Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: McKay on 18/12/2014 00:26:50
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I think I have discussed this somewhere on forum. This or another, but cant find the thread anymore and I want to learn more about this.
If gravity is the curvature of space and objects "fall" in to the gravity well because they are following a curved path, then, well, that can only happen if the object is moving, isn't it so? I understand there is still molecular and sub-atomic motion in matter and this would be the major contributing factor if this is true.
But then escape velocities exist and I get really confused.
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What's the problem? There is still molecular and sub-atomic motion in matter that is shot straight up.
Except if we give the matter a huge amount of upwards speed. Then the internal motion almost freezes, so the the matter should become almost weightless.
Let's say we shoot a photon straight up from the event horizon of a black hole, the photon stays in one place, does not lose energy or momentum ... yes it seems to be true that things going upwards at the speed of light are weightless.
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If gravity is the curvature of space and objects "fall" in to the gravity well because they are following a curved path, then, well, that can only happen if the object is moving, isn't it so?
First off you're thinking of spacetime curvature, not space curvature. And spacetime is curved only when tidal forces are present. If the field is uniform then the spacetime is flat. However even in that situation objects which are not supported will fall in the field. If the particle is supported then it will still have weight which means that gravity is still acting on it just as gravity is acting on you as you sit on your chair.
I understand there is still molecular and sub-atomic motion in matter and this would be the major contributing factor if this is true.
You've been talking about general relativity which is a classical theory and as such it doesn't take into account the atomic structure of matter. Whether there is subatomic motion is irrelevant to the motion of the body as a whole.
So yes, gravity works on objects which are at rest.
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If gravity is the curvature of space and objects "fall" in to the gravity well because they are following a curved path, then, well, that can only happen if the object is moving, isn't it so? I understand there is still molecular and sub-atomic motion in matter and this would be the major contributing factor if this is true. But then escape velocities exist and I get really confused.
It's really simple provided you've read the original material by Einstein. A concentration of energy, usually in the guise of matter in the guise of a star, "conditions" the surrounding space, the effect of this diminishing with distance. See Einstein's Leyden Address (http://www-history.mcs.st-and.ac.uk/Extras/Einstein_ether.html) for that. Then imagine you could place optical clocks at various locations throughout an equatorial slice through the Earth and surrounding space. Clocks go slower when they're lower, so when you plot all your clock rates, what you get is a plot like this:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F2%2F22%2FSpacetime_curvature.png%2F250px-Spacetime_curvature.png&hash=a568150c038971e59eb7c8d6e572dbec)
GNUFDL image by Johnstone, see Wikipedia (http://en.wikipedia.org/wiki/Riemann_curvature_tensor)
That's a depiction of Riemann curvature. It's basically a picture of curved spacetime. Like Pmb said, space isn't curved. See the Baez (http://math.ucr.edu/home/baez/einstein/node2.html) website and note this: "not the curvature of space, but of spacetime". Curved spacetime isn't curvature of space and curvature of time. It's a curvature in your plot of measurements of motion through space over time. It's a curvature of "the metric", metric being to do with measurement. And note that the force of gravity depends on the slope of the plot at some location, not on the curvature. Like Pmb said, that's to do with the tidal force. Also note this (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html) on the Baez website:
"Einstein talked about the speed of light changing in his new theory. In his 1920 book "Relativity: the special and general theory" he wrote: "... according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers."
Those clocks I referred to are optical clocks. And they go slower when they're lower because light goes slower when it's lower. See this Shapiro quote (http://en.wikipedia.org/wiki/Shapiro_delay):
"The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of decreasing gravitational potential."
People refer to this speed of light as the "coordinate" speed of light. The locally-measured speed of light is the speed that's constant, because of a tautology (http://arxiv.org/abs/0705.4507) wherein we define the second and the metre using the motion of light. Anyway, like Einstein said (http://einsteinpapers.press.princeton.edu/vol7-trans/156?highlightText=%22speed%20of%20light%22), light curves because the speed of light varies. There's a nice gif showing this on Ned Wright's deflection and delay (http://www.astro.ucla.edu/~wright/deflection-delay.html) article where you can read this: "In a very real sense, the delay experienced by light passing a massive object is responsible for the deflection of the light."
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.astro.ucla.edu%2F%7Ewright%2FEinstein-wavelets-75.gif&hash=90c19f44af64e060d75969fcfc93939f)
Light doesn't curve because spacetime is curved. It curves because the speed of light is lower near the floor. It's a bit like the way a car veers when it encounters mud at the side of the road. Or like the way sonar waves curve (http://fas.org/man/dod-101/navy/docs/es310/SNR_PROP/snr_prop.htm). Once you know that and you know about the wave nature of matter, and pair production and electron diffraction and magnetic moment and spinors, it's quite easy to work out why matter falls down. And it is because of that sub-atomic motion. Think of an electron as a wave going round and round, then simplify it to a wave going round a square path. Then imagine the horizontal sections curve down a little, like this:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.thenakedscientists.com%2Fforum%2Findex.php%3Faction%3Ddlattach%3Btopic%3D52410.0%3Battach%3D19140%3Bimage&hash=9526106ba51d3349f1db50d3ccd39dc1)
The electron falls down. And just as general relativity predicts, light is deflected twice as much as matter because only the horizontal component of the matter wave curves downward. See Albrecht Giese's description (http://ag-physics.org/gravity/) which is similar. There's things he says that I don't like, but I think the gist of his explanation is correct.
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Light doesn't curve because spacetime is curved. It curves because the speed of light is lower near the floor.
Caution: There are different uses of the term curve in general relativity. It this instance John is not using it to refer to curved spacetime. He's using it to refer to the fact that in the non-inertial frame that the observer is at rest in, e.g. a uniform gravitational field or a uniformly accelerating frame of reference, the worldline of a photon is not straight, but curved. As Feynman said, since light has energy and anything that has energy has mass then light has mass, it follows that there is a gravitational force acting on the photon and that's accelerating it. Just because the speed of light changes with potential that doesn't explain why the light moves from places having different potentials.
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Caution: There are different uses of the term curve in general relativity. It this instance John is not using it to refer to curved spacetime. He's using it to refer to the fact that in the non-inertial frame that the observer is at rest in, e.g. a uniform gravitational field or a uniformly accelerating frame of reference, the worldline of a photon is not straight, but curved.
Correct. If you flick a marble across a tilted board, the path of the marble is curved, but the board isn't.
As Feynman said, since light has energy and anything that has energy has mass then light has mass, it follows that there is a gravitational force acting on the photon and that's accelerating it.
I'm a Feynman fan, but I have to say he didn't understand gravity. See for example chapter 42 of the Feynman Lectures (http://www.feynmanlectures.caltech.edu/II_42.html). He thought curved spacetime incorporated curved space, and obviously never read Einstein referring to inhomogeneous space (http://einsteinpapers.press.princeton.edu/vol7-trans/192?highlightText=%22neither%20homogeneous%22).
Just because the speed of light changes with potential that doesn't explain why the light moves from places having different potentials.
It's what Einstein said repeatedly, and it's what others said, and it makes perfect sense. As you know light doesn't curve "because spacetime is curved", and the interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with.
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I'm a Feynman fan, but I have to say he didn't understand gravity
I've heard you say a lot of incorrect things and this one is near the top of the list.
See for example chapter 42 of the Feynman Lectures (http://www.feynmanlectures.caltech.edu/II_42.html).
What about it? What in that chapter do you claim is wrong?
He thought curved spacetime incorporated curved space,...
Please clarify. If space is curved then spacetime is curved. What's wrong with that?
and obviously never read Einstein referring to inhomogeneous space (http://einsteinpapers.press.princeton.edu/vol7-trans/192?highlightText=%22neither%20homogeneous%22).
So what? First of all that section is very difficult to read. It's expressed in a language that is now almost 100 years old and as such unclear. In any case there are very few physicists who've read all of Einstein's papers. Why should Einstein be any different?
It's what Einstein said repeatedly, and it's what others said,....
Yet you have no proof that I'm wrong, do you? All you know is that Einstein said something similar to this but not exactly what I was saying. He never demonstrated this for all possible gravitational fields. He only did it for a uniform gravitational field and the gravitational field of the sun. In those instances its true.
What is what Einstein said? I'm saying that the speed of light varying with position is insufficient to cause light to be deflected. And that is a fact. It's clearly another one of the many facts in physics that you're unaware of.
An example of this was published back almost 100 years ago in the following paper:
On The Gravitational Field Produced by Light, Tolman, Ehrenfest and Podolsky, Physical Review, Vol. (37), March 1, 1931, pg 602-615.
You can also find it in the following textbook on relativity and cosmology:
Relativity, Thermodynamics and Cosmology by Richard C. Tolman, Dover Pub.
I worked this out and uploaded it onto my website for just such an occasion. If you can follow the math then do so. See: http://home.comcast.net/~peter.m.brown/gr/grav_light.htm
If the light is moving parallel to the beam in one direction then its deflected. If its moving in the opposite of that direction than its not deflected but keeps moving in a straight line. Otherwise its deflected.
... and it makes perfect sense.
Sure it makes sense. But just because something makes sense it doesn't mean that there's more to it and the paper above is a perfect example.
As you know light doesn't curve "because spacetime is curved", and the interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with.
Of course I know. I wrote a paper on it 15 years ago. If I'm correct then that's how you learned of it, isn't it?
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I'm a Feynman fan, but I have to say he didn't understand gravity. See for example chapter 42 of the Feynman Lectures (http://www.feynmanlectures.caltech.edu/II_42.html).
Actually in that chapter he talks about the relativistic mass of the photon. :)
The same result can be obtained in still another way. A photon of frequency ω 0 has the energy E0 =ℏω0. Since the energy E0 has the relativistic mass E0 /c2 the photon has a mass (not rest mass) ℏω0 /c2, and is “attracted” by the earth.
This is another example of Feynman saying that light is attracted to the earth because it has mass. :)
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I've heard you say a lot of incorrect things and this one is near the top of the list.
No you haven't, and I'm not wrong, because I'm with Einstein.
What about it? What in that chapter do you claim is wrong?
Feynman thought space is curved when spacetime is curved. That's wrong. When spacetime is curved, space is inhomogeneous, such that when you plot the inhomogeneity using eg light clocks, there's a curve in your plot.
Please clarify. If space is curved then spacetime is curved. What's wrong with that?
See above. Read what Baez said, note the bit about "the distinction is crucial". Gravity is nothing to do with curved space. Your pencil falls down because the space in the room you're in is inhomogeneous. Not because space is curved. And not because spacetime is curved.
So what? First of all that section is very difficult to read. It's expressed in a language that is now almost 100 years old and as such unclear. In any case there are very few physicists who've read all of Einstein's papers. Why should Einstein be any different?
Because Einstein was the author of general relativity, and when you read what he said, you understand how gravity works. When you don't, you come up with all sorts of erudite tosh like light curves because spacetime is curved or matter tells space how to curve.
You have no proof that I'm wrong, do you?
No, I can't prove that your non-explanation is wrong.
All you know is that Einstein said something similar to this but not exactly what I was saying. He never demonstrated this for all possible gravitational fields. He only did it for a uniform gravitational field and the gravitational field of the sun. In those instances its true.
Einstein said what he said repeatedly: light curves because the speed of light varies. Shapiro said it, Ned Wright said it, Don Koks the Baez editor said it. Stop dismissing all that in favour of your own preconception.
What is what Einstein said?
That light curves because the speed of light varies with position. The "coordinate" speed of light doesn't vary because of gravity, gravity is there because the speed of light varies.
I'm saying that the speed of light varying with position is insufficient to cause light to be deflected. And that is a fact. It's clearly another one of the many facts in physics that you're unaware of.
It isn't a fact. You're wrong. Einstein was right.
An example of this was published back almost 100 years ago in the following paper: On The Gravitational Field Produced by Light, Tolman, Ehrenfest and Podolsky, Physical Review, Vol. (37), March 1, 1931, pg 602-615. You can also find it in the following textbook on relativity and cosmology: Relativity, Thermodynamics and Cosmology by Richard C. Tolman, Dover Pub.
Find what? What page? Is it online and freely available? When was it written? A vague reference to a textbook does not counter my link to that Einstein actually said.
I worked this out and uploaded it onto my website for just such an occasion. If you can follow the math then do so. See: http://home.comcast.net/~peter.m.brown/gr/grav_light.htm
This is no good. You say since a light rays move on null geodesics. That's a tautology.
Sure it makes sense. But just because something makes sense it doesn't mean that there's more to it and the paper above is a perfect example.
No it isn't a perfect example. A perfect example would address light moving past a star.
Of course I know. I wrote a paper on it 15 years ago. If I'm correct then that's how you learned of it, isn't it?
Of course I did. That's why I quoted your exact words. Now go and read what Einstein said, and this time pay attention. And try to point out where my explanation for gravity is incorrect or could be improved.
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Actually in that chapter he talks about the relativistic mass of the photon. :)
And you and I both know that that's a measure of energy, and that a concentration of energy causes gravity, and that "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".
The same result can be obtained in still another way. A photon of frequency ω 0 has the energy E0=ℏω0. Since the energy E0 has the relativistic mass E0 /c2 the photon has a mass (not rest mass) ℏω0 /c2, and is “attracted” by the earth.
This is another example of Feynman saying that light is attracted to the earth because it has mass. :)
Well it's wrong, because light is "attracted" twice as much as matter. Again see Ned Wright's deflection and delay (http://www.astro.ucla.edu/~wright/deflection-delay.html) article:
"Before Einstein developed the full theory of General Relativity he also predicted a deflection of 0.875 arcseconds in 1913, and asked astronomers to look for it. But World War I intervened, and during the war Einstein changed his prediction to 1.75 arcseconds, which is twice the Newtonian deflection."
Besides, saying light falls down because it has a mass of sorts gets things back to front. Matter falls down because of the wave nature of matter. We can make electrons out of light in pair production. And we can diffract 'em. And the electron has a magnetic moment (http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment#Magnetic_moment_of_an_electron). And the Einstein-de Haas effect (http://en.wikipedia.org/wiki/Einstein%E2%80%93de_Haas_effect) demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics. And when we annihilate the electron with a positron, what do we get? Light. Just draw a square of light, with the horizontals curved down a little, and you soon see how gravity converts internal kinetic energy aka potential energy into external kinetic energy.
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And you and I both know that that's a measure of energy, and that a concentration of energy causes gravity, and that "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".
You have it backwards. There is only one reason that energy is a source of gravity and that's because there is an equivalence between mass and energy. There is no other reason. This is exactly what Einstein and other gravitational physicists argue. E.g. Misner, Thorne and Wheeler state the same thing in their text Gravitation.
Well it's wrong, because light is "attracted" twice as much as matter.
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"Before Einstein developed the full theory of General Relativity he also predicted a deflection of 0.875 arcseconds in 1913, and asked astronomers to look for it. But World War I intervened, and during the war Einstein changed his prediction to 1.75 arcseconds, which is twice the Newtonian deflection."
Once again you're misinterpreting the facts. The reason that Einstein was off by a factor of two was that at the time of his calculation in 1911, i.e. the last one before he got GR right, was due to the fact that he didn't take into account the curvature of space. When he accounted for the curvature of space he got the right value. It turns out that the curvature of space accounts for an exact value of a factor of two in the amount of deflection.
Let's drop this nonsense. It has nothing to do with the topic of the thread.
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And you and I both know that that's a measure of energy, and that a concentration of energy causes gravity, and that "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".
You have it backwards. There is only one reason that energy is a source of gravity and that's because there is an equivalence between mass and energy. There is no other reason. This is exactly what Einstein and other gravitational physicists argue. E.g. Misner, Thorne and Wheeler state the same thing in their text Gravitation.
Well it's wrong, because light is "attracted" twice as much as matter.
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"Before Einstein developed the full theory of General Relativity he also predicted a deflection of 0.875 arcseconds in 1913, and asked astronomers to look for it. But World War I intervened, and during the war Einstein changed his prediction to 1.75 arcseconds, which is twice the Newtonian deflection."
Once again you're misinterpreting the facts. The reason that Einstein was off by a factor of two was that at the time of his calculation in 1911, i.e. the last one before he got GR right, was due to the fact that he didn't take into account the curvature of space. When he accounted for the curvature of space he got the right value. It turns out that the curvature of space accounts for an exact value of a factor of two in the amount of deflection.
Let's drop this nonsense. It has nothing to do with the topic of the thread.
Pete the factor of 2 pops up a lot in the equations to do with gravitation so I'm in your camp.
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Does gravity only work on moving objects?
The first good estimate of the Earth's mass was produced by the Cavendish experiment (http://en.wikipedia.org/wiki/Cavendish_experiment), which measured the attraction between heavy balls in a torsion balance. This attraction still exists when the balls are stationary, relative to each other.
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Jeffrey: Pete's explanation and his reference to Feynman and "photon mass" don't account for the factor of two wherein light is deflected twice as much as matter.
You have it backwards. There is only one reason that energy is a source of gravity and that's because there is an equivalence between mass and energy. There is no other reason. This is exactly what Einstein and other gravitational physicists argue. E.g. Misner, Thorne and Wheeler state the same thing in their text Gravitation.
MTW is wrong in some important respects. Again see this (http://einsteinpapers.press.princeton.edu/vol6-trans/197?highlightText=gravitatively%20) where Einstein said "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". And do note that mass does not feature in the stress-energy-momentum tensor:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Ff%2Ffe%2FStressEnergyTensor_contravariant.svg%2F236px-StressEnergyTensor_contravariant.svg.png&hash=370f52ee872d28294b676ab0285ffcab)
Once again you're misinterpreting the facts. The reason that Einstein was off by a factor of two was that at the time of his calculation in 1911, i.e. the last one before he got GR right, was due to the fact that he didn't take into account the curvature of space. When he accounted for the curvature of space he got the right value. It turns out that the curvature of space accounts for an exact value of a factor of two in the amount of deflection.
So give us a reference to the paper of circa 1914 where Einstein calculated the correct deflection.
Let's drop this nonsense. It has nothing to do with the topic of the thread.
It has everything to do with the topic of this thread. I've given McKay an explanation that hopefully clarifies things for him, with robust references to Einstein and others. You're just being all not invented here because you have no explanation. There are no magical mysterious rays of attraction-at-a-distance pulling a photon down. Its path curves because of something local. And it isn't the curvature of spacetime, or the curvature of space, it's the inhomogeneity of space. Light veers like a car veers when it encounters mud at the side of the road. Like the way you steer a tank. A curvature of rays of light can only occur when the speed of light varies with position. That's what Einstein said. Why won't you accept it?
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The first good estimate of the Earth's mass was produced by the Cavendish experiment (http://en.wikipedia.org/wiki/Cavendish_experiment), which measured the attraction between heavy balls in a torsion balance. This attraction still exists when the balls are stationary, relative to each other.
The quarks are moving. Freeze the balls - attraction disappears.
But why does bouncing up and down increase weight? Now that's a mystery.
Let's see ... Space is rapidly flowing downwards near a balck hole, so I conclude that space is slowly flowing downwards near the earth. So bouncing up and down increases the drag, for some reason.
Moving horizontally increases the drag twice as much as moving up and down, for some reason.
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Pete the factor of 2 pops up a lot in the equations to do with gravitation so I'm in your camp.
You're correct. All for different reasons. For example, if you have a gas of photons then the pressure of the gas contributes to its inertia just as much as the energy does.
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And you and I both know that that's a measure of energy, and that a concentration of energy causes gravity, and that "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".
As I explained above, its more accurate to refer to the energy-momentum tensor as a mass tensor. Einstein in his 1916 GR review paper wrote
The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in a symmetrical tensor of second rank, the energy-tensor.
When he said nothing more or less than energy he meant that an increase in one is coincident with an increase in the other and vice versa.
When deriving Einstein's field equations one has to replace Newtonian mass with relativistic mass. See:
http://home.comcast.net/~peter.m.brown/gr/einsteins_field_equations.htm
An article was written about this tensor not too long ago. The article is called
Mass-Energy-Momentum in General Relativity. Only there because of Spacetime? by Dennis Lehmkuhl, Oriel College, Oxford University. September 16, 2008.
http://philosophyfaculty.ucsd.edu/faculty/wuthrich/PhilPhys/LehmkuhlDennis2008Man_MassEnergyMomentumGR.pdf
Abstract - I describe how relativistic field theory generalizes the defining property of material systems to possess mass to the requirement of them having a mass-energy-momentum density tensor Tuv (energy tensor for short) associated with them. I argue that according to general relativity Tuv is not an intrinsic property of matter, looking at how the energy tensor for a relativistic material system can be derived in a Lagrangian framework. It will become evident that the matter fields alone are not sufficient for such a derivation. The metricfield guv plays a prominent role in obtaining the energy tensor of a material system, and occurs explicitly in a generic Tuv . Accordingly, since guv represents the geometry of spacetime itself, the properties of mass, stress, energy and momentum should not be seen as intrinsic properties of matter, but as relational properties that material systems have only in virtue of their relation to spacetime structure.
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Does gravity only affect moving objects? No.
A "relative gravimeter" is essentially a sensitive force balance, which measures the extension of a spring or the current required by an electromagnet to suspend a superconductor. In either case the test mass is stationary.
Classical textbook measurements of G admittedly detect the asymmetry of a swinging torsion pendulum in the presence of a large mass, but the underlying physics is the theoretical deflection of a stationary bob weight.
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Does gravity only affect moving objects? No.
A "relative gravimeter" is essentially a sensitive force balance, which measures the extension of a spring or the current required by an electromagnet to suspend a superconductor. In either case the test mass is stationary.
Classical textbook measurements of G admittedly detect the asymmetry of a swinging torsion pendulum in the presence of a large mass, but the underlying physics is the theoretical deflection of a stationary bob weight.
Sub-atomically the are moving. I mentioned this.
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Does gravity only affect moving objects? No.
A "relative gravimeter" is essentially a sensitive force balance, which measures the extension of a spring or the current required by an electromagnet to suspend a superconductor. In either case the test mass is stationary.
Classical textbook measurements of G admittedly detect the asymmetry of a swinging torsion pendulum in the presence of a large mass, but the underlying physics is the theoretical deflection of a stationary bob weight.
Sub-atomically the are moving. I mentioned this.
I think that what you are trying to say is that since sub atomic particles have internal motion they can never be considered at rest. If with respect to each other two masses can be considered stationary then gravity will act on the internal motions of the sub atomic particles to cause an attraction between them. Correct me if I am wrong on this point.
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Piffle. The constituent atoms and subatomic bits of a body may well be moving but
(a) they are moving at random and therefore the net motion within the body is zero
(b) G does not depend on temperature and
(c) as far as astonomers can tell, G has the same value for rocks and gases.
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Piffle. The constituent atoms and subatomic bits of a body may well be moving but
(a) they are moving at random and therefore the net motion within the body is zero
(b) G does not depend on temperature and
(c) as far as astonomers can tell, G has the same value for rocks and gases.
It isn't my viewpoint I was trying to clarify what the poster actually meant.
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Sub-atomically the are moving. I mentioned this.
The laws of physics as we know them for gravity are classical in nature since as of yet there is no quantum theory of gravity. The sub-atomic world is described by quantum mechanics. What we know about quantum mechanics is that there is no such thing as something being at rest in the quantum world. So physics has nothing to say about your question. However we do know that macroscopic objects which are at rest have an average motion of rest so that allows us to speak of them as being at rest.
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Don't know. Everything uniformly moving is in a geodesic. That can be translated to them being 'at rest', ignoring any definition of a speed they may have found. That as there exist no 'golden standard' for defining it in a uniform motion. You can't pick a suns light for it without knowing what 'speed' this sun would have, and you also have to define it, relative what? But speeds are overall a strange concept, as you according to relativity can 'shrink' a universe at 'relativistic speeds' close to lights. And doing so something more than just that speed you defined comes into play.
=
Also, a better definition of what a ultimate speed is, than 'c', doesn't exist. And 'c' will be measured to be 'c', no matter what 'speed' you otherwise define to yourself, your planet, solar system or galaxy. Doesn't matter, it's still 'c'. And that one is truly interesting.
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Pete said:
"What is what Einstein said? I'm saying that the speed of light varying with position is insufficient to cause light to be deflected. And that is a fact."
This is a very important point. Light being slowed IS insufficient to cause the deflection of light as can be demonstrated by a photon traveling directly away from the centre of gravity. In these circumstances there will be no change of trajectory. It is only by following an angular path to the direction of a gravitational field where we find deflection. The question is do we need tidal forces for this to occur or can it occur in a flat gravitational field?
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Pete said:
"What is what Einstein said? I'm saying that the speed of light varying with position is insufficient to cause light to be deflected. And that is a fact."
This is a very important point. Light being slowed IS insufficient to cause the deflection of light as can be demonstrated by a photon traveling directly away from the centre of gravity. In these circumstances there will be no change of trajectory. It is only by following an angular path to the direction of a gravitational field where we find deflection. The question is do we need tidal forces for this to occur or can it occur in a flat gravitational field?
Not only that but consider a beam of light directed along the x-axis. The potential varies with the distance from the beam so that the speed of light varies with distance from the beam. However if a photon was moving parallel to the beam and in the direction of flow of the energy then it wouldn't be deflected. See
http://home.comcast.net/~peter.m.brown/gr/grav_light.htm