Subject: Re: Numbers
From: Leonard Timmons
Date: Fri, 17 Jan 1997 21:38:03 -0500
David K. Davis wrote:
> ... The point is not that discovery of Pi is some supreme measure
> of intelligence, but rather that Pi is in some sense objective and there
> waiting to be disovered by whomever - it is not a social artifact. We
> think of things existing physically, located in space somewhere. But where
> does Pi exist? That's why I speak of the "space " of logical possibility.
This "space of logical possibility" sounds to me like a property space
where we take one of the properties of a real object and ignore it.
That property is the object's position in 3D space. In this property
space everything that is identical except for 3D position, now occupies
the same location. Let's consider the electron as you have done
below. All electrons become a new thing called the "electron prototype".
But such an object, once it is created, also has another property called
number. This property tells us how many electrons are in the universe.
Suddenly a number has appeared, but it results from us discarding
information about the world around us. As far as I can tell, all numbers
are produced in this way. If we discard enough properties of the world
around us (like charge, for instance) ultimately we are left with only
the property called number which cannot be further reduced.
> There's an intermediate kind of example: the electron. Electrons exists
> througout the universe and are, as far we know, absolutely identical. They
> are all perfect instantiations of one electron. Does this general
> electron, apart from its zillions of instantiations, exist? One has to say
> yes in recognition of this identity across the universe. There is
> something very abstract about the electron and yet it exists, exists
> everywhere, and is real. Pi may not have any one perfect instantiation,
> and yet it too exists, exists everywhere, and is real.
But the electrons are not identical. We have to ignore their different
positions in order to make such a statement. In order to say that
the prototypical electron actually exists in a world without humans,
we have to say that any two electrons can be replaced by one another
(with the remainder of the universe held constant) and the universe would
be no different. To me, this seems entirely reasonable and would argue
for the actual existence of your prototypical electron. It would,
however, also argue for the actual existence of numbers, since
your prototypical electron would also have as a property the number
of electrons that exist.
> Modern physics has
> made clear how tenuous is the boundary between the realms of abstract
> logical space and real physical space. I think the modern physicist must
> feel that they are trying to discover how nature does mathematics.
And if numbers exist and are real and are fundamental (a lot of suppositions
to be sure) is matter just the numerals that result from their existence?
Number would be the only real property in the universe and numerals would
provide variations on the theme since a single preferred representation of
any number (127 for instance) would seem unreasonable.
-leonard
Subject: Re: paradox
From: candy@mildred.ph.utexas.edu (Jeff Candy)
Date: 17 Jan 1997 22:52:27 GMT
Ron Shepard:
|> It seems that there should be a difference between proving/confirming
|> relations between members of finite sets and those of infinite sets. If
|> there are a finite number of objects, then confirmation of "All non-black
|> things are non-ravens" does indeed make progress toward proving that all
|> ravens are black; in principle, if the process were continued until all
|> non-black objects were tested, we would have the complete proof. But if
|> there are an infinite number of such non-black objects, then little, or
|> perhaps even no progress at all has been made.
Bingo.
If you limit yourself to axiomatic set theory, then you get
nowhere -- at least nowhere interesting. If you care to discuss
the problem, rather, in the context of statistics or decision
theory, it becomes far more complicated.
At the level of the "raven paradox", for example, all physical
constants (c, G, eps_0, ...) are not only unknown, but ill-defined.
Now, the next time someone well-trained in logic tells you that
you can't prove the existence or non-existence of god, you can
mention the parallel with _reality_ vs. the raven paradox.
-------------------------------------------------------------------
Jeff Candy The University of Texas at Austin
Institute for Fusion Studies Austin, Texas
-------------------------------------------------------------------
Subject: Re: A case against nuclear energy?
From: meron@cars3.uchicago.edu
Date: Fri, 17 Jan 1997 22:55:59 GMT
In article <32E02184.6115@erols.com>, Dennis Nelson writes:
>meron@cars3.uchicago.edu wrote:
>>
>> In article <32DE8A53.1D18@spam.com>, Greg Chaudion writes:
>> >Jim Carr wrote:
>> >
>> >{Cut}
>> >
>> >> The attitude of the US military towards weapons testing was that
>> >> of a nation still at war with a dangerous enemy. They did not
>> >> test when winds were blowing the wrong way, but they did not delay
>> >> tests when conditions were uncertain. Compared to other effects
>> >> of government policies, the risk was not that bad and the exposures
>> >> of downwinders cannot be compared to what Slotin got -- or what a
>> >> person being treated for cancer gets, for that matter.
>> >
>> >So, you are justifying the deaths of civilians because the big bad wolf
>> >was at the door.
>>
>> Yes. Do you realize how many civilians did die in various countries
>> due to a lack of preparadness for war.
>
>And how many died due to thorough preparations for war? Bogus argument.
Nothing bogus. Check numbers and compare. Consider that it was the
lack of preparadness of western democracies for war that convinced
Hitler that in spite of WWI experiences his conquest plans stand a
chance.
>> >Was not a similar defense used during the war crime trials after WWII.
>>
>> No. Else the whole top brass of the Allied military would've to stand
>> trial too. It was well understood that civilians may get hurt in the
>> course of military operations. What was considered a crime (though
>> even this only selectively so) was intentional targeting of civilians,
>> not compelled by any military rationale.
>
>Exactly. Both sides losts their minds along with their morality during the
>second world war.
Really? Well, yes, lots of it could've been prevented by an outright
surrender to Hitler, right?
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Subject: GR Problem Restated
From: gpenney@thezone.net (George Penney)
Date: 18 Jan 1997 02:54:33 GMT
GR---Equivalence Problem
When Einstein put forth his Equivalence Principal using the elevator thought
experiment,he reasoned that a beam of light entering the elevator through a w
indow,(let's say located 1/4 distance from the top),would curve downward and
strike the opposite wall at a lower point than where it entered if the elevat
or were accelerating upward.He concluded that light would also bend in the vi
cinity of a Gravitational Field produced by Mass,saying there was no way to
determine if the elevator had accelerated or entered a Gravitational Field.
Let's carry this to the limit!!.If we increase the acceleration,the radius
of curvature will become smaller,thus the beam will hit the opposite wall fu
rther down.If we keep on increasing the acceleration the beam will eventually
almost hit the floor,then go to the left,then upward,then to the right again,
finally going in an endless circle.
No:1 What will be the acceleration of the elevator(in m/s^2),to produce this
No:2 What will be the dia of the circle of light?What would be the limit as
to how small the dia could be?(if you wish and if need be assign your
own dimensions to the elevator).
When I first posted this article on the sci.physics NG,as GR problem,some of
the responses ranged from---this is totaly incorrect to maximum deflection
would make the beam just hit the opposite floor to the only circle was in my
head.
Oooo.K.I'll do some adjustments here as I don't think you seen what I was
getting at.(no one ever did give the value of acceleration for max curvature)
NOW----Suppose as the beam was starting to bend I accelerate the elevator to
the Right,then Down,then to the Left,then Up----What Now??.The elevator would
be accelerating in a circular manner,but to the observer inside he would obse- rve the light to be going in a circle!!.
The important thing to note here is the relationship between accelleration
and MASS!!,for if the acceleration is changed it affects the lightbeam as wo
uld be the case if we were talking about light in the vincinity of mass,if
we were to increase or decrease the mass it would vary the curvature of the
light.
With this in mind,what would be the right amount of mass to cause a lightbe
am to orbit it?(i'll take a few punches on this I expect).If you say light
has no mass so it would not go into orbit the way a body of mass would,(as
for example a planet around a star),it must follow the curvature of space
determined by the mass and if the mass is large enough it must confirm to the
elevator analogy.---What difference would it make if the large mass were rot
ating at i'ts maximum and draging spacetime around with it?
Finally what would the elevator equivalent of light going into a Black Hole?
(in terms of the elevator's acceleration).Don't reply that it would enter the
elevator and not come back out,because in the original problem it would not
go back out through the window it entered.And I forbid you to put a window
at some location on the opposite side(or anywhere else).No such trickery,as
this is my modified thought experiment,so lets stick to the conditions I've
set.
George Penney
Subject: Re: What is the Cause of Time Dilation?
From: savainl@pacificnet.net (Louis Savain)
Date: Fri, 17 Jan 1997 18:41:51 GMT
In article , Keith Stein
wrote:
[Reposting via different server. Sorry if double post]
> Louis Savain writes
>> Concepts like geodesics and inertial paths in spacetime
>>>>are simply dumb.
> right!
>
>> And no amount of rationalization or
>>>>obfuscation is going to change that.
> right!
>
>> Too bad some of you are having
>>>>trouble grasping this. And also, too bad if some of you take offense.
> right!
>
>> Time is always derived by applying the equation t = d/v.
> Wrong!
>
> Surely the concept 'time' must preceed the concept of 'velocity'.
It may indeed precede 'velocity' but maybe not, as I willingly
concede that our understanding of reality is almost entirely
inductive. In this light, I don't understand how you can be so sure
that time must precede velocity. :-) At any rate, I have what I
think is *deductive* proof that it does not, but being human and
eminently fallible, I'm always willing to change my mind in the face
of strong evidence to the contrary.
When you say that time precedes motion, I assume that you mean that
time is a more fundamental physical concept than motion and that it
can exist independently of motion. Apparently, in your view, motion
needs time. I, OTOH, take the position that time is an entirely
abstract mathematical notion that cannot be divorced from velocity or
change. I think I perfectly understand your position since I used to
subscribe to the same view but I've changed my mind over the years.
Here's the reason:
As soon as you separate time from motion/change, time becomes a
dimension of its own. I call this separation the "reification of
time". You must then explain the concept of the 'passage of time'. I
believe that the phrase 'passage of time', is objectively an oxymoron.
Why? Because the word 'passage' is indicative of some form of travel
or motion. 'Passage of time' then means that, either objects stand
still and time just passes by, or that time stands still and objects
move in time. Whichever way you want to look at it, it is logically
and mathematically impossible for either interpretation to be correct.
The passage of time must obey the equation v = t/t. This equation
always gives the dimensionless value 1, which says nothing about
change or motion. It is a meaningless number in and of itself.
> What is your definition for 'v' in the above equation, Louis ?
Well I believe that the traditional way of measuring velocity in
terms of time (as in 'miles per hour' or 'meters per second') may be
intuitive but is highly misleading. It should be the other way
around, i.e., time should be measured in terms of velocity. IOW, if
we create a unit of measurement for velocity called, let's say a
"zeno", time should then be measured in 'meters per zeno'. So then
velocity should be regarded as a mere quantitative phenomenon like
mass or charge. Velocity is a change in position and its measure is
merely a quantitative measure of change. The higher the number, the
faster the change. Time is abstract and is inversely proportional to
velocity. To insist that velocity must be described in terms of time
is not unlike insisting that mass must be described in terms of its
abstract inverse, 1/mass. It is not necessary, IMO.
As an aside, notice that I say "describe" instead of "define". This
is because I'm always taken aback by what I've been calling "physics
by definition". For example, physicists have no qualm about defining
the slowing of clocks as "time dilation", a very injurious practice
IMO, especially since the concept of time is linked to all sorts of
misconceptions. Should not the internal velocity of a clock mechanism
be just that, velocity? Why redefine 'the measure of velocity' to
mean 'the measure of time' and reify time (another absurd practice) in
the process? It's highly unnerving when you think about it because
the confusion that ensues from this "damnable" practice makes it
almost impossible to discuss special relativity. Besides, how can
anyone define nature? Should we not be *describing* it instead of
defining it and be ready to change our description if a new discovery
warrants it? Food for thought.
Having said all that, it pays to revisit the notion of the 'passage
of time' in this new light. We have already determined that time
cannot be divorced from velocity. So from whence cometh our notion
that time passes even in the absence of motion in 3-D "space"? This
is a very disturbing state of affairs, because here we have a
situation where time apparently exists without motion. How can that
be possible if time is abstract and cannot be divorced from motion as
we have shown above? Well it is *not* possible. Logic wins
**always**. There must be motion or velocity somewhere in order to
obtain time. This is inescapable.
To solve this nearly impossible quandary one must postulate motion
along a fourth dimension. And, as we have just shown, this fourth
dimension cannot possibly be a temporal dimension a la spacetime. The
so-called "spacetime continuum" is hopelessly flawed as a model of
reality. So what then? What else is there? Why, a spatial dimension
of course! And here is the bombshell, the piece de resistance so to
speak: The entire matter of the known universe must be moving along a
fourth spatial dimension. More food for thought.
In conclusion and retrospect, the 'passage of time', with its
implication of motion in the word 'passage', is not that far off after
all. There is indeed a passage or a travel taking place, but it is
not a travel in time, but a "travel" along a fourth spatial dimension.
Here I'm careful to put "travel" in quotes because I have very
specific definitions for concepts like travel and motion. Let me just
say for now that I don't believe that motion involves going from one
place to another in an extrinsic substantive space, (thank you Mr.
Zeno!) as I consider myself a staunch nonlocalist and nontemporalist.
>>> What is new in this century is the unification of space and time.
>> Which is the biggest nonsense to ever come out of science.
> right!
>--
>Keith Stein
I am glad I got only one wrong assertion out of five in your
judgement. That's something to be happy about. :-) Maybe we should
form a club. But then again, maybe not, as I'm sure you'll find new
things to disagree with in this article. :-) I apologize for its
length.
Best regards,
Louis Savain
Subject: Re: Utter Futility of Arguing about God
From: "Bruce C. Fielder"
Date: Fri, 17 Jan 1997 20:39:02 -0600
Religion is based on "faith", science is based on "observation".
These are not mutually exclusive.
For example, consider a world is which any sinwas Imediately punished
-say, by pain. How many people would brave the pain to 'sin' when the
punishment was imediately there?
Of course, this eliminates the proposition of 'free will'. After all,
if you are imediately punished, "free will" can hardy be said to apply.
At best, god would be selecting the stupid.
By extension, ANY type of proof for the existence of god is infringement
upon our free will. (If YOU had proof of god's existance, how stupid
would you have to be to knowingly choose hell?) And, if proof was
available, but only to those who had studied science (or theology), god
would obviously be favouring those who were rich enough to study -
clearly contradicted by anyone's version of the scriptures.
Therefore, if god exists, s/he cannot be proved or disproved by anything
we may discover in science.
Logic cannot prove or disprove God; but it can prove that no matter what
we learn about the world, it has no bearing upom whether God exists.
Subject: Re: Missing Plutonium
From: meron@cars3.uchicago.edu
Date: Fri, 17 Jan 1997 23:02:06 GMT
In article <32DFF759.1FF@hydro.on.ca>, Dan Evens writes:
>Alan "Uncle Al" Schwartz wrote:
>> The toxic radiological hazard from ingestion is incredible. The weapon
>> forthcoming would not be a nuclear device, it would be a bunch of aerosol
>> cans. Think about infiltrating a deodorant manufacturer.
>
>Not all that incredible. If it is plutonium oxide, it is roughly
>as chemically poisonous as caffeine. You don't see too many terrorists
>hijacking coffee shipments and threatening to blow them up.
>
>Radiologically, the radioactive isotopes of iodine are far more
>troublesome because they are heavily concentrated by many orgranisms,
>including humans.
>
>The mythology surrounding plutonium as "most toxic substance" is
>based on the so-called "hot particle theory." This is the notion
>that a lethal dose of plutonium is the amount which, if it held
>still in one place in a human lung, would cause cancer. This
>notion is clearly false as such small particles DON'T hold still.
>
Yes, such silly scenarios always generate unrealistic results. It is
like saying "Since one gram of TNT, in the right location, can easily
kill a person, then a conventional bomb of one ton can kill million
people". As we know, it doesn't work this way.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Subject: Re: Can a Black Hole have a Charge?
From: browe@netcom.com (Bill Rowe)
Date: Fri, 17 Jan 1997 23:06:22 GMT
John Jordano wrote:
>Given the condition that an excess of positively charged particles were
>to fall into a black hole, would the black whole exhibit a positive
>charge?
>My intuition says "Yes," but if so, how does the "information" about the
>charge inside of the event horizon get communicated outside of the
>horizon? It's my understanding that the effect of a charge is carried
>by the electromagnetic force, and that the force carrying particle for
>the EM force are photons. If photons can't escape from a black hole,
>then how can the black hole exhibit the positive charge?
>If you accept the reverse, though, and assume that a black hole would
>*not* exhibit any excess positive or negative charge it had swallowed,
>then you can "destroy" charge by letting it fall into the black hole,
>which violates the principle of conservation of charge.
>Similarly, how does a black hole exhibit gravity? If you take for
>granted that a black hole exhibits gravity (one of it's defining
>features), then how does the force of gravity get transmitted? We don't
>have any evidence to support it, but let's assume for a moment there are
>force carrying particles for gravity, as there are for other three
>forces, and let's call them gravitons. For gravity to be exhibited by
>the black hole, gravitons must be emitted by the black hole. The
>definition of the event horizon of a black hole, however, is that
>nothing can ever leave. Am I missing something, or is this a
>contradiction in our current understanding of black holes?
I don't have a good answer to your first question, that is can a black
hole be charged and if so how is that manifest outside the event
horizion. Hoever, you second question about gravitions and gravity
escaping a black hole are more easily answerd.
It is important to realize the need for a particle such as a graviton
to transmit the force of gravity only arises in quantum theories of
gravitation. I do not mean to suggest I can solve this problem for
quantum gravity. What I would point out is the best description we
currently have of gravity is general relativity.
General relativity desribes gravity as a curvature of spacetime. The
points inside the event horizon of a black hole are merely those point
where the curvature of spacetime is so great no light like path exists
beyond the event horizon.
At the event horizon spacetime is continuous. Beyond the event horizon
the curvature of spacetime is not as great an light like paths extend
to any arbitrary distant point. Since there is continuity, there will
be some curvature of spacetime outside the event horizon. This is what
we will see as gravity. Remember, curvature of spacetime and gravity
are one and the same in general relativity.
Subject: Re: FTL Comm
From: Alexander Borghgraef
Date: Fri, 17 Jan 1997 23:51:40 +0100
Alex Tsui wrote:
>
> I was just wondering, suppose two persons were 10 light years away
> from each other, and they were strong enough to hold a 10 light years
> long rod that could not be stretched nor be contracted. if 1 of the
> person pulls or pushes the rod, will the person 10 light year years
> away immediately sense the change? IF he was able to do that, then
> wouldn't that be regarded as FTL comm?
Yes it would be FTL-comm, but no, it doesn't work. There is no such
thing as a solid rod: when you apply force to a solid object,you
generate a pressure wave travelling through the object, thus causing it
to move.This pressure wave travels at the sound of speed in the material
the object is made of.(hardly FTL, is it? :)
--
Darn right! No government should be allowed to keep a taxpaying!, god
fearing! citizen from strapping a couple hundred thousand Estes rocket
motors to a kerosene tanker with the hope she ll make orbit. If it
lands on some stupid, third world country, well it serves them right
for not investing in an ABM system!
- Someone in sci.space.policy -
Subject: Re: A case against nuclear energy?
From: meron@cars3.uchicago.edu
Date: Fri, 17 Jan 1997 23:38:52 GMT
In article <32E02575.717A@erols.com>, Dennis Nelson writes:
>steve perryman wrote:
>>
>> Greg Chaudion wrote:
>>
>> Who's defending evil? What's the death of a few civilians compared to
>> all life on the planet? It may sound cruel, but given the choice I would
>> sacrifice a few (yes, even myself) if I was absolutely sure that it would
>> preserve more life than it would destroy.
>
>And just how would you be "absolutely sure that it would preserve more life
>than it would destroy?" There's the rub. You have to place yourself in
>a position of wisdom and knowledge of which you are incapable.
True, nobody can ever be absolutely sure. Thus, the position of "Don't
act unless absolutely sure" always translates to "don't act, period".
But, one has to be aware that a decision not to decide, or not to act,
is still a decision and it may carry consequences. Chamberlain found
it out in 1939.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Subject: Re: Orch OR explained
From: Jack Sarfatti
Date: Fri, 17 Jan 1997 19:43:57 -0800
roland cook wrote:
>
> On Fri, 17 Jan 1997, Jack Sarfatti wrote:
>
> clip....
>
> Can you, or anyone, explain to us laymen, why quantum collapse due to
> gravitation is necessary at all in any theory of consciousness? What
> requires this extreme position?
>
> Roland Cook
You're asking the wrong guy. Roger Penrose is a genius. His intuition
may be correct in the end even though his particular "E = h/T" idea is
wrong for the reason Brain Josephson (another genius) has given. On the
other hand, there is an alternative quantum gravity model for
consciousness offered by Dimitri Nanopoulos which is of the back-active
GRW type. The connection of back-action to GRW is given in the book The
Undivided Universe by Bohm and Hiley. See my
http://www.hia.com/hia/pcr/bohmtht.htm
While back-active models of inner felt experience do not require quantum
gravity they are compatible with it. Quantum gravity would be one way to
get the universal objective "quantum friction" of the GRW objective
reduction model. In Bohm's version, the collapse to a particular
eigenfunction is visualized as the capture of the classical rocklike
hidden variable into a basin of attraction in classical configuration
space. The basin of attraction is set up by the thoughtlike
eigenfunction that is the end-result of the collapse. In the back-active
extension of quantum mechanics to post-quantum mechanics, Stapp's idea,
is that only one eigenfunction really survives objectively because the
back-active quantum friction obliterates the other "empty"
eigenfunctions. The back-action also means that the surviving
eigenfunction is continually reconstructing itself. That is, it is
adapting to the sensory information input imprinted on it by the
back-action. Stapp is able to explain memory this way as well. It's in
his book.
Basically, the back-action model is equivalent to a non-classical i.e. a
nonlocal form-dependent "active-informational" post-quantum neural
network at the sub-microtubular level. The back-action corresponds to
the neural net changing its weights. However, the post-quantum "neurons"
are the lone electrons, i.e., Eccles gates, controlling the conformation
of the dimers. This is how the macro-classical neurons couple to their
subunits. The classical neurons are the I/O devices of the post-quantum
biocomputer. The CPU is nonlocal and form-dependent at the sub-dimer
level in the microtubules.
Subject: Re: Missing Plutonium
From: larryt@pmafire.inel.gov (Larry L. Taylor)
Date: Fri, 17 Jan 1997 08:34:52 -0600
In article <32DE2D18.1D3D@cdc.com>, Dave Monroe wrote:
> Saw on the CBS evening news last night where
> the US shipped 80 grams of plutonium to Viet Nam
> prior to the war for one reason or another.
> When the commies overran the south, our guys
> grabbed the wrong container and the Viet Cong
> were left with the goods.
>
> Anybody know if 80 grams of plutonium could be
> used to make a small weapon?
>
Not a nuclear device - if that's what you mean with your question.
The single parameter mass limit ( the quantity of material that cannot
be made to go critical regardless of how it is packaged or moderated) is
about 600 gms for Pu-239. Achieving the 'prompt' criticality necessary
for a nuclear explosion requires perhaps 10 times that amount of material
as a minimum.
I would refer your to either of Richards Rhoades books on the history
behind the development of the fission (The Making of the Atomic Bomb) and
fusion (Black Sunday) bombs (both from the US _and_ the Russian
perspective). They are a both rather lengthy treatises, but read
something like a Tom Clancy novel, replete with diagrams and details of
the spying activities by the communists. You could also refer to a book
published in 1992 titled "The Los Alamos Primer: The First Lectures on How
To Build An Atomic Bomb" by Robert Serber for more details associated with
what it takes to build a nuclear device.
> --
> David S. Monroe David.Monroe@cdc.com
> Software Engineer
> Control Data Systems
> 2970 Presidential Drive, Suite 200
> Fairborn, Ohio 45324
> (937) 427-6385
--
"When it's my turn to die, I want to go quietly in my sleep, like my
grandfather -- not kicking and screaming, like the passengers in his
car..."
Larry L. Taylor
Systems Engineering, LITCO
Subject: Re: [QUESTION] Why negative ground?
From: Peter Berdeklis
Date: Fri, 17 Jan 1997 16:56:30 GMT
On Wed, 15 Jan 1997, Ken wrote:
> Doug Jones said:
>
> >In ice, protons and negative holes are mobile.
>
> Please tell me where you got this interesting tidbit. Any ice, or
> just water ice? Why does it behave in a manner different from
> other solids? If the protons are in motion, what supports the
> crystal lattice? Why is a proton, which is 2000 times more massive
> than an electron, moving instead of the electron?
This is true of water ice definitely. I don't know about other forms.
Remember that water is H2O, and in the molecule the electrons of the
hydrogens fill the outer shells of the oxygen molecule (this causes the
dipole of H2O). Therefore the electrons are tightly bound to the oxygen
and are not free to move as charge carriers as they are in metals.
As to why the hydrogen ions (protons) move as charge carriers, that is
still a matter of some debate. From Hobbs, _Ice Physics_:
"It is believed that the movemnet of a proton along a hydrogen bond
occurs by quantum mechanical tunnelling (with virtually zero activation
energy) through the potential barrier of the double-minimum potential of
the hydrogen bond which links the oxygen of a H3O+ ion with neighbouring
oxygen atom. ... the mobility of the proton is determined by a complex
realaxation process involving the absorption of one proton and the
emission of another. During this process one proton of the ion undergoes
a transition from the ground state to the excited vibational state in the
hydrogen bond."
Basically one proton pushes the next out of the way, and so on down the
line. The crystal lattice is never broken because the whole line of
protons move together.
Hobbs goes on to point out that not everyone agrees with this theory, but
it is accepted that protons are the charge carriers in ice.
---------------
Peter Berdeklis
Dept. of Physics, Univ. of Toronto
Subject: Re: Gravity a property of Energy, too?
From: "Bruce C. Fielder"
Date: Fri, 17 Jan 1997 21:51:04 -0600
Excuse me, but I believe that the first proof of relativitry theory (you
know, mass is equivilent to energy) was in 1917, when the bending of the
light around the sun indicated that the energy of the sun
(gravitational, mainly) was bending the light in EXACT agreement with
Einstein's predictions. It's been seen. It does exist. Of course, the
experiment was only conducted 80 years ago... who knows where Eric
lives.
Eric Flesch wrote:
>
> On Wed, 15 Jan 1997 06:41:08 -0600, steveb@tds.bt.co.uk wrote:
> > If mass is considered as "condensed energy" does this imply that
> >sufficient energy would exhibit a gravity field?
>
> All of the "Yes" answers notwithstanding, it must be noted that the
> gravitation of energy has never been observed. General Relativity,
> which posits such a energy-gravity link, is only a theory. A theory
> which will in time be superseded by another theory.
>
> Don't believe them. If it's never been seen, it doesn't exist.
> Energy does not gravitate.
>
> Eric
Subject: Einstein 14 GR
From: Jack Sarfatti
Date: Fri, 17 Jan 1997 20:48:24 -0800
How Einstein created the classical general theory of relativity of the
gravitational field.
“The special theory of relativity owes its origin to Maxwell’s equations
of the electromagnetic field ... the latter can be grasped formally in a
satisfactory fashion only by way of the special theory of relativity.
Maxwell’s equations ate the simplest Lorentz-invariant field equations
that can be postulated for an antisymmetric tensor derived from a vector
field. ... we know ... from quantum phenomena that Maxwell’s theory does
not do justice to the energetic properties of radiation. ... to Mach’s
question: ‘how does it come about that inertial systems are physically
distinguished above all other coordinate systems?’ this [special] theory
offers no answer.
That the special theory of relativity is only a first step ... became
completely clear to me only in my efforts to represent gravitation in
the framework of this theory. In classical [Newtonian] mechanics,
interpreted in terms of the field, the potential of gravitation appears
as a scalar field (the simplest theoretical possibility of a field with
a single component). Such a scalar theory of the gravitational field
can be made invariant under the group of Lorentz transformations. ...
(1) From .... special relativity it was clear that the inertial mass
... increases with the total energy ( ... e.g., with the kinetic
energy).
(2) From very accurate experiments (especially from the torsion balance
experiments of Eotvos) it was empirically known with very high accuracy
that the gravitational mass of a body is exactly equal to its inertial
mass.
It followed from (1) and (2) that the weight of a system depends in a
precisely known manner on its total energy. ... The acceleration of a
system falling freely in a given gravitational field is independent of
the nature of the falling system (especially therefore also of its
energy content). .. within the structure of the special theory of
relativity there is no niche for a satisfactory theory of gravitation.”
Einstein’s key idea -- the equivalence principle.
“Now it came to me: the fact of the equality of inertial and
gravitational mass, i.e., the fact of the independence of the
gravitational acceleration from the nature of the falling substance, may
be expressed as follows: In a gravitational field (of small spatial
extension) things behave as they do in a space free of gravitation, if
one introduces into it, in place of an “inertial system,” a frame of
reference accelerated relative to the former.
If then one interprets the behavior of a body with respect to the latter
frame of reference as caused by a ‘real’ (not merely apparent)
gravitational field, it is possible to regard this frame as an ‘inertial
system’ with as much justification as the original reference system.
So, if one considers pervasive gravitational fields, not apriori
restricted by spatial boundary conditions, physically possible, then the
concept of the ‘inertial system’ becomes completely empty. The concept
of ‘acceleration relative to space’ then loses all meaning and with it
the principle of inertia along with the paradox of Mach.
The fact of the equality of inertial and gravitational mass thus leads
quite naturally to the recognition that the basic postulate of the
special theory of relativity (invariance of the laws under Lorentz
transformations) is too narrow, i.e., that an invariance of the laws
must be postulated also relative to nonlinear transformations of the
coordinates in the four-dimensional continuum.
Goodbye to naked coordinates.
This happened in 1908. Why were another seven years required for the
construction of the general theory of relativity? The main reason lies
in the fact that it is not so easy to free oneself from the idea that
coordinates must have a direct metric significance. ...
We start with an empty, field-free space, as it occurs -- related to an
inertial system -- within the meaning of the special theory of
relativity, as the simplest of all imaginable physical situations. If we
now think of a noninertial system introduced by assuming that the new
system is uniformly accelerated against the inertial system (in a
three-dimensional description) in one direction (conveniently defined),
then there exists with reference to this system a static parallel
gravitational field. The reference system may be chosen to be rigid,
Euclidean in its three-dimensional metric properties. But the time in
which the field appears as static is not measured by equally constituted
stationary clocks. From this special example one can already recognize
that the immediate metric significance of the coordinates is lost once
one admits nonlinear transformations of the coordinates. To do the
latter is, however, obligatory if one wants to do justice to the
equality of gravitational and inertial mass ....
If, then, one must give up the notion of assigning to the coordinates an
immediate metric meaning (differences of coordinates = measurable
lengths, or times), one cannot but treat as equivalent all coordinate
systems that can be created by the continuous transformations of the
coordinates.
The general theory of relativity, accordingly proceeds from the
following principle: Natural laws are to be expressed by equations that
are covariant under the group of continuous coordinate transformations.
This group replaces the group of the Lorentz transformations of the
special theory of relativity, which forms a subgroup of the former.
... the general principle of relativity .. leads us to ... those systems
of equations that in their general covariant formulation the simplest
ones possible; among these we shall have to look for the field equations
of physical space. Fields that can be transformed into each other by
such transformations describe the same real situation.”
This is Einstein’s classical definition of objective reality. Objective
reality is the set of all real situations each one of which is invariant
under the group of all nonlinear continuous transformations of
coordinates. Objective reality is independent of the knowledge of the
observer. Note, that in Bohm’s version of quantum mechanics the
classical configuration space is more fundamental than physical space.
Wheeler’s classical superspace is the configuration space for general
relativity.
“Of which mathematical type are the variables (functions of the
coordinates) that permit the expression of the physical [metric]
properties of space ?... Which equations are satisfied by those
variables .... we do know with certainty a special case: that of the
‘field-free’ space in the special theory of relativity. Such a space is
characterized by the fact that for a properly chosen coordinate system
the expression
ds^2 = dx1^2 + dx2^2 + dx3^2 - dx4^2 (1)
belonging to two neighboring points, represents a measurable quantity
(square of distance), and thus has a real physical meaning. Referred to
an arbitrary system this quantity is expressed as follows:
ds^2 = gikdxidxk (2)
whereby the indices run from 1 to 4. The gik form a (real) symmetrical
tensor. If, after carrying out a transformation on field (1), the first
derivatives of the gik with respect to the coordinates do not vanish,
there exists a gravitational field with reference to this system of
coordinates ... but of a very special type ... this special field can be
characterized invariantly:
(1) Riemann’s curvature-tensor Riklm, formed from coefficients of the
metric (2), vanishes.
(2) The trajectory of a mass-point in reference to the inertial system
(relative to which (1) is valid) is a straight line, hence an extremal
(geodesic). This last statement, however, is already a characterization
of the law of motion based on (2). ...
The universal law of physical space must be a generalization of the law
just characterized. I now assumed that there are two steps of
generalization:
(a) the pure gravitational field
(b) the general field (which is also to include ... the electromagnetic
field).
The case (a) was characterized by the fact that the field can still be
represented by Riemann metric (2), i.e., by a symmetric tensor but
without a representation of the form (1) (save on an infinitesimal
scale). ... This means that in the case (a) the Riemann tensor does not
vanish ... a field law must hold that is some generalization (loosening)
of this law. If this generalized law also is to be of the second order
of differentiation and linear in the second derivatives, then only the
equation obtained by a single contraction
0 = Rkl = g^imRiklm
was a prospective field law in the case (a). It appears natural ... to
assume .. the geodesic line is still to represent the law of motion of
the material point.
It seemed hopeless to me at that time to venture the attempt of
representing the total field (b) ...
In Newton’s theory one can write the field law of gravitation thus:
Laplacian of the gravitation potential vanishes
valid wherever the density of matter .. vanishes. In general one has
Poisson’s equation ... In the relativistic theory of the gravitational
field, Rik takes the place of Laplacian of the gravitation potential. On
the right hand side we shall then have to replace [the density of
matter] also by a tensor. Since we know from the special theory of
relativity that the inertial mass equals the energy, we shall have to
put on the right-hand side the tensor of energy density -- more
precisely, of the entire energy density that does not belong to the pure
gravitational field. In this way one arrives at the field equation
Rik - (1/2)gikR = -kTik
The second member on the left-hand side is added becaue of formal
reasons; for the left-hand side is written in such a way that its
divergence, in the sense of the absolute differential calculus, vanishes
identically.”
This ensures local conservation of all energy-stress currents in
physical space. “Absolute” means objective invariance under all
nonlinear continuous coordinate transformations. This is also called
tensor calculus. Tensor equations have invariant forms under these
generalized transformations. Tensors have “square roots” called
“spinors”. Penrose has generalized these spinors to “twistors” on a
complexified spacetime where the different kinds of spacetime infinities
are represented by finite points.
“Not for a moment ... did I doubt that this formulation was merely a
makeshift .... If anything in the theory as sketched ... can possibly be
claimed to be definitive, ... it is... the limiting case of a pure
gravitational field and its relation to the metric structure of space
...
The peculiarity of these equations likes, on the one hand, in their
complicated structure, especially their nonlinear character with respect
to the field [gij] variables and their derivatives, and, on the other
hand, in the almost compelling necessity with which the transformation
group detrmines this complicated field law. If one had stopped with the
special theory of relativity, I.e., with the invariance under the
Loretnz group, then the field law Rik = 0 would remain invariant also
within the frame of this narrower group. But, from the point of view of
the narrower group, there would be no off-hand grounds for representing
gravitation by a structureas involved as the symmetric tensor gik If ..
one would find sufficient reasons for it, there would then arise an
immense number of field laws out of ... gik, all of which are covariant
under Lorentz transformations (not however under the general group).”
Note, in general, as you restore symmetries, going to deeper levels of
objective physical reality, I.e., as you “loosen” the structure, you
filter out possible field laws. Things get simpler. As you go the
opposite way i.e. breaking symmetries, the number of possible field laws
increase indicating an increasing diversity and complexity in possible
phenomena. This is exactly what happens in the expansion of the universe
out of the relatively simple big bang. This is the mathematics of groups
and their representations. The thoughtlike quantum pilot-waves of
physical reality are representations of rocklike objective invariants of
groups of transformations between different frames of reference. This
includes frames in “internal spaces” inside of physical space.
