However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in both directions symmetrically in the box, then the total momentum is zero in the box's frame of reference but the energy is not. Therefore the light adds a small contribution to the mass of the box. This could be measured--in principle at least--either by the greater force required to accelerate the box, or by an increase in its gravitational pull.
The use of words can make a lot of confusion. Unfortunately, the word "mass" has been used in two different ways in physics. One was the way Einstein used it in E=mc^2, where mass is really just the same thing as energy but measured in different units. This is the same "m" that you multiply velocity by to find momentum. It's also the mass that provides the source of gravitational effects. Light has this "m" because it has energy (E) and momentum (p). So it is indeed affected by gravity- not just in black holes but in all sorts of less extreme situations too. In fact, the first important confirmation of General Relativity came in 1919, when it was found that light from stars bends as it goes by the Sun.
The other way "mass" is often used, especially in recent years, is to mean "rest mass" or "invariant mass", which is sqrt(E^2-p^2*c^2)/c^2. This is invariant because it doesn't change when you describe an object at rest or from the point of view of someone who says it's moving. Obviously that's a good type of "mass" to give when you want to make a list of masses of particles. For
light, E=pc, so this "m" is zero. There is no point of view from which the light is standing still!
Mike
In physics, light or other forms of electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational field (and which could be said to have climbed "uphill" out of a gravity well) will be found to be of longer wavelength when received by an observer in a region of weaker gravitational field. If applied to optical wave-lengths this manifests itself as a change in the colour of the light as the wavelength is shifted toward the red (making it: less energetic,longer in wavelength, and lower in frequency) part of the spectrum. This effect is called gravitational redshift and other spectral lines found in the light will also be shifted towards the longer wavelength, or "red," end of the spectrum. This shift can be observed along the entire electromagnetic spectrum.
Light that has passed "downhill" into a region of stronger gravity shows a corresponding increase in energy, and is said to be gravitationally blueshifted.
Proposed by R. V. Pound and G. A. Rebka Jr. in 1959,[1] and was the last of the classical tests of general relativity to be verified (in the same year). It is a gravitational redshift experiment, which measures the redshift of light moving in a gravitational field, or, equivalently, a test of the general relativity prediction that clocks should run at different rates at different places in a gravitational field. It is considered to be the experiment that ushered in an era of precision tests of general relativity.
disagree.
Note on Theory vs Practice: "While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account."
Already will/did. But then/now you've used those two lost minutes re-over, and did the same thing, forming a never-ending loop. Thanks, buddy. Now there is no way out of this conversation.
Someone needs to launch a series of spheres of various materials (ferrous and several nonferrous,) and see if the effect is merely related to mass. Be a kick in the ass if turns out to be related to volume instead.
That sir is *exactly* the point. Observed measurements are at odds with our model. There is no "period" at this point, but rather an exclamation point. Paradox and inconsistency are not to be feared, they are just the flags raised when something worthy is noticed.
The beautiful thing about the scientific method is that is requires peer review. Truth isn't a matter of what one claims they've done, it also requires that other people repeat the experience. Its better still when different methods are used (to avoid systemic errors) and the same results yet obtain. Its not like, "whose truth", because there is only one. What actually *is*, is truth. There is no, "well gravity accelerates at about 32 meter/sec^2 to me", and someone else says, "oh no, the acceleration of gravity might be that for you, but for me it is 3200000 meter/sec^2". It is what it is. To suggest that when you talk to Mary the sky is blue (she is a Scientist), but when you talk to Fred the sky is green (after all, he is a priest, he understands what the Book says about the green-ness of the sky). This is to trivialize what *truth* means, and make slogans such as: "black is white", and "war is peace", and "the truth is a lie", come to horrible nightmare life. Compartmentalization as you suggest allows various deluded people to get along, sure, since they shift gears and go with a different delusion as needed to get along. Just don't mistake this for TRUTH. It ain't that.
I would even go so far as to suggest that the very fact that you can talk about "both truths" mean you don't know what truth is. Are there 4 quarters in a dollar? Or are there 3? Is it necessary to believe there are both 3 and 4 quarters in a dollar? Why?
Finally, to suggest that doing whatever you think is best makes ones decisions good decisions is like saying, "yeah, well, ok, he was *sure* the rope would hold, and well maybe the bus of kids did die, but lets build a statue to this man who did what he thought was right". Sometimes, I think you'd agree, actual consequences of actions based on willful behavior gets counted, too. Like, "Opps, oh shit, I thought putting the match in the gas tank was a good idea, I mean it seemed funny, and now, well, my family is *dead*." Grrr...
Often the root cause of straw man arguments, application of fallacy of the consequent, and most especially ad hominem attacks is simply this: that they don't like you.
"Mutation is random, selection is not." So Intelligent Design works at least in so far as mate selection. At least for those intelligent enough to choose an intelligent mate...
Well, someone once said "the truth will set you free". He was reputed to be a great teacher. If you assume that some people don't want to know the truth, and further that some people don't want to be free, then perhaps you are right. Still, most children have a natural curiosity regarding the world and its wonders. Should children have to likewise grow up blindly ignorant because their parents are willfully so? How fair a world is that? I would suggest that good parents should agree to, and even desire to accept a certain amount of suffering as their children embrace truth.
Agreed that if we could get them to take enough Physics to get through Statistical Mechanics, the difficulty of presenting Evolution would be markedly reduced. Good luck with that. On the other hand, if successful, you'd probably take care of any number of other related problems;-)
Actually this is part of the Reagan myth. In reality, the average annual returns where higher under Carter than Reagan. Fewer under-18 yr olds were living in poverty under Carter than Reagan. Carter surely didn't contribute to an increased percentage debt to GDP ratio, while Reagen *doubled* the national debt, out spending every president before him added together. By objective measures, Clinton was better for the economy than Reagan. Its just a fact, no matter how much people liked listening to "the ol' gipper".
I should have included a winking smiley face;-)
I was trying to quote from The Big Chill:
Michael: I don't know anyone who could get through the day without two or three juicy rationalizations. They're more important than sex.
Sam Weber: Ah, come on. Nothing's more important than sex.
Michael: Oh yeah? Ever gone a week without a rationalization?
All other presidents since WWII have contributed nothing to the Gross Federal Debt (as % of GDP) except for Reagan, George Bush, and George W. Bush. It is fair to say that postwar (WWII) debt is a creation of the GOP. This is *not* "politics as usual" and *is* historically significant.
Interestingly enough, if you track the market and label the time axis based on who is power at that time, the market has historically done slightly better with a democrat at the helm. Not sure if that is *really* a measure of "prosperity", as it doesn't measure any quality-of-life indicators, just market growth. Capital growth is at least somewhat related to prosperity, though. "The humorist Will Rogers reportedly suggested that, in order to find the place where the Republican Party was formed, one should find out where the first business was formed." This seems more humorous than true, however.
Normal, intelligent people don't care much about national politics because they know that as individuals they have zero impact on the operations of the broken and corrupt system. That is the *rational* response.
Methinks you confuse "rational" with "rationalize".
But hey, rationalization is more important than sex. Think not? Every try to go a day without three really juicy rationalizations?;-)
Slashdot Mirror
disagree.
Note on Theory vs Practice: "While gravitational redshift refers to what is seen, gravitational time dilation refers to what is deduced to be "really" happening once observational effects are taken into account."
...and even more so on what you mean by "definition".
Already will/did. But then/now you've used those two lost minutes re-over, and did the same thing, forming a never-ending loop. Thanks, buddy. Now there is no way out of this conversation.
Someone needs to launch a series of spheres of various materials (ferrous and several nonferrous,) and see if the effect is merely related to mass. Be a kick in the ass if turns out to be related to volume instead.
Physics can be done in crayon just fine, thank you very much! Color coding the variables is quite useful :-) And more fun than anatomy coloring books.
Gravity doesn't work like that.
That sir is *exactly* the point. Observed measurements are at odds with our model. There is no "period" at this point, but rather an exclamation point. Paradox and inconsistency are not to be feared, they are just the flags raised when something worthy is noticed.
The beautiful thing about the scientific method is that is requires peer review. Truth isn't a matter of what one claims they've done, it also requires that other people repeat the experience. Its better still when different methods are used (to avoid systemic errors) and the same results yet obtain. Its not like, "whose truth", because there is only one. What actually *is*, is truth. There is no, "well gravity accelerates at about 32 meter/sec^2 to me", and someone else says, "oh no, the acceleration of gravity might be that for you, but for me it is 3200000 meter/sec^2". It is what it is. To suggest that when you talk to Mary the sky is blue (she is a Scientist), but when you talk to Fred the sky is green (after all, he is a priest, he understands what the Book says about the green-ness of the sky). This is to trivialize what *truth* means, and make slogans such as: "black is white", and "war is peace", and "the truth is a lie", come to horrible nightmare life. Compartmentalization as you suggest allows various deluded people to get along, sure, since they shift gears and go with a different delusion as needed to get along. Just don't mistake this for TRUTH. It ain't that.
I would even go so far as to suggest that the very fact that you can talk about "both truths" mean you don't know what truth is. Are there 4 quarters in a dollar? Or are there 3? Is it necessary to believe there are both 3 and 4 quarters in a dollar? Why?
Finally, to suggest that doing whatever you think is best makes ones decisions good decisions is like saying, "yeah, well, ok, he was *sure* the rope would hold, and well maybe the bus of kids did die, but lets build a statue to this man who did what he thought was right". Sometimes, I think you'd agree, actual consequences of actions based on willful behavior gets counted, too. Like, "Opps, oh shit, I thought putting the match in the gas tank was a good idea, I mean it seemed funny, and now, well, my family is *dead*." Grrr...
Often the root cause of straw man arguments, application of fallacy of the consequent, and most especially ad hominem attacks is simply this: that they don't like you.
Indeed. For most people I'd suggest that feeling certain was more a function of their limbic system than their gray cells.
"Mutation is random, selection is not." So Intelligent Design works at least in so far as mate selection. At least for those intelligent enough to choose an intelligent mate...
ID is also extremely controversial exactly because of the audacity of not having any evidence.
It is exactly that you think about it that is the proof you've risen above the herd ;-)
Well, someone once said "the truth will set you free". He was reputed to be a great teacher. If you assume that some people don't want to know the truth, and further that some people don't want to be free, then perhaps you are right. Still, most children have a natural curiosity regarding the world and its wonders. Should children have to likewise grow up blindly ignorant because their parents are willfully so? How fair a world is that? I would suggest that good parents should agree to, and even desire to accept a certain amount of suffering as their children embrace truth.
Agreed that if we could get them to take enough Physics to get through Statistical Mechanics, the difficulty of presenting Evolution would be markedly reduced. Good luck with that. On the other hand, if successful, you'd probably take care of any number of other related problems ;-)
Actually this is part of the Reagan myth. In reality, the average annual returns where higher under Carter than Reagan. Fewer under-18 yr olds were living in poverty under Carter than Reagan. Carter surely didn't contribute to an increased percentage debt to GDP ratio, while Reagen *doubled* the national debt, out spending every president before him added together. By objective measures, Clinton was better for the economy than Reagan. Its just a fact, no matter how much people liked listening to "the ol' gipper".
Actually the market did less well under Reagan than Clinton.
I was trying to quote from The Big Chill:
Note: one such quality-of-life indicator is poverty
National Debt History (as percentage of GDP) by President
Even more interesting is who is responsible for our current debt : Presidents and the Federal Debt
All other presidents since WWII have contributed nothing to the Gross Federal Debt (as % of GDP) except for Reagan, George Bush, and George W. Bush. It is fair to say that postwar (WWII) debt is a creation of the GOP. This is *not* "politics as usual" and *is* historically significant.
Interestingly enough, if you track the market and label the time axis based on who is power at that time, the market has historically done slightly better with a democrat at the helm. Not sure if that is *really* a measure of "prosperity", as it doesn't measure any quality-of-life indicators, just market growth. Capital growth is at least somewhat related to prosperity, though. "The humorist Will Rogers reportedly suggested that, in order to find the place where the Republican Party was formed, one should find out where the first business was formed." This seems more humorous than true, however.
In Business Law they taught us that negligence is legally a form of intent.
But hey, rationalization is more important than sex. Think not? Every try to go a day without three really juicy rationalizations?
I don't know, "fiscally conservative and socially liberal" sounds like a democrat. Republicans are fiscally liberal and socially conservative...