the bell jar experiment where you pump the air out of a container containing a sound creating device. So they should also be aware that air provides a medium for sound transmission and that the lack of it prevents the propagation of sound.

You say that he gets a null result is any weather. But this would not be the case in a high wind if the device is not enclosed. (And why would it be? They already know that air provides a medium, and they would want to test sound's response to moving air.

Thus your Dr. Aphos would only expect to get a non null reading if the Earth moved with respect to the air surrounding it, but that would create a measurable wind that could be felt.

Thus he must conclude that the Earth carries its air( the sound medium) with it.

He also has no evidence that the air extends much beyond the surface of the Earth. ( in fact, barometric readings would show that the air thins with altitude.) He doesn't detect any sounds that originated from points far removed from Earth. (And no way to detect the sound equivalent of stellar aberration.)

Thus he has no reason to postulate an all prevading medium of sound that fills space and that the Earth moves in respect to.

The upshot is that there is no way that he would ever come up with the equivalent of the Lorentz transformations while experimenting with sound, as you suggest.

Now, this is an excellent response- one that I would've wrote had I
not been so busy. You have grasped the moral of OneEye's parable above when you wrote "Thus he must conclude that the Earth carries its air( the sound medium) with it. ". Like in the case with sound, if light propagates through a medium, it can only be a constant c on Earth for all observers if the medium was stationary with respect to the Earth (i.e., moving along with it like our atmosphere).

And as you concede above that there would not be a null reading for sound if the medium was moving with respect to the Earth (or vice versically, the Earth was moving with respect to the medium), the same logic applies for light, whether it propagates wave-like through a stationary ether (as was assumed in the 19th century), or at a constant c through empty space like a particle since an absolutely stationary frame (such as the 19th century lumineferous ether) is mathematically equivalent to having no ether.

Thus, the MM esperiment null result contradicts the hypothesis of a constant c in vacuo (or in a stationary ether) and we arrive at the moral of the parable- a constant c can only be achieved if the medium was stationary with respect to the lab. This is also equivalent to source dependency of propagating phenomena in the case of particle propagation through empty space.

Dr. Aphos's parody of the Lorentz Transformation was to show that if one were to interpret the result of a constant c as a consequence of the length contraction and time dilation factors from SR, one would get different factors, depending on the type of propagating phenoma we used (sound carried inside a lab with a windspeed with the magnitude of the Earth's motion through empty space but in the opposite direction, or light propagating independently of source speed through the vacuum) as the value of c in the LT. Obviously, LT's time dilation and space contraction has nothing to do with real changes in physical space nor time but are mathematical tools to force a presupposed result of the value c.

 

[Janus]

Now, this is an excellent response- one that I would've wrote had I
not been so busy. You have grasped the moral of OneEye's parable above when you wrote "Thus he must conclude that the Earth carries its air( the sound medium) with it. ". Like in the case with sound, if light propagates through a medium, it can only be a constant c on Earth for all observers if the medium was stationary with respect to the Earth (i.e., moving along with it like our atmosphere).

And as you concede above that there would not be a null reading for sound if the medium was moving with respect to the Earth (or vice versically, the Earth was moving with respect to the medium), the same logic applies for light, whether it propagates wave-like through a stationary ether (as was assumed in the 19th century), or at a constant c through empty space like a particle since an absolutely stationary frame (such as the 19th century lumineferous ether) is mathematically equivalent to having no ether.

Thus, the MM esperiment null result contradicts the hypothesis of a constant c in vacuo (or in a stationary ether) and we arrive at the moral of the parable- a constant c can only be achieved if the medium was stationary with respect to the lab. This is also equivalent to source dependency of propagating phenomena in the case of particle propagation through empty space.

Dr. Aphos's parody of the Lorentz Transformation was to show that if one were to interpret the result of a constant c as a consequence of the length contraction and time dilation factors from SR, one would get different factors, depending on the type of propagating phenoma we used (sound carried inside a lab with a windspeed with the magnitude of the Earth's motion through empty space but in the opposite direction, or light propagating independently of source speed through the vacuum) as the value of c in the LT. Obviously, LT's time dilation and space contraction has nothing to do with real changes in physical space nor time but are mathematical tools to force a presupposed result of the value c.

No, the problem is that Dr, Aphos cannot determine how sound travels beyond the close proximity of the Earth. We, on the other hand can determine how light travels beyond Earth, and we detect light coming from objects removed a great deal from Earth. And due to the movement of the Earth with respect to these sources, we see Stellar Aberration (A shifting in the apparent positons of the stars over the course of a year). We also have the Maxwell equations that determine the speed of light in a vacuum to be constant. Add in the results of the MME.

If the Earth moved in respect to the Ether, then we would see stellar aberration and get a positive result from the MME.

If the Ether moves with the Earth, we get a Null result from the MME, and don't see stellar aberration.

What we actuallyget is a null MME result and stellar aberration. This, combined with the results of the Mawell equations, results in the consclusion the the Speed of light is constant for all observers, and that there is no need for an ether.

Dr, Aphos however does not have the sonic equivalent of the Maxwell equations, nor the sonic equivalent of stellar aberration. He does have the abiltiy to determine that air is the medium of sound propagation, and that air movement gives a positive result with his experiment.

Conclusion, Dr. Aphos' experiments and observations are not an analogy for light, and would not produce the same type of conclusion as those done with light.



MENTOR HAT ON
Be forewarned, I will not let this thread degrade into an argument over the validity of Relativity, those arguments belong in TD.

 

[Eyesaw]

How do you know what the title of the "essay" was supposed to mean? Are you confriming my suspicions? If someone is going to call some "essay" a parable, I actually infer that I should take it with a grain of salt. Since when does calling something a parable elevate it to a level of scrutiny?




Well, I was not aware of this qualification. I thought that OneEye would have appreciated my response:
, together with the fact that no one else had seemed to bother. Did you, Eyesaw, not have one single comment in the entire week that this essay was posted without reply? Why, only now that I have responded, do you chose to retort? Come to think of it, I don't recall you having ever responded to anything that OneEye has written, yet I have seen you respond in a few of OneEye's threads (to other posters).




You know, I have never really given any serious consideration to substituting c for the speed of sound. So, I never thought that I had to explain such a thing. Perhaps that makes me a poor scientist.

The only similarity that I consider between light and sound is the mathematical formulation of both phenomena as waves. Beyond that, I do not attach any physical significance, and I do not consider the similarity to be significant. They are even, mathematically, completely different kinds of waves (i.e. longitudinal vs. transverse). Why not suggest a gratuitous relativistic analogy between light and waves in the ocean (which are at least transverse)? Wave nature itself is not what led to SR. I can point out that the reasoning is flawed without reading through the entire "essay," which, might I add IMO, is a credit to OneEye's organisation and clarity.




I do not deny the fabulousness. What I adduced from OneEye's parable was a flaw in the line of reasoning that ignores the crucial behavior indicated by Maxwell's equations.

I have been busy and didn't see the post until recently. I had written
a little critique on this parable before your response to this thread but
after a little thought, I realized that my quibble did not really alter
the conclusion of the essay so I didn't post it. The complaint I had was similar to yours and janus's in that sound waves are not quite comparable to
light. For example, sound waves don't travel in a vacuum while light apparently does so Dr. Aphos's dispensing of the medium for sound becomes unrealistic. However, after deeper reflection, I came to note that a stationary medium of propagation for sound is mathematically equivalent to
a constant propagating speed through a vacuum, making Dr. Aphos's analogy correct. Dr. Aphos's act of dispensing the ether for sound is of course a reference to Einstein's getting rid of the stationary ether for light.

The much simpler explanation that wasn't explored when SR was in vogue and the MM esperiment showed a null result was the possibility that the ether was moving with the massive bodies.

 

[OneEye]

Janus,

Ah, now this is the sort of response I was hoping for - thoughtful, thorough, apropos. Thank you so much for taking so much time and thinking my post through!

I do confess to premeditatively skewing the parable a little: A people who were so sonically adept would surely, as you say, conclude that sound travels through the medium of air. And the effect of wind on the speed of sound could hardly go unnoticed to a people whose only telemetric sense was sound. But I cheated, and assumed that these two discoveries were still inchoate rather than explicit. And if Dr. Aphos's theory preceded these other two propositions, then (assuming it is accepted,) Dr. Aphos' version of special relativity would tend to derail the other two conclusions, since it would lead to a dogmatic ether-independent theory of sound which would prove extremely hard to unseat. Further, given the right scientific climate, Dr. Aphos's experiment might even have been taken as conclusive proof that sound does not use air as a medium!

I must disagree with you on one point, though: Your assurance that the observation of a varying speed of sound would affect the conclusions of Dr. Aphos's theorizing is probably not true. We observe light to travel at various speeds through various media, but this does not prevent us from concluding that c is an upper limit. We simply use the highest observed value of c.

In addtion, since Dr. Aphos has no conception of the size of the universe, he has no reason to believe that local conditions (i.e., the presence of an atmosphere) do not pertain throughout the universe (which would, therefore, necessarily be rather small).

Then also, just as wind "pollution" would have changed the results of Dr. Aphos's experiment, so would light pollution have interfered with the Michelson-Morley experiment. One can reasonably assume that Michelson and Morley isolated their experiment from errant light sources. One could also reasonably assume that Dr. Aphos isolated his experiment from errant sound sources - hence isolating it from wind effects.

Ultimately, I agree that you have found the weak spot in the parable. But the weak spot that you are pointing out may not be such a great weakness as it first appears. And, as AI Researcher Warren McCullough is reputed to have often said, "Don't bite my finger - look where I'm pointing!"

Thoughts which might come from this:

1) Had Dr. Aphos been possessed of other faculties, he would have been able to observe things which clearly traveled faster than the speed of sound. But, since one cannot use sound to observe things moving faster than sound, Dr. Aphos is limited by his own powers of observation. As are we.

2) Had Dr. Aphos been able to move his experiment "faster than a slow walk", would he have noticed the sort of interference he was looking for? Almost certainly. So if we were able to move our optical apparatus at a significant fraction of c (say, .1c), would we see different results? I have no idea, but then, I suspect that no-one does.

3) Might sound also be subject to relativistic effects? This is, to me, the most exciting question. I can conceive of a few rather inexpensive experiments which might show a Lorentz-type tranform for sonic emitters which move at a significant fraction of the speed of sound.

Anyway, thank you again for taking the time to work this through. I appreciate your feedback.

 

[OneEye]

Come to think of it, I don't recall you having ever responded to anything that OneEye has written, yet I have seen you respond in a few of OneEye's threads (to other posters).

By the way, and for the record: No, there is no relation between "OneEye" and "EyeSaw" - aside from our mutual engagement on the Physics Forums, and the curious fact that we both have noms de plume which are six letters long and contain the term "Eye". Perhaps we will have a laugh on the board one day by discussing the reasons for this curious coincidence.

I must admit that, one time, on one other board of a very different nature, I had two aliases going at once. One was an erudite intellect; the other was a numbskull. However, that board was political in nature and submitted itself well to a particular sort of psychological experiment. On this board, however, I would expect that psychology is irrelevant, and so I can promise that I will never engage in "Starthrower" kinds of theater here. And, if I engage in a board with a given persona, I will stick with that persona whenever I am on that board.

Eyesaw is Eyesaw; OneEye is OneEye - neither is in any way the other. If you are talking to me, you are talking to OneEye, not Eyesaw. If you are talking to OneEye, you are talking to only me.

(By the way, if I had it to do over again, my handle on this board would be "Reference Mollusc." Man, I love that phrase!)

 

[Janus]

Janus,

Ah, now this is the sort of response I was hoping for - thoughtful, thorough, apropos. Thank you so much for taking so much time and thinking my post through!

I do confess to premeditatively skewing the parable a little: A people who were so sonically adept would surely, as you say, conclude that sound travels through the medium of air. And the effect of wind on the speed of sound could hardly go unnoticed to a people whose only telemetric sense was sound. But I cheated, and assumed that these two discoveries were still inchoate rather than explicit. And if Dr. Aphos's theory preceded these other two propositions, then (assuming it is accepted,) Dr. Aphos' version of special relativity would tend to derail the other two conclusions, since it would lead to a dogmatic ether-independent theory of sound which would prove extremely hard to unseat. Further, given the right scientific climate, Dr. Aphos's experiment might even have been taken as conclusive proof that sound does not use air as a medium!

I must disagree with you on one point, though: Your assurance that the observation of a varying speed of sound would affect the conclusions of Dr. Aphos's theorizing is probably not true. We observe light to travel at various speeds through various media, but this does not prevent us from concluding that c is an upper limit. We simply use the highest observed value of c.

The difference here is that we have theoretical grounds for the speed of light in free space being the highest possible value.
With sound, It travels faster the more rigid the medium. Dr. Aphos has no theoretical basis for assuming a top velocity for sound, as he has no reason to exclude the possibility of an perfectly rigid substance for which the speed of sound is infinite. In that case, the Lorentz transformations reduce to the Galieian transformations.

In addtion, since Dr. Aphos has no conception of the size of the universe, he has no reason to believe that local conditions (i.e., the presence of an atmosphere) do not pertain throughout the universe (which would, therefore, necessarily be rather small).

Then also, just as wind "pollution" would have changed the results of Dr. Aphos's experiment, so would light pollution have interfered with the Michelson-Morley experiment. One can reasonably assume that Michelson and Morley isolated their experiment from errant light sources. One could also reasonably assume that Dr. Aphos isolated his experiment from errant sound sources - hence isolating it from wind effects.

Then he would be isolating it from the very effect that he is trying to measure.

Ultimately, I agree that you have found the weak spot in the parable. But the weak spot that you are pointing out may not be such a great weakness as it first appears. And, as AI Researcher Warren McCullough is reputed to have often said, "Don't bite my finger - look where I'm pointing!"

Thoughts which might come from this:

1) Had Dr. Aphos been possessed of other faculties, he would have been able to observe things which clearly traveled faster than the speed of sound. But, since one cannot use sound to observe things moving faster than sound, Dr. Aphos is limited by his own powers of observation. As are we.

No, he is not limited by his lack of sight in order to detect faster than sound movement. He could very easily set up a device that could propel an object at these speeds and use clocks, (with their faces in brail) to time it. the clocks could be rigged to start and stop mechanically.

2) Had Dr. Aphos been able to move his experiment "faster than a slow walk", would he have noticed the sort of interference he was looking for? Almost certainly. So if we were able to move our optical apparatus at a significant fraction of c (say, .1c), would we see different results? I have no idea, but then, I suspect that no-one does.

But we have been able to test the predictions of Relativity. We now have clocks sensitive enough to detect its effects at velocities we can achieve.

3) Might sound also be subject to relativistic effects? This is, to me, the most exciting question. I can conceive of a few rather inexpensive experiments which might show a Lorentz-type tranform for sonic emitters which move at a significant fraction of the speed of sound.

No, sound does not produce any relativistic effects. Sound does require a medium and its velocity is measured with respect to that medium. Light does not require a medium, and its velocity is a constant to all observers.

 

[OneEye]

What we actually get is a null MME result and stellar aberration. This, combined with the results of the Mawell equations, results in the consclusion the the Speed of light is constant for all observers, and that there is no need for an ether.

Janus: I don't mean to trip your mentor trigger, and I am not presently making any proposals, but your assessment is only true if the hyphothetical ether is "rigid" WRT the Earth throughout the entire universe. If the putative ether has some degree of fluidity (as the tensor may be thought to have), then it can be effectively static WRT Earth within the Earth's neighborhood, and at more distant locales be "in motion" WRT Earth (i.e. Earth is moving relative to the ether), thus supporting both the null MME result and stellar aberration.

Again, I am not seriously proposing the existence of an ether (though I must say, I have come to see the MME as much less conclusively anti-ether because of this analogy,) and at present I don't care whether there is an ether or not.

Nor am I waging an assault on SR. My specific intent is to use the parable above to investigate and illuminate SR. Particularly, I believe that SR can stand as valid without accepting some of the unprovable dogmatic baggage which travels along with SR. I am beginning to suspect that SR may be a general principle of finite-velocity measurement wave media, and so I think it possible that there may actually be a separate SR for sound. If so, then this helps separate the strict, factual, mathematical construction from some of the unfortunate philosophical paraphernalia which is promoted as fundamental to the scientific construct of SR.

Hope this helps clear things up. I am not gunning for SR or trying to prove an ether - just trying to find a way to contemplate the principles of SR and thus to examine some of the philosophical elements.

 

[OneEye]

No, sound does not produce any relativistic effects. Sound does require a medium and its velocity is measured with respect to that medium. Light does not require a medium, and its velocity is a constant to all observers.

Here is where I have my doubts. I think that sound does, indeed, behave in a relativistic way. (By which I mean, Special Relativity - and which gloss I use here passim.)

For instance: When an object moves toward me, its sonic emissions are Doppler-shifted "blue" - likewise, when an object moves away from me, the sonic emissions are Doppler-shifted "red". However, the speed of sound, as measured by the stationary observer, remains unchanged.

Every observation and argument which Dr. Einstein makes in the first ten sections of Relativity (regarding light-based measurement of distance and time with regard to two co-moving observers) can also be made with regard to similary-constructed sonar measurements. Why, then, should we not also take the next step and include Section XI?

What I am saying is that I think that, yes, it is probable that relativity is sonic as well as photonic, and this helps us understand what relativity is actually describing - which is different from the philosophical ontology which is usually elaborated from the strict mathematical nature of relativity.

And, to my mind, the presence or absence of a medium is irrelevant to this question - neither helps nor hinders the case. We are used to thinking of relativity as only photonic. But I believe that the theory will work sonically as well.

I certainly welcome your help in clearing this up if I am wrong. But I cannot think of a case in Relativity where we may not consider the case of sound as being equivalent to that of light. Perhaps, with your greater education, experience, and insight, you can be of help here.

 

[Janus]

Janus: I don't mean to trip your mentor trigger, and I am not presently making any proposals, but your assessment is only true if the hyphothetical ether is "rigid" WRT the Earth throughout the entire universe. If the putative ether has some degree of fluidity (as the tensor may be thought to have), then it can be effectively static WRT Earth within the Earth's neighborhood, and at more distant locales be "in motion" WRT Earth (i.e. Earth is moving relative to the ether), thus supporting both the null MME result and stellar aberration.

No, because when the light reached the neighborhood of the Earth it would enter that part of the ether that was traveling with the Earth and would be drug along with it. This prevents any observer on the surface of the Earth from seeing any Stellar Aberration, or at the very least would reduce the degree of its measurement to below that which we actually measure. Our observations do not support that. What you are suggesting is call "ether drag" and it was one of the first suggestions made and discounted.

Again, I am not seriously proposing the existence of an ether (though I must say, I have come to see the MME as much less conclusively anti-ether because of this analogy,) and at present I don't care whether there is an ether or not.

Nor am I waging an assault on SR. My specific intent is to use the parable above to investigate and illuminate SR. Particularly, I believe that SR can stand as valid without accepting some of the unprovable dogmatic baggage which travels along with SR. I am beginning to suspect that SR may be a general principle of finite-velocity measurement wave media, and so I think it possible that there may actually be a separate SR for sound. If so, then this helps separate the strict, factual, mathematical construction from some of the unfortunate philosophical paraphernalia which is promoted as fundamental to the scientific construct of SR.

If you suspect this than you have completely missed the meanings of the fundamental principles of SR. It is not only that light has a finite velocity in vacuum, but that velocity is fixed for all observers, regardless of their mutual relative velocities, this not something that holds for just any wave.

 

[Janus]

Here is where I have my doubts. I think that sound does, indeed, behave in a relativistic way. (By which I mean, Special Relativity - and which gloss I use here passim.)

For instance: When an object moves toward me, its sonic emissions are Doppler-shifted "blue" - likewise, when an object moves away from me, the sonic emissions are Doppler-shifted "red". However, the speed of sound, as measured by the stationary observer, remains unchanged.

But, if there were an observer moving with that object and he was listening to a tone produced by you, then he would also hear the Doppler-shift, but he would measure a difference in the speed of the sound emmited by you (and in fact, if he measured the speed of the sound formt he object next to him, he would note that its speed would depend on what direction it was traveling with respect to his motion. . And here in lies the difference; with sound you can determine who is moving with respect to the medium propagating the sound.

Wiith light however, both observers would still observe the Doppler shift, but each would also measure both the light they receive and transmit as having the same velocity with respect to themselves. Both observers would measure the speed of light as 300,000 km/sec relative to themselves. (rather than one observer measuring the speed of light as c+v or c-v)

Every observation and argument which Dr. Einstein makes in the first ten sections of Relativity (regarding light-based measurement of distance and time with regard to two co-moving observers) can also be made with regard to similary-constructed sonar measurements. Why, then, should we not also take the next step and include Section XI?

No, they can't. If you concluded that, then you misconstrued something.

 

[energia]

I like your Parable

I even like the writing style

as far as comparisons to MMX and aether, the analogy is only plausable if electromagnetic radiation (light waves) are oscillations of aether

Janus makes a good point here...

They also would likely have done the bell jar experiment where you pump the air out of a container containing a sound creating device. So they should also be aware that air provides a medium for sound transmission and that the lack of it prevents the propagation of sound.

You say that he gets a null result is any weather. But this would not be the case in a high wind if the device is not enclosed. (And why would it be? They already know that air provides a medium, and they would want to test sound's response to moving air.

that such a society would have come to the conclusion though day to day experience alone that air exists - since it gets windy at times

they would have discovered that the speed of sound is not constant for all observers since doppler shifts occur with passing sound sources

they might use the horrifying phenomenon of lightning striking trees and other objects followed a moment later by loud thunder, a delay which blind persons would surely notice - as evidence that electricity travels much faster than sound


I like the Parable whether or not it makes a sound (pun intended) analogy

I think the subject of whether or not aether moves with respect to objects of mass in space and on the Earth should be discussed without using the sound analogy, (since soundwaves are produced by oscillations in air pressure, and in fact should be called pressure waves)

unless you're suggesting that light is produced by oscillations in aether

in either case the premise has little to do with relativity
since sound has no relativistic properties

it makes a great TD topic - why is Theory Development treated like the Siberia of Physics Forums

"if you don't watch it - I shall send this topic to (gasp!) Theory Development" :yuck:

I think TD is the best forum - since it serves to test standard theories as well as new theories and ideas - it should not be thought of as a punishment
like 18th century New South Wales or Devil's Island

 

[OneEye]

But, if there were an observer moving with that object and he was listening to a tone produced by you, then he would also hear the Doppler-shift, but he would measure a difference in the speed of the sound emmited by you

Ah, and here is where we disagree. Because, in order to be able to measure the speed of sound between us, he would have to know the distance between us, and he would have to have a useful time base. But, if he used sound to measure the distance between us, his sonic "rods" would be (apparently) lengthened (WRT my rods) as he measured the steadily-decreasing distance between us, and the ticks from my sonic clock would be Doppler-shifted upward in his frame, hence providing a time dilation effect. I think that you are counting on being able to use light measurements to factor out these transformations and to render "true" length and time measurements, but if one uses strictly sound for distance and simultaneity measurements, one sees (I believe) an exact parallel of the photonic argument of Relativity.

(and in fact, if he measured the speed of the sound formt he object next to him, he would note that its speed would depend on what direction it was traveling with respect to his motion)

Which seems to me to be an exact equivalent to what Dr. Einstein says:

Relativity, Appendix I (Simple Derivation of the Lorentz Transformation):

Those space-time points which satisfy (1) must also satisfy (2). Obviously, this will be the case when the relation

$$(x^\prime-ct^\prime)=\lambda(x-ct)\eqno 3$$​

is fulfilled in general, where $\lambda$ indicates a constant; for, according to (3), the disappearance of $(x-ct)$ involves the disappearance of $(x^\prime-ct^\prime)$.

If we apply similar considerations to light rays [but here, we would substitute sound waves] which are being transmitted along the negative x-axis, we obtain the condition:

$$(x^\prime+ct^\prime)=\mu(x+ct)\eqno 4$$​

And here in lies the difference; with sound you can determine who is moving with respect to the medium propagating the sound.

This is true; with sound, the medium can act as a reference frame, thus implicating a "truly stationary" coordinate system. However, this is not significant, since we cannot absolutely answer the question as to whether the air reference frame is "really" moving or whether we are.

Wiith light however, both observers would still observe the Doppler shift, but each would also measure both the light they receive and transmit as having the same velocity with respect to themselves. Both observers would measure the speed of light as 300,000 km/sec relative to themselves. (rather than one observer measuring the speed of light as c+v or c-v)

I have never heard of a sonic equivalent of The Experiment of Fizeau. Have you? I would be most interested to find whether $V=v+w$ when one measures sound propagation in a moving medium.

Every observation and argument which Dr. Einstein makes in the first ten sections of Relativity (regarding light-based measurement of distance and time with regard to two co-moving observers) can also be made with regard to similary-constructed sonar measurements. Why, then, should we not also take the next step and include Section XI?

No, they can't. If you concluded that, then you misconstrued something.

A little more explanation would help here.

 

[robphy]

One difference between light and sound that might be worth pointing out here is that the Doppler formulas differ.

For sound (in the absence of wind),
if the source approaches a stationary receiver
then $$f'=\frac{c_{sound}}{c_{sound}-v_{source}}f$$
if the receiver approaches a stationary source
then $$f'=\frac{c_{sound}+v_{receiver}}{c_{sound}}f$$
if the source and receiver approach each other
then $$f'=\frac{c_{sound}+v_{receiver}}{c_{sound}-v_{source}}f$$


For light,
$$f'=\sqrt{\frac{c_{light}+v}{c_{light}-v}}f$$
where $$v$$ is the relative velocity between the source and receiver.

 

[Janus]

Ah, and here is where we disagree. Because, in order to be able to measure the speed of sound between us, he would have to know the distance between us, and he would have to have a useful time base.

No, he wouldnt. All he has to do is measure is the speed of sound relative to himself. All he needs are two sound sensors placed a distance apart and moving with him, and measure how long it takes from the time the sound first hits the first sensor till is hits the second. He has to know nothing about the distance between us. With sound he will get different answers. With light he will always get the same answer. This is the fundamental difference.

But, if he used sound to measure the distance between us, his sonic "rods" would be (apparently) lengthened (WRT my rods) as he measured the steadily-decreasing distance between us, and the ticks from my sonic clock would be Doppler-shifted upward in his frame, hence providing a time dilation effect. I think that you are counting on being able to use light measurements to factor out these transformations and to render "true" length and time measurements, but if one uses strictly sound for distance and simultaneity measurements, one sees (I believe) an exact parallel of the photonic argument of Relativity.

No, he doesn't because he will measure a different velocity for sound relative to himself depending on how he is moving wrt the medium. Again, with light you always measure the same speed of light regardless of your movement.


Which seems to me to be an exact equivalent to what Dr. Einstein says:




This is true; with sound, the medium can act as a reference frame, thus implicating a "truly stationary" coordinate system. However, this is not significant, since we cannot absolutely answer the question as to whether the air reference frame is "really" moving or whether we are.

Yes it is significant, because for light there is no medium for which you can measure its velocity or your velocity wrt. If there were, there would be no Relativistic effects.

I have never heard of a sonic equivalent of The Experiment of Fizeau. Have you? I would be most interested to find whether $V=v+w$ when one measures sound propagation in a moving medium.

I have. In fact, there are a number of companys that manufacture Sonic Anemometers that measure wind speed by that very measurement.

A little more explanation would help here.

The simple fact is that there are no relativistic effects due to the speed of sound.

 

[turin]

I don't even know why I bother.

 

[OneEye]

All,

It's probably time to put this one to bed. I will leave the last word to my correspondents. I confess that I must retrench somewhat from my original position, especially after robphy's very helpful post.

Just three observations before I relinquish this discussion:

1) I come away with a serious reconsideration of my initial proposition because of the fact of the mediating nature of the atmosphere when applying the principles of the relative nature of time and distance to sound. Undoubtedly, the fact that sound's velocity can be measured relative to its medium is a powerful and important consideration. But, in order to fully rest on this consideration as a defense for a Newtonian interpretation of sonic measurement, one must assume that it is oneself that is moving rather than the medium. Such an assumption is substantiated by the fact that one has the atmosphere/earth relationship and light-based measurements to ground the atmospheric measurements. But such correlations have no value in, say, the center of an opaque nebula, or 1000 meters below the surface of the ocean, or 1000 kilometers down into the Jovian atmosphere. However, to my mind, these consideration are sufficient to cast reasonable doubt on the original proposition. And given that reasonable doubt, I don't expect to get any farther with this idea in this particular venue.

2) I will repeat my averment that Dr. Einstein's philsophical proofs for the relativity of simultaneity, distance, and time (as propounded in, if I recall correctly, Sections VIII, IX, and X of Relativity) are as applicable to sound as they are to light. The Doctor's arguments are not at all arguments regarding light, nor are they at all dependent on the invariance of the speed of light. Dr. Einstein's arguments are, rather, general arguments regarding observation and motion which are as appropriate to sound as to light - or to a BB machine gun in a darkened room.

3) Although there was a good deal of beneficial opposition in this discussion, I cannot help the feeling that some correspondents were sometimes engaging in the same sort of "of course not" ideation which attends those who are unable to make the jump from Newtonian mechanics to relativistic contemplation. I feel that some of the responses were tainted by a stubborn orthodoxy rather than a real willingness to fully engage the idea on the table. However, there was enough thoughtful consideration to counteract this influence (even on the part of those who seemed to be thus entangled), and so I feel that the whole show was a good one in the end.

Credits​

Janus: Thanks for taking the time. I doubt that you found this much in the way of edifying, but you stuck with it. Goodonya!

Eyesaw: Thanks for your support. We both suspect, I think, that there is more than a germ of an idea still left here. May this be useful to you.

energia: Thanks for your kind comments. I enjoy writing, and I am glad that you enjoyed reading.

robphy: Thanks for injecting valuable mathematical rigor into the discussion. Right timing, right level of detail, just the right influence. Nice touch!

turin: I don't know why you bother, either. If novel or unorthodox speculation is not to your taste, then perhaps this is not the right place for you - and perhaps scientific investigation is not your true home. May you find a place of comfort!

In any case, I hope that everyone had a good time (except turin, whom, I am afraid, did not), was edified, and enjoyed exploring some peculiar ideas.

[size=-1]No subatomic particles were destroyed or harmed in the evolution of this thread.[/size]

 

[energia]

maybe we can continue the discussion of aether in 'Michelson-Morley Experiment Revisited'

or start a new thread in Theory Development

aether theory is one of my favourite subjects