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acerola

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Does God play dice?

According to the current understanding of quantum theory, the answer is yes. Not only we cannot predict the behavior of quantum objects, but also the behavior is not defined until we measure it.

Is this really correct? Does the electron "know" what he is going to do and we just can't predict it or the electron chooses at random his acts?
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erostosthenes

the electron doesn't 'know' anything, of course. the psi wave function is more like a guide along which the electron may or may not appear when measured. but really, this comes down to the fact that electrons are not corpuscular entities, they are simply a grouping of statistical information.
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When a single electron goes through a small slit, it may turn left, right or head forward, due to diffraction and interference of its wave behavior.

He doesn't know whether he will turn left or right until he does. And we can't predict it.

So, is it our limitation of not beeing able to predict the behavior or is it the way nature behaves?
God does not play dice, they know the final outcome. God gives man a limited set of information so that Man may play dice.

But the electron going through the slit turns both left and right and is reflected and yet not reflected in the half silvered mirror so whatever He did in between produces the results our theories predict.
the electron is not turning left or right or going straight because it is NOT A CORPUSCULAR ENTITY. it is a wave, and this is how you get diffraction patterns. however, if you probe the path between the slit and the backplate, you see the electron in one place, and it 'appears' as though it somehow chose some sort of angled path. but in fact, it chose every path, you just simply can't observe every path, you can only observe one. i don't mean to sound derisive, but you should probably study quantum mechanics first before you make false statements about a subject you're not totally familiar with.
In Roger Penrose's 'Emperors new mind' he states that the electron goes through both paths. It *is* a corpuscular entity, not a wave. That your physics produces predictable results by considering it to be a wave or a probability density does not make it so. All these tricks like sum over histories and wave functions and superstrings and such are simply that, Tricks that Man has invented to help him predict nature. The question however is "Does God play dice" to which I say NO since God understands nature but won't tell us His rules.
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"it is NOT A CORPUSCULAR ENTITY"

They have dual behavior. They are both particles and waves. How do you explain the photoelectric effect? Compton effect? It is photons and electrons behaving like particles. In this example (diffraction), they are behaving like waves.

"you get diffraction patterns"

You get a diffraction pattern if you shot many electrons. How about if you shoot a single electron? It will arrive at a single point in the wall behind the slit. This point may be just in front of the slit, to the left or to the right.

"should probably study quantum mechanics first before you make false statements about a subject you're not totally familiar with."

I have a M.Sc. in physics. I've studied 4 semesters of quantum mechanics. And I have had this discussion in class with some teachers, who all have Ph.D. in physics.

When you measure someting in quantum mechanics, you have a probability of measuring A and a probability of meauring B. The question is whether the nature itself is probabilistic or the probability comes from our experimental limitations.
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erostosthenes,

Do you know who said "God does not play dice"? Do you know why?
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http://www.lactamme.polytechnique.fr/Mosaic/images/DIFF.32.0.16.D/display.html

This page has the results of an experiment of electron diffraction. On the top you see the diffraction pattern, because you shot many electrons. In the bottom you see the single points (one for each electron shot). Notice that when shooting single electrons the electron doesn't arrive always at the same point. It "chooses" where he is going.

The slides arrangement are a little confusing. The bottom left is the first one and the top right is the last one.
acerola, I think eratosthenes (sp?) suggests that I don't understand quantum mechanics rather than you not understanding it, and that's true. I don't remember how to do the sums and half of them have changed since I did physics at school anyway.

You will probably take the problem to the grave with you same as Einstein did, I don't think we will have a universal theory in our lifetimes. That we can teleport light or use some other trick to make one particle assume the state of it's twin when we read it's value does not prove our theory is correct.
yes i know einstein said god does not play dice with the universe. i also know that he said it cos he never really liked quantum mechanics. he was on the side of the Copenhagen camp which included people like Bohr. however, einstein also said that nature presents itself only once, and in the form of physical theory. not twice, once in reality, the second in theory which we compare to 'reality'. regardless, it's useless to throw around quotes to win an argument ;). does god play dice with the universe? well, i don't believe in god, but if i did, i'd say yes. on very small scales, he's rolling dice. but on larger scales, he's rolling trillions and trillions of them, and you're seeing the overall, average result. and for the single electron - if you shoot a beam of highly focused electrons so that only one enters the slit at any time, you still get diffraction patterns as long as you're not probing between the slit and detector. i've done it myself since i'm also a physicist. and i don't follow everything einstein says as if it's gospel. in the end, this question comes down to opinion, not facts. are you a matrix theorist like heisenberg, or a wave theorist like shroedinger. i'm on shroedinger's side.
for diffraction patterns, i meant to say interference patterns :p...
Tell me the difference between something that behaves truly randomly, and something that behaves in a way that is determined by controlling factors which are inherently hidden?

I think if you can answer this question, you will answer the main one.
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Truly randomly obeys Bell's inequality
Local hidden variables does not.
yes exactly, local hidden variables have been disproven already by Bell (though he intended the opposite i hear).

Bell's inequality:

|P(a,b)-P(a,c)|<_ 1+P(b,c) for any arbitrary hidden variable lamda. (i've skipped the derivation for time's sake)

now let's say the vector c makes a 45 degree angle with vectors a and b, then quantum says P(a,b)=0 and P(a,c)=P(b,c)=-[sqrt2]^-1.

left side gives .707 right side gives .293, which is not larger or equal to the left side, therefore any hidden variable is not compatible with quantum mechanics, and god (whoever He is) does indeed play dice ;).
If there are no hidden, unknown parameters, why is it that young men "on the town" will
ask every "Sheila" who passes by: "will you or won't you?"
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I was receiving the email notifications of the comments posted here, but was a little afraid to check on them. But for my surprise, unlike the other questions I posted, this discussion is at a very high scientific level, and not full of philosofy and religion as the other ones.

You guys really understood the question. Is nature random? Or is nature deterministic and unpredictable?

erostosthenes, I also don't belive in god and also think that nature is random. I even like this idea because a world where everything is deterministic is a world with a pre-written history. And I like the idea that the future is blank for us.

gbentley, you took the words out of my mouth ;p. I was once discussing with some friends the definition of existence. We concluded that something that can't be detected or measured doesn't exist. And when discussing with some teachers they gave us that the scientific definition of existence: "interacting directly or indirectly with the human beeing." So if hidden variables can't be detected in any way, they don't exist at all.
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"are you a matrix theorist like heisenberg, or a wave theorist like shroedinger"

First of all, I'm an experimentalist. I work with applied optics but I really like quantum optics and intent to study it someday.

I'm not sure I undestood your question, but here is how I understand quantum mechanics: the electron is a particle, but the probability of measuring it is a wave.

I think it was Bohr who once said that what is important is what you measure. The mathematics behind it was just a way to predict the measurement. He said that it was pointless to try to understand the mathematics behind it.
well that was what i was getting at earlier. do you believe there is such a thing as 'reality' that is separate from physical theory, or as einstein believed, does nature present itself only once - on paper, and there is no such thing as reality. either way, heisenberg's matrix mechanics (which treats the electron as a particle or some kind of knot of statistical information) only works (by working, i mean it accurately predicts behaviour) for free electrons (so far). shroedinger's theory, which treats electrons and photos as waves only, works in all cases. now, one could argue that the mathematics and the interpretation need not go together, but that's for a different topic i think. at this point, you can pretty much believe whatever you want about the nature of an electron. Born scattering is ambiguous about this, that is to say, you can treat the electrons as particles or as waves and you get the same exact thing. i think i'm getting off topic now :Þ.
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"shroedinger's theory, which treats electrons and photos as waves only, works in all cases"

The "Copenhagen School", which is the most widely accepted interpretation of quantum mechanics, doesn't treat the electron either as one or the other, but as both. It is both a particle and a wave. When you detect it, it is a particle. The photoelectric effect and Compton effect show that electrons and photons are particles. But quantum mechanics introduce a new concept: probability. Probability oscillates like waves. Probability flows. And you can have probability densities. So, it is not like the electron is a wave, but the probability of measuring it is.

When you have a electron in a hydrogen atom orbit, it is not spread. It is not a charge or a mass distribution. The electron is still a particle but its probability is spread around the nucleus, like a stationary wave. If it were a charge or mass distribution (i.e. electron is purely a wave), you could measure parts of the electron on the orbit. But when you do measure, you always measure the full electron. So the electron itself is not spread like a wave. It is still a particle, but its probability is spread like a wave.

"Born scattering is ambiguous about this, that is to say, you can treat the electrons as particles or as waves and you get the same exact thing"

Same is true for the photoelectric effect and Compton effect. You can solve the problem either using Shroedinger equation or treating them as little balls. This reinforces the idea that the electron is both a wave and a particle: a particle with mass and charge and a wave of probability.
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"do you believe there is such a thing as 'reality'"

The only correct answer is: I don't know.

Physics is about measuring and calculating stuff. A phylosofical interpretation is only useful, in my opinion, if it helps you measure or calculate something.

This question is much like asking "what is charge", "what is a field", "what is mass", etc. The only answer is: they are stuff you measure and/or calculate.

Nature is like a game of chess. We look at it and write down the rules. But nobody asks why the pieces move like that.

Furthermore, if the 'reality' can't be measured or detected, directly or indirectly, it doesn't exist.
I was going to get in on this discussion, but then I read all of the posts and have decided that there are too many semantic pseudo-debates, and poor ole acerola appears to have been looking for philosophical observations rather than the quasi-scientific blather about someone's failed  interpretation of quantum mechanics. I think the "firing a single electron" experiments are extraordinary subjects for thought and discussion. But the idea that "if you can't measure or detect it, it doesn't exist" is a mumbo-jumbo, physics-cum-philosophy comingling, moving target statement . . . like the sophomoric assertion that everything is relative.

How about an 'idea', acerola? What would define an idea as measurable or detectable? Verbalized cerebral activity?

Steve
Something doesn't have to be observable by everybody to exist. I can certainly detect an idea in my mind, hence it exists. The fact that you can't is irrelevant.
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If you believe in soul or spirit or God or something like that, I respect your belief and will not argue with you.

But if you don't, then all you think is based on your brain activity. So an idea is composed by neural connections in your brain and electrical/chemical stimulus. When you think, you can detect electromagnetic waves coming from your brain. So, an idea is brain activity. You can detect brain activity. But our science is not advanced enought to "read" the ideas from someones brain. But they are detectable. So they exist.
If there is no God, then the question as stated would not be valid.  It would be
equivalent to asking whether Martians played dice.  Now, there was a time, however,
when few people had any idea whether or not there were any Martians.  So, it might make
some vague sense to ask if they played dice.  We now have ample evidence that life on
Mars is quite unlikely.

In a similar vein, we have ample evidence that the universe itself is nothing
like the mental image of the universe that people in ancient times held.  They
built and evolved their ideas of a deity based on their existing knowledge of the
universe.  Modern religious "leaders" have been forced to alter their preached vision
of a deity so much that it is nothing like what the ancients believed.  For example,
official Catholic teaching now holds that evolution is probably true, but that the "soul"
somehow entered into beat-men only a relatively short time ago.  If you pin down religious
thinkers still more about "where" heaven or hell might be located, they will quickly get
into a metaphysics approach that no longer holds that these are physical places.

Anyway, if we are honest with ourselves, we should start investigating the sources of faith
within human minds.  That inevitably leads to a study of human emotions, with the clear
suggestion that ALL religious metaphors are ARTIFACTS of the human condition, and are
VIRTUAL ones to boot.

Think about the ideas expressed here:

http://home.ntelos.net/~write/memes.html

Typo above: "beat-men" should be "beast-men".
I don't know whether or not I believe in God but it's interesting to me that people who profess not to believe in God set up a strawman argument which essentially states that there's not some humanoid with super powers way up in heaven somewhere looking down on us poor, weak mortals.

If I do believe in God it is as a sort of collective good will of men . . . which athiest activists say is too vague to take seriously . . . and it makes the question of whether or not he plays dice irrelevant or more of the rediculous nature as in "can God make a rock so big that even he can't lift it". Moreover, I would not agree that we can't predict quantum events or the behavioral determinism of electrons except to the extent that 10,000 years ago we couldn't clone sheep or perform brain surgery or hit a home run over the Green Monster at Fenway Park. I think that the very fact that we've been able to establish a framework for studying quantum theory implies an eventual understanding.

Also, I believe that saying we can't predict quantum objects is a misstatement of quantum theory. We cannot predict the outcome of a specific quantum event, but we can come very close to predicting the outcome of a large number of events . . . more or less like flipping a coin or rolling dice once vs. 1 million times.

There's a fatalist view of the universe which says that everything is infinitely knowable, maybe that defines God.

Steve
> If I do believe in God it is as a sort of collective good will of men.

Past and current conflicts among religious groups don't support the conclusion: "good will of men".
I don't give a rat's patooty about "past and current conflicts among religious groups" or the Pope's opinion or the thoughts and actions of The Great Big Right Reverend Jesse Jackson or any muslim or jew or buddist or Billy Graham or a Berkley Outer Space Acid Head or name your poison. I would agree that modern religion is in large part a sham.

Before Gutenburg screwed things up with the printing press, only a miniscule number of people could read and therefore those who could read who also owned Bibles were free to inflict their interpretation of scripture on an unsuspecting, knavish public, and many if not most of them had agendas that had nothing to do with catholicism or christianity. Things really haven't changed much since then.

By the way, I'd agree that "good will of men" is a pretty weak way of stating what I meant . . . I suppose that if I had St. Thomas Aquinas' cognitive power and William F Buckley's control over language, I might have come up with something a little more profound . .  . but thanks for sharing.

Steve
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Please, guys, you misunderstood the question. This is NOT a religious question/discussion. God is used in the question in the sense Einstein used. The question is whether nature is deterministic or random. God is just a figure of speech. For science, god does not exist.

The thread about god existance is in another topic group. THIS THREAD IS NOT ABOUT GOD! Let's keep ourselves in-topic. Religion discussions are endless.
You are correct and I apologise for wasting valuable bandwidth.

However I stand by my statement that although we cannot predict the outcome of a specific quantum event, we can come very close to predicting the outcome of a large number of events . . . more or less like flipping a coin or rolling dice once vs. 1 million times.

Not being able to predict the track of every water molecule in a flowing river has nothing to do with determinism and everything to do with the relatively primitive nature of our measuring equipment. Predicting molecular movement in a river is a function of being able to monitor what is now an overwhelming number of events not proof of non-deterministic behavior.

If we know the "precise" mass and luminosity of a star we can predict that it will supernova (assuming that it's sufficiently massive) in a number of years, but at this stage we cannot specify the day, hour, minute and second . . . which is a matter of slicing time into increasingly smaller units and measuring mass and luminosity more precisely.

I would argue (because I am poorly educated) that this is a simple argument of scale. We can predict where a mortar round will land with great precision because of the limited number of variables involved and the sophistication of our measuring equipment. 10,000 years ago this would have seemed fantastic if not impossible. Our understanding of ballistics has nothing to do with deterministim, just as our lack of understanding of quantum mechanics or quantum chromodynamics has nothing to do with disproving the theory of determinism.

The "Dice" question raised by Einstein, I see, still causes controversies at dinner parties.

Obviously in order to measure something one has to interact with it in some way, and the obvious problem is how intrusive is that going to be? When one considers the energies involved with electrons it is quite obvious that the interaction energy for measurement is not insignificant! Hence dual or even triple behaviors!

Schrödinger's approach to the problem was to integrate, which according to Wittgenstein, necessitated the abolition of discussion about the object. The "mode" of the period was Monte Carlo which introduced randomness into almost everything. In fact one of the most famous usage of "randomness" namely Random Pertubations was THE tool of Richard Feynman in the fifties. This all depressed Einstein who uttered his famous remarke after getting nowhere with gravity.

BUT! There is obviously a relationship between energy and space which manifests itself in various forms: the slit experiment, quantum tunneling and (a non-random related effect) the quantum numbers. Indeed black hole event sufaces are related to the energy contained within. All of these things must be part of a wider, deeper effect (ie: degenerates thereof) and there is no reason to suppose that this is "random". In fact it may be that it is all deterministic - only that the number of degrees of freedom are SOOOOOOOO large it all appears random. Thank God for that, otherwise my Monte Carlo methods would not work!

Thanks, BigRat. To an untrained eye, football players just run around randomly once the play starts . . . and it would be absurd to say that their behavior is unpredictable simply because of the number of choices they make once the play starts.

Steve
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The probabilities present in quantum mechanics don't have the same nature as the probabilities present in statistical physics.

When you take a deterministic theory, such as classical mechanics or classical eletrodynamics, and apply it to a many-body problem (with many degrees of freedom), it is impossible to solve it exactly. So you use statistical physics and thermodynamics to predict the behavior of the system. The theory is not probabilistic for few particles, but for large systems you must use probabilities.

Quantum mechanics is different. When you apply it to two particles, such as the hydrogen atom, you solve it exactly but still got probabilities. The probability is part of quantum mechanics. It doesn't come from statistical methods. You may also use statistical physics with quantum mechanics for larger systems when needed.

The problem of the electron and the slit is a one particle problem where the slit performs a measurement. You cannot make statistics for one particle (although some very few physicists say otherwise).
acerola: You are confusing issues. The problems in classical dynamics, which one cannot solve exactly, have to do with functional representation. The use of statistical methods is not intrinsic to the problem.

In Quantum Mechanics the issue was and still is that measurement requires interaction and that disturbs the "event" being measured. Consequently in order to "discuss" these things one talks of a whole. Integration. The next problem was interaction. Since one could not dicuss a single entity and it's interaction one was forced to discuss a "whole", enter probablistic theory. Not that these means have been ineffective, quite the contrary, but they are just means to an end. There is no reason to believe that the objects are intrinsically so.

All of this took place at a time when Logical Positivism was being rejected. This philosophy maintained a deterministic world but was at odds with things like Brownian movement. People began to think that it was not that Logical Positivism needed one more block in the foundations but that the entire structure was malfounded.

Many people are not satisfied with the Wittgensteinian approach in QM. The slit experiment shows that the understanding of a coherant theory is incomplete. It does seem however that the only acceptable approach is to think out theories based on abstract concepts, work them many years and hope that the predict reality. String theory is an extremely good example of this. The problem is that it contradicts the "measure and abstract" procedure introduced by our eighteenth centuary gentelmen scientists.

And finally one must not forget that these is a great deal of crap produced by many significant people. Only a few years ago someone wanted to monitor gravitational waves form the center of our galaxy by means of a large barrel like object. Needless to say the stress vibrations which MIGHT be caused by a wave were far exceeded by orders of magnitude by the thermic vibrations of the tings operating temperature.

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"You are confusing issues."

You are the one confusing probabilities that come from large number of variables with probabilities in small systems in quantum mechanics. You said:

"In fact it may be that it is all deterministic - only that the number of degrees of freedom are SOOOOOOOO large it all appears random"

When you have a deterministic system, in classical mechanics/electrodynamics for example, with a large number of particles (and degrees of freedom) you can't solve the system for every particle, so you use statistical physics to solve it. But with one or two particles, you can solve the problem exactly and without probabilities.

On the other hand, with quantum mechanics, even when you have just one or two particles, there are intrinsic probabilities in it, even though you can sove the problem exactly.

The question whether god plays dice is about "intrinsic" probability and not "statistical" probability.
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"The problems in classical dynamics, which one cannot solve exactly, have to do with functional representation."

What do you mean by "functional representation"? A functional, as I understand, is a function of functions, used, for example, in variational calculus. Anyway, as you said previously, a large system (3 or more particles without constrains) can't be solved exactly.

"The use of statistical methods is not intrinsic to the problem."

Is the solution intrinsic to the problem? Of course not. There is usually more than one way of solving a problem. Where did I say that otherwise?
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"Since one could not dicuss a single entity and it's interaction one was forced to discuss a "whole", enter probablistic theory"

I disagree. You can make an experiment with a single entity. You can work with a single electron, a single photon, a single atom. And even with single entities we get probabilities.

Once again, don't mix statistical probabilities, the ones you are talking abount when referring to "whole" and "integration" and intrinsic probability, the one we have in quantum mechanics when dealing with single entities.
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"It does seem however that the only acceptable approach is to think out theories based on abstract concepts, work them many years and hope that the predict reality"

Isn't this the opposite of the scientific method? Isn't this what Aristotle used? Think first, test later. Galileo showed that we must first make the experiment and then propose the theory. Reality must come before theory.
I have trouble with the concept of "intrinsic probability".  For example:

> But with one or two particles, you can solve the problem exactly and without probabilities.

Can you provide any reference to experiments in which an isolated, single electron
was created and measured accurately?

My point is that there probably is no case outside of the laboratory in which a
single electron occurs.  So, what gives with this "intrinsic probability"
thing?
single electrons occur quite commonly in nature. otherwise we would not see balmer and lyman lines in the spectroscopy of the sun. the aurora borealis is caused by ionized particles (atoms which have had 1 or 2 electrons stripped off) hitting the atmosphere. so clearly, single electrons are not laboratory oddities.
besides, wasn't the main question answered already?
By functional representation regarding so-called exact solutions I meant the general problem created by integration. For example 1/x is a simple polynominal function whose integral is logx which involves the transcendental e. There are similar examples, eg: Bessel functions, using transcendental gamma, and so on.
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"1/x is a simple polynominal function"

1/x is not a polynomial function. Polynomial functions are in the form:

a0 + a1*x + a2*x^2 + a3*x^3 + ...

You can, however, use a Taylor series to represent 1/x as a polynomial function with infinite terms.

"general problem created by integration"

I still don't get the problem. Every regular function can be integrated, even though not all of them have anti-derivative. And in nature we only have regular functions. So what is the problem with integration?
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"besides, wasn't the main question answered already"

The discussion is still going on. And the main question require other questions to be answered first. So far:

- Do hidden variables exist?

- Does intrinsic probability really exist or is quantum mechanics a kind of statistical physics?

The most accepted answers among physicists are:

- No, hidden variables don't exist.

- Yes, instrinsic probability really exist and quantum mechanics is not statistical physics.

But there are still some other great questions hidden in the main question, and I am waiting for them to appear in the discussion.
> single electrons occur quite commonly in nature

I don't think so.  They may be individually discrete, but there are ALWAYS many
others in the crowd.
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"Can you provide any reference to experiments in which an isolated, single electron was created and measured accurately?"

I think I get your point.

First, the only way to "create" a electron is to make the energy-mass conversion and create a electron-postiron pair. Usually, when you want to experiment with single electrons you just rip it from a atom and isolate it.

In a CRT (cathodic ray tube), such as the ones present in television sets and monitors, it is possible to control the flow of electrons and shot one single electron at a time. You can make experiments such as the slit experiment this way.

In the photoelectric effect you can shoot a single photon that rips a single electron from a piece of metal.

In the Compton effect you also shoot a single photon that collides with a single electron. The electron changes its momentum/energy and shoots back another photon with a different energy/momentum then the first one.

There are also other quantum objects that can be isolated. You can shoot silver atoms through a magnetic field to measure its spin. There is a 50% chance that the atom has a spin up and 50% chance that it has a spin down. If you shoot a single atom, it will either go up or down. If you shoot 1000 atoms, around 500 will go up and the rest will go down.
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Ok, I gave the exemples but forgot the conclusion:

The question "is quantum mechanics deterministic" is ambiguous. You must define what you mean by deterministic.

For example, Shroedinger's equation is deterministic. If you have a initial state Psi(0) you will have one and only one final state Psi(t). So in this sence, it is deterministic.

But, when you measure an observable, you get only one of the probabilities. And after the measurement you collapse the wave funciton Psi you measured to the value you just measured.

For exeample, lets say:

Psi = 50%spin-up + 50%spin-down

before the measurement. If you measure it and get spin-up, then right after the measurement you Psi funciton becomes:

Psi = 100%spin-up

So, Psi evolves in a deterministic way (Shroedinger's equation), but the measurement instroduces a pertubation that is not deterministic.
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Ok, forgot the conclusion again:

"So, what gives with this "intrinsic probability" thing?"

The measurement. Unlike classical phisics, your measurement interfere with the experiment. And, as I explained before, the probabilities only appear when you measure. Without the measurement, quantum mechanics would be deterministic (in the sense that a initial state will evolve to a unique final state).


"From: pleasenospam  Date: 07/05/2002 09:47AM PST  
> single electrons occur quite commonly in nature

I don't think so.  They may be individually discrete, but there are ALWAYS many
others in the crowd. "


please remember that electrons are fermions and so are very much distinguishable in a crowd, and in fact, must be to obey the pauli exclusion principle.
> Does the electron "know" what he

a) No, electron is stupid matter
b) No, electron is not god, quark or man
c) No, electron is genderless
d) * No, this question is invalid for subject of a dice_rolling_god
...ergo...
Answer = "No" (4-0)

> "God gives man a limited set of information so that Man may play dice."

-ditto

> "something that behaves in a way that is determined by controlling factors which are inherently hidden?"

- ~ditto

> "can God make a rock so big that even he can't lift it".

- ...interesting

> "with a large number of particles (and degrees of freedom)"

- not quite, IMO. The term freedom implies volition and choice. IMO it is merely about laws/rules, such as in term: "dispersion"

SteveJ, any thoughts that you may lean more (~religion) towards Jungian than Einstonian?

> "- Do hidden variables exist?"

ans> incomplete question, so no. More appropriate methinks, is about hidden (unknown) law, rule, relationship, habit,

ans> come to think of it, ditto self that term: "hidden" is also invalid to the question(s), for it implies an intent to be obscure when that is unnecessary. The obscurity in itself is sufficient, no intent is requisite to be either present or absent

> " there are ALWAYS many others in the crowd."

I'd similar thought when borealis brought up. Stripping a single electron from each of 1000 molecules does not in itself directly imply 1000 single electrons as a result, given multitudinal possible collections and/or recombinations (that may not necessarily require time gap for the entity to be single).

> "is it our limitation of not beeing able to predict the behavior or is it the way nature behaves? "

a) Yes, you are limited
b) No, (and/or yes) the term: "nature" also implies potential for volition, which changes the question to having the term: "god" to begin with Caps_On
c) Yes, electron "behaves", as does other matter that has not volition
The approach taken is attempt to segregate the rules, laws, of whatever process, be it from a god or what have you,

From what may in science fiction be referred to as sentient types, or in religious terms as creatures having choice. Each may include more than humankind.

Much of the problem in the thread seems to revolve upon capability to understand laws and make measurements, god or no god. Just because a more primitive being cannot measure or detect an electron or even an internal organ, does not cause the organ to cease to exist. Similarly for a 'solid' rock that cannot detect that it has some content of silicon. The silicon exists, whether the rock detects it or not.

As above, so below...:

More macroscopically, did Pluto exist prior to achieving a name in the book of (hu)mankind? Or Neptune? Or Chiron?

If you skimp on religious or philosophical aspects, then I reject any argument that things do not exist when your senses are underachievers.
it's not as if physicist can't see what the controlling factors are and so they throw their hands up and say only god can know or something just as ridiculous. hidden variables (ANY hidden variables or invisible controlling factors for those of you who seemingly refuse to let go of this) have been proven to NOT BE CONSISTENT with quantum mechanics. since quantum mechanics works perfectly for everything, i'm not about to give it up just so i can squeeze some notion of god that doesn't play dice or yahtzee or whatever into my life. the latter half of this discussion has turned into semantics and it doesn't seem as if anyone is reading the previous half before they reply.
He e-, which came first . . . philosophy or science?

It seems that this post is polarizing: the notion that reality is the here and now, regardless of our ability or lack of ability to understand a particular component such as electron behavior AND a general if not arrogant willingness to believe that if we can fit the behavior of the electron into some set of abstract mathematical rules no matter how absurd the consequential implications may be then we can define reality.

It isn't at all odd that the post seems to return inexorably to a discussion of god or God because, despite what scientists may believe or preach, science isn't like instrument flight: you can't simply define existence by intrument readings. I suppose that if I'd spent my entire adult or academic life studying physics and some smug lay person told me that I just wasn't smart enough to design the instrument or see the reality I'd react the same way erosthenes reacts. Sorry, no offense intended.

I think the "does (G,g)od play dice?" question is simply another way of asking whether or not we can ever fully understand the behavior of all matter. Why is it that throughout history, so many scientists have insisted that we can when in the face of history it's obvious that we can't. Which isn't to say that TV is magic, or that carbon dating is guess work, or that scientific research is futile. On the contrary, it's unending.



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First of all, once again, THIS IS NOT A RELIGIOUS QUESTION!!!

The word god is used for historical reasons (Einstein used it). It is a figure of speech. The meaning of the question is:

Is nature random or is it deterministics?

Second, the definition of existence is:

"Something that CANNOT be detected does not exist"

and NOT

"Something that wasn't still detected doesn't exist"

So, Pluto exists because it CAN be detected. Before detecting it, we didn't know of his existence, but it doesn't mean it didn't exist.

In physics you can prove something exists. You just have to detect it. But the fact that you didn't detect something doesn't mean it does not exist.

DETECTED -> EXISTS
UNDETECTED -> no conclusion (ASSUMED doesn't exist until otherwise proved)

If something CANNOT be detected, not now not ever, then it doesn't exist.
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So, since no one detected hidden variables we assume they don't exist. IF someone detects them, them the theory will be changed. But the present experimental/theoretical knowledge on quantum mechanics indicate that they really won't be detected.
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Science changes when needed.

You live by a lake and only sees white ducks every day on the lake. If someone asks you about the lake, you will say "the lake only has white ducks". But then someday you see a black duck in the lake. Next time you are asked about the lake you will say "the lake has white and black ducks".

If a new experiment (seeing the black duck) doesn't agree with the theory (lake only has white ducks) then we must change the theory (lake has both white and black ducks). That is the scientific method.

Maxwell predicted the theoretical existence of electromagnetic waves. But before Hertz detected them experimentally, they were considered by many, including Maxwell himself, as beeing a "mathematical coincidence". Of course electromagnetic waves existed before Hertz. But since we hadn't detected them we assumed they didn't exist.
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"He e-, which came first . . . philosophy or science?"

What is better? Something old or something new?
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"you can't simply define existence by intrument readings"

That is the physical/scientific definition of existence. It is different from the philosophycal/religious definitions.

Can you give me an example of something that exists and can't be detected by instruments?

"see the reality"

I like Bohr's definition of reality as beeing everything that we feel, either directly with our sences or through instruments.

All those philosophycal definitions of reality are very cool, but come on, let's be more REAListic. Is life a dream? Are we in the Matrix? If you want to believe in that, that is ok. I prefer to be skeptical.
> So, Pluto exists because it CAN be detected. Before detecting it, we didn't know of his existence, but it doesn't mean it didn't exist.

And that is why I think garbage like Zen shouldn't exist!

BTW: acerola -- you have points available elsewhere. See the lounge forum for a link.

"So, since no one detected hidden variables we assume they don't exist."

That's not exactly correct. Hidden variables were proven not to exist if quantum mechanics is correct (msg to the religious: please don't spin this off into science can't be correct cos we can't know god or something else that just as easily defeats the purpose of this debate). See our discussion above of Bell's inequality.
> First of all, once again, THIS IS NOT A RELIGIOUS QUESTION!!!

tough. Einstein (I believe) used the god_term religiously - just not like the religions of others, of which he was aware and preferred to be distinguished from.

But may be similar, let us see.... here goes:

god makes matter and man
man has choice
choice means dice were thrown, outcome unknown
The cosmos is a gigantic game of billiards.
The billiard balls have a variety of attributes.
Perhaps one has:
speed, size, mass, spin
but when one hits the other, there is no choice for them of the consequences. the consequences were preselected for them by the rules of the game.
The balls have no sentience or volition of their own

Human can contrive to put some english on ball, or rocket accelerator. This can lead to alternative observed behaviors when billiard balls meet, these do remain following existing pattern of behavioral rules by that wheel of law. Human does not transmit volition or sentience or will through the cue to the ball.

Human, OTOH, has the sentience, volition, and will to change or adapt behavior (and survive, at times instinctually, from learned expectations of things yet to be seen). While human more adaptive to the unforeseen, human cannot either predict the future nor to see into it.

Therefor, the dice are thrown, one can often guess the outcome at a certain rate or frequency, and if one tries to win the game through bets based upon statistical projections, one will frequently lose, since the house gets its cut first.

Ans = no, god does not play, but human observer ever will
Maybe the rules of the game are not fixed. Perhaps the rules themselves are subject to chance.
"the only thing constant around here is change"
SunBow,

I don't know if you understood what I meant.  When I suggested that the rules
of the game might change over time, I was not referring to this thread or even Experts
Exchange.  Instead, I was wondering if the whole universe might be subject to rules
that are evolving, willy-nilly, over time.  Why not?  Nothing we see in the sky
makes any sense.
> I don't know if you understood what I meant.

Apparently I did. Intention was to support your argument, add-in/include what is now a cliche over here, and yet distance myself as much as possible from the recent claims of pro-claimed astronomers/scientists in findings that some rules are already changing, but at distances of > 20 billion light years. Using justification that their predictive formulae are off at certain increased levels of precision. (since their formula and understanding of physics are correct, it leaves only that the universe is adding and changing laws right before their very eyes, and they are self-nominated discoverers)
> Nothing we see in the sky makes any sense.

Oh, except on that one. Something I read recently reminds me that really, the sky makes too much sense for something that would be expected (by who?) to be completely random.

In short, deficiency in randomness. Implication of that left open. Maybe food for another thread.

Still, I have troubles on constellations, how they were of any sense so early on in human history.
> the rules keep changing over time

So now not only does God play dice, he changes their shape and numbers "willy nilly" so that even if you begin to understand the physics of dice hitting a craps table any sort of predictability about their behavior becomes impossible? I think that the Occam's razor view would be that we simply don't understand the rules.

> Nothing we see in the sky makes sense

If I hold a newspaper too close to my eyes it becomes unreadable. If I hold it too far away it becomes unreadable. I don't think this is a property of the newspaper.
> even if you begin to understand the physics of dice hitting a craps table

IMO there is also human factor to consider. The god set up the rules, which may well be fixed. Then there came mankind with freedom of choice. A long time ago the human roled bones, preferably of ancesters, in attempt to understand the rules of the god. LATER, the human made a six sided die, and chose to role pairs (in some bars several pairs). Human also changed the location of where the die go, migrating from ground to floor to table-top.

Odds are, that you won't find either the dice nor the craps table elsewhere in universe. The human also had capability to name the bones, lately called dice, such as in this thread. Neither dice nor craps table gave themselves name, but they were formed up easily enough under existing rules, needing, requiring no change to existing rules. Yet they remain a new phenomena, comparatively, due to influence of mankind, in search of understanding the universe and its behavior.

Within the room, you can still here the phrase: "Roll them bones!"

For the question, the god may change rules as we go. If die are six-sided today, they could have been 7 or better, eight sided die on yesterday. The last night the rules were changed. The human would have no knowledge of prior universe of the rules where eight sided dice were used, so the human would only be able to remember them as if they fir rules of today ... as six sided dice. But no matter. Whether the rules change today is not necessary to the question in this approach.

Once there came the time of the giving human the freedoms to learn and to choose, the dice were effectively rolled at that transition point, and any move on part of human is another roll building upon the initial one that enabled human to do so. In a sense, the human roll is emulating that moment, in mimickry of the first one, in image of the god that enabled dice creation under existing rules. This extends the influence of that first roll, so one could then extend that god is still rolling through the wrists of the human. But it is not necessary for the god to influence the wrist or the physics or the sides of the dice anymore, sitting back in an easy chair and watching it all develop is ok in this approach to an answer that can still support that:

> Does God play dice?

Ans: Yes
> If I hold a newspaper too close to my eyes it becomes unreadable...

This supports the notion that things just don't seem so disorganized to this being a universe having properties of true randomness in creation
I'm not quite sure I understand your "this supports . . ." comment. Im simply saying that randomness is relative.
:-)  even better
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"Hidden variables were proven not to exist if quantum mechanics is correct"

you said "proven" and "if" in the same sentence. i am not defending hidden variables. i really dont like that hipothesis. and yes, hidden variables and quantum mechanics are not consistent with each other. the guys who want to prove them want, in a way, to prove quantum mechanics wrong.
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"Maybe the rules of the game are not fixed. Perhaps the rules themselves are subject to chance"

man, lets hope not! imagine that someday the rules about interactions between electrons and protons change. all computers would stop working. we would probably die too. imagine if gravity suddently became less attractive, or repulsive. earth would come out of its orbit and travel around the galaxy. that would be madness!
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once again, this is not a religious question. even if einstein himself was religious, this question isnt. i know because i am asking it.

in a more scientific way, the question is: "is nature random or deterministic?". if we knew all the rules of the universe and had a machine to measure all the variables without interfering with the system, would we be able to predict what is going to happen with 100% certanty?
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about the rules of the universe changing.

if known rules were changing, would there be a rule for this change? in other words, if nothing in the universe is constant, can we make any kind of theory/prediction?
> imagine that someday the rules about interactions between electrons and
> protons change. all computers would stop working. we would probably die too.
> imagine
if gravity suddently became less attractive

Actually, I meant very TINY changes over eons of time, but enough that conditions in
distant galaxies might be far different than on earth.

My point is that we only ASSUME that in the far reaches of space the rules are the
same as here, and with that ASSUMPTION we make further ASSUMPTIONS (now calling them
PREDICTIONS) as to the CONDITIONS that might hold there.
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"I meant very TINY changes over eons of time"

i saw you comments later, sorry. would those tiny changes be predictable or the rate of change would be changing also?
>  would those tiny changes be predictable or the rate of change would be changing also?

The words: "predictable" and "rate of change" suggest some sort of order.  I am
suggesting JUST THE OPPOSITE!  What I am proposing is that cumulative random changes
in the rules might not be uniform, and that would dictate different predictions for
events in different parts of the visible universe. If that could be the case, claimed
observations from earth could very well trick the observers into making extrapolations
from earth rules as to the nature of the universe as a whole.

Take biology as an example.  On a planet otherwise physically comparable to earth,
biology might be impossible.  That would not change the physics of light transmission.

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I think Newton was the first one to discuss this hypothesis. He wrote in his work principia that he was assuming that everything he measured in the lab applies to the whole universe.

Also, the basis of Einsteins special relativity is that the physical rules (in this case classical electrodynamics) is the same for all referentials, with any speed and anywhere.

The search for constants in nature is a fundamental aspect of physics. All theories are based on conservation laws and numerical constants.

If the rules were changing, at some point they would cause serious consequences. But as far as we can observe, distant stars are pretty much the same as nearby ones. The hydrogen spectrum (the light that hydrogen emmits) is the same for the sun and for distant stars (except for the redshift). So it is reasonable to assume that far away and long ago things were the same as they are now. Also, when observing the movement of pairs of distant stars, they seem to have a normal gravitational behavior.

The hipothesis of variable constants is a very complicated one. Unless we have some strong experimental evidence that it happens, we should try to solve the easier problem, which is extremely difficult already. Why create new problems when the ones we have are already near impossible to solve?

Thats why i like quantum mechanics. we are only worried with what happens in the lab. we dont really care what happens at distant stars or long ago. we leave that for cosmologists.
Last night without warning, while everyone was asleep, everything in the universe doubled in size. The AP Wire Service has been unable at this time to determine any past frequency of such a momentous event.
> was assuming that everything he measured in the lab applies to the whole universe.

uni=1
::applies to one whole verse, not all verses

> hipothesis of variable constants is a very complicated one.

Mine simpler. My variables are not yet measured, or are otherwise unused in equations, so their influencing factors and scales remain to be determined.
Everyone here would probably agree that one explanation for the gravity that we all
observe is that EVERYTHING, down to the smallest atom, is expanding at a uniform rate.
Thus, it would agree with all of our experimental evidence, including elevators
to produce a sensation of gravity.

And, since everything is relative, the ONLY way we could know that even our own bodies
are expanding would be that sensation of gravity.

Plus, of course, a determination that the universe as a whole is expanding at an
ACCELERATING rate.  Or at least space is.
The question expressed Einstein's frustration at not being able to get his head around it.
Since then we have learned more, and there is a suspicion that the brain state itself may be implicated in descriptions of the state of the world.  That would be ironic, and the ultimate joke would be that Einstein's denial actually contributes to the paradoxes he laboured over.

The discussion on Monty Hall's game has lead me to understand that the "presenting" rules of a game are everything when calculating probability, and the existence of absolute rules is an illusion.  And although I have difficulty justifying this statement, I think that applies equally to an electron as a human. Or if you like, any system has a set of "presenting" rules.  

The probability decisions made in the frame of reference of a "player" depend on that players knowledge function.
There seems to be a "transform" that will cause the reality of the player to change, in spite of the probabilities within the player's own frame of reference.

Another intruiging thing is that probability in the individual case loses its meaning.  Is only meaningful when it can be transformed into a rule - but how is an individual system able to "know" that something did not happen because it could not happen?  The only way for this to work, is for the thing itself to actually participate in its non-happening and its happening somehow.  probability and statistics are therefore an illusion, they must be artifacts of various "participative processes".

So it is really no surprise when Feynman discovers that a 'particle' takes 'all' paths into its calculation. So the nature of time must be some kind of "transform", like a Bayes likelihood function.

I think that participation must be fundamental, and particles, probability functions and multiplicity of existence to various degrees and in various contexts must be artifacts of the participative processes and their interactions.

We are so busy trying to explain participation amngst the particularisations we see, that we may have gotten it around the wrong way.  Perhaps particularisation needs to be explained beginning from a basis of the participatory universe.  

(We could even postulate that mind is axiomaticaly participative, but constrained to be fragmented by circumstance.)

In sum: "Everything Affects Everything"
Or (converse?): "Everything is Affected by Everything"
Which could lead to: "Everything is Everything"
But shouldn't that have been in the beginning?
Well, I dropped my ruler, gonna do a dice thread substitution (heh, er, hmmm?)
Sure, but not in a loose poetic sort of way, but in a rigorous defined and describable sort of way.  

In particular, we have to watch language like a hawk.

It is conceivable for example that there is only one electron in the universe, and has only ever been one. Then a lot depends on wht you mean by time and space, by existence, by identity, by uniqueness, and by cause and effect.
> It is conceivable for example that there is only one electron in the universe

It is more than conceivable.
It is the nature of TheArchitect.

Likewise, there is only one thumb
(~blueprint)
[TheThumb hath neither left nor right. Those be separate concepts. It hath nail (singular).]
I still say you cannot ignore man in the equation. God made eath and moon, maybe by playing dice, maybe not. God made man. Mand has same ruleset as rest of universe. Man plays dice. Dice are played in universe. In universe, dice are played.

Use your own means to develop set theory towards conclusion, but I claim it goes with the obvious. Man in universe playing dice -> dice are played in universe.

Now if you want to apply dice to a specific phenomenon, that is separate question. Like rules for dice, there be rules for the others. Beware the leaping extrapolations.
Does god play dice ?  Hmmm
Can we understand Chaos ????  Hmmm
Will we ever understand Chaos ???? Hmmm
Is Chaos "Random" or is there a MASSIVLY COMPLEX ANSWER  which looks random to STUPID humans !
Who can tell ?

I beleve :
1) Chaos can be understood !
2) BUT Humans are too mentally limited as a whole to understand..

But we are trying eg: The Earth Simulator

go on google and search for the earth simulator !!

Good Luck.
"Not only does God play dice with the universe, but he also throws them where they cannot be read."

Do you know the original author of this perceptive line?
Answer- It was Hawking - but I saw a similar quote about loaded dice published earlier.  Here's a good one:

"There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened."
 -- Douglas Adams
I cant Belive ........Dice & universe
Was a quote from Albert Einstein and it was meet by the genaral public with ridicual.....

Funny that most of Einstien's theory's were only belived/found to be true after he was dead.
Chaos is merely a rough attempt at foretelling when we do not know the initial state of all the players involved.

And Einstein was indeed proven wrong as he was on the static universe point.... Hey where's my cat gone?
HippyWarlock  . . . Einstein was proven wrong? About what?
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About Quantum Mechanics.
SteveJ - ? About the universe being static, Hubble showed the stars predominantly red-shifting and therefore moving away from us.

And as ozo says, about QM

Thanks.

I guess I didn't know that he was dogmatic about a static universe.
To keep the universe static he invented the Cosmological Constant, which he called his biggest blunder.
Now observations suggest it may really exist.
If I had only known........................ I would have been a locksmith

What's proof got to do with it?
Define 'proof'
proof is when you start with a hole and some bits, and all the bits fit into the hole with no bits left over or missing.  
In science you never know if you have all the bits, or too many, or the right size hole, and some other guy has a hole that fits bits into it as well, or he can even put your hole into his hole, and your hole can be fuzzy and maybe the hole is a hill from another perspective and and and and and and and and
So time has nothing to do with proof?
Sure it does.  You tend to get better fits as time goes on.  And especially better questions.  Thats it.
I wonder... If an object such -as the sun- can be shown -indeed has been shown- , to bend light... and we know that everything is relative, including space itself because the bending of light indicates the bending or warping of space... and we know that many objects in nature are not single particles, but rather groupings of particles... and we know that groups of particles often revolve... and we know that objects have different apparent gravities when in motion and that groups of objects in motion can produce waveform effects relative to a relatively fixed object when revolving... does that mean that since an electron might be several revolving particles - tightly bound- that as they turn about they will effect the space about them, warping space, with a differential, does this mean that our observation of the particle being in two spaces merely mean that to our instrumentation the warped space has produced a lense effect ?

Think of it this way, if our moon was not one object, but two objects revolving about each other, wouldn't our cycles of tides reflect a different wave pattern than they do now ? Of course the coupled system would warp space in interesting ways! To small spaces, small particles obviously seem larger. To objects observing fast moving particles, space warps in interesting ways (waves)that often seem to over represent the apparent relative size or location of the fast moving particle.

My point is, it may not be a "he"; an electron is likely a "them".

Is the interesting thought of the day are we accurately measuring spaces traveled by light, if light (or another type of fast moving particle) is a coupling of fast moving particles and fast moving particles warp space in a wobbling motion wouldn't those particles cover more ground? I have ridden a motorcyle in my youth beside a man who was very steady. If I was as steady as he, I would travel about the same milage over a hundred miles or so, by odometer. If I were a squid, and roamed about my lane, I would go noticeably further by those same odometers.  wadeedward
OK I am not the physics expert you need, but I have some comments none-the-less:

" and we know that everything is relative, including space itself because the bending of light indicates the bending or warping of space..."

Be careful with meaningless phrases such as "everything is relative".  They have a seductive ring, and are picked up in everyday speech, especially if you are a trendy social relativist - but I do not believe Einstein used the word, or if he did, he didn't like to use the word "relativity".  I think they convinced him to use it to make his paper more catchy, but he preferred to think in terms of "invariants" rather than relativism.

"does that mean that since an electron might be several revolving particles - tightly bound"

You should be informed that there is absolutely NO experimental evidence in a hundred years of looking, for ANY internal structure to the electron.  Even though it has properties of charge, mass and spin.  On the theory side, there is no way to assemble these properties into a coherent picture, even with relativity and quantum theory taken into account.   Forget about little balls and planets and such, that just creates an even bigger mess.  A major problem is the energy of a charge interacting with its own field, as you can imagine the field density must get pretty high and you zoom in.  So high in fact that you get infinity in the math for the field energy which is just plain wrong.   In fact the mathematical fudge has a grand name "re-normalisation" but its still just that, a fudge.  It is just possible that there is a kind of space-time vortex involved, like some kind of mini-black hole, to create the apparent properties we see from the outside, but that is all speculative until a grand unified theory (GUT) is agreed on.

As far as being in several places, or its mass being distributed in momentum space - well none of this behaviour is exclusive to electrons. so:
"Does this mean that our observation of the particle being in two spaces merely mean that to our instrumentation the warped space has produced a lense effect ?"
The answer must be no.

"is a coupling of fast moving particles and fast moving particles warp space in a wobbling motion wouldn't those particles cover more ground?"
Interesting question - I think you are saying if particles exchange places as they move, then they move further?  Except that the exchange of places is not a physical movement.  This is where it gets really spooky.  You can effectively exchange places or other properties for particles even when they are moving in opposite directions.  The only way to get a grip on all this quantum stuff is to start all over with the quantum rules and toss those cues balls in the cupboard along with the sticks and the whole table.
I did a bit of googling about - here is an interesting "loop model" that suggests that you can create an electron model by having a "mini particle" in a very small loop moving near the speed of light.  That way the relativistic effects combine give you the energy and magnetic properties you need.
http://www.stormingmedia.us/96/9647/A964783.html
Topic: Railroad tire electrical vorticies and the the Electro Thermal Hypothesis of Stress in Railroad Tires as it relates to observed activities with regard to an individual electron

Hmmmm, did Einstein say everything is relative? I must have missed that... I thought it was a much smaller gentleman. But no matter. It seems an observation doesn't really mean anything was observed anyway; how then can simple men know if one's relative position (what I was referring to was indeed spatial / observational relativity, a SUBJECTIVE IN WHICH NOTHING IS INVARIENT? READ ON FOR WE SHALL SEE...).

I'm too simple a man to worry about "experimental math"; perhaps I'd know how to condense a cube had I paid more attention....

What I do know is that physicists still wonder about cloud chambers. And there are Electrical engineers that still haven't figured out that there are "angles" in some equations that merely refer to the angle one lays a wire on a horseshoe to make a more  or less efficient electromagnet. (This relivation alone is worth the read to many of you I suspect!)

I am saying I don't buy it. Particles exist, they behave in predictable ways. Electrons can be made to dance, and if "when" they pass through slit "a" they "produce" pattern "b" that does in no way mean they are directly responsible for that effect. Building a mathematical model that somehow ignores the fact that charges do converge in observable ways in the stratosphere to make for lenses when the Air Force so desires that lens would seem to be myopic to this casual scientist. Yes it is quite a leap to say that maybe backscatter radar physics might apply to individual streams of electrons moving through a slit, but to ignore that there is a world of rational physics is just as silly. Methinks

OK, take string theory, which seems to say that points are not but string like things might indeed be would seem to me obvious implications of normal physics in the real world of the railroad engineer. Though I admit it is a stretch, calisthenics are good for the mind, so please bear with me.

When a railroad tire runs along it's track parts of that tire are always moving decidedly backward, some are if you will at rest, and practically none of it's parts are going the same speed as the train.
These discrepancies will tend to distort said tire and indeed have been known to derail many a train as the tires explode from the stresses , some of them electro thermal, of this distortion. I suppose someone out there might know what fields interact with themselves within the tire, but I would trust God knows more than I do.

I did mention "my" hypothesis of electro thermal stress in rail road tires didn't I?  (A topic I made up! (?)OH Goodness me! A hypothesis no group of physics professors "agreed upon"! I must be a rogue!) But fact they are. Prove it to yourself. Build a wheel of copper say four feet in diameter. Spin it. measure the electrical potential on the edge and at center.... wow! They are different! Now speed the spin up and slow it down. Wonderbar! A definitive relationship TO POTENTIAL. But the wheel on a train has many velocities? Wow! There you are, at  the fields in play with the Lord.

What has changed? The relative position of the tire in Space? The Spin is the same RPM, but one effect is uniform, and the other not? Well, I was crippled years ago, and the DHS hates me. (Department of Human Services) I'll be lucky to avoid prison for child support "violations". (I "owe" $100,000 to a working RN who is a contributor to my being crippled, until I pay to be hurt again or even killed this time I am by law prohibited from seeking the schooling I so desperately need.) It is up to more "worthy" souls to test my hypothesis, what say you? Want to measure the current generated by a moving tire at different points around it's edge and in it's internal area / volume? Then you can at least say you've studied, rather than merely prognosticated on the work of others. (As I seem barely able to do) Why question God with poetry if physicists we be?

                                                                                Blood and Fire,
                                                                                     wadeedward
PS: I am sorry for having such a big fat head, I know everyone is smarter and more qualified than I, and I know everyone has "done more physic" (sic). If this has been done and I'm sure it has please let me know about it, I certainly can't afford ther paper....
So you know about diffaction patterns.  Good.  Thinks of the world around you, reality, as a secondary phenomenon.  Think of reality itself as diffraction patterns.  Now imagine the patterns are made from the thing diffracting with itself on another scale.  Then you got the picture.