If I used my magic obliterator to magically make the sun disappear, would Earth go flying off into space at the same moment or would it continue to orbit the missing sun for the 8 minutes it would take the last rays of light to reach us? The latter.
This is where they say gravitons come in as a particle that conveys gravity which doesn't make any sense. Why doesn't it make any sense? Photons are particles which convey electric and magnetic forces, do you have a problem with them too?
Anyway, you don't need to appeal to graviton particles to answer the above question. Even in classical general relativity, the answer is still "8 minutes later", since that's how long for gravitational waves of spacetime curvature, traveling at the speed of light, take to reach the Earth.
One hypothesis of gravity is that it is an exchange of 'gravitons'. If this hypothesis is indeed correct, then it does indeed make sense to ask how these gravitons can escape a black hole. And I don't know the answer to that. Static gravitational fields are mediated by virtual gravitons, which can travel at any speed, including faster than light. However, you cannot use them to transmit information, i.e., changes in the field from inside the horizon.
With this image, it is spacetime that bends so there's no meaningful question for how gravity 'escapes' from it. Right. Classically you can see that the exterior field does not depend on the interior field, and that gravitational radiation generated inside the hole can't get out.
If we suspend physics and assume that one could take measurements inside the event horizon, wouldn't those detectors "see" a whole shitload of photons coming in from the outside? Yes. This Java applet has a visualization (if you set the observer distance to less than the Schwarzschild radius at 2.0 M. You should rotate the view to face outward.)
(There's no need to "suspend physics"; there's no physical reason why you can't take measurements within an event horizon, as long as you're comfortable with the fact that you'll die soon afterward and won't be able to transmit your data to anyone outside of the hole).
However, the mediating particles themselves are not affected by the force they mediate. Otherwise the universe would disappear up its own arse. Hence, gravity is not affected by gravity. Actually, most mediating particles are affected by the force they mediate, including gluons, the hypothetical gravitons, and IIRC the W bosons.
In gauge theory, a non-Abelian gauge group will in general lead to a nonlinear Yang-Mills theory with self-interacting fields, in contrast to the linear Abelian theory of electrodynamics.
Because gluons, the mediator of the strong nuclear force, themselves carry strong ("color") charge, it's possible for them to bind to each other. (See glueballs in quantum chromodynamics.)
Similarly, gravity gravitates: gravitons interact with each other, because they have energy and anything with energy gravitates. This idea holds even in classical general relativity: gravitational fields themselves gravitate. Analogously to QCD glueballs, general relativity can have gravitational geons, which are regions of gravitational field which hold themselves together under their own gravity. (You might think that a vacuum black hole has that property too, but I'm talking about purely non-singular field configurations.)
The existence of a single solar mass black hole has nothing to do with any of the facts I stated. They hold no matter what the mass of the black hole, so long as it's not comparable in size to the planet's orbit itself.
(FYI, the smallest known black hole candidates are about 3 solar masses, with a size of about 18 km in diameter, i.e., about half the size of a neutron star.)
I'm not going to waste my time on this thread any more since you persist in not paying attention to what I'm saying.
As I said several times, I am not claiming that dark matter has been shown to exist through its gravitational effects, nor that observed gravitational phenomena have been proven to be due to dark matter.
I am merely saying that dark matter, if it exists, does have observable gravitational effects. This is to correct an earlier poster, who implied that dark matter should be dismissed as a theory because dark matter has no observable consequences.
(On the other hand, I will claim that it is very likely that dark matter does exist, on the basis of observed gravitational phenomena, as it explains far more phenomena than the ones Wiltshire is trying to explain. Dark matter can simultaneously account for galactic rotation curves, galactic superclusters, large scale early universe structure formation, cosmological expansion, and other effects — not to mention forms of dark matter being independently and naturally predicted by the Standard Model of particle physics and most extensions thereof.)
It is highly unlikely that a black hole would have planets orbiting it, as the planets would have insufficient mass to keep from simply falling in to the black hole, If the Sun collapsed into a black hole, its gravitational pull on the Earth wouldn't change.
that is to say the overwhelming mass of the black hole would place the barycenter of the black hole and any accompanying planet well inside the event horizon, Maybe you're talking about supermassive black holes, but if you're talking about black holes in solar systems, formed from collapsed stars, that's not true. A black hole is not "overwhelmingly massive"; it generally has less mass than the star it formed from, since some mass may be lost during the collapse. (Unless it gains a lot more later...)
Furthermore, as the Earth-Sun barycenter is well outside the Sun's Schwarzschild radius, it would be outside the event horizon of a solar-mass black hole, too. Not that the location of the barycenter even matters to the stability of the orbit.
There are exoplanets — the first discovered, actually — known to orbit neutron stars, which are only 10-20 km in radius. There's no reason why planets couldn't orbit black holes too.
Other people have answered your question (radiation cannot escape from inside the horizon, but it can still generate a static external field), but here is a FAQ with more detail, including the quantum picture.
While I can't give you numbers since I'm going from memory, but there used to be a theoretical limit to black hole size. There has never been a theoretical limit to the size of a generic black hole. (Technically, the observable universe could be in a giant black hole.) But back when people thought the only way a black hole could form was from the collapse of a single star, there was a practical limit on the size of an astrophysical black hole: if it forms from stellar collapse, it can't be more massive than the most massive stars. Everyone recognized that black holes can get larger by swallowing more mass, but it was a long time before people seriously considered the possibility of supermassive black holes actually existing.
Not quite what? What does your lengthy response have to do with anything I said?
Look, I'm just pointing out that the original poster was claiming that dark matter should be rejected because dark matter can have no observed gravitational effects, when the whole idea of dark matter was invented BECAUSE it has observable gravitational effects. I'm not claiming that dark matter exists, I'm just claiming that if it does exist, it has gravitational effects and cannot be rejected because it has no observable consequences. It does have observable consequences, independent of whether or not it's actually there.
I know dark matter has been inferred gravitationally, but the point is that the gravitational effects of dark matter, if it exists, are by definition detectable. The original poster was suggesting that we should conclude dark matter "isn't there" because it can't be detected through gravity effects, which is absurd.
The Universe is thought to be expanding mainly due to the red shift of light from distant galaxys Also because of the blackbody cosmic background radiation, the observation of hotter ambient temperatures in galaxies closer in time to the Big Bang, the observed ratios of light element nucleosynthesis from the Big Bang, etc.
Is it not possible that after travelling huge distances light "slows down" and exhibits a red shift. Such a theory, besides contradicting relativity, has numerous problems in explaining observations. See here for an incomplete list of failures of such "tired light" theories, as well as more detail on some of them here.
Your proposed mechanism in particular wouldn't explain supernova light curves (their light is redshifted but the supernova also goes more slowly the further away it is, consistent with the redshift being due to time dilation from cosmological expansion, not "slow light"). You haven't proposed any concrete mechanism, but I suspect it would have to also lead to blurring unless you can think of some way for light to "slow" without changing momentum! There are problems with explaining the cosmic background, etc.
History proves that what ever a scientist tells you is wrong. History doesn't "prove" any such thing. But if you're honestly taking the position that all science is wrong, I think you have more serious problems than merely objecting to some point of cosmology.
If you cannot detect something at all with light or gravity effects, then it very likely isn't there. Um, the whole point of dark matter is that it has detectable gravitational effects. (As does dark energy, which this article is about.) Why do you think the theory was invented?
Some people have mentioned that relativity does not impose a maximum temperature, since although it has a maximum particle speed, kinetic energy and therefore temperature is infinite.
However, when you bring thermodynamics into it, things become more complicated.
Thermodynamics is derived from the statistical behavior of large collections of particles. The thermodynamic laws are derived from the partition function, which is a sum of the form exp(-beta E), where beta ~ 1/T is inverse temperature and E is the energy of a state of the system. The sum is over all the possible states.
In some systems, the number of states increases exponentially with energy, so the sum eventually diverges even though each term is an exponentially decaying function. The temperature at which this happens is the Hagedorn temperature mentioned in TFA. You can think of this situation as "entropy winning over energy", as the number of states determines the system's entropy.
In particular, in relativistic quantum field theory, relativity requires that it be possible to create particles matter-antimatter pairs if you put enough energy in the system.
One thing that can happen in some relativistic systems (though it doesn't have to happen) is that when you put enough energy into a system, it mostly goes into creating new particles instead of making existing particles go faster. Thus, the Hagedorn temperature: as you reach it, all the energy you're putting in to heat the system goes into particle production, and nothing goes into raising their temperature. (This is not the only way in which a system can have a Hagedorn limit, nor do all relativistic systems have this limit, but it can happen.)
TFA implies that this limit only exists in string theory. But it exists in other theories as well. For instance, quantum chromodynamics, the theory of the strong nuclear force, has a Hagedorn limit. But in QCD, it is thought that it's not a true maximum temperature. Rather, the divergence of the partition function there signals the presence of a phase transition, from quarks confined in hadrons to a free quark-gluon plasma. Perhaps in string gas cosmology it's a true limit; I don't know much about that.
If the entropy increases even faster than exponentially, you can get weird situations like negative heat capacities, i.e., where adding more energy to a system lowers its temperature! There, you actually take kinetic energy from existing particles and put it into particle creation, creating so many new particles that the overall temperature of the system decreases.
Incidentally, the beta factor mentioned above in the partition function explains another point in TFA, about negative temperatures. In statistical thermodynamics, you can see that the key parameter is not temperature T, but inverse temperature beta ~ 1/T. As you increase temperature towards infinity, beta decreases to towards zero from above, so hotter temperatures correspond to smaller betas. You can imagine how a negative beta, then, corresponds to an even hotter temperature than any positive beta. In other words, negative temperatures are hotter than positive temperatures. As beta is decreased smoothly through zero from above, temperature increases to positive infinity, jumps discontinuously to negative infinity, and then approaches zero temperature from the other side. The hottest temperature, then, is -0 K — or rather, the limit as you approach 0 K from below, instead of above (which is a different limit from the perspective of the more fundamental parameter beta).
I don't exaggerate. Uh huh. Let's just jump to a fantasy scenario of prison rape and permanent sex offender status. No exaggeration there.
Name one instance in which someone has been prosecuted, let alone convicted, for someone else hijacking their wifi to download child porn to a computer not belonging to them. One you've done that, we can narrow that down to the instances involving prison rape and sex offender registries.
Most individuals can't get past the stage of hiring a lawyer who's good enough to defend that point. There's no fine nuance that requires fancy legal footwork.
I did point this out in my original message, which you don't seem to have read. I read it, it's just wrong.
The unknowing user whose home wifi got hijacked (or who mistakenly downloaded the wrong thing) goes to jail for a very long time and is systematically raped and tortured by the inmates for being a "child molester" only to have to register as a sex offender for the rest of their lives when/if they get out, because of existing laws. If that were true, they wouldn't need this new law.
Right now, if someone else uses your Internet connection (home wifi or if you're an ISP) to download child porn, the law can't really do anything to you. They can only punish the actual downloader.
Under the new law, if someone else uses your public Internet service to download child porn, and you demonstrably know about it, but you don't report it, then they can... make you pay a fine.
That's a far cry from sending you to jail for a very long time where you are systematically raped and tortured and have to register as a sex offender for the rest of your life.
Were these the same floats that initially indicated that the oceans were *cooling* and not warming, but which were later recalibrated to report "accurate" temperature data? Yes.
All MOND states (last time I checked) is that gravities falloff rate is slower at long distances. MOND is weirder than that. Instead of modifying gravity at some length scale as you suggest, MOND makes the gravitational force dependent on a body's acceleration instead of just its position.
MOND's main problems are that (1) it can't account for as many phenomena as can dark matter (it does great on galactic rotation curves but not so great at, say, cosmology), (2) it's hard to make consistent with relativity (Bekenstein has a proposal but it has a number of free parameters that appear to require fine tuning to match observations), (3) there is fairly direct evidence for dark matter (e.g., the Bullet Cluster) so even if MOND is true, it doesn't really achieve its original goal of replacing dark matter.
It's better to play the numbers you excluded than the ones you retained. 10-10-10-10-10 is just as likely as 34-95-89-24-61. But because people think it's less likely, they tend not to pick it. Which means that you should pick it, since you're no less likely to win, but are less likely to have to share the prize with someone else.
He's doing this because he doesn't like that he's being quoted by creationist nutjobs to support their unscientific positions, and he wants to stick it to 'em; he would never have retracted otherwise. It's a completely self-serving, hypocritical and irrational action He probably is retracting it because he's being quoted by creationist nutjobs. But it's not hypocritical or irrational. The paper WAS flawed. Sure, the creationism bit may have spurred him to retract it instead of quietly ignoring the errors, but there is nothing fundamentally wrong with retracting an erroneous paper.
Slashdot Mirror
Anyway, you don't need to appeal to graviton particles to answer the above question. Even in classical general relativity, the answer is still "8 minutes later", since that's how long for gravitational waves of spacetime curvature, traveling at the speed of light, take to reach the Earth.
(There's no need to "suspend physics"; there's no physical reason why you can't take measurements within an event horizon, as long as you're comfortable with the fact that you'll die soon afterward and won't be able to transmit your data to anyone outside of the hole).
Hence, gravity is not affected by gravity. Actually, most mediating particles are affected by the force they mediate, including gluons, the hypothetical gravitons, and IIRC the W bosons.
In gauge theory, a non-Abelian gauge group will in general lead to a nonlinear Yang-Mills theory with self-interacting fields, in contrast to the linear Abelian theory of electrodynamics.
Because gluons, the mediator of the strong nuclear force, themselves carry strong ("color") charge, it's possible for them to bind to each other. (See glueballs in quantum chromodynamics.)
Similarly, gravity gravitates: gravitons interact with each other, because they have energy and anything with energy gravitates. This idea holds even in classical general relativity: gravitational fields themselves gravitate. Analogously to QCD glueballs, general relativity can have gravitational geons, which are regions of gravitational field which hold themselves together under their own gravity. (You might think that a vacuum black hole has that property too, but I'm talking about purely non-singular field configurations.)
The existence of a single solar mass black hole has nothing to do with any of the facts I stated. They hold no matter what the mass of the black hole, so long as it's not comparable in size to the planet's orbit itself.
(FYI, the smallest known black hole candidates are about 3 solar masses, with a size of about 18 km in diameter, i.e., about half the size of a neutron star.)
I'm not going to waste my time on this thread any more since you persist in not paying attention to what I'm saying.
As I said several times, I am not claiming that dark matter has been shown to exist through its gravitational effects, nor that observed gravitational phenomena have been proven to be due to dark matter.
I am merely saying that dark matter, if it exists, does have observable gravitational effects. This is to correct an earlier poster, who implied that dark matter should be dismissed as a theory because dark matter has no observable consequences.
(On the other hand, I will claim that it is very likely that dark matter does exist, on the basis of observed gravitational phenomena, as it explains far more phenomena than the ones Wiltshire is trying to explain. Dark matter can simultaneously account for galactic rotation curves, galactic superclusters, large scale early universe structure formation, cosmological expansion, and other effects — not to mention forms of dark matter being independently and naturally predicted by the Standard Model of particle physics and most extensions thereof.)
Furthermore, as the Earth-Sun barycenter is well outside the Sun's Schwarzschild radius, it would be outside the event horizon of a solar-mass black hole, too. Not that the location of the barycenter even matters to the stability of the orbit.
There are exoplanets — the first discovered, actually — known to orbit neutron stars, which are only 10-20 km in radius. There's no reason why planets couldn't orbit black holes too.
Other people have answered your question (radiation cannot escape from inside the horizon, but it can still generate a static external field), but here is a FAQ with more detail, including the quantum picture.
"Again, not quite:"
Not quite what? What does your lengthy response have to do with anything I said?
Look, I'm just pointing out that the original poster was claiming that dark matter should be rejected because dark matter can have no observed gravitational effects, when the whole idea of dark matter was invented BECAUSE it has observable gravitational effects. I'm not claiming that dark matter exists, I'm just claiming that if it does exist, it has gravitational effects and cannot be rejected because it has no observable consequences. It does have observable consequences, independent of whether or not it's actually there.
Regulation #13754: All of sakdoctor's monetary savings and possessions are herewith legally redistributed to Ambitwistor.
I know dark matter has been inferred gravitationally, but the point is that the gravitational effects of dark matter, if it exists, are by definition detectable. The original poster was suggesting that we should conclude dark matter "isn't there" because it can't be detected through gravity effects, which is absurd.
Your proposed mechanism in particular wouldn't explain supernova light curves (their light is redshifted but the supernova also goes more slowly the further away it is, consistent with the redshift being due to time dilation from cosmological expansion, not "slow light"). You haven't proposed any concrete mechanism, but I suspect it would have to also lead to blurring unless you can think of some way for light to "slow" without changing momentum! There are problems with explaining the cosmic background, etc. History proves that what ever a scientist tells you is wrong. History doesn't "prove" any such thing. But if you're honestly taking the position that all science is wrong, I think you have more serious problems than merely objecting to some point of cosmology.
First recorded use of a heliograph: 405 BC, metal shields used to shine signals across a battlefield.
Some people have mentioned that relativity does not impose a maximum temperature, since although it has a maximum particle speed, kinetic energy and therefore temperature is infinite.
However, when you bring thermodynamics into it, things become more complicated.
Thermodynamics is derived from the statistical behavior of large collections of particles. The thermodynamic laws are derived from the partition function, which is a sum of the form exp(-beta E), where beta ~ 1/T is inverse temperature and E is the energy of a state of the system. The sum is over all the possible states.
In some systems, the number of states increases exponentially with energy, so the sum eventually diverges even though each term is an exponentially decaying function. The temperature at which this happens is the Hagedorn temperature mentioned in TFA. You can think of this situation as "entropy winning over energy", as the number of states determines the system's entropy.
In particular, in relativistic quantum field theory, relativity requires that it be possible to create particles matter-antimatter pairs if you put enough energy in the system.
One thing that can happen in some relativistic systems (though it doesn't have to happen) is that when you put enough energy into a system, it mostly goes into creating new particles instead of making existing particles go faster. Thus, the Hagedorn temperature: as you reach it, all the energy you're putting in to heat the system goes into particle production, and nothing goes into raising their temperature. (This is not the only way in which a system can have a Hagedorn limit, nor do all relativistic systems have this limit, but it can happen.)
TFA implies that this limit only exists in string theory. But it exists in other theories as well. For instance, quantum chromodynamics, the theory of the strong nuclear force, has a Hagedorn limit. But in QCD, it is thought that it's not a true maximum temperature. Rather, the divergence of the partition function there signals the presence of a phase transition, from quarks confined in hadrons to a free quark-gluon plasma. Perhaps in string gas cosmology it's a true limit; I don't know much about that.
If the entropy increases even faster than exponentially, you can get weird situations like negative heat capacities, i.e., where adding more energy to a system lowers its temperature! There, you actually take kinetic energy from existing particles and put it into particle creation, creating so many new particles that the overall temperature of the system decreases.
Incidentally, the beta factor mentioned above in the partition function explains another point in TFA, about negative temperatures. In statistical thermodynamics, you can see that the key parameter is not temperature T, but inverse temperature beta ~ 1/T. As you increase temperature towards infinity, beta decreases to towards zero from above, so hotter temperatures correspond to smaller betas. You can imagine how a negative beta, then, corresponds to an even hotter temperature than any positive beta. In other words, negative temperatures are hotter than positive temperatures. As beta is decreased smoothly through zero from above, temperature increases to positive infinity, jumps discontinuously to negative infinity, and then approaches zero temperature from the other side. The hottest temperature, then, is -0 K — or rather, the limit as you approach 0 K from below, instead of above (which is a different limit from the perspective of the more fundamental parameter beta).
For a little more about the Hagedorn temperature, read this historical essay and this paper (section 2). Wikipedia has a good discussion of negative temperature.
If it was an air burst, as is plausible from the damage done, one wouldn't expect to find an impact crater or a meteorite.
Yeah, I was about to say that Tufte wouldn't be caught dead making graphs in Excel — it's the antithesis of his visual explanations.
Name one instance in which someone has been prosecuted, let alone convicted, for someone else hijacking their wifi to download child porn to a computer not belonging to them. One you've done that, we can narrow that down to the instances involving prison rape and sex offender registries. Most individuals can't get past the stage of hiring a lawyer who's good enough to defend that point. There's no fine nuance that requires fancy legal footwork. I did point this out in my original message, which you don't seem to have read. I read it, it's just wrong.
Right now, if someone else uses your Internet connection (home wifi or if you're an ISP) to download child porn, the law can't really do anything to you. They can only punish the actual downloader.
Under the new law, if someone else uses your public Internet service to download child porn, and you demonstrably know about it, but you don't report it, then they can
That's a far cry from sending you to jail for a very long time where you are systematically raped and tortured and have to register as a sex offender for the rest of your life.
Yes, they do wash up on shore (sometimes they're even found), and yes, they are continually replaced.
MOND's main problems are that (1) it can't account for as many phenomena as can dark matter (it does great on galactic rotation curves but not so great at, say, cosmology), (2) it's hard to make consistent with relativity (Bekenstein has a proposal but it has a number of free parameters that appear to require fine tuning to match observations), (3) there is fairly direct evidence for dark matter (e.g., the Bullet Cluster) so even if MOND is true, it doesn't really achieve its original goal of replacing dark matter.
It's better to play the numbers you excluded than the ones you retained. 10-10-10-10-10 is just as likely as 34-95-89-24-61. But because people think it's less likely, they tend not to pick it. Which means that you should pick it, since you're no less likely to win, but are less likely to have to share the prize with someone else.