Proof Of My Fundamental Equation

[Doctordick]

Obviously my earlier post, “The Most Critical Question!” did not clear the air at all. I have reread a number of posts on that thread and come to the conclusion there are some important misrepresentations which need to be addressed. Perhaps this post will break some new ground. Since “The Most Critical Question!” thread has now become such a morass of confusing and irrelevant contentions, I am entering this as a new thread.

 

To begin with, what I have presented on this forum is not a theory; it is a mathematical proof. Actually a rather simple and straight forward proof with far reaching and subtle implications. I came up with the proof as a graduate student in the middle sixties but found no worthwhile implications for almost twenty years. It seems that it is not my proof which has actually generated any real complaints, but rather it is those implications which I point out which disturb you so greatly. But most important it is your mental perception of it being a theory which distorts any attempt to understand my presentation.

 

I have never attempted to examine a classical limit for Dick's presentation and I did not mean to define it as [imath]K=i\hbar[/imath], I only said it would involve the phases approaching zero; I hadn't specified anything more exactly about how and I think in the end it would boil down to adding the things in QM the aren't in his presentation. At that point, of course, it would become the von Neumann formalism instead of Dick's formalism. :doh:

Absolute idiocy! It is quite clear that Anssi is the only person here who has any comprehension at all of what I am saying. “Formalism” is no more than another word for a theory and, as I have commented many times, I have not presented a theory of any kind. What I have presented is a proof of a specific constraint implied by my definition of an explanation; quite a different thing.

 

There is no such thing as “Dick's formalism”. I have never presented my fundamental equation as a formal attack on any problem. It is rather a solution to a very important question. What I have asserted is that any “valid” explanation must yield expectations which can be represented as solutions to that equation! (Where “valid” is defined to be “there exists no known data which in any way contradicts that explanation”.) One thing that is very significant. That result is proved without in any way making any assumption that the consequences of that explanation have been actually fully determined. That is probably the single most important issue everyone overlooks.

 

Qfwfq and modest (and Erasmus by the same token) should be well aware of the fact that no modern theory makes the claim of being universally valid (under my definition of valid). They all require that some very specific assumptions be made about the circumstances being discussed before they can be deemed applicable. What is significant is that it is exactly those assumptions where the errors of science occur.

 

I am reminded of the final exam of the Quantum Mechanics course I took in my first year in graduate school. It was an essay test (quite unusual in physics exams). The circumstances were given as follows:

 

Every publication dealing with Quantum Mechanics in any way has vanished (library fires, book burnings by civil unrest ... whatever; they just don't exist anymore).

 

Every person on Earth (other than you) who knew anything about Quantum Mechanics has died (again, how this came to be is not the issue; it is no more than a postulate behind the essay).

 

And finally, you have exactly one hour to live.

 

The examination consisted of writing down what you think would most benefit the redevelopment of Quantum Mechanics by the scientists of the world. (It was allowed that one could presume they had an understanding of Classical Newtonian Mechanics.)

 

As it turned out, I was the only student still writing when the bell rang. When I brought my paper to him, the professor told me (as he took my paper) that, considering what we covered in the class, no one knew enough Quantum Mechanics to write for an hour without padding the thing with undefendable baloney.

 

What I had done was to write down every experiment I could think of where Classical Mechanics gave the wrong answer; finishing, in each case, with an example of the mathematics which would yield the correct result without, in any way, presenting any of the standard QM interpretations as to what was going on or why the mathematics yielded the correct result. (Apparently the other students spent most of their time giving arguments for the standard QM interpretations of reality).

 

Anyway, he later called me to his office to give my paper back to me, marked A++, and told me that he gave me the highest grade in the class. (I don't think he called anyone else to his office, but I could be wrong.)

 

The biggest single error the both of you make is presuming your examples are “valid” explanations when you cannot prove that they are.

 

Qfwfq, you and I had a big argument some five years ago concerning relativity. I held that Newton was bright enough to come up with the modern relativistic transformations had someone pointed out the logical difficulties embedded in his assumption that all clocks could be physically set to agree (he was well aware of the finite speed of light by the way). You essentially asserted that no one could have convinced him of that and I denied your assertion. The issue goes directly to the question of “validity” as I have defined it. Classical Mechanics is not and never was a “valid” theory; it was only approximately valid under rather restricted circumstances. The fact was that it just was just never examined carefully enough to bring the problems up.

 

Right. Exactly. The FE, as it stands now, does not make allowance for such a thing.

Of course it doesn't and it should be clear to you that your example (classical mechanics) is not a “valid” explanation. It only yields reasonable answers under some serious erroneous assumptions.

 

Until you can show me a specific error in my deductions, I hold that my proof is correct. When I show that Schrödinger's equation, Dirac's equation, Maxwell's equation, the relativistic transformations and the five forces of modern physics are all approximate solutions to my equation, what I am showing is that these theories are indeed approximately valid. Approximately valid does not mean absolutely “valid”. However, they are closer to being valid than are most explanations one runs into. In fact, they are close enough to being valid that I was able to specifically point out, in detail, what those assumptions had to be.

 

And, by the way, Qfwfg, your examples are consistently inadequate to the issue under discussion. They consistently presume gobs and gobs of underlying explanation is valid without any complete examination of that explanation whatsoever. Your Sudoku example is the extreme of the lot as it presumes your explanation of paper, pencils and a writing surface is a valid underlying explanation on which your solution is to be built: i.e., you totally misrepresent what I am saying. You bring it forth as a counter example to my proof and, as I said earlier, if it is indeed a true counter example to my proof then it must also be a counter example to Schrödinger's equation, Dirac's equation, Maxwell's equation, the relativistic transformations and the five forces of modern physics as these are all approximations to my equation. And I know you would not be stupid enough to make that kind of assertion.

 

But back to modest's complaints!

 

My objection, and Will's objection, is that classical mechanics cannot be a solution of the FE as it is now (and Dick's claim is that "the symbols used to communicate any internally consistent explanation must obey the FE" as it stands now). Dick's presentation does not allow the introduction of new axioms. He proposes it as a tautology.

Yes, what I have presented is exactly that: a tautological extension of my definition of an explanation: a restatement of the constraints implied by that definition and nothing more; as such, no additional axioms are or ever will be required. Your axioms are presumed constraints on your explanation which have to be added to the background information before your “formalism” can be expressed (to use Qfwfq's terms).

 

I don't think Dick is making any argument about reality (he is very carefully avoiding that).

No I am not making any arguments about reality at all; other than the fact that any “explanation” of “reality” is an explanation and “reality” is very clearly defined to be “the entirety of all the available information”: i.e., that is clearly the information your explanation of reality must explain. This is in contrast to most other explanations where “gobs and gobs” of presumed information is totally ignored: i.e., the underlying explanation being presumed is totally incomplete and unexamined.

 

Dick is, however, saying that a proper explanation of any data set must be quantum mechanical in nature (a notion for which I obviously disagree).

You have this roughly backwards. I am saying that quantum mechanics is closer to being valid than most theories. And your insertion of “any data set” ignores the fact that the data set being explained consists of “all known data”. It is, without a doubt, seen in your minds eye as embedded in a presumed background of understood data (the underlying ignored and unproved explanations).

 

I've, in fact, given a relevant quote of Dick's: "until that information is available to us, the outcome is in the future and is only determinable as a probability. Thus it is that the mechanism to be used is quantum mechanics which overtly recognizes probabilistic outcomes."

Again, by omitting significant constraints, you have twisted what I said into something that I never asserted. Your assertion that probabilistic outcomes are unnecessary makes the assumption that the “theory” standing behind your explanation of what is going to happen is 100% valid and that no incorrect prediction can ever occur. But you present this without admitting the presumptions you make in presenting that very theory. Again, I am quite confident you wouldn't make such an idiotic statement if you understood what you were saying.

 

I agree, but I've seen Anssi and Dick talk about the problem before many times, so it is not unfamiliar to me. The question is:

 

If we cannot know the true nature of reality then how can we develop a worldview that usefully represents that reality?

Now that is a roughly accurate statement of the difficulty. And the answer to the question lies in my fundamental equation. The world view is constructed through millions upon millions of “by guess and by golly” propositions. What is important is that it doesn't make any difference what the theory behind the solution is. What is important is that it is approximately valid and the closer it is to valid the better.

 

What is totally ignored by the scientific community is communication itself. You have a world view and everyone else also has a world view. Your explanation of the means of communication itself is bounded by the fact that you are interpreting that communication to be consistent with your world view.

 

There is a presumption being made there. Once you establish your belief in the meanings of the majority of those communication elements (something achieved around the age of two) you are presuming the other's world view maps one to one into your world view. Now, if both world views are perfectly 100% valid (valid under my definition) such a mapping can exist. However, if that world view is not perfectly valid, the existence of such a mapping is an invalid presumption.

 

What I have shown via my proof is that the definition of an explanation itself stands behind any solution to that mapping problem. Without the truth of the issues standing as a result of that proof, one cannot develop a consistent mapping between two independently developed world views. However, since any valid explanation must obey my equation, what ever is represented by that “i” index in my world view can be mapped into whatever is represented by some “i” index in your world view by virtue of the similar probabilities of the expectations generated by that world view. If my expectations match your asserted expectations (as per the mapping presumed) we further presume we are talking about the same thing. What is important to recognize is that the presumption is not necessarily true. When our explanations are invalid (by my definition of valid) that mapping is bogus and realization of that fact has some profound subtle consequences simply not recognized by the scientific community.

 

As Anssi has stated, it is all semantics.

 

By the way, there are some subtle issues in probability theory which can be shown to be invalid.

 

Ignorance is its own reward. Your world views are built on ignorance and, until they are perfectly valid, they are fundamentally bogus. When they are perfectly valid, they do not constitute truth; they are merely valid representations of the past. Induction (a procedure known to yield invalid results) is the source of your belief that valid explanations of the past yield knowledge of the future. The apparent truth in that presumption is a result of the shear volume of past information as compared to the volume of “present” information: i.e., the probability of decent results remaining decent with additional information is reasonably large if the world view is reasonably close to valid.

 

Have fun -- Dick

[Qfwfq]

Dick, call it a tomato. I don't call it a theory and I do call it a formalism.

 

What I have asserted is that any “valid” explanation must yield expectations which can be represented as solutions to that equation! (Where “valid” is defined to be “there exists no known data which in any way contradicts that explanation”.)

Given that you say it is a mathematical proof, you need to mathematically define what you mean by "known data" and I would like to see how the definition implies your thesis.

 

Qfwfq, you and I had a big argument some five years ago concerning relativity. I held that Newton was bright enough to come up with the modern relativistic transformations had someone pointed out the logical difficulties embedded in his assumption that all clocks could be physically set to agree (he was well aware of the finite speed of light by the way). You essentially asserted that no one could have convinced him of that and I denied your assertion.

Convinced him of what? I believe you are erroneously reporting something I said. BTW the speed of light being finite is not a sufficient condition upon which to draw the conclusion about spacetime coordinate transformations.

 

Your Sudoku example is the extreme of the lot as it presumes your explanation of paper, pencils and a writing surface is a valid underlying explanation on which your solution is to be built: i.e., you totally misrepresent what I am saying.

I addressed the very same objection from Anssi and I tire of repeating things. Sudoku can be cast as a purely mathematical thing and the fictional efforts were only a manner of getting the idea across. You always raise this same objection and I always point out that you do the same thing yourself; you make examples which rely on gobs of things being valid.

 

You bring it forth as a counter example to my proof and, as I said earlier, if it is indeed a true counter example to my proof then it must also be a counter example to Schrödinger's equation, Dirac's equation, Maxwell's equation, the relativistic transformations and the five forces of modern physics as these are all approximations to my equation. And I know you would not be stupid enough to make that kind of assertion.

I dearly hope I would not be so stupid. For one thing, that's not what I did.

 

Induction (a procedure known to yield invalid results) is the source of your belief that valid explanations of the past yield knowledge of the future. The apparent truth in that presumption is a result of the shear volume of past information as compared to the volume of “present” information: i.e., the probability of decent results remaining decent with additional information is reasonably large if the world view is reasonably close to valid.

Don't worry about teaching the problem of induction to me, nor to Modest. We've both read quite enough about it to know about the above matters. Mind though that it isn't quite so simple either.

[Doctordick]

Dick, call it a tomato. I don't call it a theory and I do call it a formalism.

Well then you better define for me exactly what you mean by a formalism.

 

Given that you say it is a mathematical proof, you need to mathematically define what you mean by "known data" and I would like to see how the definition implies your thesis.

Known data is whatever is listed under the “i” index. That collection of data which your explanation explains including sufficient internal information to deduce the implied semantics used to define the internal relationships presumed for that collection (from the perspective of your explanation).

 

Convinced him of what? I believe you are erroneously reporting something I said. BTW the speed of light being finite is not a sufficient condition upon which to draw the conclusion about spacetime coordinate transformations.

Well, I can't quote it as the current form of the forum does not retain anything that old. Since you are a member of the elite you may be able to obtain the original posts. If so, have a look at the thread “Is 'time' a measurable variable?” (begun May 4, 2006), read posts 84 through 87 posted June 7, through June 11, 2006.

 

In my opinion, the speed of light being finite together with Galilean relativity, both of which he well understood, does yield some major logical difficulties with setting clocks to agree. That was quite clear to me when I was nine years old and first heard of the problem of setting clocks in a moving train (without being given any arguments about relativity or space time at all). I seriously doubt Newton was dumber than I was.

 

I addressed the very same objection from Anssi and I tire of repeating things. Sudoku can be cast as a purely mathematical thing and the fictional efforts were only a manner of getting the idea across.

Well then, cast it as a purely mathematical thing via a list of the required fundamental elements and we can discuss the issue.

 

I dearly hope I would not be so stupid. For one thing, that's not what I did.

At the moment, I am afraid that is a matter of opinion so let's not worry about it.

 

Don't worry about teaching the problem of induction to me, nor to Modest. We've both read quite enough about it to know about the above matters. Mind though that it isn't quite so simple either.

That is nice to know; however, simple or complex, it has no bearing on my deductions.

 

Have fun -- Dick

[modest]

It is quite clear that Anssi is the only person here who has any comprehension at all of what I am saying.

 

I would be somewhat frightened had I the same to say about any assertion I made.

 

In my opinion, the speed of light being finite together with Galilean relativity, both of which he well understood, does yield some major logical difficulties with setting clocks to agree.

 

No.

 

The speed of light being invariant along with Galilean relativity has logical difficulties. That the speed of light is finite is not enough to have led Newton to the conclusion of relativistic mechanics. You might as well be saying "the speed of sound is finite which should have led Newton to derive relativistic mechanics". It is the finite *and* invariant nature of C that makes Galilean relativity wrong, not the finite nature of any particular signal.

 

In fact, yes, let's quote that...

 

But back to the point that Newton could have recognized the difficulty had he happened to think of the problem of setting his clocks from an ideal perspective. Let us set up a thought experiment using nothing not known by Newton. First, as I commented, Newton certainly believed in "relativity": the idea that the description of physical experiments could be transformed into alternate frames of reference. Secondly, he knew the speed of light was finite as he himself observed the difference in the apparent orbits of the moons of Jupiter caused by the finite speed of light.

 

All one would have had to do is describe a thought experiment involving examination of the same experiment from a rest position and a moving carriage as described in an ideal circumstance (both being inertial frames). Let the two examiners each possess a glass plate set parallel to the direction of motion an infinitesimal distance apart, one at rest with respect to observer number one and the other at rest with respect to observer number two. Let them each set up a coordinate system (make it a polar coordinate system with theta equal zero in the direction of motion for simplicity) on their respective glass plates and reckon their times from a infinitely accurate clock positioned at the origin of their coordinate system setting t=0 to the moment the two origins are in the same position.

 

Now let the two observers examine a phenomena which takes place between the two plates, recording the time and position of the significant events in that phenomena. I think we are all pretty sure we know exactly what Newton would initially do: he would presume to describe the phenomena via the rest observers measurements and then use Euclidean general relativity to transform the measurements into the moving observers coordinate system. Now all we have to do is point out the physical problems in that solution: essentially the problem of determining who is actually at rest.

 

He has obviously made the assumption that measurements in the direction of travel are the same for both observers. Challenge him to prove that those measurements have to be the same: i.e., that the acceleration to the other frame did not change the characteristics of the measurement devices used by that observer. If he responds that relativity itself requires they be the same then one can shift to the problem of defining time at the various positions in the coordinate system. No matter what he suggests, a problem with his solution can be brought up as it simply is not an internally self consistent solution and I believe Newton would have been able to see that fact.

 

Special relativity can be deduced directly from the idea that the speed of light is the same for both observers.

 

You started with the premise "he knew the speed of light was finite as he himself observed the difference in the apparent orbits of the moons of Jupiter caused by the finite speed of light" and ended with an entirely different premise: "Special relativity can be deduced directly from the idea that the speed of light is the same for both observers."

 

Now, If you don't understand the difference between:

 

The speed of light is finite.

and

 

The speed of light is invariant.

then you have absolutely no business telling Newton what he could or could not have deduced.

 

He could not have found relativistic mechanics any more real or convincing than classical mechanics because he could not have known that there was a finite invariant speed.

 

It is very difficult to believe you don't know this.

 

~modest

 

EDIT --->

 

BTW the speed of light being finite is not a sufficient condition upon which to draw the conclusion about spacetime coordinate transformations.

 

Yes, exactly!

 

Honestly, DD, you know what you are saying is wrong? Yes?

[Qfwfq]

Well then you better define for me exactly what you mean by a formalism.

Dick, I'm writing in English. I'm not using my own little language with my own little idiosynchrasies and I did not say that statement as part of a mathematical proof.

 

Known data is whatever is listed under the “i” index. That collection of data which your explanation explains including sufficient internal information to deduce the implied semantics used to define the internal relationships presumed for that collection (from the perspective of your explanation).

Thanks a lot :rolleyes: but you add nothing useful to uphold your case. You show that, as I guessed, you're claiming that it must be so for any set of data, since any candidate data can be "known data" according to this definition, from which follows that your claim could only be true for an absolutely trivial condition. IOW, what is the use of an explanation being such that no data could contradict it?

 

Thanks Modest for quoting that old post and addressing it and a few other things, saves me a bit of the huge volume of work here. I browsed those posts and, sure enough, what I argued was not what Dick reported me to have said.

 

In my opinion, the speed of light being finite together with Galilean relativity, both of which he well understood, does yield some major logical difficulties with setting clocks to agree. That was quite clear to me when I was nine years old and first heard of the problem of setting clocks in a moving train (without being given any arguments about relativity or space time at all). I seriously doubt Newton was dumber than I was.

Having read his Principia and having read your posts, I even more seriously doubt it. Dick, even the task between station and moving train is conceptually simpler according to Galilean relativity. If one doesn't actually do it in a case where discrepancies are appreciable, one couldn't be aware of incorrect assumptions. If one does do it in such a case, finding unexpected discrepancies, it is epistemologically akin to getting the Michelson Morley results, from which a mathematician can deduce the Minkowskian spacetime geometry. Mind, Newton was smart but in his day they hadn't had the idea of alternative geometries, despite centuries of research over Euclid's fifth; this is the only reason why even if he had known the M&M results he might not have done such a neat job as Minkowsi. He'd have done a least as well as the young hippie though.

 

Well then, cast it as a purely mathematical thing via a list of the required fundamental elements and we can discuss the issue.

I would prefer to doubt you being even dumber than me, much worse than being dumber than Newton, but I might expect it to be obvious. Each complete sudoku is a matrix and it is no problem to define the requisites of it being valid; it is also obviously possible to bijectively map the possible pairs of values for the indices onto 81 values of a single index. You're wanting me to teach you this kind of thing?

 

At the moment, I am afraid that is a matter of opinion so let's not worry about it.

Er, opinion about me being stupid? Or about what I did and didn't do? :rolleyes:

 

That is nice to know; however, simple or complex, it has no bearing on my deductions.

Why did you take the care to tell us about it then?

 

In any case you misused the term probability in a manner which Carnap was, quite justly, criticized for. One could talk about a degree of corroboration and it is often quantified by the [imath]\chi^2[/imath] statistic, I think though that entropy can be used as a very relevant statistic in discussing how much sense it makes to have confidence in the expectations. What did you think about examples of apophenia, about the Bible Code and similar things?

 

So then, how to distinguish which expectations one might bet all one's property on and which to not even bet a penny on?

[joekgamer]

The way I see it, you are being hindered by misunderstandings through terms not being defined the same way by everybody. I think it would help your argument be understood by others (including me) if you would make a list of the terms you use. For example, what is your definition of 'valid'?

[Qfwfq]

For example, what is your definition of 'valid'?

Dick's definition, in the OP (4th paragraph) and which I quoted, rests on the notion of "known data" and at my request he supplied his definition of that too. I then drew my conclusions from it in my previous post.

[Qfwfq]

If means something else, then could you please clarify?

no, please don't, because it is dragging decidedly off topic.

:steering:

 

Moderation note: the posts quoted here and 5 preceding it have been moved to thread "Discussion of Feedback Loops, AI, etc.", because they are about different topics

[AnssiH]

Just noticed this thread, and yeah it is going a bit off topic. For what it's worth, I did find the OP quite clear. As long as people understand how and why this is not a theory about reality at all, but rather a logical analysis about explanations or models or world views (with rather striking implications about our current world views), I suppose the main purpose of the OP would be fulfilled. Polymath, if you want, I can try and explain what DD is referring to.

 

In the meantime, a popular side topic seems to be whether or not it would have been possible for Newton to arrive at special relativity. Getting slightly off-topic but it's somewhat interesting, so maybe I'll make a comment too, especially since so far the comments reflect some rather common and naive misconceptions about the history of special relativity...

 

Having read his Principia and having read your posts, I even more seriously doubt it. Dick, even the task between station and moving train is conceptually simpler according to Galilean relativity. If one doesn't actually do it in a case where discrepancies are appreciable, one couldn't be aware of incorrect assumptions. If one does do it in such a case, finding unexpected discrepancies, it is epistemologically akin to getting the Michelson Morley results, from which a mathematician can deduce the Minkowskian spacetime geometry. Mind, Newton was smart but in his day they hadn't had the idea of alternative geometries, despite centuries of research over Euclid's fifth; this is the only reason why even if he had known the M&M results he might not have done such a neat job as Minkowsi. He'd have done a least as well as the young hippie though.

 

First, the M&M result was not necessary to form special relativity. Einstein has claimed that he did not even know about this experiment when he wrote the original paper about special relativity. Certainly he did know about various attempts to measure the properties of aether though, but the important fact is that the considerations that led to special relativity arose from more subtle difficulties, whose root can be traced back to the violation between Maxwell's equations, and Galilean principle of relativity. The experiments made these problems more obvious(i.e. forced people to look more closely), but they lived in different shapes and forms in the subtleties of the definitions that existed in the world view of the time. I.e. various suggestions to solve these problems arose from careful examination of the definitions that already existed.

 

These attempts to solve the violation between Maxwell and Galileo led to violations in other important aspects of the physics world view of the time, and/or contained unobservable asymmetries between moving bodies. For instance, several aether theories had a subtle violation of reaction principle, which could be shown to lead to perpetual motion, and so on and so forth. Understanding these sorts of violations requires some thinking about the details of the underlying ideas, and it is nowhere near as simple as you guys make it seem.

 

Second, the formulation of Minkowskian spacetime is not in any way a necessary component of special relativity. That formulation does not appear in the original paper of special relativity; Minkowski came up with it after reading the said paper, and Einstein did not think about the issue in those terms at that point.

 

So winding back to the time before special relativity, Maxwell's equations were widely accepted as valid, but they contained the c, which was interpreted as the speed of the propagation of undulations of aether of some sort. This creates an obvious violation between the Galilean principle of relativity, and aether. You could just as well say at this point, that the finite speed of light and the Galilean principle of relativity were at odds (Together with a plethora of other assumptions of course).

 

It was commonly thought that thus the Galilean principle of relativity is wrong (aether would not comply), and trying to measure the properties of aether was all the rage among experimental physicists.

 

After some more experimental work and careful thinking, the physicists were forced to take into account the more subtle details of the definitions of their world view, which generated many different flavours of length contractions and time dilations, as necessary consequences of the idea of aether. Elastic, inelastic, dragged by matter or static, these definitions pretty much led to circumstances where natural observers could not objectively agree with time and length measurements, nor with simultaneity, and this is all prior to special relativity.

 

So at this point, the Galilean principle of relativity was thought to be valid for natural observers, yet invalid in ontological sense. I.e. "it just looks symmetrical to us because it is fundamentally impossible to measure otherwise, but it's not really symmetrical" was the attitude.

 

The contribution of Einstein was to disregard asymmetries to properties that could not be observed by natural observer anyway. He basically viewed them as meaningless metaphysics, and was convinced that there exists a simpler way to express the electrodynamics of moving bodies, a way which would not violate the Galilean principle of relativity in any hypothetical sense either. It was the moving magnet and conductor problem that led him to define simultaneity as it must appear to natural observers anyway. The paper is called "On the electrodynamics of moving bodies" because it was a solution to what was essentially an epistemological paradox at that point. It was not called "Here's to Michelson and Morley". It did not make arguments about relativistic spacetime. I think to Einstein it was just a way to remove asymmetry from something that was symmetrical to us from the point of view of the information actually available to us. Ignorance -> symmetry and all that, sounds reasonable, yes?

 

I think this was pretty interesting commentary about the topic;

http://www.bourbaphy.fr/darrigol2.pdf

 

I recommend reading at least the 1st page and "Einstein's theory" starting from page 15. Couple of selections;

 

I am more and more convinced that the electrodynamics of moving bodies, as it is presented today, does not agree with the truth, and that it should be possible to present it in a simpler way. The introduction of the name 'ether' into the electric theories has led to the notion of a medium of whose motion one could speak of without being able, I believe, to associate a physical meaning to this statement. I believe that electric forces can be directly defined only for empty space, [which is] also emphasized by Hertz. Further, electric currents will have to be regarded not as 'the vanishing of electric polarization in time' but as motion of true electric masses, whose physical reality seems to result from the electrochemical equivalents.... Electrodynamics would then be the science of the motions in empty space of moving electricities and magnetisms.

 

What he was after was a way to express electromagnetism in a way that would not contain undefendable (=meaningless) asymmetry to it. It was this desire which led him to different path from other physicists, and this also allowed him to be convinced of the validity of his definitions, as long as the best competing theories were also valid. It was essentially a reformulation of the best aether theories (Lorentz's basically), just removing the metaphysical aspects;

 

In the introduction to this paper, Einstein remarks that magneto-electric induction receives two very different interpretations in Lorentz's theory, according as it is the magnet or the electric conductor that is moving with respect to the ether. In the first case the motion of the magnet implies the existence of an electric field e within the conductor (such that [imath]\nabla \times e = -\partial b/ \partial t[/imath])). In the second case, there is no electric field within the conductor, and the Lorentz force ([imath]v \times b[/imath] per unit charge) is responsible for the motion of the electrons. Yet the induced current only depends on the relative motion of the coil and the magnet.

 

Emphasis mine. You have to understand that M&M did not lead to relativity. Explanations to M&M existed. What he wanted to do was to create definitions that would play the same role as Lorentz's theory, but without undefendable asymmetries.

 

It occurred to Einstein that, since universal simultaneity is an assumption that cannot be proved (making the clocks agree and all that), simply defining observer-dependent notion of simultaneity would not only be possible (people knew it was), but would yield entirely self-coherent transformations for Maxwell's equations, and it would take care of all the problems that Lorentz' theory was taking care of. I don't think he cared much about any metaphysical implications of that definition at that time. Minkowski's interpretation surfaced a lot of those later.

 

So what about Newton, would it have been possible for him to come to similar realization about signal speeds, simultaneity and Galilean symmetries? It really is hard to say, but it's certainly not impossible. It probably would have been harder to swallow at the time, and also he had his theory of corpuscular light, which is at least superficially in agreement with the Galilen principle of relativity (in the form of emission theory).

 

But on the other hand, emission theory was at least at Einstein's time problematic because of subtleties having to do with signals getting mixed up in many cases. If Newton were able to see problems with emission theories (I have no idea what's the case), he would not have been too far away from seeing a violation between Galileon relativity and finite speed of light. The connection between finite signal speeds and setting clocks to agree would have been in his reach, and it is entirely possible he would have come to think of the consequent possibility of redefining simultaneity.

 

But not without thinking about it!

 

Think about it.

 

-Anssi

[Doctordick]

So what about Newton, would it have been possible for him to come to similar realization about signal speeds, simultaneity and Galilean symmetries? It really is hard to say, but it's certainly not impossible. It probably would have been harder to swallow at the time, and also he had his theory of corpuscular light, which is at least superficially in agreement with the Galilen principle of relativity (in the form of emission theory).

The real issue is, could you have convinced Newton that his picture of the problem (that all clocks could be set to agree) contained assumptions. Once he realized there were real assumptions in that picture, I think he would have attacked them. The real problem is that people didn't seriously think about the definition of time (and they don't even today) but rather simply assume their emotional convictions are correct.

 

The connection between finite signal speeds and setting clocks to agree would have been in his reach, and it is entirely possible he would have come to think of the consequent possibility of redefining simultaneity.

 

But not without thinking about it!

 

Think about it.

Sorry Anssi but I doubt anyone here besides you and I is going to think about it. People don't like to think; they just like to know!

 

Have fun -- Dick

[Qfwfq]

Anssi, you equivocate on what people say and sometimes don't even get the basics of logic straight, and so you accuse folks of sharing naive misconceptions. :rolleyes:

 

Darrigol's seminar was interesting to read but your summary is a bit of a hash and your argument doesn't support the contention about Newton. But of course, you deduce from this that I disagree with the premises, eh?

 

I increasingly see that, no matter what I tell you, no matter how I put it, it's never much use and I don't have nearly enough patience to insist. I was inclined to make yet another effort in that other thread but after reading this I doubt I will say much more on the matter.

 

First, the M&M result was not necessary to form special relativity.

Of course it wasn't. Did I imply so?

 

Einstein has claimed that he did not even know about this experiment when he wrote the original paper about special relativity.

In the very .pdf you linked to, Darrigol says he did. I also read elsewhere that he is reported to have said he didn't, but not seriously, and at other times that he did. Of course it was the nature of the equations of electromagnetism that were troublesome and people were making various efforts to sort it out. I had seen many different accounts of the history, even before Darrigol's.

 

What Minkowski did was to tidy up what the young hippie had done. His reaction was at first resentful but then he realized his former math professor was right, it was a better presentation of the same thing. Whether it is true to say "not in any way a necessary component" is a semantic issue.

 

This creates an obvious violation between the Galilean principle of relativity, and aether. You could just as well say at this point, that the finite speed of light and the Galilean principle of relativity were at odds (Together with a plethora of other assumptions of course).

Why don't you think about it, but much more carefully?

 

So at this point, the Galilean principle of relativity was thought to be valid for natural observers, yet invalid in ontological sense. I.e. "it just looks symmetrical to us because it is fundamentally impossible to measure otherwise, but it's not really symmetrical" was the attitude.

Actually, this was prevalent since Galileo and Newton. The transition from "we can't know" towards "no such thing" came later, mainly with Mach, only EM dragged away from it.

 

The contribution of Einstein was to...

...have been a great admirer of Mach.

 

I recommend reading at least the 1st page and "Einstein's theory" starting from page 15.

Don't worry, I read the whole thing. I have also more than once read Einstein's 1905 SR and 1916 GR papers. BTW if you had read the whole of Darrigol you would have seen that Poincarè also considered the ether a metaphysical notion. Perhaps one called the bottle half full, the other called it half empty, or maybe their concerns just differed.

 

So what about Newton, would it have been possible for him to come to similar realization about signal speeds, simultaneity and Galilean symmetries? It really is hard to say, but it's certainly not impossible.

Just to set records straight, I said that, at Newton's time, nothing was known that gave a reason to question the coordinate transformations between moving observers. If you think there was such a reason, only not so obvious, think about the following questions and think carefully because it doesn't seem to be your habit, judging by your post:

 

Shortly after Newton published his Principia, Tom thought: "Good golly, knowing that light propagates at a finite speed through the ether, Galileo's transformations need to be revised!" and Bob, elsewhere, thought: "Good golly, knowing that sound propagates at a finite speed through the air, Galileo's transformations need to be revised!" Can these both be valid reasons? Can one be and the other not? Why? Motivate your opinion carefully.

Edited March 11, 2011 by Qfwfq
dumb typo + copy-paste effect :-]

[AnssiH]

Anssi, you equivocate on what people say and sometimes don't even get the basics of logic straight, and so you accuse folks of sharing naive misconceptions. :rolleyes:

 

Right...

 

You know, I didn't really expect to understand what your exact stance is on the matter from your post, but I did remember you have commented yourself that it wasn't just the M&M experiment that led to relativity. Which was just all the more reason to think that your post in this thread was not really a serious attempt to explain anything to other readers, but rather felt like just an excellent way to give bad impressions to them. How do you think people who don't know about the history of relativity would read your post? Do you care at all about properly explaining something to people?

 

So my message was and still is that I do not appreciate the impression that those short accounts would give to most readers. They give the impression that getting to relativistic definitions requires these types of experiments. As if there are no other routes of thought to reaching essentially the same definitions. I know you don't explicitly say that without Minkowskian geometry it would have been impossible, but the impression that non-knowledgeable people would get is that missing Minkowskian geometry would be in some way a problem. While you know perfectly well it is not, at all.

 

Likewise the complaints that finite signal speeds are not enough to reach relativity. I know you know perfectly well that finite signal speeds are what cause serious issues in any methods of setting clocks to agree, and add Galilean relativity principle to those difficulties, and you have some material to think about already. That's the root of relativistic definitions, with or without Maxwell's definitions, and regardless what the history of relativity is, and you know it perfectly well.

 

And since you are complaining that I don't understand what you mean, are you sure you understand what DD means when he says Newton could have come up with relativistic definitions already at his time, had he come to think about appropriate difficulties/undefendable aspects of his world view? In particular, the problems associated with getting clocks to agree. If you do understand, then why oh why do you bring up M&M?

 

I don't really have any big complaints to your other comments, my main complaint is about giving bad impressions about the issue.

 

-Anssi

[AnssiH]

Shortly after Newton published his Principia, Tom thought: "Good golly, knowing that light propagates at a finite speed through the ether, Galileao's transformations need to be revised!" and Bob, elsewhere, thought: "Good golly, knowing that sound propagates at a finite speed through the air, Galileao's transformations need to be revised!" Can these both be valid reasons? Can one be and the other not? Why? Motivate your opinion carefully.

 

Admittedly, it is hard for me to believe that you are asking this seriously but yes of course Tom could have thought exactly the same thing as Einstein did; while one can assign speed to a volume of air in a coordinate system (making sound waves comply to Galilean principle of relativity), assigning speed to the ether which is spanning the entire universe is a meaningless notion. And before you ask, yes I know Einstein had more reasons to think about that. I think I commented about those reasons in my post.

 

Newton's train of thought would have been rather corpuscular light too (probably try emission theory for a fit first), so I'm thinking more about the situation where he'd have to come up with an objective way of making clocks agree, and thinking of the subtle complications that moving coordinate systems give to that situation.

 

-Anssi

[Qfwfq]

Anssi, you are insinuating that I deliberately attempt to mislead others. Anssi, this is ludicrous.

 

I have good reasons for being concise too, most of all people are free to look up the things I mention without delivering a full lecture about them. Your post did not come across as being only to clarify what I said to the ignorant masses, you were implying that Modest and I have these misconceptions.

 

...Tom could have thought exactly the same thing as Einstein did; while one can assign speed to a volume of air in a coordinate system (making sound waves comply to Galilean principle of relativity), assigning speed to the ether which is spanning the entire universe is a meaningless notion.

How could Newton have been sure of the difference between Tom and Bob's argument?

 

Don't get me wrong, it's clear that they can't both be conclusive and neither can it be that Bob's is and Tom's isn't. If you think Newton could have been sure Tom's is, more than Bob's is, think more carefully. For one thing, I forgot to mention a rather subtle thing, too often overlooked: ether wasn't the real problem with the principle of relativity (and Maxwell and Lorentz were certainly aware of this too). And I should think more carefully about Dick's argument and understand it better?

 

Another thing, which I omitted in my previous post. Did you notice the fact that the perpetual motion Darrigol discusses, seemingly attributing it to Poincarè, is non sequitur? Even if Poincarè made this blunder, it wouldn't support Dick's case because, in order to make the same mistake, Newton would have had to be just as dumb. :doh:

[AnssiH]

Anssi, you are insinuating that I deliberately attempt to mislead others. Anssi, this is ludicrous.

 

I have good reasons for being concise too, most of all people are free to look up the things I mention without delivering a full lecture about them. Your post did not come across as being only to clarify what I said to the ignorant masses, you were implying that Modest and I have these misconceptions.

 

I would in fact appreciate if you didn't say something like that at all, being that I don't believe for a second that you wouldn't understand the connection between finite signal speeds and clock synchronization, and thus you should be able to see what DD is talking about, without jumping to "hey finite signal speeds don't lead to relativity!". I mean I'm sure you know perfectly well that DD understands something as simple as special relativity, and you should be able to see he is talking about the possibility of uncovering the inherent circularity of these definitions (time, speed, distance) and the impact of the realization that the signal speeds are finite.

 

I don't know about Modest but I do expect you to understand these things perfectly well, which is why it irritates me that you seem to too often just reply with the first thought that pops into your mind, without further thinking.

 

How could Newton have been sure of the difference between Tom and Bob's argument?

 

Don't get me wrong, it's clear that they can't both be conclusive and neither can it be that Bob's is and Tom's isn't. If you think Newton could have been sure Tom's is, more than Bob's is, think more carefully. For one thing, I forgot to mention a rather subtle thing, too often overlooked: ether wasn't the real problem with the principle of relativity (and Maxwell and Lorentz were certainly aware of this too).

 

Now that's exactly the thing; using Lorentz's theory with the aether would be perfectly fine in the sense that natural observer can't tell the difference between that and Minkowski spacetime anyway (superficially anyway). Like Einstein commented on the letter, he was just thinking there must be a way to describe reality without using such a meaningless idea. That is, if there is no information available to us about the velocity of the aether (which is so by the very definition of aether, as per Lorentz's theory), then there ought to be valid way to represent what we know, in a terminology where that aspect does not exist.

 

It is just another case of "if we can't tell where the origin of the universe is, then our terminology ought to be symmetrical in terms of where the origin is. Otherwise we have made an undefendable assumption".

 

Let me re-iterate that I see all this aether stuff as a different track from how Newton could have arrived at relativistic time definitions. It's just the route that physics took, but not really the only possible route for arriving there. The most important bit lies in the self coherent definitions of distance, speed and time, in the case that clock synchronization must be performed via finite signal speeds.

 

Another thing, which I omitted in my previous post. Did you notice the fact that the perpetual motion Darrigol discusses, seemingly attributing it to Poincarè, is non sequitur? Even if Poincarè made this blunder, it wouldn't support Dick's case because, in order to make the same mistake, Newton would have had to be just as dumb. :doh:

 

No I didn't and I have not investigated that issue carefully, I sort of don't even want to get into it too deep, it's just so full of subtleties that is not even funny. My perspective is that any aether theory should be workable into a self-coherent (and thus valid) explanation of reality, if you carefully modify it. The only problem is that it probably ends up incredibly complex, full of tiny little special rules everywhere.

 

-Anssi

[Qfwfq]

I don't believe for a second that you wouldn't understand the connection between finite signal speeds and clock synchronization, and thus you should be able to see what DD is talking about, without jumping to "hey finite signal speeds don't lead to relativity!".

You're making an undefendable assumtion here. Which? :rolleyes:

 

...you seem to too often just reply with the first thought that pops into your mind, without further thinking.

Are you sure? Is that what I did above? Nah. Usually I think there would be too much to say, if you don't think about it properly; sometimes I put a great deal of thought into the brief reply but, alas, trying to stimulate a bit of thought in you is no use. You just believe what you said there, without further thinking.

 

Now that's exactly the thing; using Lorentz's theory with the aether would be perfectly fine in the sense that natural observer can't tell the difference between that and Minkowski spacetime anyway (superficially anyway).

But that wasn't the problem at all. Meantime:

It is just another case of "if we can't tell where the origin of the universe is, then our terminology ought to be symmetrical in terms of where the origin is. Otherwise we have made an undefendable assumption".

Newton did not have the conceptual tool of equivalenve classes and that's why he discussed things in terms of absolute rest, despite the simpler geometry and no reason to go through all the tricky stuff Lorentz and Poincarè did. It was later that the term inertial coordinates came about, seen as the class of all the possible choices ex aequo. That was when the ether was seen as superfluous, until EM made it appear useful again. As an aside, Mach's criticism of Newton supposed that he made the assumption of inherent impossibility of empirically distinguishing absolute rest but, not so; Newton was troubled by it and did grope for and speculate about the poosibility of some day observing it. It was just a bit beyond him, back then, and he even came nigh on the idea of Mach's principle but missed it by a slight conceptual leap.

 

I sort of don't even want to get into it too deep, it's just so full of subtleties that is not even funny.

Actually it is a rather gross error, but I agree there's no point going into it in detail unless you make it necessary. Mostly, you mentioned it despite that it could not have been a reason for Newton to question the coordinate transformations. Moreover, you would do well to understand that the part of Darrigol's paper, concerning Poincarè's analysis, shows that Minkowski vs. Galileo-Newton is not the same matter as Mach vs. Newton. Unfortunately, this distinction is more subtle than the perpetual motion blunder or, at least, your post shows that you can't see it despite thinking about these things (and even saying what you did, right after the above quote).

 

So, can you tell us why you think Tom's argument should have been more conclusive than Bob's, back at that time? Are you sure there isn't something missing in the premises? First of all, can you specify more exactly what you meant, each time you wrote "finite signal speeds" in your post? There is the possibility that you are making tacit assumptions, as if Newton could have been and was aware of them, or that you believe them unnecessary and hence Newton didn't need them.

[AnssiH]

Just a quick reply since haven't had much time to look over here, but let it be said this is not to dismiss what you are saying, rather I think we may practically understand each others on things that matter...

 

You're making an undefendable assumtion here. Which? :rolleyes:

 

...except maybe here because I don't have any idea; too many possibilities as to what you could be referring.

 

Are you sure? Is that what I did above? Nah. Usually I think there would be too much to say, if you don't think about it properly; sometimes I put a great deal of thought into the brief reply but, alas, trying to stimulate a bit of thought in you is no use. You just believe what you said there, without further thinking.

 

Well I have quite consciously chose to use very "e-primish" language almost all the time, such as "to me it seems like you are..." etc; I am quite conscious I can only talk about what impression I have about your responses, and of course I realize that impression is only formed by the text I see and how I interpret it.

 

But that wasn't the problem at all. Meantime:Newton did not have the conceptual tool of equivalenve classes and that's why he discussed things in terms of absolute rest, despite the simpler geometry and no reason to go through all the tricky stuff Lorentz and Poincarè did. It was later that the term inertial coordinates came about, seen as the class of all the possible choices ex aequo. That was when the ether was seen as superfluous, until EM made it appear useful again. As an aside, Mach's criticism of Newton supposed that he made the assumption of inherent impossibility of empirically distinguishing absolute rest but, not so; Newton was troubled by it and did grope for and speculate about the poosibility of some day observing it. It was just a bit beyond him, back then, and he even came nigh on the idea of Mach's principle but missed it by a slight conceptual leap.

 

Yeah he was troubled by the idea, and perhaps he could have also thought about the circularity of the definitions of spatial distances, speed, and time, when synchronizing the clocks always takes "time". I believe the point DD was trying to make - and which I would agree with - is simply that it is possible to recognize the circularity of one's own assumptions related to those definitions, and it is possible to uncover subtle inconsistencies which are solved via relativistic definitions (or rather logically equivalent of). Physics came about to those definitions via aether theories, but there are other possible routes.

 

Actually it is a rather gross error, but I agree there's no point going into it in detail unless you make it necessary. Mostly, you mentioned it despite that it could not have been a reason for Newton to question the coordinate transformations.

 

Now this is where you seem to be reading me wrong, so I'm sorry if my first post to this thread was not quite clear but it should be read as its first part just describing the history of physics (how we came to this), which is something I laid down just so people could perhaps think about the issue and perhaps realize that the route which got us there is not the only possibility. And the second part, in the very end, is just a simple comment about whether or not Newton could have had the material to reach relativistic definitions through careful thinking (basically via some other route). I thought this intention was clear from my post (and from my later responses) but maybe not.

 

Moreover, you would do well to understand that the part of Darrigol's paper, concerning Poincarè's analysis, shows that Minkowski vs. Galileo-Newton is not the same matter as Mach vs. Newton.

 

I don't really see it that way either. The idea that the concept of aether turned out physically meaningless is entirely something I said in reference to the history of physics. I don't see Newton having had similar problem to that (being that he was thinking in terms of corpuscular theories, albeit I do not know if he had a stance on emission theories), all that I'm saying is that he could have thought about the circularity of the definitions of "length", "time" and "speed", and the subtleties that arise from the inability to measure these things without making assumptions.

 

So, can you tell us why you think Tom's argument should have been more conclusive than Bob's, back at that time? Are you sure there isn't something missing in the premises?

 

You are talking about a premise where the concept of aether exists, and where the signal speeds are finite? Are you referring to the possibility of things like emission theories (i.e. varying signal speeds)? If you are, certainly those possibilities can be taken as obeying galilean relativity (if there wasn't further problems with them), but in all those possibilities the circularity of the abovementioned definitions remains.

 

First of all, can you specify more exactly what you meant, each time you wrote "finite signal speeds" in your post? There is the possibility that you are making tacit assumptions, as if Newton could have been and was aware of them, or that you believe them unnecessary and hence Newton didn't need them.

 

I am simply referring to the issues arising from the need to know the signal speed in order to synchronize the clocks, and the need to synchronize the clocks in order to know the signal speed.

 

-Anssi