This happens because electromagnetic fields warp space-time in very specific ways in general relativity, and the gravitational field itself is responsible for coupling the charges to the electromagnetic fields; this is easier to see in action in the Hilbert-Palatini variational principle formulation of general relativity.
Wait, wait; electromagnetic fields warp space-time? My (non-university-based) understanding of GR only includes that masses warp space-time; now you're telling me that charges warp space-time too? I've only ever thought about GR in gravitational terms; does GR cover all 4 fundamental forces or just gravity and electromagnetism? *head asplode*
Everything warps space-time in GR (and all other alternative theories of gravity since Einstein)*: if it has energy content, momentum (linear or angular), pressure or stress, then it warps space-time. In GR, this comes because of the contracted Bianchi identities I mentioned earlier. These identities are algebraic identities, meaning they always hold; and by virtue of the core equations of GR, they force the conservation of the stress-energy-momentum tensor to hold everywhere. If something had stress, energy or momentum and that something didn't gravitate, it would cause detectable violations in the conservation of stress-energy-momentum according to GR; and this would violate the fundamental principles at the core of GR -- most notably, the equivalence principle and the principle of general relativity.
However, the strong and weak forces have the "disadvantage" of being short-ranged enough that it is usually understood that quantum effects are extremely important when dealing with these forces; and they are short-ranged enough that it is usually understood that gravitational effects are negligible. Regardless of whether or not these assumptions are correct, they have the effect of causing most physicists to avoid studying the nuclear forces in depth from the perspective of GR. This doesn't mean that physicists don't do it -- for example, a former colleague of mine did just that in his doctoral thesis, studying the effects of neutrino confinement in the life cycle of supernovae -- it just means that it is not too common.
* GR is still the best of them all because it is the simplest -- it has one "free" parameter, which is fixed by the requirements of compatibility with Newtonian gravitation in its domain of validity, and it is so successful that all other theories are ranked according to how well they match the predictions of GR.
To be quite frank, I think that this answer is terrible and should never be used. Ever.
Black holes, such as the Reissner-Nordström, are a feature of general relativity; virtual photons (and virtual particles in general) are a feature of quantum field theory. Trying to explain how general relativity black holes interact by using a different theory which is completely and thoroughly incompatible with general relativity at a fundamental level is not an explanation at all.
Why is Hawking radiation a well-accepted hypothesis even though it heavily mixes GR and QM?
Moreover, the very idea of the eletromagnetic field (and other fields) being "mediated by photons" is alien to general relativity -- this idea also has its origins in quantum field theory. While the idea might be useful when doing "semi-quantum" gravity analysis, there is no need to use this when talking about general relativity proper. And who knows, the very notion of particle-mediated fields may turn out be wrong when an actual theory of quantum gravity is found.
The actual answer for the question is conservation of stress-energy-momentum: given the expression for electromagnetic energy in terms of the potential fields, you can deduce Maxwell's equations from the contracted Bianchi identities (see this for some information on these identities) on all but a few hyper-surfaces in which the electric and magnetic fields are orthogonal; and if you have Maxwell's equations, the Lorentz force can be deduced from those very same contracted Bianchi identities, regardless of the geometry of the situation.
This happens because electromagnetic fields warp space-time in very specific ways in general relativity, and the gravitational field itself is responsible for coupling the charges to the electromagnetic fields; this is easier to see in action in the Hilbert-Palatini variational principle formulation of general relativity.
I have to confess that all this goes well over my head.
Why is Hawking radiation a well-accepted hypothesis even though it heavily mixes GR and QM?
There. :-p
More seriously, it is a hypothesis which is accepted pending confirmation -- it makes sense given what we understand of QM, and is a way of solving the information paradox of black holes (which is one of the many ways in which QM and GR are incompatible). But without evidence, it will never amount for more than a hypothesis.
Warp wrote:
I have to confess that all this goes well over my head.
I will try to make it simpler: two of the bedrock principles behind general relativity are the equivalence principle and the principle of general relativity. There are others, but these are by far the most important because they are (a) testable, (b) tested and (c) expected to be present in all theories of gravity to come, even in theories of quantum gravity.
The principle of general relativity is the ultimate form of the principle of relativity: it says that the laws of Physics are the same for all observers. Contrast earlier versions which stated that only for inertial observers. This principle basically states that the laws of Physics must be written in tensorial form, as tensor equations are valid for any coordinate system you pick (this latter form was explicitly stated by Einstein as the "principle of general covariance", but most authors nowadays consider it redundant).
The principle of equivalence states that gravity and acceleration are equivalent -- more specifically, that any gravitational field is locally equivalent to acceleration of the observer in the absence of gravity; it is often stated as the fact that active and passive gravitational masses are equivalent to inertial mass (see this). It also has the distinction of being one of the most well tested principles in Physics.
The principle of equivalence couples everything to the gravitational field: for example, a beam of light in a gravitational field moves in the same way in relation to a freely-falling observer as it would in the absence of gravity from the perspective of an accelerating observer -- hence, it must bend in a gravitational field. In the same way, that beam of light must lose energy as it "climbs" a gravitational field (away from the source) and gain energy as it falls down that gravitational field (towards the source) -- i.e., gravitational redshift.
The laws of conservation of energy and conservation of momentum are replaced in relativity (special or general) by the law of conservation of the stress-energy-momentum tensor. As I said, it is an automatic algebraic feature of the theory. This, combined with the principles of equivalence and general relativity, is enough to make everything warp space-time -- for example, if a beam of light bends in a gravitational field (as it must, because of the equivalence principle), it must cause its own gravitational field or conservation of stress-energy-momentum will fail, which is algebraically impossible.
I hope I managed to clear it up a bit, instead of further muddying the issue...
The principle of general relativity is the ultimate form of the principle of relativity: it says that the laws of Physics are the same for all observers. Contrast earlier versions which stated that only for inertial observers. This principle basically states that the laws of Physics must be written in tensorial form, as tensor equations are valid for any coordinate system you pick (this latter form was explicitly stated by Einstein as the "principle of general covariance", but most authors nowadays consider it redundant).
I once read a wonderful introduction to special relativity (IIRC from a book) which was surprisingly easy to understand. It started with the simple assumption that the speed of light in vacuum is the same for all (intertial) observers (which I think is a fair assumption to make because it's a measurement result rather than a mere hypothesis), and from that single assumption it deduced the Lorentz transformations in a logical and easy-to-follow way. It was rather illuminating. (Of course this was many, many years ago, and damned if I remember any of it now.)
I'm assuming from your explanation that the general relativity equations can likewise be deduced by making the further assumption that the speed of light in vacuum is the same for all observers regardless of their state (ie. inertial or accelerating) and that gravitational mass and inertial mass are the same thing. I'm assuming this naturally leads to the result of curved spacetime. Is that about correct?
I hope I managed to clear it up a bit, instead of further muddying the issue...
Yes, it was a bit clearer, but it didn't really answer the question of how a black hole can have an electric charge (which can be measured from the outside).
Why is Hawking radiation a well-accepted hypothesis even though it heavily mixes GR and QM?
Who knows, but I have a better question... why is gravity said to be a curvature of spacetime, when it contradicts the theory of gravitons and a superforce? Einstein wanted to unify gravity and electromagnetism, so why did he create a theory that says that gravity behaves in a completely different way than other forces?
Joined: 11/22/2004
Posts: 1468
Location: Rotterdam, The Netherlands
Warp wrote:
I once read a wonderful introduction to special relativity (IIRC from a book) which was surprisingly easy to understand. It started with the simple assumption that the speed of light in vacuum is the same for all (intertial) observers (which I think is a fair assumption to make because it's a measurement result rather than a mere hypothesis), and from that single assumption it deduced the Lorentz transformations in a logical and easy-to-follow way. It was rather illuminating. (Of course this was many, many years ago, and damned if I remember any of it now.)
If you ever happen to remember what book that was, I'd be interested in knowing.
Joined: 11/23/2010
Posts: 14
Location: Peotone, IL, USA
Dada wrote:
Warp wrote:
I once read a wonderful introduction to special relativity (IIRC from a book) which was surprisingly easy to understand. It started with the simple assumption that the speed of light in vacuum is the same for all (intertial) observers (which I think is a fair assumption to make because it's a measurement result rather than a mere hypothesis), and from that single assumption it deduced the Lorentz transformations in a logical and easy-to-follow way. It was rather illuminating. (Of course this was many, many years ago, and damned if I remember any of it now.)
If you ever happen to remember what book that was, I'd be interested in knowing.
Ditto.
www.NintendoLegend.com -- One gamer's quest to play and review every American-released NES game!
I once read a wonderful introduction to special relativity (IIRC from a book) which was surprisingly easy to understand. It started with the simple assumption that the speed of light in vacuum is the same for all (intertial) observers (which I think is a fair assumption to make because it's a measurement result rather than a mere hypothesis), and from that single assumption it deduced the Lorentz transformations in a logical and easy-to-follow way. It was rather illuminating. (Of course this was many, many years ago, and damned if I remember any of it now.)
Strictly speaking, you also need the principle of (special) relativity (i.e., that the laws of Physics are the same for all inertial observers), plus the assumptions of spatial homogeneity and isotropy and memorylessness (for example, the proper time cannot elapse differently depending on the past history of an observer, but only in its current state of motion). This way of deducing relativity comes all the way back to Einstein, although he left the latter 3 assumptions unstated.
Warp wrote:
I'm assuming from your explanation that the general relativity equations can likewise be deduced by making the further assumption that the speed of light in vacuum is the same for all observers regardless of their state (ie. inertial or accelerating) and that gravitational mass and inertial mass are the same thing. I'm assuming this naturally leads to the result of curved spacetime. Is that about correct?
Regarding the idea, yes; but it rather more involved than that of special relativity. The principles of general relativity which Esintein originally used are:
- equivalence principle;
- principle of general relativity/principle of general covariance;
- Mach's principle;
- correspondence principle: general relativity must agree with Newtonian universal gravity for weak gravitational fields and low velocities, and with special relativity in the absence of gravity;
- principle of minimal gravitational coupling: no unnecessary terms should be added when making the transition from special to general relativity. This principle is rather vague, and was used implicitly by Einstein.
Note that the constancy of the speed of light is neither a principle nor a consequence of general relativity; in fact, it changes along a gravitational field. The important property of light -- that it travels in space as fast as in time, and is forever being reach of massive objects -- is preserved because the main feature of space-time is kept -- simply put, any sufficiently small region of space-time in general relativity "looks like" a piece of space-time in special relativity.
Modern treatments usually dispense with the deduction from these principles, except for historical purposes, and use a different and much more efficient approach.
Warp wrote:
Yes, it was a bit clearer, but it didn't really answer the question of how a black hole can have an electric charge (which can be measured from the outside).
In the same way as you can have gravity: the field is in place before the formation of the black hole, and the presence of an event horizon does not make the charge (or mass, for gravity) cease to exist. Changes in the electromagnetic field from within the event horizon, if any, cannot propagate beyond the event horizon, but the field does not cease to exist -- that would violate conservation of charge, energy and momentum.
nfq wrote:
Who knows, but I have a better question... why is gravity said to be a curvature of spacetime, when it contradicts the theory of gravitons and a superforce? Einstein wanted to unify gravity and electromagnetism, so why did he create a theory that says that gravity behaves in a completely different way than other forces?
This answer has several answers, and several levels of answers. Lets see:
1) theory of gravitons: there is no such thing, really. Gravitons are theoretical constructs which are supposed to mediate gravity in a quantum field formulation of gravity, but gravitons have never been observed and there is no quantum field theory of gravity yet. This means that, for now, your question would still make as much sense as it does now if you substitute "invisible pink unicorns" for "gravitons" :-p.
2) Einstein developed general relativity before quantum mechanics was finalized, and long before quantum field theory. The weak and strong nuclear forces weren't even known yet, and their unification wasn't even dreamt of yet. Einstein started trying to unify gravity and electromagnetism decades after general relativity, and by making electromagnetism into something analogous to what gravity had become -- i.e., by "geometrizing" the electromagnetic field. So your question is also wrong from a historical point of view, as well as the methodology by which Eisntein (and others) were attempting the unification of the forces.
3) Relativity (special and general) ends up dealing with the structure of space-time. It was quantum mechanics which had to be adapted to be compatible with special relativity, not the other way around. By analogy, it is expected that quantum field theories will have to be adapted into the curved space-time of general relativity, even if the field equations of general relativity have to be changed.
4) Special relativity is incompatible with gravity. There have been many, many attempts to dispense with general relativity by making a classical force-field gravitational field within the flat space-time of special relativity. All such attempts were either logically inconsistent (i.e., the theory predicted gravitational attraction would exist and conservation of energy would always be present, but also predicted that conservation of energy would only happen if there was no gravitational attraction), physically unsound (i.e., predicting gravitational waves that had negative energy), experimentally incorrect or identical to general relativity but with unobservable extra features (such as an extra unobservable flat background space-time). Combine with (3), above, at your leisure.
5)At the end of the day, general relativity is still the best theory we have for gravity. Since it predicts gravity to be the curvature of space-time, than that is what gravity is -- until a better theory arrives.
5)At the end of the day, general relativity is still the best theory we have for gravity. Since it predicts gravity to be the curvature of space-time, than that is what gravity is -- until a better theory arrives.
Also note that there exists numerous experimental evidence for spacetime curvature which corroborate the predictions of GR. Einstein himself made several predictions based on GR which were later corroborated by measurements. General relativity is not purely theoretical, as it has concrete practical applications (the most famous one of them being probably GPS, which would show systematic errors if they were calibrated according to newtonian mechanics or even special relativity, but which work very precisely when calibrated according to GR equations).
There is, in fact, so much overwhelming evidence of the accuracy of GR that whenever something seems to contradict it, it's usually assumed that there's a secondary factor being at play which is not being accounted for. The famous Pioneer anomaly and flyby anomaly are examples. (Also the dark matter hypothesis is an example of this.)
but gravitons have never been observed and there is no quantum field theory of gravity yet. This means that, for now, your question would still make as much sense as it does now if you substitute "invisible pink unicorns" for "gravitons" :-p.
But spacetime curvature hasn't been observed either, so couldn't that be called "invisible pink unicorn curvature"? We have observed effects of gravity, like gravitational lensing, but not the curvature of spacetime. Mathematically it's a good theory though, and it makes good predictions. Btw, shouldn't the orbits of planets be circular, and not elliptical, according to the spacetime curvature theory (because of the uniform curvature of spacetime around celestial bodies)?
I understand that General Relativy allows the distance between two points in space (and consequently the distance between two particles) to grow faster than c
Can someone explain how this works, in very simple language?
Sage advice from a friend of Jim: So put your tinfoil hat back in the closet, open your eyes to the truth, and realize that the government is in fact causing austismal cancer with it's 9/11 fluoride vaccinations of your water supply.
but gravitons have never been observed and there is no quantum field theory of gravity yet. This means that, for now, your question would still make as much sense as it does now if you substitute "invisible pink unicorns" for "gravitons" :-p.
But spacetime curvature hasn't been observed either, so couldn't that be called "invisible pink unicorn curvature"? We have observed effects of gravity, like gravitational lensing, but not the curvature of spacetime.
There is no practical meaningful distinction here between "observing X" and "observing the effects of X". We haven't observed electrons, only the effects of electrons in bubble chambers and other detectors. We haven't observed Newtonian gravity, only its effect on sticking my bum to the seat.
The difference with gravitons is that we haven't observed any phenomena which are better predicted by a graviton theory of gravitation than by the alternatives. The evidence we have gives no reason to favour gravitons over other explanations of gravity. We have observed phenomena which are best explained by curved spacetime.
Btw, shouldn't the orbits of planets be circular, and not elliptical, according to the spacetime curvature theory (because of the uniform curvature of spacetime around celestial bodies)?
I don't think that spacetime is uniformly curved around celestial bodies. It is more strongly curved the closer you get to the body.
But spacetime curvature hasn't been observed either, so couldn't that be called "invisible pink unicorn curvature"? We have observed effects of gravity, like gravitational lensing, but not the curvature of spacetime.
It depends on your definition of "observed"; for all but the most pedantic definitions, space-time curvature has been observed, while gravitons haven't. This is because only curved space-time theories of gravity can account for all observed phenomena in the observed magnitude, whereas flat space-time "theories" of gravity can't and graviton "theories" have had no predictions observed that are unique to them.
nfq wrote:
Btw, shouldn't the orbits of planets be circular, and not elliptical, according to the spacetime curvature theory (because of the uniform curvature of spacetime around celestial bodies)?
When it is all accounted for, general relativity actually predicts that orbits aren't even elliptical, but are ellipses that precess around one of the foci. And this is nicely confirmed by experiment. This all happens because curvature isn't uniform, as rhebus said.
This all happens because curvature isn't uniform, as rhebus said.
I think that "curvature isn't uniform" is a confusing statement when nobody has defined what "uniform curvature" means.
In classical physics you can think of a gravity well as if it was a funnel whose "slope" depends on the distance squared from the celestial body (iow. the farther you get away, the more "horizontal" the surface of this funnel gets, and the exact slope of this surface is the distance squared). In a way, if the "slope" of the gravity well is strictly defined by the distance squared, one could define that as "uniform curvature" (similarly as one could argue that the surface of a parabolic antenna is "uniformly parabolic").
If you think you had a physical funnel shaped like that and you put a small ball on it and give it an initial velocity, unless this velocity is just perfectly right and its direction perfectly perpendicular to the central depression, it will make an elliptical path on the surface of the funnel (assuming no friction, as is the case in empty space). Thus it's not all that strange that planets have elliptical orbits.
If you think you had a physical funnel shaped like that and you put a small ball on it and give it an initial velocity, unless this velocity is just perfectly right and its direction perfectly perpendicular to the central depression, it will make an elliptical path
Good point, but if you can't accept such perfection, how come planets are a perfect distance away from the sun in this gravity based solar system model? If the speed was slightly more, the planets would be thrown out from the solar system and if they were slightly closer they would spiral/fall into the sun (like in your example about the ball). That's why I think there's other factors/forces except gravity and speed that make planets stay in their path. Another problem with gravity is that you need an intial cause/bang that causes everything to move.
Good point, but if you can't accept such perfection, how come planets are a perfect distance away from the sun in this gravity based solar system model? If the speed was slightly more, the planets would be thrown out from the solar system and if they were slightly closer they would spiral/fall into the sun (like in your example about the ball).
This actually isn't true. If you take an object in an orbit with no friction and activate its thrusters momentarily it will enter the orbit that passes through the point it thrusted at and is slightly wider/narrower. However, if the thrusting is TOO strong in the outward direction it will become a parabolic or hyperbolic orbit, as it is moving away faster than the thusly weakening gravity will ever be able to grab hold of it. However, before that point, there are many many kinds of elliptical paths an orbiting object can and will orbit.
The only reason why an object that gets too close to a planet crashes is because friction in the atmosphere makes it lose speed, fall more and more vertically and then it hits the planet. If the planet had no atmosphere and no radius, then tightening its orbit would just make it a tighter ellipse - gravity + no acceleration + no friction = a path that follows a conic, which is one of: circle, ellipse, parabola, hyperbola.
Good point, but if you can't accept such perfection, how come planets are a perfect distance away from the sun in this gravity based solar system model? If the speed was slightly more, the planets would be thrown out from the solar system and if they were slightly closer they would spiral/fall into the sun (like in your example about the ball).
No. Warp had it right, and you seemed to agree with him. Then you contradict him by saying something completely different.
As Warp said, if a planet in a circular orbit moves slightly faster, it will have a slightly larger and more elliptical orbit. If it's slower, it will have a slightly smaller and more elliptical orbit. Neither of these situations is catastrophic.
To leave the solar system, a planet (say, Earth) needs to reach escape velocity, which is far greater that its current orbital velocity. A slight increase would not be nearly enough to send any of the 8 planets out of the solar system. Similarly, a slight decrease in velocity will not cause the Earth, or any other planet, to spiral into the sun; you'd need to kill almost all of its momentum to get that to happen. A slight perturbation ain't gonna do it.
IOW, the planet's orbits are not so delicate as you seem to think. Look at the orbits of comets: they are highly elliptical, but they are in no danger of either leaving the solar system, or of hitting the sun. If earth's speed slowed down by half - not just a slight perturbation, but losing fully half of its speed - its orbit would look more like one of these comet orbits. It wouldn't be in any danger at all of hitting the sun.
Finally, all of the planets have elliptical orbits. None of the orbits are perfect circles. So, based on your argument, should all of the planets have already hit the sun or left the solar system?
Another problem with gravity is that you need an intial cause/bang that causes everything to move.
Gravity, on its own, doesn't need any such thing. Two bodies at rest will start to move due to gravity. They are each other's first movers. This is true in GR and in Newtonian gravity.
The "first mover" argument is often used by intelligent designists to try to somehow "disprove" physics. However, it is wrong for many reasons. For one, it is now known that it is quite possible for there to be an unmoved mover as explained above.
(I hope that, whether or not you believe in ID, you are posting in a thread called "physics questions" in order to learn something about physics, and not just to try to prove physics wrong. I have no interest in showing you why the ID arguments are false unless you have an interest in learning something about physics.)
IOW, the planet's orbits are not so delicate as you seem to think.
The fragility of planetary orbits is not caused by a planet requiring a precise orbital speed to maintain orbit (because as noted, a change in speed would simply change the shape of the orbit and seldom a collision or flinging the planet out of the system).
The fragility of planetary orbits comes from the fact that the solar system is an n-body system, which is quite unpredictable and easily unstable. A 2-body system is quite stable, but an n-body system isn't quite so. The reason why we only have 8 planets and a bunch of smaller rocks, and the solar system being relatively "empty" (rather than being littered with small rocks all over) is because only the objects which happened to have stable orbits in this n-body system remained, the rest collided with them or were flung out of the system.
The fragility of planetary orbits comes from the fact that the solar system is an n-body system, which is quite unpredictable and easily unstable.
A general n-body system is unstable. The solar system is not, because the attractive forces between the planets is negligible compared to the attractive force between the sun and the planets. The planetary orbits are not fragile.
A general n-body system is unstable. The solar system is not, because the attractive forces between the planets is negligible compared to the attractive force between the sun and the planets. The planetary orbits are not fragile.
They may be negligible in the short term. However, they are not negligible in the long run, during the billions of years that the solar system has existed. Any "tug" a planet experiences, no matter how small, will start accumulating when it happens enough times.
Isaac Newton solved the 2-body problem, and it was completely clear to him why it's a stable system. However, when he tried to solve a 3-body problem (eg. the Sun-Earth-Moon system) he was unable to find a stable solution, and could not understand how the solar system can maintain stability. (He attributed it to supernatural forces.) Later work in astrophysics solved the problem and it's now clearer how an n-body system can be stable.
The only reason why an object that gets too close to a planet crashes is because friction in the atmosphere makes it lose speed,
shouldn't gravity cause it to lose speed too, and make it crash? that's what gravity does, right... it attracts things towards itself, and when both are close enough, the motion stops.
rhebus wrote:
Gravity, on its own, doesn't need any such thing. Two bodies at rest will start to move due to gravity. They are each other's first movers.
but they will just move towards each other and then the motion stops. and something had to move them apart from each other in the first place, for them to be able to move towards each other.
Look at the orbits of comets: they are highly elliptical, but they are in no danger of either leaving the solar system, or of hitting the sun.
it's a little strange that such a weak force like gravity can hold them in their orbits. but some comets will leave the solar system. it will take a long time though.
Finally, all of the planets have elliptical orbits. None of the orbits are perfect circles. So, based on your argument, should all of the planets have already hit the sun or left the solar system?
i think if only gravity and speed is holding them in their orbits, they should have all crashed or left the solar system (lol), because it would be too big of a coincidence for the speed and distance to be just right for them to stay in their orbits for billions of years. everything in the universe should be in one giant ball of matter. but i guess that's kinda what the big bang theory says was in the beginning.
the orbits of planets are slightly elliptical, but i would call them circles because they're almost perfect circles. i say the earth is round too, even though it's not perfectly round (nothing in nature is). btw, i don't think the orbits have anything to do with ID.
For one, it is now known that it is quite possible for there to be an unmoved mover as explained above.
not really, because like i said earlier there had to be something that moved them apart in the first place, right? so how could they be unmoved movers?
(I hope that, whether or not you believe in ID, you are posting in a thread called "physics questions" in order to learn something about physics, and not just to try to prove physics wrong.
yeah, i'm just posting my thoughts. i don't claim them to be the truth, haha.
Warp wrote:
The reason why we only have 8 planets and a bunch of smaller rocks, and the solar system being relatively "empty" (rather than being littered with small rocks all over) is because only the objects which happened to have stable orbits in this n-body system remained, the rest collided with them or were flung out of the system.
could be, but there's no evidence of that because if it happened that way, then the evidence crashed into the sun.
i think the theory of gravity becomes even more problematic on galactic level, but i'm not sure i'm gonna get into that now.
(He attributed it to supernatural forces.) Later work in astrophysics solved the problem
shouldn't gravity cause it to lose speed too, and make it crash? that's what gravity does, right... it attracts things towards itself, and when both are close enough, the motion stops.
Gravity also does not affect speed in the transverse direction. At any point in the trajectory, gravity will point from one body to the other, and unless their relative velocity is entirely in this direction, they will move without crashing (as long as they are sufficiently far away).
nfq wrote:
but they will just move towards each other and then the motion stops.
Whoever told you that did you a disservice... if it was a school, go get your money back.
nfq wrote:
it's a little strange that such a weak force like gravity can hold them in their orbits. but some comets will leave the solar system. it will take a long time though.
Jump off of a 10-story building to see how "weak" it is. Gravity may be weak compared to the other fundamental forces, but it is always attractive; the other forces have charges that cancel out on macroscopic scales (or even intra-atomic scales, for strong and weak nuclear forces) and end up being almost throughly negligible on the inter-planetary scale.
nfq wrote:
i think if only gravity and speed is holding them in their orbits, they should have all crashed or left the solar system (lol), because it would be too big of a coincidence for the speed and distance to be just right for them to stay in their orbits for billions of years. everything in the universe should be in one giant ball of matter. but i guess that's kinda what the big bang theory says was in the beginning.
Ah, guesswork. Nothing is more out-of-place in science than pure wild-***** guesses.
Let me ask you a question: do you know the history of how Neptune (and later Pluto) was discovered? By your comments, I would bet large sums of money that the answer is "no". So here it goes:
Both Neptune and Pluto were discovered through theory before they were observed.
Yeah, you read that right. Physicists since Newton have been calculating the orbits of planets using Newton's equations and comparing them to astronomical observation. In the early 19th century, as accuracy of astronomical observations increased, they started to notice discrepancies between the calculated and observed positions of Uranus for which they had no explanation. After some proposed that an as yet undiscovered planet could be the cause, they calculated, using the theory, where this planet would have to be, its mass and speed in order to account for the observations. Then, looking at the calculated position, they found Neptune. There was an element of luck, because the orbit of Neptune was similarly perturbed by Pluto, which was eventually found in the same way.
So, to reiterate: gravity, speed and distance are enough to keep the solar system stable for billions of years? Yes; we know this by direct computation and observation, not by guessing.
Is it a "coincidence" that they are "just right"? No, and no: there is considerable leeway in the orbits that still keep the solar system functional. Moreover, you have it backwards: the solar system isn't stable because the positions and speeds of the planets are "just right", but they are "just right" because the solar system would have disintegrated long ago if they were not.
Not that "stable" means "pretty" or "ordered": there is evidence of several powerful collisions at the beginning of the solar system, including one strong enough (with a Mars-sized object) to blast enough material from the Earth to form the Moon while the Earth itself was being formed.
nfq wrote:
the orbits of planets are slightly elliptical, but i would call them circles because they're almost perfect circles.
Tell that to Pluto. But no, they are not circles and they are not elliptical: the orbits are messy, having oscillations around the "elliptical" orbit that is due to the gravitational interaction with the other planets and moons. And even the elliptical orbit precesses around the Sun due to the interactions with other planets and due to general relativistic effects. All these effects are observable, have been observed and are accounted by theory, by the way -- some being predicted by theory before being observed.
Almost perfect circles? Bah.
nfq wrote:
i say the earth is round too, even though it's not perfectly round (nothing in nature is).
Round != spherical. The Earth is round, but it is not a sphere.
nfq wrote:
btw, i don't think the orbits have anything to do with ID.
Yeah, right. I know that this cannot be really true because of this:
nfq wrote:
not really, because like i said earlier there had to be something that moved them apart in the first place, right? so how could they be unmoved movers?
Busted. I was going to reply to the rest of your post, until I reached this. This alone shows that you are not really sincere about wanting to learn anything, and should be regarded in this thread as just a troll.
Either that or you are pulling a Poe. Either way, further replying to you is a waste of time.
Edit: Forgot this:
DarkKobold wrote:
Warp wrote:
I understand that General Relativy allows the distance between two points in space (and consequently the distance between two particles) to grow faster than c
Can someone explain how this works, in very simple language?
In simple language? Let me try. Space-time in general relativity is an integral participant in the dynamics of a system. It is warped by matter, and in turn, tells matter how to move, which warps it depending on how it moves and so on.
In particular, global solutions of the equations of general relativity show that space-time, in its entirety, is not static; it may expand and contract (globally). This will affect the distances between objects in it; and since space-time is not a material object, it is not limited by the speed of light for the rate of expansion.
One common analogy is a balloon: here, the rubber represents space-time. Place dots on the surface of this balloon to represent stars. When you fill the balloon (representing the expansion of the Universe), the distance between the dots will increase, even though the dots themselves haven't moved in the surface of the balloon.
The stars (dots, in the analogy) cannot move faster than (or even at) the speed of light because they are massive objects; but space-time itself has no such limitation.
Gravity, on its own, doesn't need any such thing. Two bodies at rest will start to move due to gravity. They are each other's first movers.
but they will just move towards each other and then the motion stops. and something had to move them apart from each other in the first place, for them to be able to move towards each other.
No, something did not have to move them apart. They could have started like that. The first mover argument is based on a false premise - that motion cannot come from non-motion - and the thought experiment demonstrates this falsehood.
Finally, all of the planets have elliptical orbits. None of the orbits are perfect circles. So, based on your argument, should all of the planets have already hit the sun or left the solar system?
i think if only gravity and speed is holding them in their orbits, they should have all crashed or left the solar system (lol), because it would be too big of a coincidence for the speed and distance to be just right for them to stay in their orbits for billions of years.
You're not listening to our arguments -- that the solar system is a stable system. You haven't attempted to address them, yet you still claim the solar system is held together by "coincidence" and the speeds have to be "just right". Wrong and wrong. This is what I meant by saying I suspect you may not wish to learn about physics, but rather complain about your perceived problems with it.
btw, i don't think the orbits have anything to do with ID.
Yeah, right. I know that this cannot be really true because of this:
nfq wrote:
not really, because like i said earlier there had to be something that moved them apart in the first place, right? so how could they be unmoved movers?
Busted. I was going to reply to the rest of your post, until I reached this. This alone shows that you are not really sincere about wanting to learn anything, and should be regarded in this thread as just a troll.
Either that or you are pulling a Poe. Either way, further replying to you is a waste of time.
I don't know how much you have read nfq's past posts, but at least previously he has clearly expressed his "open-minded" philosophy, meaning that he has a strong belief in many of the purported extraterrestrial and supernatural phenomena that are so popular among pseudoscientists, ufologists, paranormalists and many other "new age" movement representatives. Knowing this, it's not surprising for him to express doubt on established science, because that's one of the key tenets of that kind of people.
Anyways, this argument about the solar system (and galaxies) being somehow paranormal (in the sense that they "couldn't" remain in orbit by natural means) is IMO unusually dense. There's nothing unclear about orbital trajectories and how they work. The math may be slightly complex, but in principle anybody should be able to corroborate it.
As for how these eight planets and the big bunch of smaller rocks have got the "precise fine-tuned orbits" needed to remain stable, the answer is pretty simple: In the beginning there were millions and even billions of small rocks, with more or less randomized orbits. From these billions of rocks the majority had unstable orbits and ended up colliding with each other (forming planets) or the Sun, or were flung out of the system. Only a few of them happened to have stable orbits, and they remained. You could say it's natural selection: From the billions of objects the ones which by chance had stable orbits were naturally selected to remain, while all the others went away (mostly by collisions). It's like you put a big bunch of rocks of different sizes in a bucket full of holes and started shaking it: Only the rocks which are larger than the holes will "get selected" to remain, while the smaller ones will drop out. The exact same principle of why antibiotic-resistant bacteria are a really big problem nowadays. There's nothing strange about this.
