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Confused about Determinism and Bell's theorem watch

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    I have quite an interest in the concept of determinism, that is, the idea that from the moment the big bang occured (if we accept that model), everything that was going to happen was fixed and unchangeable. In a nutshell, determinists argue that everything that has ever happened is a direct result of an unbroken chain of causal events.

    We're not talking big things here like WW2, we're talking down to the atomic level. If you follow determinism properly, the positioning of every atom in your body at this moment in time was predetermined by the original structure of the big bang, every hair on your head, every neuron in your brain - there was never any alternative outcome.

    Obviously, with determinism, free will goes out the window. You have the illusion of free will, but ultimately, every decision you make, no matter how small (even when you blink or neurons fire in your brain), it was always going to happen.

    Now, I feel many people miss the point of determinism and often start talking about major events or big decisions. But lets stay on the atomic level here because, if we do that, all events can be taken into account and we don't lose focus.

    Now, I see many people claiming that determinism cannot exist because Quantum Physics has demonstrated that there is no such thing as "hidden variables", mostly thanks to Bell's theorem. However, I am not very maths minded, and I find it very VERY hard to understand the arguments Bell's theorem puts forward. I also don't understand how he manages to claim that there are no such things as "hidden variables".

    In my, non science, mind, it is a bit crazy to assume that we humans can experience or measure ALL variables and it seems very likely that our understanding of certain elements of the universe is massively flawed or incomplete. For example, just because we don't understand why sub-atomic particles act in seemingly random ways (to the extent they can only be expressed in terms of probability) does not mean that they really do... surely we just don't understand it?

    Basically, can anyone explain to me how Bell's theorem disproves determinism???

    Sorry, I wrote that very fast and I could have been a little more clear...
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    Seemingly, no one else understands it either...
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    This thread is one of the many reasons why I wish I had done physics.
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    (Original post by Socmyoligy)
    I have quite an interest in the concept of determinism, that is, the idea that from the moment the big bang occured (if we accept that model), everything that was going to happen was fixed and unchangeable. In a nutshell, determinists argue that everything that has ever happened is a direct result of an unbroken chain of causal events.

    We're not talking big things here like WW2, we're talking down to the atomic level. If you follow determinism properly, the positioning of every atom in your body at this moment in time was predetermined by the original structure of the big bang, every hair on your head, every neuron in your brain - there was never any alternative outcome.

    Obviously, with determinism, free will goes out the window. You have the illusion of free will, but ultimately, every decision you make, no matter how small (even when you blink or neurons fire in your brain), it was always going to happen.

    Now, I feel many people miss the point of determinism and often start talking about major events or big decisions. But lets stay on the atomic level here because, if we do that, all events can be taken into account and we don't lose focus.

    Now, I see many people claiming that determinism cannot exist because Quantum Physics has demonstrated that there is no such thing as "hidden variables", mostly thanks to Bell's theorem. However, I am not very maths minded, and I find it very VERY hard to understand the arguments Bell's theorem puts forward. I also don't understand how he manages to claim that there are no such things as "hidden variables".

    In my, non science, mind, it is a bit crazy to assume that we humans can experience or measure ALL variables and it seems very likely that our understanding of certain elements of the universe is massively flawed or incomplete. For example, just because we don't understand why sub-atomic particles act in seemingly random ways (to the extent they can only be expressed in terms of probability) does not mean that they really do... surely we just don't understand it?

    Basically, can anyone explain to me how Bell's theorem disproves determinism???

    Sorry, I wrote that very fast and I could have been a little more clear...
    First of all, congratulations on creating an interesting and meaningful thread. You don't see many on this sub-forum nowadays.

    Bell's Theorem doesn't disprove Determinism, despite what dogma-swallowing Physics students will tell you. Bell starts from certain assumptions, such as Hidden Variables and Locality, and derives an absurd conclusion from them. Now, any one of the assumptions he started off with could have been responsible for the absurd conclusion, so all Bell's Theorem tells you is that either Hidden Variable Theory or Locality or both are wrong.

    The following spoiler contains information about how Bell's thought experiment works. You don't need it to understand the logical framework of the argument in its purest form; it can be skipped. You might want to read it to see where the ideas came from, though.

    Spoiler:
    Show
    There are many different "Bell arguments" that all give roughly the same results, but here is a crude summary of one. Imagine a device that shoots out pairs of particles in opposite directions. Let's imagine also that there are detectors placed either side of the setup that detects certain properties about the particles when they arrive at the detector - for example, whether their spin is up or down (don't worry about what spin is). Now, according to non-Hidden Variable Quantum Mechanics, the particles do not possess a definite "spin" when they're flying through the air: their properties are not determined or caused; they act probabilistically. Hidden Variable Theory would say that the spin of the particles is definite and determined, only we can't know what that spin is.

    Now, let's suppose that we've experimentally determined that whenever you measure one particle in a detector to have a certain spin, its partner will always be measured to have the opposite spin. According to non-Hidden Variable Theory, what's happening is that both particles have indeterminate spins until one reaches a detector, at which point the measurement process imposes definite spins onto the two particles.

    It's clear that, under this interpretation, Locality is violated. [Locality is when the causes of an event happen right next to that event. If I kick a ball, that obeys locality because the cause of the ball's movement is next to it. In this experiment, one particle is instantly affecting another from across the room, which is obviously contrary to locality.]

    Of course, the Hidden Variable Theorist/Determinist disagrees totally about what's actually happening here. To him, the particles both have definite spins even while they're going through the air. There is no breach of locality. The particles having opposite spins isn't the result of one being measured and then somehow affecting its partner from across the room. Rather, they always had opposite spins, even while they were traveling through the air; and this opposite-ness was caused by something else, say, the make-up of the device that shot out the particles.


    Bell says: suppose the Hidden Variable Theorist is correct. If it is, we can make certain predictions about the number of particles arriving with certain spins at the detector. These predictions turn out to be wrong. If you're interested in the exact Maths of the argument, which isn't at all complicated, then tell me and I'll write it out. But, for now, it suffices to say that the predictions about the number of particles arriving with a certain spin turn out to be wrong. This has been confirmed by experiment.

    One of our original assumptions - mainly, Hidden Variables and Locality - have to be wrong. You have to give up one of them. It doesn't necessarily have to be Hidden Variables, though. So Determinism can be retained, but only at the expense of Locality.

    (If you want the Maths, ask. It's really easy, honest; even I managed to understand it!)
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    (Original post by littleshambles)
    This thread is one of the many reasons why I wish I had done physics.
    Loser :p:

    EDIT: Though, to be fair, you don't need much Physics knowledge to understand it (and you certainly don't need much Maths knowledge to understand the inequalities).
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    (Original post by shamrock92)
    Loser :p:

    EDIT: Though, to be fair, you don't need much Physics knowledge to understand it (and you certainly don't need much Maths knowledge to understand the inequalities).
    I'd like to see the maths, if you don't mind
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    (Original post by Anonhummus)
    I'd like to see the maths, if you don't mind
    Ok; here's a simple Bell's inequality.

    I talked vaguely about spin earlier. Well let's suppose that there's three different axes along which our detectors can measure spin: x, y and z. We can position our detector to measure the spin along any one of these axes - a way to picture this is measuring the rotation of the Earth along the equator, or along the line going through the North and South poles, or any arbitrary straight line going through the Earth. In each axis, we can either get a positive value or a negative value. So the possible results of any measure are: x positive, x negative, y positive, y negative, z positive, z negative. Also recall that the particles have opposite spins, so if one particle has x positive spin then its partner has x negative spin, and vice versa.

    Now here's the Maths. To introduce some notation, let N(Lx+, Ly-, Lz+) represent the number of particles emitted in a given period to the left of the detector with spin x positive, y negative, z positive. Similarly, let N(Rx-, Ry-) represent the number of particles emitted in a given period to the right of the detector with spin x negative, y negative - z spin doesn't matter, in this case.

    Now, if we presume that the particles are determined by Hidden Variables prior to measurement, it follows that a particle with x positive and y positive spin as it enters the detector was either (x+, y-, z+) or (x+, y-, z-) - it had to have a definite z spin value according to Hidden Variable Theory. Therefore

    N(Lx+, Ly-) = N(Lx+, Ly-, Lz+) + N(Lx+, Ly-, Lz-). (Equation 1)

    Likewise, N(Lx+, Lz-) = N(Lx+, Ly+, Lz-) + N(Lx+, Ly-, Lz-). (Equation 2)

    Now consider the left particles that have spin x positive and z negative - (Lx+, Lz-). It's obvious that the number of these particles arriving in a given period - N(Lx+, Lz-) - must be more than the number of particles arriving with (Lx+, Ly-, Lz-), as (Lx+, Ly-, Lz-) is a subset of (Lx+, Lz-). Therefore

    N(Lx+, Lz-) \geq N(Lx+, Ly-, Lz-). (Equation 3)

    Similarly, N(Ly-, Lz+) = N(Lx+, Ly-, Lz+) + N(Lx-, Ly-, Lz+) \geq N(Lx+, Ly-, Lz+). (Equation 4)

    Now, if we use Equation 4 to subsitute in N(Ly-, Lz+) in for N(Lx+, Ly-, Lz+) in Equation 1, and we use Equation 3 to substitute in N(Lx+, Lz-) for N(Lx+, Ly-, Lz-) in Equation 1, we end up with

    N(Lx+, Ly-) \leq N(Ly-, Lz+) + N(Lx+, Lz-). (Equation 5)

    This is essentially a prediction made by Hidden Variable Theory about the spins of the particles that will be detected. So we want to test this prediction. Unfortunately, the detectors can only detect one axis of spin at once; so we can't test for N(Lx+, Ly-) directly, as that would involve testing two axes at once. But we know that the right particle will be measured to have opposite spin to the left particle. So

    N(Lx+, Ly-) = N(Lx+, Ry+) - so we're just determining N(Ly-) by measuring N(Ry+), where N(Ry+) represents the number of particles in a given time period arriving at the right detector with spin y positive.

    Therefore, Equation 5 entails

    N(Lx+, Ry+) \leq N(Ly-, Rz-) + N(Lx+, Rz+).

    Now, that's a "Bell inequality" - a mathematical prediction about what results will occur, assuming the existence of both Locality and Hidden Variables. Tragically, this inequality is measured as being incorrect. This means that one of our assumptions - Locality or Hidden Variables - must have been wrong.
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    Many thanks for posting this. I'm currently reading some material about locality and bells theorem. Part of this states:

    "If we assume that the two detectors are far enough apart, and the measurements are done at almost exactly the same time, then locality says that nothing which happens at one of the measurements can affect the result of the other one."

    However, how can we be sure that there is not some "unknown force" that we simply cannot measure or comprehend that actually does somehow link the two electrons being fired? It kind of seems that we are clinging on to certain assumptions that we know ALL the variables and then, when we get unexpected results, claim locality has been violated?

    I'm going to keep reading so I may end up answering my own question...
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    (Original post by Socmyoligy)
    However, how can we be sure that there is not some "unknown force" that we simply cannot measure or comprehend that actually does somehow link the two electrons being fired?
    That "unknown force" would be a Hidden Variable. We can't know that it doesn't exist - it is, after all, hidden! But we can show that Hidden Variables and Locality together lead to incorrect results.

    (Original post by Socmyoligy)
    It kind of seems that we are clinging on to certain assumptions that we know ALL the variables and then, when we get unexpected results, claim locality has been violated?
    We can derive Bell inequalities by presuming just that Hidden Variables exist and that Locality exists. Generally speaking, they're the only necessary assumptions.
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    Bell's Theorem doesn't conclusively disprove philosophical Determinism (-not to be conflated with Newtonian Determinism). Bell's Theorem starts from certain assumptions, such as Hidden Variables and Locality, and derives an absurd conclusion from them. Now, any one of the assumptions he started off with could have been responsible for the absurd conclusion, so all Bell's Theorem tells you is that either Hidden Variable Theory or Locality or both are wrong.

    There are many different "Bell arguments" that all give roughly the same results, but here is a crude summary of the thought experiment (later to become a real experiment). Imagine a device that shoots out pairs of particles in opposite horizontal directions. Let's imagine also that there are detectors placed either side of the setup that detects certain properties about the particles when they arrive at the detectors - for example, how they are spinning (don't worry about what spin is for now). Now, according to the Copenhagen Interpretation, the particles do not possess a definite "spin" when they're flying through the air: their properties are not determined or caused; they act probabilistically. In contrast, Hidden Variable Theory would say that the spin of the particles is definite and determined, only we can't know what that spin is.

    Let's suppose that we've experimentally determined that whenever you measure one particle in a detector to have a certain spin, its partner will always be measured to have the opposite spin. So if I measure a particle to have negative spin, its partner will be measured to have positive spin.

    What's going on here? According to the Copenhagen Interpretation, what's happening is that both particles have indeterminate spins until one reaches a detector, at which point the measurement process imposes definite spins onto the two particles. It's clear that, under this interpretation, Locality is violated.

    What's Locality?
    Locality is when the causes of an event happen right next to that event. If I kick a ball, locality is obeyed because the cause of the ball's movement is next to it. In this experiment, one particle is instantly affecting another from across the room, which is obviously contrary to locality.


    Of course, the Hidden Variable Theorist/philosophical Determinist disagrees totally about what's actually happening here. To him, the particles both have definite spins even while they're going through the air. There is no breach of locality. The particles having opposite spins isn't the result of one being measured and then somehow affecting its partner from across the room. Rather, they always had opposite spins, even while they were traveling through the air; and this opposite-ness was caused by something else, say, the make-up of the device that shot out the particles.

    So who's right? What's really happening? This is where Bell's Theorem comes in: Bell proves that the assumptions behind Hidden Variable Theory, when combined with Locality, give absurd results.

    So here's the important bit. I talked vaguely about spin earlier. Let's refine this idea a little, and suppose that there's three different axes along which our detectors can measure spin: x, y and z. We can position our detector to measure the spin along any one - and only one - of these axes. (A handy (if inaccurate) way to picture this is measuring the rotation of the Earth along the equator, or along the line going through the North and South poles, or any arbitrary straight line going through the Earth.) Along each axis, we can either get a positive value or a negative value of spin. So the possible results of any measurement are: x positive, x negative, y positive, y negative, z positive, z negative. Also recall that the particles have opposite spins, so if one particle has x positive spin then its partner has x negative spin, and vice versa.

    Now here's the Maths. To introduce some notation, let N(Lx+, Ly-, Lz+) represent the number of particles emitted in a given period to the left of the detector with spin x positive, y negative, z positive. Similarly, let N(Rx-, Ry-) represent the number of particles emitted in a given period to the right of the detector with spin x negative, y negative - z spin doesn't matter, in this case.

    Now, if we presume that the particles are determined by Hidden Variables prior to measurement, it follows that a particle with x positive and y positive spin as it enters the detector was either (x+, y-, z+) or (x+, y-, z-); it had to have a definite z spin value according to Hidden Variable Theory. Therefore

    N(Lx+, Ly-) = N(Lx+, Ly-, Lz+) + N(Lx+, Ly-, Lz-). (Equation 1)

    Likewise, N(Lx+, Lz-) = N(Lx+, Ly+, Lz-) + N(Lx+, Ly-, Lz-). (Equation 2)

    Now consider the left particles that have spin x positive and z negative - (Lx+, Lz-). It's obvious that the number of these particles arriving in a given period - N(Lx+, Lz-) - must be more than the number of particles arriving with (Lx+, Ly-, Lz-), as (Lx+, Ly-, Lz-) is a subset of (Lx+, Lz-). Therefore

    N(Lx+, Lz-) \geq N(Lx+, Ly-, Lz-). (Equation 3)

    Similarly, N(Ly-, Lz+) = N(Lx+, Ly-, Lz+) + N(Lx-, Ly-, Lz+) \geq N(Lx+, Ly-, Lz+). (Equation 4)

    Now, if we use Equation 4 to subsitute in N(Ly-, Lz+) in for N(Lx+, Ly-, Lz+) in Equation 1, and we use Equation 3 to substitute in N(Lx+, Lz-) for N(Lx+, Ly-, Lz-) in Equation 1, we end up with

    N(Lx+, Ly-) \leq N(Ly-, Lz+) + N(Lx+, Lz-). (Equation 5)

    This is essentially a prediction made by Hidden Variable Theory about the spins of the particles that will be detected. So we want to test this prediction. Unfortunately, the detectors can only detect one axis of spin at once; so we can't test for N(Lx+, Ly-) directly, as that would involve testing two axes at once. But we know that the right particle will be measured to have opposite spin to the left particle. So

    N(Lx+, Ly-) = N(Lx+, Ry+) - so we're just determining N(Ly-) by measuring N(Ry+), where N(Ry+) represents the number of particles in a given time period arriving at the right detector with spin y positive.

    Therefore, Equation 5 entails

    N(Lx+, Ry+) \leq N(Ly-, Rz-) + N(Lx+, Rz+).

    Now, that's a "Bell inequality" - a mathematical prediction about what results will occur, assuming the existence of both Locality and Hidden Variables. Tragically, this inequality is measured as being incorrect. This means that one of our assumptions - Locality or Hidden Variables - must have been wrong.

    You have to give up one of them. It doesn't necessarily have to be Hidden Variables, though. So Determinism can be retained, but only at the expense of Locality.
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    RE the above: I just wanted to have those two posts as one so I can link to it. Thanks
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    Read quite a bit more and, you are right, the maths isn't that hard. Very interesting stuff.

    So, in a nutshell, the theory proves that either the universe is non-local or the universe is indeterminate?

    However, there are a hell of a lot of assumptions going on and I guess that is the danger of building theories on theories, although I understand that, to some extent, Bell's theorem can be actually tested.
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    The problem, if you give up locality, how do you maintain the speed of light law?
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    (Original post by Socmyoligy)
    Read quite a bit more and, you are right, the maths isn't that hard. Very interesting stuff.

    So, in a nutshell, the theory proves that either the universe is non-local or the universe is indeterminate?

    However, there are a hell of a lot of assumptions going on and I guess that is the danger of building theories on theories, although I understand that, to some extent, Bell's theorem can be actually tested.
    You're right that how the two assumptions are relevant to the derivation is not entirely rigorous. Because of this, it's still being debated whether Bell's Inequalities are what they say they are, and whether they disprove what they say they disprove.

    A lot of physicists could give a fiddler's either way, as both theories (for now) make the same predictions, which means they're equivalent in some sense - though, as I have argued before, this view is a dangerous and probably inconsistent one.

    Anyway, well done for creating a decent thread. :top:
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    It makes me wonder if QP is a bit like a sudoku puzzle. You know, when you are doing a sudoku puzzle, all the numbers are falling into place and you think that you have nearly cracked it. Then you get to the final few numbers and realise that, due to a mistake you made right at the start, the the puzzle is not solveable.

    It makes you wonder whether physics has made some fundamental errors at the start and now we are in a situation where we can't move forward unless we go back. But then again, my knowledge of physics is tiny. It's just how I feel having read about Bell's theorem.
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    (Original post by Socmyoligy)
    The problem, if you give up locality, how do you maintain the speed of light law?
    That's the problem. (In fact, if you can have things travelling faster than light, then you can almost certainly have one person seeing a ladder that is bigger than a garage fit into the garage while another person travelling at a different speed sees the ladder crash straight into the back of it, along with manifold other paradoxes.)
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    (Original post by Socmyoligy)
    It makes me wonder if QP is a bit like a sudoku puzzle. You know, when you are doing a sudoku puzzle, all the numbers are falling into place and you think that you have nearly cracked it. Then you get to the final few numbers and realise that, due to a mistake you made right at the start, the the puzzle is not solveable.

    It makes you wonder whether physics has made some fundamental errors at the start and now we are in a situation where we can't move forward unless we go back. But then again, my knowledge of physics is tiny. It's just how I feel having read about Bell's theorem.
    Well, I wouldn't worry too much about that. Revisions of these starting assumptions have lead to the most massive advances in science. In fact, what we're discussing - Quantum Mechanics - was a fundamental revision of Determinism and a break with traditional physics. But we've managed to readjust despite these big corrections; and, indeed, without QM, we wouldn't have the computers we have. If anything, these big falsification events where fundamental parts of the theory are revised strengthen my faith in science as progressing, albeit a Lakatosian faith.
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    Shamrock92's posts explain it very well in a simple, albeit mathematical, way. I wanted to add something about locality but I've forgotten it now that I've reread the entire thread!

    Will post it if I remember but well done thanks for this interesting thread. :cool:
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    (Original post by Socmyoligy)
    I have quite an interest in the concept of determinism, that is, the idea that from the moment the big bang occured (if we accept that model), everything that was going to happen was fixed and unchangeable. In a nutshell, determinists argue that everything that has ever happened is a direct result of an unbroken chain of causal events.

    We're not talking big things here like WW2, we're talking down to the atomic level. If you follow determinism properly, the positioning of every atom in your body at this moment in time was predetermined by the original structure of the big bang, every hair on your head, every neuron in your brain - there was never any alternative outcome.

    Obviously, with determinism, free will goes out the window. You have the illusion of free will, but ultimately, every decision you make, no matter how small (even when you blink or neurons fire in your brain), it was always going to happen.
    Ok I know next to nothing about physics so I'm going to ignore that part.

    But I'm always so surprised when people reach the conclusion that because any decision you make was always going to happen, it isn't free. I'm not trying to make the case for straight-forward compatibalism, but rather that it seems to make sense to talk about free will without determinism.

    Making a decision for any event (not WW2 but let's say a basic one to go to do the shopping) only counts as a decision if it is made up of various determining factors. It would seem odd if I preferred shopping to starvation, knew that I had to do it today and had enough money and wanted to go shopping, but then just didn't do it. That would be randomness, and so decisions seem much less free than if they do all have determining factors.

    To consider the self as divorced from one's history, upbringing, genes etc. seems entirely incoherent.

    But yes...have no idea on the physics
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    (Original post by *Katie*)
    Ok I know next to nothing about physics so I'm going to ignore that part.

    But I'm always so surprised when people reach the conclusion that because any decision you make was always going to happen, it isn't free. I'm not trying to make the case for straight-forward compatibalism, but rather that it seems to make sense to talk about free will without determinism.

    Making a decision for any event (not WW2 but let's say a basic one to go to do the shopping) only counts as a decision if it is made up of various determining factors. It would seem odd if I preferred shopping to starvation, knew that I had to do it today and had enough money and wanted to go shopping, but then just didn't do it. That would be randomness, and so decisions seem much less free than if they do all have determining factors.

    To consider the self as divorced from one's history, upbringing, genes etc. seems entirely incoherent.

    But yes...have no idea on the physics
    Well, a hard determinist would argue that from the moment the big bang occured, you were always going to write what you just wrote, down to the last full stop and comma. It is not a case of determining factors, it is a simple case that every atom in the universe, every electron and proton, was always going to end up in a certain way. It's the notion that everything that has ever happened, and ever will happen, is simply the combined result of one massive causal relationship. Everything... down the the last atom in the universe.

    So, in this sense, no, free will has gone. It is a sobering concept, that the original arrangement of the big bang determined everything else that would ever happen.

    I'd like to get to grips more with the physics behind the various agruements for and against this position, but my brain prevents me - oh well, it was always going to be the case...
 
 
 
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