A Look at Quantum "Spookiness"
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Erops - 03 Mar 2006 15:47 GMT A Look at Quantum "Spookiness"
The results of quantum theory were described as "spooky" by Drs. Einstein, Podalsky, and Rosen because quantum theory seemed to reject "objective reality". They believed that all observed effects must be produced by "local" causality. Their conclusion resulted from their firm belief that information could not travel faster than the velocity of light. Indeed, if this were the case, quantum theory would indeed be "spooky". Quantum theory required, for example, that "paired photons" maintain polarizations which were opposite in direction . If the polarization angle of one of the "paired photons" were changed, the polarization angle of the other photon of the pair must instantaneously change to match. ("Paired photons" are produced by the self annihilation of an artificial atom composed of an electron and a positron. They are polarized in opposite directions and are emitted in opposite directions. Their polarization angle is, of course, random with respect to the external world.)
Since the "paired photons" are emitted in opposite directions, they rapidly become separated in space. The required instantaneous coupling of their polarization implies that information must travel at an infinite velocity and, since these personages were firmly committed to the idea that information could not be transmitted faster than the velocity of light, they had to conclude that the process was "spooky" and required the existence of "hidden variables". (These allegedly "hidden" variables are not necessarily hidden, one of them for example, is the polarization coupling of "paired photons".Since this coupling had been shown to propagate at an "impossible" infinite velocity, it was necessary for orthodox physics to accept the idea of "spookiness". If the effect were accepted without the idea of "spookiness" it, the existence of an absolute velocity reference frame for space (i.e.- the Aether) would have to be accepted. Since this is currently dogmatically unacceptable, a problem remained.
An alternative explanation, proposed by the "Copenhagen School" of physicists asserted that there was no objective reality, there was only the reality as seen by the observer. This interpretation led to Schroedinger's Cat Paradox which asserted that a cat in a closed box that would be subject to cyanide poisoning if the decay of a radioactive atom was detected by instruments within the box. It was further asserted that, since the decay of the atom and thus the death of the cat, the creature was both dead and alive until an external observer opened the box and looked. The reasoning behind this was the idea that an event does not occur until it is observed. This does not seem to be an objectionable idea, per se, but the observation that counts in this Paradox is the decay of the radioactive atom, not the observation by an external observer. The cat is not both alive and dead prior to his observation, it is one or the other, but not both. The fact that the observer does not know is meaningless. It is only attributed as having meaning as a result of intellectual sloppiness. Schroedinger's Cat Paradox is not a paradox.
A different approach to resolving the "spookiness" of Quantum theory is the idea of Parallel Universes. In this interpretation, each particle in the Universe creates an unobservable twin every time it makes a quantum "decision" The result is that each particle creates an unobservable "Parallel Universe" at virtually every instant of time occurring since our Universe began. When one considers the number of particles in the Universe, the number of ways in which they can interact, and the number of instants of time since the Universe began, the number of Universes which are required under this theory is, incredibly, at least 10^160. What is equally incredible is that each of these Universes contains the same amount of energy as our own and each of its particles occupies the same space at the same time as do its brothers. This interpretation seems to have a large number of believers of high reputation. In spite of this, the writer has no qualms about asserting that any physicist who would accept such a concept is in the wrong line of work. I understand that Wal-Mart is hiring.
When one examines the concept that information cannot propagate faster than the velocity of light one finds that it is based on the fact that information is almost always encoded in the form of energy. Since the Lorentz Transformation for energy is 1/(1-V^2/C^2)^0.5 (the same as the Lorentz Transformation for Length), it is obvious why information cannot propagate faster than the velocity of light. At the velocity of light, the Lorentz Transformation for Energy becomes infinite. The transformation becomes imaginary! Information encoded in the form of energy certainly cannot propagate faster that the velocity of light. When information is encoded in the form of the polarization angles of "paired photons", however, this limitation does not occur. Changing the polarization angle of a photon does not change its energy. As a result, no energy transfer is involved in changing their polarization angles. If one extracts the Lorentz Transformation for Angle using the conventional Lorentz Transformations, one find that this transformation is unity since angle is equal to a LENGTH along an arc divided by the LENGTH of the radius of that arc. Accordingly, the Lorentz Transformation for Angle becomes ((1-V^2/C^2)/(1-V^2/C^2))^0.5 or unity. One might conclude, therefore, that the relativistic processes do not impose a velocity limit on the propagation of the polarization angle of the "paired photons" and it is reasonable to expect that velocity to be infinite. "Spookiness" is not needed.
Physicists have also concluded that even if information could be transmitted by the use of "paired photons", that information could not be decoded singe the polarization angle of the "paired photons" emitted by their source was completely random. This apparent limitation is not fundamental problem, it is a signal to noise ratio problem. The information is actually being transmittted but it is swamped by the noise level of background photons. If the singal to noise ratio of the transmission could be sufficiently improved,communicating over a distance at a quasi-infinite velocity would be found to be perfectly feasible. The most dangerous part of this conclusion is that it would establish the existence of "absolute time" and the existence of the classical Aether and would demolish the hare-brained concept of "space-time". (For diagram see http://einsteinhoax.com/cf53.htm. Omit the 45 degree polarizers. They may destroy the polarization coupling.)
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Tao - 03 Mar 2006 17:56 GMT >A Look at Quantum "Spookiness" > [quoted text clipped - 9 lines] > polarization angle of the other photon of the pair must instantaneously > change to match. Actually this is not a very accurate description of the situation. It is about determining the polarization, not changing it. The key thing is that one can measure the polarization in two directions which are incompatible observables in quantum mechanics, so the results cannot be explained merely by the states the particles started off in. Which direction to measure can be chosen by a central controller communicating simultaneously with each end of the experiment.
If you read the papers about Aspect's experiment (which verified Bell's theorem empirically), as I have, you will see Bell's result is only visible in the statistics, not in any individual measurement. No-one has found any way to use this effect to communicate faster than light, and very few people expect this to ever happen.
Daniel Pitts - 04 Mar 2006 16:47 GMT > >A Look at Quantum "Spookiness" > > [quoted text clipped - 23 lines] > way to use this effect to communicate faster than light, and very few people > expect this to ever happen. Although, they have proven conclusivly that the aformentioned effect is real. Not by statistics, but by concrete mathimatics. Instead of coupling two photons, they used three photons, and the math became "Always" (Quantum Spookiness) or "Never" (Einstein Hidden Variables). Turns out its "Always"
Tao - 04 Mar 2006 18:07 GMT >> >A Look at Quantum "Spookiness" >> > [quoted text clipped - 37 lines] > "Always" (Quantum Spookiness) or "Never" (Einstein Hidden Variables). > Turns out its "Always" It is possible my intended meaning was not clear. The effect is in the statistics of the measurements, and can be seen when one collates the experimental data from both (or all three) afterwards, but at the time, there is no way for any of the participants to use the effect to communicate with another at faster than the speed of light.
One article I read on this said that when a participant makes a measurement it "determines an aspect of reality". This aspect of reality is immediately known at another point connected by quantum entanglement. The reason this cannot be used to communicate is that the person who made the measurement did not specify what the aspect of reality was (for example, whether the photon was vertically polarised), he merely measured it. From measurements made at the other end, the other participant cannot determine anything about what the first person did. We can only be sure that if the other person measures the vertical polarisation, his measurement will be determined by the measurement that the first person made.
Is this clear now?
Daniel Pitts - 05 Mar 2006 00:51 GMT > >> >A Look at Quantum "Spookiness" > >> > [quoted text clipped - 56 lines] > > Is this clear now? Yes... But, what if entangled particles are actually different facets of the same underlying particle? Maybe there is no such thing as "one photon" entangled with another "one photon". Maybe once they are entangled, the actually become a single entity that exists at more than one physical point.
Tao - 08 Mar 2006 00:32 GMT >> >> >A Look at Quantum "Spookiness" >> >> > [quoted text clipped - 74 lines] > entangled, the actually become a single entity that exists at more than > one physical point. Yes, it's absolutely right to think of the two photons as two parts of a single quantum mechanical object.(called a pair of coupled photons) until a measurement of the polarization of one of them is made. This "immediately" fixes the polarization of the other photon, but also breaks the coupling, in the sense that nothing you do to one of the photons afterwards will have any further implications for the other photon (i.e. if anyone made any measurements on one of the photons, the new information would not be useful to predict what a measurement on the other photon would be.
Fortunately this is made clear by the "bra-ket" formulation due to Dirac. When you write down the quantum states, you can see the way two photons can be "entangled" and it also shows how when one makes a measurement they become "untangled".
Let a single photon 1 in a vertically polarized state be:
| V1 > and a single photon 1 in a horizontally polarized state:
| H1 > If photon 1 is unpolarized it is a state which is 50% of each:
1/2 | V1 > + 1/2 | H1 >
{ a photon could also be polararized at any other chosen angle, and these states can be mixed together in various ways, but that's just confusing the issue unnecessarily }
Suppose we start with paired photons of random polarisation. We write the state where they are both vertically polarised
| V1 > (x) | V2 > and the state where they are both horizontally polarised
| H1 > (x) | H2 > Each of these is what is called a tensor product of the individual photon states. A state that is a tensor product of states of the individual photons is not entangled, because the behaviour of each of the photons does not depend at all on anything you do to the other one.
The initial state in the experiment is given as:
1/2 | V1 > (x) | V2 > + 1/2 | H1> (x) | H2 >
Which says there's 50% chance they are both vertically polarized and 50% chance they are both horizontally polarized. This is an "entangled", or "coupled" or or "correllated" state. This is because it is impossible to write this as a single tensor product of the states of two different photons. It is entangled because any measurement of polarization of one photon acts on this state in a way which gives you information about the other photon.
If we make a measurement of the polarization of one of the photons in the vertical direction, mathematically we apply an operator to that state above and the rules say that we get either:
| V1 > (x) | V2 > or else
| H1 > (x) | H2 >
{with a real polarizing filter, the latter would be the case where it reflected}
Either of these is no longer an entangled state, as it is a tensor product of the states of two separate photons, so it behaves like two separate photons. No measurement on one photon will tell you any more about the other one.
At the risk of being repetitive, if the state of two particles cannot be written as a tensor product of a state of one particle and a state of the other particle, they are entangled.
Daniel Pitts - 08 Mar 2006 15:37 GMT > >> >> >A Look at Quantum "Spookiness" > >> >> > [quoted text clipped - 152 lines] > written as a tensor product of a state of one particle and a state of the > other particle, they are entangled. That explains some to me, thanks.
So, what happens if I somehow alter (without mesuring) the polarization of one of the photons? Does the other photon change? In other words, given A is entangled with B, if you change A by 10 degrees, does B change by 10 degrees as well?
What about alterations that are unobservable?
Sorry if these are newb questions.
floppy01@idirect.com - 08 Mar 2006 20:57 GMT You are all thinking in small scale ! YOU CAN'T UNDERSTAND IT UNLESS YOU CAN SEE IT FROM THE OUTSIDE !
Everything that occurs in this reality is a Relative function. A Relative function must occur within a Holistic environment, it must exist within an environment. We exist within a permanent four dimensional construct known as Space - Time. This is the Holistic construct.
Events occur in series, and what everyone is missing, is that not only do Relativistic Events occur, but so do Holistic Events.
Again, Space - Time is a single but huge unit. If we do not monitor an Event that is in progress, then the event becomes an Holistic Event, meaning it is an Event which includes the circumstances that extend across time. All possible paths of Photons, for instance, are seen at the same time from the holistic point of view. For the event of this nature to take place, a conditional or entangled agreement has been met.
If, however, we do monitor an Event in progress, then that becomes a smaller event that breaks down the possibility of the larger Holistic event from occurring. And so it becomes a mere Relativistic event, and the collapse of the possible Holistic event takes place.
If we do not do monitor an Event in progress, but instead become part of an Event such as setting the polarity of a polarized light filter, then the Event of determining the polarity of a second Photon, as do we, also becomes part of an Holistic event.
And so, if you attempt to create a Relativistic explanation of Relativistic / Holistic events, then this will be no easier than squeezing a 3 dimensional object into a 2 dimensional plane. The explanation of a car going up a hill or down a hill can not be explained if up and down do not known of or included in the attempts to explain the phenomena.
Disregard Holistic events, and you will remain NOW HERE, getting NOWHERE in your achievements.
Gentleman, you are still thinking 3 dimensionally.
Think about it, give it a shot, or shoot it down without thought like all ****** of the ******* do.
Tao - 09 Mar 2006 01:46 GMT >> >> >> >A Look at Quantum "Spookiness" >> >> >> > [quoted text clipped - 194 lines] > > Sorry if these are newb questions. Well the answer in the case we were looking at is this.
starting with the state:
1/2 | 0_1 > (x) | 0_2 > + 1/2 | 90_1> (x) | 90_2 >
i.e. 50% chance that both are polarized at 0 degrees and 50% chance that both are polarized at 90 degrees.
If you make a measurement of the polarization of one photon in _any_ direction, you immediately know what the polarization of the other photon is. For example, if you measure the polarization of the 1st photon in the direction 45 degrees, you either find it is polarized at 45 degrees or it is polarized at 135 degrees (just like horizontal = not vertical, only twisted around a bit).
When you have done this, you immediately know the second photon has the same polarization, either 45 degrees in one case, or 135 degrees in the other. This gives us a state like:
| 45_1 > (x) | 45_2 > i.e. both photons are polarized at 45 degrees.
But once you have done this once, the photons are unentangled, and you can't do anything to one photon that tells you anything more about the other one. For instance, once you have found the polarization of both photons is at 45 degrees, if you then measure the polarization of the first photon at 90 degrees, there's a 50% chance you find it is and a 50% chance that it isn't (which means it's polarized at 0 degrees).
But the polarization of the second photon stays at 45 degrees, since it is no longer coupled. So we just get a state like:
| 0_1 > (x) | 45_2 > or
| 90_1 > (x) | 45_2 > There are very simple mathematical rules for exactly what happens when you apply any measurement to any sum of tensor products of states that gives exactly the results above.
Tao - 09 Mar 2006 19:43 GMT >>> >> >> >A Look at Quantum "Spookiness" >>> >> >> > [quoted text clipped - 250 lines] > apply any measurement to any sum of tensor products of states that gives > exactly the results above. Unfortunately, I overstated the case above. Doing the calculation, it is clear that one does not get a certain polarization for the second photon for all possible choices of the angle of the filters, just a increased probability in general. My argument for this is as follows:
The rules for measurement on 1 photon are easy. If it is polarized at an angle a and you measure the polarization at angle b , the probabilty is (cos(a-b))^2 that it gives "true" and 1-(cos(a-b))^2 that it gives "false".
i.e. < M(b) | a_1 > = cos(a-b)^2
If you tensor this photon state with the state of another photon, measurements applied to the first photon don't affect the state of the second:
< M(b) | a_1> (x) | c_2 > = cos(a-b)^2 | c_2>
and the rule can be extended to a applying a measurement to one of a pair of coupled photons, by applying it to each component separately:
<M(b)| applied to 1/2 | 0_1 > (x) | 0_2 > + 1/2 | 90_1 > (x) | 90_2 >
= (1/2)(cos(b))^2 | 0_2 > + (1/2)(cos(90-b))^2 | 90_2 >
so in this case, our knowledge about the polarization of the second photon is only perfect when a measurement was made at either 0 degrees or 90 degrees (180 or 270 degrees are the same, of course).
Unfortunately, the worst case is where we make a measurement at 45 degrees (or 135, 225, 315 ), when this is:
(1/2)(cos(45))^2| 0_2 > + (1/2)(cos(45))^2 | 90_2 > = (1/4) | 0_2 > + (1/4)
| 90_2> so in this case we know nothing about the polarization of the other photon (any measurement of the polarization of the second photon gives a positive result 50% of the time).
However, it is possible to have situations where _any_ measurement of polarization of the first photon will give some (but not perfect) imformation about the second photon. For example, if we know that the two photons have identical polarization, but no idea what that is, the state is an integral from theta=0 to theta=2*pi of
1/(2*pi) | theta_1 > (x) | theta_2 >
{a state where both photons are polarized at the same random angle theta between 0 and 2*pi}
Measuring the polarization of the first photon at some direction phi gives an integral over theta of 1/(2*pi) (cos(phi-theta))^2 | theta_2 >
Making a measurement of the polarization of the second photon at angle phi gives an integral over theta of 1/(2*pi) * (cos(phi-theta))^4
The ratio of the probabilities (which is the conditional probability that the polarization of the second photon agrees with the measurement of the first) is the ratio of the integral of cos^4(theta) to the integral of cos^2(theta).
This is 0.75.
So, in this case there is a 75% chance that the polarization of the second photon agrees with that of the first, for measurements of polarization in any direction.
Any questions/comments/improvements?
Tao - 19 Mar 2006 00:01 GMT ...and of course when I talked about probabilities, I meant to refer to the mod squared of the bra-ket. as is clear in the (correct) numbers.
>>>> >> >> >A Look at Quantum "Spookiness" >>>> >> >> > [quoted text clipped - 327 lines] > > Any questions/comments/improvements?
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