Tensorman

Indeed, it is an arbitrary assertion which cannot be proved. There isn't any logical contradiction in the hypothesis that there isn't an upper bound to the number of particles in the universe.

The curved spacetime of general relativity doesn't need an explanation by some "real thing" (apart from the mass that causes the curvature) anymore than the 3-dimensional space of classical physics needs an explanation by some "real thing". It's only that we take the latter for granted, as we've in our life always experienced a 3-d space where Euclidean geometry applies accurately. We could as well ask: why has space just 3 dimensions? Why is its geometry Euclidean? We don't suppose that there is some "real thing" that causes this behavior, nevertheless it is part of reality, we never see a fourth or a fifth or whatever dimension, just the three we know. The desire to "explain" the curved geometry of GR is caused by the fact that it goes against our intuition, we think it's "obvious" that space is 3-dimensional and Euclidean and not curved and that time is an absolute, independent variable, but it is our intuition that is wrong, which is due to the fact that the direct effects of the curvature are not part of our everyday experience, as they are too small to be observed in daily life. So we tend to look for an explanation that describes the unintuitive theory in terms of the classical, intuitive theory with some extra factor added. Instead we should accept that reality isn't always in accordance with our intuition. In fact this is the same thing that makes Quantum Mechanics so difficult to understand, as we would like to rewrite it in classical terms that are in accordance with our intuition, which is doomed to failure, however.

I agree. I strongly advise against changing the name. There is no real disadvantage in keeping the name, that is only imagination.

The principle of relativity - that is, the physical laws should be the same in all intertial reference frames - combined with the constancy of the speed of light. From that the Lorentz equations follow automatically.

What Lorentz did was posing an ad hoc solution for the negative result of the MM experiment, that was expressed in his equations. The next thing he did, was trying to explain these with a primitive atomic theory (quantum mechanics with its precision to 12 decimal places was still far away), which was not very succesful. Of course that doesn't in any way diminish his genial contribution to the theory of relativity. Einstein's genial move was to find a much simpler explanation of the Lorentz equations, leading to his famous e = mc^2 equation and later to his graviational theory, of which the special theory is just a special case. That all many times experimentally confirmed over a century. The ether theory is really dead as a doornail.

It isn't nonsense, as the slowing down of the clocks is a real effect that will cause a permanent difference in elapsed time, even if the objects no longer move with respect to the observer. In other words, you can get physically younger than your grandchild by making a long trip through space with high speed. Of course this is in practice far beyond our current technology, but the principle has been experimentally verified.

At least some of them were connected to his writing. The octopus is indeed an illustration in Les travailleurs de la mer (and that scene was also the inspiration for the fight with the octopus in Jules Verne's Vingt mille lieues sous les mers, IIRC Verne even made a reference to Hugo that in his text). I have the complete novels by Hugo and they contain many of his illustrations. They are not great art, his drawings are a bit amateurish, but I wouldn't like to miss them. Apparently they are not in the translated versions. In Les misérables some of his illustrations are in fact funny caricatures of some of the characters in the book. I just browsed his Notre Dame de Paris, but I found no illustrations there (but I'll look more carefully later).

That time is different in moving systems and that this is not just some kind of "optical illusion" is proved by the fact that there is a measurable time lag that persists even if the frames are no longer moving with regard to each other. When someone is traveling through space with a speed that is close to the speed of light and comes back on Earth after say 10 years in his own time (he has physically aged 10 years) he may find that his son who remained on Earth is (physically) older than himself. Now this human experiment may be far beyond our current technology, but the effect does exist and has been demonstrated experimentally. How can you explain that with an aether theory? And for that matter, how does an aether theory explain the equivalence between mass and energy, the famous E = mc^2 equation?

Can you be a bit more explicit? In what way does Einstein's interpretation deny the notion of a metaphysically given reality?

What is wrong in Einstein's interpretation?

I've explained this already in post #160, which you ignore. You seem to be more interested in finding apparent contradictions by taking statements out of their context, looking for a gotcha, but you don't address the arguments themselves. You call that "seriously"? You think that an example with a Crystal Ball in a discussion about determinism deserves serious consideration? Again you're deliberately obtuse, so that I have to spell it out for you: of course when I talk about states of the computer this implies a given input. Then I have a suprise for you: Newtonian physics, relativistic physics and even chaos theory are completely deterministic theories. But of course you know better than all those dumb physicists. I've seen many intelligent, thoughtful reactions in this thread by people who take arguments seriously, but not from you. Yes, I know. Chaitin omega numbers and Solovay machines, fascinating stuff.

Of course it is a deterministic program. Why should that be a contradiction? Of course I mean a running computer, not one that is turned off or destroyed by an axe. I think I don't have to spell out such obvious conditions. If someone tells you that car X can attain a speed of 200 km/h, do you ask then: what about when the fuel tank of the car is empty?

You ignore the context of my statements. The first one refers to the prediction of a system in which the predictor is part of the system, which leads to the infinite loop and the essential impossibility of prediction (apart from the practical impossibility of using parameters which are known with infinite precision in a chaotic system and the external influence on small particles). The second example (playing dice) is a simple isolated system which is not sensitive to external influences (hurricanes excepted) in which the predictor is not part of the system. I'm not saying that deterministic systems are never predictable (then we wouldn't be able to build a working computer or any other machine), but that deterministic systems are not necessarily predictable. You see only a contradiction when you take my statements out of context.

Of course there is something wrong with such a program, that is exactly my point: as such a program couldn't work, prediction of future states such a deterministic system is impossible, that was the crux of my argument. A computer is a deterministic machine par excellence. The state of the machine at any time is determined by its previous state. If this were not so, no useful program would be possible. You couldn't perform the simplest of calculations on a non-deterministic machine, as you would get different outcomes every time you performed the same calculation.

In your analogous reasoning you keep ignoring an essential difference between the two cases, which I've mentioned before: while "life" is just a label we attach to certain complex systems, determinism is an observed property of physical systems that is independent of the size or the complexity of those systems, unless you pose some mystical intervention that for large systems mysteriously disables determinism. There isn't a shred of evidence for such a mysterious intervention, that some large systems seem to be indeterministic is due to the fact that it is practically impossible to describe those systems completely. I can illustrate that with another analogy: a famous quote by Einstein is "God doesn't play dice", where "playing dice" is a metaphor for randomness. Yet there is in fact nothing random in throwing a die: if we could measure all the parameters (velocity, position, mass, etc.) of the hand-die-table system accurately enough, we could in principle predict the outcome, as this is a deterministic system. As it is in practice impossible (perhaps it might be possible using a sophisticated throwing machine), we use the die as a generator of random outcomes. The randomness we observe is not a fundamental randomness however, it is the result of the in practice unpredictable variation of the parameters of a deterministic system.

Not for determinism in the brain. See for example: M. Tegmark, Importance of quantum decoherence in brain processes, Phys. Rev. E 61, 4194-4206 (2000), or Maximilian Schlosshauer, Decoherence and the Quantum-to-classical Transition, Ch. 9: Observations, the Quantum Brain and Decoherence, Springer 2007. Contradictions do not exist, but determinism does exist in reality. Your computer for example is a deterministic machine. The solution to the prediction paradox is simple: it is impossible to predict the future, even in principle. Determinism does not imply predictability. Even a simple classical and deterministic system like the molecules in an ideal gas is unpredictable. First it would be necessary to measure the parameters of the molecules with infinite precision, which is impossible. Second, even if we assume for the sake of argument that we could measure those parameters exactly, we cannot isolate the system from external influences. Borel showed already in 1914 that the gravitational effect of the displacement of a small rock at the distance of Sirius by a few centimeters would completely change the behavior of the individual gas molecules here on Earth, so we would have to know the parameters of the whole universe with infinite precision, which is of course impossible. The prediction paradox is easily solved: as the predictor is part of the system the future of which he wants to predict, he must also predict his own predictions as these may influence future events, and also those predictions, etc. This results in an infinite regress, or an infinite loop. That means that the time needed for the calculations to predict the future is infinite, which makes prediction of the state of the system at any time in the future impossible.

Apparently you don't understand the essential difference between the example of life and that of determinism. Life is an emergent property, it is defined as the property of certain complex systems consisting of inanimate parts that can grow, self-replicate etc. Such systems don't become inanimate by a detailed description in terms of its inanimate parts, as the term "life" refers to the whole system (or subsystems that are large enough, like cells) and not to the individual molecules. On the other hand determinism is a fundamental property of classical physical systems. If you combine two (three,.., many) deterministic systems the new system is necessarily also deterministic, unless you suppose that by merely combining them suddenly some mysterious non-deterministic element is created. However, that is mysticism and therefore rejected by science. That we do seem to observe non-determinism in complex systems is only the result of the fact that we have to use very incomplete data, in a full description it is still deterministic. Really, it isn't that difficult.

This analogy doesn't hold. The property of being alive is the result of a special configuration of inanimate particles. There is some arbitrariness where we draw the line between living parts and inanimate parts, but in general we can say that a cell is a living entity while it can grow, reproduce itself etc., using the DNA/RNA machinery that forms the basis of all life on Earth, while the individual molecules in the cell like the DNA molecule or a protein molecule are not alive. On the other hand, if we build a system consisting of deterministic subsystems then, no matter how complex the total system is, in a complete description it is still a deterministic system. Due to its enormous complexity the deterministic substrate is in general hidden to us (except when it is the subject of a specialized study done by neuroscientists) and therefore the total system may surprise us with unexpected actions. Conscious thoughts (that we observe by introspection) are not sufficient to determine future thoughts of the brain, they form an incomplete, reduced description that is not deterministic: a given state at that level of description does not contain sufficient information to determine a later state of the system. As we in daily life only deal with consciousness (our own and that of others) in terms of thoughts, we see only a non-deterministic system with "free will", but it would be wrong to conclude that therefore the system in a complete description (in terms of the fundamental building blocks) is also indeterministic. There is no contradiction between the non-deterministic character of the world of thoughts and the fact that it is a deterministic system in a complete description in terms of fundamental building blocks.

Merely thinking doesn't make it so, but that would be at least compatible with our knowledge of physics. But "freely choosing to focus" on a fact is in itself already a choice, so that's merely shifting the problem from one choice to a previous choice. I do not claim that I can prove that determinism exists. I only claim that the argument that determinism can't be true while we experience "free will" when we introspect, is not valid, as the determinism would be invisible to our introspection. That said, it's not true that there are no arguments for determinism. There is scientific evidence that the brain at the functional level (synapses, firing neurons etc.) can be treated as a classical system. Now all classical systems are deterministic systems (which should not be confused with predictable systems). Claiming that the brain is an exception is an extra hypothesis - and an extraordinary one at that. As I've shown, it is not a necessary hypothesis to explain our perception of "free will" and Occam's razor tells us that we should not multiply unnecessary hypotheses. That we still know very little about the processes in our brain that correspond to our thinking is not relevant, as the principle is quite general and doesn't depend on the specific details. It's the same principle that we use when we reject the claim of the construction of a working perpetual motion machine without knowing the details of that particular machine: the laws of thermodynamics are so strongly validated that there is no need to examine the details of the machine to reject the claim.

That is the crucial point. We may think that our choice might have been different, but that doesn't prove that it is so. Before we make our choice we cannot predict which choice we'll make and therefore all the possibilities seem still to be open. But in fact the decision process may be completely determined: we may weigh the merits of the different options, reasoning what the consequences of each choice will be. This weighing process will be influenced by our experience, memory, feelings, genetic constitution, current input via the senses, etc. Sometimes the process will be rather straightforward, while all factors strongly favor one particular outcome. In other cases the arguments and factors will be more balanced so that the choice is more difficult. Especially in the latter case we'll have a strong feeling that different options are possible. But this all is not in contradiction with the notion that the whole thinking process, including making a choice, is in fact a deterministic process. We cannot observe the inevitability of our thinking process, as observing is itself a thinking process and you'd have to observe that process too, etc., leading to an infinite regress. We can only reason about what we can consciously observe, and at that level the determinism is necessarily invisible, so a final choice may seem to appear out of the blue, while it is in fact determined by the processes of myriads of firing neurons.

The prediction of the Mercury perihelion precession (that is: the part that cannot be explained by Newtonian mechanics) follows from Einstein's field equations, i.e. his gravitational theory, in particular from the Schwarzschild solution for a spherical symmetric field around a star. But as Brian0918 remarked, the special theory with its time dilation and matter/energy equivalence is a special case of the general theory, you cannot accept general relativity without special relativity, a confirmation of the general theory is indirectly also a confirmation of the special theory.

There are two contrary effects: time in the GPS satellites runs slower (than on earth) while they move relative to the Earth (the well-known time dilation), and it runs faster while gravity up there is weaker. The clocks must be corrected for the combined effect (the gravity component dominates); with the calculated correction they work fine. See for example here.

That's no crap, but solid science. It has been experimentally verified many times. Belief has nothing to do with it.

It's both of course! There is no dichotomy. Just as a letter (or the radio waves of a broadcast) you receive is a fact and a carrier pigeon for information. Whether it originates from a natural source or from an intelligent source makes no difference in this respect.

That is an interesting question, that can be answered at two levels: (1) how do we know that the radio signal comes from outer space and not from a source on Earth? (2) If we know that its origin lies outside the solar system, how do we know that it comes from an intelligent source and that is isn't caused by some natural phenomenon? The first question isn't difficult: with our radio telescopes we can easily determine where the signal comes from - if it is from outer space, the position of the source will move with the apparent daily motion of the stars. The second question is more difficult to answer. Suppose it is a signal that is deliberately sent to announce the existence of an extraterrestrial intelligence, how could we recognize it as such? We can make a guess by thinking how we would announce our existence via a radio signal to possible extraterrestrial civilizations. The general consensus is that a mathematical approach is the best way. An extraterrestrial intelligence might be quite different from us, but one thing is certain: if they are advanced enough to listen to radio signals from outer space, they must have a knowledge of mathematics that is comparable to ours. They must know for example what prime numbers are and they'll probably know the characteristics of finite groups. Such knowledge can easily be coded, for example by enumerating the first 1000 prime numbers or the orders of the finite simple sporadic groups. A binary code will be understood universally, as it is the simplest code. There are systems for building a message, starting from scratch by showing a simple code, and use this to generate more complex codes. In the 1960's Hans Freudenthal designed such a language, which he called LINCOS. Suppose we receive a signal from outer space which we can decode with a simple decoding system into a list of the first 1000 prime numbers, how certain can we be that it comes from an intelligent source and that it is not the accidental result of a random signal? An analogy may be helpful here. Suppose in a bridge game, where the cards are supposed to be shuffled well before being dealt, we get the "perfect" bridge deal: every player has a complete suit in one color. We may then safely assume that this deal is not the result of a random shuffling, but that someone has been tampering with the cards. Why do we know that? After all the probability of the perfect deal is exactly the same as that of any other particular, average, deal. The point is that the perfect deal has a very special significance to us, it would for example be a good "fisherman's yarn" to tell, or it could be a joke. Even if we estimate the probability that someone will rig the cards for this reason as very small, it is still enormously larger (literally trillions of times) than the probability that this special deal will come up by chance, so our conclusion that someone has rigged the cards is warranted (you should never believe someone who tells you he got such a deal accidentally!). The same argument may be used when we receive information from an extraterrestrial source that we recognize as something very special. The difference is that we have no data for an estimate of the probability that an extraterrestrial intelligence exists and will announce its existence. But if the message seems to build up a system of communication in a way that is similar to LINCOS and if the amount of meaningful information that we can extract is large enough, the conclusion that it comes from an intelligent extraterrestrial source will become inescapable.