>The Will of the people decides what is right and >wrong in a Republic with strong Democratic ties. >If the majority of the public finds that there is >no place for Communism in America, then policy >should be made on that Will.
No... we have a Bill of Rights to guarantee that the majority of the public does *not* completely determine things. If 99.9% of the population wanted to exclude everyone with red hair, it wouldn't matter. The right to espouse communist views is protected by the 1st amendment. What you're saying is pretty scary.
You read a math text and find out that almost everything that post said is wrong. The definitions of simply connected and compact are, as others pointed out, not at all what the previous poster claimed they were.
mathworld.wolfram.com is generally a good reference for looking up definitions...
Uh... sort of. First of all, the cross product isn't just any outer product, it's an antisymmetrised one, more of a wedge product than a tensor product. Anyhow, you can certainly do similar things in other dimensions, but the objects you get won't all be "of the same type", in a loose way of speaking. Somewhat more precisely, only in 3 dimensions do we have that the spaces of 1-forms and 2-forms have the same dimension, so that if a and b are one forms, (a/\ b) can be somehow identified with another one form. Even in 3 dimensions there really isn't a canonical way to do this, which is why cross products end up needing an orientation (the whole right-hand rule thing, which is rather arbitrary).
I agree that Hatcher's book is good, although I'm just beginning to learn this stuff. We're using that as the text in Math 263 at Chicago - taught by J.P. May. May has a book as well, "A Concise Course in Algebraic Topology," which is highly categorical in its perspective. I'm struggling to figure out limits and colimits, so I'm afraid I haven't made it past the second chapter yet, but there seems to be a lot of good stuff in that book.
At a more basic level, Munkres "Topology" is good for point-set stuff, but also has some algebraic topology.
It isn't about algebraic topology, but I very highly recommend Milnor's "Topology from the Differentiable Viewpoint" and his book on Morse Theory. Guillemin & Pollack also give a very good treatment of differential topology. And Thurston's book on three-dimensional geometry and topology is awesome, but I think I would have had a very hard time getting through much of it without the class I took on it in the fall.
This reminds me of another anecdote - which I believe is true. I don't recall who it is about, though. The story is that at a seminar, a respected mathematician was giving a proof when someone questioned one step. The speaker said, "it is clear," and moved on. A bit later, he turned back to the questioner and said "it can be shown," then continued once more with the talk. A few minutes later, he paused, thought for a few seconds, turned to the questioner, and said "It is well-known." Moving on with the argument, a few minutes later he paused again, turned once more to the questioner, and said: "It is wrong."
It's always easy to take things for granted that look obvious; to some extent one always has to do this. The trick is knowing when you can do it and be right.
Although relativistic physics does predict a sort of "inherently linked" spacetime, as you say, it is still the case, in a well-defined way, that this spacetime has 3 space + 1 time dimensions. It is not necessarily possible that we can find some global time coordinate and dissect the spacetime into 3-dimensional space "slices", but it is still true that locally spacetime always resembles Minkowski space. The Lorentz group is SO(3,1), the metric has signature (3,1); these things don't change. There is no absolute time or space, but counting the number of dimensions of each type is always possible. We tend to say that spacetime is 3+1 dimensional, but this is not intended to suggest that we can find some sort of global coordinate system with 3 space and 1 time coordinates.
Ordinary non-relativistic quantum mechanics, on the other hand, maintains the idea of a separate time dimension while treating spatial coordinates as operators. It's only in relativistic QM, and quantum field theory (QFT), that quantum effects and special relativity are reconciled. But this does not take general relativity into account, so QFT actually maintains the idea of global (but not absolute!) space + time coordinates, in a certain sense. We can't determine the position of a particle exactly, however (and there are problems with constructing "time-of-arrival" operators... but I'm getting in over my head with that comment.)
Also, there are elementary particles in quantum physics. We might never be completely sure that at some huge energy scale, the particles we think are elementary are not composite, but there are certainly particles which, from the standpoint of current theory, seem to be elementary.
>Seriously, I'm amazed that gravity hasn't been
>experimented with on smaller scales. Would that be
>something that requires zero-g and objects in a
>vacuum, or do you get other problems, like
>electrostatic/electromagnetic forces or even
>gravity of surrounding objects on those scales that
>make gravity difficult to measure directly at that
>resolution?
Apparently the current limit is now somewhat less than a millimeter, but still on the order of a millimeter. Yes, it is very difficult to test. A group at the University of Washington has developed small-scale gravity tests; see http://www.npl.washington.edu/eotwash/shortr.html for an explanation.
Basically, you have the right idea; it's hard to screen out all of the other effects at a scale that small, which is why studies at the millimeter scale are extremely difficult.
>1 - If a charged particle drops into a black hole
>it has to change black hole's chargebecause of
>conservation.
This is correct - charge, momentum, and angular momentum are all globally conserved, so far as we can tell.
Note that "mass" is not *really* conserved - this is especially obvious in certain decays of elementary particles (i.e., electron+positron -> photon+photon; you end up with 0 mass). What *is* conserved is the energy-momentum four-vector (E, p), and for any one particle E^2 - p^2 = m^2. Mass only is conserved in the nonrelativistic limit. But I digress...
>2 - It also happens to be the case that no
>information can be obtained from (if you excuse
>the term) "inside of" event horizon,
This is basically true: no information is obtained. It is said that "black holes have no hair." But they do have a few properties - charge, mass, and angular momentum are essentially it. (Temperature and entropy also, but these depend on mass.)
>determine mass changes and angular momentum
>changes because it changes the shape and size of
>event horizon.
This is somewhat true; I'm not sure I would have expressed it in terms of "shape and size." I have to admit my knowledge of the black hole solutions in general relativity is fairly rudimentary, so I'm not sure in exactly what way that is true, but I think it is. There is a metric - called the "Kerr black hole" - that describes black hole solutions that spin; I think when they have charge there is another term. But the thing to note is that the metric of spacetime is actually different for different values of black hole spin, or charge. You'll also see a change in the electromagnetic potential (phi, A) outside the black hole for the charged case. So there are external effects.
>So how can charge be preserved if it doesn't
>affect event horizons properties? How can you
>tell total charge of a black hole?
The simple answer is: Maxwell's equations. Anything with charge, even a black hole, will change your electromagnetic potentials.
In other words, black holes tend to wear their charge, angular momentum, and mass "on the outside", in some sense.
The essential reason is that the "fundamental Planck scale" is ~ 1 TeV in LED (large extra dimension) theories. Gravity is a "bulk" field (propagates in all dimensions) while the standard model fields are localized, so this affects them differently. The gist of it is, if you put enough energy in a small enough region, you make a black hole. If there are more dimensions, the size of that region is bigger, so it's not as difficult to make black holes.
Let me try to outline what's going on: I'm getting this from "Black hole production in TeV-scale gravity, and the future of high energy physics" by Steven Giddings (hep-ph/0110127 on arxiv.org). It's a nice article to start with, if you want to dig into the literature on this.
(By the way, this is using the "warped" extra dimension model but the general ones are similar.)
The Planck mass in D dimensions is M_p^(D-2) = (2 pi)^(D-4) / (4pi G_D) with G_D the gravitation constant. It turns out (M_4 / M_p)^2 = (M_p)^(D-4)V_{w}, with V_{w} the "warped volume" of the extra dimensions. (I'm not being very rigorous here; in fact this is how the volume is defined, and the ratio is given by a certain integral in terms of the warped metric.) This is essentially a sort of "Gauss law" argument, over the extra dimensions.
Now, let's consider a black hole with radius r_h much less than the geometrical scale R_c of the extra dimensions. It turns out that for a black hole of mass M, spin J, in the J = 0 limit, we have r_h = 2 [C M / M_p^(D-2) ]^[1 / (D-3)] where C is some constant in terms of D that I don't want to bother writing. The Hawking temperature looks like T_h = (D-3)/(4pi r_h). This description is valid roughly for M_p > 1.1 TeV -.8 TeV for D = 6 - 10.
Black hole cross-section was assumed to be geometrical (pi (r_h)^2), but as I mentioned in another post this is questioned (look up papers by Voloshin - but Giddings questions those), and there may be an exponential suppression. Anyhow, the important point is that, once you take all this into account, you get that the cross section sigma grows when D is larger, i.e. you don't have to put energy into as small a region if there are more dimensions.
>antimatter is not a very exotic thing, normal
>matter with reverse charge reverse spin. Once in
>the blackhole there is no telling whether what fell
>was matter or antimatter, they all behave the same
>(increase black hole's mass, that is, and nothing
>else.)
Sorry for being so pedantic, but they also affect its charge and angular momentum. So you're essentially right, except that if you know, for instance, that either an electron or positron fell into a black hole, and you could somehow monitor its charge, you could distinguish which.
Actually, there are some people working on combinatorial quantum gravity models, though I don't know enough about them to be very informative. Look up "spin networks" or "spin foams."
Detection of signatures of large extra dimensions wouldn't actually offer direct experimental evidence for string theory. Yes, string theory predicts extra dimensions, but it isn't necessarily the only theory that does.
Direct evidence for string theory at any point in the near future is highly doubtful. We just can't get good evidence of such high energy scales. We could see associated effects, like extra dimensions or supersymmetry, but those don't necessarily imply string theory.
These are actually completely different theories. What you call "multiple universes" sounds a lot like the Everett "many worlds" interpretation of quantum mechanics, i.e. that we can think of "wave function collapse" as a branching of the universe into different possibilities. Most people tend to think of this more as a way of looking at QM rather than an actual claim that other "universes" exist, and it certainly doesn't suggest any way of making contact with these other "universes."
The idea of extra dimensions, on the other hand, simply implies that there are more spatial dimensions in the universe than it appears. Of course, there seem to be 3, plus one time dimension, but it's possible there are others that are visible on in small-scale (high-energy) effects. This has nothing to do with other universes.
>Is this detecting the Hawking radiation from an
>evaporating hole, or is it detecting other effects?
Yes, this is essentially what happens. The decay is actually somewhat more complicated; there is an initial "balding" phase in which the black hole loses its hair, along with a "spin-down" phase... after this, there's a very quick evaporation with high sphericity. Go to http://arxiv.org and search for "black hole production"; some recent papers by Giddings have details. It was believed for a while that the cross-section is geometric, which would lead to a good chance of detecting these in the next generation of colliders if large extra dimension (LED) models are correct. A paper by Voloshin indicates, on the other hand, that the cross-section is really exponentially suppressed by the black hole action. I'm not sure this has quite been settled completely.
The basic idea behind all this, by the way, is that there may be extra dimensions which are large compared to the Planck scale (up to a millimeter in size - that's about as far as gravity has been probed!). Gravity would be a field in "the bulk", that is it propagates in all the dimensions, but the standard model fields are localized on some sort of 4-dimensional "brane." There are actually a couple of different models with large extra dimensions - one is the ADD model (Arkani-Hamed, Dimopolous, Dvali) and another is the Randall-Sundrum or "warped extra dimension" model. Searching on arxiv.org for any of these names should get you links to the papers.
The basic reason for looking into all of this is the hierarchy problem, namely that the gravitational force is far weaker than the other forces. The electroweak scale is on the order of one TeV (= trillion electron volts, where one electron volt is about 1.6*10^-19 Joules). Gravity, on the other hand, is associated with a much higher energy scale. To explain this, the ADD model proposed that maybe the fundamental Planck scale is actually on the order of a TeV, like the electroweak scale. In other words, they solve the hierarchy problem by saying there is no hierarchy. Gravity propagates in more dimensions, so that its effect in our four-dimensional part of the universe looks much weaker. The other fields are localized in such a way that this ratio doesn't take any effect for them, so we see them at the "true" Planck scale on the order of a TeV.
It just so happens that the TeV scale is what we're looking at with current colliders, which is why there's so much interest in this lately. But cosmic rays give an alternate approach. Keep in mind that these ideas are very speculative, but still worth looking into.
>You seem to be saying that we need 2^N amount of
>space to store the spins? No we don't. You said
>it yourself: there are 2^N possible values that
>can be stored, and this requires precisely N
>amount of storage space. Say we have ten
>particles, that requires ten bits to store the
>spins, not 2^10 (1024) bits!.
Oops... I was in a hurry:-) Still, it's a large number of particles, so N is huge, and when you start addressing trying to also store their positions and velocities in any sort of detail (which is a bit of a problem in itself, due to Heisenberg) you see that even obtaining the data, much less storing them, is a bit of a problem. Not to mention that you still have to transfer that information to the site where the object is to be reconstructed, which takes finite time, sometimes large finite time.
>I guess the only thing preventing us from moving
>big stuff really comes down to the equipment and
>being able to handle the massive amount of data
>that would be generated in a 'timely' fashion.
Those are two major problems; there are plenty of others. There is a *huge* difference in "transporting" single photons and transporting larger objects. A photon has essentially two possible states (the helicity; left-handed or right-handed). Let's suppose all we needed was such spin information from every particle in a person's body in order to transport them. Try figuring out how many megabytes of information that is: we have 2^N possible values, where N is the number of particles. Divide by 2^23 to convert to megabytes. 23 is a lot smaller than N, so we may as well say it's still 2^N. N is really, really big. And now we consider that we need to get a lot more information right. Like the relative positions and velocities of the particles. We wouldn't want to transport someone and find his hand is flying away from him, would we? And how are we to extract this kind of information in the first place? Sure, entanglement is nice for say 5 particles, and for dealing with simple quantum states. It doesn't do you much good for much larger numbers of particles; and you generally have to have things beginning in the same place to entangle them.
I'm no expert in this particular area, but I think I understand basic quantum mechanics well enough to tell you that transporters are, almost certainly, never going to happen.
>>Particles that can all have the same EXACT
>>state, in quantum mechanical terms, are called.
>>They fill and occupy available states in a
>>certain way, described by a Bose distribution.
>
>Um, no. Bosons are (by definition) particles
>with integer spin (0, +1, -1, etc.).
The two definitions are more or less equivalent, according to a result known as the "spin-statistics theorem." Let me try to give a rough explanation of what this means (but not why it's true, because that's fairly complicated). Particles with integer spins (bosons) have Bose-Einstein statistics (note this is not quite the same as saying they form Bose-Einstein condensates). Bose-Einstein statistics mean, essentially, that when you exchange two of them, you get no effect. Fermi-Dirac statistics, on the other hand, have anticommuting particles so that exchanging two of them gives you a minus sign. Of course, this is implies that xx = -xx = 0, so you can never have two particles in exactly the same state when they obey Fermi-Diract statistics (that's the Pauli exclusion principle). The spin-statistics theorem assures us that particles obeying Fermi-Dirac statistics have half-integer spins, i.e., are fermions.
You're only partially right. Quantum gravity may be at a much higher energy scale, but we can still begin looking for signs of things like large extra dimensions. Or, for that matter, supersymmetry, which is of course fairly important for deciding whether or not string theorists are correct about things.
>but gain this could still turn out to be a total
>failure. and thats a hell of a lot of energy
>they ae using to make this mini black hole. So
>no matter what why you want to look at it (black
>hole taking out the generator, Overload lead to
>explosion) there is a lot of risk here. And
>thats what I want to get across.
There is no threat. First, a few hundred GeV is not a lot of energy. It is a lot relative to the masses of fundamental particles (proton mass is ~ 1 GeV) but not compared to the sorts of energy scales you're used to dealing with on an everyday basis. Second, the goal of the accelerator is *not* to create a black hole, but to probe new physics at this high energy scale, like (hopefully) the Higgs mechanism (giving us a better understanding of electroweak symmetry breaking), and (again, hopefully) supersymmetry. There are many very good signs that we will learn a lot about physics in these energy scales, gaining insight into mechanisms that were previously out of the reach of our colliders.
Electron-positron colliders are in some ways cleaner (in terms of the data we get from them) than proton-antiproton colliders (like the Tevatron at Fermilab or the planned LHC at CERN). The problem with building them is they must be linear; particles moving in a circle lose energy (it's called synchrotron radiation), and since electrons are so light they lose a *lot* of energy, so we can't use them in circular colliders like we can protons. One possible future alternative is a muon collider; muons are heavy enough to not emit much synchrotron radiation, so we could use them in a future collider, and the physics of muons is much like that of electrons, so we keep the "cleanness." This is farther in the future, though. One difficulty is that muons are harder to produce than electrons or protons; one way might be hitting a fixed target with a beam to produce pions, which then decay into muons.
Anyway, my point is that the physics going on here is fairly well constrained by what we already know, so no disasters will happen. We will learn about physics in a bit more detail than we currently know about it, though, and a linear electron-positron collider has advantages that other types of colliders we could currently build don't. (Of course, it has its disadvantages too, but getting data from multiple kinds of experiments is important to be able to understand the results). There is absolutely no threat of a "mini black hole" eating the Earth, or the collider, or much of anything else. There's no sense worrying about disasters here. The decision to make is whether public funds should be spent on basic research, not on any dangers of this research.
>This doesn't make much sense. Say, for example,
>our sun suddenly collapsed into a black hole.
>Now, correct me if I'm wrong, but it would still
>have the same gravitational pull. Just because
>you make things smaller does not mean their mass
>increases.
That's right. People are worrying over nothing. Of course, there are big differences very near the black hole, but not at any reasonable distance scale. Tiny black holes aren't much of a threat to anything.
Don't give in to ignorance and hatred
on
More On Tragedy
·
· Score: 2
I know probably no one will read this, but I felt like I should write it nonetheless. First, my condolences to all those who know people who were lost in the disasters Tuesday. I'm fairly sure no one that I know was near those areas, but still I can never remember being so shocked and sickened. The thing that bothers me most today, though, are reports of ignorant Americans who are terrorizing innocent Islamic citizens in America. The local news here in Louisville carried a story of a local Islamic woman who was told by the owner of a store that he was going to get a gun and if she didn't leave by the time he returned he would shoot her. The woman, of course, was completely innocent; in fact her sister was a victim of the attack on the World Trade Center. This sort of ignorant hatred disgusts me. In its own way, although on a smaller scale, this is just as evil and reprehensible as the terrorists attacks themselves. No form of bigotry should be tolerated. Let us judge the terrorists by their actions, not by their religious beliefs. And remember that even flag-waving, apparently patriotic citizens of the U.S. are just as much enemies of our country if they turn on their fellow citizens.
>KMBZ radio reports Kansas City, MO has gas at
>$5/gallon, and another of $4/gallon in
>Louisville, KY.
Here in Louisville, gas is not *that* expensive. On the other hand, rumors of impending gas price hikes did lead to it being almost impossible to drive anywhere because of all the people trying to get gas in fear of it going up. Some of the outlying towns in southern Indiana did have higher gas prices, according to the local news (they showed $2.65 at some places; I don't know if it was more elsewhere). The mayor made a statement earlier that gas prices will be kept from skyrocketing, and that any reports of price-gouging will be investigated. The real problem isn't the price, it's that people aren't keeping their heads and acting sensibly about the rumors.
Let's all try to use a little caution in discriminating rumors from fact. I was amazed by the reports and footage today of how New Yorkers acted calmly and so many were able to evacuate the WTC. Just think how much worse this all could have been if people didn't keep their wits about them. We all need to keep that in mind, to avoid economic consequences or hasty assumptions about reprisals.
And, as with everyone in the U.S. and most of the world right now, my condolences to all those who have been affected by this tragedy. I can't find the words to express how angry and shocked I am right now.
>Unfortunately, recent boson precession measurements show the Standard Model is wrong. Oh well, it's still kinda nice
>to explain mass. Even in a dead model!
I don't believe this is "unfortunate" and it certainly isn't a bad thing for Fermilab. In addition to looking for the Higgs, there will be searches for new physics (i.e. physics beyond the standard model) in Fermilab run 2 data, just as in run 1. SUSY (supersymmetric) Higgs possibilities will be examined as well as the standard model Higgs. And in general, most physicists have thought that the standard model was inadequate, hence all of the theoretical work on SUSY, superstring theory, additional extended spatial dimensions, and other ways of going beyond the standard model.
You said "boson precession measurements." I assume you're alluding to the muon g-2 experiment? I believe they claim 99% confidence for a value that does not match the standard model. While that is compelling, it's just not enough sigmas to be decisive.
A couple of other notes... I'm just an undergrad, so people with more experience in physics can feel free to correct me:
Don't expect to see an announcement of the Higgs discovery right away. It will take time to collect enough data for a "discovery," although I suppose Higgs-like events could show up relatively soon. Also, I think the Higgs is harder to detect in p-pbar collisions than in e+ e- collisions (as at LEP) because the decay modes leading to the Higgs are closer to some background processes. But perhaps someone who knows more about this could explain.
And last, a technical note for all the Slashdotters who think every article should relate to Linux. Most of the work being done at Fermilab is on Linux, specifically Fermilab Linux, which is based on RedHat. For the CDF experiment, the Run 1 code was written in Fortran, but most Run 2 code is in C++. There are a number of modules which process event data, and TCL scripts are used to set module parameters and the order in which modules are run. ROOT is used to interactively run C++ scripts for data analysis based on the output of these modules. I don't know much about how D0 operates but I believe it's similar.
zpengo wrote: Linux has brought together mortal enemies, and has promoted a spirit of peace, love, and understanding. (Or something like that).
Not quite. MacOS X isn't Linux; it's a BSD system. Still, I think you're right, the increased portability of software to the Mac hardware will be nice.
Cire wrote: (I'm not a coder) But... Why can't someone port Xlib over to macos X? It's got all of the unix goodies, like gcc and emacs built in. How hard would it be?
I think that is essentially what has already been done. Xlib requires an X server, though. That was the original poster's point: X would run much faster on MacOS X if, rather than working the way X normally does and going through a server, it just called MacOS APIs directly. This would lose the advantage of X's network features, but a lot of people don't use those anyway.
Slashdot Mirror
>The Will of the people decides what is right and
>wrong in a Republic with strong Democratic ties.
>If the majority of the public finds that there is
>no place for Communism in America, then policy
>should be made on that Will.
No... we have a Bill of Rights to guarantee that the majority of the public does *not* completely determine things. If 99.9% of the population wanted to exclude everyone with red hair, it wouldn't matter. The right to espouse communist views is protected by the 1st amendment. What you're saying is pretty scary.
You read a math text and find out that almost everything that post said is wrong. The definitions of simply connected and compact are, as others pointed out, not at all what the previous poster claimed they were.
mathworld.wolfram.com is generally a good reference for looking up definitions...
Uh... sort of. First of all, the cross product isn't just any outer product, it's an antisymmetrised one, more of a wedge product than a tensor product. Anyhow, you can certainly do similar things in other dimensions, but the objects you get won't all be "of the same type", in a loose way of speaking. Somewhat more precisely, only in 3 dimensions do we have that the spaces of 1-forms and 2-forms have the same dimension, so that if a and b are one forms, (a /\ b) can be somehow identified with another one form. Even in 3 dimensions there really isn't a canonical way to do this, which is why cross products end up needing an orientation (the whole right-hand rule thing, which is rather arbitrary).
I agree that Hatcher's book is good, although I'm just beginning to learn this stuff. We're using that as the text in Math 263 at Chicago - taught by J.P. May. May has a book as well, "A Concise Course in Algebraic Topology," which is highly categorical in its perspective. I'm struggling to figure out limits and colimits, so I'm afraid I haven't made it past the second chapter yet, but there seems to be a lot of good stuff in that book.
At a more basic level, Munkres "Topology" is good for point-set stuff, but also has some algebraic topology.
It isn't about algebraic topology, but I very highly recommend Milnor's "Topology from the Differentiable Viewpoint" and his book on Morse Theory. Guillemin & Pollack also give a very good treatment of differential topology. And Thurston's book on three-dimensional geometry and topology is awesome, but I think I would have had a very hard time getting through much of it without the class I took on it in the fall.
This reminds me of another anecdote - which I believe is true. I don't recall who it is about, though. The story is that at a seminar, a respected mathematician was giving a proof when someone questioned one step. The speaker said, "it is clear," and moved on. A bit later, he turned back to the questioner and said "it can be shown," then continued once more with the talk. A few minutes later, he paused, thought for a few seconds, turned to the questioner, and said "It is well-known." Moving on with the argument, a few minutes later he paused again, turned once more to the questioner, and said: "It is wrong."
It's always easy to take things for granted that look obvious; to some extent one always has to do this. The trick is knowing when you can do it and be right.
Although relativistic physics does predict a sort of "inherently linked" spacetime, as you say, it is still the case, in a well-defined way, that this spacetime has 3 space + 1 time dimensions. It is not necessarily possible that we can find some global time coordinate and dissect the spacetime into 3-dimensional space "slices", but it is still true that locally spacetime always resembles Minkowski space. The Lorentz group is SO(3,1), the metric has signature (3,1); these things don't change. There is no absolute time or space, but counting the number of dimensions of each type is always possible. We tend to say that spacetime is 3+1 dimensional, but this is not intended to suggest that we can find some sort of global coordinate system with 3 space and 1 time coordinates.
Ordinary non-relativistic quantum mechanics, on the other hand, maintains the idea of a separate time dimension while treating spatial coordinates as operators. It's only in relativistic QM, and quantum field theory (QFT), that quantum effects and special relativity are reconciled. But this does not take general relativity into account, so QFT actually maintains the idea of global (but not absolute!) space + time coordinates, in a certain sense. We can't determine the position of a particle exactly, however (and there are problems with constructing "time-of-arrival" operators... but I'm getting in over my head with that comment.)
Also, there are elementary particles in quantum physics. We might never be completely sure that at some huge energy scale, the particles we think are elementary are not composite, but there are certainly particles which, from the standpoint of current theory, seem to be elementary.
>Seriously, I'm amazed that gravity hasn't been
>experimented with on smaller scales. Would that be
>something that requires zero-g and objects in a
>vacuum, or do you get other problems, like
>electrostatic/electromagnetic forces or even
>gravity of surrounding objects on those scales that
>make gravity difficult to measure directly at that
>resolution?
Apparently the current limit is now somewhat less than a millimeter, but still on the order of a millimeter. Yes, it is very difficult to test. A group at the University of Washington has developed small-scale gravity tests; see http://www.npl.washington.edu/eotwash/shortr.html for an explanation.
Basically, you have the right idea; it's hard to screen out all of the other effects at a scale that small, which is why studies at the millimeter scale are extremely difficult.
>1 - If a charged particle drops into a black hole
>it has to change black hole's chargebecause of
>conservation.
This is correct - charge, momentum, and angular momentum are all globally conserved, so far as we can tell.
Note that "mass" is not *really* conserved - this is especially obvious in certain decays of elementary particles (i.e., electron+positron -> photon+photon; you end up with 0 mass). What *is* conserved is the energy-momentum four-vector (E, p), and for any one particle E^2 - p^2 = m^2. Mass only is conserved in the nonrelativistic limit. But I digress...
>2 - It also happens to be the case that no
>information can be obtained from (if you excuse
>the term) "inside of" event horizon,
This is basically true: no information is obtained. It is said that "black holes have no hair." But they do have a few properties - charge, mass, and angular momentum are essentially it. (Temperature and entropy also, but these depend on mass.)
>determine mass changes and angular momentum
>changes because it changes the shape and size of
>event horizon.
This is somewhat true; I'm not sure I would have expressed it in terms of "shape and size." I have to admit my knowledge of the black hole solutions in general relativity is fairly rudimentary, so I'm not sure in exactly what way that is true, but I think it is. There is a metric - called the "Kerr black hole" - that describes black hole solutions that spin; I think when they have charge there is another term. But the thing to note is that the metric of spacetime is actually different for different values of black hole spin, or charge. You'll also see a change in the electromagnetic potential (phi, A) outside the black hole for the charged case. So there are external effects.
>So how can charge be preserved if it doesn't
>affect event horizons properties? How can you
>tell total charge of a black hole?
The simple answer is: Maxwell's equations. Anything with charge, even a black hole, will change your electromagnetic potentials.
In other words, black holes tend to wear their charge, angular momentum, and mass "on the outside", in some sense.
The essential reason is that the "fundamental Planck scale" is ~ 1 TeV in LED (large extra dimension) theories. Gravity is a "bulk" field (propagates in all dimensions) while the standard model fields are localized, so this affects them differently. The gist of it is, if you put enough energy in a small enough region, you make a black hole. If there are more dimensions, the size of that region is bigger, so it's not as difficult to make black holes.
.8 TeV for D = 6 - 10.
Let me try to outline what's going on: I'm getting this from "Black hole production in TeV-scale gravity, and the future of high energy physics" by Steven Giddings (hep-ph/0110127 on arxiv.org). It's a nice article to start with, if you want to dig into the literature on this.
(By the way, this is using the "warped" extra dimension model but the general ones are similar.)
The Planck mass in D dimensions is M_p^(D-2) = (2 pi)^(D-4) / (4pi G_D) with G_D the gravitation constant. It turns out (M_4 / M_p)^2 = (M_p)^(D-4)V_{w}, with V_{w} the "warped volume" of the extra dimensions. (I'm not being very rigorous here; in fact this is how the volume is defined, and the ratio is given by a certain integral in terms of the warped metric.) This is essentially a sort of "Gauss law" argument, over the extra dimensions.
Now, let's consider a black hole with radius r_h much less than the geometrical scale R_c of the extra dimensions. It turns out that for a black hole of mass M, spin J, in the J = 0 limit, we have r_h = 2 [C M / M_p^(D-2) ]^[1 / (D-3)] where C is some constant in terms of D that I don't want to bother writing. The Hawking temperature looks like T_h = (D-3)/(4pi r_h). This description is valid roughly for M_p > 1.1 TeV -
Black hole cross-section was assumed to be geometrical (pi (r_h)^2), but as I mentioned in another post this is questioned (look up papers by Voloshin - but Giddings questions those), and there may be an exponential suppression. Anyhow, the important point is that, once you take all this into account, you get that the cross section sigma grows when D is larger, i.e. you don't have to put energy into as small a region if there are more dimensions.
>antimatter is not a very exotic thing, normal
>matter with reverse charge reverse spin. Once in
>the blackhole there is no telling whether what fell
>was matter or antimatter, they all behave the same
>(increase black hole's mass, that is, and nothing
>else.)
Sorry for being so pedantic, but they also affect its charge and angular momentum. So you're essentially right, except that if you know, for instance, that either an electron or positron fell into a black hole, and you could somehow monitor its charge, you could distinguish which.
Actually, there are some people working on combinatorial quantum gravity models, though I don't know enough about them to be very informative. Look up "spin networks" or "spin foams."
Detection of signatures of large extra dimensions wouldn't actually offer direct experimental evidence for string theory. Yes, string theory predicts extra dimensions, but it isn't necessarily the only theory that does.
Direct evidence for string theory at any point in the near future is highly doubtful. We just can't get good evidence of such high energy scales. We could see associated effects, like extra dimensions or supersymmetry, but those don't necessarily imply string theory.
These are actually completely different theories. What you call "multiple universes" sounds a lot like the Everett "many worlds" interpretation of quantum mechanics, i.e. that we can think of "wave function collapse" as a branching of the universe into different possibilities. Most people tend to think of this more as a way of looking at QM rather than an actual claim that other "universes" exist, and it certainly doesn't suggest any way of making contact with these other "universes."
The idea of extra dimensions, on the other hand, simply implies that there are more spatial dimensions in the universe than it appears. Of course, there seem to be 3, plus one time dimension, but it's possible there are others that are visible on in small-scale (high-energy) effects. This has nothing to do with other universes.
>Is this detecting the Hawking radiation from an
>evaporating hole, or is it detecting other effects?
Yes, this is essentially what happens. The decay is actually somewhat more complicated; there is an initial "balding" phase in which the black hole loses its hair, along with a "spin-down" phase... after this, there's a very quick evaporation with high sphericity. Go to http://arxiv.org and search for "black hole production"; some recent papers by Giddings have details. It was believed for a while that the cross-section is geometric, which would lead to a good chance of detecting these in the next generation of colliders if large extra dimension (LED) models are correct. A paper by Voloshin indicates, on the other hand, that the cross-section is really exponentially suppressed by the black hole action. I'm not sure this has quite been settled completely.
The basic idea behind all this, by the way, is that there may be extra dimensions which are large compared to the Planck scale (up to a millimeter in size - that's about as far as gravity has been probed!). Gravity would be a field in "the bulk", that is it propagates in all the dimensions, but the standard model fields are localized on some sort of 4-dimensional "brane." There are actually a couple of different models with large extra dimensions - one is the ADD model (Arkani-Hamed, Dimopolous, Dvali) and another is the Randall-Sundrum or "warped extra dimension" model. Searching on arxiv.org for any of these names should get you links to the papers.
The basic reason for looking into all of this is the hierarchy problem, namely that the gravitational force is far weaker than the other forces. The electroweak scale is on the order of one TeV (= trillion electron volts, where one electron volt is about 1.6*10^-19 Joules). Gravity, on the other hand, is associated with a much higher energy scale. To explain this, the ADD model proposed that maybe the fundamental Planck scale is actually on the order of a TeV, like the electroweak scale. In other words, they solve the hierarchy problem by saying there is no hierarchy. Gravity propagates in more dimensions, so that its effect in our four-dimensional part of the universe looks much weaker. The other fields are localized in such a way that this ratio doesn't take any effect for them, so we see them at the "true" Planck scale on the order of a TeV.
It just so happens that the TeV scale is what we're looking at with current colliders, which is why there's so much interest in this lately. But cosmic rays give an alternate approach. Keep in mind that these ideas are very speculative, but still worth looking into.
>You seem to be saying that we need 2^N amount of
:-) Still, it's a large number of particles, so N is huge, and when you start addressing trying to also store their positions and velocities in any sort of detail (which is a bit of a problem in itself, due to Heisenberg) you see that even obtaining the data, much less storing them, is a bit of a problem. Not to mention that you still have to transfer that information to the site where the object is to be reconstructed, which takes finite time, sometimes large finite time.
>space to store the spins? No we don't. You said
>it yourself: there are 2^N possible values that
>can be stored, and this requires precisely N
>amount of storage space. Say we have ten
>particles, that requires ten bits to store the
>spins, not 2^10 (1024) bits!.
Oops... I was in a hurry
Thanks for pointing out that mistake.
>I guess the only thing preventing us from moving
>big stuff really comes down to the equipment and
>being able to handle the massive amount of data
>that would be generated in a 'timely' fashion.
Those are two major problems; there are plenty of others. There is a *huge* difference in "transporting" single photons and transporting larger objects. A photon has essentially two possible states (the helicity; left-handed or right-handed). Let's suppose all we needed was such spin information from every particle in a person's body in order to transport them. Try figuring out how many megabytes of information that is: we have 2^N possible values, where N is the number of particles. Divide by 2^23 to convert to megabytes. 23 is a lot smaller than N, so we may as well say it's still 2^N. N is really, really big. And now we consider that we need to get a lot more information right. Like the relative positions and velocities of the particles. We wouldn't want to transport someone and find his hand is flying away from him, would we? And how are we to extract this kind of information in the first place? Sure, entanglement is nice for say 5 particles, and for dealing with simple quantum states. It doesn't do you much good for much larger numbers of particles; and you generally have to have things beginning in the same place to entangle them.
I'm no expert in this particular area, but I think I understand basic quantum mechanics well enough to tell you that transporters are, almost certainly, never going to happen.
>>Particles that can all have the same EXACT
>>state, in quantum mechanical terms, are called.
>>They fill and occupy available states in a
>>certain way, described by a Bose distribution.
>
>Um, no. Bosons are (by definition) particles
>with integer spin (0, +1, -1, etc.).
The two definitions are more or less equivalent, according to a result known as the "spin-statistics theorem." Let me try to give a rough explanation of what this means (but not why it's true, because that's fairly complicated). Particles with integer spins (bosons) have Bose-Einstein statistics (note this is not quite the same as saying they form Bose-Einstein condensates). Bose-Einstein statistics mean, essentially, that when you exchange two of them, you get no effect. Fermi-Dirac statistics, on the other hand, have anticommuting particles so that exchanging two of them gives you a minus sign. Of course, this is implies that xx = -xx = 0, so you can never have two particles in exactly the same state when they obey Fermi-Diract statistics (that's the Pauli exclusion principle). The spin-statistics theorem assures us that particles obeying Fermi-Dirac statistics have half-integer spins, i.e., are fermions.
You're only partially right. Quantum gravity may be at a much higher energy scale, but we can still begin looking for signs of things like large extra dimensions. Or, for that matter, supersymmetry, which is of course fairly important for deciding whether or not string theorists are correct about things.
>but gain this could still turn out to be a total
>failure. and thats a hell of a lot of energy
>they ae using to make this mini black hole. So
>no matter what why you want to look at it (black
>hole taking out the generator, Overload lead to
>explosion) there is a lot of risk here. And
>thats what I want to get across.
There is no threat. First, a few hundred GeV is not a lot of energy. It is a lot relative to the masses of fundamental particles (proton mass is ~ 1 GeV) but not compared to the sorts of energy scales you're used to dealing with on an everyday basis. Second, the goal of the accelerator is *not* to create a black hole, but to probe new physics at this high energy scale, like (hopefully) the Higgs mechanism (giving us a better understanding of electroweak symmetry breaking), and (again, hopefully) supersymmetry. There are many very good signs that we will learn a lot about physics in these energy scales, gaining insight into mechanisms that were previously out of the reach of our colliders.
Electron-positron colliders are in some ways cleaner (in terms of the data we get from them) than proton-antiproton colliders (like the Tevatron at Fermilab or the planned LHC at CERN). The problem with building them is they must be linear; particles moving in a circle lose energy (it's called synchrotron radiation), and since electrons are so light they lose a *lot* of energy, so we can't use them in circular colliders like we can protons. One possible future alternative is a muon collider; muons are heavy enough to not emit much synchrotron radiation, so we could use them in a future collider, and the physics of muons is much like that of electrons, so we keep the "cleanness." This is farther in the future, though. One difficulty is that muons are harder to produce than electrons or protons; one way might be hitting a fixed target with a beam to produce pions, which then decay into muons.
Anyway, my point is that the physics going on here is fairly well constrained by what we already know, so no disasters will happen. We will learn about physics in a bit more detail than we currently know about it, though, and a linear electron-positron collider has advantages that other types of colliders we could currently build don't. (Of course, it has its disadvantages too, but getting data from multiple kinds of experiments is important to be able to understand the results). There is absolutely no threat of a "mini black hole" eating the Earth, or the collider, or much of anything else. There's no sense worrying about disasters here. The decision to make is whether public funds should be spent on basic research, not on any dangers of this research.
>This doesn't make much sense. Say, for example,
>our sun suddenly collapsed into a black hole.
>Now, correct me if I'm wrong, but it would still
>have the same gravitational pull. Just because
>you make things smaller does not mean their mass
>increases.
That's right. People are worrying over nothing. Of course, there are big differences very near the black hole, but not at any reasonable distance scale. Tiny black holes aren't much of a threat to anything.
I know probably no one will read this, but I felt like I should write it nonetheless. First, my condolences to all those who know people who were lost in the disasters Tuesday. I'm fairly sure no one that I know was near those areas, but still I can never remember being so shocked and sickened. The thing that bothers me most today, though, are reports of ignorant Americans who are terrorizing innocent Islamic citizens in America. The local news here in Louisville carried a story of a local Islamic woman who was told by the owner of a store that he was going to get a gun and if she didn't leave by the time he returned he would shoot her. The woman, of course, was completely innocent; in fact her sister was a victim of the attack on the World Trade Center. This sort of ignorant hatred disgusts me. In its own way, although on a smaller scale, this is just as evil and reprehensible as the terrorists attacks themselves. No form of bigotry should be tolerated. Let us judge the terrorists by their actions, not by their religious beliefs. And remember that even flag-waving, apparently patriotic citizens of the U.S. are just as much enemies of our country if they turn on their fellow citizens.
>KMBZ radio reports Kansas City, MO has gas at
>$5/gallon, and another of $4/gallon in
>Louisville, KY.
Here in Louisville, gas is not *that* expensive. On the other hand, rumors of impending gas price hikes did lead to it being almost impossible to drive anywhere because of all the people trying to get gas in fear of it going up. Some of the outlying towns in southern Indiana did have higher gas prices, according to the local news (they showed $2.65 at some places; I don't know if it was more elsewhere). The mayor made a statement earlier that gas prices will be kept from skyrocketing, and that any reports of price-gouging will be investigated. The real problem isn't the price, it's that people aren't keeping their heads and acting sensibly about the rumors.
Let's all try to use a little caution in discriminating rumors from fact. I was amazed by the reports and footage today of how New Yorkers acted calmly and so many were able to evacuate the WTC. Just think how much worse this all could have been if people didn't keep their wits about them. We all need to keep that in mind, to avoid economic consequences or hasty assumptions about reprisals.
And, as with everyone in the U.S. and most of the world right now, my condolences to all those who have been affected by this tragedy. I can't find the words to express how angry and shocked I am right now.
>Unfortunately, recent boson precession measurements show the Standard Model is wrong. Oh well, it's still kinda nice
>to explain mass. Even in a dead model!
I don't believe this is "unfortunate" and it certainly isn't a bad thing for Fermilab. In addition to looking for the Higgs, there will be searches for new physics (i.e. physics beyond the standard model) in Fermilab run 2 data, just as in run 1. SUSY (supersymmetric) Higgs possibilities will be examined as well as the standard model Higgs. And in general, most physicists have thought that the standard model was inadequate, hence all of the theoretical work on SUSY, superstring theory, additional extended spatial dimensions, and other ways of going beyond the standard model.
You said "boson precession measurements." I assume you're alluding to the muon g-2 experiment? I believe they claim 99% confidence for a value that does not match the standard model. While that is compelling, it's just not enough sigmas to be decisive.
A couple of other notes... I'm just an undergrad, so people with more experience in physics can feel free to correct me:
Don't expect to see an announcement of the Higgs discovery right away. It will take time to collect enough data for a "discovery," although I suppose Higgs-like events could show up relatively soon. Also, I think the Higgs is harder to detect in p-pbar collisions than in e+ e- collisions (as at LEP) because the decay modes leading to the Higgs are closer to some background processes. But perhaps someone who knows more about this could explain.
And last, a technical note for all the Slashdotters who think every article should relate to Linux. Most of the work being done at Fermilab is on Linux, specifically Fermilab Linux, which is based on RedHat. For the CDF experiment, the Run 1 code was written in Fortran, but most Run 2 code is in C++. There are a number of modules which process event data, and TCL scripts are used to set module parameters and the order in which modules are run. ROOT is used to interactively run C++ scripts for data analysis based on the output of these modules. I don't know much about how D0 operates but I believe it's similar.
zpengo wrote: Linux has brought together mortal enemies, and has promoted a spirit of peace, love, and understanding. (Or something like that).
Not quite. MacOS X isn't Linux; it's a BSD system. Still, I think you're right, the increased portability of software to the Mac hardware will be nice.
Cire wrote: (I'm not a coder) But... Why can't someone port Xlib over to macos X? It's got all of the unix goodies, like gcc and emacs built in. How hard would it be?
I think that is essentially what has already been done. Xlib requires an X server, though. That was the original poster's point: X would run much faster on MacOS X if, rather than working the way X normally does and going through a server, it just called MacOS APIs directly. This would lose the advantage of X's network features, but a lot of people don't use those anyway.