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Author | Topic: A Proposed Proof That The Origin of The Universe Cannot Be Scientifically Explained | |||||||||||||||||||||||||||||||||||||||||||
Son Goku Inactive Member |
I just realised that the Kochen Specker theorem can be proved in a reasonably comprehensible way way, so I'll give it a try.
The system I'm going to look at for the theorem is a system composed of two particles with spin-1/2 and I'm only concerned about their spin and nothing else, not momentum, position, e.t.c. There are four possible basic states this system can be in:Particle 1 is spin up, Particle 2 is spin up Particle 1 is spin up, Particle 2 is spin down Particle 1 is spin down, Particle 2 is spin up Particle 1 is spin down, Particle 2 is spin down Up here means spinning anticlockwise around the z-axis, down is spinning clockwise around the z-axis. This means there are four basic binary measurements I can perform. A binary measurement is an experimental test with only a yes/no answer. These are:Is particle 1 spin up? (P1) Is particle 2 spin up? (P2) Is particle 1 spin down? (P3) Is particle 2 spin down? (P4) The answers to all of these are either yes or no, which I will model mathematically with 0 or 1. So if I measured particle 1 to be spin down, I'd have P3 = 1. If particle 2 was measured to not be spin up, I'd have P2 = 0. However Quantum Mechanics say that the sum of all these answers must be 1: P1 + P2 + P3 + P4 = 1. This basically means that all of them, must have the value 0, except for one. So I have four pieces of equipment which each measure one of P1,P2,P3 and P4. This is the basic set up.
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Son Goku Inactive Member |
Now the particular P1, P2, P3, P4 measurements I gave above are not the only possible yes/no measurements. For instance I could ask if particle 1 and particle 2 were spin up. This would be P5, let's say.
Cabello has found that there are nine sets of four measurements you can make (he didn't include P1) where quantum mechanics predicts the answers must sum up to 1. These are:P4 + P3 + P5 + P6 = 1 P4 + P2 + P7 + P8 = 1 P9 + P10 + P5 + P11 = 1 P9 + P12 + P8 + P13 = 1 P3 + P2 + P14 + P15 = 1 P10 + P12 + P15 + P16 = 1 P17 + P18 + P6 + P11 = 1 P17 + P19 + P7 + P13 = 1 P18 + P19 + P14 + P16 = 1 It doesn't matter what each of these measurements are especially just that:(i) Quantum Mechanics that if you take one set and measure each P with a piece of equipment, then the answers must sum up to 1. This means only one of the P's you pick will be measured to be 1. (ii) Each particular P measurement appears in two of the sets. So, now the weird part. If particles have real actual properties, something underneath the randomness of quantum mechanics, you would be able to predict whether you would get 0 or 1 for each P if you knew those properties. So assume particles have real properties. Then we have:(i) Those properties, to match the predictions of quantum mechanics, confirmed by experiment, must only predict one of the P-measurements in each set to be 1 and the rest to be 0. (ii) Since the particles do not know which experiment you are going to perform and they are supposed to have properties independent of your measurements, then if they predict P4 = 0 in the first list, they must also predict P4 = 0 if you choose the second list. They don't know which set of P-measurements you are going to choose to make. Condition (i) says then that the real properties will predict one of the P values in each list to be 1. If you Mark this value this means there are nine marked values, an odd number. Condition (ii) says that if you mark a value in one list, it must be marked in the other list it appears in. This means there must be an even number of marks. Hence assuming particles have real properties implies that you must mark an even number of entries and an odd number of entries. This is impossible/contradictory, hence the existence of real properties is logically refuted. Particle do not possess definite independent properties. QED.
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nano Member (Idle past 1320 days) Posts: 110 Joined: |
Very interesting. Thanks.
So, can we draw any conclusions about the nature of reality from this? I think any conclusions must be limited because certainly electrons have a defined mass and charge.
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Son Goku Inactive Member |
Well in quantum mechanics what we call a single electron is actually just a collection of probabilities that always returns 1/2 when you measure the "total spin". There is even some ambiguity in defining a state with two electrons.
The conclusions are pretty strong, experimental results are not decided in advance by the pre-existing "objective" properties of particles, since particles do not possess such things.
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Son Goku Inactive Member |
I will explain what happens in the Hawking-Hartle no-boundary proposal, otherwise the whole discussion might just revolve around a failure of my approximation of the effect in normal English.
Basically quantum mechanics has a device, the path integral, which takes in two different states and outputs the chance to go from one to the other. These states could be "Electron at location x at time t1" and "electron at location y at time t2". This path-integral is one way of encoding the laws of quantum physics. People had started to apply this idea to gravity in the early 1980s. Hawking and Hartle found the pretty strange result that if you input the following two states: 1. The Null Set2. Expanding universe containing matter The path-integral gave a non-zero probability to go from one to the other, hence quantum laws can produce a universe from the null set. Perhaps there are better way of describing this than "nothing but laws". However I should say the null set above is genuinely the null set of mathematics.
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Dr Adequate Member (Idle past 312 days) Posts: 16113 Joined: |
Perhaps there are better way of describing this than "nothing but laws". However I should say the null set above is genuinely the null set of mathematics. Yes ... but ... the thing I'm worrying about ... I think that a "nothing" with laws applying to it is not actually nothing. Because it has qualities, in that it has a way in which it tends to behave. You say that it's the null set, but I think that the set of aardvarks which are elephants (a null set) does not have any tendency to create a universe. If every logical characterization of the null set had to make a universe, then we'd be knee-deep in them. It has to be a "null set" with the property of obeying certain laws. There may be an ambiguity here between what you mean by "null set" as a physicist and what I mean as a mathematician. I am most grateful to you for explaining the physics.
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Tangle Member Posts: 9512 From: UK Joined: Member Rating: 4.8 |
Dr A writes: There may be an ambiguity here between what you mean by "null set" as a physicist and what I mean as a mathematician. .....and between what I mean as someone who runs a telephone company. The problem is that the term "nothing" only has meaning to the rest of us when it's inside something else. There's nothing for dinner. It falls over and refuses to get up when there's nothing on it's own, doing nothing. Nothing explains something, something doesn't explain nothing. Edited by Tangle, : Friggin' quotes again....Life, don't talk to me about life - Marvin the Paranoid Android
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Dr Adequate Member (Idle past 312 days) Posts: 16113 Joined: |
Mmm ... I don't completely follow the point that you're trying to make. I don't say that your point is wrong, but I think that you should express it sufficiently formally that I know whether I agree with it or I don't.
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Tangle Member Posts: 9512 From: UK Joined: Member Rating: 4.8
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We can understand the phrases
"I have something in my pocket" and "There is nothing in my pocket." But the phrase, "There is nothing outside my pocket" means, well nothing. We can also understand "There is something in the universe" But we can't understand there is "nothing outside the universe" because our minds don't have a way of catching hold of non-reality. Nothing means something when it's defined by other things. But as soon as it really means nothing - on it's own - with nothing real or imagined to set it against, we, or at least I, can't understand what it means. And I suspect it means nothing - that is, it's meaningless. The universe is very definitely not nothing, we're creatures built of something, used to experiencing our physical reality so the concept of a boundless universe with nothing beyond, is beyond normal imaginings. Or at least beyond mine and certainly beyond the normal useage of language.Life, don't talk to me about life - Marvin the Paranoid Android
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onifre Member (Idle past 2979 days) Posts: 4854 From: Dark Side of the Moon Joined: |
Nothing means something when it's defined by other things. But as soon as it really means nothing - on it's own - with nothing real or imagined to set it against, we, or at least I, can't understand what it means. And I suspect it means nothing - that is, it's meaningless. I used to get into these discussions here before. I've since then strayed away and mostly lurk when they're going on. The 'meaningless' description is how I see it too having been explained that very thing by Cavediver once before. I'm totally comfortable with that. - Oni
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1.61803 Member (Idle past 1532 days) Posts: 2928 From: Lone Star State USA Joined: |
Nothing denotes no thing. There is Nothing or there is something. If there were nothing we would not be here to ponder it. It being nothing. Oh here we go again!
"You were not there for the beginning. You will not be there for the end. Your knowledge of what is going on can only be superficial and relative" William S. Burroughs |
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Stile Member Posts: 4295 From: Ontario, Canada Joined: |
Dr Adequate writes: Stile writes: For example: "What is the explanation for velocity?""Velocity is distance over time." "But why is velocity disance over time?" Well, that does have an answer: "By definition". Exactly.What I'm trying to say is that the universe may have an answer that we can understand... the ultimate explanation may be "By definition" if our understanding of the universe can reach that point. Our understanding may not be able to reach that point. Perhaps by lack of intelligence, or perhaps by impossibility. But, it is possible that the ultimate answer to the universe is a "just so" explanation that comes out of the definition of the properties we can understand (like time, distance, velocity...). And, if it does, then the answer is possibly obtainable. And then, if it is possible and obtainable, then it is likely that it will be scientifically explained.Therefore, however unlikely it may be, it is not "impossible" for the origin of the universe to be explained scientifically.
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Son Goku Inactive Member |
Dr Adequate writes:
You are probably right, but I don't know how to really see what those properties are. Your next sentence provides a possible clue.
I think that a "nothing" with laws applying to it is not actually nothing. Because it has qualities, in that it has a way in which it tends to behave. You say that it's the null set, but I think that the set of aardvarks which are elephants (a null set) does not have any tendency to create a universe. If every logical characterization of the null set had to make a universe, then we'd be knee-deep in them. It has to be a "null set" with the property of obeying certain laws.
Yes indeed, this null set does have some origin. Basically standard Quantum Gravity gives you the probability for one three dimensional space to be produce from another. This is the analogue of normal quantum mechanics where you work out the probability to go from one position to another. So you have a three dimensional space and you compute the probability that that space will "jump" to being a different space , just as a particle may quantum tunnel from one point to another. This probability is worked out as follows:(a) Take the set of all four dimensional spaces which have and as the boundaries on either side (I mean this in the sense that a cylinder has circles on either side.) An individual such space is . (b) Compute the total curvature of each one of these spaces. This is . The contribution to the probability by a given space is (c) You know have a function giving the contribution of certain four dimensional space to the probability. Sum/Integrate this function over the space of all possible four dimensional spaces . the result is the probability that will jump to . What Hawking and Hartle considered was the choice:A = Null Set B = The three dimensional space describing the early universe at a given time. There are four-dimensional space which have this choice as boundaries, namely spaces with no boundary at one end, which is a null set boundary, hence the no-boundary proposal. If you work out the calculation (a)-(c) you get a non-zero number. So a null set can tunnel into a full three-dimensional space. However I suspect you are right and really this is "the null set in the context of Quantum Gravity Theory". What I don't know is how to express this null set as being a thing in terms of material objects.
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Dr Adequate Member (Idle past 312 days) Posts: 16113 Joined:
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What I'm trying to say is that the universe may have an answer that we can understand... the ultimate explanation may be "By definition" if our understanding of the universe can reach that point. But "by definition" is a different sort of answer to a different sort of question. It's not the sort of answer you could give to a question about the causes of things. The "why" in "why is velocity distance over time?" is actually a different "why" to the "why" in the question (for example) "why did John Wilkes Booth kill Abraham Lincoln?"; and when we are answering it the "because" is a different "because". In the first case, it is because we have defined velocity to be distance over time, whereas in the second case it is not because we defined "John Wilkes Booth" as being "whatever killed Abraham Lincoln". To answer the second question, we'd have to talk about things like slavery and the Confederacy and the Civil War.
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1.61803 Member (Idle past 1532 days) Posts: 2928 From: Lone Star State USA Joined: |
If I may................The "because" is a big one.
No one likes when a parent says "because" I said so. However, it may very well come down to that. At some level, reality may be bound to some basic, simplistic statement. That is just the way it is man."You were not there for the beginning. You will not be there for the end. Your knowledge of what is going on can only be superficial and relative" William S. Burroughs
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