Re: Michelson-Morley experiment

From: RP (no_mail_no_spam_at_yahoo.com)
Date: 01/01/05 

Date: Sat, 01 Jan 2005 00:55:15 -0600

Androcles wrote:

> "RP" <no_mail_no_spam@yahoo.com> wrote in message
> news:33lqv6F3vdj4vU1@individual.net...
>
>>
>>Androcles wrote:
>>
>>
>>>"RP" <no_mail_no_spam@yahoo.com> wrote in message
>>>news:33ll0pF42b7omU1@individual.net...
>>>
>>>
>>>>Androcles wrote:
>>>>
>>>>
>>>>
>>>>>"RP" <no_mail_no_spam@yahoo.com> wrote in message
>>>>>news:33lhevF41q390U1@individual.net...
>>>>>
>>>>>
>>>>>
>>>>>>Androcles wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>"RP" <no_mail_no_spam@yahoo.com> wrote in message
>>>>>>>news:33lcj0F418475U1@individual.net...
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>hasuinterceptor wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>>Hi guys!
>>>>>>>>>
>>>>>>>>>This is my visit to this here forum. I'm googled it out because
>>>>>>>>>I have
>>>>>>>>>a question (or, as some might say it, a series of 'hidden'
>>>>>>>>>questions)
>>>>>>>>>regarding the Michelson-Morley experiment.
>>>>>>>>>
>>>>>>>>>Here are two links to the experiment just in case:
>>>>>>>>>
>>>>>>>>>http://en.wikipedia.org/wiki/Michelson-Morley_experiment
>>>>>>>>>http://scienceworld.wolfram.com/physics/Michelson-MorleyExperiment.html
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>This experiment was meant to prove the existance of ether (and
>>>>>>>>>it
>>>>>>>>>failed, of course). Now, people are telling me that this
>>>>>>>>>experiment
>>>>>>>>>also proves that the speed of life is stable and is not
>>>>>>>>>dependant on
>>>>>>>>>the speed or state of the observer (A. Einstein's theory).
>>>>>>>>>
>>>>>>>>>Can anyone possibly explain to me how is that? I've went through
>>>>>>>>>this
>>>>>>>>>experiment in my mind for very long, but was unable to reach a
>>>>>>>>>rational conclusion as to this matter.
>>>>>>>>>
>>>>>>>>>I would appretiate any help.
>>>>>>>>
>>>>>>>>Special relativity explains the null result by setting the speed
>>>>>>>>of light as an observational constant. IOW, by setting the
>>>>>>>>apparatus perpetually *at rest* with respect to the medium in its
>>>>>>>>own frame. That is, if it isn't moving wrt the medium, then there
>>>>>>>>would be no fringe shift expected. The difference between this
>>>>>>>>theory, and the absolute ether theory, is that their predictions
>>>>>>>>differ when the state of motion of the apparatus is changed.
>>>>>>>>Since the Earth changes in its motion wrt any given inertial
>>>>>>>>frame over the course of the year, then the absolute ether theory
>>>>>>>>cannot maintain that the apparatus was at rest wrt the medium on
>>>>>>>>every trial. I.e. it could only have been at rest for a single
>>>>>>>>moment, at most, wrt the medium. The special relativistic
>>>>>>>>solution is thus in keeping with the results, and the absolute
>>>>>>>>ether is an impossibility, i.e. it was disproved by the
>>>>>>>>experiment(s).
>>>>>>>>
>>>>>>>>Proofs of the truth of any given theory is however an
>>>>>>>>impossibility, and because of this, neither does MMX prove that
>>>>>>>>special relativity is the 'de facto' correct theory. The
>>>>>>>>evolution of theory depends upon the process of elimination, that
>>>>>>>>is, it is possible to *disprove* theories but not to prove them.
>>>>>>>>Some theories may account equally as well for a particular
>>>>>>>>phenomenon as do other competing theories. The one may OTOH take
>>>>>>>>as general premises views that are contradicted by experiments in
>>>>>>>>other domains. These experimentally falsified theories are thus
>>>>>>>>clearly only *accidentally* successful in the domain to which
>>>>>>>>they apply well, i.e. they are special cases of a more general
>>>>>>>>theory, and their terms were improperly interpreted. By
>>>>>>>>successive elimination of faulty theories such as these, the most
>>>>>>>>generally successful of them are established and retained until
>>>>>>>>yet more general solutions are developed. This applies without
>>>>>>>>question to special relativity, in that it was soon discovered
>>>>>>>>that its domain was limited to inertial frames.
>>>>>>>>
>>>>>>>>The MMX disproves the *absolute ether* theory in that an absolute
>>>>>>>>ether, through which light propagates in wave-like motion, would
>>>>>>>>have resulted in the observation of fringe shifts. No fringe
>>>>>>>>shift was observed, that is, none that corresponded to motion wrt
>>>>>>>>an absolute space (absolute ether). IOW, the MMX proved only one
>>>>>>>>thing, i.e. that light doesn't propagate through a fixed
>>>>>>>>(stationary in all points wrt itself) medium.
>>>>>>>>
>>>>>>>>There are however several competing theories remaining that also
>>>>>>>>were not disproved by the experiment. OTOH, each of those
>>>>>>>>theories makes quantitative predictions in other domains as well,
>>>>>>>>and many can thus be filtered out through other means. The most
>>>>>>>>successful of those, in the macroscopic domain, has been general
>>>>>>>>relativity, of which special relativity is a limiting case valid
>>>>>>>>when there are no gravitational fields present in the system
>>>>>>>>under study, or a good approximation when those fields are
>>>>>>>>negligible in magnitude. Though it isn't the most intuitive
>>>>>>>>solution, it is the most versatile theory by far (of those that
>>>>>>>>have been considered), in that it describes the greatest number
>>>>>>>>of behaviors with the least number of premises. Though special
>>>>>>>>relativity successfully accounts for the null result of the MMX,
>>>>>>>>it isn't a general solution, no more so than some of its
>>>>>>>>competitors, and was later superseded by general relativity for
>>>>>>>>this very reason.
>>>>>>>>
>>>>>>>>As Androcles notes, the ballistic model of light equally well
>>>>>>>>explains the null results of the MMX. What he consistently fails
>>>>>>>>to note, however, is that special relativity *is* a ballistic
>>>>>>>>model, one that simply defines the terms *time* and *distance*
>>>>>>>>differently than does Newton. Thus the equations of motion in
>>>>>>>>special relativity differ in form from those that Androcles
>>>>>>>>expects.
>>>>>>>>
>>>>>>>>Don't get into the relativity debate. I argued for years against
>>>>>>>>special relativity only to find that it was my very objections
>>>>>>>>that were the premises that led to general relativity. The
>>>>>>>>problem seems to be that those handful who actually understand
>>>>>>>>the theory are typically inept at relating that understanding.
>>>>>>>>And then there are those who claim to understand it but don't,
>>>>>>>>and are prone to make statements on its behalf that simply do not
>>>>>>>>follow from the theory. IOW, there are idiots on both sides of
>>>>>>>>the debate, and your best bet is to forget about trying to have
>>>>>>>>serious discussion about it on usenet.
>>>>>>>>
>>>>>>>>Richard Perry
>>>>>>>
>>>>>>>
>>>>>>>Good advice, Richard. However, I have difficulty with your
>>>>>>>assertion
>>>>>>>that GR is a valid model since it takes no account of such
>>>>>>>empirical
>>>>>>>data as
>>>>>>>
>>>>>>>http://www.androc1es.pwp.blueyonder.co.uk/Compare.JPG
>>>>>>>
>>>>>>>Both diagrams have distance vertically and time horizontally. The
>>>>>>>vertical distance is many many light years. The observer is at top
>>>>>>>and
>>>>>>>the source at bottom.
>>>>>>>
>>>>>>>In the upper diagram, the speed of light is constant and the
>>>>>>>spacing between the lines occurs at transmission, whereas in the
>>>>>>>lower diagram the speed of light is added to the speed of the
>>>>>>>source, the spacing between the lines occurs only at the position
>>>>>>>of the observer. Either way, the observer sees the same effect,
>>>>>>>but must invoke general relativity's time dilation for the upper
>>>>>>>diagram. See
>>>>>>>http://nobelprize.org/physics/laureates/1993/taylor-lecture.pdf
>>>>>>>If we add velocities, the lower diagram is correct and the
>>>>>>>interval between the pulses is regular at transmission, but is
>>>>>>>seen to be irregular, but if we believe what we see then the
>>>>>>>pulses are transmitted irregularly at source.
>>>>>>>
>>>>>>>I strongly suggest that Occam's Razor makes the lower diagram the
>>>>>>>correct one.
>>>>>>>
>>>>>>>I see nothing of value in pretending spacetime is distorted "out
>>>>>>>there"
>>>>>>>
>>>>>>>to make agreement with our subjective observations. Objectively,
>>>>>>>the velocity of light must be source dependent.
>>>>>>>
>>>>>>>You say "The special relativistic solution is thus in keeping with
>>>>>>>the results, [of MMX]" but I have to take issue with that.
>>>>>>>
>>>>>>>The x-axis arm of MMX is length contracted by
>>>>>>>
>>>>>>>xi = (x-vt)/sqrt(1-v^2/c^2) and the y-axis arm has no contraction.
>>>>>>>
>>>>>>>Standing alone, that might then be in agreement with Lorentz's
>>>>>>>analysis
>>>>>>>
>>>>>>>of contraction and re-introduce the aether. Except for one thing:
>>>>>>>
>>>>>>>Michelson was assuming would be c-v, c+v in one arm but not the
>>>>>>>other.
>>>>>>>
>>>>>>>Einstein claims it to be c (the same c) in both arms.
>>>>>>>
>>>>>>>Same speed of light, one arm shorter than the other. That
>>>>>>>produces a shift.
>>>>>>>
>>>>>>>Now, if Einstein had proposed a longitudinal time dilation and not
>>>>>>>a transverse time dilation, it might still possibly manage to be
>>>>>>>fringeless,
>>>>>>>
>>>>>>>and indeed Einstein DOES say tauX = (t-vx/c^2) / sqrt(1-v^2/c^2).
>>>>>>>
>>>>>>>What is definitely missing is tauY = (t-vY/c^2) /
>>>>>>>sqrt(1-v^2/c^2).
>>>>>>>
>>>>>>>He got into trouble with his transverse and longitudinal mass,
>>>>>>>too.
>>>>>>>
>>>>>>>Androcles
>>>>>>
>>>>>>There is no contraction of either arm in special relativity, the
>>>>>>interferometer is at rest wrt the medium in its own frame.
>>>>>
>>>>>
>>>>>Then
>>>>>xi = (x-vt)/sqrt(1-v^2/c^2)
>>>>>is totally meaningless drivel.
>>>>>
>>>>>"Examples of this sort, together with the unsuccessful attempts to
>>>>>discover any motion of the earth relatively to the ``light medium,''
>>>>>suggest that the phenomena of electrodynamics as well as of
>>>>>mechanics possess no properties corresponding to the idea of
>>>>>absolute rest. They suggest rather that, as has already been shown
>>>>>to the first order of small quantities, the same laws of
>>>>>electrodynamics and optics will be valid for all frames of reference
>>>>>for which the equations of mechanics hold good. We will raise this
>>>>>conjecture (the purport of which will hereafter be called the
>>>>>``Principle of Relativity'') to the status of a postulate, and also
>>>>>introduce another postulate, which is only apparently irreconcilable
>>>>>with the former, namely, that light is always propagated in empty
>>>>>space with a definite velocity c which is independent of the state
>>>>>of motion of the emitting body. These two postulates suffice for the
>>>>>attainment of a simple and consistent theory of the electrodynamics
>>>>>of moving bodies based on Maxwell's theory for stationary bodies.
>>>>>The introduction of a ``luminiferous ether'' will prove to be
>>>>>superfluous inasmuch as the view here to be developed will not
>>>>>require an ``absolutely stationary space'' provided with special
>>>>>properties, nor assign a velocity-vector to a point of the empty
>>>>>space in which electromagnetic processes take place. " -- Einstein
>>>>>1905.
>>>>>
>>>>>"The law of the propagation of light in vacuo would then have to be
>>>>>replaced by a more complicated law conformable to the principle of
>>>>>relativity. The development of theoretical physics shows, however,
>>>>>that we cannot pursue this course. The epoch-making theoretical
>>>>>investigations of H. A. Lorentz on the electrodynamical and optical
>>>>>phenomena connected with moving bodies show that experience in this
>>>>>domain leads conclusively to a theory of electromagnetic phenomena,
>>>>>of which the law of the constancy of the velocity of light in vacuo
>>>>>is a necessary consequence. Prominent theoretical physicists were
>>>>>therefore more inclined to reject the principle of relativity, in
>>>>>spite of the fact that no empirical data had been found which were
>>>>>contradictory to this principle."--Einstein 1920.
>>>>>
>>>>>
>>>>> If OTOH we
>>>>>
>>>>>
>>>>>
>>>>>>assume a frame in motion wrt the interferometer, then the speed of
>>>>>>light is c both ways wrt our moving frame, but however the arms are
>>>>>>now in motion. Thus wrt our moving frame, the two-way speed of
>>>>>>light is c/gamma^2 wrt the longitudinal arm and c/gamma wrt the
>>>>>>transverse arm. Thus the longitudinal arm must be contracted by a
>>>>>>factor 1/gamma in order to provide a null result. You can
>>>>>>alternately use your ballistic model in a Galilean context to
>>>>>>provide the same result. You're not only frame jumping, but mixing
>>>>>>models as well.
>>>>>
>>>>>
>>>>>What are you talking about?
>>>>>It is YOUR OTOH, not mine.
>>>>>If anyone is frame jumping or mixing models, you are.
>>>>>Androcles.
>>>>
>>>>I've never found an error in the math applied to MMX, it is
>>>>derivable directly from Euclid without even reference to special
>>>>relativity.
>>>
>>>
>>>
>>>>a Galilean context it yields LET.
>>>
>>>
>>>Really. How so?
>>>
>>>
>>>
>>>
>>>>By redefining time and distance, LET was transformed into SR. The
>>>>difference is only one of interpretation.
>>>
>>>
>>>I think you are somewhat misguided into imagining I am a LET
>>>supporter.
>>>
>>>
>>>
>>>
>>>>OTOH, it was a mere supposition that only the longitudinal arm length
>>>>is non-invariant; I once posted a mathematical proof that a
>>>>lengthening of the transverse arm will serve equally as a solution,
>>>>and moreover that there are also an infinite number of solutions
>>>>involving changes in lengths of both arms that will provide for the
>>>>same end result. There is a single ratio that must be maintained (per
>>>>experiment), but there are infinite mathematical methods of
>>>>maintaining it, i.e. there are infinite numbers of "sets of premises"
>>>>that are workable.
>>>>
>>>>The appeal of the LET/SR approach is that the math is simpler, and in
>>>>the absence of a fixed medium, it seems reasonable (whether "true" or
>>>>not) that light speed be defined as constant, a definition that
>>>>immediately negates those infinite other scenarios. There is nothing
>>>>absolute about premises of SR, i.e. they are not "true", they are
>>>>simply "true within context".
>>>>
>>>>As for your argument: There are two methods of stating the speed of a
>>>>thing, the first being its speed wrt a given frame, the second being
>>>>its speed wrt a given frame as measured in yet another frame.
>>>
>>>
>>>In MMX, three.
>>>1) with respect to the medium (Lorentz)
>>>2) with respect to the source (Galileo)
>>>3) with respect to the detector. (Einstein)
>>>
>>>The result of MMX eliminated aether as medium,
>>>but left air, source and detector in a single frame, all relatively
>>>at rest.
>>>
>>>
>>>
>>>
>>>>Light speed can indeed be c-v in the latter, within the special
>>>>relativistic context. Your objections to Einstein's use of c-v seem
>>>>to indicate that you are superposing this expression over the first
>>>>definition of speed, which is a fallacy, since light speed is always
>>>>c in the first definition.
>>>
>>>
>>>Quote:
>>>"It follows, further, that the velocity of light c cannot be altered
>>>by composition with a velocity less than that of light.
>>>For this case we obtain V = (c+w)/(1+w/c) = c."
>>>Unquote.
>>>Reference :
>>>http://www.fourmilab.ch/etexts/einstein/specrel/www/
>>>
>>>
>>>
>>>>Until you understanding the difference between these two measures of
>>>>speed, then you're bound to repeat the same fallacious arguments
>>>>indefinitely. I'm not making an attempt to flame you, I'm just
>>>>stating what appears to me to be the error in your arguments.
>>>
>>>
>>>>Richard Perry
>>>
>>>Likewise.
>>>You appear to be labouring under the delusion that I support LET.
>>>Nothing could be further from the truth. I support the theory of
>>>Ritz,
>>>not Einstein and not Lorentz.
>>>
>>>Androcles
>>>
>>
>>I've looked at Ritz, and a million other alternate theories, and don't
>>subscribe to any of them, because none are based entirely upon lab
>>data.
>
>
> Your choice. I'll accept that none are complete
>
>
>
>>OTOH, what sort of experiment can you suggest to invalidate SR?
>
>
> Shoot the moon with a laser from ISS and pick up the reflection
> with HST. Most equipment is in place. Even cheaper, use Roemer's
> method but with Cassini at Saturn as the clock.

What you cannot do is determine the displacement between source and
detector except by measuring the time-like interval required for a
photon to traverse that distance and then dividing the speed of light
by that time-like interval. Thus you will necessarily measure the same
speed of light that you used to find the displacement. It's quite
circular for sure, but it is also quite unassailable. OTOH, what isn't
circular in the mathematics of physics? E=IR for instance, is circular
in quite the same way, but who can deny its utility? It works, and it
works very well.

>
>
>>Light speed is *defined* as constant.
>
>
> Not well-defined, since it isn't.

Check with NIST on this, I'm certain that you'll find that it is in
fact defined well.
>
>
>> You simply cannot invalidate what has been defined to be true.
>
>
> Sure I can. I could define the speed of sound to be constant if
> I chose, but it wouldn't be well-defined and would be quickly
> invalidated.

No, it would not be invalidated if carried through to completion. By
this I mean that you would have to redefine other parameters as well
in order to maintain a consistency. It can be done, but it would be
quite messy.

> Ptolemy define the Earth as the centre of the universe
> and that lasted 1400 years. Anyone can define anything they like.

And Special Relativity reinstated that view.

> Einstein said
> "the velocity of light in our theory plays the part, physically,
> of an infinitely great velocity."

By this he meant only that particles interact instantly, but that the
time here differs from the time there, and thus there is always a
measured delay. It gets complicated maintaining this view, absorber
theory and such, but that's immaterial to your argument that it's a
definition. It isn't, it's just an observation or better an
interpretation. By replacing c with oo the lorentz transform reduces
to the Galilean transform. Thus his interpretation is mathematically
consistent.

> Reference :
> http://www.fourmilab.ch/etexts/einstein/specrel/www/
>
> That's a definition, and nonsense.
>
>
>
>>And so, even though the agreement with lab data was obtained via
>>redefinition of the data, I can only argue at this point that it
>>accidentally gets good results,
>
>
> Empirical data doesn't need redefinition. Only the model that
> interprets it can be changed.

Einstein quipped "If you can't fit the theory to the data, then change
the data". Upon first reading this sounds like an absurd notion, but
upon careful consideration it was actually a quite insightful
approach, even a logically necessary approach. Circularity, as I've
already noted above, is the only means of providing unassailable
mathematical relationships. In a universe in constant flux, if you
don't initially and arbitrarily define some constants, then you'll
never have a possibility of deriving a consistent set of physical
laws. IOW, you have to start somewhere with a bit of decisiveness, and
what's more decisive than proposing an arbitrary rule and then forcing
the data into conformity, even if that means redefining measurements
and measurement procedures. In retrospect I see this statement as
nothing less than pure genius.

>
> Data: a stick in water appears bent.
> Model: I believe what I see, the stick is bent.
> Model: The speed of light in water is less than the speed of
> light in air. The stick only appears bent.
> The data doesn't change, the interpretation does.
>
> Data: Rainbow.
> Model: God made it as a sign from heaven. (see Old Testament)
> Model: The refractive index of water differs with EM frequency.
> The data doesn't change, the interpretation does.
>
> Data: delta-cepheus brightens and dims periodically (5 days).
> Model: The star is pulsating.
> Model: The star is in tiny orbit obeying Kepler's laws
> and the speed of the light we see it by is source dependent.
> The data doesn't change, the interpretation does.
>
> It's all a matter of subjectivity vs objectivity.

Indeed.

>
>
>
>> i.e. that it is a special macroscopic case of a more detailed
>>underlying electromagnetic reality. But then I'm not the only one
>>making this claim; quantum mechanics has been around longer than I
>>have. I've also noticed recently that Einstein inserted a proviso in
>>one place to his special relativistic claims, to the extent that "I
>>know that these phenomena can be explained by complicated
>>interactions, as outlined by Lorentz and others, but special
>>relativity produces the result without regard to these details." Exact
>>wording escapes me, as does its location. IOW, he is here admitting
>>that the theory is not fundamental.
>
>
> He isn't even mathematically correct.

Perhaps he hadn't fully understood his wife's theory at the time of
that writing ;)

> "But the ray moves relatively to the initial point of k, when measured
> in the stationary system, with the velocity c-v, so that x'/(c-v) = t."
> and
> "It follows, further, that the velocity of light c cannot be altered by
> composition with a velocity less than that of light.
> For this case we obtain V = (c+w)/(1+w/c) = c."
> are contradictory statements.
> I am currently in dispute with Randy Poe on the validity of Einstein's
> equation
> ½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v)).
> Poe has arrogantly said that he can derive the Lorentz equations based
> on this, and I KNOW he cannot.
> Follow the thread and watch what happens. I can safely predict the
> outcome. Whether he throws up his hands and calls me idiot as Alan
> Schwartz would do, or capitulates gracefully (very unlikely, it is not
> human nature to do so) he will not succeed. It isn't that I will snip
> and ignore his points, I shall answer them, as I answer yours. I
> try to inject a little levity, sure, and I'm certainly vicious with
> those
> those that are vicious toward me, but I will NOT accept mystery
> as a solution.

Poe is probably finding that the task that he set forth for himself is
harder than he expected it to be. There is one other premise that must
be introduced in order to derive the lorentz transform, namely
symmetry. Unless each of two observers perceive the same relative
speed between them, lorentz is a futile quest. By arbitrarily defining
the respective observations as asymmetrical a number of other
transforms can be derived, all being equally workable, even though
seemingly absurd. Space and time can be distorted to ones liking as
long as one grinds his optics to prescription.

>
>
>>There is also this to take into consideration, one of his arguments in
>>favor of relatively of simultaneity, was that simultaneity *must* be
>>relative, else we could not progress in time.
>
>
> Well of course. Supernova 1987A did not take place in 1987. That
> was only when we observed it. It occured 170,000 years before that.
> The Minkowskian sqrt( x^2 + y^2 + z^ + ict ^2) merely relates
> that the occurrence was simultaneous with our observation.

Incorrect. What it means is that when it emitted that light, the Earth
was that far along in its now.
>
>>IOW, progression in time ensues as a sort of feedback effect; the time
>>that you are progressing into must already exist...somewhere. That
>>somewhere being every other frame in which you are not presently in.
>>That was the one consideration that I could never get past without
>>arriving at the same conclusion.
>>
>>Richard Perry
>
>
>
> I cannot agree. That involves the concept of predetermination
> and contradictory free will.

Point being? Free will can't even be defined without contradicting
oneself.

> A purely philosophical debate without
> any way of being resolved.

Of course it can be resolved. It's called physics. Every action has a
predetermined reaction associated with it. Complexity is a separate
issue, but regardless of complexity, repeatability of effects and
predetermination are virtually synonymous.

> Science is the observation, investigation
> and explanation of the occurences or phenonema in Nature, not
> the subjectivity of the human psyche. I'm discussing physics, not
> psychology. I refuse to speculate on whether or not my actions
> tomorrow are pre-ordained. I will insist (albeit subjectively) that
> my actions tomorrow are my choice, tomorrow. We all have
> 20-20 hindsight and 0-20 foresight. Saying "I told you so" is
> only a guess based on probability, not a certainty.
>

It's a philosophical issue only for those regard it as a philosophical
issue. For some it's a simple matter of empirical observation, and
thus a matter of science. When you make statements containing terms
such a *choice*, then you should probably make some sort of effort to
explain how choice and predetermination are incompatible. My computer
makes several choices every second, and yet there was never any
argument as to what the outcome would be.

Richard Perry

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