Does god play dice??
This is a summery and comments to Hawking's public lecture "Does god play dice" which simply explains the bases of quantum mechanics, u can find the site address below.
- classical 19th century ideas, dating back to Laplace "determinism": a hot body, like a piece of hot metal, should give off radiation. It would lose energy in radio waves, infra red, visible light, ultra violet, x-rays, and gamma rays, all at the same rate.
- Planck: The energy in the packets or quanta, is higher for ultra violet and x-rays, than for infra red or visible light. This means that unless a body is very hot, like the Sun, it will not have enough energy, to give off even a single quantum of ultra violet or x-rays. That is why we don't get sunburn from a cup of coffee.
- quantum mechanics: first put forward in 1900, by the German physicist, Max Planck
- 1926, that Werner Heisenberg, another German physicist, pointed out that you couldn't measure both the position, and the speed, of a particle exactly. To see where a particle is, one has to shine light on it. But by Planck's work, one can't use an arbitrarily small amount of light. One has to use at least one quantum. This will disturb the particle, and change its speed in a way that can't be predicted. To measure the position of the particle accurately, you will have to use light of short wave length, like ultra violet, x-rays, or gamma rays. But again, by Planck's work, quanta of these forms of light have higher energies than those of visible light. So they will disturb the speed of the particle more. It is a no win situation: the more accurately you try to measure the position of the particle, the less accurately you can know the speed, and vice versa. This is summed up in the Uncertainty Principle that Heisenberg formulated; the uncertainty in the position of a particle, times the uncertainty in its speed, is always greater than a quantity called Planck's constant, divided by the mass of the particle.
- Laplace's vision, of scientific determinism, involved knowing the positions and speeds of the particles in the universe, at one instant of time. So it was seriously undermined by Heisenberg's Uncertainty principle. How could one predict the future, when one could not measure accurately both the positions, and the speeds, of particles at the present time? No matter how powerful a computer you have, if you put lousy data in, you will get lousy predictions out.
- Einstein was very unhappy about this apparent randomness in nature. His views were summed up in his famous phrase, 'God does not play dice'. He seemed to have felt that the uncertainty was only provisional, but that there was an underlying reality in which particles would have well defined positions and speeds, and would evolve according to deterministic laws, in the spirit of Laplace. This reality might be known to God, but the quantum nature of light would prevent us seeing it, except through a glass darkly. Einstein's view was what would now be called, a hidden variable theory. Hidden variable theories might seem to be the most obvious way to incorporate the Uncertainty Principle into physics. They form the basis of the mental picture of the universe, held by many scientists, and almost all philosophers of science. But these hidden variable theories are wrong (??). The British physicist, John Bell, who died recently, devised an experimental test that would distinguish hidden variable theories. When the experiment was carried out carefully, the results were inconsistent with hidden variables. Thus it seems that even God is bound by the Uncertainty Principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion. (??)(comment: so if we can't see or put laws to something with our very limited abilities, let's keep trying till we figure it out, not deny it just cause we can't see it, or else we'll make a set of rules to every thing completely far from the truth of that thing just because it is convenient to our limited abilities, so we would deny the wisdom of a higher power behind this universe, be it a god or a goddess or a multitude of them just because, no matter what genius we possess, we can't yet grasp the laws on which this universe was built, because of a silly experiment in one of our mortal labs we speak of the creators of this universe as if we possessed their exact immortal qualities?! This is ridiculous. It is not that I'm defending the wisdom of that higher power, I'm far from it, but I believe that I can protest to the idea of a just creator based on the pain we see surrounding us, or on a personal painful experience, cause I am ACTUALLY suffering and I don't care what the greater good is, all I know is that I want that pain to STOP NOW, but call a creator a gambler based on my limited brains and wits?! When that person creates a similar universe then he can call the creators anything he wants, any way in Hawking's case the painful experience is quite clear).
- Quantum mechanics, was put forward by Heisenberg, the Austrian, Erwin Schroedinger, and the British physicist, Paul Dirac. Dirac was hawking's predecessor but one, as the Lucasian Professor in Cambridge. Quantum mechanics has been around for nearly 70 years.
- it is a completely different picture of the physical universe, and of reality itself. In quantum mechanics, particles don't have well defined positions and speeds. Instead, they are represented by what is called a wave function. This is a number at each point of space. The size of the wave function gives the probability that the particle will be found in that position. The rate, at which the wave function varies from point to point, gives the speed of the particle. One can have a wave function that is very strongly peaked in a small region. This will mean that the uncertainty in the position is small.
But the wave function will vary very rapidly near the peak, up on one side, and down on the other. Thus the uncertainty in the speed will be large. Similarly, one can have wave functions where the uncertainty in the speed is small, but the uncertainty in the position is large.
The wave function contains all that one can know of the particle, both its position, and its speed. If you know the wave function at one time, then its values at other times are determined by what is called the Schroedinger equation. Thus one still has a kind of determinism, but it is not the sort that Laplace envisaged. Instead of being able to predict the positions and speeds of particles, all we can predict is the wave function. This means that we can predict just half what we could according to the classical 19th century view. Although quantum mechanics leads to uncertainty, when we try to predict both the position and the speed, it still allows us to predict, with certainty, one combination of position and speed.
However, even this degree of certainty, seems to be threatened by more recent developments. The problem arises because gravity can warp space-time so much, that there can be regions that we don't observe.
- Laplace wrote a paper in 1799 on how some stars could have a gravitational field so strong that light could not escape, but would be dragged back onto the star. He even calculated that a star of the same density as the Sun, but two hundred and fifty times the size, would have this property. But although Laplace may not have realised it, the same idea had been put forward 16 years earlier by a Cambridge man, John Mitchell, in a paper in the Philosophical Transactions of the Royal Society. Both Mitchell and Laplace thought of light as consisting of particles, rather like cannon balls, that could be slowed down by gravity, and made to fall back on the star.
- But a famous experiment, carried out by two Americans, Michelson and Morley in 1887, showed that light always traveled at a speed of one hundred and eighty six thousand miles a second, no matter where it came from. How then could gravity slow down light, and make it fall back. This was impossible, according to the then accepted ideas of space and time. But in 1915 Einstein put forward his revolutionary General Theory of Relativity. In this, space and time were no longer separate and independent entities. Instead, they were just different directions in a single object called space-time. This space-time was not flat, but was warped and curved by the matter and energy in it. "In order to understand this, considered a sheet of rubber, with a weight placed on it, to represent a star. The weight will form a depression in the rubber, and will cause the sheet near the star to be curved, rather than flat. If one now rolls marbles on the rubber sheet, their paths will be curved, rather than being straight lines." ??
- In 1919, a British expedition to West Africa looked at light from distant stars that passed near the Sun during an eclipse. They found that the images of the stars were shifted slightly from their normal positions. This indicated that the paths of the light from the stars had been bent by the curved space-time near the Sun. General Relativity was confirmed.
Questions by the blogger:
- distant stars mean that the images are not real, but the old places of where the stars used to be, so did they pass the sun at an eclipse at that time or at a previous time? Or mathematically speaking the stars in their real positions were supposed to pass the sun at that time? I think they meant the last possibility
- why not assume that the solar flairs affected the light of the stars passing the sun and not the time-space curvature?
- How black holes are formed:
Consider now placing heavier and heavier, and more and more concentrated weights on the rubber sheet. They will depress the sheet more and more. Eventually, at a critical weight and size, they will make a bottomless hole in the sheet, which particles can fall into, but nothing can get out of. What happens in space-time according to General Relativity is rather similar. A star will curve and distort the space-time near it, more and more, the more massive and more compact the star is. If a massive star, which has burnt up its nuclear fuel, cools and shrinks below a critical size, it will quite literally make a bottomless hole in space-time, that light can't get out of. Such objects were given the name Black Holes, by the American physicist John Wheeler, who was one of the first to recognize their importance, and the problems they pose. In a black hole bodies are governed by their total mass, and the state of rotation.
- do black holes emit radiation?
black holes aren't completely black. Quantum mechanics causes them to send out particles and radiation at a steady rate. What is though of as empty space is not really empty, but it is filled with pairs of particles and anti particles. These appear together at some point of space and time, move apart, and then come together and annihilate each other. These particles and anti particles occur because a field, such as the fields that carry light and gravity, can't be exactly zero. That would mean that the value of the field, would have both an exact position (at zero), and an exact speed or rate of change (also zero). This would be against the Uncertainty Principle, just as a particle can't have both an exact position, and an exact speed. So all fields must have what are called, vacuum fluctuations. Because of the quantum behavior of nature, one can interpret these vacuum fluctuations, in terms of particles and anti particles, as I have described. These pairs of particles occur for all varieties of elementary particles. They are called virtual particles, because they occur even in the vacuum, and they can't be directly measured by particle detectors. However, the indirect effects of virtual particles, or vacuum fluctuations, have been observed in a number of experiments, and their existence confirmed. If there is a black hole around, one member of a particle anti particle pair may fall into the hole, leaving the other member without a partner, with which to annihilate. The forsaken particle may fall into the hole as well, but it may also escape to a large distance from the hole, where it will become a real particle, that can be measured by a particle detector. To someone a long way from the black hole, it will appear to have been emitted by the hole. This explanation of how black holes ain't so black, makes it clear that the emission will depend on the size of the black hole, and the rate at which it is rotating.
The radiation of a black hole will be otherwise independent of what went into the hole. It doesn't matter whether you throw television sets, diamond rings, or your worst enemies, into a black hole. What comes back out will be the same (what?? Nothing comes out of a black hole). These virtual black holes are so small, a hundred billion billion times smaller than the nucleus of an atom
Even the limited predictability of the Uncertainty Principle disappeared, when the effects of black holes were taken into account. The loss of particles and information down black holes meant that the particles that came out were random. One could calculate probabilities, but one could not make any definite predictions. Thus, the future of the universe is not completely determined by the laws of science, and its present state, as Laplace thought. God still has a few tricks up his sleeve.
Comment by the blogger: after reading this lecture, I think that even science is influenced by political and social common view of a certain era, the era of Einstein was still an era of belief and religion, now it's the era of man gods
Hawking's public lectures: http://www.hawking.org.uk/lectures/lindex.html
Hawking's universe: http://www.pbs.org/wnet/hawking/html/home.html
- classical 19th century ideas, dating back to Laplace "determinism": a hot body, like a piece of hot metal, should give off radiation. It would lose energy in radio waves, infra red, visible light, ultra violet, x-rays, and gamma rays, all at the same rate.
- Planck: The energy in the packets or quanta, is higher for ultra violet and x-rays, than for infra red or visible light. This means that unless a body is very hot, like the Sun, it will not have enough energy, to give off even a single quantum of ultra violet or x-rays. That is why we don't get sunburn from a cup of coffee.
- quantum mechanics: first put forward in 1900, by the German physicist, Max Planck
- 1926, that Werner Heisenberg, another German physicist, pointed out that you couldn't measure both the position, and the speed, of a particle exactly. To see where a particle is, one has to shine light on it. But by Planck's work, one can't use an arbitrarily small amount of light. One has to use at least one quantum. This will disturb the particle, and change its speed in a way that can't be predicted. To measure the position of the particle accurately, you will have to use light of short wave length, like ultra violet, x-rays, or gamma rays. But again, by Planck's work, quanta of these forms of light have higher energies than those of visible light. So they will disturb the speed of the particle more. It is a no win situation: the more accurately you try to measure the position of the particle, the less accurately you can know the speed, and vice versa. This is summed up in the Uncertainty Principle that Heisenberg formulated; the uncertainty in the position of a particle, times the uncertainty in its speed, is always greater than a quantity called Planck's constant, divided by the mass of the particle.
- Laplace's vision, of scientific determinism, involved knowing the positions and speeds of the particles in the universe, at one instant of time. So it was seriously undermined by Heisenberg's Uncertainty principle. How could one predict the future, when one could not measure accurately both the positions, and the speeds, of particles at the present time? No matter how powerful a computer you have, if you put lousy data in, you will get lousy predictions out.
- Einstein was very unhappy about this apparent randomness in nature. His views were summed up in his famous phrase, 'God does not play dice'. He seemed to have felt that the uncertainty was only provisional, but that there was an underlying reality in which particles would have well defined positions and speeds, and would evolve according to deterministic laws, in the spirit of Laplace. This reality might be known to God, but the quantum nature of light would prevent us seeing it, except through a glass darkly. Einstein's view was what would now be called, a hidden variable theory. Hidden variable theories might seem to be the most obvious way to incorporate the Uncertainty Principle into physics. They form the basis of the mental picture of the universe, held by many scientists, and almost all philosophers of science. But these hidden variable theories are wrong (??). The British physicist, John Bell, who died recently, devised an experimental test that would distinguish hidden variable theories. When the experiment was carried out carefully, the results were inconsistent with hidden variables. Thus it seems that even God is bound by the Uncertainty Principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion. (??)(comment: so if we can't see or put laws to something with our very limited abilities, let's keep trying till we figure it out, not deny it just cause we can't see it, or else we'll make a set of rules to every thing completely far from the truth of that thing just because it is convenient to our limited abilities, so we would deny the wisdom of a higher power behind this universe, be it a god or a goddess or a multitude of them just because, no matter what genius we possess, we can't yet grasp the laws on which this universe was built, because of a silly experiment in one of our mortal labs we speak of the creators of this universe as if we possessed their exact immortal qualities?! This is ridiculous. It is not that I'm defending the wisdom of that higher power, I'm far from it, but I believe that I can protest to the idea of a just creator based on the pain we see surrounding us, or on a personal painful experience, cause I am ACTUALLY suffering and I don't care what the greater good is, all I know is that I want that pain to STOP NOW, but call a creator a gambler based on my limited brains and wits?! When that person creates a similar universe then he can call the creators anything he wants, any way in Hawking's case the painful experience is quite clear).
- Quantum mechanics, was put forward by Heisenberg, the Austrian, Erwin Schroedinger, and the British physicist, Paul Dirac. Dirac was hawking's predecessor but one, as the Lucasian Professor in Cambridge. Quantum mechanics has been around for nearly 70 years.
- it is a completely different picture of the physical universe, and of reality itself. In quantum mechanics, particles don't have well defined positions and speeds. Instead, they are represented by what is called a wave function. This is a number at each point of space. The size of the wave function gives the probability that the particle will be found in that position. The rate, at which the wave function varies from point to point, gives the speed of the particle. One can have a wave function that is very strongly peaked in a small region. This will mean that the uncertainty in the position is small.
But the wave function will vary very rapidly near the peak, up on one side, and down on the other. Thus the uncertainty in the speed will be large. Similarly, one can have wave functions where the uncertainty in the speed is small, but the uncertainty in the position is large.
The wave function contains all that one can know of the particle, both its position, and its speed. If you know the wave function at one time, then its values at other times are determined by what is called the Schroedinger equation. Thus one still has a kind of determinism, but it is not the sort that Laplace envisaged. Instead of being able to predict the positions and speeds of particles, all we can predict is the wave function. This means that we can predict just half what we could according to the classical 19th century view. Although quantum mechanics leads to uncertainty, when we try to predict both the position and the speed, it still allows us to predict, with certainty, one combination of position and speed.
However, even this degree of certainty, seems to be threatened by more recent developments. The problem arises because gravity can warp space-time so much, that there can be regions that we don't observe.
- Laplace wrote a paper in 1799 on how some stars could have a gravitational field so strong that light could not escape, but would be dragged back onto the star. He even calculated that a star of the same density as the Sun, but two hundred and fifty times the size, would have this property. But although Laplace may not have realised it, the same idea had been put forward 16 years earlier by a Cambridge man, John Mitchell, in a paper in the Philosophical Transactions of the Royal Society. Both Mitchell and Laplace thought of light as consisting of particles, rather like cannon balls, that could be slowed down by gravity, and made to fall back on the star.
- But a famous experiment, carried out by two Americans, Michelson and Morley in 1887, showed that light always traveled at a speed of one hundred and eighty six thousand miles a second, no matter where it came from. How then could gravity slow down light, and make it fall back. This was impossible, according to the then accepted ideas of space and time. But in 1915 Einstein put forward his revolutionary General Theory of Relativity. In this, space and time were no longer separate and independent entities. Instead, they were just different directions in a single object called space-time. This space-time was not flat, but was warped and curved by the matter and energy in it. "In order to understand this, considered a sheet of rubber, with a weight placed on it, to represent a star. The weight will form a depression in the rubber, and will cause the sheet near the star to be curved, rather than flat. If one now rolls marbles on the rubber sheet, their paths will be curved, rather than being straight lines." ??
- In 1919, a British expedition to West Africa looked at light from distant stars that passed near the Sun during an eclipse. They found that the images of the stars were shifted slightly from their normal positions. This indicated that the paths of the light from the stars had been bent by the curved space-time near the Sun. General Relativity was confirmed.
Questions by the blogger:
- distant stars mean that the images are not real, but the old places of where the stars used to be, so did they pass the sun at an eclipse at that time or at a previous time? Or mathematically speaking the stars in their real positions were supposed to pass the sun at that time? I think they meant the last possibility
- why not assume that the solar flairs affected the light of the stars passing the sun and not the time-space curvature?
- How black holes are formed:
Consider now placing heavier and heavier, and more and more concentrated weights on the rubber sheet. They will depress the sheet more and more. Eventually, at a critical weight and size, they will make a bottomless hole in the sheet, which particles can fall into, but nothing can get out of. What happens in space-time according to General Relativity is rather similar. A star will curve and distort the space-time near it, more and more, the more massive and more compact the star is. If a massive star, which has burnt up its nuclear fuel, cools and shrinks below a critical size, it will quite literally make a bottomless hole in space-time, that light can't get out of. Such objects were given the name Black Holes, by the American physicist John Wheeler, who was one of the first to recognize their importance, and the problems they pose. In a black hole bodies are governed by their total mass, and the state of rotation.
- do black holes emit radiation?
black holes aren't completely black. Quantum mechanics causes them to send out particles and radiation at a steady rate. What is though of as empty space is not really empty, but it is filled with pairs of particles and anti particles. These appear together at some point of space and time, move apart, and then come together and annihilate each other. These particles and anti particles occur because a field, such as the fields that carry light and gravity, can't be exactly zero. That would mean that the value of the field, would have both an exact position (at zero), and an exact speed or rate of change (also zero). This would be against the Uncertainty Principle, just as a particle can't have both an exact position, and an exact speed. So all fields must have what are called, vacuum fluctuations. Because of the quantum behavior of nature, one can interpret these vacuum fluctuations, in terms of particles and anti particles, as I have described. These pairs of particles occur for all varieties of elementary particles. They are called virtual particles, because they occur even in the vacuum, and they can't be directly measured by particle detectors. However, the indirect effects of virtual particles, or vacuum fluctuations, have been observed in a number of experiments, and their existence confirmed. If there is a black hole around, one member of a particle anti particle pair may fall into the hole, leaving the other member without a partner, with which to annihilate. The forsaken particle may fall into the hole as well, but it may also escape to a large distance from the hole, where it will become a real particle, that can be measured by a particle detector. To someone a long way from the black hole, it will appear to have been emitted by the hole. This explanation of how black holes ain't so black, makes it clear that the emission will depend on the size of the black hole, and the rate at which it is rotating.
The radiation of a black hole will be otherwise independent of what went into the hole. It doesn't matter whether you throw television sets, diamond rings, or your worst enemies, into a black hole. What comes back out will be the same (what?? Nothing comes out of a black hole). These virtual black holes are so small, a hundred billion billion times smaller than the nucleus of an atom
Even the limited predictability of the Uncertainty Principle disappeared, when the effects of black holes were taken into account. The loss of particles and information down black holes meant that the particles that came out were random. One could calculate probabilities, but one could not make any definite predictions. Thus, the future of the universe is not completely determined by the laws of science, and its present state, as Laplace thought. God still has a few tricks up his sleeve.
Comment by the blogger: after reading this lecture, I think that even science is influenced by political and social common view of a certain era, the era of Einstein was still an era of belief and religion, now it's the era of man gods
Hawking's public lectures: http://www.hawking.org.uk/lectures/lindex.html
Hawking's universe: http://www.pbs.org/wnet/hawking/html/home.html
posted by nadia @ 9:42 PM
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