Free Republic
Browse · Search
News/Activism
Topics · Post Article

Skip to comments.

Written in the skies: why quantum mechanics might be wrong
Nature News ^ | 15 May 2008 | Zeeya Merali

Posted on 05/18/2008 10:40:38 PM PDT by neverdem

click here to read article


Navigation: use the links below to view more comments.
first previous 1-5051-78 last
To: Eye On The Left
'Tis Ok. My doctorate is in molecular collision theory, so I still remember some of it.

Cheers!

51 posted on 05/20/2008 5:24:11 AM PDT by grey_whiskers (The opinions are solely those of the author and are subject to change without notice.)
[ Post Reply | Private Reply | To 49 | View Replies]

To: grey_whiskers

I wasn’t poking fun at you, but rather myself (you certainly seem to have an excellent understanding of these subjects). In any case, what I wrote about time and energy is apparently correct. I got it out of a not too old physics text book titled Basic Concepts in Relativity and Early Quantum Theory (by Robert Resnick). Many people can grasp the position and momentum uncertainty correlation, but are somewhat puzzled by the time and energy one.


52 posted on 05/20/2008 5:48:13 AM PDT by Eye On The Left
[ Post Reply | Private Reply | To 51 | View Replies]

To: djf; All

You know, a fascinating question arises from this whole non-locality/Belle’s Theorem business: Since it states that quantum entities (photons, etc) which were once ‘entangled’ with each other at the subatomic level, then later separated, theoretically to unlimited distances, somehow remain in a state of instantaneous quantum connection with each other, then, since the entire universe was once quantumly entangled (within the big bang singularity), might the universe today be in some sort of instantaneous communication with itself? A single quantum entity? I once asked this question to Roger Penrose (Hawking’s mentor) at a lecture he gave a few years ago at Columbia University. He really loved the question which seemed to have never crossed his mind. Unfortunately, he went off into some related discussions which I didn’t quite follow.


53 posted on 05/20/2008 6:00:03 AM PDT by Eye On The Left
[ Post Reply | Private Reply | To 50 | View Replies]

To: Eye On The Left

I have wondered about these types of questions. I am interested in physics and math not so much for the actual results, as the theoretical implications. Epistemology and heuristics.

There is another very interesting result of Bell.

According to Einsteins theory, we can “rotate” the four dimensional space so that “time” becomes a linear dimension, and one of the linear dimensions rotates to become time.

The gist of this is that Bells theorem that talks about non-locality of space applies equally well - to time.

So, it would seem at least, that it is not theoretically impossible for you to open up your door tomorrow and see a baby pterodactyl there.

Or possibly - and I emphasize this is just educated speculation - change the past.

I have Bell’s set of lectures “Speakable and Unspeakable in Quantum Mechanics” I can understand alot of it, but in some places, the math is just too daunting.

And BTW, the last I heard, the Aspect experiments have been done, and managed to completely and decisively prove that Bell was right. That non-locality is a fact.


54 posted on 05/20/2008 6:11:41 AM PDT by djf
[ Post Reply | Private Reply | To 53 | View Replies]

To: xJones

Thanks for that bit of rich history.

I understand Edward Teller (The father of the H bomb) was also close to Enrico Fermi. I cannot imaging the outcome of W.W. 2 if the Germans had gotten hold of Teller.

Although the Germans were so arrogant and filled with race superiority syndrome, they would not have listened to such a “stupid Jew”.


55 posted on 05/20/2008 6:19:04 AM PDT by PSYCHO-FREEP (Juan McCain....The lesser of Three Liberals.")
[ Post Reply | Private Reply | To 8 | View Replies]

To: djf
And BTW, the last I heard, the Aspect experiments have been done, and managed to completely and decisively prove that Bell was right. That non-locality is a fact.

http://en.wikipedia.org/wiki/Bell_test_experiments

56 posted on 05/20/2008 6:22:34 AM PDT by Eye On The Left
[ Post Reply | Private Reply | To 54 | View Replies]

To: Flashlight; samtheman
I appreciate your comments, and mostly agree. I think samtheman means something slightly different by “random” than Flashlight and I mean. A better word might be “undetermined.”

In the physical world, all events are determined, and what appears as “undetermined” is just our ignorance of the minutiae of physical influences involved. The principle is this: every physical entity will be have in the same way in the same context.

That's where QM indeterminism is unique, and it's not exactly the kind of indeterminism people think it is, and includes an element of ignorance, but not in the sense that we just do not know, but cannot know.

The indeterminism, in the case of QM, happens to be very precise. We know exactly the degree of indeterminism in quantum events—it is always a factor of Planck's constant. It has nothing to do with what we usually call randomness.

While I happen to think the math is right, and that mathematically it will never be possible to “measure” a particle’s position and it's momentum simultaneously, there is a mistake in assuming that all characteristics can be described exactly in terms of mathematics. For example, we know there is an exact ratio between the legs and hypotenuse of an isosceles triangle, or between the radius and circumference of a circle, but all such ratios cannot be expressed exactly, mathematically. There is also the little matter of Planck's constant. As important as it is, no one asks why it is. It is just assumed because it, “fits the phenomena,” but no one knows (or even asks apparently) the explanation for why that number and not another.

Interesting, too, is the fact all this "indeterminism" is very determinisitic--such as the half-life of racioactive substances.

Mostly thinking out loud here. Forgive my rambling.

Hank

57 posted on 05/20/2008 6:58:14 AM PDT by Hank Kerchief
[ Post Reply | Private Reply | To 50 | View Replies]

To: djf; All
The gist of this is that Bells theorem that talks about non-locality of space applies equally well - to time.

Isn't that where the instantaneous stuff comes in?

http://en.wikipedia.org/wiki/EPR_Paradox

http://en.wikipedia.org/wiki/Copenhagen_interpretation

http://en.wikipedia.org/wiki/Many-worlds_interpretation

58 posted on 05/20/2008 6:59:26 AM PDT by Eye On The Left
[ Post Reply | Private Reply | To 54 | View Replies]

To: neverdem; All
Here's something I found years ago relating quantum mechanics to biological mechanisms such as ourselves...

Lothar Schäfer is the author of the book, In Search of Divine Reality - Science as a Source of Inspiration, . The book is, in essence, a brilliant description of the encounter of Science and Religion, wherein Schäfer proposes “that the traditional conflict between the two disciplines is mainly one involving classical, Newtonian Science; and many of its most pressing issues have obtained an entirely different meaning by the change in world view effected by the discovery of Quantum Mechanics.”

Lothar Schäfer is the Edgar Wertheim Distinguished Professor of Physical Chemistry at the University of Arkansas in Fayetteville. He received his Ph.D. (in Chemistry) from the University of Munich in 1965, and is the recipient of numerous awards for his scientific work. His current research interests include topics in Applied Quantum Chemistry and Molecular Structural Studies by Electron Diffraction.

On the Foundations of Metaphysics in the
Mind-like Background of Physical Reality

by Lothar Schäfer

That the basis of the material world is non-material is a transcription of the fact that the properties of things are determined by quantum waves, - probability amplitudes which carry numerical relations, but are devoid of mass and energy. As a consequence of the wave-like aspects of reality, atoms do not have any shape - a solid outline in space - but the things do, which they form; and the constituents of matter, the elementary particles, are not in the same sense real as the real things that they constitute.

Rather, left to themselves they exist in a world of possibilities, “between the idea of a thing and a real thing”, as Heisenberg wrote, in superpositions of quantum states, in which a definite place in space, for example, is not an intrinsic attribute. That is, when such a particle is not observed it is, in particular, nowhere.

In the quantum phenomena we have discovered that reality is different than we thought. Visible order and permanence are based on chaos and transitory entities. Mental principles - numerical relations, mathematical forms, principles of symmetry - are the foundations of order in the universe, whose mind-like properties are further established by the fact that changes in information can act, without any direct physical intervention, as causal agents in observable changes in quantum states. Prior to the discovery of these phenomena information-driven reactions were a prerogative of mind. “The universe”, Eddington wrote, “is of the nature of a thought. The stuff of the world is mind-stuff”.

Mind-stuff, in a part of reality behind the mechanistic foreground of the world of space-time energy sensibility, as Sherrington called it, is not restricted to Einstein locality. The existence of non-local physical effects - faster than light phenomena - has now been well established by quantum coherence-type experiments like those related to Bell’s Theorem. If the universe is non-local, something that happens at this moment in its depths may have an instantaneous effect a long distance away, for example right here and right now. By every molecule in our body we are tuned to the mind-stuff of the universe.

In this way the quantum phenomena have forced the opening of a universe that Newton’s mechanism once blinded and closed. Unintended by its creator, Newton’s mechanics defined a machine, without any life or room for human values, the Parmenidian One, forever unchanging and predictable, “eternal matter ruled by eternal laws”, as Sheldrake wrote. In contrast, the quantum phenomena have revealed that the world of mechanism is just the cortex of a deeper and wider, transcendent, reality. The future of the universe is open, because it is unpredictable. Its present is open, because it is subject to non-local influences that are beyond our control. Cracks have formed in the solidity of the material world from which emanations of a different type of reality seep in. In the diffraction experiments of material particles, a window has opened to the world of Platonic ideas.

That the universe should be mind-like and not communicate with the human mind - the one organ to which it is akin - is not very likely. In fact, one of the most fascinating faculties of the human mind is its ability to be inspired by unknown sources - as though it were sensitive to signals of a mysterious origin. It is at this point that the pieces of the puzzle fall into place. Ever since the discovery of Hume’s paradox - the principles that we use to establish scientific knowledge cannot establish themselves - science has had an illegitimate basis. Hume was right: in every external event we observe conjunction, but infer connection. Thus, causality is not a principle of nature but a habit of the human mind. At the same time, Hume was not right in postulating that there is no single experience of causality. Because, when the self-conscious mind itself is directly involved in a causal link, for example when its associated body takes part in a collision, or when the mind by its own free will is the cause of some action, then there is a direct experience of, and no doubt that, causal connections exist. When this modification of the paradox is coupled with the quantum base, a large number of pressing problems find their delightful solutions.

Like the nature of reality, the nature of knowledge is counter-intuitive, and not at all like the automatic confidence that we have in sensations of this phenomenon. The basis of knowledge is threefold. The premises are experience of reality, employment of reason, and reliance on certain non-rational, non-empirical principles, such as the Assumptions of identity, factuality, permanence, Causality, and induction. Where do these principles come from? Neither from an experience of external phenomena, nor from a process of reasoning, but from a system program of the self-conscious mind. By being an extension of the mind-like background of nature and partaking of its order, mind gives the epistemic principles - those used in deriving knowledge - certainty. Since they are not anchored in the world of space-time and mass-energy but are valid nevertheless, they seem to derive from a higher order and transcendent part of physical reality. They are, it can be assumed, messengers of the mind-like order of reality.

In the same way, moral principles. Traditional societies based their social order on myths and religious explanations. By assuming a purpose in the world, they told people why things are the way they are, and why they should act the way they were supposed to act. In the “animist ontogenies” values and knowledge derived from a single source, and life had meaning in an “animist covenant” as Monod called it. By destroying the ontological base of the animist explanations, - their astronomy, physics, and chemistry, - science also destroyed the foundations of their values.

In this process Monod saw the origin of the contemporary sickness in culture, das Unbehagen in der Kultur: on the one hand science is the basis for our power and survival; on the other, it has broken the animist covenant, rendered life meaningless in the process, and disconnected the world of values from the world of facts.

The sickness of spirit and the concomitant erosion of moral standards are the great danger for the future of mankind, already apparent in the public adoration of violence and debased behavior. At its roots is the unsolved question, on whose authority are the moral principles to be based now that the authority of the animist myths has been found lacking?

For those who are willing to listen, the answer is: on the authority of mind. In the same way that the self-conscious mind grants certainty to the epistemic principles, it invests authority in the moral principles. Like the former, the moral principles are non-empirical and non-rational, - not derived by a process of logic nor verified by experience - messengers from a higher reality beyond the front of mass-energy sensibility.

Epistemic principles give us a sense of what is true and false; moral principles, of what is right and wrong. The former establish the certainty of identity, permanence, factuality, causality; the latter, of responsibility, morality, honesty. By the same process that allows us to accept, without possible verification, the epistemic principles, we can also accept the authority of the moral principles. Violation of any one of them will put us in contrast to the nature of reality. If the nature of the universe is mind-like, it must be assumed to have a spiritual order as well as a physical order. As the epistemic principles are expressions of physical order, the ethical principles are expressions of the spiritual order of physical reality. By being an extension of the transcendent part of the nature and partaking of its order, mind establishes the authority of the ethical principles.

The challenge of reality and the ability to explore it are wonderful gifts to mankind. Understanding reality requires refinement of thought. That is, it has to do with culture. It requires an effort, is not afforded by automatic, intuitive reflex. Making sense of the world takes the response to a challenge, not the complacency of common sense. It is one and the same as striving for the moral life. An important part of it is the need to become aware of the specific character of human nature, to recognize “the human mystery” as Eccles called it: the mystery of how mind and body interact, how self-conscious human beings with values emerged in an evolutionary process supposedly based on blind chance and brutality. The evidence is growing that there is more to human nature than the laws of physics or chemistry, more to the process of evolution than blind chance and brutality; that evolution is more than, as Monod wrote, “a giant lottery, and human beings live at the boundary of an alien world that is deaf to our music and indifferent to our hopes and suffering and crimes”.

The barbaric view of reality is mechanistic. It is the easy view of classical science and of common sense. In epistemology mechanism is naive realism, the view that all knowledge is based on unquestionable facts, on apodictically verified truths. In physics mechanism is the view that the universe is clockwork, closed, and entirely predictable on the basis of unchanging laws. In biology, mechanism is the view that all aspects of life, its evolution, our feelings and values, are ultimately explicable in terms of the laws of physics and chemistry. In our legal system, mechanism is the view that the assumption of precise procedural technicalities constitutes perfect justice. In our political system, mechanism is the view that the assertion of finely formulated personal rights constitutes the ideal democracy. In our public administration, it is the view that responsible service manifests itself by the enforcement of finely split bureaucratic regulations. All of these attitudes are the attitudes of barbarians.

The quantum phenomena have taught us that, without naive realism, knowledge is possible. They have taught us that, without naive animism an ethic of knowledge, as Monod has called it, and a life with values are possible. Principles exist which are valid even though they cannot be verified. The discovery of the quantum phenomena has established a new covenant - between the human mind and the mind-like background of the universe - one that provides a home again to the homeless and meaning to the meaningless life. Whether or not the human mind is separate of the brain, as Sherrington and Eccles thought, I do not know. But I do not doubt that it is human only in some parts, and in others shares in the mind-like background of the universe. It is now possible to believe that the mind is the realization of universal potentia, a manifestation of the essence of the universe. Therefore, the only good life is in harmony with the nature of reality.

59 posted on 05/20/2008 7:01:09 AM PDT by Eye On The Left
[ Post Reply | Private Reply | To 1 | View Replies]

To: William Tell
William,

Sorry I did not see your post earlier.

You mean if we knew exactly what every atom in a die was going to do, we could predict the behavior of the die?

Not exactly. I mean, at the macro level, all physical events are determined. If they were not, the behavior of everything from computers to lasers would be unreliable. Except for manufacturing errors, they are entirely reliable. If you knew the exact amount of energy and momentum applied to a pair of dice, and coefficient to friction of the material the landed on and the angle at which they landed (the entire physical context, in other words) you would know exactly what they would do. Every time that identical context was repeated (if it could be) the behavior of the dice would be identical.

I do not think that behavior has anything to do with the indeterminate (not random) quantum behavior.

A thought for you. Quantum mechanics treats particles as discrete. The wave nature of these “particles” (which is analog) is ignored.

Not make an argument for my view, just telling you what it is.

Hank

60 posted on 05/20/2008 7:21:15 AM PDT by Hank Kerchief
[ Post Reply | Private Reply | To 25 | View Replies]

To: grey_whiskers

Only useful links to Ives and Bridgman are through Amazon if they still carry their books. Internet has fallen down on the job.


61 posted on 05/20/2008 7:23:17 AM PDT by RightWhale (You are reading this now)
[ Post Reply | Private Reply | To 38 | View Replies]

To: grey_whiskers

‘Debris from the U.S. intercept of a spy satellite in February and from China’s anti-satellite test in Janaury 2007 is still orbiting Earth’

Don’t have time to worry about quantum mechanics right now when space junk refuses to be cooperative.


62 posted on 05/20/2008 7:25:15 AM PDT by RightWhale (You are reading this now)
[ Post Reply | Private Reply | To 37 | View Replies]

To: stig
Why is matter quantized but time is continuous?

Is it? There is the theory, traditional, good enough, but if math is a problem try philosophy. In particular Husserl. I would recommend Whitehead but there is nothing in English.

63 posted on 05/20/2008 7:34:41 AM PDT by RightWhale (You are reading this now)
[ Post Reply | Private Reply | To 41 | View Replies]

To: Hank Kerchief

That’s some very interesting rambling. Thanks for sharing your thoughts.

My post was more of a tangent off on the subject of game probabilities, which is a different animal than the probability of one wave form collapsing out of all the possible wave forms an a quantum system.

Shuffling a deck of cards is very deterministic, it’s just impossible for the human eye and mind to follow the cause-effect chains that end up in the “random” shuffle.

Quantum mechanics is different than that.

Nevertheless, game probabilities are a good analogy in some respects, don’t you think?

Just as the chances of getting dealt 13 spades in a bridge hand is very remote (but possible), so outcomes of experiments in particle physics do allow for the occasional occurrence of a highly improbable event.

Or am I wrong to think that the analogy is apt?


64 posted on 05/20/2008 7:54:28 AM PDT by samtheman
[ Post Reply | Private Reply | To 57 | View Replies]

To: RightWhale
The microwave background might be a local phenomenon and have nothing to do with quantum mechanics.

I agree. It is far more likely that we simply don't fully understand Cosmology and the background radiation. QM has been going pretty strong for a while. It is interesting though.

Good thing the Bible didn't have alot to say about this stuff, otherwise these posts might turn into pages long flames.

65 posted on 05/20/2008 8:16:39 AM PDT by Paradox (Politics: The art of convincing the populace that your delusions are superior to others.)
[ Post Reply | Private Reply | To 27 | View Replies]

To: stig
"Why is matter quantized but time is continuous?"

Maybe time is more contiguous than continuous. Not moving, just re-appearing in a neighboring slice of Planck time like the procession of images on a 35mm film strip and the phenomena of after-images creating the illusion of continuous, smooth motion. Does that make sense?

66 posted on 05/20/2008 9:15:29 AM PDT by Eastbound
[ Post Reply | Private Reply | To 41 | View Replies]

To: samtheman
Hmmm, let's see. Off the top of my bald hear:

The probability of being dealt all spades is not less than the probability of being dealt any other particular hand.

As an analogy, I don't think it fits Quantum indeterminism, because it does not allow for just anything to happen. The uncertainty is limited. I suppose if you think of all possible hands being the limiting factor (Planck's constant?), it might be. Honestly haven't given as much thought as it deserves.

Hank

67 posted on 05/20/2008 9:27:53 AM PDT by Hank Kerchief
[ Post Reply | Private Reply | To 64 | View Replies]

To: xJones

Interesting post, good enough place to bookmark this thread.


68 posted on 05/20/2008 9:57:40 AM PDT by Kevmo (SURFRINAGWIASS : Shut Up RINOs. Free Republic is not a GOP Website. ItÂ’s a SOCON Site.)
[ Post Reply | Private Reply | To 8 | View Replies]

To: Hank Kerchief
The probability of being dealt all spades is not less than the probability of being dealt any other particular hand.
Yes, that's true. But the probability of being dealt ANY particular hand (in which you name all 13 cards by suit and face-value in advance) is exceedingly low (56!/13!), it's just that "all spades" is an easy way to specify one of those particular hands.

What I should have said is that the probability of being dealt a WINNING hand, in poker, for example, varies inversely with the ranking of that hand. You're going to get more single-pairs dealt to you in your life than you are royal-straight-flushes, even thought the probability of any PARTICULAR single-pair hand (if I specify 2h, 2s, 5c, 9d, ks, for example) is the same as expecting royal-straight-flush in spades.

And even the word "probability" is somewhat suspect. If you play 10,000 hands of poker a year, you will CERTAINLY see more crappy hands than you will great hands (crappy and great as per definitions within the game).

The more I think of it, the more I think this is a good way to explain QM to the lay person, even though cards, of course, are definitely not quantum events but causal on a macro level just like a baseball, if it's hit with enough force in the right direction, will go sailing over the fence.

69 posted on 05/20/2008 11:39:47 AM PDT by samtheman
[ Post Reply | Private Reply | To 67 | View Replies]

To: SunkenCiv

Thank you for the ping. It is my personal opinion (personal, not calculated) that Physics will not resolve the separation between quantum mechanics and relativity until it accepts the notion that every particle contains a little smidge of time, a small degree of space, and energy. The variable expressions of both dimension Time and dimension Space must be resolved in continua of combinatoric expressions before calculations for ultimate measurement will be possible ... Ol’ Werner will continue his laughing until that is accomplished.


70 posted on 05/20/2008 12:39:07 PM PDT by MHGinTN (Believing they cannot be deceived, they cannot be convinced when they are deceived.)
[ Post Reply | Private Reply | To 46 | View Replies]

To: RightWhale
Don’t have time to worry about quantum mechanics right now when space junk refuses to be cooperative.

OR as "Spaceman" Bill Lee of the Boston Red Sox said circa 1975, "With Skylab falling you have to pitch faster."

Cheers!

71 posted on 05/20/2008 7:40:51 PM PDT by grey_whiskers (The opinions are solely those of the author and are subject to change without notice.)
[ Post Reply | Private Reply | To 62 | View Replies]

To: Eye On The Left
Robert Resnick, of Halliday and Resnick fame?

Be still my heart!

(...or is that Holiday Inn Express and Resnick ?)

Cheers!

72 posted on 05/20/2008 7:44:46 PM PDT by grey_whiskers (The opinions are solely those of the author and are subject to change without notice.)
[ Post Reply | Private Reply | To 52 | View Replies]

To: MHGinTN

Interesting.


73 posted on 05/20/2008 9:50:27 PM PDT by SunkenCiv (https://secure.freerepublic.com/donate/_______________________Profile updated Monday, April 28, 2008)
[ Post Reply | Private Reply | To 70 | View Replies]

To: Hank Kerchief
For example, we know there is an exact ratio between the legs and hypotenuse of an isosceles triangle, or between the radius and circumference of a circle, but all such ratios cannot be expressed exactly, mathematically...

you lost me. any geometric ratio can be expressed exactly, mathematically. what's an example of a "ratio that cannot be expressed exactly, mathematically"?

74 posted on 05/20/2008 11:32:37 PM PDT by Flashlight
[ Post Reply | Private Reply | To 57 | View Replies]

To: Hank Kerchief
Hank Kerchief said: "Quantum mechanics treats particles as discrete. "

The whole point of quantum mechanics is that sometimes the particles can be treated as discrete and sometimes they can't. Regardless of how we treat the "particles", they will behave as the quantum theories predict, sometimes inconsequentially close to the predictions of newtonian physics; sometimes quite different.

75 posted on 05/21/2008 9:04:56 AM PDT by William Tell (RKBA for California (rkba.members.sonic.net) - Volunteer by contacting Dave at rkba@sonic.net)
[ Post Reply | Private Reply | To 60 | View Replies]

To: samtheman
samtheman said: "Or am I wrong to think that the analogy is apt?"

I believe that you are exactly correct. The proto-typical example I recall is of a "particle" in a potential well. The particle has a finite amount of kinetic and potential energy.

Classical physics predicts that the particle cannot leave the well, because there is insufficient energy to escape. Quantum physics predicts that there is a small probability that the particle can leave the well, appearing outside the well. I believe this is referred to as "tunneling".

I don't think that radioactivity of many substances is possible without this effect. The particles emitted from radioactive nuclei shouldn't be able to escape the nucleus; but they DO.

Quantum physics is not just classical physics with uncertainty thrown in. It is more complicated than that. Quantum physics predicts events which can't happen given the constraints of classical physics.

76 posted on 05/21/2008 9:12:58 AM PDT by William Tell (RKBA for California (rkba.members.sonic.net) - Volunteer by contacting Dave at rkba@sonic.net)
[ Post Reply | Private Reply | To 64 | View Replies]

To: Eastbound
Eastbound said: "creating the illusion of continuous, smooth motion. Does that make sense? "

It makes sense to me.

If I gave you a length standard and told you it was 1 meter long, but in fact it was 1.01 meters long, you could measure things forever without detecting that the standard was wrong.

Similarly, we are forced to measure durations using whatever we adopt as a measure of "time". It may just be that we can't observe any lack of continuity in time because of the tools we have to measure it.

The ancients believed that there were a few pure substances and that they consisted of "atoms" which, as the name implies, were indivisible. Using the tools they had, they were not going to be able to observe the particles inside atoms. Nor were they ever going to properly explain all the phenomenon that are the result of atoms not being indivisible.

77 posted on 05/21/2008 9:23:46 AM PDT by William Tell (RKBA for California (rkba.members.sonic.net) - Volunteer by contacting Dave at rkba@sonic.net)
[ Post Reply | Private Reply | To 66 | View Replies]

To: Flashlight

“what’s an example of a ‘ratio that cannot be expressed exactly, mathematically’?”

I gave two examples. When expressed they are called “irrational” numbers, which really means a number which cannot be perfectly expressed as a ratio [it has nothing to do with rationality].

But I’ll give you one detailed example. It is Bertrand Russell’s recasting of Euclid’s explanation of incommensurables arising from the Pythagorean theorem.

“In a right-angled isosceles triangle, the square on the hypotenuse is double the square on either side. Suppose each side is an inch long; then how long is the hypotenuse? Let us suppose its length is m/n inches. Then m²/n²=2. If m and n have a common factor, divide it out, then either m or n must be odd. Now m²=2n², therefore m² is even, therefore m is even, therefore n is odd. Suppose m=2p. Then 4p²=2n², therefore n²=2p² and therefore n is even, contra hyp. Therefore no fraction m/n will measure the hypotenuse. The above proof is substantially that in Euclid, Book X.” (Bertrand Russell, History of Western Philosophy)

The reason I like this is because it illustrates that what are called irrationals and often expressed as incomplete decimals are not just a problem of precision. Irrationals are things which cannot technically be expressed mathematically—there is no number, positive or negative, that represents the ratio between the hypotenuse and either leg of an isosceles right triangle.

Hank


78 posted on 05/22/2008 6:08:24 AM PDT by Hank Kerchief
[ Post Reply | Private Reply | To 74 | View Replies]


Navigation: use the links below to view more comments.
first previous 1-5051-78 last

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
News/Activism
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson