God’s playing dice explaining the butterly effect! How idiotic! The butterly effect doesn’t really concern itself with indeterminacy (which is the point in Einstein’s quote), a quantum mechanical concept.

@ Ashok.

You had better not step out of the confines of Fowler’s worship onto scientific concepts. Einstein’s comment “God doesnt play dice” is not a totally related to quantum mechanical concepts. Though, permit me to say, whatever happens at the quantum mechanical level is what happens in the world we can perceive. Einstein’s comments related directly to the Heisenberg’s Uncertainty principle, but the comment
( as Prof. Stephen Hawking explains it) goes to show that Einstein seemed to have felt that the uncertainty was only provisional: but that there was an underlying reality, in which particles would have well defined positions and speeds, and would evolve according to deterministic laws.
The chaos theory a.k.a the butterfly effect practically means that the world around us is actually indeterminate. That the future CANNOT be fully determined.
For further professional insights into the relation, you may do well to read “Does God Play Dice?: The
Mathematics of Chaos” by Ian Stewart

Einstein’s comment questions the probabilistic nature of quantum theory. This theory, pertains to events involving atoms and particles smaller than atoms, events such as collisions or the emission of radiation. In all these situations the theory is able to tell what will probably happen and not what will certainly happen. It is important to note that Einstein was not questioning the use of probabilities in quantum theory (as a measure of temporary ignorance or error), but the implication that the individual microscopic events are themselves indeterminate, unpredictable, random.

The classical idea of casuality (i.e. the idea that the present state is the effect of an anterior state and cause of the state which is to follow) implies that in order to predict the future we must know the present, with enough precision. But, for quantum events this is impossible in view of Heisenberg’s Uncertainty Principle. It was thought, however, that order reigned at human dimensions, but, in more recent times, with chaos theory and non-linear dynamics, we have got used to the fact that non-predictability is omnipresent in the physical world.

All these facts have undermined our familiar ideas about space, time, matter, casuality. So, it appears that God plays indeed dice with the physical universe.

. . . Einstein’s comment “God doesnt play dice” is not a totally
related to quantum mechanical concepts. Though, permit me to say,
whatever happens at the quantum mechanical level is what happens in
the world we can perceive. Einstein’s comments related directly to the
Heisenberg’s Uncertainty principle . . .

> Well, the uncertainty principle is an integral part of quantum mechanics; it most certainly is a quantum mechanical concept. How can the quote relate to as well as not relate to quantum mechanics at the same time?

> And this is irrelevant: “whatever happens at the quantum mechanical level is what happens in the world we can perceive”

. . . show that Einstein seemed to have felt that the uncertainty was
only provisional: but that there was an underlying reality, in which
particles would have well defined positions and speeds, and would
evolve according to deterministic laws . . .

> Exactly. I thought that was the standard interpretation of Einstein’s quote.

. . . The chaos theory a.k.a the butterfly effect practically means
that the world around us is actually indeterminate. That the future
CANNOT be fully determined . . .

> I’m sorry; your understanding of the basic idea of the theory is incorrect. Chaos refers to the high level of dependence of a system on initial conditions; it does not refer to the uncertainty that quantum mechanics predicts. Chaos says that it is extremely difficult to determine the variables of interest as a function of time (say) not so much because the equations connecting them are difficult to find as because their values at a particular “initial” time are extremely hard to measure. Indeterminate means that which doesn’t have a fixed value to be measured; it means there is nothing to be found. Chaos only says that certain variables are very hard to predict because of the problem in measuring.

. . . Einstein’s comment questions the probabilistic nature of quantum
theory. This theory, pertains to events involving atoms and particles
smaller than atoms, events such as collisions or the emission of
radiation. In all these situations the theory is able to tell what
will probably happen and not what will certainly happen. It is
important to note that Einstein was not questioning the use of
probabilities in quantum theory (as a measure of temporary ignorance
or error), but the implication that the individual microscopic events
are themselves indeterminate, unpredictable, random . . .

> I know.

. . . The classical idea of casuality (i.e. the idea that the present
state is the effect of an anterior state and cause of the state which
is to follow) implies that in order to predict the future we must know
the present, with enough precision. But, for quantum events this is
impossible in view of Heisenberg’s Uncertainty Principle . . .

> So far so good. Except that quantum mechanics too has this prediction-of-the-future-by-means-of-the-present. Only it asks for the wavefunction and the like, which don’t have direct physical meanings.

. . . It was thought, however, that order reigned at human dimensions,
but, in more recent times, with chaos theory and non-linear dynamics,
we have got used to the fact that non-predictability is omnipresent in
the physical world . . .

> Confused ideas. The non-predictability in non-linear dynamics is due to the measuring problem I mentioned (and computational problems?), whereas the quantum unpredictability is due to the inherent uncertainty in the variable, i.e. the classical variables don’t fixed values at a given time; there are only fixed expectation values (rarely, though, the state function of the system will be an eigenfunction of the operator corresponding to the variable of interest, and you’ll have one fixed value).

> Now I’d like to point out a terrible mistake you’ve made. You misspell causality. So it is very evident that you have no idea where the word came from and possibly what it means. It relates to cause and causal.

> Overall, you have done an admirable job of mixing irrelevant facts, rambling explanations, and glaring mistakes.

@ Ashok. Thanx for your sustained interest in correcting my mistakes(?). I’m sure you would do better to try a study of the chaos theory. The interpretations you called “wrong” are not mine, but of Prof. Stephen Hawking. I’m much more inclined towards believing Hawking’s interpretations than the interpretation of one of my juniors.

Wait a minute. You haven’t stated which are Hawking’s opinions (rather convenient I must say). I suspect you copied the interpretation given by him of Einstein’s comment from somewhere and would like everyone to believe that everything you said came from Hawking.

hhhhmmm… so in ur opinion how would you explain how connections in the world affect everything in the world, do you
actually believe that there is a butterfly effect and are world events
really linkd together