Shachar Shemesh <shac...@shemesh.biz> writes: > Dotan Cohen wrote: > > Oleg, I understood that the universe has 11 or so dimensions, and that > 5 or six can even be measured. But the wikipedia article that you > link to claims only 3+1. I have googled a bit but found only very > technical explanations, or baby facts with no explanations. Can you > sum it up for someone who is familiar with relativity, but is not a > physicist? Thanks.
Ouch! We need a new list - science for Linux geeks or sth like that. Mea culpa! Essential disclaimer: I am not, nor have I ever been, a string theorist. > I'll do my best as another non-physicist, and then Oleg (or anyone > else) can correct me where I'm wrong. <Shachar's response stripped, but *only* because anyone can find it in the archives - see below.> I will not attempt to address any of the points that Shachar mentioned, but the essence of his response is quite correct. Various numbers of dimensions come from string theories, superstring theories, membrane theories, and so on. We'll call them "string theories" collectively. You mention 11 dimensions, there have also been theories predicting 10, 26, 119 (or at least a hundred and something, I don't recall the details, and there have been quite a few of those), or whatever. These are mathematical theories that start from various symmetry considerations, and usually operate on mathematical constructs, be it 1-dimensional strings or multi-dimensional surfaces ("membranes", or "branes" for short). Observable phenomena, e.g., particles, are particular "resonances" or "eigenstates" corresponding to oscillations of those strings or membranes, similar to different musical notes corresponding to particular resonant states of a guitar or a violin or a piano string. This is where "strings" and "membranes" get their names from - they must be oscillating "lines" or "surfaces" to produce particles we can observe. Now, if a string or a membrane oscillates the oscillation has some energy and, by relativity, this energy can be related to the mass of the corresponding particle. Now you do the math to fit the observations. E.g., a photon, that travels with the speed of light, must be massless. It turns out that this can happen only if the string/membrane/whatever world has so many dimensions (the value of "so many" depends on the theory, it may be 11, or 26, or sth else). How do these theories reconcile the 10/11/26/115/etc. dimensions with the observed 3+1 of the "macro" world? They devised a notion that the extra dimensions are "compactified", i.e., in the other dimensions the world is so small that it cannot be measured, at least not at attainable energies (and at the required energies it is not clear to me if any theory predicts that Heisenberg's uncertainty principle can be overcome). Now, as Shachar wrote, this is all mathematics. To become physics, these theories must make predictions that can be empirically verified. Physics, unlike philosophy, is an empirical science. Unfortunately, the zillion and a half of various string theories predict observable effects at energies that are many orders of magnitude higher than anything modern particle accelerators can produce. In fact, the preferred method (beyond arguments related to mathematical elegance) of picking "most promising" theories out of the multitude is based on the minimal energy at which the theory predicts an observable effect. Mind you, they pick the theory that predicts an effect at the lowest energy as "promising" *not* because they think chances are it will be correct, but because it will be the first to check if and when they get enough billions or trillions to build an accelerator that is 100 times more powerful than the current most powerful one. This is part of the reason why these guys are so keen to build more and more powerful "colliders". So, to sum up, as far as physics, the empirical science, knows there are 3 spatial and 1 temporal dimensions. There are a zillion and a half complicated mathematical theories of various degrees of elegance that predict various number of dimensions (there is indeed a subclass that predicts 11), the extra dimensions must be "compactified" in order not to spook the imaginative (or not[1]) non-mathematicians. None of these theories makes any prediction that is practically verifiable at the current level of experimental technology. If and when the relevant experiments are performed either (some of) the theories will be rejected or we'll find out that the Universe is more fascinating than we thought. Until then you are welcome to retell your favourite version of theory vs. practice witticism. Now, if you'll excuse me, I have plans for tonight that are restricted to 3+1 dimensions. ;-) [1] Gauss said of one of his former students, "He became a poet, he didn't have enough imagination to become a mathematician." -- Oleg Goldshmidt | p...@goldshmidt.org _______________________________________________ Linux-il mailing list Linux-il@cs.huji.ac.il http://mailman.cs.huji.ac.il/mailman/listinfo/linux-il