It's all a matter of the distinction between rest mass and effective mass. Rest mass is mass that a quanton has when it has zero energy. Effective mass is the mass that it "effectively" has when it is in an excited state.
Because the energy imparted to a quanton increases its momentum, this can be accounted for in equations by increasing its effective mass. Both effective and rest mass are "mass", but there is a subtle difference between them.
No. p = mv isn't relativistically correct. You just get E = pc.
Sorry about that, perhaps I was a little bit hasty. The development of the deBroglie relationship actually goes more like this:
E = hc/lambda. Also, E^2 = p^2v^2 + m_0^2c^4.
We can equate the two of these, because they are both valid for light. Also, for light, v = c, and m_0 = zero. Thus
hc/lambda = pc
h/lambda = p.
That was just the derivation of the deBroglie relationship, nothing more.
It is energy and momentum that are related, not energy and mass. There is a fine line between the two. For instance, when calculating reactions, you must conserve energy (a scalar quantity) and momentum (a vector quantity), not energy and mass.
Some confusion arises from people quoting the equation
E=mc^2
but this is an abridged version, and many people leave out some critical subscripts. In actual fact, it should be
E^2 = (p^2)(c^2) + (m_0^2)(c^4)
where p is the momentum of the quanton, and m_0 is its REST mass. Thus, for photons with no rest mass, take the square root of both sides and substitute p = mv, where v=c, the speed of light, and
E = mc^2
It is also from this simplified equation that we can substitute the energy of a wave (E = hc/lambda) and get the deBroglie relationship
h/lambda = mc = p
Now, back to the subject at hand, both of you are kind of correct. Light has no rest mass, but light with any amount of energy does have momentum (which can be interpreted as it having mass, but only loosely). If light bends because it is travelling in a straight line through curved space-time, it is only travelling in that straight line because it has momentum, and that momentum is being conserved.
Well, maybe not, but we do sell an awful lot of power to the Americans. Lots is generated at hydro dams in northern Quebec and Labrador, and shipped to New England.
Sorry, I should have been more clear. What I meant was that typists using typewriters need a lot of force on the keys to generate a clear letter on the page. It is quite difficult to generate this amount of force with your wrists resting on the desk. Try it yourself if you've got an old typewriter lying around.
Anyway, my theory is that CTS was not a problem in the age of typewriters precisely for this reason. Since the typists did not (and could not) rest their wrists on the desk, they did not put pressure on the carpal tunnel, which is what many typists using computer keyboards do now.
Of course, it could also be that CTS was only recognized recently, along with the host of other RSI's. Who really knows. All I know is that my wrists don't hurt if I don't rest them on the desk while I'm typing, even if it's for long periods of time.
Sorry, but I'd have to disagree with you on the topic of a wrist rest. I'm guessing the one on your laptop is made of the hard plastic case that encloses the guts of your machine.
Resting your wrists on that while typing will put pressure on the carpal tunnel, increasing your risk of developing CTS. Personally, whenever my wrists start to hurt from long periods of typing, I move my keyboard to the edge of my desk so that I can't rest my wrists on anything, which I tend to do when I get lazy.
If you can't get out of the habit of resting your wrists when typing, you may want to look into getting some form of better support (I don't know how effective those gel wrist rests are).
Personally, I have a theory that typists did not suffer from CTS, even though they typed all day long, simply because they did not rest their wrists. It was impossible to generate enough force to create a clear letter on paper with a typewriter unless the hands were positioned above the keyboard, with the wrists not resting on anything. Thus, they had to have their wrists raised all day, and there was no extra pressure on the carpal tunnel. This is a big difference from what a lot of "lazy keyboarders" do today.
Another bonus of not resting your wrists is that your arms will get tired every once and a while, forcing you to get up and do something else. This is the perfect time for some of those stretches and exercises that are suggested by all the ergonomicists (sp?)
Update:
Here is the current score, I asked bot#1 "What kind of car?" and it replied "What kind of cars are there?" which I fed into bot#2, resulting in the following thread:
Me: What kind of car?
1: What kind of cars are there?
2: The kindest. (pun?)
1: Is that a fact.
2: All my information is completely factual.
1: Give me an example.
2: For example, eukaryotes. (WTF?)
1: Can you think of another example?
2: I think about all sorts of thinks.
1: Why?
2: The explanation is rather complicated.
1: I have time.
2: My estimate is that it will take more than 6000 years.
1: Where did you get your estimate?
2: From my botmaster.
1: Does your botmaster give good advice?
2: If I were your robot, do you think it should botmaster give good advice?
Okay, bot#2 is degenerating rapidly. I know this is just romanticism, but it seems like bot#1 had more of a personality. Perhaps that's because it was giving responses to somewhat standard questions and statements, whereas bot#2 had to deal with the crap that came out of bot#1.
This whole thing kind of reminds me of the conversations that the two AI's had in Chrichton's The Terminal Man except much more primitive. Perhaps it's closer to the "conversations" that the paranoid and the psychologist programs had (was that mentioned in GEB: EGB?)
Well, here's one for you. I opened up two copies of the AI page and started feeding the responses of the Chatbots into each other. Unfortunately, I hit a loop, so now my fun is over.
It seems that both my Chatbots would rather be driving a car. And whenever I state "I would rather be driving a car." they just mimic that right back to me.
1. I really like this quote from the article: "Our analysis strongly suggests that it is difficult to understand how any of these mechanisms can explain the magnitude of the observed behaviour of the Pioneer anomaly," the team says.
I interpret this as "our reasearch sez we're completely baffled."
2. I swear, it's drag from the ether. You don't witness this with planets, because they have a much higher mass/frontal area ratio.
3. Maybe the universe is expanding/contracting at different speeds in different locations. Um, assume that we are remaining the same size, that means the rest of the universe is contracting with respect to our solar system. This was the basis for a Sci-Fi short story I read once. One solar system was shrinking while the rest of the universe was expanding. They found out when they sent astronauts up, and one of them dropped a sapphire and it was huge. Anyone know the title/author?
4. Basis for a Voyager episode: different time scales in different parts of the universe. If time is moving more slowly out there (in a gradient of course), then the probe would still "think" it was going the correct speed, but it would in fact seem to be going too slow for us.
5. Um, how does the special theory of relativity take into account the fact that gravity does affect time? Never mind, they probably already thought of that...
what these wires could do for the speed of your future pocket computer!
In my opinion, not much. The largest obstacle in the way of infinitely fast computers is the switching time of the FETs and BJTs used to make up the logic gates etc. These largely arise from the resistance, capacitance and inductance of the material in the transistors themselves, which must be made with semiconductors.
These wires are conductors (sorry for stating the obvious) and thus could not be used to fabricate a transistor using any conventional (or even known) methods. So, I'm sorry folks, but the best way to faster computers is still probably decreasing the size of the gates on the transistors.
Well, I got halfway through the other comments, and haven't seen a thread bringing up this point yet, so...
Has anyone given any thought to how a stationary permanent space elevator will restrict the number of orbits available? No more equatorial orbits at all, at any height (except geosynch), and any orbits that cross the equator (say, the polar orbits that many spy satellites are on) would have to be VERY carefully calculated so that they would be in a resonance pattern with the elevator, and miss it every time. Well, that covers every orbit possible, doesn't it.
Other people's thoughts on this?
PS - credit to Larry Niven Rainbow Mars for bringing up that objection.
My optics are a little rusty
on
Tractor Beam?
·
· Score: 1
but IIRC, in order to get any appreciable level of refraction, the object performing the refraction needs to be of the same order of magnitude as the wavelength of the waves being refracted. This means that, for example, a car would cause significant refraction in light of wavelengths of around 3 metres. That puts it firmly in the radio wave section of the spectrum.
Now, I may be wrong, but it seems to me that the longest wavelength laser still works in the infrared region of the spectrum, nowhere near the metre-range of radio waves, so no appreciable diffraction would occur to short-wavelength light on macroscopic objects.
Also, I would like to know why the more intense light would incinerate objects. The light is not being absorbed, therefore its energy of h_nu is not being converted to heat. If the photon is just being diffracted, then more photons would mean more diffracted photons, and more "rebound", but not more heat.
Well, we're taking an RTOS course right now, but it doesn't do anything useful. All it does is run a bunch of special test programs to make sure we understand things like interprocess communication, memory management, and preemption.
Our fun classes deal more with hardware, and with programming the hardware directly. Microprocessor interfacing, digital design, etc. I like to think that we get a lot of the hands-on knowledge without having to delve into the tedious mathematical proofs that programs work that CS students have to do.
Now Scott Adams is not only spying on us at work, he's also reading/.:)
Re:They ain't engineers...
on
Beer In Space
·
· Score: 2
You hit the nail on the head there.
I can't recall exactly how all the forces add up
In the case of the yo-yo whirling about your head, the two balanced forces are the tension in the string pulling the yo-yo in, and with equal force pulling your hand (holding the other end of the string) out. Through muscluar control and friction, this force is transferred from your hand to the earth. Balance acheived.
They ain't engineers...
on
Beer In Space
·
· Score: 2
'Cause we engineers know that there's no such thing as centrifugal force. Centripital force exists, yes. It is the force that holds a spinning object to the centre of its axis - example, the tension (force of) in the string attached to the yo-yo you're winging around your head.
There actually is no outwards force when you wing something around in a circle.
Our Univ. class has an unwritten rule. If your cell phone interrupts the prof, at the end of the class you have to stand on your desk and do the chicken dance. So far, it has only been enacted(sp?) three or four times. They are going to try to apply this rule to the entire department.
We all know that dinosaurs were killed largely by second-hand smoke. Just imagine the size of the cigarettes it would take to give a brachiosaurus a nicotine buzz...
Those aren't *really* jr. high girls saying that they want to cyber with you. It's actually a 400lb man, wearing a foodstained shirt and boxers, with his hand in his pants, getting off on his fantasy that he is a jr. high girl being fscked by a high profile exec at a law firm, which is who you are pretending to be.
Now, I wholly approve of this as an outlet for your sexual tension, but please, don't ever believe that they are who they say they are, and for god's sake, never agree to meet with them.
Ha ha ha ha ha! I loved the time I tried that as a sadist bastard! One of my friends gave a guy nothing but a trailer and an outdoor toilet and hot-tub. He kept inviting chicks over, and they'd get in the hottub, but whenever he tried to get some, they'd smack him. Also, he wouldn't let his guy sleep or eat. It got to the point where the guy would be walking to get the mail and would collapse on the ground for a couple of hours. Ha ha ha ha!
Slashdot Mirror
It's all a matter of the distinction between rest mass and effective mass. Rest mass is mass that a quanton has when it has zero energy. Effective mass is the mass that it "effectively" has when it is in an excited state.
Because the energy imparted to a quanton increases its momentum, this can be accounted for in equations by increasing its effective mass. Both effective and rest mass are "mass", but there is a subtle difference between them.
No. p = mv isn't relativistically correct. You just get E = pc.
Sorry about that, perhaps I was a little bit hasty. The development of the deBroglie relationship actually goes more like this:
E = hc/lambda. Also, E^2 = p^2v^2 + m_0^2c^4.
We can equate the two of these, because they are both valid for light. Also, for light, v = c, and m_0 = zero. Thus
hc/lambda = pc
h/lambda = p.
That was just the derivation of the deBroglie relationship, nothing more.
This is a tricky question.
It is energy and momentum that are related, not energy and mass. There is a fine line between the two. For instance, when calculating reactions, you must conserve energy (a scalar quantity) and momentum (a vector quantity), not energy and mass.
Some confusion arises from people quoting the equation
E=mc^2
but this is an abridged version, and many people leave out some critical subscripts. In actual fact, it should be
E^2 = (p^2)(c^2) + (m_0^2)(c^4)
where p is the momentum of the quanton, and m_0 is its REST mass. Thus, for photons with no rest mass, take the square root of both sides and substitute p = mv, where v=c, the speed of light, and
E = mc^2
It is also from this simplified equation that we can substitute the energy of a wave (E = hc/lambda) and get the deBroglie relationship
h/lambda = mc = p
Now, back to the subject at hand, both of you are kind of correct. Light has no rest mass, but light with any amount of energy does have momentum (which can be interpreted as it having mass, but only loosely). If light bends because it is travelling in a straight line through curved space-time, it is only travelling in that straight line because it has momentum, and that momentum is being conserved.
Hell, they already do...
Well, maybe not, but we do sell an awful lot of power to the Americans. Lots is generated at hydro dams in northern Quebec and Labrador, and shipped to New England.
Sorry, I should have been more clear. What I meant was that typists using typewriters need a lot of force on the keys to generate a clear letter on the page. It is quite difficult to generate this amount of force with your wrists resting on the desk. Try it yourself if you've got an old typewriter lying around.
Anyway, my theory is that CTS was not a problem in the age of typewriters precisely for this reason. Since the typists did not (and could not) rest their wrists on the desk, they did not put pressure on the carpal tunnel, which is what many typists using computer keyboards do now.
Of course, it could also be that CTS was only recognized recently, along with the host of other RSI's. Who really knows. All I know is that my wrists don't hurt if I don't rest them on the desk while I'm typing, even if it's for long periods of time.
Sorry, but I'd have to disagree with you on the topic of a wrist rest. I'm guessing the one on your laptop is made of the hard plastic case that encloses the guts of your machine.
Resting your wrists on that while typing will put pressure on the carpal tunnel, increasing your risk of developing CTS. Personally, whenever my wrists start to hurt from long periods of typing, I move my keyboard to the edge of my desk so that I can't rest my wrists on anything, which I tend to do when I get lazy.
If you can't get out of the habit of resting your wrists when typing, you may want to look into getting some form of better support (I don't know how effective those gel wrist rests are).
Personally, I have a theory that typists did not suffer from CTS, even though they typed all day long, simply because they did not rest their wrists. It was impossible to generate enough force to create a clear letter on paper with a typewriter unless the hands were positioned above the keyboard, with the wrists not resting on anything. Thus, they had to have their wrists raised all day, and there was no extra pressure on the carpal tunnel. This is a big difference from what a lot of "lazy keyboarders" do today.
Another bonus of not resting your wrists is that your arms will get tired every once and a while, forcing you to get up and do something else. This is the perfect time for some of those stretches and exercises that are suggested by all the ergonomicists (sp?)
forgot to close my italics. Sorry. That'll teach me to use the preview button.
directed distributed cognition == brainstorming.
Otherwise known as a bunch of different people thinking about the same problem.
Update: Here is the current score, I asked bot#1 "What kind of car?" and it replied "What kind of cars are there?" which I fed into bot#2, resulting in the following thread:
Me: What kind of car?
1: What kind of cars are there?
2: The kindest. (pun?)
1: Is that a fact.
2: All my information is completely factual.
1: Give me an example.
2: For example, eukaryotes. (WTF?)
1: Can you think of another example?
2: I think about all sorts of thinks.
1: Why?
2: The explanation is rather complicated.
1: I have time.
2: My estimate is that it will take more than 6000 years.
1: Where did you get your estimate?
2: From my botmaster.
1: Does your botmaster give good advice?
2: If I were your robot, do you think it should botmaster give good advice?
Okay, bot#2 is degenerating rapidly. I know this is just romanticism, but it seems like bot#1 had more of a personality. Perhaps that's because it was giving responses to somewhat standard questions and statements, whereas bot#2 had to deal with the crap that came out of bot#1.
This whole thing kind of reminds me of the conversations that the two AI's had in Chrichton's The Terminal Man except much more primitive. Perhaps it's closer to the "conversations" that the paranoid and the psychologist programs had (was that mentioned in GEB: EGB?)
Well, here's one for you. I opened up two copies of the AI page and started feeding the responses of the Chatbots into each other. Unfortunately, I hit a loop, so now my fun is over.
It seems that both my Chatbots would rather be driving a car. And whenever I state "I would rather be driving a car." they just mimic that right back to me.
Ah well, it was fun while it lasted.
or even better, the Olson twins as Stewie stand-ins, Fifteen Minutes of Shame
"Blast! I am victorious!"
"Whose leg do you have to hump to get a dry martini around here?"
1. I really like this quote from the article:
"Our analysis strongly suggests that it is difficult to understand how any of these mechanisms can explain the magnitude of the observed behaviour of the Pioneer anomaly," the team says.
I interpret this as "our reasearch sez we're completely baffled."
2. I swear, it's drag from the ether. You don't witness this with planets, because they have a much higher mass/frontal area ratio.
3. Maybe the universe is expanding/contracting at different speeds in different locations. Um, assume that we are remaining the same size, that means the rest of the universe is contracting with respect to our solar system. This was the basis for a Sci-Fi short story I read once. One solar system was shrinking while the rest of the universe was expanding. They found out when they sent astronauts up, and one of them dropped a sapphire and it was huge. Anyone know the title/author?
4. Basis for a Voyager episode: different time scales in different parts of the universe. If time is moving more slowly out there (in a gradient of course), then the probe would still "think" it was going the correct speed, but it would in fact seem to be going too slow for us.
5. Um, how does the special theory of relativity take into account the fact that gravity does affect time? Never mind, they probably already thought of that...
Thanks for listening!
what these wires could do for the speed of your future pocket computer!
In my opinion, not much. The largest obstacle in the way of infinitely fast computers is the switching time of the FETs and BJTs used to make up the logic gates etc. These largely arise from the resistance, capacitance and inductance of the material in the transistors themselves, which must be made with semiconductors.
These wires are conductors (sorry for stating the obvious) and thus could not be used to fabricate a transistor using any conventional (or even known) methods. So, I'm sorry folks, but the best way to faster computers is still probably decreasing the size of the gates on the transistors.
Well, I got halfway through the other comments, and haven't seen a thread bringing up this point yet, so...
Has anyone given any thought to how a stationary permanent space elevator will restrict the number of orbits available? No more equatorial orbits at all, at any height (except geosynch), and any orbits that cross the equator (say, the polar orbits that many spy satellites are on) would have to be VERY carefully calculated so that they would be in a resonance pattern with the elevator, and miss it every time. Well, that covers every orbit possible, doesn't it.
Other people's thoughts on this?
PS - credit to Larry Niven Rainbow Mars for bringing up that objection.
but IIRC, in order to get any appreciable level of refraction, the object performing the refraction needs to be of the same order of magnitude as the wavelength of the waves being refracted. This means that, for example, a car would cause significant refraction in light of wavelengths of around 3 metres. That puts it firmly in the radio wave section of the spectrum.
Now, I may be wrong, but it seems to me that the longest wavelength laser still works in the infrared region of the spectrum, nowhere near the metre-range of radio waves, so no appreciable diffraction would occur to short-wavelength light on macroscopic objects.
Also, I would like to know why the more intense light would incinerate objects. The light is not being absorbed, therefore its energy of h_nu is not being converted to heat. If the photon is just being diffracted, then more photons would mean more diffracted photons, and more "rebound", but not more heat.
Well, I guess I'll just have to make the obvious joke about who goes down, while the other stays up...
Well, we're taking an RTOS course right now, but it doesn't do anything useful. All it does is run a bunch of special test programs to make sure we understand things like interprocess communication, memory management, and preemption.
:)
Our fun classes deal more with hardware, and with programming the hardware directly. Microprocessor interfacing, digital design, etc. I like to think that we get a lot of the hands-on knowledge without having to delve into the tedious mathematical proofs that programs work that CS students have to do.
Plus, our mascot isn't a giant pink tie
2001 Dilbert Desk Calendar
/. :)
Sunday, February 11
Now Scott Adams is not only spying on us at work, he's also reading
You hit the nail on the head there.
I can't recall exactly how all the forces add up
In the case of the yo-yo whirling about your head, the two balanced forces are the tension in the string pulling the yo-yo in, and with equal force pulling your hand (holding the other end of the string) out. Through muscluar control and friction, this force is transferred from your hand to the earth. Balance acheived.
'Cause we engineers know that there's no such thing as centrifugal force. Centripital force exists, yes. It is the force that holds a spinning object to the centre of its axis - example, the tension (force of) in the string attached to the yo-yo you're winging around your head.
There actually is no outwards force when you wing something around in a circle.
Which is the first step to contacting those sex-crazed Syreen...
First contact with the Spathi.
Our Univ. class has an unwritten rule. If your cell phone interrupts the prof, at the end of the class you have to stand on your desk and do the chicken dance. So far, it has only been enacted(sp?) three or four times. They are going to try to apply this rule to the entire department.
We all know that dinosaurs were killed largely by second-hand smoke. Just imagine the size of the cigarettes it would take to give a brachiosaurus a nicotine buzz...
Those aren't *really* jr. high girls saying that they want to cyber with you. It's actually a 400lb man, wearing a foodstained shirt and boxers, with his hand in his pants, getting off on his fantasy that he is a jr. high girl being fscked by a high profile exec at a law firm, which is who you are pretending to be.
Now, I wholly approve of this as an outlet for your sexual tension, but please, don't ever believe that they are who they say they are, and for god's sake, never agree to meet with them.
Ha ha ha ha ha! I loved the time I tried that as a sadist bastard! One of my friends gave a guy nothing but a trailer and an outdoor toilet and hot-tub. He kept inviting chicks over, and they'd get in the hottub, but whenever he tried to get some, they'd smack him. Also, he wouldn't let his guy sleep or eat. It got to the point where the guy would be walking to get the mail and would collapse on the ground for a couple of hours. Ha ha ha ha!