Physics Problems For The New Age 237
In May, we ran a story on ten
"math problems for the new age."
ContinuousPark writes: "Last month, at the end of a conference on superstring theory at the University of Michigan, a group of physicists chose ten of the hardest problems in their field. They range from 'simple' ones like 'What is the lifetime of the proton and how do we understand it?' to obscure ones like 'Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?' Resolve one today, get a Nobel Prize tomorrow. This
NY Times article
has the details." And unfortunately, says the Times,
"'Just because' is not considered an acceptable answer." Darn, there goes my Nobel.
Re:My question: Is time continuous or discrete? (Score:1)
Re:Let's keep things in perspective. (Score:1)
1) Where the hell are my keys ?
Re:Prime Numbers (Score:1)
Re:Prime Numbers (Score:1)
That is just a blatantly false statement. There are many patterns, the most obvious one being that the product of any number of consecutive primes starting at 2 plus 1 is a prime.
I don't understand either (Score:1)
Right idea, almost all data/info contained is lost (Score:1)
The encyclopedia is much too macro to be a decent example.
Nope, that's simple arithmetic (Score:1)
Re:The *s proof that all odd numbers are prime. (Score:1)
Re:Let's keep things in perspective. (Score:1)
You're expecting drunk people to think about being objective?
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Re:Let's keep things in perspective. (Score:1)
One problem that Cramer mentions that no one else seems to, however, is the causality problem. I often wonder if science as a paradigm can even deal with this sort of problem as causality is implicit in experimentation.
Re:That's is SOOOO simple. (Score:1)
--EMN
Re:Prime Numbers (Score:1)
Hmm. I believe the correct statement is that "1 plus the product of any n consecutive primes starting at 2 is either a prime number or has a prime factor greater than n."
why epicycles == hidden dimensions (Score:1)
The interesting thing about string theory is that we may now be running into some serious limits on the degree to which we can experimentally verify our theories. Some of these limits may be fundamental, and tied into the theories themselves (as with Heisenberg's principle), but they may also be economic or otherwise practical - the problems involved in building accelerators with high enough energies to detect some of the artifacts of these theories may become insurmountable in future.
Even if string theory succeeds (which it hasn't yet) in providing a perfect explanation which integrates and explains all forces and dimensions, we still may not know whether the entities it postulates actually exist in any real sense. Unless we can get some kind of fairly direct (experimental) evidence of the hidden dimensions and strings (or branes), we won't know whether perhaps there's an entirely different mathematical solution waiting in the wings, which may use different undetectable entities to explain the same phenomena. In either case, the question of whether those entities truly exist becomes rather irrelevant, if we can't detect them directly. All we can say is that "the universe behaves as if our theory is valid, and therefore the entities it proposes may have some physical correlate".
This bears some resemblance to what the Copenhagen interpretation says of quantum theory, so this philosophical ground has been covered before. However, quantum theory has the benefit that all the objects it proposes have either been experimentally detected, or else are not central to the theory, but rather predicted by it. With string theory, we are indeed returning to the era of epicycles and hidden variables.
Of course, we hope that this situation will change in future, whether because of new experiments or different theories. Until this happens, lay people and physicists alike are right to treat string theory with a greater degree of skepticism than even the notoriously unintuitive quantum theories.
Wrong! (was Re:Looking for the patent clerk.) (Score:1)
Don't forget that it was Hilbert who wrote the righthand side of the basic general relativity equation (matter tensor).
Just because a "mildly" educated Joe Blow knows the names of whopping 2 physicists - Einstein and Hawking - doesn't mean he's right.
Re:Call for changes (Slightly OT) (Score:1)
Re:Call for changes (Slightly OT) (Score:1)
Please see www.infidels.org [infidels.org] for some though-provoking essays.
Re:Call for changes (Slightly OT) (Score:1)
You've watched way too many episodes of 'Star Trek'
Re:Here's a question, if anybody knows- (Score:1)
Re:OT - And if you want the ketchup out... (Score:1)
Re:Let's keep things in perspective. (Score:1)
Many SSC opponents were naive in thinking that if the SSC were cancelled, the funds would go to other disciplines. But that money only existed for one purpose -- kill the project and you kill the money, too
This is incorrect. No one assumed that the money would flow to the other fields. What the SSC did effectively do was to suck the air (and money) from other projects though, as congress wanted to limit the money given to the scientists. What many SSC opponents knew was that the zero sum game of science funding was about to get tremendously worse due to the funding problems in the SSC. Why should the condensed matter physicists have to lose funding for their research just to let the SSC continue? I speak from experience, after watching the funding in the grant that I was working under get sucked dry as monies shifted around to bolster the SSC at the expense of other science.
That this ever happened in the first place (despite the protestations that it never would) was unfortunate. Unfortunately, my group was the norm and not the exception. The grant program managers explained to us what had happened.
You also wrote
Maybe, but are they similarly far less intrigued by black holes, wormholes, the origins of the universe, superstrings, etc.?
I would expect that they are highly focussed on CJS (aka Mad Cow disease) and the issues surrounding the processing of food, food borne illness, how to prevent contamination, are they infected, what CJS actually is (a prion, or disease state of a protein, folded in a different conformation) than they are about black holes, superstring theory, and other things that aren't likely to kill them because they ate a bad burger. You also write:
By the way, while I contest many of your points -- because I'm in high-energy physics -- I will freely admit that the most interesting science book I've read in years is Kauffman's At Home in the Universe on biology, biochemistry, evolution, etc.
I personally encourage healthy debate. I had many such debates in grad school over this with friends in HEP and friends in my own field of computational condensed matter physics. One of the most fundamental points of such debates is can we afford to do the science, as well as can we afford not to. I personally argue that not all mountains should be climbed because we can (with a nearly infinite expenditure of energy), but we need to pick our mountains more carefully. My apparant focus on the biological aspects comes with a recent shift in career to a bioinformatics focus (which is a beautiful application of statistical mechanics).
Then again I also think that we (in the US) spend far too little money on basic research, and we treat our graduate students very much like slave labor (or indentured servants, or even middle class kids on the government dole). The investment in basic research almost always pays off (economic analysis seems to put the internal rates of return at ~30% or so... I wish my stocks did as well).
Re:More on epicycles (Score:1)
As you have no doubt realized, when I referred to "epicycles added to epicycles" I was repeating what I had heard elsewhere (probably in elementary school) and accepted as fact.
I learn something on slashdot every day!
Torrey Hoffman (Azog)
Re:11-dimensional superstrings, etc. (Score:1)
As far as the math and the books go - I guess the ideal book for me would be something that carefully defined and explained all these terms like Standard Model and Gauge Fields, and then went on to give some overviews of the proofs. I suspect I won't be able to understand all the math in the books you mentioned, but I can certainly read calculus and discrete math equations, so I'll see how far I get...
Thanks again. Posts like yours make Slashdot worth reading.
Torrey Hoffman (Azog)
Re:I like these ideas (Score:1)
What about Computer Science?
As a current undergraduate student looking towards an academic career, I know a list of unsolved problems in CS (perhaps not including Math and AI?) would be a great help in focusing my course selection.
Or even better, why not establish an online database of unsolved questions in every discipline? Each question could include some links to background information, a list of researchers who were known to be working on them, perhaps a method for companies and individuals to offer financial incentives (much like Paul Erdos used to).
As an aside, if anyone has any links or suggestion for topic selection, I'd greatly appreciate it.
Re:(1 * 1 == 1) || (1 * 1 == 0) (Score:1)
Re:Those are easy (Score:1)
note to moderators: this ain't redundant. the guy asked a question. and nobody replied yet. (i think)
Re:Your Logic Is Flawed (Score:1)
Re:(1 * 1 == 1) || (1 * 1 == 0) (Score:1)
or something like that. maybe i'm just not awake.
then again, I really really really really screwed up in terms of my physics class... ugh. painful.
Re:Prime Numbers (Score:1)
#0. if this was true, number theorists would be idiots :)
#1. the sieve of Eratosthenes.
#2. multiplying a couple primes and adding by 1 is not always a prime--it just isn't divisible by the primes that were used in computing the product. However, the primes may be primes, but that still wouldn't help much--you would still have to check whether they're primes or not.
oh. and I hate number theory.
Re:Fundamental questions to the universe.... (Score:2)
Re:Those are easy (Score:2)
Surely you mean the answer is 42...
On a side note, does anyone have a login-free link for this? For reasons best known to itself, NYT have lost my login details, and I really can't be bothered to re-register.
Re:What are the essential CS questions? (Score:2)
Note that
and
are in part arguably physics questions (i.e., "how fast can you make transistors switch?", "how fast an optical switch can you make?", etc.).
The question
strikes me as being a more purely CS question (although with stuff such as Adelman's DNA computing it might not be pure CS either - toss in a little chemistry...).
Now, I'd put "is P = NP?" on the list....
Re:epicycles (Score:2)
Steven E. Ehrbar
Re:11-dimensional superstrings, etc. (Score:2)
Within a certain framework, yes. One of the most perplexing things about the Standard Model is that it doesn't contain gravity. There are many straightforward ways to extend it, all of them wrong (WRT gravity). Richard Feynman explored this in detail in "The Feynman Lectures on Gravity" (look for this in a library). But to really understand these lectures requires quite a bit of background knowledge. This is, for instance, why we think the "graviton" is spin-2. Extending the Standard Model in a straightforward way requires the graviton to be spin 2. Of course, it doesn't work. But within the framework of existing theories, you can rigorously prove that it has to be spin-2. There are a finite number of "actions" which can be written down in this framework. (action being the equation from which equations of motion are derived, by minimizing/maximizing the action) Each of these can be explored in turn, and rigorously proven to be wrong.
The next question is: "is our framework wrong?" The Standard Model is a set of "Gauge Theories", that is Quantum Field Theories which posess a certain gauge symmetry (represented by a Lie group). Now there's a mouthful to scare off the lay person. ;) String Theory/M-Theory is attempting to explore this, by starting from the simple assumption that particles, rather than being point entities, contain a continuous degree of freedom. (that is, parameterized by x,y,z,t and one extra, continuous, internal degree of freedom...hence "string") This theory has turned out to be significantly more complex than one might imagine at first, and we're not done trying to figure out the theory.
For instance, you can straightforwardly prove that string theory can only exist in 26 dimensions. If you add supersymmetry it requires 10 dimensions. If you go to M-theory (which still isn't well defined) it requires 11 dimensions. Each of these is rigorously provable.
Supersymmetry solves a nasty problem in field theories of renormalization in certain calculations. It turns out that by adding a fermion (1/2 integer spin) for every boson (integer spin) and vice-versa, that you exactly cancel many divergences. This is clearly desirable. A theory with divergences should be treated with skepticism. But where are these extra particles? Supersymmetry was discovered in the context of string theory and carried over into field theories because of this nice property. You can have a string theory without it, but it clearly does not correspond to our universe.
I often wonder if there is a better framework. The Standard Model/Gauge Fields framework was very confusing (because of certain apparent problems like renormalization...which turned out to be a calculational problem, rather than theoretical) when it was first introduced, but it has turned out to be extremely useful in calculation.
Gad, I'm rambling again...that's what I get for answering posts in my field. ;)
ah, books. I'm most familiar with graduate texts, so I'll give those. I don't read lay books because they frustrate me. (I need the math dammit!) These are the "canonical" texts in the field, those most respected in the physics community. There are others, I cannot speak for their quality, but I have used all in the following list, and can recommend them. I can handle the math: good luck, these are not easy reading, and often require a close examination of relevant equations. Note that this is the course regimen for a graduate degree in physics. If you make it through all these books, you should consider applying to a local university and getting a masters in Physics. This isn't light reading. Usual starting point for this material is an undergraduate degree in physics (though math or some engineering may suffice).
hep-th/####### and similar references can be obtained electronically at www.arxiv.org.
Hope this is useful, --Bob
Re:Question #4 (Score:2)
Did he also say "erectron" instead of electron?
Re:Prime Numbers (Score:2)
Heck, we haven't even been able to solve relatively minor prime-related problems, like the twin primes conjecture: Are there infinitely many pairs of primes of the form n and n+2? Or a followup, which I thought of but have no idea if anyone's done any research on, which I call 'quad primes': pairs of twin primes of the form n, n+2, n+6, n+8. It's easy to show that except for 3 and 5, all twin primes are of the form 6k-1 and 6k+1, and similarly that except for 5-7-11-13 all quad primes are of the form 30k+(11,13,17,19). But past that, who knows?
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1/137+? (Score:2)
Re:# 8 just doesn't seem to fit (Score:2)
always increases, so this causes a bit of a problem.
No it doesn't. Substitute "planet" for "black hole" - gravitational potential energy is decreased, and entropy goes down. The second law refers only to closed systems.
If i have a solar-powered robot that organizes my sock drawer, that doesn't violate the second law because it's using energy to do so. A black hole sucking in an encyclopedia is using up energy (gravitational potential energy) to do so.
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Re:# 8 just doesn't seem to fit (Score:2)
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Re:I don't understand either (Score:2)
While it might not be technologically possible for humans to reassemble the information, it would be technically possible for, say, someone with root access to the universe, to look at the state of the entire universe, and follow the trajectories of the zillions of ash particles back to their original locations, and determine exactly what the book used to be like.
To explain another way: Pretend you're a fatalist. That means that given the state of everything in the universe at time t, it it possible to determine what the state will be at time t+1. Well, neglecting black holes, you could also say that given the state of the universe at time t, you could determine what it was at time t-1. But black holes screw that up.
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Re:Let's keep things in perspective. (Score:2)
Some will take issue with these points. That is fine and arguably quite good. A healthy debate on the visibility of science is good for the country and the world.
Admittedly I am biased, as I am not an HEP person. My dissertation was on molecular dynamics studies of semiconductors. What I saw while in graduate school was projects like the SSC draining all the money out of science. When the NSF went before congress to ask for more money, congress balked, as it was after all funding this massive white albatross. Couldn't all scientists use it?
Arguably that was part of the problem, the lack of congressional education. The other part of the problem was the selling of HEP as Physics. It isn't, and it has demonstratably damaged the entire research community when that view was pushed. Yet there are still some that push it (see the article pointed to at the root of this thread).
No, the interesting problems in physics come from all the physics disciplines. The High Energy Physics (HEP) types still haven't learned that interesting physics to the public and interesting High Energy Physics are not identical. I would suspect that people in the U.K. are far less intrigued by the parity violation experiments as they are with protein folding diseases, specifically prions that are suspected to cause CJS. That is biophysics, biochemistry, biology, condensed matter physics, etc. The binding of small molecules to receptor sites to promote or inhibit life processes is arguably more interesting, and related to molecular dynamics, molecular recognition, statistical mechanics, etc. It is also the basis for drug discovery, without which we would have no pharmaceutical products.
Re:# 8 just doesn't seem to fit (Score:2)
So, information 'disappearing' into a black hole *does* appear to violate the second law of thermodynamics. Which means something else must balance it out.
What about hawking radiation though? Could that not be seen as increasing the entropy in the universe?
Re:11-dimensional superstrings, etc. (Score:2)
You say the current model of particle physics is the simplest model that is possible, and it's difficult to explain why.
That sounds a little like what we call a "hardness" proof in computer science.
I have a very good theoretical computer science background. Sometimes in computer science we can prove what we call "hardness" of a problem. That is, for some problem like multiplying two n-bit numbers, there is no algorithm that can do it in less than f(n) steps on some rigorously defined hardware (probably a virtual machine). These results are very difficult to obtain in general, and a lot the ones we do know aren't very good. For instance, it is easy to show that there is no way to sort n items in less than n steps, regardless of what algorithm you use, because you have to look at each item at least once.
Anyway...
When you say there is "no simpler theory" do you mean that it is possible to rigorously prove that? For instance, can you prove that any theory of particle physics that matches experimental results must be supersymmetric, or must have at least 11 spatial dimensions, or whatever?
If it's really too hard to explain in a Slashdot post, can you recommend a good book? I can handle the math - layperson stuff like "Shrodinger's kittens and the search for reality" is easy reading for me.
Thanks!
Torrey Hoffman (Azog)
Re:Prime Numbers (Score:2)
BTW. 2*3*5*7*11*13 + 1 = 30031, which is non-prime because 30031 = 59 * 509.
But these are all easy! (Score:2)
- Yes, they are a direct by-product of the topological shape of spacetime, and that shape is the only possible shape.
- QG itself can't, but you can derive the creation of time from the topology of space. The perception of time is just a side-effect of the way our consciousness works.
- Protons are "wrapped" across the entire temporal dimension, like a loop, and thus appear to live forever, unless you radically distort spacetime.
- Yes, and it actually is not broken
- The "temporal dimension" is an illusion of consciousness. It is really just a highly expanded spatial dimension. Only three spatial dimensions have expanded because n-banes only need three dimensions of freedom to do all of the topologically possible transformations they can undergo.
- This is a direct fallout of the "shape" of the temporal dimension.
- No, it doesn't yet.
- The information does not go anywhere - it is stored in the topology of spacetime. This confusion comes from failing to consider time as a dimension capable of information storage.
- This is an artifact of only considering gravity in the 3 expanded dimensions
- Yes, again it is just an artifact of the shape of spacetime.
I have delightfully simple mathematical proofs for all of these, but alas, this text entry box does not allow me to paste in equations... =;-PRe:I don't understand either (Score:2)
Unfortunately, the universe doesn't work that way. Classical mechanics is deterministic, but quantum mechanics is not. We can't trace back to an earlier state of the universe, because we can only find the probability of one state evolving into another.
I'm not at all an expert, but I think this question is a lot more complex than most posts are making it sound. If problem #8 could be solved so easily by saying "the information is lost; the entropy difference is made up for by gravitational potential energy or Hawking radiation or some combination thereof," then the physicists who made this list would have said that.
It would be nice if someone who knows more about the underlying problems than I do could explain. However, this looks vaguely related to something known as the holographic principle, which seems to be important in string theory. My (very limited) understanding of it is that the equations of string theory could work on a smaller-dimensional subset... in other words, everything inside the universe might just be some sort of "reflection" of something on the "surface" of the universe. The theory that information inside black holes is reflected on the surface seems to be very similar. I'm fairly sure - correct me if I'm wrong - that the current theory is that a black hole's entropy is related to its surface area; i.e., when something falls into a black hole, the surface area increases by the same amount that the entropy of the rest of the universe decreases.
As I said, my understanding of this physics is limited, but one thing I do know is that quantum states can not be copied or destroyed. This is the source of some interesting differences between classical computers and quantum computers. Black holes seem to violate this.
By the way, if anyone reading this thread is unfamiliar with Hawking radiation, that's one thing I can explain... Black holes have a tendency to "evaporate." They give off particle/antiparticle pairs, so that they aren't entirely "black." On the other hand, these particles don't contain any of the information that actually goes into a black hole. They're more or less empty of information; black-hole radiation follows a statistical distribution that is roughly the same as the distribution of energy emitted from the sun (i.e., they work like blackbodies). As black holes emit this energy, they lose mass (remember E=mc^2?) and, correspondingly, "evaporate" over time. Because of this, every black hole can be said to have a temperature, which is determined from the Stefan-Boltzmann formula F=sigma*T^4, where F is the energy flux (watts per square meter) coming out of the black hole. So, a black hole shrinks over time. The question is: as it shrinks, does any information that was lost in it come back out?
If I get around to it, I might dig through some books later today and see if I can understand more about the issues involved here. I'm pretty sure it isn't a simple question, and there are very good reasons for it to be part of the list.
Re:Call for changes (Slightly OT) (Score:2)
I would rather that science be treated like the religion that it is, and like all religions have its problems talked about in a meaningful manner.
Or, the microscopic world is so different from the everyday macroscopic world where we live in, that we lack proper language to describe extremely small (or large) phenomena.
But what should scale have to do with anything? Any properly described event will happen the same way no matter how much, or how little, enery or matter is a part of the equation. That we recongize a difference is part of the problem.
OT - And if you want the ketchup out... (Score:2)
I support the EFF [eff.org] - do you?
Re:Question #4 (Score:2)
Yes, the pions are mesons, composed of two quarks. When running simulations we tend to use both electrons and pions for detector simulations. The simulated data from pions tends to be very easy to compile and use to check whether one detector is better than another. I slipped up because I had been using pion simulationed events in my last project.
Patterns (Score:2)
2+1 = 3
(missed)= 5 (2x2+1)
2x3+1 = 7
11 (2x5+1)
13 (2x2x3+1)
17 (2x2x2x2+1)
19 (2x3x3+1)
23 (2x11+1)
29 (2x2x7+1)
2x3x5+1 = 31
His statement should have read more like, "no one has yet to discover *any* pattern that completely maps out the prime numbers."
:)
Veldrane
Re:Let Go of the Frog! (Score:2)
"Why does the Cambridge combinatorial hierarchy (a mathematics construct, pure and simple) generate the observed scale constants with great accuracy whereas standard theory does not?"
Let Go of the Frog! (Score:2)
"Why does the Cambridge combinatorial hierarchy (a mathmatics construct, pure and simple) generate the observed scale constants, such as vacuum energy, with great accuracy, whereas standard theory is off by 10 to the 120'th power?"
Re:My question: Is time continuous or discrete? (Score:2)
Most Quote Punctuation Ever In A Slashdot Story? (Score:2)
8 single-quotes
I think we have a "winner"!
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Re: Fermat (Score:2)
Actually, he wrote that note in the margin of Arithmetica by Diophantus. In that book, the problem posed by Diophantus was to express a square rational number (a fraction), as the sum of 2 other square numbers.
Fermat's note stated that he had a marvellous proof of a related problem but that the margin was too small to contain it. I find it hard to believe that a mathemetician such as Fermat would make that sort of reference based on a specific case (n=4). More likely, he had a general case worked out which never saw the light of day. Considering the difficulty of the proof by Wiles, it is unlikely that Fermat's would have held up under scrutiny. But that is something which will probably remain a mystery :)
Best regards,
SEAL
Re:Geek Movie Physics/Physiology (Score:2)
Re:WTF is a "curled-up dimension"? (Score:2)
Re:Consolidated effort (Score:2)
Someone's already been working on it, actually:
Society for Interdisciplinary Studies [knowledge.co.uk]
Very fascinating stuff. I first heard of them from the back of a James P. Hogan book.
That's is SOOOO simple. (Score:2)
The answer is: Yes. Now were's that Nobel prize when I need it????
kwsNI
Damn, I tried. (Score:2)
kwsNI
That's the beauty of it. (Score:2)
kwsNI
Answer:Quesiton #8 should be rephrased (Score:2)
No. Everyone knows first posts are faster than light. At least they appear faster.
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Quesiton #8 should be rephrased (Score:2)
Re:Prime Numbers (Score:2)
This is a method used to calculate *a* prime number. It's not unique in that manner. There are many others.
What it is *not* is a pattern to the prime numbers. Hell, there is no known pattern to the non-prime numbers either. Guess what though, I can take any power of two, and it won't be a prime number. Yes! I figured out the pattern!
Wait, here's another. Multiply the number five by any other number. Wow! I found another!
In short, the word pattern: You keep using that word. I do not think it means what you think it means.
Re:Call for changes (Slightly OT) (Score:2)
Science is about revising our view of the universe to be closer and closer to the way the universe actually acts.
Mathematics is a compression method. It compresses large amounts of explanation into small symbols which can be understood in an open-source kind of way. I use that term because 1. You can get your hands on the proofs for the mathematics we use today. 2. You are both allowed and encouraged to use and revise those proofs to show new principles. "Going back to first principles" is a much-lauded activity. Mind you, much like GPL, you are required (For some value of required) to point out the original data. If you built upon the theory of relativity, for example, and then claimed to have done all the work yourself, you would be professional crucified.
The big important thing to recognize is that as we form new theories we find ways to explain old behavior. Saying we shouldn't move on until we explain every open space in our logic today is like saying we shouldn't go to Mars when we still have hunger on our planet. Advances in space-based technology have consistently percolated down through the human strata to ensure a better way of life for [nearly] all mankind. (Sorry, I refuse to be PC.) My point is of course that by making advances in science, we solve old riddles. Some of those riddles would doubtless not be solvable without this new knowledge. So I think your initial exasperated expression of desire is at best uninformed.
Re:WTF is a "curled-up dimension"? (Score:2)
Can somebody please explain how a "dimension" can be "curled up tiny"?
I'll try...
First, think of an infinite 1 dimensional surface ... a line. Now, as you know from geometry, the line has infinite extent. This is what we normally think of when we think of a "dimension". It is "1-dimension" since we need 1 parameter to describe a position along its length. It is an infinite dimension since the value of that position parameter can vary from -\infty to +\infty
Now, we'll think of a finite 1 dimensional surface. Take a line segment and connect the ends, and we get ... a circle! It is also "1 dimensional" since we need 1 parameter, and it is finite, since that parameter can vary from (say) 0 to 2\pi
When formulated in the right way, there is nothing that prevents you from doing physics where the dimensions are finite instead of infinite (I admit that it would be quite difficult using the techniques normally taught in an undergraduate setting). And, generally speaking, there is nothing that prevents you from doing physics with more than three space and one time dimension (although again, it is generally quite difficult using undergraduate techniques).
Now, we bring it all together; while a particular string theory requires that our universe be ten dimensional (for the mathematical consistency of the "supersymmetry algebra" of the theory), the theory itself doesn't specify which of those dimensions are finite, and which of them are infinite (eventually, we would hope to come up with a theory which DID make that specification, starting from basic assumptions, but we aren't there right now). What makes that specification right now is our experiments, which say that there are at least 3+1 "large" dimensions (nearly infinite). Thus, those extra 6 dimensions must be finite, or "curled up".
Incidentally, the fact that we can't see those extra dimensions (if they exist) tells us something (that "something" depends on exactly how you assume that they have compactified). Generally, it tells us that they must be smaller than a certain size, otherwise they would have manifested themselves in experiments, usually as deviations from the Newtonian gravitational force. The fact that we haven't seen any such deviations tells us that the "size" of the "dimension" must be very small.
Rereading what I just wrote, I'm not sure it helps, but I hope it does!
Re:I like these ideas (Score:2)
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Re:Prime Numbers (Score:2)
The most interesting "pattern" is the Prime Spiral. Get a sheet of graph paper. Write a "1" in the center square. Go one square to the right and write a "2". Move down and write "3". Continue in a clockwise pattern incrementing each number by one until you get to 100-200. Now circle all the prime numbers and you will see an interesting pattern. (or better yet, search for prime spiral on Google and see someone else do the hard work)
Re:Looking for the patent clerk. (Score:2)
In any case, this is only potentially true for Einstein in the case of his work on the photoelectric effect. Special and general relativity were conceived as a world-famous, extremely prominent physicist.
epicycles (Score:2)
Firstly, they were backed by religion. Everything orbited the Earth, if you recall, and according to both the Church and Aristotle, they orbited in circles (aristotle claimed the solar system was geometrically perfect - each body orbited the earth on a sphere, inside of which was inscribed a regular polygon). One could argue that force of habit is as binding as religion, but probably not win that argument, in tht force of habit does not possess axemen.
Secondly, until Newton's gravity, epicycles were more accurate, ie, they gave results consistent with observation. Once Newton's gravity was on the field, Kepler showed how to compute the correct ellipses, and the simpler argument was more correct.
So two points are worth remembering here - one, that epicycles were the best solution to a geocentric orbital model - a model which could not be discarded b/c of the catholic church; and two, more advanced (ie, complex) physics had to be invented to compute the simpler explanation.
Today there is no religious body powerful enough to squash disagreeable science. World views we have accepted a priori bind our perceptions, but we have learned to question all our instincts these days. Also, simpler explanations don't fall out of a system until we are mired inside a more complex explanation, and made familiar with the system we're trying to model. I recall what a professor once told me:
Re:Prime Numbers (Score:2)
It's a good try, though.
Steve
40 years... (Score:2)
More on epicycles (Score:2)
This is what happened: Aristotelian physics required that all motions in the heavens to be circular, so some astronomers introduced epicycles to account for retrograde motion. Ptolemy incorporated this in his magnificient theory. Now, the story goes:
(taken from de Vaucouleurs, Gerard (1957)), it's just that this is wrong! First, where is the evidence that there was any significant observational progress. Have a good look, and you'll see that there wasn't any observational progress, so they had no reason whatsoever to introduce additional epicycles. The observational progress didn't come until Tycho Brahe, after Copernicus.
Now, the whole thing culminated in 1963, Robert Horace Baker wrote an article in the Encyclopedia Britannica stating that 40 to 60 epicycles were added to each planet, which is absurd, they would have needed a Beowulf cluster to compute the positions of the planets if they did that... ;-) At least with the math they had available.
Baker further said that Alfonso X stated that if he had been there at creation, he would have given the good lord a few hints. Alfonse X computed (well, as a patron) the Alfonsine Tables, that astronomers needed to determine the expected positions of the planets.
Owen Gingerich [harvard.edu] bashed the myth in 1968 by recomputing the Alfonsine Tables, and found that they were based on a pure Ptolemaic model with only minor corrections to the parameters used by Ptolemy.
I have been trying to figure out why this myth came to be and how it propagated. I haven't had time to do much research on it lately, and I won't tire you with my stuff, but I have an old essay about it [astro.uio.no] for those interested.
Now, the myth has been uncritically accepted by a number of canons, most notably Thomas Kuhn. I have read a couple of his books, and I'm a bit uncertain how important it is for his philosophy, but it is clearly motivating him to go in the direction he does. Gingerich told me on the History of Astronomy Discussion List [wvnet.edu] that Kuhn was very embarrased when he told him about it.
It is very important to note, IMHO, that Ptolemy went away from Aristotelian physics a long way, and that allready in the 10th century (i.e. before Aristotle was made compatible with Christianity by Thomas Aquinas), the criticism against him gained strength. Ptolemy had to introduce several concepts, among them, the equant. The epicycle itself is not consistent with Aristotelian physics, because the circular motion should be around the centre of the universe, namely the earth. Now, could it be that Copernicus was mainly motivated by lack of proper physics as opposed to merely mathematical constructs?
Finally, as others has mentioned, Copernican cosmology had no advantage over Ptolemaic cosmology in terms of accuracy, also as shown by Owen Gingerich. The breakthrough in accuracy came with Kepler.
Re:11-dimensional superstrings, etc. (Score:2)
Re:Looking for the patent clerk/Einstein's credit (Score:2)
The concept of special relativity had been in development for several years..
It was not the concept of relativity, it was the mathematics of what would later be called special relativity. The concept of relativity in this theory is mostly if not exclusively due to Einstein, who arrived at it from purely physical considerations. He did not need that mathematics.
As far as GRT and Gauss is concerned... What credit do you think deserves someone who even does not have guts to publish one's ideas. That's precisely what happened to Gauss who never published his idea that the space can be curved because he was afraid to be laughed at...Mach might have some impact on GRT, perhaps even negative. Einstein pursued Mach's ideas, but this turned out to be a blind alley: GRT does not realize the so called Mach principle that Einstein tried to incorporate in GRT. Poincare had nothing of substance to contribute to GRT at all, unlike to the mathematics of SRT. As far as Leibnitz is concerned- I can only guess that his ideas were very vague and certainly of no impact on Einstein.
So much about where the credit is really due...
Once you eliminate the impossible... (Score:3)
That's typically how the "logic" in science's attempts to describe reality functions, and it functions quite well that way, Godel be dammed.
Or in other words:
"I think X is so"
"This experiment foo tests X"
"If foo fails, X cannot be true"
"If foo succeeds, X may be true, and can probably be treated as true until something better comes along"
As far as the quantum mechanical property that observing changes the observed, that isn't as screwed up as you seem to think. Instead, consider how one might "observe" something at a quantum mechanical scale. Anything bounced off a quantum mechanical particle with sufficient energy to perform a "measurement" is locally "large" enough to affect whatever it is you're observing.
Consider a basic thermometer. If I take your temperature, the amount of heat energy drawn off into the themometer is not enough to materially affect your overall temperature. But if I take that same thermometer and attempt to take the temperature as a drop of liquid nitrogen, the heat energy in the (room temperature) thermometer will boil off the nitrogen, and thus alter it.
It's just a question of scale, not metaphysics.
What is the heaviest element known to science?? (Score:3)
This new element has no protons or electrons, thus having an atomic number of zero. It does, however, have 1 neutron, 125 assistant neutrons, 75 vice neutrons and 111 assistant vice neutrons, giving it an atomic mass of 312.
These 312 particles are held together by a force called morons, that are surrounded by vast quantities of lepton-like particles called peons. Since it has no electrons, Administratium is inert. However, it can be detected as it impedes every reaction with which it comes into contact. According to the discoverers, a minute amount of Administratium causes a single reaction to take over four-days to complete when it would normally take less than a second.
Administratium has a normal half-life of approximately three years; it does not decay but instead undergoes a reorganization in which a portion of the assistant neutrons, vice neutrons and assistant vice neutrons exchange places. In fact, an Administratium sample's mass will actually increase over time, since with each reorganization some of the morons inevitably become neutrons forming new isotopes.
This characteristic of moron promotion leads some scientists to speculate that Administratium is spontaneously formed whenever morons reach a certain quantity in concentration. This hypothetical quantity is referred to as "Critical Morass".
You will know it when you see it.
Re:11-dimensional superstrings, etc. (Score:3)
I totally agree that it's hard to come up with other answers. Of course I don't think that scientists should stop doing physics.
The problem is, (and I should have made it clearer in my earlier post) I really get the impression that most physicists today are just trying to "patch up" these theories. And there are so many holes that there is lots to do, so they all keep pretty busy.
Is anyone (other than crackpots) even trying to come up with an alternative explanation? Or is it true, as another response to my post said, that "string theory IS the simpler theory.". If so, why are there so many different string theories, and what's with the M-theory "unifying" them but "adding complications"?
Are there physicists out there writing journal articles that say:
"Let's assume that all this string theory stuff is just wrong. Instead of patching holes in it (adding epicycles!) here's an alternative explanation..."
Torrey Hoffman (Azog)
Geek Movie Physics/Physiology (Score:3)
- True invisibility (not that refractive/ablative Predator-camo stuff) is complete transparency to light
- Human vision is transduction of light energy to electrochemical stimuli
- An invisible guy's lenses (light not refracted, focused, flipped) and retina (light not transduced) are transparent to light energy
wouldn't an invisible man be blind? Haven't heard this one discussed - just wondered.Re:I like these ideas (Score:3)
I find this rather hard to believe... can you give me any examples? Ideally, examples of original and/or important discoveries... My undergrad number theory prof told us an interesting story about when he was at Utah... seems one day the math dept got a packet in the mail from an amateur mathematician. It had several pages filled with Pythagorean triples. The person who sent them in said he did it because he thought they "might be helpful". Unfortunately, the problem of identifying Pythagorean triples has been completely solved, so all of his work was for nothing...
A few months ago I saw a list of unsolved mathematical problems that required no special knowledge to understand
Any chance you happen to remember where you saw it? Sounds interesting... My personal favorite is the Collatz problem (also called many other things...): define C(x) = 3*x+1 if x is odd, and C(x) = x/2 if x is even. Consider iterating C on a natural number N. Does C^n(N)=1 for some n? (Hint: it's true for N assuming Fermat wasn't bluffing or erred in his proof, then a simpler method awaits rediscovery.
I think it's pretty much assumed that Fermat didn't have a proof... partly because (as best as we can tell) he made that note several years before his death, and he had a proof in the case n=4. The generally accepted theory is that he thought this proof would work for the general case, and so he made that note in the margin. When he realized it didn't work, he didn't go back and scratch out that note...
Published lists of unsolved problems that can be comprehended by a layman may increase interest and make science "real" again for a lot of people who view things like physics and chemistry as voodoo.
It's not too hard to do for math, but are there any of these types of lists for physics or chemistry?
The *s proof that all odd numbers are prime. (Score:3)
1 is prime and odd, 3 is prime and odd, 5 is, 7 is, 9 isn't but that's probably just statisical error, 11 is, 13 is, well that's good enough for me.
The computer scientists proof that all odd numbers are prime.
1 is prime and odd, 3 is, 5 is, 7 is, 7 is, 7 is, 7 is
MSs proof that all odd numbers are prime.
1 is prime and odd, 3 is, 5 is, 7 is, [BSOD!]
Well it was holding true up until it crashed so it must be true.
Re:Call for changes (Slightly OT) (Score:3)
Although one could say that the problem must stem from the Schrodinger Equation, which is one of the four fundamental equations like F=ma, and therefore it must be changed, it also seems to be inexplicably correct. People have stopped and said, maybe we need to rethink everything up to this point, because this just shouldn't be happening. Einstein did, he questioned quantum mechanics until he died. Every question he threw at it, everytime he tried to throw a wrench in the gears, he failed. Some of his questions have only been answered in the past 20 years, but they have been answered.
Quantum mechanics has been poked, prodded, attacked, and verbally abused and yet it keeps on showing us that it is correct. All of the scientific data taken to try and disprove things like the Uncertainty Principle has failed. We cannot do any better than hbar. We have to deal with the duality of waves and particles. All of the evidence shows that it is correct.
Sure there are holes, the standard model for particles is full of them. People are trying their hardest to patch them, a good example is question #4. Supersymmetry was theorized as a fix for the standard model, and it wasn't the first, there were others with funny names like Technicolor.
Einstein placed the cosmological constant into his relativity equation because he wanted the universe to be static rather than expanding or collapsing. Now there is talk of re-introducing the cosmological constant, in a slightly different form, but never less it has been talked about to try and explain some of the holes.
Superstring theory is just another patch, a way of trying to understand the universe. Other theories don't cut it, they have gapping holes. Superstring theory surfaced because something wasn't quite right and someone tried to fix it.
Most of the physics done today is patch work. Something isn't working right so we need to find out why.
Looking for the patent clerk. (Score:3)
a different list, from slightly less-drunk people (Score:3)
note that the definition of "physics" being used here is pretty broad. :-)
Re:Prime Numbers (Score:3)
There are many ways to calculate prime numbers, yes. Calculations are not patterns.
To help you out a bit, there is a pattern to the following series: 1, 4, 9, 16, 25,
Can you guess this pattern? Good job. Know what the 1000th number in this list would be? Good job. Did you have to know the values of any other elements in the list, or did you just need to know the pattern? I think you understand.
Oh, and the 1000th prime number is 7919. Useful stuff to know.
Re:11-dimensional superstrings, etc. (Score:3)
Why didn't they try harder to find a simpler explanation?
I'm a grad student in particle theory, so take what I say with a grain of salt. In a sense that isn't easy to relate to a lay person (because they are technical and require acquisition of a vocabulary and rigorous definitions that I'm not well equipped to explain), the current model of particle physics IS the simplest theory that is possible (meaning anything simpler gets the wrong answer). Whether it be within the Standard Model or with M-theory, you start by writing down the simplest mathematical description you can, and then check the consequences.
The complications all arise in the last step, checking the consequences. Those calculations are often horrifically difficult. This is not unlike the example you cite of Newtonian gravity: you COULD write down a more complicated model that agrees with experiments, but the inverse square law works very well, and is incredibly simple. Unfortunately, even this simplest possible model becomes calculationally intractable when you try to do something as seemingly simple as the three body problem, which is unsolvable (in a technical sense) except in a few highly contrived circumstances.
String theory is the same thing. Write down the absolutely most trivial and general equations you can that are consistent with the known "properties" of the universe, turn the crank, and see what comes out....but you get stuck in the process of turning the crank.
As to whether there are physicists trying to come up with a simpler set of explanations; yes, there are, but anything that has been tried that IS simpler is KNOWN to be wrong. Since these theories are mathematical, you can convince yourself that there AREN'T simpler theories that you have missed (in a certain highly technical sense....), because those classes of theories makes predictions which are wrong.
Of course, it may turn out that a more complicated fundamental theory may turn out to be simpler to calculate with, and hence be simpler in a different sense.
#8 (Score:3)
This question could be resolved by checking your reference frame. If I am someone outside of the black hole, dropping my copy of Webster's in, I never actually see that copy of Webster's hit the event horizon. Instead, it approaches it more and more slowly, the image growing ever redder and ever dimmer. From my reference frame, it never actually enters the black hole. It may be very red and very dim, but just 'cause I can't read it, doesn't mean that it is not there. Locking that Webster's in a box doesn't count as information loss. Thus, no information loss.
From the reference frame of someone (someone due to die a quick and short death) inside the event horizon, I would see a Webster's plunging in towards me. Still, no information loss.
Black holes were also once called "frozen stars," due to the fact that the "history" of a black hole (as Thorne puts it) is contained just above the event horizon -- the star's surface would appear to be there, if it weren't so red(-shifted) and dim. Somewhere in Wheeler's gravitation there's a nice calculation on how long it takes something to become practically invisible (red/dim) as it plunges towards the event horizon.
What is troubling for my two cent explanation is the problem of the matter that was there when the collapse began, which would be the neutron-laden core of a supernova. That definitely seems like lost information.
Black holes do all kinds of fun things, like violate baryon conservation and lepton conservation, in big ways. They do pose some very interesting questions. Of course, we don't have any really handy to test out stuff like Hawking radiation and whatnot on, so we won't know if our theory meets reality. We've detected black holes, but we haven't gotten up close enough to really know if what we predict about them in regards to particle production is true.
Re:Yeah but they still (Score:3)
Average American male loses 4 socks per year. Call it 125,000,000 million males in US. That is about a billion socks every 2 years. This has been going on for at least 50 years.
Do you think you could hide 25,000,000,000 socks without the odd one showing up every once in a while? With that many socks missing you would think we'd be tripping over them regularly.
The answer of Life, the Universe and Everything... (Score:3)
The real question, of course, is how much wood would a woodchuck chuck if a woodchuck could chuck wood. Now _there's_ some Nobel material!
You owe Slashdot a copy of the best Oracularities...
Yeah but they still (Score:3)
--
You're a unique individual, just like everyone else.
New Age Physics Problems (Score:4)
--
Question #4 (Score:4)
We only hope that the NLC, or Tesla, is built. Right now particle physicists around the world are trying to scrape up the ~$9 billion that it would require to build one of them.
I know that some of you will say, "We already have particle accelerators that can reach TeV (Tera Electron Volts), why do we need the NLC?" The particle accelarators today that can reach TeV, like the Tevatron at Fermilabs, accelerate Hadrons like protons. Although the physics gained from accelerating Hadrons is very useful, it cannot give us the information necessary for supersymmetry. Hadrons are composed of three quarks, and therefore when they collide not all six quarks are hitting at the same time, generally only one quark hits one quark. These kind of reactions are useful but not what we need. We need a particle accelerator that can accelarate leptons, like electrons and pions, to the TeV scale. When electrons hit we are getting the entire center of mass energy at one point at one time. This allows for physics that is extremely useful to supersymmetry.
I am just an undergrad so my understanding of this next aspect is kind of shakey. From what I have been able to understand, hadron colliders are really good for understanding the forces between particles, whereas lepton colliders are really good for discovering new particles. In order to prove, or disprove, supersymmetry we need to see if sparticles (supersymmetric particles) exist, therefore we need lepton colliders. Today the most powerful lepton collider in the US is SLAC (Stanford Linear Accelerator). [stanford.edu]
The Answer is Easy (Score:4)
Mike Roberto
- GAIM: MicroBerto
Re:Looking for the patent clerk. (Score:4)
I hope you were joking, my friend. The concept of special relativity had been in development for several years, perhaps starting when Maxwell suddenly noticed that his equations weren't invarient under Galilean (Newtonian) transformations. If you study a bit of rudimentary E&M (say a bar magnent moving through an electric field) you see that the E vector will not be the same in all inertial reference frames... think a little bit and viola, you have Lorentzian transformations.
Ever wonder why the special relativity transforms you learn in intro physics aren't Einsteinian transformations? Hrm...
Also, GTR was a clever amalgomation of theories developed by several thinkers, including Gauss, Leibniz (read the letters between Clark, a Newtonian advocate and Leibniz and you see the beginnings of a relativistic nature of space and time (though not nearly as sophisticated as GTR)), Mach, and Poincare.
Of course, this dosen't take away from the genius of Einstein, but still, it dosen't give credit where credit is due.
In Steven Weinberg's book, Gravitation and Cosmology (Wiley and Sons, 1972) there is an excellent first chapter on the development of this science. It's a good book overall, you should check it out.
Prime Numbers (Score:4)
My favorite unanswered questions like this are those which are easy to explain but relatively impossible to figure out. For example, no one has yet to discover *any* pattern in the prime numbers. I can explain that question to my grandmother. Difficult questions aren't always complicated to explain.
Where's my Nobel? (Score:4)
People PLEASE! Do I have to spell out everything for you? The answer is obviously 'NO'.
This is 3rd grade stuff, people.
D
11-dimensional superstrings, etc. (Score:5)
Whenever I read about these incredibly complex theories, like 11 dimensional superstrings, the M-theory, "sparticles", and what have you, it just reminds me of the "theories of planetary motion" that people used to come up with before they realized the earth goes around the sun.
To explain the observed motion of the planets in a way consistent with the sun going around the earth, they invented "epicycles", which were essentially loops within loops on the hypothical orbits. This went on for years, with the epicycles getting more and more complicated. They built amazing geared machines to simulate the motion of the planets. Now we look back at them and shake our heads, thinking "Why didn't they look for the simpler explanation? Why did it take so long for a Copernicus to come along?"
I don't mean to dis modern physics... but I can't help thinking that in 100 years, people will look back on M-theory and sparticles and laugh, saying "Why didn't those people realize how ridiculous those theories are? Why didn't they try harder to find a simpler explanation?"
Maybe the real world really is that complicated. But history would indicate otherwise.
Torrey Hoffman (Azog)
Let's keep things in perspective. (Score:5)
This point reminds me of a listing posted to slashdot a couple of months ago of the top ten algorithms of all time. It just so happened that all ten were numerical algorithms, reflecting the bias of the poster in that case as well. A more objective list requires a more universal panel.
Re:The Answer is Easy (Score:5)
Where can I buy clothing from Gap?
er, not quite what i had in mind, thanks, Jeeves.
I think i'd sack my butler if he was making money on the side selling crappy products whilst working for me.
Re:# 8 just doesn't seem to fit (Score:5)
But the point is that the singularity means, for all we can tell, the complete destruction of everything except the raw mass of the particles that fall into it.
Using the encyclopedia is a bad pun; imagine dropping something simpler, like a salt grain down instead. The salt grain contains information about its structure and if you were clever enough you could figure out where it came from and how long ago. That information vanishes in a black hole.
I like these ideas (Score:5)
A few months ago I saw a list of unsolved mathematical problems that required no special knowledge to understand and I thought it was a really good idea since it might get your average person interested in solving one of these problems. For example, Fermat's last theorem has been proven, but using very complex math that was unknown at the time he wrote his little note in the margin. The concept behind the theorem is pretty intuitive, and assuming Fermat wasn't bluffing or erred in his proof, then a simpler method awaits rediscovery.
Published lists of unsolved problems that can be comprehended by a layman may increase interest and make science "real" again for a lot of people who view things like physics and chemistry as voodoo.