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##### Current Law Students / Re: Legal Reasoning
« on: May 30, 2008, 01:13:46 PM »
Bell's Inequality in Detail

To explain away this quirky paradox, some scientists said that there were "hidden variables" that exist in the photons that allow them to behave this way. Hidden variables are variables that we have yet to discover. They would be aspects of each of the photons that are the same, since they were entangled, but that did not depend on the other photon.

Bell proved mathematically that this was impossible with this inequality:

Number(A, not B) + Number(B, not C) >= Number(A, not C)

David M. Harrison, a physicist at the University of Toronto, explains it this way:

Quote
In class I often make the students the collection of objects and choose the parameters to be:

A: male
B: height over 5'8"
C: blue eyes

Then the inequality becomes that the number of men students who do not have a height over 5'8" plus the number of students, male and female, with height over 5'8" but who do not have blue eyes is greater than or equal to the number of men students who do not have blue eyes. I absolutely guarantee that for any collection of people this will turn out to be true.

What does this have to do with quantum mechanics? Here goes: you can shoot photons at a detector that detects the arrival time of the photon, and the photon's energy. If energy and arrival time were absolute values, that is, if the energy and arrival time of the photon exists whether it is measured or not, then the values would have to satisfy Bell's inequality, regardless of hidden variables.

The Punch Line: Does Quantum Mechanics Violate the Inequality?

In experiment after experiment Bell's Inequality is not violated, but instantaneous communication, or "spooky at a distance", seems to occur. If you rule out instantaneous communication, Bell's Inequality is violated. The most interesting experiment was carried out by a physicist at the University of Geneva, Switzerland, Nicolas Gisin in 1997. He split a single photon into two "smaller" photons (which meant they were entangled) and sent them down fiber optic cable in opposite directions. When the photons where about 10 kilometers apart they ran into a detector. Gisin found that even though a large distance separate the photons, something done to one photon at one end very much affected the photon at the other end...instantaneously.

What does this mean?

Let's take a look at assumptions. Here we invent two assumptions:

Quote
All birds have wings.
Everything that has wings flies.

We can conclude from these two assumptions that all birds fly. If we find a bird that has wings but doesn't fly, we know that at least one of our assumptions was wrong. In this case, it's obviously the last assumption (all the birds I know have wings).

It's interesting to know that Bell's Theorem has assumptions, too. They are:

Quote
Logic is valid.
There is a reality separate from its observation.
No information can travel faster than light.

The last assumption is called locality. Locality says that everything that is bound by relativity, everything that can't go faster than light, is local. If something is non-local it is thought to be part of a larger reality.

So which assumption is wrong in Bell's Theorem? Nobody knows.

Logic could be wrong. In 1930, Kurt Gödel proved that any theory proposed for the foundation of mathematics will be either insufficient for mathematics, incomplete, or inconsistent. This was a wild and crazy thing for a logician to do, as it essentially proved that logic was incomplete. There may be no reality separate from its observation. This is where physics melds with philosophy and religion. Could it be that the universe only exists because we are conscious of it? Perhaps we only exist because someone or something is conscious of us? The EPR paradox isn't the only paradox that raises this possibility. Erwin Schrödinger proposed a way to link the classical world that humanity knows to the quantum world of electrons and protons. He proposed that in a closed box one could put a live cat, a vial of poison gas, a geiger counter that smashes the vial if it detects radiation, and a radioactive atom. In an hour, the atom's likelihood of having decayed is 50%. In quantum mechanics, before you measure whether of not the atom decayed, it actually exists in a superstate of both decayed and not decayed. It's not that you just don't know, it's that it actually exists in both states at the same time. Thus, after an hour's time, before you peer into the box to see if the kitty is alive or dead, it must exist in a superstate of both dead and alive. If a tree falls in the forest and no one is around, did it actually exist at all? Information might be able to travel faster than light. Consider a one-dimensional creature, we shall call him a 1d, that exists on a line. Everything the 1d creature knows is in terms of length and nothing else. Then along comes a two dimensional creature, call him 2d. The 1d can measure the length of the 2d, but isn't aware of anything else. In fact, it's possible for the 1d to measure two lengths for a single 2d, making the 1d think that the 2d exists in two places at once, and in his universe he does! The same could be true for our universe.

The popular press likes to claim that quantum physics allows for faster than light communication of information. So far, physicists have not come to this conclusion. Dr. Ken Caviness, chair of the Physics Department at Southern Adventist University in Tennessee, says this:

Quote
I don't know of anyone in the field who seriously proposes instantaneous communication. On the contrary it seems that despite quantum entanglement information cannot be extracted from the system without some (at most) light-speed exchange of information.

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##### Current Law Students / Re: Einstein and the EPR Paradox
« on: May 30, 2008, 12:56:24 PM »

Here it is an interesting article on the issue:

By the 1920s, it had become clear to most physicists that classical mechanics could not fully describe the world of atoms, especially the notion of "quanta" first proposed by Planck and further developed by Albert Einstein to explain the photoelectric effect. Physics had to be rebuilt, leading to the emergence of quantum theory. Werner Heisenberg, Niels Bohr and others who helped create the theory insisted that there was no meaningful way in which to discuss certain details of an atom's behavior: for example, one could never predict the precise moment when an atom would emit a quantum of light. But Einstein could never fully accept this innate uncertainty, once famously declaring, "God does not play dice." He wasn't alone in his discomfort: Erwin Schrödinger, inventor of the wave function, once declared of quantum mechanics, "I don't like it, and I'm sorry I ever had anything to do with it."

In a 1935 paper, Einstein, Boris Podolsky and Nathan Rosen introduced a thought experiment to argue that quantum mechanics was not a complete physical theory. Known today as the "EPR paradox," the thought experiment was meant to demonstrate the innate conceptual difficulties of quantum theory. It said that the result of a measurement on one particle of an entangled quantum system can have an instantaneous effect on another particle, regardless of the distance of the two parts. One of the principal features of quantum mechanics is the notion of uncertainty: not all the classical physical observable properties of a system can be simultaneously determined with exact precision, even in principle. Instead, there may be several sets of observable properties–position and momentum, for example–that cannot both be known at the same time. Another peculiar property of quantum mechanics is entanglement: if two photons, for example, become entangled –that is, they are allowed to interact initially so that they will subsequently be defined by a single wave function–then once they are separated, they will still share a wave function. So measuring one will determine the state of the other: for example, with a spin-zero entagled state, if one particle is measured to be in a spin-up state, the other is instantly forced to be in a spin-down state.

This is known as "nonlocal behavior." Einstein dubbed it "spooky action at a distance." It appears to violate one of the central tenets of relativity: information can’t be transmitted faster than the speed of light, because this would violate causality. It's worth noting that Einstein wasn’t attempting to disprove quantum mechanics; he acknowledged that it could, indeed, predict the outcomes of various experiments. He was merely troubled by the philosophical interpretations of the theory, and argued that, because of the EPR paradox, quantum mechanics could not be considered a complete theory of nature. Einstein postulated the existence of hidden variables: as yet unknown local properties of the system which should account for the discrepancy, so that no instantaneous spooky action would be necessary. Bohr disagreed vehemently with this view and defended the far stricter Copenhagen interpretation of quantum mechanics. The two men often argued passionately about the subject, especially at the Solvay Conferences of 1927 and 1930; neither ever conceded defeat.

There have been numerous theoretical and experimental developments since Einstein and his colleagues published their original EPR paper, and most physicists today regard the so-called "paradox" more as an illustration of how quantum mechanics violates classical physics, rather than as evidence that quantum theory itself is fundamentally flawed, as Einstein had originally intended. But the paper did help deepen our understanding of quantum mechanics by exposing the fundamentally non-classical characteristics of the measurement process. Before that paper, most physicists viewed a measurement as a physical disturbance inflicted directly on the measured system: one shines light onto an electron to determine its position, but this disturbs the electron and produces uncertainties. The EPR paradox shows that a "measurement" can be performed on a particle without disturbing it directly, by performing a measurement on a distant entangled particle. Today, quantum entanglement forms the basis of several cutting-edge technologies. In quantum cryptography, entangled particles are used to transmit signals that cannot be intercepted by an eavesdropper without leaving a trace. The first viable quantum cryptography systems are already being used by several banks. And the burgeoning field of quantum computation uses entangled quantum states to perform computational calculations in parallel, so that some types of calculations can be done much more quickly than could ever be possible using classical computers.

byraze, Einstein never liked Quantum Mechanics. Even though he virtually invented the quantum theory of light, the more he rolled the ideas of quantum mechanics around in his mind, the more he rejected the idea that it was complete -- or even worked at all. He didn't like the idea that the momentum of a particle, if it's position was known, was completely unknowable -- random. He said, "God does not play at dice with the universe." Neils Bohr, one of the greatest physicists working with quantum mechanics, wittily replied, "Quit telling God what to do!" But Einstein wasn't the only one who didn't like the theory. In 1935 he got together with two other like-minded physicists, Boris Podolsky and Nathan Rosen, and wrote a famous paper entitled Can Quantum-Mechanical Description of Physical Reality be Considered Complete? We now refer to it as simply the EPR Paradox (no wonder, since the other title flows off the tongue so well). It wasn't until 1964, 29 years after the EPR Paradox was published, that serious proof was established that Einstein and friends had good reason to be worried. That was the year John S. Bell published his mathematical proof, a theorem that elegantly proved that if momentum and position were absolute values (that is, they exists whether they were measured or not) then an inequality, now called Bell's Inequality, would be satisfied (Pool). Einstein's position was clear: "I think that a particle must have a separate reality independent of the measurements. That is an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it.

What Exactly is the Problem?

In the EPR paradox, Einstein and friends imagined a scenario that would let you measure, say, both the position and momentum (as an example) of a particle with absolute certainty, a big no-no in quantum mechanics. A perfect example is the case of the neutral pion. A pion is a subatomic particle (very small) that decays into two photons, each with opposite spins. These are difficult concepts to understand, but all you really need to know is this:

- The pion has no spin. Imagine a baseball just sitting there, not spinning. Pretty simple.
- When the pion decays (a common occurrence in the subatomic world) it no longer is a pion. It splits into two photons that shoot away from each other in opposite directions.
- Photons have spin, but these two photons came from a pion with no spin. So, since you know the spin of one photon, you can find out the spin of the other photon because their spins have to add up to no spin at all. Imagine our baseball that was not spinning all of the sudden flies apart into two golf balls, each spinning in opposite directions.

Because the photons came from a single pion, it is said that they are entangled. You'll see what I mean. One of the photons flies to the right. You first measure it's spin along the x-axis with absolute certainty (quite possible). But, alas, quantum mechanics won't let you measure the y-axis spin, since you already know the x-axis spin. So you go to the second photon that flew to the left. You already know its x-axis spin without even measuring it: it is the exact opposite of the other photon. The paradox is this: Can you measure the y-axis spin of the second photon with absolute certainty even though you already know it's x-axis spin without measuring it? Duh, of course you can, says Einstein. How would the second photon "know" you measured the first photon? But quantum mechanics says you can't measure the y-axis spin with absolute certainty. It doesn't matter if the two photons were separated by an inch or 10 miles, the very instant you measure the first photon's x-axis spin, the y-axis spin of the second photon is impossible to measure. Relativity says that the "knowledge" of the measurement of the first photon can only travel the speed of light. But quantum mechanics requires the "knowledge" of the measurement to be instantaneous, because they have been entangled. Einstein called it "spooky action at a distance". If you understood all that, the rest of this is a piece of cake. If you didn't, don't worry, the rest is still interesting (you could always ask a question). So who's right? Ah, how the plot thickens when Bell comes on the scene.

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##### Current Law Students / Re: Que Sera sera
« on: May 30, 2008, 12:51:07 PM »

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##### Current Law Students / Re: INSTITUTIONAL DENIAL ABOUT THE DARK SIDE OF LAW SCHOOL
« on: May 30, 2008, 12:38:36 PM »
Tom Cruise is nothing when it comes to closet cases. Have you heard about Elvis Costello?

And to think he's a bigot and a racist (but what I am talking about -- is it not that the biggest bigots are those who can easily be bigoted)

During a drunken argument with Stephen Stills and Bonnie Bramlett in a Columbus, Ohio, Holiday Inn hotel bar, in the late 1970s Costello referred to James Brown as a "jive-ass n i g g e r," then upped the ante by pronouncing Ray Charles a "blind, ignorant n i g g e r."

A contrite Costello apologised at a New York City press conference a few days later, claiming that he had been drunk and had been attempting to be obnoxious in order to bring the conversation to a swift conclusion, not anticipating that Bramlett would bring his comments to the press. According to Costello, "it became necessary for me to outrage these people with about the most obnoxious and offensive remarks that I could muster." In his liner notes for the expanded version of Get Happy!!, Costello writes that some time after the incident he had declined an offer to meet Charles out of guilt and embarrassment, though Charles himself had forgiven Costello ("Drunken talk isn't meant to be printed in the paper"). In a Rolling Stone interview with Greil Marcus, he recounts an incident when Bruce Thomas was introduced to Michael Jackson as Costello's bass player and Jackson said, "I don't dig that guy...".

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##### Current Law Students / Re: The Da Vinci crock
« on: May 30, 2008, 12:34:26 PM »

To date, it has been proposed that the superior cardiac protection provided by carvedilol is not a consequence of hemodynamic variances but rather is due to its additional antioxidant effects. Studies in animals suggest that antioxidant effects may be protective in myocardial ischemia and may help retard the progression of atherosclerosis. Carvedilol decreases nitric oxide, the chemical that causes endothelial dysfunction and apoptosis (programmed cell death). In addition, carvedilol decreases the expression of structural extracellular proteins, an effect that reverses cardiac remodeling.

Is there some kind of cohort or case-control study confirming this?

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