Randomness

[Amn]

I once played a game with my bro where one thinks of a number and the tries to guess it. It was semisuccessful especially after we have trained a bit. The number would lie in range from 0 to 10.

After that i dont really think random is possible in real world, be it hardware or software or in nature. At least we think nature is random, because the amount of parameters is comparable with the resultant random value itself, which makes it highly efficient, but still not really random, since it turns out to be a function of its parameters, while random number is not.

In that sense, even CryptoGenRandom is an algorithm that is simply is an improval over the old rand(), while both plotted would generate some distinguishable patters in some form or another.

****, i dont even know - perhaps if we plot the human DNA for all the humans on Earth - will we find any pattern ? Or if we plot the amount of texture spots on a tigershark, will we find a pattern ? :)

Just a food to the though, i am interested in these kinda things.
Happy discussion !

[galathaea]

Many researches in the foundation of mathematics have attempted definitions of random, but the results are still not universally accepted. The most convincing modern attempt (in my opinion) has been the information theoretical approach coupled with computation theory:

A sequence is termed random (in a given expression language) iff all descriptions of the sequence require expressions at least the information content of the sequence.

The difficulties with this approach are

The definition is expression language dependent.
Even random sequences have a likelihood of including non random subsequences.

In my opinion, the first objection is less of a problem if one uses category theory as a mathematical (and indeed a language) foundation, where all mathematical expressions are decomposable into primitive logical mappings and objects. The second objection, though, has been the subject of numerous philosophical papers, as it implies that the only sequences that might qualify are infinite sequences (countable and beyond).

The definition provided is often interpreted in terms of compression algorithms and information entropy. This is not quite as general an interpretation as the given one, but it does illustrate the general concept. The basis of the definition of randomness is one of predictability.

And this brings us to the topic of quantum mechanics. There are processes in quantum mechanics that are unpredictable, in a mathematical sense (in terms of observer predictability to future event states observed). Even Bohm's classic hidden variable models of quantum mechanics (which disproved vonNeumann's no-go "theorem") cannot overcome this, and the standard prediction inequalities prove that this can be either interpreted in terms of subquantum nonlocality or an inherent indeterminism in the logic of space-time. This is why quantum cryptography in the future will be such a great advance (as well it can detect interception observations).

Anyway, its my opinion that there is true spontaneity in the universe, and that we can harness the randomness available. Its just not as simple as flipping a coin...

[Amn]

Very good point galathaea :)

You will be surprised if i say, i believe NOTHING in universe is of true spontaneous character. I believe everything follows the golden rule of cause and effect. I may be alone on this, but i am deeply convinced nothing can be true random.

We humans know as much as we do, not a yota more. Even quantum mechanics will be split into underying sciences in the future i believe, that perhaps will prove that even quantum level jumps are caused by some underlying process :)

But i think this is fascinating discussion nevertheless.. God knows how many people have argued on this.

Reminds me of the movie my signature comes from....Where one astronomer opposed the view of another on the existence of God, while they are actually talking about the same thing, while both defend THEIR point of view based on "different" facts.. :)

[galathaea]

You are of the Einsteinian opinion that "God does not play dice with the universe". I, on the other hand, believe the Goddess is much more of a merry prankster...

Very interesting...

[SolarFlare]

Originally posted by Amn
After that i dont really think random is possible in real world, be it hardware or software or in nature. At least we think nature is random, because the amount of parameters is comparable with the resultant random value itself, which makes it highly efficient, but still not really random, since it turns out to be a function of its parameters, while random number is not.
To elaborate on this, you could hypothetically obtain a "random" number from where an electron is in an atom, or a series of atoms, because the observation is so unnoticeable and indirect and changes frequently and unpredictably (with available observation/science). Along these lines, you could also obtain a "random" number by counting the number of drops of water that have evaporated from a square mile of the ocean over the past second because it is completely unrelated to any other part of the code.

Since science itself is based solely on the idea that cause->effect, random is a mathematical concept only. A scientist could observe the rotational velocity and gravitational acceleration on a flipped coin to determine whether it would land heads or tails, but a mathematician would say half likely heads and half likely tails. The mathematician is saying that as long as you don't attempt to figure out how the scientist made his measurements or what methods he used, then the outcome of the flip is random, because from a human's observation, the outcome was unclear until the coin hit the ground.

So basically the coin flip was and wasn't random at the same time, depending on what else you knew.

[Yves M]

This reminds me of a story I read about problems in Cryptography in WW2. Besides the whole Enigma thing, people used stuff called one-time pads. Basically the sender and reciever had to have the same code (which was usually generated at home, before the sender left for an undercover mission) which was a "completely random" list of numbers (between 1 and 26 or more to allow for spaces & special symbols). The code was as long (or longer) than the actual text so theoretically impossible to break.

The only hiccup was that the random sequences were generated by humans, and so weren't "completely random". If for example the sequence was generated by shuffling a deck of cards, then if the same person always shuffled the cards, he (or she) was always using the same method to shuffle. Moreover if there were three aces in a row, he might think that this is not really random and shuffle again, thereby distorting the randomness.

Flipping a coin isn't really random either. Each person has his own technique and it's rather likely that that will favor one of the outcomes, or favor series of outcomes etc. Moreover it's hard to come by perfectly balanced coins ;) People who have practiced this a lot can tweak the outcome. Same for dice ;)

[SolarFlare]

That is true about distortions due to imperfections in the coins, etc.

But if you have, say, a quantum (a type of elementary particle) which could be in one of two states, each of which the likelihood (not the same as random) is one half, then if someone else measures and records this state, it is 100% random to you.

[AnthonyMai]

You will be surprised if i say, i believe NOTHING in universe is of true spontaneous character. I believe everything follows the golden rule of cause and effect. I may be alone on this, but i am deeply convinced nothing can be true random.


"TRUE RANDOM" is defined not as something totally un-predictable, but as something that can only be predicted with a computation as complicated as the length of the sequence itself.

So, yes, every thing in the universe, down to the detail of what state each particle is in, is completely deterministic. But to carry out such determination, you would have to use a quantum computer that consumes the energy of the whole universe, and continupusly run from the birth of the universe until now. What would you say about that? I would say that using the definition of random, the event of the universe is them a pure random sequence.

Your golden rule of cause and effect is not golden at all. To have causes and effects you have the implied presumption of the time and time moves only forward, since cause always happen at a time before effect. In modern physics, the very existance of time itself is being questioned. Time is probably mostly a concept of some sort of statistical average.

Here is some of my spare time research result. Let's assume our universe is, like some said, a black hole. We know from the Hawking theory that a black hole's entropy can be calculated merely from its surface area. My calculation shows the number comes to 1x10^122. Then I calculated the total computation a quantum computer can carry out, assuming it has the total energy of our universe, and assuming it has been computing since the birth of our universe, and I come to the same number, 1x10^122. I guess this coincident supports both the notion that our universe is a black hole, and some other's notion that our universe is a giant quantum computer.

[AnthonyMai]

Any one interested may have a look at this web site:
http://www.edge.org/3rd_culture/lloyd2/lloyd2_index.html

[SolarFlare]

Originally posted by AnthonyMai
Here is some of my spare time research result. Let's assume our universe is, like some said, a black hole. We know from the Hawking theory that a black hole's entropy can be calculated merely from its surface area. My calculation shows the number comes to 1x10^122. Then I calculated the total computation a quantum computer can carry out, assuming it has the total energy of our universe, and assuming it has been computing since the birth of our universe, and I come to the same number, 1x10^122. I guess this coincident supports both the notion that our universe is a black hole, and some other's notion that our universe is a giant quantum computer.
I wouldn't go so far as to say that, since the definitions of the measurements are based on each other. You're saying, "Assume A is true. Therefore, A." It doesn't actually tell you anything about A even though it appears to. You are right about what you called "true random," however. If the measurement is calculated with enough complication, then it is nearly useless and the observation remains random.

[galathaea]

I am extremely interested in Anthony Mai's post, but there are some inconsistencies and physical misconceptions that I feel required to object to.

Claim 1: Let's assume our universe is, like some said, a black hole.

Okay, on this one you will have to clarify... Some of the "multiverse" theories claim that our universe could have been created by a blackhole creating event in a separate universe (through a tunnelling/expansion stage) and that we may still be linked to this mother universe through an umbilical ER bridge, much like the Reissner-Nordstrom spacetimes. But a blackhole, by definition, would not be a good definition of our universe, as there is too much space-time / mass for such a qualification (and this has nothing to do with whether our universe is open or closed...). Maybe this is a confusion of the idea that the universe may be finite but unbounded (a 3-sphere topology) which is not the same topology as a Schwarzschild topology...

Claim 2: We know from the Hawking theory that a black hole's entropy can be calculated merely from its surface area.

Not quite true... They are related concepts mathematically only by analogy. It is part of Hawkings analogy of the laws of thermodynamics with the laws of black hole dynamics, a metaphor. And the correct analogy is dS with dA. In other words, there is an analogy in the change direction requirements only. The actual equations actually show different form integrals and different, incompatible work terms...

Claim 3: My calculation shows the number comes to 1x10^122.

Love to see that calculation. Or, actually, I'd love more explanation on where the area comes from for our universe, particularly if it is, as most physicists suspect, unbounded (yet finite)... And this is for real. I'm not making a point here. I just can't accept this claim without an explanation.

Claim 4: Then I calculated the total computation a quantum computer can carry out, assuming it has the total energy of our universe, and assuming it has been computing since the birth of our universe, and I come to the same number, 1x10^122.

Now, this seems to be hand waiving. There are many possible theoretical components in any given QC design. Some of those elements have zero theoretical energy requirements (and only thus maintenance energy consumption), so I do not know which design has been chosen here to arrive at this number. More on this in a sec...

Claim 5: I guess this coincident supports both the notion that our universe is a black hole, and some other's notion that our universe is a giant quantum computer.

So now the general QC has become our universe. But our universe does not consume any energy, even including zero-point quantum fluctuations. This is the quantum version of conservation of energy. Unless some inverted method of Casimir sonoluminescence is being proposed here that I have not noticed...

Listen, Anthony Mai. I do not disagree with your main point. I too believe that the universe is a giant computer, both syntactically and semantically. I believe that this calculation's goal is completely unpredictable (but through a different line of reasons, as stated in my previous posts). In fact, I see this computer in much the same tradition as the Jewish mystics viewed Sam-a-el, the blind, insane creator. But I have a lot of concern about the reasons you provided, as it appears to me (and I am often myopic, myself) that it is more of an obfuscation to convince, as many do not have the experience necessary to actually counter your claims. This is why I have posted this reply. Not as a disagreement with your conclusion but as a challenge of your lemmas.

[Amn]

Originally posted by galathaea
Bla bla, blablabla bla bla blablablablabla
and blabla scientific talk i dont understand a tiny bit of blablabal :D


ARE YOU KIDDING ME ?

No seriously listen man, can i call you later, i was thinking to build a UFO prototype with a propulsion system based on magneto-gravitational waves, but couldnt find the right man for the job until now..Care to join me ? :D

Where do you have this kind of knowledge from ? Is it a PhD in quantum physics and astronomy I smell here ? :p

I read the article too, but my ears started to shake after a while -so i had to close the page and return to my daily life ;)

[SolarFlare]

Originally posted by galathaea
Claim 3: My calculation shows the number comes to 1x10^122.
[/list]
Love to see that calculation. Or, actually, I'd love more explanation on where the area comes from for our universe, particularly if it is, as most physicists suspect, unbounded (yet finite)... And this is for real. I'm not making a point here. I just can't accept this claim without an explanation.

I'd have to say the same... the science just doesn't hold itself up unless you have facts.

I too believe that the universe is a giant computer, both syntactically and semantically.
Isn't it strange to think that every action you make and every thought you have is all just a step in a calculation?

It's one of the reasons religion was created, but let's not go there just yet ;).

[Amn]

With all due respect, i stopped thinking our universe may be a computer.

A computer is a device tightly linked to time or the 4th dimension here. This implies that its dependent on it, and practice proves this fact rather well. Our universe on the other hand DEFINES the 4th dimension, and thus cannot be depending on it in any way. Also i then can state that its "computations" are not based on time, this also means that the processes happening in real life are not suspendable, not accelerateable, and cannot be schedulled. This makes me reject the thought about Universe being a computer. It MAY have resembleance to a computer, but without a link to time it cant be one.

What it is i dont know of course =)

[SolarFlare]

Originally posted by Amn
With all due respect, i stopped thinking our universe may be a computer.
Keep in mind that I also am not certain what it is, but I will, for the next minute, advocate for it.

Time is merely another dimension which is entered into the calculation. A computer manipulates matter (and possibly other particles) in space to produce a solution at the end of the time it takes to calculate. Likewise, our universe may be manipulating matter (and possibly other particles) in space and time to produce a solution at the end of the lifetime of the universe (the end of the calculation).

[Amn]

Originally posted by solarflare

Keep in mind that I also am not certain what it is, but I will, for the next minute, advocate for it.

Time is merely another dimension which is entered into the calculation. A computer manipulates matter (and possibly other particles) in space to produce a solution at the end of the time it takes to calculate. Likewise, our universe may be manipulating matter (and possibly other particles) in space and time to produce a solution at the end of the lifetime of the universe (the end of the calculation).

Ok if I understand correctly, the entire lifetime of the universe is like a single computer instruction, and not a program. Hence time slice approaches zero right ? Are we talking major time versus minor time ?

I guess it makes sense what you said then :)

[galathaea]

No, I am completely self-taught in these respects, and unfortunately have no such credentials :(. But I am very obsessive in nature and have been studying this for over 10 years (this = quantum mechanics, general relativity, gneral theories on the structur and logic of our universe). It is a religious fascination with me, as I must know what we have actually "seen" of our univers to date and what remains veiled in the mist of the unknown. To me, it is an alchemical journey...

But about the computer... I have no qualms viewing myself as part of a computation since I don't believe the computation is determined. Just as I have no problem seeing myself as part of a living Goddess of all life, even though she may still be quite young and impressionable and be making some serious mistakes on this planet right now... I view myself as an active part, not a passive one.

And what I meant by the universe being a computer is much more linguistics based. You see, I view a calculation as a transformation of a category collection/statement into another such object. I then see us able to express fundamental particles/strings/branes as sentences in such a category and the time evolution operator acts as the processor clock cycle. In other words, the laws of the universe are the processor and the actual state of the universe is the information operated on...

[galathaea]

So as not to get things mixed up with my other posts...

TOM, what did you use to make those great graphs? Did you do that yourself? I've been thinking of getting some graphical correlation display programs at work (as the human eye will pick up a lot of order that may be quite complex for a computer) and was contemplating my choices. They were great quality, simple and direct!

6 bits or digits. Perhaps we'll never know. Perhaps it is unknowable. Was the question as random as the answers? The mist is thick and thickening...

[SolarFlare]

Originally posted by galathaea
6 bits or digits. Perhaps we'll never know. Perhaps it is unknowable. Was the question as random as the answers? The mist is thick and thickening...
In the house of wang miao, a little more than a week ago:

He is typing. The screen says, how to produce a 6 bit random integer. i means how to control the bits. The phone rings. He goes to answer it. We can only hear half the conversation: "Oh, hello there, I was wondering when you'd call... no, I haven't done that yet... yes, but... I told you, Tuesday is too soon... fine... okay, then, I'll be there... yes, I heard you, you said the alley off of Maple Street... okay okay I'll bring it... I just need to turn off my computer and I'll be there... bye... yeah, sure, screw you too." He goes back to the computer. Scrolls down. Submit Reply. He thinks to himself: I need to get an answer to this fast or I'm dead... Man, I am not looking forward to this... The mouse clicks on Start->Shut Down...->Shut Down. He walks out of his apartement for the last time. The next day, the headline to the local paper reads: Master programmer hospitalized in gang brawl. Unfortunately, he is still on the respirator at the local hospital, and has not yet recovered from the coma... To be continued...

[SolarFlare]

Basically, my idea of random is if the observer does not know the outcome of a situation, or how to predict it.

So here's an interesting situation: Imagine you flip a coin. It's 50/50, right? Okay, now imagine your friend flips a coin. He knows what it landed on, and you don't. He says to you, "There is a 70% chance it's heads, and 30% chance it's tails." What do you think about the coin?

[AnthonyMai]

This is not a proper forum to discuss profound physics questions. But since some asked how I come to the conclusion that the universe's entropy, if our whole universe is a black hole, and the total calculation the universe has carried out assuming it is a giant quantum computer, comes to the same number, which is about 1x10^122. Here is how these numbers are obtained.

1.Look at this web site to see how the total computation of the universe quantum computer has carried out can be cauculated.
http://www.edge.org/3rd_culture/lloyd2/lloyd2_index.html
I used slightly different method to calculate it, but comes to the same number, 1x10^122.

2.The Hawking theory gives the fomula for the entropy as simple as this, in natural units:
S = A/4 (A being the surface area of the black hole)

Plug in the dimentional constants to get the fomula most people are more comfortable with, rather than the natural unit, you get:
lnW = (PI*R^2*C^3)/(hbar*G)
Here R is the radius of our universe. SInce our universe has been in existance for about 20 billion years, R is about 20 billion light years. The final result would be about 1x10^122

The odd for some huge dimention-less numbers to have the same magnitude is so small, that people tend to believe they are somewhat indeed connected. This line of thought was actually started by one of the greated a physicists, Dirac. Yes, I truely believe Dirac's big number hyperthesis.

To the one who only knows our universe to be 4 dimentional. Too bad now it looks more like a 11 dimentional universe. I hope soon they will have a 11 dimentional universe theory that give raise to the marvelous big number 1x10^122.

Before that happens, every thing is just speculation, certainly.

[Tom Frohman]

TOM, what did you use to make those great graphs? Did you do that yourself? I've been thinking of getting some graphical correlation display programs at work (as the human eye will pick up a lot of order that may be quite complex for a computer) and was contemplating my choices. They were great quality, simple and direct!

They were generated in Matlab.

[Amn]

Your golden rule of cause and effect is not golden at all. To have causes and effects you have the implied presumption of the time and time moves only forward, since cause always happen at a time before effect. In modern physics, the very existance of time itself is being questioned. Time is probably mostly a concept of some sort of statistical average.


As much as you may speculate about time being not what we think it is, and even not what the most clever bunch of us think it is, it is without doubt the most profound and monumental force in the known space. Without time, whatever it is, no other process that affects the state of the universe as an object, will happen. Without time there are no black holes, because there is no gravity, without black holes, there is no universe which is assumed to be a black hole itself. These kind of speculations are a mere tea-talk if you ask me, because we are so unmature to argue on this, but yet very few actually are willing to stop, because the topic is tempting :D

Still i name it golden rule, because simply i at least count time as being "there". And if its there, it sure affects the rule of cause and effect. I simply view my existence as a mathematical function of its parameters. Its just so many of them, that the function behavior approaches to random, but yet cant be one, as a number of parameters, as someone here said is unbound but finite. The time being a concept of some sort of statistical average doesnt prohibit it to be a one of those parameters.

[SolarFlare]

Originally posted by AnthonyMai
My calculation shows the number comes to 1x10^122. Then I calculated the total computation a quantum computer can carry out, assuming it has the total energy of our universe, and assuming it has been computing since the birth of our universe, and I come to the same number, 1x10^122. I guess this coincident supports both the notion that our universe is a black hole, and some other's notion that our universe is a giant quantum computer.

First off, it is extremely wrong to claim someone else's work as your own. From this basis alone, it would be acceptable to morally, if not scientifically, reject your theory. For the sake of your reputation and validity of your words, never ever do that again.


The Hawking theory gives the fomula for the entropy as simple as this, in natural units:
S = A/4 (A being the surface area of the black hole)

Plug in the dimentional constants to get the fomula most people are more comfortable with, rather than the natural unit, you get:
lnW = (PI*R^2*C^3)/(hbar*G)
Here R is the radius of our universe. SInce our universe has been in existance for about 20 billion years, R is about 20 billion light years. The final result would be about 1x10^122

Okay... you could be a bit more descriptive about your mathematical reasoning, but it looks alright. The problem is, you've based your reasoning on a number of "facts" that are not accepted in the scientific world today, only by that guy you stole your work from, Seth Lloyd. First of all, I have never heard any source say the age of the universe is 20 billion years. The oldest I have heard (and I do read a lot) is about 16 billion. Second of all, you assume that the universe is a sphere in three spacial dimensions. Most astronomers would want to lock you up in a closet for that assumption. Now, I'm not saying you're wrong, but keep in mind, that calculation of yours doesn't mean anything in favor of or against "your" theory.

[AnthonyMai]

First off, it is extremely wrong to claim someone else's work as your own. From this basis alone, it would be acceptable to morally, if not scientifically, reject your theory. For the sake of your reputation and validity of your words, never ever do that again.


It's my own independent calculation although it comes to the same number of Seth Lloyd. And I am sure there are some one else other than Seth Lloyd who did the same calculation, too. Heck its just a calculation. There is no issue of who steals whose calculation.

The calculation of black hole entropy using our universe as a black hole doesn't seem to have been carried out by Seth Lloyd, at least on his web site. I did it myself. But I am pretty sure there are some one who probably has done the same calculation. Are you going to say that I stealed from some one or some one stealed from me?

When big numbers are involved, one or two order magnitude difference is nothing. There are only estimates of how big our universe is. Any thing from 10 billion to 20 billion light years are valid. Finally frankly speaking, you don't seem to have the knowledge background to even discuss the validity of my calculations. End of discussion.

[SolarFlare]

Originally posted by AnthonyMai
It's my own independent calculation although it comes to the same number of Seth Lloyd. And I am sure there are some one else other than Seth Lloyd who did the same calculation, too. Heck its just a calculation. There is no issue of who steals whose calculation.
When asked to show your calculation, you instead showed his. There is a difference between writing a theorem and understanding a theorem.

frankly speaking, you don't seem to have the knowledge background to even discuss the validity of my calculations. End of discussion.
First of all, no that's not going to be the end of the discussion. It's going to be the end of the shouting match. I don't mind discussing this, but if you're going to try to get a cheap shot like that then it's an argument, not a discussion. Also, there you go saying they're your calculations again. But since you seem so passionate, exactly what is your superior training?

[SolarFlare]

I must say I am impressed with your resume.

[galathaea]

Okay, the calculations above are intended to reach a particular conclusion about the univers and randomness that I support. However, the calculations still have numerous errors (many of which were already covered and not responded to), so I will continue to point out where the lemmas are failing.

Claim 1:

The Hawking theory gives the fomula for the entropy as simple as this, in natural units: S = A/4 (A being the surface area of the black hole)


No. It doesn't. I wonder where Mai got this "fact". The Hawking theory gives

dM = [1/(8 pi)] kappa dA + Sigma_H dJ
which is metaphorically similar to
dE = T dS + work terms

dA and dS are only related as analogies. The "correct" entropy of a black hole is always calculated to be approximately zero because there is only one state it is known to be in (all particles at the singularity -- or on the ring singularity for charged Kerr black holes), whereas the quantum state space it could be in is quite large...

Claim 2:

Plug in the dimentional constants to get the fomula most people are more comfortable with, rather than the natural unit, you get:
lnW = (PI*R^2*C^3)/(hbar*G)
Here R is the radius of our universe. SInce our universe has been in existance for about 20 billion years, R is about 20 billion light years. The final result would be about 1x10^122


This is incorrect on all levels. First, the right side is not a dimensionless quantity (check it out... I get km^2 / J as the simplest -- of course I can expand out J, but you get the idea). Second, it is not even a legitamate expression of what you desire (removing the natural units of the first equation). I will accept the 20 billion calculations even though the most recent guesstimates on this today would put it around 12-13 billion (but this controversial) and the rate of expansion for most of the time of the univers has been much less than c (though there likely was a Guth expansionary phase during the early force decoupling/phase transitions), so Ill give that to Mai. However, I still have seen no explanation for the black hole thing in the first place...

Claim 3 (out of order):

Look at this web site to see how the total computation of the universe quantum computer has carried out can be cauculated.
a web site I checked out and saw more handwaiving
I used slightly different method to calculate it, but comes to the same number, 1x10^122.


Really, I think this is hand waiving. There is no foundational reason for this calculation over one that gives 10^90 or 10^130. The main source of hand waiving is in the original QC calculation (where there is no explanation of the component model used for the fundamental particle calculation). Everything else is simple scaling...

Now, the funny thing is I agree with Dirac that there may be something unusually profound about the 10^40 scale. But this argument that Anthony Mai is giving appears only to be of the type that is obscurity for authority.

Anthony, you are a very intelligent young man, and are interested in many great things. But I would suggest checking out these sources for the real scientific skizzy...

Robert M. Wald's General Relativity
P. D. B. Collins, A. D. Martin, and E. J. Squires Particle Physics and Cosmology
Jayant V. Narlikar and T. Padmanabhan Gravity, Gauge Theories, and Quantum Cosmology
Michio Kaku's Quantum Field Theory
and the Penrose, Rindler series Spinors and Space-Time

These will give you a better understanding of the type of calculations you are attempting and a better foundation to make the claims you wish. As well, there are many good resources on Quantum Computing (non of which I have available at the moment) that might clarify some of your conceptions about energy consumption...

[galathaea]

Finally frankly speaking, you don't seem to have the knowledge background to even discuss the validity of my calculations. End of discussion.

This seems to really confirm my authority through obscurity claim...

[galathaea]

In my dimensional analysi, I forgot to carry over a s^2 term in the denominator. Once I realized that the mass terms didn't cancel, I forgot to finish my calculation. I'm sorry if this has confused anyone trying to follow my earlier discussion, but the terms are still not dimensionless (for the mass terms) and the rest of the discussion follows...