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Author Topic:   Missing Matter
shalamabobbi
Member (Idle past 2848 days)
Posts: 397
Joined: 01-10-2009


Message 76 of 104 (501774)
03-07-2009 4:45 PM
Reply to: Message 73 by Son Goku
03-07-2009 5:14 AM


Re: bump
Hi Son Goku,
Thanks for all the posts for the cosmological laymen.
I have a rather rambling thought about the chosen basis representation. Is there a way to look for basis representations that might be missed? I am imagining perhaps a computer program that evaluates all possible basis representations and looks for any resulting simplifications that might result. If you were to run it upon a planetary model expressed in x, y, z coordinates, it would spit out r, theta, phi as a basis representation to look at, for example.
I don't know if this makes any sense, as maybe the equations don't involve a large number of variables etc.
I'm just curious if a basis might be found that points to something that *is* particle/field rather than one or the other.
(edit added)
As you can see by the question, I don't understand enough to know if viewing particle wave duality as a single *something* would reduce the rank and create a dependent basis from an independent basis. I am wondering if particle wave classical manifestations are the 'reality' in the ultimate sense or if there might be another viewpoint to replace it, that makes more sense and falls out of the physics. (end edit)
If this is nonsense, feel free to ignore. I don't know much upon the subject.. Thanks.
Edited by shalamabobbi, : No reason given.

This message is a reply to:
 Message 73 by Son Goku, posted 03-07-2009 5:14 AM Son Goku has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 77 of 104 (501786)
03-07-2009 5:41 PM
Reply to: Message 68 by Son Goku
12-18-2008 12:21 PM


Re: Quantum Probability 1
Yes it does make sense and don't for one minute think that my lack of response equals a lack of interest!!!
I will no doubt be back soon with my conceptual 'recap' and more questions but in the meantime please note that a lack of response does not equal a lack of interest.
It is just harder to engage and less obvious to pursue than the more accessible "creationist are wrong" debates.
Long may the SG masterclass continue.

This message is a reply to:
 Message 68 by Son Goku, posted 12-18-2008 12:21 PM Son Goku has not replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 78 of 104 (502014)
03-09-2009 10:30 AM
Reply to: Message 74 by Son Goku
03-07-2009 5:59 AM


Re: Quantum Probability 2
As Straggler said, I'm happy you're continuing as well. But I don't have much to say right now.
Except for this:
All because nature cares about which way things are multiplied.
Was there a specific reason you said "multiplied" here? That is, I would have said:
All because nature cares about which way things are measured.
Is there a difference that is escaping me?
Basically, I don't see nature having a problem with multiplication. It's just that you end up with different numbers to muliply depending on the order of taking the measurement.

This message is a reply to:
 Message 74 by Son Goku, posted 03-07-2009 5:59 AM Son Goku has replied

Replies to this message:
 Message 79 by Son Goku, posted 05-29-2009 6:17 PM Stile has seen this message but not replied

  
Son Goku
Inactive Member


Message 79 of 104 (510302)
05-29-2009 6:17 PM
Reply to: Message 78 by Stile
03-09-2009 10:30 AM


Re: Quantum Probability 2
Hey Stile, apologies for the ludicrously long delay teaching and research has me busy!
Anyway on to your question, which will lead nicely into entanglement.
Was there a specific reason you said "multiplied" here? That is, I would have said:
All because nature cares about which way things are measured.
Is there a difference that is escaping me?
Basically, I don't see nature having a problem with multiplication. It's just that you end up with different numbers to muliply depending on the order of taking the measurement.
In this case the multiplication is directly related to the order in which things are measured. However in some cases the multiplication can't really be interpreted that way, an example of which will be in my next post.

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Son Goku
Inactive Member


Message 80 of 104 (511928)
06-12-2009 8:20 PM


Entanglement
This post is a slight detour to explain entanglement and hopefully with the terminology I've introduced I can make it quite simple.
In Quantum Probability 2, I described quantum mechanics as a probability theory which cares about multiplication. To use technical language a noncommutative probability theory.
Obviously this allows different phenomena than regular probability, the best example being entanglement.
The basic idea is the following experiment:
Two observers are at a great distance from each other, let's say ten light years. Half way between the observers there are two particles each of which must have a spin of 1/2 and the total spin must be 0, so they have spins in the opposite direction to the each other.
The particles are sent off, one to one observer and one to the other observer. Observer 1 sees its particle spinning up and observer 2 sees its particle spinning down. Not too surprising, exactly what you would expect. Things can turn out differently of course and sometimes observer 2 will see their particle spinning up and observer 1 will see theirs spinning down.
So far so good.
Now what if observer 1 keeps measuring the spin in the up-down direction, but observer 2 measures it in the left-right direction.
There are four possible outcomes of this experiment:
Observe 1: Up Observer 2: Right
Observe 1: Up Observer 2: Left
Observe 1: Down Observer 2: Right
Observe 1: Down Observer 2: Left
If the observers do this experiment hundreds of times, they will see statistical correlations in their data. The spin in the left-right direction of one particle is correlated with the spin in the up-down direction of the other particle, despite the fact that the particles are widely separated by light years.
At first one would imagine that one particle is "causing" an effect in the other particle, even though they are light years apart, somehow influencing its spin. This is what some have called "spooky action at a distance".
However as anybody familiar with statistics has heard, correlation is not causation. In order to establish causation we need to perform a few other statistical checks beyond correlation. The particles fail these tests. So it is not causation which is occuring. The particles are not actually affecting each other's spins magically at a distance.
Rather the fact is that QM is a new probability theory which allows new correlations. Correlations stronger than those in regular probability theory. Hence things can be correlated in a way that is impossible in good old "probability due to lack of knowledge". In some sense the particles are more closely connected initially than was possible in any previous theories, be they probabilistic or deterministic theories.
We say the particles are entangled, a new quantum phenomena.
Edited by Son Goku, : Title

  
Son Goku
Inactive Member


Message 81 of 104 (513025)
06-24-2009 6:54 AM


Quantum Probability 4
I will use my notation from Quantum Probability 3, where:
{2}(.....) is a two particle list
and
{5}(.....) is a five particle list
Now I will introduce relativity into the mix. First of all a brief recap of the crucial insights of relativity.
Rel1: In pre-relativistic physics there was a quantity called mass, which measured a body's ability to resist being accelerated. There was also energy, which measured the ability to do work. In relativity, mass becomes a form of energy. Hence a physical system can decrease its resistance to motion to gain an increase in its ability to do work and vice versa.
Rel2: If two events are separated in such a manner that one would have to "travel-faster-than-light" to move between them, then they cannot communicate and can not have any possible influence on each other.
Rel3: Space and time are unified into a single spacetime. This isn't too important for this post.
Somehow one has to implement these points into quantum theory. To make quantum particles obey special relativity. This is the problem of relativistic quantum theory.
However there is also another problem, I have only described particles so far with quantum theory. I haven't dealt with fields, such as the electromagnetic field. This is the problem of the quantum theory of fields.
The solution to these problems turns out to be one and the same.
First of all let's consider Rel1 and what it implies.
A very fast moving particle possesses high energy due to its motion. It is possible that this energy could be "turned into" mass to produce another particle. In general a system of many particles with lots of energy can lose some energy and gain some particles.
This means that I could start with a two particle list like
{2}(.......)
and eventually end up with a four particle list like:
{4}(.......)
So I need a new way of evolving in time that allows me to move between lists.
Now for Rel2. This means that my quantum theory can not allow influences to travel faster than light.
So how can I move between different numbered lists and prevent things traveling faster than light?
Now let's look at applying quantum mechanics to field, for instance the electromagnetic field. For a field I should have lists which give all the averages possible for all observables of a field instead of for a particle.
There are an absolutely huge number of lists in this case, since you can observe a lot more things with a field then with a particle. However if you look at these lists there is some structure inside.
Basically some of the lists for the field behave as if nothing is going on, I'll call them a vacuum list:
{0}(......)
Another bunch of lists act like nothing is going on, except there is one "small lump" of mass/energy of the field moving around in a quantum way. It turns out that these lists act exactly like lists for one single particle, in fact there is no difference. These lists are the lists for a single particle. So I can use my old notation:
{1}(......)
It turns out there are field lists which act like two particles:
{2}(......)
three particles:
{3}(......)
and so on.....
However since all these lists are simply lists of the original field, they are all connected and over time they can move from one to the other, allowing particles to be created and destroyed.
Also since fields like the electromagnetic field naturally obey relativity, that is they never move faster than light, this fact is now automatically built into the lists.
This is quantum field theory, where particles are seen to be a consequence of quantum mechanics and fields. Different fields give different particles, e.g.
Electromagnetic field => Photons
Dirac field => Electrons
Next I'll try to deal with some of the physics that comes out of quantum fields.
I just wanted to ask, is any of this making any sense?

Replies to this message:
 Message 82 by Stile, posted 07-13-2009 9:13 AM Son Goku has not replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 82 of 104 (514837)
07-13-2009 9:13 AM
Reply to: Message 81 by Son Goku
06-24-2009 6:54 AM


Re: Quantum Probability 4
Hi Son Goku, sorry I didn't reply for a while.
I did read this a while ago, and I do still check it and read it over and am interested in (and thankful for) your descriptions.
Son Goku writes:
I just wanted to ask, is any of this making any sense?
Yes, and maybe no.
Yes - I understand everything you're talking about in a when-you're-talking-about-it sense. That is, I get the different bits and pieces you're describing and I understand the details you've provided.
Maybe No - My problem is that I am unaware of how all the details and different bits come together to give us anything. I think I'm a bit lost in the forest and think I'm in a small group of trees
I cannot identify your goal or the main reasoning behind such descriptions right now. However, I may just be waiting for this:
Next I'll try to deal with some of the physics that comes out of quantum fields.
...such a talk may clear up all my current fogginess
Please proceed whenever you have the time. I can only give you my word that it is greatly appreciated. Hopefully there are some other lurkers gaining insights from your time and effort here as well.

This message is a reply to:
 Message 81 by Son Goku, posted 06-24-2009 6:54 AM Son Goku has not replied

  
Son Goku
Inactive Member


Message 83 of 104 (517120)
07-29-2009 4:13 PM


Bell's theorem.
Just a brief explanation of this theorem since it comes up so often, for instance about three years ago RAZD started an interesting discussion on it.
As I've already explained, Quantum theory is a noncommutative probability theory. Very early on people proposed that the probability in QM came from lack of knowledge or ignorance. Basically that there was a hidden theory underneath, a real honest old fashioned theory and QM was just some statistical approximation.
However statistics due to ignorance is always (stress on always) commutative probability. Bell realised that this meant the only way you could say QM was a statistical approximation was if you could find some commutative probability theory which could simulate QM.
In 1964 he proved that the only if the commutative probability theory was nonlocal could it simulate QM. That is only if it allowed transmission of information faster-than-light.
This actually leads to a popular misconception about QM. QM is not nonlocal, it's totally local. Nothing is transmitted faster-than-light. Rather any theory which tries to replicate QM while claiming the probability is due to ignorance must be nonlocal.
Anyway next post I promise I'll have actual physics.

Replies to this message:
 Message 84 by cavediver, posted 07-29-2009 5:25 PM Son Goku has not replied
 Message 85 by Straggler, posted 08-01-2009 6:57 PM Son Goku has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 84 of 104 (517129)
07-29-2009 5:25 PM
Reply to: Message 83 by Son Goku
07-29-2009 4:13 PM


Re: Bell's theorem.
Gotta say that that's one of the nicest explanations I've seen Though no doubt there's going to be some questions around what you mean by commutative and noncommutative

This message is a reply to:
 Message 83 by Son Goku, posted 07-29-2009 4:13 PM Son Goku has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 85 of 104 (517577)
08-01-2009 6:57 PM
Reply to: Message 83 by Son Goku
07-29-2009 4:13 PM


Re: Bell's theorem.
Hello. Yes I am still reading and yes I think I am still following.
This actually leads to a popular misconception about QM. QM is not nonlocal, it's totally local. Nothing is transmitted faster-than-light. Rather any theory which tries to replicate QM while claiming the probability is due to ignorance must be nonlocal.
Here you are referring to exactly the sort of "spooky action at a distance" type misconception mentioned in Message 80 right? The difference between correlation and causation as per:
SG talking about entanglement in msg 80 writes:
However as anybody familiar with statistics has heard, correlation is not causation. In order to establish causation we need to perform a few other statistical checks beyond correlation. The particles fail these tests. So it is not causation which is occuring. The particles are not actually affecting each other's spins magically at a distance.
In other words there is no faster than light communication of any sort occurring between entangled particles. Exactly as per Bell's theorem. Right?
So can we totally discount the possibility of a "real, honest and old fashioned" theory underlying QM on this basis? Or is this still considered a meaningful possibility? Is anyone working on such a thing?
Edited by Straggler, : No reason given.

This message is a reply to:
 Message 83 by Son Goku, posted 07-29-2009 4:13 PM Son Goku has replied

Replies to this message:
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Son Goku
Inactive Member


Message 86 of 104 (521876)
08-30-2009 5:32 AM
Reply to: Message 85 by Straggler
08-01-2009 6:57 PM


Re: Bell's theorem.
I apologise for the eons it took to respond....
Here you are referring to exactly the sort of "spooky action at a distance" type misconception mentioned in Entanglement (Message 80) right? The difference between correlation and causation as per:
Yes, precisely.
In other words there is no faster than light communication of any sort occurring between entangled particles. Exactly as per Bell's theorem. Right?
Yes. Sorry to be so short, but you are simply exactly correct.
So can we totally discount the possibility of a "real, honest and old fashioned" theory underlying QM on this basis? Or is this still considered a meaningful possibility? Is anyone working on such a thing?
No, not entirely. Although we do know that if it is true, it must be pretty damn weird to the point where you would wonder if it was any better than QM.
First of all, if there were such a theory what we now call quantum mechanics would simply be a statistical approximation or probability due to ignorance, i.e. commutative probability. From Bell's theorem we know that commutative probability can only replicate noncommutative probability if it is nonlocal. So this theory would have information being transferred faster then light, but in such a way that this transfer of information can never be observed or used so that special relativity still holds. Which seems a little odd to me, to have some effect which for the consistency of the theory must never be observed.
Also, due to the Kochen-Specker theorem (see my post "Interpretations") we know the theory must give up a few other things. Since you want it to be a good old fashioned theory that replicates QM it must give quantities definite values, i.e. something is really spin up or spin down. However the Kochen-Specker theorem says that you then have to give up value realism or noncontextuality.
Giving up noncontextuality would mean that what an experiment means depends on context, for example my experiment to measure an electron's spin in the z-direction in Dublin when Frank measures a electron's spin in the x-direction in Guatemala City is a actually a different experiment to me measuring an electron's spin in the z-direction when Frank measures it in the y-direction. i.e. I'm measuring a different quantity of property of the elextron in both experiments, because even though I'm doing the exact same thing the global context is different.
Giving up value realism would be equally bizarre, to quote the Stanford Encyclopedia of Philosophy:
Stanford Encyclopedia of Philosophy on violation of value realism writes:
Put in a crude example, this would amount to saying that to ask for a system's energy is a well-defined question, while to ask for the square of the system's energy is not, even if, from our answer to the first question and trivial mathematics, we have a well-defined answer at hand.
So we can't totally discount the possibility of these theories, but they have to be weird to the point where you actually wonder is it really any better then QM. They have to give up noncontextuality and locality or give up value realism and locality, which in my opinion makes them worse than QM.
For instance one way you have a universe which talks to itself faster-than-light in a way that can never be detected and where what quantity one looks at depends on what everything else is doing. Not even the value of the quantity, but the quantity itself!
The other way you also have the faster-than-light communication and where just because some quantity is measurable doesn't mean that things related to it by trivial mathematics, like the square of the quantity, have a meaning or exist.
Are either of these really worse than QM? In QM everything is local, things don't depend on context, if I can measure something I can measure another thing related to it. What QM has is that probability is noncommutative, which is difficult to interpret and understand. Is this really worse than the above?
A few people work on these alternate theories, but quite often it is a lot of hard work to replicate QM and in the end the theory is stranger than QM, harder to use and quite often (not always) can't be made to obey special relativity.
Edited by Son Goku, : Small addition.

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vikas11 
Suspended Member (Idle past 5288 days)
Posts: 2
Joined: 10-05-2009


Message 87 of 104 (528198)
10-05-2009 6:25 AM


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Edited by Admin, : Ambiguate link.

  
Son Goku
Inactive Member


Message 88 of 104 (539585)
12-17-2009 12:05 PM


Nielsen on the need for QM
Although I am going to try and finish these posts sometime in the next thousand years, I just thought anybody here might like to check out:
Why the world needs quantum mechanics | Michael Nielsen
Michael Nielsen is quantum computation expert, one of the top in the field and author of one of the best text books on the subject. Here he tries to explain why our intuitive understanding of the world must be wrong and some new theory (e.g. quantum mechanics) is needed. Check it out!
Edited by Son Goku, : Title

  
Son Goku
Inactive Member


Message 89 of 104 (555564)
04-14-2010 8:22 AM


Magnetic Moment of the Electron.
Alright, so as I promised about nine months ago (!), I'll start discussing some physics and how quantum field theory deals with it. In order to do this I will discuss one of the most famous calculations in Quantum Electrodynamics (QED), the calculation of the magnetic moment of the electron, which basically was what got Julian Schwinger his 1965 Nobel Prize. This will allow me to discuss a sticky issue in physics called renormalization.
Quantum Electrodynamics is the quantum field theory of electrons interacting with photons.
Okay, so let's set up the problem. The magnetic moment of the electron is basically a measure of how much an electron is affected by a magnetic field. Just like charge decides how much it is affected by an electric field.
Historically, before quantum field theory came on the scene, Dirac had calculated the magnetic moment of the electron to be 2 using an older theory of his creation.
Schwinger attempted to get a more accurate answer using QED. To this he basically analysed how the list of probabilities for a single electron, {1}(......) in my notation above, change in the presence of a magnetic field. Inside those changes will be the electrons magnetic moment.
Unfortunately the equations are far, far too difficult to solve. So people came with an idea, approximate QED. The idea is that you start off with the theory where electrons and photons don't interact and work things out there. Then you work out things in a theory where they interact once and once only for all time, then a theory where they interact twice, e.t.c. By adding these results together, you slowly approach the correct theory.
Schwinger only consider the first two cases which affect the magnetic moment, namely one interaction and three interactions. These cases are symbolised by Feynman diagrams:
The one interaction diagram:

The three interaction diagram:

In the first term the solid lines are the electron and the wavy line is a photon from the magnetic field which causes it to move, the electron's reaction to this photon is its magnetic moment.
In the second term, the electron emits its own photon, then gets kicked by the photon from the magnetic field and then reabsorbs the photon it emitted. This diagram has a loop in it and effects due to diagrams with one loop are called (incredibly) one-loop effects.
Everybody could work out the first term, which gave the same result as Dirac, that the magnetic moment was 2.
However the second term posed a problem, when calculated the answer was infinity. For over a decade nobody really knew what to do with this, perhaps QED was just nonsense. In fact most people thought this.
However Julian Schwinger came up with a brilliant solution. In calculating these diagrams we have neglected something. In the calculations, the electron's charge "e" that appears is shifted by one loop effects itself and we can't compute this diagram without taking this into account. Pretending that the electron's charge stays the same is what gives the infinity. If we replace the electron's charge by its shifted value, then the diagram suddenly becomes finite.
Replacing the unphysical "unshifted" quantities with their physical "shifted" replacements is called renormalization and it is the procedure which saved quantum field theory.
Now that the second diagram was finite, Schwinger simply added the two results together to get the following for the electron's magnetic moment:
2.0023228
Which is only slightly off 2. However very shortly afterward experiments showed this result was incredibly accurate.
Today people have gone all the way up to diagrams with four loops to get:
2.00231930436170
Which agrees with experimental measurements to ten parts in a billion, making this number the most accurately verified prediction in all of physics.

Replies to this message:
 Message 90 by Straggler, posted 04-14-2010 7:51 PM Son Goku has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 90 of 104 (555662)
04-14-2010 7:51 PM
Reply to: Message 89 by Son Goku
04-14-2010 8:22 AM


Re: Magnetic Moment of the Electron.
Just to let you know that I (and no doubt others) are still following this!!
I hope to read your post properly soon and ask questions at some point after. Hopefully in less than 9 months time......
And to those unfamiliar with this on-off long running thread - It is a masterclass in advanced physics for simpletons that anyone interested in such things should take note of.

This message is a reply to:
 Message 89 by Son Goku, posted 04-14-2010 8:22 AM Son Goku has not replied

  
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