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Post by speakertoanimals on Oct 4, 2010 15:47:30 GMT 1
Indeed. Gravitational potential (in the Newtonian approximation) is calculated by taking the strength of gravity at a point (g(h) say), and multiplying by the infinitesimal distance (height), g(h)dh. Hence if g varies with height, you have an integral to perform. As I said before, Einstein predicted an effect even in a uniform gravitational field. The relation is that the gradient of the gravitational potential gives the strength of the gravitational field, so that the SAME value of gravitational potential doesn't mean the gradient (hence strength of gravity) is the same. Mind you, I will admit that this is a common mistake, thinking that it is the strength of the gravitational field that matters, as is shown in this essay on GPS and time dilation: triangulum.nl/Werkgroepen/documentatie%20werkgroepen/Snaartheorie/GPS%20essay.pdfEasy mistake to make, since for bodies like the Earth, higher generally means weaker gravitational field.
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Post by carnyx on Oct 4, 2010 16:07:21 GMT 1
@speaker-to-animals
I'm sorry, but you may have forgotten that when Newton talks about 'g', he means the attractive <i>force</i> between masses, which varies as the inverse square of the distance.
And a matter of observation, there can be no 'uniform gravitational field' where every point has the same gravitational potential right across the 3D field.
(PS I suspect you are thinking about potential <i>energy</i> on a localised basis, where potential energy PE = Mh)
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Post by carnyx on Oct 4, 2010 16:20:23 GMT 1
@eamonshute,
And so a clock on saturn's surface will differ in the ratio of 1.065 from one on the earth's surface, no matter how much the two planets differ in mass.
And I am sorry to have inadvertently misled anyone if I said gravitational potential (energy) when I should have said gravitational force.
But there again, 'gravitational potential' as Mh is a construct and is not physical, but potential and also contingent, so it should not have confused things for very long, really.
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Post by eamonnshute on Oct 4, 2010 16:42:05 GMT 1
@eamonshute, And so a clock on saturn's surface will differ in the ratio of 1.065 from one on the earth's surface, no matter how much the two planets differ in mass. Not true. To lift a rock into space from Saturn would need more energy than from Earth, because the gravity decreases more slowly with altitude. Similarly, a photon would be red-shifted by more. In fact, a black hole with enough mass can have a gravity of 1g, or even less, at the event horizon, but the time dilation would be infinite.
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Post by Progenitor A on Oct 4, 2010 17:30:25 GMT 1
@speaker-to-animals I'm sorry, but you may have forgotten that when Newton talks about 'g', he means the attractive <i>force</i> between masses, which varies as the inverse square of the distance. And a matter of observation, there can be no 'uniform gravitational field' where every point has the same gravitational potential right across the 3D field. (PS I suspect you are thinking about potential <i>energy</i> on a localised basis, where potential energy PE = Mh) Indeed, STA has the capacity to muddy the clearest water It should be stated again THERE IS NO SUCH THING AS A UNIFORM GRAVITATIONAL FIELD (in the sense of a uniform acceleration toward a point) STA does no appear to realise that if she is talking about a uniform acceleration (as she was) then she is NOT talking about gravitational acceleration, where it is fundamental that acceleration is proportional to the inverse square of the distance away from the centre of mass. In her quite silly example of a lift with uniform acceleration, it is quite evident that the lift is not accelerated by a gravitational filed as one end of the lift would be at accelerated at a different rate to the other. Therefore her example has nothing to do with time varying due to gravitational field, but to a uniform accelerating field
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Post by carnyx on Oct 4, 2010 17:32:03 GMT 1
eamonnshuteThe weight of a mass of 1kg on the surface of the Earth would weigh 1.065Kg on the surface of Saturn. And so, any timing device would exhibit the same kind of difference in measurement. And with regard to your statements concerning a black hole, I suspect they are wrong, because AFAIK their existence has not been proven, and they may even turn out to non-existent pathological artefacts of mathematical formulae.
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Post by speakertoanimals on Oct 4, 2010 17:46:04 GMT 1
Might I just add, NOT my 'silly example' but the very thought experiment Einstein used to realise that gravity should effect clocks as well as speed.
It is only for point masses that gravitational force varies as inverse square. Same is true for electrostatic force between point charges, butu that doesn't stop the concept of a uniform electric field being both useful and totally physical.
Same goes for uniform gravitational fields.
And neither of this changes one whit the simple fact that the Einsteinian prediction for gravitational time dilation, in the simple Newtonian approximation (if effects small, can take the first-order term in the Taylor series) depends on gravitational potential, and not on gravitational field strength.
I just suspect some posters would rather eat their own foot than admit that I have it correct, and they are wrong...............
Wrong again. Uniform gravitational field means the gradient of potential is uniform in size and direction, not that potential is constant.
I dunno, if you can't admit you are wrong, you will never learn! Unless your ego really does require you to seriously maintain the position that Einstein was a numpty.................
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Post by carnyx on Oct 4, 2010 18:40:35 GMT 1
speakertoanimals, Here is a sentence from your most excellent link; "Gravity makes clocks run slow. That is, in a gravitational field, the rate at which clocks tick depends on the position in this field. Since the gravitational force exerted by the Earth on a satellite is less the greater its distance to the surface, on-board clocks will run faster than those on Earth." Now, if you go back to Post 1 you wil find that this is exactly what was said. And the reason WHY clocks run faster or slower is that the local gravitational FORCE affects ALL sensible time-measuring mechanisms. I hope you can go back and consider the rest of what was said in Post 1, as it now may be of more interest to you.
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Post by speakertoanimals on Oct 4, 2010 18:57:43 GMT 1
speakertoanimals, Here is a sentence from your most excellent link; "Gravity makes clocks run slow. That is, in a gravitational field, the rate at which clocks tick depends on the position in this field. Since the gravitational force exerted by the Earth on a satellite is less the greater its distance to the surface, on-board clocks will run faster than those on Earth." Now, if you go back to Post 1 you wil find that this is exactly what was said. And the reason WHY clocks run faster or slower is that the local gravitational FORCE affects ALL sensible time-measuring mechanisms. I hope you can go back and consider the rest of what was said in Post 1, as it now may be of more interest to you. If you had READ my message, you would have seen that I posted this as an example of someone else GETTING IT WRONG! Yes, right in that different positions (i.e., different heights) in a gravitational field give different rates, but WRONG in making the link that it is difference in field strength that gives the effect, rather than difference in gravitational potential............... Anyway, saying that since pendulum clocks are effected by field strength, therefore so is time, is just daft, given that a pendulum clock won't tick at all in weightless conditions, yet time still passes. Be brave, just admit you've got it wrong, and LEARN something instead!
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Post by carnyx on Oct 4, 2010 19:20:05 GMT 1
speakertoanimalsA 'field strength' at a specific point in a gravitational field is the g-force and direction at that point. That is all you can measure. And as for time measurement with a pendulum, if that is all that you have with you as a time measuring device, then that is the only result you <b>can</b> have. ( see Post 1 for an explanation) The behavious of a prendulum is the result of having a time-measure that is wholly dependent on g and length, and so is competely 'dependent' on it. In fact, a pendulum makes a good accelerometer (i.e. a g-meter) (BTW, with regard to the effect of pendulum length, for fun try googling 'schuler tuning' ... which was an aspect of my job a few years ago.)
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Post by Progenitor A on Oct 4, 2010 19:53:01 GMT 1
speakertoanimalsA 'field strength' at a specific point in a gravitational field is the g-force and direction at that point. That is all you can measure. And as for time measurement with a pendulum, if that is all that you have with you as a time measuring device, then that is the only result you <b>can</b> have. ( see Post 1 for an explanation) The behavious of a prendulum is the result of having a time-measure that is wholly dependent on g and length, and so is competely 'dependent' on it. In fact, a pendulum makes a good accelerometer (i.e. a g-meter) (BTW, with regard to the effect of pendulum length, for fun try googling 'schuler tuning' ... which was an aspect of my job a few years ago.) For someone (SBTA) who insists that a gravitational field can have constant acceleration in the direction of force, SBTA is not worth while bothering with OK as a 'thought' experiment, but outside 'thought' there is (to our knowledge) no gravitational field that has constant acceleration wrt to distance from cog. Under those conditions , therefore the consideration of (gravitational) time dilation is dependent upon the (usual) gravitational variation of acceleration with distance from the centre of gravity. (Just reserving this for posterity) Just to point out, the original post repeats a misconception, that time is affected by the local strength of the gravitational field. This is totally wrong. In relativity, what effects time is not the gravitational field strength, but differing heights in a gravitational field -- hence we have a gravitational time dilation even in a totally UNIFORM gravitational field. And given that gravitational time dilation/gravitational redshift has been tested over GPS altitudes, over the height of a tower, and now over a height of 33cm: www.sciencenews.org/view/generic/id/63657/title/Everything_really_is_relativeWhich blows the first post right out of the water. Moral -- try to learn the BASICS of a subject, before trying to build some supposed alternative theory of time on it. Else you end up looking like a right idiot.
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Post by speakertoanimals on Oct 5, 2010 11:57:41 GMT 1
Don't blame me, blame Einstein!
And it is perfectly sensible, just as a constant electric field is perfectly sensible.
First, is if your mathematical equations for your physics are any good, they should be able to describe situations that although not exactly realisable in practise, are nevertheless not ruled out as unphysical. So, a constant gravitational field OVER SOME FINITE REGION has no problems with infinite force, or infinite energy. It is perfectly physical. Hence if your physics is to be logically consistent, it ought to be able to describe that situation as well.
Second, from a practical point of view, consider the following. Suppose out in empty space, far from any other planet or star, we set up a flat, dense plate (a Bouguer plate). For an infinite plate, the gravitational field strength is everywhere perpendicular to the plate, and doesn't depend on distance. For a FINITE plate, you get an approximation to this, constant gravitational field over some region not too far from the plate compared to size of plate. Since you can approximate a constant field to a given degree of approximation over a finite region just by making the plate big enough, then the truly constant gravitational field is a sensible limit in this case.
If the situations with the finite plate and almost constant fields are physical, then the limiting case had better be as well.
This is actually a common idea in physics. We all know that taking two charged plates gives you an almost constant electric field between them, depending on the size of the plates again, hence the idea of a constant electric field had better be physical as well, else you've got real problems.
Anyone claiming to object to these ideas, or claiming they are somehow non-physical, or unimportant, is either an idiot, or someone with another agenda than actually discussing physics..............
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Post by Progenitor A on Oct 5, 2010 12:41:08 GMT 1
Don't blame me, blame Einstein! Einstein, it seems was considering an analogy of gravity as a first-order uniform accelerating field. Fine Except that there is no gravitational field that has uniform acceleration. He would have got a different result (a larger red shift) if he had modelled a real gravitational field. He postulated a body moving with uniform acceleration. The fact that the acceleration was not due to gravity could be examined by dropping two balls with 1m vertical separation in the direction of the accelerating force. In a uniform accelerating field they would reach the bottom of the lift still separated by 1m; if the lift was non-uniformly accelerated by a gravitational filed the lower ball would be accelerated more than the upper ball and by the time the lower ball reached the floor the separation would be >1m. Any measured red-shift would also be greater than for a uniform-accelerating field [And it is perfectly sensible, . Perfectly sensible except that there is no such thing -it is an abstraction. [ For an infinite plate, the gravitational field strength is everywhere perpendicular to the plate, and doesn't depend on distance. Invoking infinity is not sensible You, go on to say from Einsteins result that the time dilation does not depend upon the relative magnitudes of the gravitational fields but the difference in gravitational potential. It can simply be shown that it depends upon both and that , if you take gravity as a uniform accelerating field, you will get the wrong answer for time dilation Why you take such a silly pedantic position, such as saying the OP was WRONG (in your usual petulant manner) I do not know. Do you feel insecure?
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Post by speakertoanimals on Oct 5, 2010 13:05:18 GMT 1
No, einstein was establishing what he saw as an important physical principle (the principle of equivalence), which says that locally, a gravitational field cannot be distinguished from acceleration. Note the word, locally -- it hence specifically excludes things like gravity varying over the height of the lift, or the direction being not quite the same on different sides of the floor.
Any gravitational field, over a sufficiently small region, can be taken as constant to any specificied level of accuracy, hence your statement about gravitational fields is just stupid -- the principle of a constant gravitational field is not unphysical, in that it is a limit (as in the infinite plate case) which you can approach as closely as you like.
Did you not read my earlier post? I said quite explicitly that for a real gravitational field that varies with height, the infinitesimal change is g(h)dh, hence the actual change over a finite height is an integral, This is no way says that we are actually treating g as constant with height (what do you think g(h) means?). nor does it means that time dilation depends on the gravitational field strength per se, since what it clearly depends on is the integral that is the gravitational potential, which is NON-ZERO even in a constant field.
Stupidity upon stupidity! What do you hope to gain, apart from spreading misinformation and making yourself look stupid by continually claiming that Einstein is wrong...................
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Post by speakertoanimals on Oct 5, 2010 13:07:51 GMT 1
Unlike yourself, I obviously think that then truth matters. I prefer actual physics to common misconceptions or just plain mistakes. If you'd ever done an exam, I think you'll find that the markers take the same view.
The only one showing any sign of insecurity is yourself, in that you seem to be too insecure to admit that you might ever be wrong...........
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