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Many Worlds Theory

05112009, 06:22 AM #1
Many Worlds Theory
Kazza, someone mentioned reading the book "TimeLine", which I also read.
The book deals with your section on the collapse of the Schrodinger wave function. However, new theories(MWT, or Many Worlds Theory) say that the wave doesn't actually collapse, but each "interference" represents a different universe in which experiences parallel, but are altered by the "decision" made when each electron "chooses" to create an interference pattern.
With each decision, the universe splits into an infinity of parallel universes that contain the same people, but altered by their decisions, splitting into a new fate for each decision, into infinity.
To me, this hinges on the inability of mathematics to converge on a single truth, as in Godel's theorem, creating, of necessity, new avenues for "reality" to speciate. It seems to be a similar pattern to religion, in which an attempt to organize by a singular truth results in infinite speciation.
Does the wave function collapse into "this" reality, or does it break into infinite realities? The infinite realities theory was the basis for "TimeLine".

05112009, 04:58 PM #2
Re: Many Worlds Theory
At this stage, we simply don't know, but the Many Worlds Theory seems a bit odd. It requires that every measurement results in an infinity of worlds being created. So there are an infinte number of worlds where the only difference from our current world is the angle at which a single photon left the sun.
And then there are infinity X [B]infinity[B] worlds where the only difference is that one photon left the sun at a different angle, and the decay of a single atom of uranium Mars' crust happened at a later time.
And then there are infinity^3 worlds where the photon left at a different angle, the single atom of uranium didn't decay, and a virtual electron didn't pop in and out of existence somewhere in the void between here and the Andromeda galaxy.
etc....
It just requires sooo many worlds that I find it improbable, but there really isn't any way to know whether or not it's correct at this stage. What actually happens during the wave function collapse is one of the remaining mysteries in physics. Maybe we'll have an answer some time in the future.

05112009, 10:59 PM #3
Re: Many Worlds Theory
the existence of the wave function collapse is required in
* the Copenhagen interpretation
* the objective collapse interpretations
* the socalled transactional interpretation
* in a "spiritual interpretation" in which consciousness causes collapse.
On the other hand, the collapse is considered as redundant or just an optional approximation in
* interpretations based on consistent histories
* the manyworlds interpretation
* the Bohm interpretation
* the Ensemble Interpretation
http://en.wikipedia.org/wiki/Wavefunction_collapse
:freak3: :judges: :Last edited by lexx; 05112009 at 11:14 PM.
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05112009, 11:07 PM #4
Re: Many Worlds Theory
Where did that come from? I'm not sure that it's true. Or well, it depends on what they mean by an optional approximation. I don't think the many worlds theory explains why many measurements on a single system will yield different results to many measurements on an ensemble of identical systems, unless it includes some form of wave function collapse.
And from memory, the Bohm interpretation does do without the wave function collapse, but gives up locality, which is even weirder than the standard Copenhagen interpretation (but interesting nonetheless).

05112009, 11:12 PM #5
Re: Many Worlds Theory
Lucien Hardy, then at Oxford University in Britain, provided a beautiful illustration of the sort of paradox that arises in connection with quantum entanglement through a thoughtexperiment in 1992.
An entangled particle and antiparticle pair  an electron and a positron  is created and each flies off in the opposite direction. But their paths are made to cross at some point by strategically placed mirrors, and instead of annihilating each other as particle and antiparticle are supposed to do, they somehow manage to "be" and "not to be" at the same time and location.
Hardy considered a MachZender Interferometer (MZI), a setup containing a halfsilvered mirror, which sends a quantum particle into a superposition of states, in that it travels down two separate arms at once: the transmitted and reflected paths.
The interferometer later reunites the two paths to meet at another halfsilvered mirror, which is arranged so that if the particle has had an undisturbed journey  no encounter with any other particles or fields  it hits detector C. But if something disturbs the particle, it may hit a second detector, D.
What happens when two such interferometers positioned so that one arm of the first overlaps with one arm of the second (see Fig. 1)?
Figure 1. The overlapping paths of the electron and positron in an entangled pair
If a positron  the antiparticle of an electron – is sent through one interferometer, and an electron through the other at the same time, the two particles travelling along the overlapping arms should meet in an ‘annihilation region’ and destroy one another. Hardy showed that something much stranger happens: quantum theory predicts that both D detectors could click simultaneously. Somehow both particle and antiparticle could disturb each other, yet fail to annihilate, in the overlapping arms. This is Hardy’s paradox.
Most people tend to ‘resolve’ the paradox by pointing out that such paradoxes arise only because we make inferences that do not refer to results of actual experiments. And, if the actual measurements were performed, then standard measurement theory predicts that the system would have been disrupted in such a way that no paradoxical implications would arise.
But an international team of scientists led by Yakir Aharonov in Tel Aviv University, Israel, showed that Hardy’s thought experiment could be carried out, and that it could give new observable results, provided that weak measurements are made.
What would a weak measurement entail? It is one that does not disturb the system significantly, so it remains quantum coherent, and also sacrifices accuracy. According to Heisenberg’s uncertainty relations, an absolutely precise measurement of position reduces the uncertainty in position to zero, but produces an infinite uncertainty in momentum. But if one measures the position up to some finite precision, then one can limit the uncertainty in momentum to a finite amount.
Aharonov and his colleagues imagine such weak measurements are indeed possible, and ask what happens to Hardy’s paradox. They find the paradox far from disappearing. The results of their theoretical measurements turn out to be most surprising and to reveal a "deeper structure" in quantum mechanics, which makes it "even more paradoxical".
In the double MZI setup, it is arranged that if each MZI is considered separately, the electron can only be detected at C and the positron only at C+. However, because there is a region where the two particles overlap, there is also the possibility that they will annihilate each other.
But the clicking of D and D+ would be paradoxical. If D clicked, that means the positron must have gone through the overlapping arm, otherwise nothing would have disturbed the electron, which would have gone to C. The same logic applies if D+ clicked, that means the electron must have gone through the overlapping arm to disturb the positron. But, there has been no annihilation in either case, which is paradoxical.
Alternatively, if D has clicked, the positron must have gone through the overlapping arm. But since there was no annihilation, the electron must have gone through the nonoverlapping arm. The clicking of D+ indicates that the electron must have gone through the overlapping arm, and the positron the nonoverlapping arm. But these two statements are contradictory, which ends in paradox again.
So far, these statements are based on no measurements being made as to which arm the positron or electron actually went. If a standard detector is put in the path of the electron in the overlapping arm, we can find the electron there, but the measurement itself disturbs the path, so the electron could end up in D detector even if no positron were present. The paradox disappears.
Weak measurements however, will give different predictions. The weak measurement does not disturb the system significantly, but it will be imprecise. To make up for this, the measurement has to be repeated many times in order to get as close to the real answer as possible. (Alternatively, they can do the experiment with a large number of electronpositron pairs and measure the total number of electrons or positrons that go through each arm.) And to simplify the measurements, they concentrate only on the results when D and D+ both click. The measurements, being weak can be made simultaneously without disturbing the system or each other.
The results – based on calculating the probabilities from the complex quantum amplitudes  show that indeed, the electron and positron, each has a probability 1 of being in the overlapping region, and a probability of 0 of being in the nonoverlap region. But they could not both be in the overlapping region; and quantum mechanics is consistent with this too – the joint probability of both being in the overlapping region is 0.
Intuitively, the positron must have been in the overlapping arm otherwise the electron could not have ended at D and, further, the electron must have gone through the nonoverlapping arm as there was no annihilation. This is confirmed by the joint probability of positron being in the overlapping arm and electron in the nonoverlapping arm equals to 1. Similarly, D+ clicking means that the electron must have been in the overlapping arm otherwise the positron could not have ended at D+, and further, the positron must have gone through the nonoverlapping arm as there was no annihilation. The joint probability of the positron being in the nonoverlap region and electron in the overlap region, too, is equal to 1. But these two statements are at odds with each other, as there was only one positronelectron pair. Quantum mechanics solves this paradox by having the joint probability of electron and positron being both in the nonoverlapping branch equal to –1! That is being not merely absent, but negatively present.
Finally, "the electron did not go through the nonoverlapping arm as it went through the overlapping arm" is also confirmed – a weak measurement finds no electrons in the nonoverlapping arm, the probability of electron being in the nonoverlapping arm equals to 0. But we know that there is an electron in the nonoverlapping arm as part of a pair in which the positron is in the overlapping arm, as the joint probability of that is equal to 1. How is it possible to find no electrons in the nonoverlapping arm? The answer is given by the existence of the –1 joint probability of both electron and positron pair in the nonoverlapping arms, bringing the total number of electrons in the nonoverlapping arm to zero! So the negative presence cancels out the positive presence, resulting in absence.
Klaus Molmer of Aarhus University in Denmark, initially sceptical, now thinks he knows how to do actual weak measurements. He suggests probing the locations of a pair of ions that are first cooled down to their lowest energy state, then hit with two carefully engineered laser pulses to send them into a superposition, which would move them to positions they should never occupy. He set up the ions so they will always fluoresce, except when they are in this paradoxical superposition. As soon as the fluorescence vanishes, he carries out a weak measurement on the ions’ position using another laser. The centre of mass should lie somewhere between the pair.
But the weak measurements show that, in the paradoxical quantum state, the ions’ centre of mass actually lies outside this region.
Molmer thinks that most of what has been done todate with quantum systems employs weak measurement, only physicists haven’t realised it. And it could have practical consequences. For example, they could expose flaws in quantum cryoptography, in which it has always been supposed that disturbance caused by measurement would prevent eaves droppers decoding messages (see "Quantum information secure?" this series). But an eavesdropper who uses weak measurement would escape detection, and hence succeed in breaking the code.
All in all, reality is stranger, much stranger than we can imagine. I particularly like the idea of being positively present, absent, or negatively present simultaneously.
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05152009, 09:59 AM #6
Re: Many Worlds Theory
Of course, one of the problems of any quantum measurement is that the tools we use to measure are themselves composed of the same atomic and subatomic particles that we are measuring.
The tools themselves make a statement, "that which exists, exists" as a collection we see physically, which then measures something that does not exist until we measure it.
If we determine the existence of a particle or a wave, we are measuring it in terms of what?
That is, would the particle or wave have a meaning "in context" to some greater reality?
For example, if we select measurements that determine an electron, etc., as a particle, it has meaning in the context of our need to see it as such, and the same for the wave. By measuring, we have created a context which is not in "sync' with the larger context in which the wave is embedded.
Take a quantum computer, for example. Regular computers select a 1 or 0 as part of a decision structure, whereas quantum computers use qubits
which include both 1 and 0 as part of the decision structure.
As I understand it, you might look at the quantum computer's program while it is running, and it will give you an answer at that point which seems logical and perhaps complete as far as it runs, but the final answer, the one which is correct when all bits are processed, will be the correct, but unpredictable answer.
If we assume that the "wave" aspect of an electron is information, then we can assume an interactive computing process now in process in which the wave interacts in a holistic fashion with surroundings.
In that "undisturbed" process, statistical probabilities eliminate random effects until one apparent reality emerges.
If we look at the "information" structure of the wave to determine the existence of an electron, we alter the computational process established by the wave as it interacts within another context. We have "broken the symmetry" in which a new symmetry is created in accordance with our measurements.
However, that same symmetry may be altered to accommodate a wave or a particle from the same measurement.
That is, an electron exists within a three dimensional information space, which causes it to behave in a computation process that is interactive, corresponding to "peaks" and "troughs" in the interaction. The "reality" of the electron exists at a peak, while it is not established at its trough, the trough itself being an interaction which represents a computational process of an information wave.
If we compare it to HDTV signal as compared to older analog signal, the HDTV signal gives us an "onoff" image. It's there, or it's not.
Analog gives us image and picture continuously, but in weakened form. It is "snowy" or "grainy".
The grainy state of analog may correspond to the "computing" basis of the trough of a wave. It appears as "in" and "out", but only depleted as a signal, not switched off, as in digital.
Is it possible to consider a wave as a three dimensional process of information in which a particle exists continuously?
If the wave function is an information system that computes, then all electrons, photons, etc., measured in the double split experiment, over time, will "compute" to produce a wave effect. That is how atomic systems interact.Last edited by doojie; 05152009 at 10:02 AM.

05152009, 10:15 AM #7
Re: Many Worlds Theory
I would also point out from the statements above that if a "wave" is actually information in which the particle of the electron or atom exists, then it represents a computational process, a "1 or 0".
If so, then the computation may be a 1(particle) or 0(wave).
Of themselves, they are meaningless within a larger context, and so can appear however they are "computed".
They "compute" themselves into reality, into what we perceive as existence, not so much by statistical probability, but by the process in which waves interact, not as particles, but particles interacting as parts of a three dimensional information wave.
As they are part of the same informational process as ourselves(we are composed of atoms and electrons), they can only respond to our interventions. We determine reality to the extent we are part of that same structural reality, information computing systems.

05152009, 10:32 AM #8
Re: Many Worlds Theory
If the above two posts are accurate, the double slit experiment has a new rationale.
Assuming that the three dimensional "wave" in which the atom or electron exists is actually an informational wave, it will represent a computation process. That is, the particle representation is only part of a larger wave system represented by interactive information.
Consequently, an electron fired through the double slit need not "know" which slit to go through, but will interact as part of a computational, wavelike process AFTER it passes the slit. The wave structure in which the particle is found will determine its position in relation to other particles, as reality realigns itself into a wavelike singularity.
This would not be a "collapse" of a wave function, but actually a measurement of a particle reintegrating itself into the singular computational structure of one world.

05152009, 03:56 PM #9
Re: Many Worlds Theory
Hmm... I hope you don't take this the wrong way, but most of your understanding of how a quantum computer works is wrong. I think the problem is that you've picked up the basics, and now the questions you're asking are ones that can't be answered in a simple sentence or two. Many of them require a proper understanding of quantum mechanics. I'll do my best to explain, though.
As I understand it, you might look at the quantum computer's program while it is running, and it will give you an answer at that point which seems logical and perhaps complete as far as it runs, but the final answer, the one which is correct when all bits are processed, will be the correct, but unpredictable answer.
If you're talking about a calculation that only a quantum computer can do, then looking at the data while the computer is running will ruin the calculation. In fact, if any of the information the computer is using leaves the computer then the calculation is ruined. This is why quantum computers have to be run at very cold temperatures  it slows down their interactions with the environment.
If we assume that the "wave" aspect of an electron is information, then we can assume an interactive computing process now in process in which the wave interacts in a holistic fashion with surroundings.
In that "undisturbed" process, statistical probabilities eliminate random effects until one apparent reality emerges.
If we look at the "information" structure of the wave to determine the existence of an electron, we alter the computational process established by the wave as it interacts within another context. We have "broken the symmetry" in which a new symmetry is created in accordance with our measurements.
However, that same symmetry may be altered to accommodate a wave or a particle from the same measurement.
That is, an electron exists within a three dimensional information space, which causes it to behave in a computation process that is interactive, corresponding to "peaks" and "troughs" in the interaction. The "reality" of the electron exists at a peak, while it is not established at its trough, the trough itself being an interaction which represents a computational process of an information wave.
If we compare it to HDTV signal as compared to older analog signal, the HDTV signal gives us an "onoff" image. It's there, or it's not.
Analog gives us image and picture continuously, but in weakened form. It is "snowy" or "grainy".
The grainy state of analog may correspond to the "computing" basis of the trough of a wave. It appears as "in" and "out", but only depleted as a signal, not switched off, as in digital.
Is it possible to consider a wave as a three dimensional process of information in which a particle exists continuously?
I would also point out from the statements above that if a "wave" is actually information in which the particle of the electron or atom exists, then it represents a computational process, a "1 or 0".
If so, then the computation may be a 1(particle) or 0(wave).
0 and 1 simply need to be two discrete quantum states. It's like you have two boxes and a stone  if the stone is in the left box we say that's a 0, and if the stone is in the right box we say that's a 1.
In classical mechanics, we could toss the stone in the air, turn around, and not know which box it is in. We could say that there is a 50% chance it's a 0 and 50% chance it's a 1. However, these are only probabilities. The stone is definitely in one box.
In quantum mechanics we throw the stone in the air, turn around, and again we don't know which box it is in. When we say, though, that it's 50% 1 and 50% 0 then it actually means that both 0 and 1 are occuring simultaneously. The stone is in both boxes at the same time.
Now imagine we have lots of stones and lots of pairs of boxes. Each stone and pair of boxes represents a bit in a computer. In a classical computer, regardless of whether or not we look in the boxes, each bit is a definite 1 or 0 and thus can only interact with other boxes based on it's own state and their state.
In a quantum computer, the interactions are more complex. Each bit interacts with each other bit as both a 1 and a 0 at the same time. So whereas ten bits in a classical computer can represent any number from 0 to 1023, ten bits in a quantum computer represent every number from 0 to 1023 simultaneously.
How we actually use this to get results is a bit complicated, but if we opened up the computer and took a look at the boxes, instead of being 50% 1 and 50% 0, all of a sudden they'll become either 100% 0 or 100% 1 and we can't do any quantum calculations any more.

05162009, 10:43 AM #10
Re: Many Worlds Theory
If you're talking about a calculation that only a quantum computer can do, then looking at the data while the computer is running will ruin the calculation. In fact, if any of the information the computer is using leaves the computer then the calculation is ruined. This is why quantum computers have to be run at very cold temperatures  it slows down their interactions with the environment.
In quantum mechanics we throw the stone in the air, turn around, and again we don't know which box it is in. When we say, though, that it's 50% 1 and 50% 0 then it actually means that both 0 and 1 are occurring simultaneously. The stone is in both boxes at the same time.
Now imagine we have lots of stones and lots of pairs of boxes. Each stone and pair of boxes represents a bit in a computer. In a classical computer, regardless of whether or not we look in the boxes, each bit is a definite 1 or 0 and thus can only interact with other boxes based on it's own state and their state.
In a quantum computer, the interactions are more complex. Each bit interacts with each other bit as both a 1 and a 0 at the same time. So whereas ten bits in a classical computer can represent any number from 0 to 1023, ten bits in a quantum computer represent every number from 0 to 1023 simultaneously.
How we actually use this to get results is a bit complicated, but if we opened up the computer and took a look at the boxes, instead of being 50% 1 and 50% 0, all of a sudden they'll become either 100% 0 or 100% 1 and we can't do any quantum calculations any more.
If I understand you correctly, if I look at quantum computer at a point before the program runs, I will see 100% of 1s or 100% of 0s, but that's the end of the computation.
Likewise, if you measure the "state" of a wave or an electron, you will get one or the other, but not both.

05162009, 05:30 PM #11
Re: Many Worlds Theory
Yep, whenever you measure the qubit (a quantum bit) you will either see a 0 or a 1. It's only when nobody's looking that the qubit can be some sort of mixture of 0s and 1s. The quantum calculation depends on the qubit being in a mixture of states, so by looking at it, you change the system and destroy the information.
It doesn't even have to be someone looking, though, it can also be any sort of interaction with the environment, through a process called decoherence.

05172009, 07:40 PM #12
Re: Many Worlds Theory
anything like.....with what measure ye mete, it shall be measured to you!? as to the 0 or 1 representation!? does it indicate an all or nothing reality!? now to go look up decoherence!? :freak3: :spin2: :
Last edited by lexx; 05172009 at 07:52 PM.
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05172009, 08:50 PM #13
Re: Many Worlds Theory
here's a breif explanation!?
Before an understanding of decoherence was developed the Copenhagen interpretation of quantum mechanics treated wavefunction collapse as a fundamental, a priori process. Decoherence provides an explanatory mechanism for the appearance of wavefunction collapse and was first developed by David Bohm in 1952 who applied it to Louis DeBroglie's pilot wave theory, producing Bohmian mechanics[9][10], the first successful hidden variables interpretation of quantum mechanics. Decoherence was then used by Hugh Everett in 1957 to form the core of his manyworlds interpretation[11] . However decoherence was largely[12] ignored for many years, and not until the 1980s [13] [14]/90s did decoherentbased explanations of the appearance of wavefunction collapse become popular, with the greater acceptance of the use of reduced density matrices[5]. The range of decoherent interpretations have subsequently been extended around the idea, such as consistent histories. Some versions of the Copenhagen Interpretation have been rebranded to include decoherence.
Decoherence does not provide a mechanism for the actual wave function collapse; rather it provides a mechanism for the appearance of wavefunction collapse. The quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists, but exists — at least for all practical purposes[15] — beyond the realm of measurement. Thus decoherence, as a philosophical interpretation, amounts to either the Bohmian mechanics or something similar to the manyworlds approach.[16]
i'm currently working out my take on it!? and by the way,what did anyone think of the movie? "sphere" :freak3: :spin2: :Last edited by lexx; 05172009 at 09:17 PM.
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