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Physics Problems For The New Age
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.
...whatever remains, however improbable, must be the case.
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.
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Investigators at a major research institution have discovered the heaviest element known to science. This startling new discovery has been tentatively named Administratium.
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".
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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)
Torrey Hoffman (Azog)
"HTML needs a rant tag" - Alan Cox
- 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.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?
To within half a percent, pi seconds is a nanocentury. -- Tom Duff
The engineers proof that all odd numbers are prime.
...
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.
Disclamer - Opinion of Person
Remember some of the basic rules of quantum mechanics? That because of the act of observation that the observed changes? Again, a clear sign that something, somewhere is screwed up so completely, but nothing is ever done. Nobody ever stops and says, maybe we need to rethink everything up to this point, because this just shouldn't be happening.
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.
Disclamer - Opinion of Person
Casting a wide net and exposing the worlds problems to everyone in the population is the scientific comunities way to seek out people thay haven't previously considered. Let's not forget that the theory of relativity was concieved by one man, all alone, without contact to the "greatest minds of the day". He was a loner, an outsider, a rebel that took conventional wisdom and bent it around space time.
note that the definition of "physics" being used here is pretty broad. :-)
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.
Source code is a lot like a parachute; it needs to be open in order to function properly.
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.
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.
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.
...as everyone knows, is 42.
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!
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haven't figured out where my other matching sock goes everytime I do the wash. Seems like a blackhole or something is created with all the water rushing around a metal cylander.
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Question #4 discusses Supersymmetry. The lab group that I am part of is working with simulating supersymmetry, if you want more information on supersymmetry then go to the University of Colorado NLC group site.
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).
Disclamer - Opinion of Person
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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.
Source code is a lot like a parachute; it needs to be open in order to function properly.
'Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?'
People PLEASE! Do I have to spell out everything for you? The answer is obviously 'NO'.
This is 3rd grade stuff, people.
D
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I have only a laypersons understanding of quantum physics, so feel free to ignore me.
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)
Torrey Hoffman (Azog)
"HTML needs a rant tag" - Alan Cox
This was quite an interesting list, but let's not forget who came up with it -- a group of string theorists. The list reflects a certain... severe bias, in that ALL of the problems lie in the fields of high energy physics and cosmology. They completely ignore the equally fascinating (and much more rapidly growing) fields of condensed matter physics, biophysics, geophysics, and astrophysics (apart from cosmology). These fields promise to change our world, both in terms of the gadgets we use, to our very genetic essence, and contain problems of significant scientific merit as well.
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.
Science, like Nature, must also be tamed, with a view turned towards its preservation.
What they mean by information disappearing is that we would never be able to find out about what's in the black hole again. It would cease having an effect on the universe. Particles lost in a black hole take their history with them. You have to be realistic about this; how much information would anyone have spent time extracting from those particles anyway?
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 think this type of think is what's needed to get the average person interested in math and science again. Math used to be a hobby for a lot of people, and many discoveries were made by people in their spare time, but unfortuneately the outer boundaries of math and science are generally too specialized and complex for the average person to understand.
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.
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