Consider the phrase "Nothing yells out 'I'm a barefaced liar!' like a Slashdot reader bragging about his sexual exploits". Is 'I'm a barefaced liar' a noun? What about, "When I asked her how she felt, she yelled out 'miserable!'". Is "miserable" a noun?
Ok, obviously we're just going to have to agree to disagree. Your argument sounds to me very much like "breadth must be measured with breadth units, and length with length units, because breadth and length have different properties, namely lengthness and breadthness, and hence must be treated differently". There is a profound physics principle that it seems you're missing, but we're not going to settle this here.
Time and space are freely convertible so they are interchangeable - there is no universal distinction between the two, the distinction is very much observer dependent. The "rotation" involved, however, must be Lorentz invariant, and the metric obviously must have a (3,1) signature. Big deal.
Many coordinate systems use a mix of time and space - e.g. Kruskal-Szekeres coordinates. Time and space are equivalent and interchangeable - and there is no problem here as long as it's understood that the metric is Lorentz-invariant and has a (3,1) signature.
This is much like breadth and space are equivalent and interchangeable as long as the Euclidean metric is SO(2) invariant - as is the case for a simple rotation on the plane.
There are always exceptions, and obviously there are cases where a goto (by that or another name) is the best way to do it. But in the overwhelming number of cases, a higher-level structure will be a much better choice.
No-one's arguing the properties are different, that's why they have different labels. Heck, even different types of mass have different properties. Fundamentally, however, mass and energy are equivalent, and it's nonsense to say that one should be "properly" measured with one set of units, and the other with a different set, since they are freely convertible, and the units used simply a matter of convention.
If particle physicists find it more convenient to use GeV as units of mass, on what grounds would anyone say it's not "proper" to do so? How is it not "proper"? If we had one set of units for length, and another for breadth, and some genius found that length and breadth are equivalent (via rotation), why can't we use either units for either type of measurement? This is essentially what Einstein did with mass and energy.
You state that heat should not be measured in newton meters. However, you agree that this is simply a matter of convention, or convenience. It's like arguing that distances between cities should be measured in kilometers, and human height in centimeters. No one measures distances between cities in centimeters, but that's not due to fundamental issue, it's simply convention. If that's the case, then we don't disagree. If, however, you claim that that it's inappropriate to measure mass in GeV because of a more fundamental issue, then we'll just have to disagree, as clearly mass and energy are fundamentally equivalent.
Again, mass and energy are equivalent: a photon can be converted into a particle-antiparticle pair, with a combined mass equivalent to the energy of the photon. The energy of the photon is converted to the mass of the particle pair at will and vice versa, they are essentially the same thing with a different label.
Different types of energy are also fundamentally the same, even if they take different forms, even if they are expressed in different units. Electron volts can be converted to newton meters at will - it's just a matter of convenience for us, it's not a fundamental physics issue.
Likewise mass and energy: it's convenient for us to express them in various units, but that's merely an artifact of how we express things.
It's analogous to when the discovery was made that heat is a form of energy. We had units for heat, we had different units for other types of energy, but we discovered they are one and the same. What units we use for heat is a matter of convenience, not a matter of fundamental physics. The conversion constant in this case involves converting calories to, say, newton meters. This discussion is like someone arguing that heat should not properly be measured in newton meters because the conversion constant is not dimensionless - it misses the fundamental point that deep down, heat is KE, which is just another form of energy.
It's the coupling of the Higgs field with other particles that gives other particles their mass. It's not the Higgs boson itself that gives them their mass. No circular logic here.
Occam's Razor would indeed say that, if it wasn't the case that the Standard Model is a very well tested model for particle physics.
The Higgs mechanism is part of the Standard Model. One of the predictions of this Model is that the quantum of the Higgs field, the Higgs boson, exists. Unfortunately, if it doesn't, it means something has gone seriously wrong with the model, because it's been successful in explaining a great many things.
Unfortunatly, it's not common practice to teach QFT to undergraduates.
In any case, the Higgs boson is the particle associated with the Higgs field, much like the photon is the particle associated with the EM field. It's the Higgs field that gives massive particles their mass - and this is determined by a coupling constant in the field equations. There is no reason for the Higgs boson to be lighter than the lightest particle.
Read your comment again. Einstein showed that energy and mass are equivalent. Also, "c" is a universal constant that never changes. With these to premises, using GeV as a unit for mass is perfectly consistent, as it's also a unit of energy.
Your point may be significant to someone learning about dimensional analysis in high school, but it's not an insight into physics. It's an issue of semantics. Mass and energy are fundamentally the same.
I remember reading somewhere that some astronomy students, out of perversity, decided to continue working on the Ptolomaic system, adding additional epicycles on top of the ones that were conventional at the time to improve on accuracy, and to add the new planets discovered since then. The end result was a complex system that fairly accurately predicted planetary positions. Of course, it was all done tongue in cheek, but it does demonstrate that certain systems can be tailored ad infinitum to greater levels of accuracy - even if they are wrong in principle.
Seriously? You're recommending that book to him? Anyone that recommends that book to a physics student, for any other reason than historical interest, probably hasn't read it himself.
Disagree. Sure there is some rehashing of material that mathematicians will be familiar with, but unless said mathematicians are familiar with applications in physics, the book will cover plenty of new material for them. Take complex analysis : the initial chapter on complex analysis will be a rehash, but later chapters on its applications in QM, QFT, GR will NOT be a rehash.
That it is very broad is a good thing: it looks like the reader WANTS an overview. For further detail, good use can be made of Penrose's excellent bibliography.
I've got a maths background, and found much of the maths in this book new: much of it is idiosyncratic to physics. The holes I had in my knowledge of physics I was able to fill in via Penrose's bibliography.
I'll finally say that "Dancing Wu Li", "Tao of Physics", etc, are all pop physics that are easy to get through, but useless to learn anything. The danger with these books is that you can walk away with a completely wrong understanding of what they're on about, and you wouldn't be able to tell. They are simply too vague and "new agey", too many slippery concepts that can't be taught properly without mathematics, and dangerous without the appropriate background.
I wanted to recommend Feynman's lectures also, but it seems many others have done so already. Also Penrose's "Road to Reality", already mentioned.
What people haven't mentioned are Landau & Lifshitz's series of books, "Course on Theoretical Physics". This is stuff to read AFTER you have got through Feynman, and find his lectures too elementary. Landau is more demanding, but it will be a LONG while before you can finish reading his works.
Maybe, but my experience has been the exact opposite. As a teenager, I had plenty of experience building kits, but at the time I had little idea what how it all worked, in spite of reading all the guides, etc. I could follow instructions to build something, but I didn't have a hope in hell of calculating the exact response a circuit would have - let alone being able to design circuits from scratch. In order to do that, I had to put in hard work learning the theory at University.
Electronics is hard - don't expect to be able to understand fully it just by following simple tech guides or kit manuals. It involves some complex physics and mathematics. Without this physics and mathematics, you won't be able to really get a deep understanding of what's going on, much less be able to design electronic circuits. You may get a feel for what an EM wave does by echoing a signal down a cable - but unless you know your divs, grads, curls, your Maxwell's equations, your complex analysis, your linear algebra, you won't know how to calculate your cable's impedance from first principles, nor work out its frequency response, nor how to modulate signals to send down through it, etc, etc.
Except we just had a long trial which concluded the exact opposite, at least in the court's eyes (which are the ones that count). The court must now deal with him as though he were guilty.
I repeat: the LHC is not an advance in fundamental physics. It's an engineering marvel, sure, and we hope that it will allow us to make advances in physics, but it's not, in itself an advance.
Newton's insight into gravitation was an advance. So was the discovery of electricity and magnetism, and their unification by Maxwell. The discovery that heat was another form of kinetic energy too. The development of quantum mechanics, special and general relativity also. More recently, quantum electrodynamics, quantum field theory in general. The discovery of the strong and weak forces. The unification of electromagnetism and the weak force. The development of the standard model. And since then, as Lee Smolin says... stagnation. There's been plenty of fuss made over String Theory, but nothing testable.
The LHC may confirm the existence of the Higgs boson, and may shine a light on other aspects of particle physics. We don't know, that's in the future. For now, the LHC is a wonderful piece of machinery - but a machine is not an advance in our understanding of nature. The fact remains that since the 70s we have not had a revolution in physics in the order of anything resembling the breakthroughs I mentioned above. And as Smolin's book shows, there have been revolutions in the 20th century at the rate of almost once a decade - up to the 70s.
"If you stop to think about how science has advanced in the last 20 years your brain, like mine, might explode. DNA, human genome, genetic medical treatments, dark matter, hawking radiation, quantum related developments... all leading up to 2012?"
You're right in other respects, but this is unfortunately not the case with fundamental physics. In "The Trouble with Physics", Lee Smolin makes the case that there hasn't been a single advance in fundamental physics worth getting excited over since the '70s, when the final touches were made to the Standard Model. Pretty much the only development on that front is String Theory, which has become fashionable but is struggling to make any testable predictions.
Consider that every decade in the 20th century prior to the '70s has added considerably to our knowledge of fundamental physics. Since then, we've had nothing but speculation, nothing for the physicists of this generation to be proud of. I agree: physics is in a sorry state. Although technology is advancing in giant leaps, our fundamental understanding of the universe is proceeding nowhere near as fast.
No, it's a bit more subtle than that. This is the cat experiment, writ large. Just like the cat, the universe is hypothesised to be in an indeterminate state until measured. It has nothing to do with us *changing* the state explicitly, just like the cat experiment has nothing to do with us *changing* the state of the cat by killing it or not.
In the case of the cat, the cat is either killed or not killed by a quantum probability. We don't do the killing ourselves. The cat is in an indeterminate state until we observe it, at which point the wave function collapses, and the cat resolves to one of two states, alive or dead.
In the case of the universe hypothesis, replace a universe for the abovementioned cat.
There is nothing unusual in what the article says - it's just that quantum processes work in a counter-intuitive fashion.
In any case, the hypothesis is based on one commonly accepted interpretation of quantum mechanics, namely the Copenhagen interpretation (look it up). There are others, but they are no less counter-intuitive.
Except the earth would as a result therefore also be in an indeterminate quantum state until someone bothered to measure it. See what you did there? You created a chain of interdependent quantum states, but you did not address the question of what causes the wave function to collapse.
Slashdot Mirror
Though around 150,000 convicts were sent to Australia, we can't forget that around 50,000 were sent to the American colonies as well.
http://www.amazon.com/Bound-Iron-Chain-Transported-Convicts/dp/098367440X/ref=sr_1_1?ie=UTF8&qid=1309874514&sr=8-1
America has some claim to convict glory as well :-)
If you have to ask, you will never know.
Consider the phrase "Nothing yells out 'I'm a barefaced liar!' like a Slashdot reader bragging about his sexual exploits". Is 'I'm a barefaced liar' a noun? What about, "When I asked her how she felt, she yelled out 'miserable!'". Is "miserable" a noun?
Nothing yells out fail as much as someone trying to quote latin but getting it wrong. It's "noli me tangere".
Ok, obviously we're just going to have to agree to disagree. Your argument sounds to me very much like "breadth must be measured with breadth units, and length with length units, because breadth and length have different properties, namely lengthness and breadthness, and hence must be treated differently". There is a profound physics principle that it seems you're missing, but we're not going to settle this here.
Time and space are freely convertible so they are interchangeable - there is no universal distinction between the two, the distinction is very much observer dependent. The "rotation" involved, however, must be Lorentz invariant, and the metric obviously must have a (3,1) signature. Big deal.
Many coordinate systems use a mix of time and space - e.g. Kruskal-Szekeres coordinates. Time and space are equivalent and interchangeable - and there is no problem here as long as it's understood that the metric is Lorentz-invariant and has a (3,1) signature.
This is much like breadth and space are equivalent and interchangeable as long as the Euclidean metric is SO(2) invariant - as is the case for a simple rotation on the plane.
I have, however, no reason to force this on you.
There are always exceptions, and obviously there are cases where a goto (by that or another name) is the best way to do it. But in the overwhelming number of cases, a higher-level structure will be a much better choice.
Or even better, a COME FROM statement.
No-one's arguing the properties are different, that's why they have different labels. Heck, even different types of mass have different properties. Fundamentally, however, mass and energy are equivalent, and it's nonsense to say that one should be "properly" measured with one set of units, and the other with a different set, since they are freely convertible, and the units used simply a matter of convention.
If particle physicists find it more convenient to use GeV as units of mass, on what grounds would anyone say it's not "proper" to do so? How is it not "proper"? If we had one set of units for length, and another for breadth, and some genius found that length and breadth are equivalent (via rotation), why can't we use either units for either type of measurement? This is essentially what Einstein did with mass and energy.
You state that heat should not be measured in newton meters. However, you agree that this is simply a matter of convention, or convenience. It's like arguing that distances between cities should be measured in kilometers, and human height in centimeters. No one measures distances between cities in centimeters, but that's not due to fundamental issue, it's simply convention. If that's the case, then we don't disagree. If, however, you claim that that it's inappropriate to measure mass in GeV because of a more fundamental issue, then we'll just have to disagree, as clearly mass and energy are fundamentally equivalent.
Again, mass and energy are equivalent: a photon can be converted into a particle-antiparticle pair, with a combined mass equivalent to the energy of the photon. The energy of the photon is converted to the mass of the particle pair at will and vice versa, they are essentially the same thing with a different label.
Different types of energy are also fundamentally the same, even if they take different forms, even if they are expressed in different units. Electron volts can be converted to newton meters at will - it's just a matter of convenience for us, it's not a fundamental physics issue.
Likewise mass and energy: it's convenient for us to express them in various units, but that's merely an artifact of how we express things.
It's analogous to when the discovery was made that heat is a form of energy. We had units for heat, we had different units for other types of energy, but we discovered they are one and the same. What units we use for heat is a matter of convenience, not a matter of fundamental physics. The conversion constant in this case involves converting calories to, say, newton meters. This discussion is like someone arguing that heat should not properly be measured in newton meters because the conversion constant is not dimensionless - it misses the fundamental point that deep down, heat is KE, which is just another form of energy.
It's the coupling of the Higgs field with other particles that gives other particles their mass. It's not the Higgs boson itself that gives them their mass. No circular logic here.
Occam's Razor would indeed say that, if it wasn't the case that the Standard Model is a very well tested model for particle physics.
The Higgs mechanism is part of the Standard Model. One of the predictions of this Model is that the quantum of the Higgs field, the Higgs boson, exists. Unfortunately, if it doesn't, it means something has gone seriously wrong with the model, because it's been successful in explaining a great many things.
Unfortunatly, it's not common practice to teach QFT to undergraduates.
In any case, the Higgs boson is the particle associated with the Higgs field, much like the photon is the particle associated with the EM field. It's the Higgs field that gives massive particles their mass - and this is determined by a coupling constant in the field equations. There is no reason for the Higgs boson to be lighter than the lightest particle.
Read your comment again. Einstein showed that energy and mass are equivalent. Also, "c" is a universal constant that never changes. With these to premises, using GeV as a unit for mass is perfectly consistent, as it's also a unit of energy.
Your point may be significant to someone learning about dimensional analysis in high school, but it's not an insight into physics. It's an issue of semantics. Mass and energy are fundamentally the same.
I remember reading somewhere that some astronomy students, out of perversity, decided to continue working on the Ptolomaic system, adding additional epicycles on top of the ones that were conventional at the time to improve on accuracy, and to add the new planets discovered since then. The end result was a complex system that fairly accurately predicted planetary positions. Of course, it was all done tongue in cheek, but it does demonstrate that certain systems can be tailored ad infinitum to greater levels of accuracy - even if they are wrong in principle.
I wish I could find a link to to this.
Seriously? You're recommending that book to him? Anyone that recommends that book to a physics student, for any other reason than historical interest, probably hasn't read it himself.
The OP has a three-year university background in mathematics: he's got a BSc. He wants an MSc in astrophysics.
Disagree. Sure there is some rehashing of material that mathematicians will be familiar with, but unless said mathematicians are familiar with applications in physics, the book will cover plenty of new material for them. Take complex analysis : the initial chapter on complex analysis will be a rehash, but later chapters on its applications in QM, QFT, GR will NOT be a rehash.
That it is very broad is a good thing: it looks like the reader WANTS an overview. For further detail, good use can be made of Penrose's excellent bibliography.
I've got a maths background, and found much of the maths in this book new: much of it is idiosyncratic to physics. The holes I had in my knowledge of physics I was able to fill in via Penrose's bibliography.
I'll finally say that "Dancing Wu Li", "Tao of Physics", etc, are all pop physics that are easy to get through, but useless to learn anything. The danger with these books is that you can walk away with a completely wrong understanding of what they're on about, and you wouldn't be able to tell. They are simply too vague and "new agey", too many slippery concepts that can't be taught properly without mathematics, and dangerous without the appropriate background.
I wanted to recommend Feynman's lectures also, but it seems many others have done so already. Also Penrose's "Road to Reality", already mentioned.
What people haven't mentioned are Landau & Lifshitz's series of books, "Course on Theoretical Physics". This is stuff to read AFTER you have got through Feynman, and find his lectures too elementary. Landau is more demanding, but it will be a LONG while before you can finish reading his works.
Maybe, but my experience has been the exact opposite. As a teenager, I had plenty of experience building kits, but at the time I had little idea what how it all worked, in spite of reading all the guides, etc. I could follow instructions to build something, but I didn't have a hope in hell of calculating the exact response a circuit would have - let alone being able to design circuits from scratch. In order to do that, I had to put in hard work learning the theory at University.
Electronics is hard - don't expect to be able to understand fully it just by following simple tech guides or kit manuals. It involves some complex physics and mathematics. Without this physics and mathematics, you won't be able to really get a deep understanding of what's going on, much less be able to design electronic circuits. You may get a feel for what an EM wave does by echoing a signal down a cable - but unless you know your divs, grads, curls, your Maxwell's equations, your complex analysis, your linear algebra, you won't know how to calculate your cable's impedance from first principles, nor work out its frequency response, nor how to modulate signals to send down through it, etc, etc.
Tycho Brahms? Are you sure it wasn't Johannes Brahe?
Except we just had a long trial which concluded the exact opposite, at least in the court's eyes (which are the ones that count). The court must now deal with him as though he were guilty.
I repeat: the LHC is not an advance in fundamental physics. It's an engineering marvel, sure, and we hope that it will allow us to make advances in physics, but it's not, in itself an advance.
Newton's insight into gravitation was an advance. So was the discovery of electricity and magnetism, and their unification by Maxwell. The discovery that heat was another form of kinetic energy too. The development of quantum mechanics, special and general relativity also. More recently, quantum electrodynamics, quantum field theory in general. The discovery of the strong and weak forces. The unification of electromagnetism and the weak force. The development of the standard model. And since then, as Lee Smolin says... stagnation. There's been plenty of fuss made over String Theory, but nothing testable.
The LHC may confirm the existence of the Higgs boson, and may shine a light on other aspects of particle physics. We don't know, that's in the future. For now, the LHC is a wonderful piece of machinery - but a machine is not an advance in our understanding of nature. The fact remains that since the 70s we have not had a revolution in physics in the order of anything resembling the breakthroughs I mentioned above. And as Smolin's book shows, there have been revolutions in the 20th century at the rate of almost once a decade - up to the 70s.
The LHC is not an advance on fundamental physics. What is your point?
"If you stop to think about how science has advanced in the last 20 years your brain, like mine, might explode. DNA, human genome, genetic medical treatments, dark matter, hawking radiation, quantum related developments... all leading up to 2012?"
You're right in other respects, but this is unfortunately not the case with fundamental physics. In "The Trouble with Physics", Lee Smolin makes the case that there hasn't been a single advance in fundamental physics worth getting excited over since the '70s, when the final touches were made to the Standard Model. Pretty much the only development on that front is String Theory, which has become fashionable but is struggling to make any testable predictions.
Consider that every decade in the 20th century prior to the '70s has added considerably to our knowledge of fundamental physics. Since then, we've had nothing but speculation, nothing for the physicists of this generation to be proud of. I agree: physics is in a sorry state. Although technology is advancing in giant leaps, our fundamental understanding of the universe is proceeding nowhere near as fast.
No, it's a bit more subtle than that. This is the cat experiment, writ large. Just like the cat, the universe is hypothesised to be in an indeterminate state until measured. It has nothing to do with us *changing* the state explicitly, just like the cat experiment has nothing to do with us *changing* the state of the cat by killing it or not.
In the case of the cat, the cat is either killed or not killed by a quantum probability. We don't do the killing ourselves. The cat is in an indeterminate state until we observe it, at which point the wave function collapses, and the cat resolves to one of two states, alive or dead.
In the case of the universe hypothesis, replace a universe for the abovementioned cat.
There is nothing unusual in what the article says - it's just that quantum processes work in a counter-intuitive fashion.
In any case, the hypothesis is based on one commonly accepted interpretation of quantum mechanics, namely the Copenhagen interpretation (look it up). There are others, but they are no less counter-intuitive.
Except the earth would as a result therefore also be in an indeterminate quantum state until someone bothered to measure it. See what you did there? You created a chain of interdependent quantum states, but you did not address the question of what causes the wave function to collapse.