Well, it sort of does anyway. The factor of 2 in the exponent is exact, but the entire expression mc^2 is only valid when at rest relative to the particle in question. At some relative velocity, the expression is really (gamma)mc^2, where (gamma) is 1/(1-v^2/c^2)^-1/2.
The "throw away the textbooks" comment is a little snarky. The text I currently use, as well as most of the others in use, describe the Milky Way as *possibly* having some kind of barred shape, as there has been evidence along these lines for years. Books evolve. 15-year old books don't have much to difinitively say on the cosmological constant, either, though they may be perfectly good texts on all other phenomena.
Seconded. I use it almost daily for illustrations in homework assignments, workshops, and exams (I'm a college professor in physics). Remarkable, easy software. Combined with the LaTeX equation editor, I can import any formula or math symbol in pdf format into my illustration.
Hi! Certifiable idiot reporting for duty! My PowerBook doesn't have Bluetooth, and I'd love the horizontal/vertical scrolling capacity as well as the opportunity to use an Apple mouse, as I am fond of their design and durability. But I'll submit to your sweeping characterization! Thanks for the free judgement!
I think I agree with your first point. Science can, bascially by definition, only concern itself with those things that are non-supernatural. Perhaps there could be evidence for the supernatural, but only to the extent that the phenomenon cannot be explained by natural means. One ought to still hold to the possibility that future scientific discoveries might be able to explain the presently mysterious.
Yes, we obviously disagree as to what a Christian is. I am a follower of Christ's teachings, as I understand them, and believe him to be a human manifestation of God incarnate. I also believe in the Apostle's Creed, which by many accounts is a sufficiently small set of axioms to "test" for Christianity. Perhaps I don't pass fundamentalist muster, but I'm comfortable with that. In any case, thanks for the conversation.
Well, I would say that there are avenues of inquiry regarding humans that tend to lie in the domain of the purely physical, as opposed to those that test our "spiritual", or conscious, selves. The evidence is that the behavior of other natural objects, especially in simple systems, behaves closely according to a set of physical laws. I suppose there is still room for the supernatural in this, but there's no evidence of it yet. To the extent that there is a pervading supernatural will, its effect is thankfully in tune with physical principles.
Interestingly, I was raised Unitarian, though now I'm a member of a Methodist church and was fairly recently baptized. True, the literal readings of biblical history contradict my own professional field, but I must assume that these contradictions arise from an imperfect understanding of the text. They are brought in harmony in the realization that the Genesis stories are truly mythic in nature, communicating truths of the right relationship between God, man, and His creation. It is not necessary for me that they are literal history. It is not that I'm picking which parts I want to believe, but that I must struggle to interpret correctly those parts that are in conflict. A passage may contain spiritual or theological truth, as the parables do, and yet no historical truth. The pleasure is in the struggle for interpretation.
Christianity deals with, as you suggest, that which is not purely natural (in the scientific sense) --- the right and proper behavior of that supernatural aspect of a person we might call the "soul". Certainly I may suggest that there is some supernatural component to a human person without denying that the person is also a member of the natural world; indeed, I believe that the human form evolved according to our current theories. I don't understand why I must draw a distinction between those phenomena "influenced by humans" and those that aren't.
My Christianity is not terribly dogmatic, I don't think. What dogma bothers you? I like Christianity in that I feel it is a more precise and correct theological formulation than other religions, sort of similarly to how GR is a more precise and correct model of gravitational behavior. I could be wrong, though I must follow my conscience.
I admit to not understanding your difficulty. Why would I not subscribe to natural philosophy? I freely embrace science as our best method to understand natural phenomena. Where's the problem?
Of course my answer is, then, that there is no fundamental conflict. Hopefully that can restore some credibility. Any conflict between the two can be ascribed to an imperfect understanding of either (or both).
I can't tell if you're merely sarcastic, but yes, being an astrophysicist as well as a Christian, I am equally annoyed by those all too dismissive of theological arguments that they are unacquainted with.
Insightful? What would you like to have happen? Publish fewer articles? Not research it so much? Sheesh.
This anti-intellectualism stain in/. responders is saddening. Basically it seems to be, "I don't understand what they're talking about, so I think I'll make fun of them" or "I don't understand the thousands of papers that have been published, so I'm going to shout something superior-sounding from the cheap seats". Dismissing a beautiful and maturing field of physics with "we don't really know anything, so give up" is a sophomoric and pretentious reaction.
Sure, there's a bunch that we don't understand, but please realize that this is the way science works. Nature is too subtle for us to have canned and precise answers for her behavior. Cosmologists are rightly invigorated by the new data, and ought to be encouraged to research and refute each other's ideas.
I'll throw in a vote for OmniGraffle and OmniOutliner, OS X software from the Omni Group. They both nail what they are supposed to do so well. It is simply a pleasure to use either one of them. I use OmniGraffle at least once per day to draw diagrams for my classes and exams, export them to pdf, and import them to my LaTeX docs. OmniOutliner is a wonderful structured writing tool with simple text input and manipulation.
Oh, I just mean a distribution of dark matter that is shaped more like a ball than a disk. Astronomers call matter lying outside of the disk part of the "halo" of the galaxy --- most of the globular clusters that we know of are members of this "halo", remnants of the very early gas in the collapsing gas cloud that ultimately formed the galaxy.
1. I think so (I'm an astrophysicist, but I'm teaching now and several years removed from grad school) --- the galactic mass deficit is most readily observed in spirals of all different sizes, but it is an interesting question as to whether there is any systematic variation in distance (which would also be time). I'll have to ask around.
2. Several ways --- rotation, motion of a number of satellite galaxies, mass/light ratio, Tully-Fisher relation, and, if it's a spiral, simply by the size if we know the distance (this is pretty rough, but a decent indicator)
3. Within a galaxy, I don't think so. But intra-galactic dark matter is just one type. There is also non-luminous matter in between galaxies in clusters to account for their motion. Hot X-ray gas is one candidate, but I thought I remembered that there didn't seem to be enough of that stuff to account for cluster dynamics. Maybe this new stuff will help out, though the mass deficit was much more than this 2% if I recall correctly, and is probably non-baryonic.
3. Yes, they should. That's the problem. Outer stars and globular clusters are orbiting way to fast if all the mass in the galaxy is traced by luminous matter. A good model to account for the rotational behavior is a spherical halo (not just a disk) of non-luminous matter. This is the intra-galactic dark matter, and not relevant to the article.
Originally, the two objects were relatively close together. Now, they are far apart --- not because they have raced through space, but because the space between them has expanded. It is a subtle, but crucial, point. The light takes so long to go from one object to another because, as space expands, it has a longer way to go. If objects are separated by a few *billion* years, the expansion of space contributes significantly to both the light travel time as well as the change in the frequency of light (redshift).
Hi, maybe this will help.
A long time ago, all points in the universe were much closer together. At this time, some object emitted light in our direction. Due to the expansion of space, the distance between the object's coordinate and our coordinate has increased --- it is *not* the case that the galaxies are rushing through space; rather, the galaxies are more like objects stuck on the surface of an expanding rubber sheet. If one were to chalk off a gridded coordinate system when the sheet is unstretched, then one notices that the distance between any two coordinates (intersections on the grid) gets larger as the sheet expands. As light travels from one grid point to another, it continually has a longer distance to travel, so it takes a long time to get there. Thus, when we see light from a (now) distant object, we infer that it was emitted a long time ago when our relative distances were closer.
Yep, I just picked up the Erector Construction Set at Wal-Mart (600+ pieces and motor) for my 8-year-old. I remember how cool it was to build robust stuff with METAL! when I was a kid.
How long has it been since it was available?
Slashdot Mirror
Well, it sort of does anyway. The factor of 2 in the exponent is exact, but the entire expression mc^2 is only valid when at rest relative to the particle in question. At some relative velocity, the expression is really (gamma)mc^2, where (gamma) is 1/(1-v^2/c^2)^-1/2.
The "throw away the textbooks" comment is a little snarky. The text I currently use, as well as most of the others in use, describe the Milky Way as *possibly* having some kind of barred shape, as there has been evidence along these lines for years. Books evolve. 15-year old books don't have much to difinitively say on the cosmological constant, either, though they may be perfectly good texts on all other phenomena.
Seconded. I use it almost daily for illustrations in homework assignments, workshops, and exams (I'm a college professor in physics). Remarkable, easy software. Combined with the LaTeX equation editor, I can import any formula or math symbol in pdf format into my illustration.
Hi! Certifiable idiot reporting for duty! My PowerBook doesn't have Bluetooth, and I'd love the horizontal/vertical scrolling capacity as well as the opportunity to use an Apple mouse, as I am fond of their design and durability. But I'll submit to your sweeping characterization! Thanks for the free judgement!
...but the CNTL key is not next to the "A", as God intended. Maybe this would be configurable.
I think it's pretty "snappy"
They're probably all engineers.
Yes, we obviously disagree as to what a Christian is. I am a follower of Christ's teachings, as I understand them, and believe him to be a human manifestation of God incarnate. I also believe in the Apostle's Creed, which by many accounts is a sufficiently small set of axioms to "test" for Christianity. Perhaps I don't pass fundamentalist muster, but I'm comfortable with that. In any case, thanks for the conversation.
Interestingly, I was raised Unitarian, though now I'm a member of a Methodist church and was fairly recently baptized. True, the literal readings of biblical history contradict my own professional field, but I must assume that these contradictions arise from an imperfect understanding of the text. They are brought in harmony in the realization that the Genesis stories are truly mythic in nature, communicating truths of the right relationship between God, man, and His creation. It is not necessary for me that they are literal history. It is not that I'm picking which parts I want to believe, but that I must struggle to interpret correctly those parts that are in conflict. A passage may contain spiritual or theological truth, as the parables do, and yet no historical truth. The pleasure is in the struggle for interpretation.
My Christianity is not terribly dogmatic, I don't think. What dogma bothers you? I like Christianity in that I feel it is a more precise and correct theological formulation than other religions, sort of similarly to how GR is a more precise and correct model of gravitational behavior. I could be wrong, though I must follow my conscience.
I admit to not understanding your difficulty. Why would I not subscribe to natural philosophy? I freely embrace science as our best method to understand natural phenomena. Where's the problem?
Of course my answer is, then, that there is no fundamental conflict. Hopefully that can restore some credibility. Any conflict between the two can be ascribed to an imperfect understanding of either (or both).
I can't tell if you're merely sarcastic, but yes, being an astrophysicist as well as a Christian, I am equally annoyed by those all too dismissive of theological arguments that they are unacquainted with.
This anti-intellectualism stain in /. responders is saddening. Basically it seems to be, "I don't understand what they're talking about, so I think I'll make fun of them" or "I don't understand the thousands of papers that have been published, so I'm going to shout something superior-sounding from the cheap seats". Dismissing a beautiful and maturing field of physics with "we don't really know anything, so give up" is a sophomoric and pretentious reaction.
Sure, there's a bunch that we don't understand, but please realize that this is the way science works. Nature is too subtle for us to have canned and precise answers for her behavior. Cosmologists are rightly invigorated by the new data, and ought to be encouraged to research and refute each other's ideas.
a) Lower limits are roughly 1/20 solar mass. Less mass than this can't product the temperatures and densities needed for hydrogen fusion.
b) roughly the population dies off as M^{-2.5}, with some hard cut-off at high and low mass. There are many more low- than high-mass stars.
c) Age goes roughly as M^{-3.5} or so. High mass stars don't live very long at all.
d) Yes! Not only energy output, but elemental abundance evolution. That was my thesis.
I'll throw in a vote for OmniGraffle and OmniOutliner, OS X software from the Omni Group. They both nail what they are supposed to do so well. It is simply a pleasure to use either one of them. I use OmniGraffle at least once per day to draw diagrams for my classes and exams, export them to pdf, and import them to my LaTeX docs. OmniOutliner is a wonderful structured writing tool with simple text input and manipulation.
Oh, I just mean a distribution of dark matter that is shaped more like a ball than a disk. Astronomers call matter lying outside of the disk part of the "halo" of the galaxy --- most of the globular clusters that we know of are members of this "halo", remnants of the very early gas in the collapsing gas cloud that ultimately formed the galaxy.
2. Several ways --- rotation, motion of a number of satellite galaxies, mass/light ratio, Tully-Fisher relation, and, if it's a spiral, simply by the size if we know the distance (this is pretty rough, but a decent indicator)
3. Within a galaxy, I don't think so. But intra-galactic dark matter is just one type. There is also non-luminous matter in between galaxies in clusters to account for their motion. Hot X-ray gas is one candidate, but I thought I remembered that there didn't seem to be enough of that stuff to account for cluster dynamics. Maybe this new stuff will help out, though the mass deficit was much more than this 2% if I recall correctly, and is probably non-baryonic.
3. Yes, they should. That's the problem. Outer stars and globular clusters are orbiting way to fast if all the mass in the galaxy is traced by luminous matter. A good model to account for the rotational behavior is a spherical halo (not just a disk) of non-luminous matter. This is the intra-galactic dark matter, and not relevant to the article.
...and it's spelled "grammar".
Originally, the two objects were relatively close together. Now, they are far apart --- not because they have raced through space, but because the space between them has expanded. It is a subtle, but crucial, point. The light takes so long to go from one object to another because, as space expands, it has a longer way to go. If objects are separated by a few *billion* years, the expansion of space contributes significantly to both the light travel time as well as the change in the frequency of light (redshift).
Hi, maybe this will help. A long time ago, all points in the universe were much closer together. At this time, some object emitted light in our direction. Due to the expansion of space, the distance between the object's coordinate and our coordinate has increased --- it is *not* the case that the galaxies are rushing through space; rather, the galaxies are more like objects stuck on the surface of an expanding rubber sheet. If one were to chalk off a gridded coordinate system when the sheet is unstretched, then one notices that the distance between any two coordinates (intersections on the grid) gets larger as the sheet expands. As light travels from one grid point to another, it continually has a longer distance to travel, so it takes a long time to get there. Thus, when we see light from a (now) distant object, we infer that it was emitted a long time ago when our relative distances were closer.
Yes, mice will chew through all exposed cables, especially if you put peanut butter on them.
Yep, I just picked up the Erector Construction Set at Wal-Mart (600+ pieces and motor) for my 8-year-old. I remember how cool it was to build robust stuff with METAL! when I was a kid. How long has it been since it was available?
Floating Frogs
It's a result of you being first and foremost a resident of your state before your country. States still retain some notion of independent entities.