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Old 04-08-2005, 03:25 PM   #1
QuikSand
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Modern physics, Heisenberg, and questions of free will

On Heisenberg and the clockwork universe...


I have been trying to educate myself a bit on modern physics – a subject that I find generally interesting, despite having dropped off the real-sciences academic track many years ago. I have been listening to some lectures on relativity, and now getting into quantum mechanics. It’s a lecture series that is deliberately non-mathematical, trying to get through these topics with more description than calculation. So far, not so bad.

I’m not prepared to post a “What Do You Know” thread here, and explain relativity to everyone, but I think I understand a specific issue that has come up well enough to be troubled by it. I thought I’d share – see if some of the better minds here might be able to either straighten me out a bit, or else buck me up by saying that my skepticism is at least fair.


The issue is, essentially, getting past the notion of the “clockwork universe.” I have heard this phrase used before, to essentially describe a theory that goes something like this:

If the universe is made up of things, and the things all behave according to various physical laws relative to one another – then presumably everything that is going to happen a moment from now is simply a function of where the things are and how they are interacting. Therefore, stepping to matters of philosophy, how can there be free will? If all that is happening is a series of physical interactions of things with one another, where is there room for something like an idea in all this?

(That’s my language, not necessarily a perfect statement of the concept, but it ought to do okay)


Anyway, in the lectures, we are presented with Heisenberg’s well-known uncertainty principle, basically with a promise that this would help us out of this particular conundrum.

Simply stated (oversimplified, probably), Heisenberg says that when measuring the location and velocity of particles (things), we can never measure both with complete accuracy. And in fact, the very act of measuring things tends to disturb the things themselves, thereby contributing to the inherent error in the measurements. So, even if we had some way to warehouse all the data, we could never actually know the location and velocity of every particle in the universe, which renders the clockwork universe concept essentially impossible – we could never know that much, which would be necessary to know if we wanted to calculate everything that was going to happen.

So far, I’m on board. I get it. (And for those who understand this stuff well, I hope my simplification as been fair)


Okay – here’s where I have trouble. In my mind, I still want to say something like this:

Fine, we can’t measure everything, so we won’t be able to know where things are and how they are moving. But they still are somewhere, and they still are moving, right? So they still do, in fact, have all those various physical interactions with one another, even if we cannot measure them in any practical way.

So, if that’s the case… how do we escape from the clockwork universe concept? I buy Heisenberg’s uncertainty in measurement, but it doesn’t (intuitively, at least) translate to reality for me.



Now, I get a little shaky at this point, but I understand there is a so-called Copenhagen school of thought, which essentially suggests that anything which cannot be measured and quantified does not itself exist. (Probably a ghastly mis-summary there, I don’t really understand this leap in logic) The scientists (apparently most) subscribing to this belief argue that if something does not have effects which can themselves be measured, then it (for practical purposes) itself does not have existence. Or something like that.

And this line of thinking then leads one to conclude that Heisenberg not only determines that there is inherent imprecision in the measurement of position and velocity of particles, but indeed there is such imprecision in those things themselves. The connection between measurability and reality being the underlying link (which I don’t claim to understand).


As I understand it, this was a point of some great debate among great physicists of the 20th century. Neil Bohr, representing the emerging group of quantum thinkers, moved into this line of thinking, while other scientists like Einstein seemed reluctant to make these steps. At the moment, I’m with Einstein… not because I claim to really “know” anything, but I just haven’t been able to get my intuition around the quantum concepts, I guess.


Okay – if you’re a physics major or professional, you’re probably grinding your teeth at my mis-statements. I am trying to learn this, and am very interested in this sort of issue that gets to such a fundamental question.

Can anyone help? Or point me to a source that tries to better explain the whole concept here, or perhaps on that better summarizes the Copenhagen school of thought?

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Old 04-08-2005, 03:28 PM   #2
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Here's an item on background, better written than anything I could:

Link


Quantum Mechanics and the Copenhagen Interpretation



Eugen Merzbacher

University of North Carolina at Chapel Hill



Lecture presented at a CUNY symposium exploring scientific, historical and theatrical perspectives surrounding the events of Copenhagen,
a play by Michael Frayn

New York, 27 March, 2000



All his life, Niels Bohr struggled as he tried to express his thoughts and put them on paper, either in Danish or English or German. It did not help that he mumbled and often could not be heard, leave alone understood, by his listeners. Michael Fraynís play "Copenhagen" admirably conveys the torment that Bohr and his friends put themselves through as they groped their way toward a formulation of quantum mechanics that eventually changed how we do, teach, and learn physics.

In the midst of this upheaval in physics it was crucial to realize that, radically new as the theory was, quantum mechanics does not totally supplant the classical concepts and goals of physics. In going from classical to quantum physics the trick has always been to know what to jettison and what to retain. When I teach quantum mechanics, I find this the greatest challenge of all. In some ways, quantum mechanics resembles the game of Jeopardy. We know the answers, but must learn to ask the right questions.

Bohr won the Nobel Prize in 1922, at age 37, "for his investigations of the structure of atoms and the radiations emanating from them". In the following years, through the twenties and early thirties, he devoted most of his time and energy to a fuller understanding of the meaning of quantum mechanics. People began to speak of the "Copenhagen school", the "Copenhagen interpretation" of quantum mechanics, the "Spirit of Copenhagen", and more recently and sometimes unkindly of the "Copenhagen orthodoxy".

Bohr set out to make sense out of a number of ideas and requirements that had come to be regarded as essential features of quantum mechanics:

1. The wave-particle duality (de Broglie)

2. The uncertainty or indeterminacy relation or principle (Heisenberg)

3. The statistical character of the predictions of the theory (Born and, ironically, Schrödinger)

4. The wholeness or indivisibility of quantum states (Bohr vs. Einstein)

The wave-particle duality is traditionally illustrated by the two-slit interference experiment. A stream of particles is directed at a screen with two slits. The particles are detected one by one far away from the screen with the two holes and in various locations, many of which they could not have reached if they followed classical orbits. This behavior is the hallmark of waves producing bright and dark interference fringes by superposition of the oscillations that spread out from the two slits. Yet, what is detected are individual single particles. These can be electrons, neutrons, whole atoms or molecules and even larger objects, but of course also photons, the massless particles of light (which Einstein postulated but Niels Bohr did not really fancy). In 1923 Louis de Broglie proposed that the wavelength that can be measured by examining the position of the interference fringes is linked to the velocity of the particles of mass m by a simple reciprocity law:

where is the speed of the particle, and h is Planckís constant. The first equality applies to photons as well, since they have momentum, although no mass. Experiments immediately showed this to be correct.

At first there was the appearance of an internal contradiction here, but it was soon realized that the wave and particle aspects of matter and light are not incompatible. Instead they are inherent complementary features of one and the same thing. The reconciliation of the two seemingly contradictory properties ‚ waves and particles ‚ was achieved when it became clear that one must be extremely careful not to attribute long-familiar characteristics to the concepts "wave" and "particle", just because they have those names. The waves are not as tangible as water or sound waves, and the particles are not tiny billiard balls. The recognition that the propositions of quantum mechanics are intrinsically statistical and probabilistic was the key to resolving the seeming paradox of the wave-particle duality. This was accomplished in 1926.

A perfect harmonic (sine) wave in space has a definite wavelength and thus represents a particle (photon, electron, neutron, atom, molecule, whatever) with a sharp and precise value of its momentum, or velocity. Since the amplitude of such a wave is constant and one maximum is indistinguishable from the next, the wave does not single out any particular location. If we want a wave form to localize a particle and peak at a certain position, we must superpose two or more perfect waves by adding them together. We gain spatial definition but lose sharp momentum and get a spread of velocities instead. This kind of loss in precision of one physical quantity at the expense of greater sharpness of the values of another quantity distinguishes quantum mechanics from classical physics, where it is assumed that one can know the values of all physical quantities simultaneously with infinite precision, at least in principle. Quantitatively, these ideas are expressed in the uncertainty (or indeterminacy, or Unbestimmtheits) relations, which Heisenberg derived in 1927 and which are frequently referred to in the play. The abandonment of the ideal of perfect precision in all knowledge of physical quantities inevitably constitutes a loss, but there is a compensating gain, since quantum mechanics presents us with a wealth of different states for the description of physical processes, far in excess of the toolbox of classical physics.

The two-slit interference experiment is the textbook illustration of the wave-particle duality. Together with the de Broglie reciprocal relation between velocity or momentum of a particle and the corresponding wavelength, it leads in two steps to the uncertainty relation. The distance between the two slits, through which a single particle is sometimes said to be passing at once, gives us a measure of the uncertainty in position in the lateral direction. The deflection observed on the distant screen is a measure of the sideways momentum component, . The reciprocity of the two uncertainties is demonstrated by the superposition of waves emanating from two slits. As we bring the slits closer together, the interference pattern spreads out, and vice versa.

Several red herrings had to be disposed of in the effort to develop a unified framework to describe and predict the behavior of a vast range of physical systems. These extend from fundamental particles through nuclei, atoms and radiation to molecules and condensed matter, and into the mesoscopic domain. One of these red herrings was the heuristic notion that the theory should confine itself to dealing with observable quantities only. Since it led Heisenberg, with his incredible intuition, to the correct formulation of quantum mechanics, this mental crutch was of obvious value to the development of the theory, but it eventually became an impediment to a full understanding of quantum mechanics, especially by nonphysicists. (The history of the Aharonov-Bohm effect, around 1958-60, and even to this day, shows the danger of rigidly classifying physical quantities as observable and non-observable, and relegating the latter to second class status or worse.)

Another questionable notion is the claim that the human observer plays a more significant role in quantum physics than in classical physics, above and beyond the obvious fact that experimental tests must be prepared by humans in the laboratory, and that the entire scientific enterprise is an intellectual activity engaged in by conscious human beings. To this day, the role of the observer in quantum mechanics is often debated. Saying that "God does not play dice", with the implied corollary that only humans do play dice, Einstein hoped that at a deeper level there would be a realistic non-statistical description of nature (with a capital "N"), with no reference to an observer. On the other hand, Bohr emphasized what he considered the indispensable importance of the observer and the measuring process in quantum phenomena. Today, we are able to interpret quantum mechanics less dogmatically than either Einstein or Bohr did. We know (or have become used to the idea) that wherever there are probabilities there are alternative outcomes of experiments and tests. Ultimately, these tests provide information to an observer, of course, but the information is of a statistical nature because Einsteinís "God" does indeed play dice without human intervention. Recent articles in Physics Today with titles such as Quantum theory without observers and Quantum theory needs no "interpretation" attest to the continuing interest in and concern about these issues.

While Heisenberg was developing his new mechanics, Schrödinger unintentionally (and Dirac intentionally) brought into being a theory that accounts for the probabilities in quantum physics. We call the object of this theory simply the state, because its knowledge provides us with all the information that quantum mechanics allows us to have about the system whose condition (or state) it describes. For reasons that need not concern us, we express the state mathematically as

where the character inside the "ket" labels the particular state under consideration. This is an object to which the rules of vector algebra apply: Two states of a system can be added, and a state can be multiplied by a number. We will use the photon ‚ the particle of light ‚ to illustrate these concepts.

Since light can easily be linearly polarized and tested for its polarization (e.g., with polaroid filters), so can a photon. Photons that are polarized horizontally or vertically may be described by two basic states, . A general one-photon state is the superposition

where a and b are (complex) numbers. Their squares, , are the probabilities that the superposition represents the mutually exclusive outcomes: 100 percent, totally polarized photons in the H or V directions, respectively. For example, in the state

our photon has 60% chance of being found polarized horizontally and 40% chance of being found polarized vertically. Casually, but misleadingly, one sometimes speaks of the photon occupying both Hand V states at once ‚ analogous to passing through two slits at once. The Copenhagen interpretation provided, and still provides, the appropriate language for these new concepts. Yet, language and words can be quite treacherous. As the play reminds us, Heisenberg insisted that itís all in the mathematics. The availability of superpositions makes two-state quantum systems, or qubits, tempting tools for new methods of computation.

Our urge to see the world in terms of properties and attributes that particles "have" is strong. Even as we admit that quantum mechanics generally does not allow us to speak of a photon "having" a certain polarization, we cannot resist saying sometimes that the observation "puts" the system in a definite state of polarization and "collapses" the wave function or state. Purged of its extraneous baggage, the Copenhagen interpretation has moved our attention away from the particles that have certain properties to the properties themselves that are taken on by the particles. This may seem to be a trivial and awkward shift from a straightforward active language to a more convoluted passive mode of expression, but in quantum mechanics it makes all the difference, especially when the theory is extended to systems of several identical particles and their quantum fields. As a result, our entire concept of a physical system has had to undergo fundamental revision.

Using superpositions of the basis states , we can introduce two different new basis states, such as

or, conversely

Here, D and Dí stand for the two 45° or "diagonal" directions. Substituting these expressions into the original state, we get

which means that our state is 99% and 1% , so its polarization is very close to the diagonal (or 45° ) direction.

Next, we consider a two-photon state, labeling the two distinguishable photons 1 and 2 (or left and right, or red and blue). Evidently, there are four basic states:

The first of these states signifies a physical situation in which both photons are polarized along the horizontal, etc. Quantum mechanics allows, and indeed demands, that we should be able to construct from these basis states more general two-photon states by superposition, just as we did for one photon:

where again the (absolute value) squares of the numbers a, b, c, d, are the probabilities of detecting the particular two-photon basis state, when a measurement is made. For certain values of the coefficients the two-photon state is factorable:

If this factorization is possible, we can regard the two photons as carrying their physical information independently, without influencing one another. Generally, however, a two-particle state cannot be factored into two one-particle states. The state is then said to be entangled (verschränkt in Schrödingerís German). Entangled states are frequently referred to as weird and involving spooky actions-at-a-distance.

Schrödingerís allegorical cat. whom we also encounter in the play, is the notorious caricature of an entangled state. A radioactive nucleus, which is initially undecayed but finally decayed, takes the place of photon 1, and the cat, which is either alive or dead, symbolizes photon 2. The entire state is a superposition, not just of the live and dead states of the cat, but of two distinguishable "two-particle" states which correlate the cat states with the initial and final states of a radioactive nucleus. No such superposition has ever been observed, because of extremely rapid decoherence processes induced by even the gentlest of interactions with the environment.

Schrödingerís radioactive nucleus coupled to the cat illustrates one of the simplest examples of an entangled two-photon polarization state:

with fifty-fifty probability of finding the photons both with horizontal or vertical polarization, but never with one of them polarized along the horizontal and the other one along the vertical. It is important to remark that the same two-photon state can also be written in terms of the diagonal basis as:

Again the entanglement is apparent.

At this point, the counterfactual EPR (Einstein-Podolsky-Rosen) argument (in the version first presented by Bohm) kicks in: If, in our entangled two-photon state, photon 1 is found to have horizontal (vertical) polarization, then photon 2 is certain to be polarized the same way, horizontally (vertically). This is so even if the photons are very far apart and incapable of interacting with each other at the time of these polarization measurements, as was the case in a recent experiment, conducted in the suburbs of Geneva with a relativistic wrinkle. The doctrine of local realism, advocated by Einstein, demands that, whether it is subjected to measurement or not, photon 2 must, in an anthropomorphic way of speaking, "know" that its polarization is horizontal (vertical), and this information must be encoded in it (e.g., as the value of a hidden variable). Since we could equally well have elected to test photon 1 for polarization in the diagonal directions , bisecting the horizontal and vertical directions, local realism requires that photon 2 carries the information of its potential polarization direction unambiguously with it, although the two photons may be separated by several kilometers. In the given entangled state, Einsteinís local realism then implies that photon 2 has both 100% sharp polarization in the horizontal (vertical) direction and also along one of the diagonal directions. But in quantum theory, no such one-photon state can possibly exist! Einstein, who thought that the predictions of quantum mechanics have only statistical validity for ensembles of particles, argued that quantum mechanics is (correct but) incomplete and must allow for a more detailed deterministic and realistic description of the states of single particles (photons). Bellís inequality showed this hypothesis to be incompatible with some (although not all) of the predictions of quantum mechanics. The entangled two-photon state is, as Bohr might say, an indivisible whole, and cannot be thought of as a composite of two distinct one-photon states, which would retain their individuality and which could each carry their own sharply defined polarizations. The latter view is not consistent with the formalism of quantum mechanics.

While it is certainly important and interesting to know that quantum mechanics and local realism are incompatible, it is even more important to know what actual experiments tell us. Can entangled states (of two or more particles) be made in the laboratory, and do they in tests obey the predictions of quantum mechanics? In the past twenty years, it has finally become possible to address these questions experimentally. Several years ago, at the fiftieth anniversary celebration of the American Institute of Physics, Edward Purcell said that he was glad to be alive when Alain Aspect and his group showed that an entangled two-photon state behaves as quantum mechanics predicts (violating Bellís inequality). In recent times, the predictions of quantum mechanics, analyzed in terms of the Copenhagen interpretation, have been confirmed experimentally for ever more entangled states. This is the topic of Anton Zeilingerís subsequent talk in this symposium. The play Copenhagen has provided us once more with a memorable opportunity for examining these fundamental issues.

Last edited by QuikSand : 04-08-2005 at 03:30 PM.
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Old 04-08-2005, 03:30 PM   #3
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Alas, it seems the various formulae in the linked article didn't come through when it was pasted in - you will need to open the link to see them. Sorry 'bout that.
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Old 04-08-2005, 03:35 PM   #4
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Incidentally, much of the pasted article is beyond me. Just posted for those who are more familiar with this than I am.
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Old 04-08-2005, 03:38 PM   #5
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Here's another article on a similar vein, less number-intensive, more philosophical:


Thoughts on Physicas and Reality


Thoughts on Physics and Reality

by Ben Best

Responsible philosophy acknowledges that life requires choice and action, and that epistemological and metaphysical assumptions are presupposed both in everyday life and in the more studious or scientific pursuits of truth. Some armchair philosophers claim to be solipsists, denying the existence of other minds or an external reality, but their conduct in daily life belies their hypocrisy. Others deny the use of reason on the grounds that, for example, it is circular to use reason to justify itself and that there is no grounds external to reason by which reason can be justified. And there are many who enjoy the use of obscurity, complexity and arcane mathematics or physics to impress others or intimidate them into abandoning reason and perception of reality -- supplanted by nothing of use. These approaches use philosophy for ulterior motives and leave practical life, as well as science, effectively groundless.

I see three realms in the epistemological processes of a human being, which I designate as (1) models (2) phenomena and (3) reality. Models are the ideas a human forms about reality based on phenomena. Truth refers to the close correspondence of models with reality. This triadic view is itself a model of reality.

An armchair philosopher may claim that the biological brain in which models are constructed, and the biological sense-organs through which phenomena are processed, are so different in structure from reality itself that the gap can never be bridged. And that a correspondence between models and reality can never be verified without direct access to reality -- while humans only have access models and phenomena. But if he is preparing to leave his house and plans to use his car, he will seek phenomena from an objective reality (to improve the correspondence of his model) by checking his pocket for his car keys. Discovering no keys improves the correspondence of his model with reality and motivates the seeking of more phenomenal clues so as to correctly model and function within reality -- such as checking to see whether the keys are on his desk. The philosophical skeptic displays his hypocrisy by his conduct, and robs himself of the opportunity to make of philosophy a tool to empower his life.

Yet the skeptic is at least correct in emphasizing that reality and models of reality are distinct -- and will always and necessarily be distinct. It is erroneous to become so philosophically arrogant (as perhaps characterized by Ayn Rand) as to regard models of reality (especially her own) as perfect representations of reality. Phenomena are the windows through which reality is viewed. The receptors in the human eye represent the colors red, green, and blue as qualitatively distinct -- providing no clue that the difference is one of quantitative wavelength or that the eye has merely selected a tiny portion of the electromagnetic spectrum to be "visible". Nonetheless, other phenomena -- and model-building from those phenomena -- has given us this information. Phenomena have been used to get beyond phenomena -- to build a model of reality sophisticated enough to allow us to incorporate limitations of our perceptions.

Phenomena are more than raw sensory data. Perception is the process of a consciousness using implicit ideas or models to process sensory input. For example, the phenomenon of day alternating with night requires an induction of sensations over time. (Even if induction cannot prove theory, induction can give rise to theories.)

Models of reality have two components which may not be distinct: entities and causes. Entities cause perceptions, but causality generally refers to models of the laws or mechanisms of reality. The phenomenon of the alternation of day and night is said to be caused by the rotation of the Earth in space in its orbit around the sun. The distinction between prediction and causal determinism may be one of degree. Primitive peoples could have predicted the coming of day or night on the basis of past experience, without the visual model of earth and sun that I have presented as "casual". The explanation of the prediction can be called the cause. Similarly, one can predict that an apple dropped from a height will fall to the ground. But an understanding of the causative agent (gravity) provides a broader context for the prediction -- for example the ability to predict that the apple will not fall in a space station. Familiarity with the more general cause is itself a kind of prediction -- little is known about what gravity really is or why it exists.

Physics as the ultimate science provides the ultimate causal explanations underlying the other sciences and the general phenomena of life. Classical physics reduced physical laws to (1) Newton's laws of motion, concerning gravitational fields & forces on particles/rigid bodies, and (2) Maxwell's equations, concerning electromagnetic fields (waves). Gravitational and electromagnetic forces are the chief forces governing the macroworld, while a "strong force" and a "weak force" are the chief forces governing the atomic and subatomic microworld. Relativity demonstrated that commonsense notions of time, space and matter cannot be correct, but it did not call into question the objectivity or casual nature of reality the way orthodox interpretations of quantum theory have done.

The building of models, particularly visual models, is based on constructions from our commonsensical everyday environment. But as science explores new high velocity, ultracold or subatomic worlds, the causes and the entities involved become increasingly alien -- and so do the models. Most physicists give little thought to reality, and instead simply concern themselves with phenomena and mathematical prediction (should I say as primitives induced that day would follow night?).

Using quantum physics to resolve philosophical questions concerning reality and causality seems like little more than a "snow job", since such questions go beyond the scope of physics. The fact that physics cannot explain any specific phenomenon is no more grounds for rejecting causality than it is grounds for supporting belief in the existence of God. The alternative to a belief in a mechanistic universe is a belief in a magical universe (or a spiritual universe). One cannot live rationally while being agnostic to causality or reality -- these must at least be accepted heuristically (or denied only in some remotely irrelevant microworld).

[The physics which inspired this essay can be found in my piece The Copenhagen Interpretation of Quantum Mechanics ]

[For a collection of quotes by scientists, quasi-scientists and pseudo-scientists on the subject of quantum physics see Quotations for the Backyard Quantum Mechanic ]

[For a critique of the quantum metaphysics of Roger Penrose and New-Ager Fred Alan Wolf see my piece Comments on Two "New Age Physics" Books]
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Old 04-08-2005, 03:50 PM   #6
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I came close to understanding Heisenberg's uncertainty principle by accepting that there are no 100% probability concerning anything in quantum physics. We are accustomed to know for certain if a thing's there or not, but all you get is a probability that the thing is there when you try to measure it... translating these concepts to plain English is not easy - we totally lack precision in our language to describe it in terms other than mathematics.

Our experience is that physical things are solid and independent from us, but this is not true on the quantum level of physics. Schrodinger's cat is a good example of something that follows the laws of quantum physics. We don't know if the cat is in the box before we look into it, and by opening it we are affecting the outcome by deciding the probability of the cat being alive or dead.
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Old 04-08-2005, 03:56 PM   #7
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I'll post my findings tomorrow.

I'm of the mindset that everything can be measured. If it exists in any plane, sphere, dimension, it can be quantified. Just because we can't accurately measure it today, does not mean, to me, that is does not exist.

I stopped at mechanical physics, so my brain still hurts from perusing the stuff above.
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Old 04-08-2005, 03:56 PM   #8
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And perhaps, a dope like me, simply needs to make peace with the notion that this will never really comport with intuition, and be done with it.

I just got to the point where I was pretty comfortable with nearly all the concepts of relativity, all based on intuition... that the basic arguments of quantum physics are a bit disappointing to me, if only because they don't come easily at all. In the end, if they say it's true, I'm nt one to argue... but I really don't think I can "get" it in the same way.
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Old 04-08-2005, 03:59 PM   #9
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*de-cloaking briefly*

I am not a physics major and haven’t heard a physics lecture in years. Nonetheless, I’ve become pretty familiar with various arguments surrounding the uncertainty principle. Primarily, my point of access has been through various chaos theory, philosophy of science, and post-modernist authors who attempt to (mis-)use the work of Heisenberg for their own ends. Let me offer you a thoughts from the unscientific angle:

1) You seem to focus on the uncertainty part of the theory more than you do on the subject/object problems raised by the theory and I think that may be the source of your confusion. The notion of traditional science that there is an objective frame is problematic in a world where the experiment itself changes the result. In such circumstances, as the Copenhagen interpretation presupposes, there is an inherent inability to “know” where a particle is.

2) I think you are to that point in the problem, but I think you need to push the uncertainty even further. After all, you can continue to argue that although the subject/scientist is determining the object/result, there still is a “real,” but unknowable location. However, different schools of thought show that you can’t be secure in that conclusion. Chaos theory would generally hold that the location itself is indeterminate. That is, a particular observation by a particular scientist can cause an unpredictable location. There is no formula for the result (even if it were knowable).

3) This conclusion probably troubles you, so let me try to add another wrinkle to the problem. There is a problem of the finite in studying particles. Previously, an atom was thought to be the smallest particle and indivisible until smaller protons, electrons, quarks, etc. were discovered. I think their general scientific method in this area thinks entirely of infinite possibilities. That is, ask, “what is the smallest particle?” And then ask, “what is smaller than that?” Generally, we can think of something infinitely small even if it has no name. What are quarks made of? We don’t know, but we could certainly think that there is something smaller. (Incidentally, this provides a different problem for the clockwork universe because there are potentially an infinite number of particles that you need to know the location of - but that is irrelevant to this discussion).

However, assume that cycle ends and there are finite particles that operate according to certain laws. However, if a finite particle can only be observed by other finite particles (ie an instrument or scientist), those particles have effects on each other. As a result, the subject AND object are changed by the interaction. The result is that the universe is not so much a complex Rube Goldberg machine, but rather a series of interactions with unpredictable results. That still doesn’t address the point that you make (that unpredictability doesn’t mean non-existence), but it does help illustrate a point. Knowing is reality. The very fact that you know is not independent of the real world. Your “knowledge” is itself a series of particles (assuming a material world). From the point of observation to the understanding in your brain, knowledge is reality. It is only through a grammatical dichotomy that we separate the two ideas. And to apply “knowledge” in a non-material way (ie assuming it is a non-tangible “thought”) when your primary assumption is a wholly material world is a major problem.

Anyway, I don’t know if this helps make it clearer than the articles you have posted, but I’ve tried to explain it without using hyper-technical language that just confuses the issue.

P.S. albionmoonlight - I lost the email you sent me, so send it again if you have it - I didn’t mean not to respond - I just got caught up getting an article done for the Spring push.

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Old 04-08-2005, 04:00 PM   #10
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Quote:
Originally Posted by cartman
I'm of the mindset that everything can be measured. If it exists in any plane, sphere, dimension, it can be quantified. Just because we can't accurately measure it today, does not mean, to me, that is does not exist.

This, to me makes intuitive sense. I understand that greater minds than mine, and presumably demonstrable experimentation, suggest it's simply wrong -- but thus are the boundaries of intuition, it seems.
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Old 04-08-2005, 04:05 PM   #11
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I would recommend Huston Smith's Forgotten Truth. There are several chapters where he critiques contemporary scientific thought very effectively. You may find it helps sharpen your thinking on these matters.
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Old 04-08-2005, 04:08 PM   #12
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If a tree falls in the forest, does it make a sound? The anwser is yes, because Peter asked the trees that question, and they told him that lenny fell over last week and hasnt shut up since!

Sorry for the light response, but this stuff is over my head, maybe later I will post something more thought provoking
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Old 04-08-2005, 04:09 PM   #13
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I will confess... the whole notion of wave/particle duality is something that I don't have a very good handle on, either.
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Old 04-08-2005, 04:09 PM   #14
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This, to me makes intuitive sense. I understand that greater minds than mine, and presumably demonstrable experimentation, suggest it's simply wrong -- but thus are the boundaries of intuition, it seems.

By that logic, if something today isn't measureable, but in 50 years it becomes measurable, doesn't that contradict the theory? Maybe I'm simplying it too much, but that theory, if introduced two hundred years ago, would mean that atoms don't exist. There was no way to measure them. Then atoms were discovered and deemed measurable. Then, by that theory, proton and neutrons didn't exist, there was no way to measure them. Rinse and repeat.

I can see, though, related to thought and free will, where this could gain traction. How do you measure/quantify a thought or a dream? Today, we have no concept of how to do this. But some brainiac in the future just might figure out a way to do that.
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Old 04-08-2005, 04:11 PM   #15
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By that logic, if something today isn't measureable, but in 50 years it becomes measurable, doesn't that contradict the theory? Maybe I'm simplying it too much, but that theory, if introduced two hundred years ago, would mean that atoms don't exist. There was no way to measure them. Then atoms were discovered and deemed measurable. Then, by that theory, proton and neutrons didn't exist, there was no way to measure them. Rinse and repeat.

I can see, though, related to thought and free will, where this could gain traction. How do you measure/quantify a thought or a dream? Today, we have no concept of how to do this. But some brainiac in the future just might figure out a way to do that.

Apparently, my cloaking device is on the Fritz, but since I'm here and find this conversation to be VERY interesting, let me add a couple more points.

cartman, your intuition is one of "mis-uses" of the theory. Remember, this idea is limited to quantum mechanics, it doesn't mean that all things not currently known will be unknowable. However, the problem in a world of finite particles that interact with each other is that there is no external frame of reference. You cannot stand outside and see the particle's location without using other particles that change its location. Unless you can observe without the use of particles (and if you could, the basic assumption of a material world is again lost), there can be no way to observe the location of a quantum particle.
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Old 04-08-2005, 04:12 PM   #16
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By that logic, if something today isn't measureable, but in 50 years it becomes measurable, doesn't that contradict the theory?

I believe the Copenhagen school argument is that we're talking not of things that are unmeasurable because of the limits of our instruments, but because of their very nature.

Shaky ground, though, getting this through me...
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Old 04-08-2005, 04:16 PM   #17
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Thanks for the effort, JG. I need to chew on the latter half your point #3.


The whole concept of knowldege itself affecting reality is trouble for me. Just seems like shifty ground. It all smacks of phlogiston and ether and other since-discarded theories that once sought to explain difficult phenomena.

If there's a particle out there somewhere, doing something, without my knowledge -- I just want to believe that its interactions are based on where it actually is, and I have a hard time understanding what little old me (and what I might be able to measure or comprehend about that particle) has to do with it.

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Old 04-08-2005, 04:21 PM   #18
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Thanks for the effort, JG. I need to chew on the latter half your point #3.


The whole concept of knowldege itself affecting reality is trouble for me. Just seems like shifty ground. It all smacks of phlogiston and ether and other since-discarded theories that once sought to explain difficult phenomena.

If there's a particle out there somewhere, doing something, without my knowledge -- I just want to believe that its interactions are based on where it actually is, and I have a hard time understanding what little old me (and what I might be able to measure or comprehend about that particle) has to do with it.

I guess the one thing I would add to the mix in your thinking about the problem is to try and check yourself whenever you use a non-material concept. Things like "knowledge" and "predictions" are non-tangible "ideas" in English. However, if all "ideas" are really material (a necessary assumption of a wholly material world), then the distinctions drawn lose their power. Instead, think of what are traditionally thought of as intangibles as unknowable particles.

While this description above begs the question in a sense, it can help you bridge the gap to the "uncertain" way of thinking. If you come to believe that the intangible is really just unknowable, it makes viewing the world from a Heisenberg perspective a little easier.
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Old 04-08-2005, 04:21 PM   #19
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Another thought as someone explained it to me--

We tend to understand complex scientific subjects by anaolgy. For instance, we can think of molecules of gas as very small balls all bouncing around with each other. By and large, this use of subrelativistic Newtonian macroscopic physics to understand other concepts works for most situations (because most situations are subrelativistic and macroscopic). It is very hard for our brains, which have spent 100% of their time observing and interacting in this world to really get other situations. You may understand them intellectually, but that understanding is probably just using more and more complicated analogies to things that you understand. For example, you can learn the equations for relativity and "understand" that mass increases and length contracts, but you are probably still thinking about weight being added and rulers being shrunk. You don't really get what is happening at relativistic velocities because it is something unlike anything that you have EVER perceived.

It's like being able to understand a foreign langauge by converting it to English in your head vs. actually being able to think in that language. You can discuss concepts competently and have a sense of what is going on with either, but you don't really get it until you are doing the latter.

When it comes to quantnum mechanics, as I understand it, the fundamental nature of fundamental particles is that they are uncertain. How can that be? Doesn't everything have to exist in a particular time or place, even if we cannot measure it? The short answer is NO. Everything that you have ever known must exist in a particular time or place. But these particles are like nothing that you have ever known, and there is simply no easy way (i.e. via analogy to something familiar) to explain what they are.

None of which answers your question, but some of which may help you understand from where the frustration is coming.
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Old 04-08-2005, 04:21 PM   #20
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I believe the Copenhagen school argument is that we're talking not of things that are unmeasurable because of the limits of our instruments, but because of their very nature.

Shaky ground, though, getting this through me...


I'm with you on that one. It's starting to border a bit on faith, which goes against scientific reasoning... But as an armchair observer, I don't claim to have any in-depth knowledge of their reasonings for coming to that conclusion.
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Old 04-08-2005, 04:22 PM   #21
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The instruments used to measure are in itself part of the observation that decides the probability and thus affects the outcome of the "experiment".. as we can't remove ourselves from the universe to observe it. Thus it all goes around, like clockworks. The free will in all this would be in which way we choose to alter the universe (by making an observation in a physics experiment, for example) and which probability was going to be realized from all the infinite possibilities. It's counter-intuitive, I know - but I make no claims of understanding it. But picturing it this way works for me at least.
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Old 04-08-2005, 04:22 PM   #22
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If the universe is made up of things, and the things all behave according to various physical laws relative to one another – then presumably everything that is going to happen a moment from now is simply a function of where the things are and how they are interacting. Therefore, stepping to matters of philosophy, how can there be free will? If all that is happening is a series of physical interactions of things with one another, where is there room for something like an idea in all this?

I hate to seem like I'm boiling all of this down to a simplistic answer, but that's the result I get when I think about this. Essentially, I don't have a problem with the concept of the "clockwork universe" from a philosophical viewpoint while still believing in what we define "free will". How do I resolve the contradiction? When I boil it down, I don't truly believe in "free will" - I can't logically see how the clockwise universe concept can't be true - but I resolve this by noting that the incredible complexity of what constitutes life is such that I don't think we can ever fully unravel all the computations necessary to predict how everything works. In other words, the complexity of thought and action in living beings is so complex as to have the appearence of "free will".

Consider how difficult it is to predict the weather. While our accuracy is pretty good, it's far from perfect. Things on a macro level we understand quite well, but as we transition into the micro level we lose much of our accuracy.

It seems intuitive to me to view our universe as one in which every action has a reaction, though much of what constitutes that reaction is too subtle or too complex to gain awareness in our consciousness.

Some might view the concept of a "clockwork universe" as philosophically or spiritually lacking - that if every action can be broken down into basic physical actions and reactions, it leaves the universe a very dry place. I think what that view excludes is the magic of why things behave as they do? Why is it that the physics of our universe are what they are?
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Old 04-08-2005, 04:23 PM   #23
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I cringe every time someone talks about measurements and the Hinesburg uncertainty principle.
I doesn't say knowing one you can not measure the other, it states the other doesn't exist.

Unfortunately people usually use the measurement introducing an err example to try to explain the unexplainable.
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Old 04-08-2005, 04:25 PM   #24
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This, to me makes intuitive sense. I understand that greater minds than mine, and presumably demonstrable experimentation, suggest it's simply wrong -- but thus are the boundaries of intuition, it seems.

Well, if we think back to the "Butterfly in Tokyo, Tornado in Oklahoma" idea that little things make big changes elsewhere/when, that always made me extrapolate that to the idea of free will.

In reading these posts, for example, I got up twice to run to the kitchen and grab a handful of chips. Free will in action. But why did I get up? I was hungry. Why was I hungry? Because my stomach rumbled. Why did my stomach rumble? Becuase I haven't eaten in seven hours. Etcetera...

...or from the other side? Why did I eat chips instead of fixing a sandwich? Why did I pass up the candy bar that was sitting on the desk to leave the room? Why did I buy that particular brand of chips a week ago at the supermarket?

I could answer these questions - the answers would get more and more complex and esoteric, until I too was examining mesons and bosons on a quantum level. But it would take so much time to answer them, and so much effort and resources to predict that behavior, that I'd run out of universe to store the results in.

I suspect that if we were to take the time and effort to try to determine future events on a macro scale, we would be doomed not because the future is so unpredictable, but because the number of variables that would need to be accounted for to make any reasonable assumption is so large as to require more time and room than the universe provides. We can't build a model big enough to house the answers at anything more than an abstract probability.

More than anything else, I think THAT is why the clockwork universe is not a problem for us. No matter how deterministic the universe actually IS, we're inside it, and can't see the gears. For all intents and purposes, the complexity of the universe enforces free will on us.
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Old 04-08-2005, 04:26 PM   #25
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Apparently, my cloaking device is on the Fritz, but since I'm here and find this conversation to be VERY interesting, let me add a couple more points.

cartman, your intuition is one of "mis-uses" of the theory. Remember, this idea is limited to quantum mechanics, it doesn't mean that all things not currently known will be unknowable. However, the problem in a world of finite particles that interact with each other is that there is no external frame of reference. You cannot stand outside and see the particle's location without using other particles that change its location. Unless you can observe without the use of particles (and if you could, the basic assumption of a material world is again lost), there can be no way to observe the location of a quantum particle.

So if I am understanding this correctly, this goes back to the point that anytime you measure something, you aren't really measuring the exact state? For example, there is current running through a wire. You hook an ammeter up to measure that current. The introduction of the ammeter changes the state of the current, even minutely, in the wire. So the reading on the ammeter isn't the true state of the wire? Might be oversimplified, but is that not too far off base?

edited to fix the glaring physics mistake
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Old 04-08-2005, 04:28 PM   #26
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So if I am understanding this correctly, this goes back to the point that anytime you measure something, you aren't really measuring the exact state? For example, there is voltage running through a wire. You hook an ammeter up to measure that voltage. The introduction of the ammeter changes the state of the current, even minutely, in the wire. So the reading on the ammeter isn't the true state of the wire? Might be oversimplified, but is that not too far off base?

Except that the principle is entirely limited to quantum mechanices. Further, the statement that the reading doesn't measure the "true state" is a little off. The theory holds that their is no "true state" (or in this case "true location") of a quantum particle.
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Old 04-08-2005, 04:29 PM   #27
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Except that the principle is entirely limited to quantum mechanices. Further, the statement that the reading doesn't measure the "true state" is a little off. The theory holds that their is no "true state" (or in this case "true location") of a quantum particle.

Gotcha. That makes sense to me.
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Old 04-08-2005, 04:32 PM   #28
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I could answer these questions - the answers would get more and more complex and esoteric, until I too was examining mesons and bosons on a quantum level. But it would take so much time to answer them, and so much effort and resources to predict that behavior, that I'd run out of universe to store the results in.

I suspect that if we were to take the time and effort to try to determine future events on a macro scale, we would be doomed not because the future is so unpredictable, but because the number of variables that would need to be accounted for to make any reasonable assumption is so large as to require more time and room than the universe provides. We can't build a model big enough to house the answers at anything more than an abstract probability.

But I do not want to just settle for "it's too hard to calulate" as the answer here. I recognize that there are countless variables and effects happening... and that we can't buidl a model to understand it. But I still want it to be.


Quote:
More than anything else, I think THAT is why the clockwork universe is not a problem for us. No matter how deterministic the universe actually IS, we're inside it, and can't see the gears. For all intents and purposes, the complexity of the universe enforces free will on us.

And to me, this is a complete cop-out. I understand that it may not even matter that the universe is completely deterministic... but I want to understand why it is or is not so (or even just how we understand it to be so or not so) and am falling short on this. I won't settle for "it doesn't matter."

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Old 04-08-2005, 04:35 PM   #29
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Which suggests light behaves as a wave, not a single particle.

Hence the duality..

I'll grade myself a "B" on understanding the dual nature of light. I even follow the experiments fairly well.

Now, how about matter? ::lost::
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Old 04-08-2005, 04:35 PM   #30
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I will confess... the whole notion of wave/particle duality is something that I don't have a very good handle on, either.

Well in layman's terms, you can take light and emit a single quantifiable amount (in photons) at an object and measure the impact - typically you can shoot a single photon of light at the substance and measure the electrons that are emitted from the substance from the impact.

This suggests that light has mass and energy - particle like attributes.

However, you can also shoot a single photon at a slit in the wall (edit) larger than a photon and measure the impact on the other side of the slit (with xray material or something). You would expect that the photons would travel right though the slit and make a single dot on the other side. Instead it makes a diffraction pattern similar to a wave hitting the slit (like waves on the surface of a pond).

Which suggests light behaves as a wave, not a single particle.

Hence the duality..

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Old 04-08-2005, 04:36 PM   #31
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My response to moved at speeds so near to c that it actually preceded your own comments. Cool!
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Old 04-08-2005, 05:25 PM   #32
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Old 04-08-2005, 05:39 PM   #33
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Now, how about matter? ::lost::

Well, since light (photons) are energy we can take Einstein's equation E=mc2 which basically says energy and mass (matter) are the same thing.

More importantly you can do similar experiments on electrons which show the same wave/particle duality. And since electrons, protons, and neturons make up matter we can say that matter shows wave/particle duality. (note: I don't know if anyone ever proved it with protons and neutorns).
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Old 04-08-2005, 05:50 PM   #34
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Dola,

By the way, if you're really interested in quantum mechanics and the impacts on the universe (including explanations of Einsteins laws, and string theory (or the theory of everything) I would recommend Brian Greene's "the Elegant Universe".

It gets a bit dense at times but it's a very interesting and wide ranging book.
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Old 04-08-2005, 08:16 PM   #35
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I just received a copy of Greene's newer book The Fabric of the Cosmos, and assuming that goes well, I plan to dig back to The Elegant Universe as well. Thanks for the recommendation -- I'm on it already.
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Old 04-08-2005, 09:07 PM   #36
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But I do not want to just settle for "it's too hard to calulate" as the answer here. I recognize that there are countless variables and effects happening... and that we can't buidl a model to understand it. But I still want it to be.

But isn't this the key to your problem? The belief in free will is little more than human arrogance - the wish to believe that we're not merely a consequence of predictable mechanisms. It may well be that all we have is unpredictability.

It should also be remembered that scientific theories are not absolute truths - they're useful descriptions that allow us to "understand" phenomena. The behaviour of light - some behaviour requiring a wave model, other behaviour a particular model - illustrates this. If you treat, say the wave theory as "true", then you will have problems with other phenomena. The theory is "good" as long as you respect its limitations.

Quantum theory and Relativity are similarly two theories that are not compatible. It doesn't matter in most cases because the first deals with sub-atomic particles and the second with astronomical events. The two theories are "useful" within their own spheres but the contradictions illustrate that one or both are far from "true".

Thus we hit a problem when the two come together in the "big bang" when the astronomical is reduced to the sub-atomic. The search for a single theory (unification theory I believe they call it) is at the forefront of theoretical physics.

So, if these theories lead to philosophical problems, then there is still room for doubt as to the degree to which they validate arguments. It may be that the theories are being applied beyond the boundaries of their applicability.

I think the problem of measurement and existence arises because of a limited idea of "measurement". I think this really only implies that we should be able to interact with the phenomenon (directly or indirectly) for it to "exist" not that we should be able to "measure" in the sense of "quantity".

The problem of "intuition" and common sense I think is not with the theories but with our own mental limitations. We "understand" something when we can describe it in terms of previous experience. Just as we "understand" the idea of molecules in a gas by likening it to billiard balls on a table in three dimensions we can find nothing in our direct experience which corresponds in any meaningful way with the quantum mechanics description of sub-atomic particles. Electrons as probability distributions doesn't quite hit home like the idea of them as tiny ball bearings. The "understanding" of both relativity and quantum mechanics is through mathematics not correspondence to everyday experience.

Surely the problems of our developing "understanding" of nature comes from the limitations of human intelligence and psychology.
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Old 04-08-2005, 09:08 PM   #37
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Nicely said, Mac.
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Old 04-09-2005, 08:31 AM   #38
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Old 04-09-2005, 08:49 AM   #39
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I just received a copy of Greene's newer book The Fabric of the Cosmos, and assuming that goes well, I plan to dig back to The Elegant Universe as well. Thanks for the recommendation -- I'm on it already.


I'm on Chapter 4. It's very interesting, and even though sometimes I reread passages - it really is very well explained.

I hadn't even thought about Physics since the AP exam in high school 15 years ago, and I forgot just how interesting timespace is when you think about it. The fact that time slows down when you are in an accelerating car is just a cool thing to think about.
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Old 04-09-2005, 09:56 AM   #40
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Old 04-09-2005, 09:01 PM   #41
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I'm on Chapter 4. The fact that time slows down when you are in an accelerating car is just a cool thing to think about.

Some car if you noticed it

I believe that they did confirm this effect a couple of months ago when they synchronised a couple of atomic clocks at Heathrow airport, put one on a flight to New York and back and compared the clocks on the return. The clock that took the flight was indeed behind the one that stayed at Heathrow by the amount predicted. A very small difference of course at these velocities but one that can now be measured with today's clocks.
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Old 04-10-2005, 03:36 PM   #42
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*de-cloaking briefly*

Romulan or Klingon?
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Old 04-10-2005, 03:43 PM   #43
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Instead, think of what are traditionally thought of as intangibles as unknowable particles.

I can't wait until sports physicists find the elusive "clutch" particle.


(I apologize for the wisecracking...just my nature. I do find this discussion interesting however, I'm just not knowledgeable enough to be able to contribute much, at least not anything that isn't easily dismissed.)
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Old 04-10-2005, 04:35 PM   #44
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Some car if you noticed it

I believe that they did confirm this effect a couple of months ago when they synchronised a couple of atomic clocks at Heathrow airport, put one on a flight to New York and back and compared the clocks on the return. The clock that took the flight was indeed behind the one that stayed at Heathrow by the amount predicted. A very small difference of course at these velocities but one that can now be measured with today's clocks.

You've never driven a Mazda 323 I take it.
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Old 04-11-2005, 01:51 AM   #45
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What about the duality of Hobbes? Is he real, or is he just a stuffed tiger?
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Old 04-11-2005, 09:28 AM   #46
moriarty
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Quote:
Originally Posted by QuikSand
I just received a copy of Greene's newer book The Fabric of the Cosmos, and assuming that goes well, I plan to dig back to The Elegant Universe as well. Thanks for the recommendation -- I'm on it already.

Hmmm... I just read the description of the Fabric of the Cosmos and it sounds exactly the same as The Elegant Universe . I'm wondering what the difference is between the two. It almost sounds like he wrote Fabric based on the same material but with a less technical bent.

Last edited by moriarty : 04-11-2005 at 09:37 AM.
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Old 04-11-2005, 10:32 AM   #47
QuikSand
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I'm not sure myself... my best guess is that Fabric is really a deeper (though less scientific) exploration of the relativistic notions of space and time. Assuming I actually get some time to read in the near future (as if that term has any meaning any more) I will let you know what the basic idea seems to be.
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Old 04-18-2005, 10:39 AM   #48
dixieflatline
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Originally Posted by Quiksand
Fine, we can’t measure everything, so we won’t be able to know where things are and how they are moving. But they still are somewhere, and they still are moving, right? So they still do, in fact, have all those various physical interactions with one another, even if we cannot measure them in any practical way.

So, if that’s the case… how do we escape from the clockwork universe concept? I buy Heisenberg’s uncertainty in measurement, but it doesn’t (intuitively, at least) translate to reality for me.

Sorry to get to this late. I was talking to a friend about similiar things and stumbled on a couple of very useful webpages that might help the confusion if you haven't figured everything out yet.

Your first question is basically is: even if we can't measure all the variables about a particle as long as it they still exist then the particles should behave in known(clockwork) way.

Young did an experiment where he shot a beam of electrons through a double slit looking for diffraction. If he found diffration then electrons had to behave like waves going through the slits. That is exactly what he saw, the electrons were interacting with each other, like waves, causing a diffraction pattern to emerge. From reading your first post it sounds like you already have some grasp on this but now the fun part.

Young took his apparatus and shot single electrons through the slits. With nothing else to interact with the electrons should just go through a slit and hit his detector. But that isn't what he saw. He again found diffraction patterns. It took a while but the single electrons gradually built up to the same pattern as before. Some really neat pictures of his detector here


What's going on here? It turns out that the electrons were interacting with themselves. As the electrons pass through the slits it is equally likely to go through each slit. Once on the other side the two wavefuctions are combined again but combined like waves producing diffraction. If the world was clockwork then the elctrons would have had a specific position and velocity and gone through exactly one slit and when combining the wavefuction on the other side it would be 100% from one and 0% from the other. The only way this experiment works out is if you combine the wavefuctions 50%/50%. So which slit did the electron go through? It's just not a question that we can answer.

It seems that my scientific believes aren't exactly in high reguard so for those at home that don't believe in this wave/particle duality here is an experiment you can do at home to show quantum mechanics is necessary in understanding the universe.

Take three high quality pairs of polarized sun glasses. Setup two pair of glasses next to a light source such that no light passes through. One pair of glasses is now only letting light polarized up and down go through( | ) and the other pair is only letting light polarized left and right go through ( - ). Now add a third pair of glasses polarized at a 45 degree angle ( / ) in between the first two. Rotate the middle pair if you can't tell what direction 45 degrees is you will find it. Remarkably light now passes through all three pair. This cannot be explained classically only with wavefuctions and quantum mechanics.
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Old 04-18-2005, 11:00 AM   #49
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Quote:
Originally Posted by QuikSand
that the basic arguments of quantum physics are a bit disappointing to me, if only because they don't come easily at all.

I think it is safe to say that no one understands Quantum Mechanics. (Richard Feynman
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Old 04-18-2005, 04:31 PM   #50
judicial clerk
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Dixieflatline, Isn't there a theory that when the single electron is projected through the slits, it is ineteracting with the another "universe" that is just right "there"?

Hi JG.
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