The time-dependent Schrödinger's equation doesn't apply for massless particles. It was never intended to. It isn't relativistic. Try to apply a simple boost and you'll see it's not Poincaré invariant. The main point is that you get the same probabilities if you use a relativistic theory, but you need A LOT of work to get there.
Who said anything about Schrödinger's equation? The equations on the web page I referred to in my post are all relativistically correct. Unfortunately those equations aren't numbered, but if you look at the third equation in the section labelled "Propagation and Interference" you'll see that it was derived under the assumption of ultrarelativistic particles (whose energy is much greater than its rest mass times c^2).
I don't know of any superselection-rule -- it's possible, in theory, for the electron neutrino to have zero mass but the muon neutrino to have nonzero mass.
You can't have oscillations between massless and massive states. Remember, SR says that time stands still for massless particles. If you look at the equations for neutrino oscillations, for example here, you'll see there are expressions involving both the mass squared (for the time evolution of the wavefunction), and mass difference squared, for the mixing amplitudes. So, for quantum mechanical mixing between states, you need both non-zero masses and non-zero mass differences. There may be other, weird mixing theories which don't require mass differences, but they would be quite exotic. On the other hand, mixing of particles with zero masses would violate SR, which would be highly surprising!
That's the way I've always understood the mass/oscillation connection too. But then I thought... wait... don't photons oscillate too? They're just coherent oscillations of the EM field; oscillating back and forth between electric and transverse magnetic in free space. If there's something different about neutrino oscillation which makes it necessary for the neutrino to travel at sublight, what is it specifically?
The situation you describe with the EM field is an example of wave-particle duality. Light can behave like both a wave and a particle, but it doesn't make sense to analyze it both ways at the same time. As a wave, it does manifest itself as oscillating electric and magnetic fields and as a particle, it manifests itself as a photon, which doesn't change into a different type of particle. (There's no such thing as an "electric photon" and a "magnetic photon".)
Neutrinos, too, are described quantum mechanically by wavefunctions, and these wavefunctions have frequencies associated with them, related to the energy of the particle. But these have nothing to do with the oscillation frequencies described here, in which a neutrino of one flavor (eg. mu) can change into a different flavor (eg. tau). Quantum mechanically speaking, we say the mass eigenstates of the neutrino (states of definite mass) don't coincide with the weak eigenstates (states of definite flavor: i.e. e, mu, or tau). Without mass, there would be no distinct mass eigenstates at all, and so mixing of the weak eigenstates would not occur as the neutrino propagates through free space.
How could something have mass and so weakly interact with normal matter?
Neutrinos are thought to have a very small mass. So exceedingly small that they barely interact with anything (they also have no charge, so they are even less likely to interact).
The fact that they barely interact with anything has nothing to do with the fact that they are nearly massless. Photons are massless and they interact with anything that carries an electric charge. Electrons are much lighter than muons, but they are just as likely to interact with something. The only force that gets weaker as the mass goes down is gravity, which is by far the weakest of the fundamental forces.
How could something have mass and so weakly interact with normal matter? My understanding is that most neutrinos pass through the earth unmolested.
(insert obligatory Catholic priest joke here).
I's thought that neutrinos being massless made this possible.
I'm not sure why this was modded flamebait (is a reference to our propensity to joke about the Catholic church flamebait?), but to answer the question, being massless has nothing to do with a particle's ability to interact weakly. Quarks can interact weakly (as well as strongly and electromagnetically) and they certainly have mass. The top quark, in fact, is quite heavy.
That would be pretty amazing as it would violate the Special Theory of Relativity, one of the most tested theories of all time. The problem is, according to Special Relativity, massless particles move at the speed of light, and time does not advance for them. (If you could build a massless clock, its hands would never move.) Oscillations require a time scale. There is a time period of oscillation, or rather the probabilities of being found in a specific state (mu vs. tau, for instance) oscillate with time. Since time stands still for massless particles, this can't happen.
Am I supposed to now itemize EVERYTHING I spend? I try to do that now for business expenses, but now if I walk into Walmart to buy a $3.00 can of shaving cream because I ran out that morning mean I have to keep track of all that shit?
Only if you're claiming that can of shaving cream as a business expense. This law covers only those items you will claim as a business expense, which as you say above, you already keep track of. Items for personal use, regardless of how expensive, are not covered by these new reporting requirements. So, if you buy a $700 computer at Staples for your home business which you will claim as a deduction, you will now have to get Staples' taxpayer ID and fill in the paperwork. If you buy the same computer for your kids to do their schoolwork, you don't have to.
I've looked at these fonts, and they look very good. Is there a LaTeX package that will let me use these fonts with LaTeX yet? I think they look much more attractive than the Computer Modern fonts that ship with LaTeX.
Are there sufficient legal issues here for the Court to even take up the case?
Generally speaking, the Supreme Court takes a case when different Circuits have interpreted a law differently. Does anyone know if there are conflicting decisions on this issue in other Circuits? If not, then I doubt the Supreme Court will hear the case.
Either way the factories in China are capitalistic, not state or worker owned. It's not about who owns the factory, but how it's run.
I'm sorry, but the factories in the US are generally not state or worker owned, either. The difference is, in the US, the workers are allowed to seek employment elsewhere if they are dissatisfied with their job. Not so in a communist country. That's the difference. When you have forced employment, there's worker abuse: it doesn't matter if the factory is owned by the state or a private entity.
Do you have any idea what communism actually is? Well doesn't matter, if there is one thing that it isn't, its people working in capitalistic factories.
You're right: it isn't people working in capitalistic factories. That's a tautology. My point is that capitalistic factories, like those in the US, don't have nearly these kinds of suicide rates. Read about the Stalin years to learn more about communistic factories and farms.
It's not unique to Apple; this is capitalism itself in action.
No, this is communism in action. In a capitalist country, like the USA, the correct course of action when you are mistreated by your employer is to quit and seek employment elsewhere. Workers in communist paradises often don't have that option.
We don't read about American workers jumping off their factory roofs nearly this often.
Reading about this today, I found that the scope of this particular decision is less scary than I initially assumed -- it's limited to prisoners who meet a standard as being "sexually dangerous", so they're not just being held without due process. Apparently this applies to about 100 prisoners nationwide.
One of whom had only a 37 month sentence for possession of child pornography. No mention that he had ever touched a child. Extending a sentence from 37 months to life is pretty severe. The potential for abuse of this process is staggering. Who gets to decide if someone is "sexually dangerous"? A doctor? What are the rules of evidence and due process requirements for the forum in which that determination is made? Does someone even have to be convicted of a crime for them to be labelled as "sexually dangerous"? This is by far the most frightening decision I've seen the SCOTUS hand down in my lifetime.
Interesting that the U.S. isn't on the list. It represents a pretty huge market share of browsers, so the project might be worth it even if it's just usable in the U.S. It is nice to see that the U.S. isn't the most patent encumbered country for a change!
People are prosecuted for receiving stolen goods all the time. How is this much different?
There's a difference between stolen goods and stolen money. Imagine you own a store, and someone who (unknown to you) makes a large purchase after just having robbed a bank. In the transaction, you have received stolen money. Should you be prosecuted?
Jim Galvin of Afilias, an expert in DNSSEC, warned that a “split DNS” – where a country effectively sets up its own Internet within its borders and controls access to the global Internet - and the DNSSEC protocol “do not match very well”.
Isn't that a good thing?
Depends who you are. If you are running the global Internet, it's good. If you're running a local or national Internet, it's bad. Pretty much all technology is that way: potentially good for some, bad for others.
Ahhh I see. I was wondering where the hell you were seeing Southeast Missouri but looking at the edit history on wikipedia I see some joker (you?) put it in there in place of Harvard.
Well, if the top university can change in one day from not being on the list to be number one, I think that says something about the reliability of that list. So my point still stands.
What he found out when he went into teaching was that the school required him to take attendance because many of the students had grants that required them to miss no more then two classes or else they would lose them and they'd be given to students willing to actually show up.
I'm sorry, but that grant is a business relationship between the student and the organization that issued the grant. There should be no onus on the professor to assist the granting organization in measuring student compliance with its conditions. (It would be different, of course, if the university issued the grant, as the professor is an employee of the university.)
A comparison of these two lists show how meaningless they are. Harvard doesn't even appear in the top 20 of the first list, and it appears as No. 1 in the second list! Also, I strongly suspect the author of the Times list probably graduated from the Southeast Missouri State University. It has been number 1 (!!!!) on that list for six years. It doesn't even make the top 100 on the ARWU list.
There's definitely something strange about that.
so basically a private corporation, somewhere, probably has much more info on you than leave aside your government, but even your parents ever may have hoped to know about you.
But the point is, at some point you chose to share that information with them. There's a reason I and a lot of other people pay cash for many of the things that we buy. We don't want to give out too much information.
Now, consider a U.S. federal income tax return. It requires us to divulge all sorts of very personal information about ourselves, but, unlike Radio Shack where you can walk out without buying anything when they insist you give them your phone number, you can run into all sorts of problems if you choose not to do business with the I.R.S. So, yes, private companies may be retaining and sharing more information that we'd like, but there is still an element of choice which doesn't exist when dealing with the government.
Thankfully we don't have software patents in Europe, but does that mean we won't suffer from this?
As long as you don't try to commercially distribute your movies in the U.S. you would probably be fine. But since non-commercial licenses were already bought by the camera manufacturer, then the only advantage you'd gain by living in Europe is that you'd be able to distribute commercial films outside of the U.S. and other countries that recognize software patents. But what commercial filmmaker would want to limit his/her distribution this way?
Slashdot Mirror
The time-dependent Schrödinger's equation doesn't apply for massless particles. It was never intended to. It isn't relativistic. Try to apply a simple boost and you'll see it's not Poincaré invariant. The main point is that you get the same probabilities if you use a relativistic theory, but you need A LOT of work to get there.
Who said anything about Schrödinger's equation? The equations on the web page I referred to in my post are all relativistically correct. Unfortunately those equations aren't numbered, but if you look at the third equation in the section labelled "Propagation and Interference" you'll see that it was derived under the assumption of ultrarelativistic particles (whose energy is much greater than its rest mass times c^2).
I don't know of any superselection-rule -- it's possible, in theory, for the electron neutrino to have zero mass but the muon neutrino to have nonzero mass.
You can't have oscillations between massless and massive states. Remember, SR says that time stands still for massless particles. If you look at the equations for neutrino oscillations, for example here, you'll see there are expressions involving both the mass squared (for the time evolution of the wavefunction), and mass difference squared, for the mixing amplitudes. So, for quantum mechanical mixing between states, you need both non-zero masses and non-zero mass differences. There may be other, weird mixing theories which don't require mass differences, but they would be quite exotic. On the other hand, mixing of particles with zero masses would violate SR, which would be highly surprising!
That's the way I've always understood the mass/oscillation connection too. But then I thought... wait... don't photons oscillate too? They're just coherent oscillations of the EM field; oscillating back and forth between electric and transverse magnetic in free space. If there's something different about neutrino oscillation which makes it necessary for the neutrino to travel at sublight, what is it specifically?
The situation you describe with the EM field is an example of wave-particle duality. Light can behave like both a wave and a particle, but it doesn't make sense to analyze it both ways at the same time. As a wave, it does manifest itself as oscillating electric and magnetic fields and as a particle, it manifests itself as a photon, which doesn't change into a different type of particle. (There's no such thing as an "electric photon" and a "magnetic photon".)
Neutrinos, too, are described quantum mechanically by wavefunctions, and these wavefunctions have frequencies associated with them, related to the energy of the particle. But these have nothing to do with the oscillation frequencies described here, in which a neutrino of one flavor (eg. mu) can change into a different flavor (eg. tau). Quantum mechanically speaking, we say the mass eigenstates of the neutrino (states of definite mass) don't coincide with the weak eigenstates (states of definite flavor: i.e. e, mu, or tau). Without mass, there would be no distinct mass eigenstates at all, and so mixing of the weak eigenstates would not occur as the neutrino propagates through free space.
How could something have mass and so weakly interact with normal matter?
Neutrinos are thought to have a very small mass. So exceedingly small that they barely interact with anything (they also have no charge, so they are even less likely to interact).
The fact that they barely interact with anything has nothing to do with the fact that they are nearly massless. Photons are massless and they interact with anything that carries an electric charge. Electrons are much lighter than muons, but they are just as likely to interact with something. The only force that gets weaker as the mass goes down is gravity, which is by far the weakest of the fundamental forces.
How could something have mass and so weakly interact with normal matter? My understanding is that most neutrinos pass through the earth unmolested.
(insert obligatory Catholic priest joke here).
I's thought that neutrinos being massless made this possible.
I'm not sure why this was modded flamebait (is a reference to our propensity to joke about the Catholic church flamebait?), but to answer the question, being massless has nothing to do with a particle's ability to interact weakly. Quarks can interact weakly (as well as strongly and electromagnetically) and they certainly have mass. The top quark, in fact, is quite heavy.
That would be pretty amazing as it would violate the Special Theory of Relativity, one of the most tested theories of all time. The problem is, according to Special Relativity, massless particles move at the speed of light, and time does not advance for them. (If you could build a massless clock, its hands would never move.) Oscillations require a time scale. There is a time period of oscillation, or rather the probabilities of being found in a specific state (mu vs. tau, for instance) oscillate with time. Since time stands still for massless particles, this can't happen.
It's a shit test, and measures nothing.
You could show a little more empathy for the people who made the test you insensitive piece of shit.
Oh I get it. His name is "MrHanky".
Am I supposed to now itemize EVERYTHING I spend? I try to do that now for business expenses, but now if I walk into Walmart to buy a $3.00 can of shaving cream because I ran out that morning mean I have to keep track of all that shit?
Only if you're claiming that can of shaving cream as a business expense. This law covers only those items you will claim as a business expense, which as you say above, you already keep track of. Items for personal use, regardless of how expensive, are not covered by these new reporting requirements. So, if you buy a $700 computer at Staples for your home business which you will claim as a deduction, you will now have to get Staples' taxpayer ID and fill in the paperwork. If you buy the same computer for your kids to do their schoolwork, you don't have to.
I've looked at these fonts, and they look very good. Is there a LaTeX package that will let me use these fonts with LaTeX yet? I think they look much more attractive than the Computer Modern fonts that ship with LaTeX.
Are there sufficient legal issues here for the Court to even take up the case?
Generally speaking, the Supreme Court takes a case when different Circuits have interpreted a law differently. Does anyone know if there are conflicting decisions on this issue in other Circuits? If not, then I doubt the Supreme Court will hear the case.
Either way the factories in China are capitalistic, not state or worker owned. It's not about who owns the factory, but how it's run.
I'm sorry, but the factories in the US are generally not state or worker owned, either. The difference is, in the US, the workers are allowed to seek employment elsewhere if they are dissatisfied with their job. Not so in a communist country. That's the difference. When you have forced employment, there's worker abuse: it doesn't matter if the factory is owned by the state or a private entity.
Do you have any idea what communism actually is? Well doesn't matter, if there is one thing that it isn't, its people working in capitalistic factories.
You're right: it isn't people working in capitalistic factories. That's a tautology. My point is that capitalistic factories, like those in the US, don't have nearly these kinds of suicide rates. Read about the Stalin years to learn more about communistic factories and farms.
It's not unique to Apple; this is capitalism itself in action.
No, this is communism in action. In a capitalist country, like the USA, the correct course of action when you are mistreated by your employer is to quit and seek employment elsewhere. Workers in communist paradises often don't have that option.
We don't read about American workers jumping off their factory roofs nearly this often.
Reading about this today, I found that the scope of this particular decision is less scary than I initially assumed -- it's limited to prisoners who meet a standard as being "sexually dangerous", so they're not just being held without due process. Apparently this applies to about 100 prisoners nationwide.
One of whom had only a 37 month sentence for possession of child pornography. No mention that he had ever touched a child. Extending a sentence from 37 months to life is pretty severe. The potential for abuse of this process is staggering. Who gets to decide if someone is "sexually dangerous"? A doctor? What are the rules of evidence and due process requirements for the forum in which that determination is made? Does someone even have to be convicted of a crime for them to be labelled as "sexually dangerous"? This is by far the most frightening decision I've seen the SCOTUS hand down in my lifetime.
The article is wrong. According to the MPEG-LA, there are patents on H.264 in at least the following countries:
Germany, France, UK, Finland, Italy, Sweden, Belgium, Bulgaria, Liechtenstein, Austria, Czech Republic, Denmark, Spain, Hungary, Ireland, The Netherlands, Poland, Romania, Portugal, Slovenia, Japan, China, South Korea, Hong Kong, Singapore, Taiwan, India, Canada, Mexico, Australia
See http://www.mpegla.com/main/programs/AVC/Pages/PatentList.aspx
Interesting that the U.S. isn't on the list. It represents a pretty huge market share of browsers, so the project might be worth it even if it's just usable in the U.S. It is nice to see that the U.S. isn't the most patent encumbered country for a change!
People are prosecuted for receiving stolen goods all the time. How is this much different?
There's a difference between stolen goods and stolen money. Imagine you own a store, and someone who (unknown to you) makes a large purchase after just having robbed a bank. In the transaction, you have received stolen money. Should you be prosecuted?
From TFA:
Jim Galvin of Afilias, an expert in DNSSEC, warned that a “split DNS” – where a country effectively sets up its own Internet within its borders and controls access to the global Internet - and the DNSSEC protocol “do not match very well”.
Isn't that a good thing?
Depends who you are. If you are running the global Internet, it's good. If you're running a local or national Internet, it's bad. Pretty much all technology is that way: potentially good for some, bad for others.
I don't recall working with CMS on an IBM being all that difficult.
You beat me to it. I was going to say I can't use CMS because I no longer have a 3270 terminal, so I use Drupal instead.
Ahhh I see. I was wondering where the hell you were seeing Southeast Missouri but looking at the edit history on wikipedia I see some joker (you?) put it in there in place of Harvard.
Well, if the top university can change in one day from not being on the list to be number one, I think that says something about the reliability of that list. So my point still stands.
What he found out when he went into teaching was that the school required him to take attendance because many of the students had grants that required them to miss no more then two classes or else they would lose them and they'd be given to students willing to actually show up.
I'm sorry, but that grant is a business relationship between the student and the organization that issued the grant. There should be no onus on the professor to assist the granting organization in measuring student compliance with its conditions. (It would be different, of course, if the university issued the grant, as the professor is an employee of the university.)
A comparison of these two lists show how meaningless they are. Harvard doesn't even appear in the top 20 of the first list, and it appears as No. 1 in the second list! Also, I strongly suspect the author of the Times list probably graduated from the Southeast Missouri State University. It has been number 1 (!!!!) on that list for six years. It doesn't even make the top 100 on the ARWU list. There's definitely something strange about that.
so basically a private corporation, somewhere, probably has much more info on you than leave aside your government, but even your parents ever may have hoped to know about you.
But the point is, at some point you chose to share that information with them. There's a reason I and a lot of other people pay cash for many of the things that we buy. We don't want to give out too much information.
Now, consider a U.S. federal income tax return. It requires us to divulge all sorts of very personal information about ourselves, but, unlike Radio Shack where you can walk out without buying anything when they insist you give them your phone number, you can run into all sorts of problems if you choose not to do business with the I.R.S. So, yes, private companies may be retaining and sharing more information that we'd like, but there is still an element of choice which doesn't exist when dealing with the government.
That's not the most ridiculous thing about this. Think about it, they're looking on Facebook for people who want to be celibate.
I don't rate their chances very highly.
Yeah. Slashdot seems the more obvious place to look. Oh wait, you said "want to be celibate." Never mind.
Thankfully we don't have software patents in Europe, but does that mean we won't suffer from this?
As long as you don't try to commercially distribute your movies in the U.S. you would probably be fine. But since non-commercial licenses were already bought by the camera manufacturer, then the only advantage you'd gain by living in Europe is that you'd be able to distribute commercial films outside of the U.S. and other countries that recognize software patents. But what commercial filmmaker would want to limit his/her distribution this way?
The only way to avoid this is to ensure that they pay a transaction cost for each transaction.
Pay it to whom?