

Title: various physics questions Post by BenVitale on Jun 22^{nd}, 2008, 3:36pm Schrodinger’s cat: This is my understanding of this theoretical concept: The quantum cat exists in two states at once: it is both alive and dead at the same time  a superposition of two states. Any kind of random disturbance or interaction will destroy the exquisitely delicate mix of coexisting quantum states, forcing a single classical state to emerge instead. Meaning, it will collapse to a simple classical one, that is either dead or alive. Does this break the law of noncontradiction? As Aristotle summed it up, “One cannot say of something that it is and that it is not in the same respect and at the same time.“ Could we say: the states of Schrodinger’s cat before observation aren’t in a mutually exclusive state. In this case, the two states don’t actually contradict. Now if Schrodinger’s cat was in two states after someone looked in the box, then we’d have a problem. 

Title: Re: various physics questions Post by towr on Jun 23^{rd}, 2008, 12:47am Since Schrodinger's cat is an observer itself, the thought experiment fails. That said, it is only an interpretation of a physical phenomenon. Reifying it would be a mistake, I think. Just as it would be a mistake to consider the manyworld interpretation and pose that those many worlds actually exist, rather than conceptually. And in any case, the cat wouldn't be both alive and dead; it would be alive with 50% probability and dead with 50% probability. Which of the two is determined at observation (by any interaction with the universe at large, not necessarily by a sentient). So there is no problem with contradiction. 

Title: Re: various physics questions Post by BenVitale on Jun 23^{rd}, 2008, 10:41am Take another example, a quantum coin. Flip a coin in the quantum realm and the outcome won't be heads or tails. We will need new strategies to play traditional games in the quantum world. The quantum coin can also settle on heads and tails. We expect that quantum computers will be able to use entirely new algorithms to solve a variety of problems more efficiently than conventional machines. In quantum physics a state just gives the probabilities of finding the system in each of the possible outcomes of a measurement(well really it gives the square root of the possibility). So for example, considering the coin 1/Sqrt.{2} (Tails) + 1/Sqrt.{2} (Heads) it doesnt necessarily have to be 5050, you just change the coefficients of the possible outcome states. Also there doesnt have to be a finite number of possible outcome states, a system can have an infinite number of possible outcomes (1), (2), (3) ... and then the systems state is given by the sum of all these states each multiplied by a coefficient that gives their probability. 

Title: Re: various physics questions Post by Grimbal on Jun 26^{th}, 2008, 8:03am on 06/22/08 at 15:36:30, BenVitale wrote:
But as F. Scott Fitzgerald said: "The test of a firstrate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function." ;D on 06/23/08 at 00:47:35, towr wrote:
I wonder. What is it that makes the cat an observer? What makes it different from a cloud of particles that might well live in a superposition of states? As I see it, the cat will experience a unique outcome and could believe (provided some training in physics) that the rest of the world collapsed to a single state. But another interpretation would be that the cat split in multiple versions, each of which experiences a single outcome. I like the idea that if we do something to a particle when we observe it, then the particule does the same thing to us. It is true for gravity, why not for quantum pheonomena? If in our view the particle is in a superposition of quantum states and collapses to one when we observe it, in the view of the particle, WE are in a superposition of quantum states and OUR wave function collapse to a single state. What I wonder about with Schrodinger's cat is that when a photon splits into 2 states, each going thru a different slit, they later interact into interference patterns. Shouldn't the superposition of cats interact in a similar way? 

Title: Re: various physics questions Post by towr on Jun 26^{th}, 2008, 8:40am on 06/26/08 at 08:03:51, Grimbal wrote:
The way I tend to look at it is that with an increased number of particles, the probability gets skewed to one macro state. Whether that's a correct interpretation or not, the fact of the matter is that as long as there is any measurement, from man or machine, or animal, waveforms collapse. Quote:
But it is rather pointless, in my opinion. (Although it can be fun to consider the whole universe in one giant superposition; all the "many worlds" occupying the same spacetime/whatever at the same time.) Quote:
The term "observation" really muddles the issue, because it gives the suggestion that there is something magical entered into the equation by consciousness. But if you do the twosplit interference experiment, and set up a measurement device to check what slit the particle comes through, but you drop every measurement directly in the bin (such that no person will ever observe it), the waveform still collapse just the same, and there is no interference pattern. Quote:
(Or rather, you wouldn't notice the interference pattern if it wasn't going slow enough. And you'd have trouble pushing the cat through the slit) It'd be a very cool (http://en.wikipedia.org/wiki/Bose_einstein_condensate) cat. 

Title: Re: various physics questions Post by Grimbal on Jun 26^{th}, 2008, 2:04pm on 06/26/08 at 08:40:26, towr wrote:
That could be a reason. I have read about the idea that it is a question of critical mass. There are experiments trying to create a superposition in larger and larger systems to see if it spontaneously collapses past some point. If that's the case, an "observer" would just just be a system that tries to interact with the quantum state and is too heavy to do so in a quantum way. Quote:
I believe there is a fundamental difference between something being unknown and something being in quantum superposition. A superposition is not just a number of possible states with probabilities attached. Quote:
It is more than just a philosophical way of seeing it. You can explain quantum physics in terms of multiple realities going on side by side (a particle following different paths or being in different states simultaneously). At some times some realities disappear. The idea that some part of reality just disappears is in my opinion less satisfying that the idea that we just loose the contact to that part of reality. And that second option naturally leads to the conclusion that many universes exist side by side. 

Title: Re: various physics questions Post by towr on Jun 26^{th}, 2008, 2:32pm on 06/26/08 at 14:04:40, Grimbal wrote:
I do think it fundamentally comes down to information in a physical sense of the word though. (Which is related to a kind of knowing, but not so much in that some entity knows something). As for the different between a superposition and a collection of states with probabilities. The only difference I can see is that in the latter case, you might have that only one state is real (and the probabilities are your best guesses); whereas for a superposition the probabilities are the chance a state will become real upon measuring it. (So probability there is more like casting a mathematical die, as opposed to uncertainty in knowledge of the true state of reality.) Quote:
Also, we can keep conservation of mass, and energy etc if we stick to one universe. Not to mention problems with continuity, because the worlds don't split off neatly at decisions people make, the wavefunctions are continuous; and each point along it would split off into each own universe; for every particle; at every time. It's a bit much. However, it's neatly resolved if we leave everything in superposition. To come back to "The idea that some part of reality just disappears": they were never real in the first place. When a wavefunction collapses one of the states becomes real, the rest never were (and it wasn't real before it was observed either). 

Title: Re: various physics questions Post by BenVitale on Jun 26^{th}, 2008, 3:25pm Sorry to interrupt. I have a question : What would make a wave function to collapse? 

Title: Re: various physics questions Post by towr on Jun 26^{th}, 2008, 11:54pm on 06/26/08 at 15:25:33, BenVitale wrote:
Perhaps the wave function doesn't so much collapse, but just gets highly skewed towards one state. 

Title: Re: various physics questions Post by rmsgrey on Jun 28^{th}, 2008, 10:20am Roger Penrose speculated (possibly drawing ideas from others) in one of his books that, while small, light objects such as fundamental particles can exist simultaneously in superpositions of states, "sufficiently" different spacetimes can't superpose successfully  when the distribution of mass becomes sufficiently different between different states, a transition occurs, and the superposition collapses down to a single state (or single family of related states) 

Title: Re: various physics questions Post by BenVitale on Jun 28^{th}, 2008, 11:28am What about the standard Copenhagen interpretation? Didn't the standard Copenhagen interpretation is that the cat is neither alive nor dead? "Alive" or "dead" is what we observe when we open the box and collapse the wave function, and the probability of one observation or the other might be 50% (depending on the circumstances). But before we look, the cat exists in a nondeterministic state of superposition, that is, it is neither alive nor dead. I understand that the standard Copenhagen interpretation came under severe criticisms recently. Is it still valid or not? 

Title: Re: various physics questions Post by Grimbal on Jun 28^{th}, 2008, 3:14pm on 06/26/08 at 14:32:10, towr wrote:
What I mean is that a superposition of a top spin and a bottom spin can have a definite spin oriented left or right depending on the phases. But a particle being top or bottom with 50% chance will always be measured left or right at 50%. Also, a particle that goes through 2 slits interacts with its other self and produces inference patterns, while a particle that goes through one or the other slit doesn't. Quote:
I feel it is like being in a corridor of a hotel with many doors, you can open only the one to your room, so you don't think there is anything behind the others. Quote:
When a particle is in 2 positions simultaneously, isn't it already a multipleworld interpretation? But I agree that I am not quite happy with the idea that something that is out of reach is considered to exist. Quote:
You can not say for one state that it was never real and for the other that it becomes real. You must say it was always real. It just wasn't known. But quantum mechanics is incompatible with the idea that the state just wasn't known, as the EPR paradox demonstrates. 

Title: Re: various physics questions Post by BenVitale on Jun 29^{th}, 2008, 1:39am Is anybody familiar with the GRW theory (Ghirardi, Rimini and Weber)? According to quantum theory, a particle does not sit in just one place, but occupies many places all at once. Its true position is defined by a fuzzy blob called a "wave function", which sets out the probability of finding the particle in various locations. With time, the wave function of any particle spreads out, bleeding into an expanding volume of space, as the particle's multiple existences proliferate. Ghirardi, Rimini and Weber proposed a subtle change in the quantum rules that determine how wave functions evolve . Suppose, they said, wave functions usually spread out according to normal quantum rules, but very rarelyonce every 100 million years or so the wave function of a single particle collapses and becomes localised to a tiny region. This change scarcely affects single particles, but has a huge effect on big things. I don't really understand all of this. They take an example, a cat or any other object of similar size contains some 10^{27} particles, and even though the wave function of any one is likely to take 100 million years to collapse, there are so many particles that it is overwhelmingly likely that the wave function of at least one particle will collapse within just 10^{12} seconds. The GRW theory doesn't really explain what would make a wave function collapse, nor why it should happen only every 100 million years. I'm sure i'm missing something, even perhaps a lot of things. Could anyone clarify? 

Title: Re: various physics questions Post by towr on Jun 29^{th}, 2008, 7:30am on 06/28/08 at 11:28:44, BenVitale wrote:
I can't say that I've heard anything about criticism of the Copenhagen interpretation though, but then I'm not really involved in the QM field, it might easily have slipped passed me. 

Title: Re: various physics questions Post by towr on Jun 29^{th}, 2008, 8:01am on 06/28/08 at 15:14:44, Grimbal wrote:
But when is a particle ever in two positions at once? If you try to measure it, it's always only in one, it's never seen in two. Quote:
Just to make sure there's no confusion, my interpretation is that none of the superposed states are real before the wavefunction collapses. Not that "the real one" existed all along but was simply unknown. Quote:
Besides, any random universe can be sufficiently closely approximated in simulation by a large enough deterministic computer. ;) 

Title: Re: various physics questions Post by ThudanBlunder on Jun 30^{th}, 2008, 9:06am A timely link (http://www.guardian.co.uk/science/cern). 

Title: Re: various physics questions Post by Grimbal on Jun 30^{th}, 2008, 2:23pm on 06/29/08 at 08:01:39, towr wrote:
It can be in multiple positions as long as you don't measure it. You can hardly explain the interferences in the 2slip experiment if the photons don't go through both slits. Quote:
I see what you mean, but I don't feel comfortable with it. It is that "changing state" that bothers me. It breaks Schroedinger's equations. The other thing that bothers me is that instant action at a distance. If 2 entangled particles move away from each other, as long as you haven't measured one, the other can be in a number of quantum states. When you measure one, the wave function of the other one collapses to a definite state. It is like if your measurement forced the whole universe to align itself to it. I prefer to think that multiple universes exist, and that your measurement selects a path, affecting only yourself, not the whole universe. Since both outcomes existed before the measurement, then both exist after it. One of them is just out of reach. This being said, what makes me think like that is intuition, and quantum mechanics is notorious for offending intuition badly. 

Title: Re: various physics questions Post by towr on Jun 30^{th}, 2008, 3:16pm on 06/30/08 at 14:23:29, Grimbal wrote:
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I'm not sure you can't just see it as an interaction between waveforms though, which 'simply' results in a more certain state for the measured particle. (Similar to how many uncertain measurements average to a more certain one; the interaction between particles could 'stabilize' them with respect to each other.) Quote:
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Title: Re: various physics questions Post by Grimbal on Jun 30^{th}, 2008, 10:32pm on 06/30/08 at 15:16:09, towr wrote:
Particles are like naughty children. As long as you watch them, they behave like angels. But as soon as you turn your back they do the craziest thing you didn't even think possible. If the photon doesn't go through both slits in some way, then you don't have an interference. Quote:
Yes. Quote:
You seem to see the wave function as nothing more than some kind of probability distribution. Quote:
Of course not! I see it more like closing a door. And regarding how much can be involved, it would be interesting to see whether a whole cat can be involved. 

Title: Re: various physics questions Post by towr on Jul 1^{st}, 2008, 12:42am on 06/30/08 at 22:32:59, Grimbal wrote:
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Title: Re: various physics questions Post by BenVitale on Jul 1^{st}, 2008, 8:40am I've asked an experimental physicist about this thought experiment, about the point of this experiment. He answered: Schroedinger's cat's example is just a question of whether the atom decayed and set off a chain of events. If you get hung up on all the chain and not the atom, you've completely missed the point of the example. A thought experiment is illustrative. It does not need to take into account every tiny effect. It needs to explore a big idea, with no effects included that are so big as to dominate the outcome. The Copenhagen Interpretation of QM states that until a measurement is undertaken, that the atom simultaneously exists in two quantum states. Ignore the remainder of the window dressing. Both Schroedinger and Einstein did.... QM is a messy business. But it works extremely well. What do you guys think? 

Title: Re: various physics questions Post by BenVitale on Jul 1^{st}, 2008, 11:37am Experimental physicists don't always agree with theoretical physicists on interpretations. Is anyone familiar with the GRW theory? Source: http://philosophy.rutgers.edu/FACSTAFF/BIOS/PAPERS/LOEWER/loewerschroedingerscat.pdf 

Title: Re: various physics questions Post by Grimbal on Jul 1^{st}, 2008, 3:06pm on 07/01/08 at 00:42:45, towr wrote:
In fact, I believe photons do interact at the quantum level, or they wouldn't combine to create coherent light in lasers. But it is not like the photon splits and becomes 2 particles. I don't know how to call what it does. But some of the "stuff" the wave function is made of spreads to multiple locations and follows both paths simultaneously. It is never completely in one position or the other. But it is different from a probability because with a probability you could consider the 2 cases of the particle going through each slit and sum the results.[/quote] Quote:
But by squaring and taking the norm, you loose the phases in the wave function. And the phase allows for much more complex behavior than you can explain with probabilities. Quote:
You are in front of 2 doors, you chose one and enter the room. The door closes behind you, meaning the other room becomes inaccessible to you, but it still exists. Quote:
Frankly I don't know how many of them are on which side, but it seems to me the question is still debated. 

Title: Re: various physics questions Post by BenVitale on Jul 1^{st}, 2008, 6:51pm according to Quantum decoherence http://en.wikipedia.org/wiki/Quantum_decoherence we only have the appearance of wavefunction collapse. According to decoherence theory, even a stray photon "counts" as an observer. Any particle interacting with an object in a mixed state will collapse the superposition and put the object into a pure state. The idea is called "decoherence," and it is the reason we don't see quantummechanical effects [often] on the macroscopic level. All the billions of particles interacting with the system  atoms of air, infrared photons, etc.  all serve to keep macroscopic objects like cats out of quantum superpositions. there are some ways to observe macroscopic quantum mechanical effects, but they don't involve house pets, for example, superfluids. 

Title: Re: various physics questions Post by towr on Jul 2^{nd}, 2008, 12:44am on 07/01/08 at 15:06:07, Grimbal wrote:
Otherwise I'd expect to end up in a universe with exceedingly less people (and matter in general). Or is it a nonphysical me that's making the path through the continuum of adjacent universes? (Which has it's own set of problems). 

Title: Re: various physics questions Post by towr on Jul 2^{nd}, 2008, 12:46am on 07/01/08 at 18:51:09, BenVitale wrote:
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Title: Re: various physics questions Post by Grimbal on Jul 2^{nd}, 2008, 4:25am on 07/02/08 at 00:44:09, towr wrote:
Yes, but you experience only one path. The "other you" experiences the other path. So you might be under the impression that whatever you observe collapses to a pure state, while in fact the superposition still exists. 

Title: Re: various physics questions Post by BenVitale on Jul 2^{nd}, 2008, 8:41am Thanks towr for answering. I thought my last physics posts were being ignored. What about "superfluids"? We can observe macroscopic quantum mechanical effects with superfluids. Take a bucket of liquid helium and cool it down to within a few degrees of absolute zero, it undergoes a phase transition called BoseEinstein condensation. All the atoms hurry to enter the same quantum state, because that minimizes their total energy. So you wind up with a bucket full of atoms that have all agreed to be in the same state. And if you try to use it like a normal fluid notice it flows without viscosity. That's right, it flows without resistance through even the very smallest pores in your container, and through even the smallest pipettes. Why? Because all the atoms are already in their lowest energy state. Since they're all doing the same thing, though, the walls of a pipette can't smack them around too much  you can't smack around one, you have to smack around every single last trillion of them. Superfluids also will only permit certain values of angular momentum, e.g. 3 or 5 or 7 rotations per second. Even if you spin the bucket at 4 rotations per second from now to eternity, the helium atoms won't care. Angular momentum is quantized for their collective quantum state, and they'll only rotate at 3, 5, or 7, and never, ever at 4. You can basically consider a bucketful of liquid helium to be like one giant macroscopic quantum object. 

Title: Re: various physics questions Post by Grimbal on Jul 2^{nd}, 2008, 2:22pm That also fascinates me. Makes you feel that there is something very wrong in your understanding of the world and the truth is there at you fingertips. But you say 3, 5 or 7. Does it extend to 1 and 1, or is it an approximation? Is zero a valid angular speed? And is there a phenomenon of superposition of different speeds? 

Title: Re: various physics questions Post by BenVitale on Jul 2^{nd}, 2008, 9:49pm on 07/02/08 at 14:22:31, Grimbal wrote:
Yes, 1 and 0 are valid values for angular momentum. Usually we talk about the absolute value, but whenever direction matters we see negative spins like 1 along with positive ones. Quote:
Yes! It might surprise you to know that any quantum state can be written as a superposition of different speeds. But the same is true if the word speed is replaced by "Energy", "Position", or any other physical variable you can think of! 

Title: Re: various physics questions Post by BenVitale on Jul 3^{rd}, 2008, 12:01pm I need your help to figure this thing out. Why? Because I got ridiculed by my physics prof. [he is an experimental physicist] for showing an interest in this thought experiment. My physics prof told me that the whole Schroedinger's cat thing is something of a magnet, intentionally absurd, a metaphysical nonsense, that I should not waste my time on this, and do real physics instead. But then, I mentioned the GRW Theory (Ghirardi, Rimini and Weber) http://philosophy.rutgers.edu/FACSTAFF/BIOS/PAPERS/LOEWER/loewerschroedingerscat.pdf He got very emotional. I don't need to repeat word for word what he said to me in class, in front of everybody. In summary he belittled me for this whole Schroedinger's cat business. I'm really surprised why a physics prof would get all uptied over this theoretical physics experiment. There are theoretical physicists who don't think that this is a stupid idea, they don't think that it is a waste of time. So for now I keep my mouth shut in class about this cat thing. I have this forum to discuss about this experiment. 

Title: Re: various physics questions Post by ThudanBlunder on Jul 3^{rd}, 2008, 12:13pm on 07/03/08 at 12:01:41, BenVitale wrote:
Perhaps he is a cat lover who believes that you are trying to run before you can walk. By the way, for some reason Physics seems to be a magnet for cranks and crackpots with tunnel vision. 

Title: Re: various physics questions Post by BenVitale on Jul 3^{rd}, 2008, 12:56pm Quote:
As a matter of fact, he has a cat, because sometimes he comes to class with cat hair on his clothes. Quote:
True. I got fascinated by the Elegant Universe, Hawking's string theory on NOVA (PBS). String theory is another thing my physics prof likes to ridicule. Is it true or false that : (a) Quantum theory is highly counterintuitive (b) many physicists have trouble with it ThudanBlunder, what do you think of the different perspectives of this experiment? 

Title: Re: various physics questions Post by BenVitale on Jul 3^{rd}, 2008, 1:38pm In the Scientific American's article "The Nature of Space and Time" http://zebu.uoregon.edu/~imamura/123/lecture7/hawking.html an excerpt Quote:


Title: Re: various physics questions Post by ThudanBlunder on Jul 3^{rd}, 2008, 6:48pm on 07/03/08 at 12:56:21, BenVitale wrote:
In this case his derision is more understandable. on 07/03/08 at 12:56:21, BenVitale wrote:
I can see you a few years down the line failing your final exams but being offered a full professorship on the spot. LOL on 07/03/08 at 12:56:21, BenVitale wrote:
(a) True, as our intuition stems from classical logic. (b) Hardly true. They grew up with it and they realize it's the only game in town. What experiment? Oh, you mean this ongoing one that we are all unwittingly part of? ::) What a pity we can never observe any results without affecting them. ;D Now, what do you think of my (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_general;action=display;num=1189567036;start=38#38) theory? 8) By the way, did you know that Heisenberg was once stopped by a traffic cop while out driving? The cop said, 'Have you any idea how fast you were travelling?' Heisenberg replied, 'No, but I know exactly where I am.' 

Title: Re: various physics questions Post by towr on Jul 4^{th}, 2008, 12:31am on 07/03/08 at 18:48:41, ThudanBlunder wrote:


Title: Re: various physics questions Post by towr on Jul 7^{th}, 2008, 5:45am Here's some disturbing news: http://www.nature.com/news/2008/080702/full/454008a.html What they claim they can do there is undo measurements (of a certain kind). Why is that disturbing? Well, take a pair of entangled photons, say. Now if you measure one, the other will be in the exact same state; no matter how far apart they are. But what if you can undo a measurement? That means you can repeat observations until you see a measurement you like, which will then also be identical at the other end. All you need is a bit of good timing, and you can send information at instantaneous speed. Or so, at least, goes my understanding of the phenomenon. (I suppose it's possible some other mechanism will interfere with this scheme; it almost certainly has to.) 

Title: Re: various physics questions Post by Grimbal on Jul 7^{th}, 2008, 8:25am They don't actually undo a measurement. They do a partial measurement that is inconclusive. It only hints at one result. Then they do the opposite measurement, equally inconclusive, that hints at the opposite result. They end up now knowing anything about the quantum state. 

Title: Re: various physics questions Post by towr on Jul 7^{th}, 2008, 9:04am Of course, the measurement isn't always inconclusive. And when it's not they can't undo it either. But when it's inconclusive, they can repeat it, if they want to, until it isn't. I suppose the obstacle is that the probability is equal for it to conclude on the first or second measurement. 

Title: Re: various physics questions Post by BenVitale on Jul 7^{th}, 2008, 11:23am towr, do you have the whole article? 

Title: Re: various physics questions Post by towr on Jul 7^{th}, 2008, 11:44am on 07/07/08 at 11:23:33, BenVitale wrote:


Title: Re: various physics questions Post by BenVitale on Jul 7^{th}, 2008, 3:13pm Thanks for the link to MIT theoretical physics and for the Schroedinger's cat article. That's very cool! 

Title: Re: various physics questions Post by BenVitale on Jul 11^{th}, 2008, 11:16am Experimental vs. Theoretical physics debate. Heisenberg stated, "What we observe is not nature itself but nature exposed to our method of questioning." So theory in part constructs reality. What can we say about equipments used in experiments? Don't they determine the results? Couldn't we say that equipments construct results? The act of studying an event can change it. 

Title: Re: various physics questions Post by BenVitale on Jul 11^{th}, 2008, 1:17pm Has anyone read "The Final Theory" http://www.thefinaltheory.com/?gclid=CL2jicXSuJQCFSUqagodJnXvTQ 

Title: Re: various physics questions Post by towr on Jul 11^{th}, 2008, 1:26pm on 07/11/08 at 11:16:46, BenVitale wrote:
Reality is as it is, regardless of theory. Quote:
Would there no longer be atoms if we didn't have electron microscopes to see them with? Surely they must always have been there (well, for some 14 billion years), regardless of whether we could observe them. That we don't know something exists hasn't any bearing on whether it does. Quote:
Without the reality check of what is actually there to be measured, the whole exercise would be rather pointless. Quote:


Title: Re: various physics questions Post by ThudanBlunder on Jul 11^{th}, 2008, 1:53pm on 07/11/08 at 13:17:31, BenVitale wrote:
Probably not, and with good reason. 

Title: Re: various physics questions Post by BenVitale on Jul 11^{th}, 2008, 2:48pm on 07/11/08 at 13:53:54, ThudanBlunder wrote:
I haven't read it. I'm just curious to know whether or not has read it. I just don't have enough time to read any books unrelated to my studies. 

Title: Re: various physics questions Post by BenVitale on Jul 11^{th}, 2008, 2:51pm on 07/11/08 at 13:26:04, towr wrote:
Yes, I agree with you. Take, for example, our telescopes. From the early telescopes to the sophisticated and powerful ones of today, haven't they shaped and reshaped our theories about the size of the universe? 

Title: Re: various physics questions Post by ThudanBlunder on Jul 11^{th}, 2008, 3:07pm on 07/11/08 at 14:48:32, BenVitale wrote:
According to this guy, obviously a crank, all of modern physics is wrong. But despair not! Buy his book and you can be put right. I gave up after I read this: Q: Light slows as it passes through water or glass, causing it to bend, but how can it return to lightspeed on its own once it exits? A: This is impossible in today's science. No object in nature can speed up of its own accord after being slowed. A bullet doesn't spontaneously speed up after it is slowed by passing through a wooden block, so how does a photon of light mysteriously return to its original speed once it exits a glass block? Now correct me if I am wrong, but as photons have zero rest mass, they don't need a force to accelerate them. 

Title: Re: various physics questions Post by towr on Jul 12^{th}, 2008, 4:32am on 07/11/08 at 15:07:23, ThudanBlunder wrote:


Title: Re: various physics questions Post by BenVitale on Jul 12^{th}, 2008, 3:11pm I see your point. Thank you for taking the time and trouble to read the beginning of this nonsense. It's funny that physics attracts more wannabes, crackpots than mathematics. 

Title: Re: various physics questions Post by towr on Jul 13^{th}, 2008, 6:56am on 07/12/08 at 15:11:15, BenVitale wrote:
For example, I recall there was someone a few years back that claimed to prove the cardinality of the sets of rationals and real numbers are the same. That's pretty fundamental crackpottery right there. Of course, maths does have the advantages that you're not limited by reality (of course, one might argue theoretical physicists sometimes cross that line, like in string theory.) 

Title: Re: various physics questions Post by Eigenray on Jul 13^{th}, 2008, 7:42am on 07/12/08 at 15:11:15, BenVitale wrote:
Anyone else remember [link=http://groups.google.com/groups/search?q=jsh+group%3Asci.math]James S. Harris[/link]? Oh, and he has a [link=http://mymath.blogspot.com/]blog[/link] too. 

Title: Re: various physics questions Post by ThudanBlunder on Jul 13^{th}, 2008, 8:18am on 07/13/08 at 07:42:06, Eigenray wrote:
Yeah, I've slagged him off a few times. LOL Here is a list (not my own) of top cranks (mostly on sci.math), with reasons: 1. Ben Jebara (ajebara) for linking the negation of the axiom of choice to infinite integer solutions of FLT using a FraenkelMostowski model in which x.x.x.... exists for odd x but not for even x and in particular his observation that something that exists cannot be equal to something that doesn't. 2. Edgar E Escultura for discovering that only terminating decimals can be added and multiplied and that nonterminating decimals, including all the irrationals are illdefined. 3. James Wanless for finding out that Goldbach's conjecture is false even though his counterexample was "rather large", for solving the twin prime conjecture and indeed the 2n prime conjecture (differing by 2n rather than 2) , solving FLT, an extraordinary proof of Pythagoras' theorem, proving no odd perfect numbers exist, solving Catalan's conjecture, solving Carmichael's conjecture, an amazing proof that between n and 2n there is always a prime, a hypershort proof of Dirichlet's theorem and a fantastic proof of the Collatz conjecture. 4. James S Harris for proving FLT about 2000 times in 3 years using only very elementary methods. 5. Tleko for discovering that f(z)=z is not analytic. 6. Sollog for discovering that the primes are not randomly distributed but actually fall into 8 of 30 columns and any number which doesn't can be absolutely excluded from being a prime and JP (who is probably the same guy) for advertising this and for proving his point by using capital letters. 7. Zhang Hong for solving the continuum hypothesis in a smart way. 8. Mike Deeth (probably) for pretending to be 11, to be called Nathan and for discovering that certain things simultaneously exist and do not exist and for introducing the revolutionary technique of making childish ancient jokes with the word Cantorian substituted somewhere to prove his points. 9. Archimedes Plutonium: his achievements are too many to even think about listing  with 25349 messages he had contributed to all sorts of stuff, not just mathematics. A true renaissance guy. The fact that he solved chess is amazing enough as it is. 10. Alexander Abian for discovering that we must blow up the moon as it a source of all kinds of problems and evil. 11. Will Hunting for solving a homework exercise that was supposed to involve advanced Fourier analyis and take all semester but which, as far as I could see (and I only saw it once, so my memory might be failing me) seemed to involve transition matrices, perhaps graphs and the ohsodifficult cubing of a 4x4 (or maybe a little larger) matrix (related to the transition matrix) and having accomplished cubing a matrix he was then able to solve at first sight a problem that was supposed to have taken a Fields Medallist, specializing in the area, years. 

Title: Re: various physics questions Post by BenVitale on Jul 18^{th}, 2008, 9:35am I've been talking to a physics major student about the collapse of the wave function. I told him that the collapse of the wave function is very mysterious to me. He smiled and said that it is mysterious to him too. And, The wave function of any particle...a photon being the easiest to discuss....can occupy a large portion of space. It is only with the collapse of the wave function that the particle is observed at a single point. We don't really understand quantum mechanics. Neither does anyone else...we just have varying levels of mastery on how to manipulate the equations. 

Title: Re: various physics questions Post by BenVitale on Jul 22^{nd}, 2008, 8:01pm Here's an old and fun puzzle in physics: An averagesize adult has in the neighborhood of 2,000 square inches of skin. Multiplythis by the atmospheric pressure of 14.7 pounds per square inch, giving 30,000 pounds. That's 15 tons! Why don't we feel this enormous pressure? 

Title: Re: various physics questions Post by towr on Jul 23^{rd}, 2008, 1:02am on 07/22/08 at 20:01:49, BenVitale wrote:
We'd hardly notice ten times that, but you'll feel it if there's only a tenth. Besides, we also don't notice this enormous heat; the temperature on earth is about 100 times the average in space. But you can get used to anything, especially if you have 4 billion years of evolutionary history adapting you to the conditions. Not really a question of physics at all. 

Title: Re: various physics questions Post by BenVitale on Jul 30^{th}, 2008, 9:01am I recently had a discussion with a physics major student about String Theory, and this is what I gathered: String theory is a theory. Like all theories, it is a model, backed up by mathematics, that attempts to explain some aspect of the universe. String theory is predicated first on the world having a property called supersymmetry. Supersymmetry has never been observed,. if supersymmetry exists, string theory may still be wrong. But if supersymmetry does not exist, string theory is dead. string theories postulates that particles as we think of them can be replaced with tiny vibrating nodes in spacetime. There are many papers postulating various aspects of the strings if they exist. These papers do not make testable predictions nor is it likely that there will be a testable prediction from these papers in the forseeable future. This failure does not mean string theory is incorrect, but rather that there is no real reason to believe it at this time. String theory is completely consistent with existing data. Of course, that's by construction. Any theory that says that photons can decay into photons must be false and, of course, string theory makes no such claims. The one real success of string theory is that it provides a way to envision that all of the forces (gravity, electromagnetism, weak and strong) are all explained by a single mechanism. It also unifies the quantum world and gravity. 

Title: Re: various physics questions Post by BenVitale on Jul 31^{st}, 2008, 11:22am Here are fun riddles from the Martin Gardner puzzles in the Scientific American Magazine. (1) Suppose the Earth was in fact a perfect sphere. A steel strip is fitted around the equator, forming a tight band. That band is then cut at one point, and extra foot [30cm] of strip is welded in to the band, and with a deft flick of the band, it briefly is found in the positon where the gap between the band and the Earth is exactly the same sized all the way round the equator. The size of the gap will allow: A. A laser to be shone through the gap and thus demonstrate a spectacular diffraction pattern. B. A cigarette paper to be slipped snugly through the gap. C. A mouse to crawl through the gap. D. A cat to rush through the gap chasing such a mouse. Which answer do you think is most likely representative of the situation. (2) A group of explorers start at a point P and travel in a perfectly straight line (LEAVING A VISIBLE RED TRAIL) north until they arrive back at P. Then again leaving from P, they travel west in a perfectly straight line (leaving a visible GREEN trail this time) until they arrive back at P. BUT they notice that on the 2nd trip, the green trail does not intersect/meet the red trail. If they were living on a sphere, then the green and red trails should intersect at right angles. Question: Can these explorers be living on the surface of a sphere? If not, what could they be living on? 

Title: Re: various physics questions Post by SMQ on Jul 31^{st}, 2008, 11:36am [hide]I haven't known too many cats which will fit through a 2" gap.[/hide] ;) For myself, I like this version (http://www.ocf.berkeley.edu/~wwu/cgibin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1052722359) better, as the answer is even more surprising. SMQ 

Title: Re: various physics questions Post by BenVitale on Jul 31^{st}, 2008, 11:55am Quote:
Your link doesn't work. I got the message: This topic doesn't exist on this board. 105272235 : 1397. 

Title: Re: various physics questions Post by towr on Jul 31^{st}, 2008, 12:19pm on 07/31/08 at 11:55:12, BenVitale wrote:
(he cut off a 9 at the end) 

Title: Re: various physics questions Post by rmsgrey on Aug 1^{st}, 2008, 9:33am on 07/31/08 at 11:22:40, BenVitale wrote:
Assuming no trickery, then they're not on a sphere. The obvious example of a surface they could be on is [hide]a torus[/hide]  there are many other possibilities. 

Title: Re: various physics questions Post by BenVitale on Aug 1^{st}, 2008, 10:30am Sure they could be living on a Torus or donutshaped object. it sounds simple  except for getting a standard North South magnetic field to be set up around the donut. OR They could either be living on a sphere. On a sphere, they will have to have gone South to get back to their starting point [P]  like North along the Greenwich meridian to the North Pole, South along the international date line to the South Pole, then North again back to P. 

Title: Re: various physics questions Post by Eigenray on Aug 1^{st}, 2008, 6:58pm on 08/01/08 at 10:30:41, BenVitale wrote:
It is actually simpler on a torus than on a sphere. If we think of the torus as the square [0,1] x [0,1] in the plane with opposite edges identified, then we can just take north and west to be the directions of increasing y and decreasing x. In other words, the torus is [link=http://en.wikipedia.org/wiki/Parallelizable_manifold]parallelizable[/link] (the sphere doesn't even have one nonvanishing vector field, let alone a frame). Maybe this wouldn't be a "standard" magnetic field, but then this isn't a standard Earth either. 

Title: Re: various physics questions Post by rmsgrey on Aug 2^{nd}, 2008, 3:36am Sending an electric current around a loop of wire will give you a suitable magnetic field... 

Title: Re: various physics questions Post by BenVitale on Aug 2^{nd}, 2008, 12:58pm Quote:
The gap is 2 inches. If we assume radius r = 4000 miles. Then C = 2Pi*r and new C_{2} = 2Pi*r + 1/5280, then new r_{2} = C_{2}/2Pi = (2Pi*r + 1)/2(Pi) = r + 1/5280/(2Pi), then the gap is r_{2}  r = 1/5280/2/Pi miles. or 1/2/Pi feet or 12*2/Pi inches = 6/Pi inches = 1.90985.. inches. This gap will not allow the cat to rush in or will not be a snug fit to a cigarette paper. 

Title: Re: various physics questions Post by Christine on Aug 3^{rd}, 2008, 11:17pm Quote:
The green trail (that starts westwards) must not intersect the red trail (the one that starts northwards) until, of course, both return to the starting point. On a sphere the two trails WILL intersect before returning to start. therefore I think the explorers cannot be on a sphere. Am I missing something? BTW when you say a perfectly straight line that makes me think that it must be a geodesicon the sphere it would be two great circles which depart from the initial point at right angles. So they would meet also at right angles, at the antipodal point. 

Title: Re: various physics questions Post by Grimbal on Aug 4^{th}, 2008, 7:53am I see 2 problems: 1. If they go north all the time, they will reach the north pole and stop there. They will never reach P again. 2. By definition both lines meet at P, so the condition that they don't meet can not be satisfied, whether on a sphere or elsewhere. 

Title: Re: various physics questions Post by BenVitale on Aug 4^{th}, 2008, 5:21pm on 08/04/08 at 07:53:18, Grimbal wrote:
Sorry. I don't get it. Quote:
This is not clear to me. 

Title: Re: various physics questions Post by towr on Aug 5^{th}, 2008, 12:42am on 08/04/08 at 17:21:27, BenVitale wrote:
How can you continue in the northwards direction once you've traveled from P to the north pole? You can't, you're stuck. Quote:


Title: Re: various physics questions Post by BenVitale on Oct 14^{th}, 2008, 3:53pm Would the following qualify as a cranck: http://www.upsite.co.il/uploaded/files/251_0f2d8e2b34a229f1d05ab31eb070be32.pdf 

Title: Re: various physics questions Post by towr on Oct 15^{th}, 2008, 1:51am on 10/14/08 at 15:53:58, BenVitale wrote:


Title: Re: various physics questions Post by SMQ on Oct 15^{th}, 2008, 6:35am I also found it telling that after "discovering" that children approach the world in an organic and informal way, the first thing he tries to do is rigidify and formalize his discovery... SMQ 

Title: Re: various physics questions Post by BenVitale on Oct 15^{th}, 2008, 11:13am I thank you for answering to my post. What did you think of his representation of the Unity problem, and the nonlocality in nature? 

Title: Re: various physics questions Post by BenVitale on Dec 5^{th}, 2008, 8:52pm What do you, guys, think of this: http://www.telegraph.co.uk/scienceandtechnology/science/sciencenews/3303699/%27Wehavebrokenspeedoflight%27.html 

Title: Re: various physics questions Post by towr on Dec 6^{th}, 2008, 6:21am on 12/05/08 at 20:52:11, BenVitale wrote:
Since the article is over a year old, I'd look up the original publication and consequent responses to it. At the very least it should tell you something about what actually happened in the experiment. 

Title: Re: various physics questions Post by rmsgrey on Dec 6^{th}, 2008, 10:07am A quick look on Wikipedia (http://en.wikipedia.org/wiki/Fasterthanlight#Faster_light_.28Casimir_vacuum_and_quantum_tunnelling.29) finds: Quote:


Title: Re: various physics questions Post by BenVitale on Dec 7^{th}, 2008, 10:20am Thank you Towr and rmsgrey. Didn't the physicits at Berkeley produce an experiment where a single photon tunnelled thru a barrier and its tunneling speed was 1.7 the speed of light? 

Title: Re: various physics questions Post by Gabriel on Apr 10^{th}, 2009, 2:36pm Hello guys, I'm new to this forum, so I don't really know whether this is the correct place to post a physics problem, which I have to solve. I'm kinda stuck in that,and I hope someone can give me a little help. My scientific english isn't so good, but I will try to explain the problem: We have N nodes (we can think of them as vertice of a graph). We put resistors between them randomly, but 1. Resistors have the same resistance: R. 2. Between 2 nodes the number of maximal resistors is 1. 3. The graph doesn't have any isolated vertice/ isolated sets of vertice. (So you can walk from any of the vertice to any other of them via resistors) In result, the number of connecting resistances to a vertex can vary from 1 to N1. Measure the resistance between the endpoints of all of your resistors, and sum them up. What's the result you'll get? [hideb](N1)*R, I just can't prove it in a general situation[/hideb] I would be very grateful if someone could help. Regards, Gabriel 

Title: Re: various physics questions Post by towr on Apr 10^{th}, 2009, 2:47pm on 04/10/09 at 14:36:12, Gabriel wrote:


Title: Re: various physics questions Post by Gabriel on Apr 10^{th}, 2009, 4:26pm on 04/10/09 at 14:47:09, towr wrote:
This means to measure resistance between every two nodes, which are connected with a resistor directly. This means on my figure: Measure resistance between AE, EC, CB, BD and DC nodes, and sum them up. You will get 4R. 

Title: Re: various physics questions Post by Eigenray on Apr 11^{th}, 2009, 12:20am Interesting problem. To phrase it in terms of matrices: Suppose there are m edges connecting n vertices. Let A be the sum of the matrices E(i,i) + E(j,j)  E(i,j)  E(j,i) over each edge (i,j), where E(i,j) is the nxn matrix with a single 1 in position (i,j). Let A_{i} denote the (n1)x(n1) matrix obtained by deleting the ith row and ith column of A. Then the resistance between nodes i and j is given by the (j,j)th entry of A_{i}^{1}. So let R be the nxn matrix whose ith row is given by the diagonal elements of A_{i}^{1}, with a 0 inserted in position i; thus R(i,j) is the resistance between nodes i and j, and the problem is to show that http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif A_{i,j}*R_{i,j} = 2(n1). This generalizes as follows: suppose we have an edge between every pair (i, j) with conductance c_{i,j} (resistance 1/c_{i,j}). Let A = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif c_{i,j} ( E(i,i) + E(j,j)  E(i,j)  E(j,i) ), and R be as above. Now we need to show http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif A_{i,j}*R_{i,j} = 2(n1), the same as before. Now this is just an identity of rational functions in n(n1)/2 variables, so it can be proven for any given n at least. Code:
I'm not sure why this is true yet. In the case where all the conductances are 0 or 1, the matrix A is just the Laplacian of G, and each submatrix A_{i} has the same determinant, namely [link=http://en.wikipedia.org/wiki/Kirchhoff%27s_theorem#Kirchhoff.27s_theorem]the number of spanning trees[/link] of G. In general, I guess it is http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif_{T} http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/prod.gif_{(i,j) http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/in.gif T} c_{i,j}, where the sum is over all spanning trees T of K_{n}. So this is a common denominator for the entries of R. Suppose we wanted the sum of the resistances between every pair of vertices, not just those which are connected. That is, the (unweighted) sum, http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif R_{i,j}. Now, the sum of the ith row of R is just the trace of A_{i}^{1}, which is the sum of the roots of det( t I  A_{i}^{1} ), or the sum of the reciprocals of the roots of the characteristic polynomial det ( t I  A_{i}), i.e., 1/det(A_{i}) times the coefficient of t. So Sum(R) = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif tr(A_{i}^{1}) = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif [ 1/det(A_{i}) * { coefficient of t in det ( t I  A_{i} ) } ] = 2/det(A_{1}) * { coefficient of t^{2} in det ( t I  A ) } = 2/det(A_{1}) * http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/prod.gif http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/lambda.gif http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif 1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/lambda.gif = 2 * N * http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif 1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/lambda.gif, where http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/lambda.gif are the nonzero eigenvalues of A, since for all i, det(A_{i}) = 1/N http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/prod.gif http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/lambda.gif. Of course, this counts every pair twice, so the sum of all resistances is just N * http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif 1/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/lambda.gif. 

Title: Re: various physics questions Post by Gabriel on Apr 11^{th}, 2009, 5:12am on 04/11/09 at 00:20:18, Eigenray wrote:
I didn't know this one, and I didn't find it anywhere. Could you prove this, or at least give some pieces of advice about how can I prove it? edit: ok, I'm one step closer, I found: http://mathworld.wolfram.com/ResistanceDistance.html :) But in my opinion (3) there has some missing parts, the formula is incomplete (just have a look at (2)). But still I don't know any proof of the theorem. Some interesting things: If we allow multiple edges, the statement is still true (I tried it numerically with a 10x10 matrix) If we measure resistance at every two nodes, the result will be k*R, where k is the number of resistors. Even if there are multiple edges too. 

Title: Re: various physics questions Post by Eigenray on Apr 11^{th}, 2009, 2:46pm on 04/11/09 at 05:12:58, Gabriel wrote:
It's the matrix form of Kirchoff's law: Say there are m edges and n vertices. Let B be the m x n incidence matrix of G. If the ith edge is (a,b), then the ith row of B has 1 in position b and 1 in position a; that is, B = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif_{e_i=(a,b)} E(i,b)  E(i,a). The choice of orientation doesn't really matter, it just needs to be fixed. Let p_{a} be the potential at vertex a. Then the voltage drop across edge i = (a,b) is v_{i} = p_{a}  p_{b}, or v = B p If this edge has conductance c_{i}, then assuming there are no batteries, the current through the edge is y_{i} = c_{i} v_{i}, or y = Cv = CBp, where C is the m x m diagonal matrix with C_{i,i} = c_{i}. Now, there is a net flow f_{a} into vertex a, where f_{a} = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif_{e_i=(*,a)} y_{i}  http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif_{e_i=(a,*)} y_{i}, i.e., f = B^{t} y =  B^{t}CB p =  A p, where A is the same matrix from before, the Laplacian of G. Say we want to find the resistance between vertex j and vertex n. Fix the potential of vertex n to be 0, and drop the nth row and nth column of B. This results in the (n1) x (n1) matrix A_{n} from before. Now we pull a current of 1 out of vertex j, i.e., let f = e_{j}, and find the potential there, i.e., find p_{j} so that A_{n} * p = e_{j}. The result is R(n,j) = p_{j} = (A_{n})^{1}e_{j}. Therefore, the resistances from vertex n to every other vertex are given by the diagonal elements of A_{n}^{1}. We get a similar result by dropping any other row and column. Quote:
Interesting. I'm not quite sure why that gives the same result, but it looks like it might be easier to work with. Also note the formulas [link=http://en.wikipedia.org/wiki/Resistance_distance]here[/link], which contains the result you want. Quote:
If we put k resistors in parallel between vertices i and j, this results in a conductance c_{i,j} = k. So to sum the effective resistance over each resistor we just take http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif c_{i,j}*R(i,j). If this sum is identically 2(n1), as a rational function of the c_{i,j}, then it will be true for any values of the resistances. Quote:
Are you sure about that? Even if we just took two vertices with k resistors in parallel between them the sum should be 1/k. Or if we took a triangle, with c_{1,2} = c_{1,3} = 1, c_{2,3} = c, then the sum of resistances should be (2c+4)/(2c+1), which goes from 4, when c=0, to 1, when c=http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/infty.gif. 

Title: Re: various physics questions Post by Gabriel on Apr 12^{th}, 2009, 3:28am Thank you very much, I think I understand it now. I found the wikipedia link later too, but it doesn't prove it's statements. If I could prove that the sum of (LML)_{i,j}*R_{i,j} equals to the trace of (LM) multiplied by (2), then I could prove statement of my problem too, since if we use ML=(1/n*JI), then we get our statement (I is the identity matrix, and J is the unit nxn matrix, which has 1s at all it's entries). on 04/11/09 at 14:46:51, Eigenray wrote:
I messed it up a little bit. I calculated the sum of resistances over the edges with a for loop in octave, taking the sum of R_{i,j}*A_{i,j} (A was the adjacency matrix for me). Then, when I wanted to calculate it over all edges, I accidentally deleted R_{i,j} instead of A_{i,j}, so I calculated the sum of the adjecency matrix's entries, which is actually the spur (trace) of the Laplacian*(1), the number of resistors multiplied by 2. Stupid mistake :) :P Maybe I can prove the formula of Mathworld...I give it a try. I will use your notations, but let me use Einstein summation convention, because I can't make the Sum symbol :). Our aim is to determine resistance between vertice i and j. Hence, we pump f=(0,0...,I,0...,0,  I,0...) current in the system: I at vertice i and I at vertice j. According to your calculations, we have f= A*(p_{1}, p_{2},...,p_{n}). From this, we can derive the following formulas by calculating f_{i} and f_{j}: I =  A_{ik}p_{k}  I = A_{jk}p_{k} Now, let me use T=A+1/n*J notation, where T is gamma at mathworld, and J is the unit nxn matrix. The following can be easily derived: (A+1/n*J)p=Ap+(p_{1}+p_{2}+...+p_{n})*'/n*(1,1,1,1...1) That means, we have: (p_{1}+p_{2}+...+p_{n})*1/n*(1,1,1,1...1) +(0,0...,I,0...,0,  I,0...)= T*p so (T^1)((0,0...,I,0...,0,  I,0...)+(p_{1}+p_{2}+...+p_{n})*1/n*(1,1,1,1...1)) = p Now we prove, that T_{k,1}+T_{k,2}+...+T_{k,n}=1 It's quite easy to prove. Assume, that I = 0. Then one of our equations changes to: (T^1)(p_{1}+p_{2}+...+p_{n})*1/n*(1,1,1,1...1) = p If there isn't any current flowing into the system, the pontentials have to be equal to each other, which means T_{k,1}+T_{k,2}+...+T_{k,n}=1. We almost reached our final result, because we can write p_{i}=(T^1)_{ii}*(I)+(T^1)_{ij}*I+(p_{1}+p_{2}+...+p_{n})*1/n*((T^1)_{i,1}+(T^1)_{i,2}+...+(T^1)_{i,n}) And similarly: p_{j}=(T^1)_{ji}*(I)+(T^1)_{jj}*I+(p_{1}+p_{2}+...+p_{n})*1/n*((T^1)_{j,1}+(T^1)_{j,2}+...+(T^1)_{j,n}) By substrabting them, we get: (p_{j}p_{i}) / I=(T^1)_{ii}+(T^1)_{jj}2*(T^1)_{ij} R_{i,j}=(T^1)_{ii}+(T^1)_{jj}2*(T^1)_{ij} QED I hope I didn't make much mistakes, and that my explanation is understandable, because I'm quite tired now. At last I think I managed to understand and prove all parts of the problem, I just need the arrange my thoughts. I will post the solution of the problem in a few days, when I will have a little time. Thanks for help! 

Title: Re: various physics questions Post by BenVitale on May 15^{th}, 2009, 4:05pm I'm curious about Benford's law http://en.wikipedia.org/wiki/Benford's_law Some have made strong claims. Aren't they over the top? See articles (at the bottom of wiki page): http://www.physorg.com/news160994102.html And the law of digits at http://www.physorg.com/news98015219.html Didn't the authors just find some pattern on a small scale that somehow worked and extrapolated with the Benford's law? 

Title: Re: various physics questions Post by towr on May 16^{th}, 2009, 2:52am on 05/15/09 at 16:05:48, BenVitale wrote:
Quote:


Title: Re: various physics questions Post by BenVitale on Jul 22^{nd}, 2009, 2:38pm I've worked on a Fermi problem. I'm gonna post a proposed solution posted on the Web ... I've reached a different solution, though. The Fermi problem : When you take a single breath, how many molecules of gas you intake would have come from the dying breath of Caesar? Please read the proposed solution: http://www.hkphy.org/articles/caesar/caesar_e.html 

Title: Re: various physics questions Post by BenVitale on Jul 22^{nd}, 2009, 2:42pm Why did the author estimate thickness of the atmosphere to be 50 X 10^{3}? The thickness of the atmosphere is more difficult to pin down because its density and pressure aren't the same all the way up. How Thick is the Earth's Atmosphere? (http://www.pdas.com/atmthick.htm) it is not a very good question The air at the ground level is squeezed by the weight of all the air on top of it, so it's quite dense. The air at Mount Everest's summit doesn't have so much air above it. As a result its atmosphere never really ends, and the air just gets thinner and thinner. 

Title: Re: various physics questions Post by BenVitale on Jul 22^{nd}, 2009, 2:50pm We need a number for its thickness. I read that if we think in terms of an "effective thickness" of the atmosphere, that is to say, how high it would be if its density all the way up were the same as it is at the surface. I was told that there's some math that shows that the effective thickness of the atmosphere is the height at which the pressure of the real atmosphere has dropped to 37% of its surface value. That turns out to be about the height of Everest, which is close to 6 miles. Anybody familiar with this? 

Title: Re: various physics questions Post by rmsgrey on Jul 22^{nd}, 2009, 3:22pm on 07/22/09 at 14:50:35, BenVitale wrote:
We don't need a number for the depth of the atmosphere  just for the number of gas molecules it contains. The equivalent volume of the atmosphere if it contained the same number of molecules but at uniform pressure is only useful as a way of finding that number... 

Title: Re: various physics questions Post by BenVitale on Jul 22^{nd}, 2009, 4:21pm Quote:
do you agree with the author's estimation of the volume of earth's atmosphere? I had trouble posting the rest of my work .. I'll do it later 

Title: Re: various physics questions Post by BenVitale on Jul 22^{nd}, 2009, 10:49pm A deep breath amounts to 1 liter. Then there's the volume of earth's atmosphere: that's the area of our planet multiplied by the height of the atmosphere. I multiplied the earth's area by the effective thickness of the atmosphere gives a volume of 1,200 million cubic miles. 1200 X 4.16818183 = 5,001,818,200 ~ 5 X 10^{21}, or in shorthand notation 5e21 So if Caesar's last breath had a volume of 1 liter, it forms one part in 5e21 of the air we breathe. If your last breath was 1 liter, you just breathed in 1 X 1/5e21 = 1/5e21 liters of Caesar's last breath. All that remains is to estimate how many molecules there are in this tiny volume. It's done using an important number : the Avogadro number, that is, 1 liter of any gas contains around 2.7e22 molecules. The lungful of air you breathed contains 2.7e22 X 1/5e21 = 2.7e22/5e21 of the molecules that were in Julius Caesar's last gasp, and that works out to be 5.4 It's an average. However, the author found that the number of the molecules that comes Caesar's last exhalation is 1 molecule What do you think? Am I wrong? 

Title: Re: various physics questions Post by towr on Jul 23^{rd}, 2009, 12:30am on 07/22/09 at 22:49:21, BenVitale wrote:


Title: Re: various physics questions Post by SMQ on Jul 23^{rd}, 2009, 5:03am on 07/22/09 at 22:49:21, BenVitale wrote:
But the atmosphere is much denser near the planet than higher up! A better estimate would be to multiply average barometric pressure by the surface area of the planet to get the total weight of the atmosphere, then convert to mass and finally to mols. SMQ 

Title: Re: various physics questions Post by towr on Jul 23^{rd}, 2009, 5:09am on 07/23/09 at 05:03:20, SMQ wrote:
:P (Yeah, I know, it's a negligible difference in this case; certainly considering all the uncertainties we are dealing with already) 

Title: Re: various physics questions Post by Eigenray on Jul 23^{rd}, 2009, 5:27am on 07/23/09 at 00:30:52, towr wrote:
But how deep a breath can you really take after being fatally stabbed in the chest? 

Title: Re: various physics questions Post by towr on Jul 23^{rd}, 2009, 6:13am on 07/23/09 at 05:27:37, Eigenray wrote:


Title: Re: various physics questions Post by BenVitale on Jul 23^{rd}, 2009, 10:52am So, let's suppose it is 4 liters. We would get: 5.4 molecules / 4 = 1.35 molecules It doesn't make sense to a fraction of a molecule. This a Fermi problem, and Fermi wants us to deal with estimates. So, we end up with 1 molecule. What do you say, guys? P.S. I did multiply the earth's area by the effective thickness of the atmosphere. The effective thickness of the atmosphere being around 6 miles (Everest's altitude). The thickness of the atmosphere is more difficult to figure outsince its density and pressure are not the same all the way up. The air at the ground level is squeezed by the weight of all the air on top of it, so it's quite dense. So if we think "effective thickness" as how high it would be if its density all the way up were the same as it is at the surface. This number turns out to be 6 miles. 

Title: Re: various physics questions Post by BenVitale on Jul 23^{rd}, 2009, 1:53pm The estimation could be wrong. Why? Because we need to make huge assumptions: We need to assume that Caesar's last breath has been thoroughly mixed into the whole atmosphere and has not been permanently absorbed somewhere or lost in deep space. It takes some time for the atmosphere to be recycled by dissolving in the oceans, seas, ... and then being released or being transpired by plant life. How long? I do not know Anyone? 

Title: Re: various physics questions Post by BenVitale on Jul 23^{rd}, 2009, 1:57pm I wanted to look at it this way: Say you put 1 drop or red coloring in 1 gallon of water and stir. In a matter of moments, the solution is pink. And if you draw 1 teaspoon of water from the solution, it will contain some of the coloring. Now, granted, the earth's atmosphere is a great deal more than 1 gallon. The air from Caesar's last breath has had about 2,000 years to thoroughly mix throughout the atmosphere, and there are billions and billions (do I sound like Carl Sagan?) of air molecules in one of your breaths, so it's close to certain that at least one of the molecules you inhaled passed through Caesar. 

Title: Re: various physics questions Post by BenVitale on Jul 25^{th}, 2009, 8:32am Lots of people have the habit of drinking half a cup of tea with milk and then replenishing with tea from the pot without adding more milk. If you drink 3/4 of each cup before topping off, only a 1/4 of the original milk content remains. So, after 10 topups the final milk concentration will be reduced by a factor of (1/4)^{10} = 1/1,048,576. That's pretty strong tea. A similar process of successive dilution is used in the preparation of homeopathic medecines. A solution of the supposed therapeutic is diluted, typically with 99 parts of pure water or alcohol to one part of the original solution. The process doesn't stop there: the dilution is repeated, this time starting with the already diluted ingredient. The process of successive is repeated up to 15 times before the final solution is administered to the patient. A calculation similar to the one for working out the strength of your cup of tea gives the concentration of the homeopathic solution. It's (1/100)^{15} = 1e  30 But a 300 ml, about one full cup (1 US cup = 236.588237 ml), ... More info here (http://en.wikipedia.org/wiki/Cup_(volume)) ... of the solution would contain a total of only about 1e25 molecules. That means that the number of molecules of therapeutic ingredient in the cup would be just 1e25 X (1e  30) = 1e  5, or 1/100,000 It is not possible to have a fraction of a molecule: what this means is that there's a chance of only 1 in 100,000 that there will be one of those molecules in the cup of the solution you drink. The proponents of homeopathic remedies get around this by suggesting that the water or alcohol used in the dilution process "remembers" the earlier presence of the active ingredient. Quite an extraordinary statement !! 

Title: Re: various physics questions Post by rmsgrey on Jul 26^{th}, 2009, 4:42am The real question is why the homeopathic water remembers the drug and not, say, all the times its been part of urine  or any impurities in the air or on the glassware used in the process... 

Title: Re: various physics questions Post by towr on Jul 26^{th}, 2009, 6:54am on 07/26/09 at 04:42:54, rmsgrey wrote:
Of course, magic doesn't work either, so ... 

Title: Re: various physics questions Post by Ronno on Jul 26^{th}, 2009, 8:28am Its also not up to just 15 times. I have seen vials of drugs of potency 10M and I know there exists CM. That is the dilution is done a 100000 times. 

Title: Re: various physics questions Post by BenVitale on Sep 6^{th}, 2009, 11:37pm I'm glad the website is up again. Two Interesting Questions : Here are two interesting questions you can ponder to exercise your brainpower. The first: If you push on the end of a broomstick or iron bar and move it, does the other end move at the same time? Now that may not seem too interesting at first glance, but it directly leads to the second: Can anything move faster than the speed of light? The answers to these could have profound consequences. Don't worry if you didn't do well in your physics classes. Simple logic and a few facts will suffice for playing around with these concepts for now. We'll start with the fact that most physicists believe that nothing can move faster than the speed of light. That speed, by the way, is about 299,792,458 meters or 186,000 miles per second. It certainly seems that if you were to push or pull one end of a long bar that the other end would move at the same time. But imagine an iron bar that is ten light years long, spanning the distance between here and another planet that has intelligent life. If you push or pull this end does the other end move at the same time? If so you could transmit information through a series of movements, using Morse code, for example. You could transmit several sentences in a matter of seconds or minutes, instead of the ten years it would take to do so using radio waves or light signals. But this is contrary to the widely accepted view that nothing can move faster than the speed of light. Although the bar itself would move slowly, the information would be transmitted those billions of miles in just seconds  much faster than light or radio waves can travel (in fact, even the light of our own sun takes over eight minutes to get here). So can the other end of the bar move at the same time? Obviously either our "common sense" idea that the whole bar would move at the same time is wrong (perhaps the motion is transmitted as a wave through the bar), or... Continued here ... Two Interesting Questions (http://www.increasebrainpower.com/interestingquestions.html) 

Title: Re: various physics questions Post by towr on Sep 7^{th}, 2009, 12:24am Quote:
The observer from earth sees them going apart faster than the speed of light, but doesn't see either of them go faster than lightspeed. And neither do the observers on either rocket see anything or anyone going faster than the speed of light, because they see the universe in their own reference frame. 

Title: Re: various physics questions Post by rmsgrey on Sep 7^{th}, 2009, 5:03am Yeah, special relativity nails shut the coffin lid on the idea of rigid objects as anything other than a handy daytoday approximation. Though if you think a bit about the concept of a perfectly rigid object, and compare it to common objects that are "rigid enough"  they act like perfectly rigid objects under everyday conditions  it becomes clear that the idea of a perfectly rigid object is pretty nonphysical in newtonian physics too... 

Title: Re: various physics questions Post by SMQ on Sep 7^{th}, 2009, 5:04am First, a minor nitpick: the speed of light (in free space) is, in fact, exactly 299,792,458 meters per second. Why? By definition! The modern meter is defined to be exactly 1/299,792,458 of the distance light travels through free space in one second. The first question is an easy one: no, the ends don't move at the same time. When you push one end of the bar, the molecules of the bar that you push on push on the molecules next to them, which themselves push on the molecules next to them, and so on to the other end of the bar. This creates a compression wave which moves from your end of the bar to the other end until all the molecules are again the "preferred" distance from one another. Not only does that compression wave not move faster than the speed of light, it moves much slower than that: the speed of sound in whatever material the bar is made of. For instance, the speed of sound in iron is around 5,120 m/s, so for a 10lightyearlong iron bar, the push would take around 586,000 years to move the other end! If that seems ridiculous, remember just how massive such a bar would be, and how much force it would take to move it at all. SMQ 

Title: Re: various physics questions Post by towr on Sep 7^{th}, 2009, 5:16am on 09/07/09 at 05:04:44, SMQ wrote:
And actually, any amount of force will move it. And it will continue moving until an opposite force stops it :P 

Title: Re: various physics questions  Schrodinger's cat Post by Mickey1 on Feb 6^{th}, 2010, 1:17am A cat in the park Assume you detected a single particle through a slit using two detectors left and right perhaps equal in size  together blocking all possible particle directions. I reality you would have to wait for one registration in very low intensity beam. The quesiton is which one was the next registration, right or left? You could i) look at both detectors, ii) look at either one, or iii) take a stroll in the park. Alternativ iii) will give you the same situation as Scrodinger and his cat. If you want more drama you may attach a dramatic consequence system to one of the detectors. I see I need to add this  lets call it Schrodinger's steake. In both cases (schrodinger's cat and my cat in the park) we have models describing a known system and ii) an unknown future. There is nothing more to it than that. (Also, there is no justification for reading minddependence into Heisenberg's relation). You buy a lottery ticket and you check it a long time the drawing. You might have won or lost. Why built a model around that? Alternatively you are on your way home while another person has prepared dinner  what might it be, chicken or steake? If you were pressed to build a model around the chicken/stake or dead/alive cat, Schrodinger method is right in principle, but there are not two realities, only two model states, not the same thing. About models vs reality see my notes on the site from Berkeley http://goneri.nuc.berkeley.edu/pages2009/slides/Jensen_Comments%20to%20the%20students.pdf 

Title: Re: various physics questions Post by Mickey1 on Apr 22^{nd}, 2013, 2:09am Perhaps I should add one more – less cynical  comment about the Schrödinger cat. Let me first say that hardware, i.e. macroscopic objects, can be included in QM uncertainty. Schrödinger therefore does not attempt to introduce any counterargument to QM. He just shares a weird feeling. The debate e.g. between Bohr and Einstein on the issues about the uncertainty principle in Solvay conference 1927, included uncertainty of the position of a box. Also Heisenberg says about a hypothetical investigation of particles in a microscope to determine location: “It immediately raises the question about the position of the microscope, and its position and momentum will also be found to be subject to [the uncertainty relations]”. (The physical principles of the quantum theory, Univ. of Chicago Press, 1930, p. 22). The theory just appears strange if we use “classical intuition”. There are lots of these kind of paradoxes in QM. An even stranger aspect lies in the formulation of the principle itself: the concept uncertainty of e.g. a particle’s location assumes that it indeed possesses exact location and momentum – how else could we be uncertain of the particle's location if it never existed in the first place? The counterposition is Laplace’s: a vast intelligent being “could embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.” But let me get back to my point in this post, namely that the main requirement for a thought experiment is that it must follow the laws of physics. One can argue that Schrödinger’s cat placed in a closed room, and therefore hidden from us, does not qualify. The cat might be heard through the door. We could imagine countermeasures to this, the room being increasingly well isolated but we can also, having access to an imaginary budget, take appropriate countermeasures using xrays to see through the room. Nobel laureate Luis Alvarez studied the Second Pyramid of Chephren in Egypt using cosmic muon imaging to xray the pyramid in search for a hidden chamber. Using thought experiment techniques you might therefore always know what is going on. If you run out of muons, use neutrinos. Also, remember that a very high muon dose might kill the cat and destroy the premises of the experiment. 

Title: Re: various physics questions Post by Christine on Sep 2^{nd}, 2013, 9:57am When an eclipse of the Moon can be seen from the Earth, what can an observer on the Moon see/experience? 

Title: Re: various physics questions Post by towr on Sep 2^{nd}, 2013, 10:51am A solar eclipse. 

Title: Re: various physics questions Post by Grimbal on Sep 3^{rd}, 2013, 9:38am You would experience the delight of being in a place where nobody has been before. Or: choking to death if not properly dressed for the occasion. OK, more seriously, from the Moon you would see the Sun pass behind the Earth, resulting in pitch black darkness. Technically it could be called a sunset, since the Sun drops below the Earth horizon. 

Title: Re: various physics questions Post by anglia on Aug 20^{th}, 2015, 9:55pm Sending a electric current around a loop of wire will give a certain magnetic field. 

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