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#101




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#102




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The problem is though that when the original frame is inertial and the primed frame is noninertial γ becomes a nonconstant function of t, i.e. Δt' = γ(t)Δt. Therefore γ can not be given as a single number as, say for example, a constant proper acceleration as it's a function of t. Of course, this still proves that he is incorrect in his original idea. Why is he incorrect? Becuase the relationship between a uniformly accelerated observer and inertial observer and the relationship between an observer held stationary in a static graviational field and an inertial observer at spatial conformal infinity is not the same. What differinates them is that in the latter case the spacetime between the two observers is curved. A better comparison for the former case would be the relationship between an observer being held stationary in a static gravitational field and an freefalling observer passing close by them. 
#103




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You are trying to muddy the waters in talking about "...t going to infinity...", as that is not the scenario being discussed here. The formulae prove my original statement that clocks at 1G, whether accelerated or gravitational, run at the same rate to a high degree of precision. The term for mass is : m = m0 / sqrt( 1(v/c)^2), and references can be found in chapter XV of Einstein's book which I have already mentioned, and chapter 8 of Asimov, "The Stars In Their Courses" (and of course a myriad of others). 
#104




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In comparision the proper time of a stationary observer in a static gravational field as compared to Schwarzchild coordinate time is constant with time and hence can be expressed as a single numebr (for a given r). Is it that difficult to understand? Quote:
That's not to say that the equation isn't true when you define mass in a certain way of course, however as I've explained we don't define mass in this way any more Try reading this paper: http://www.stat.physik.unipotsdam.d...r/einstein.pdf It explores Eisntein's understanding of the concept of mass (as well as some of the problems associated with the now defunct concept of relativstic mass) 


#105




::raises hand timidly from back of room::
Can gravity potential be likened, metaphorically, to potential (ie non kinetic) energy? 
#106




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[Quote]You're still not understanding, I'm talking about the accelerated observer in Minkowski space (i.e. flat spacetime). The time dilation factor increases as t increases which means you cannot express it as a single number for acceleration = 1g as it is a function of time. In comparision the proper time of a stationary observer in a static gravational field as compared to Schwarzchild coordinate time is constant with time and hence can be expressed as a single numebr (for a given r).[Quote] If Einstein's equivalence principle is correct, you are wrong, if your quote above is correct, Einstein is wrong and there is no equivalence. 
#107




[QUOTE=tomh4040;14429193]I am not comparing IFRs with non IFRs, I am concerned only with accelerated/gravitational FRs, and their relationship to the "standard" clock. The formula for gravitational time delay was known to me; what was new was the different formula for accelerated time dilation. I had assumed, correctly as it turns out (try running the figures yourself through the 2 formulae, and work to 8 decimal places), that under 1G, whether caused by gravity or acceleration, the clocks run at (to a high degree of precision) the same rate.
[Quote]You're still not understanding, I'm talking about the accelerated observer in Minkowski space (i.e. flat spacetime). The time dilation factor increases as t increases which means you cannot express it as a single number for acceleration = 1g as it is a function of time. In comparision the proper time of a stationary observer in a static gravational field as compared to Schwarzchild coordinate time is constant with time and hence can be expressed as a single numebr (for a given r). Quote:
* the (per mass) gravity force are very slightly different  by a factor of 1 meter divided by the radius of the Earth cubed, but the difference in dilation is proportional to the difference in potential (proportional to g*dh) 
#108




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dt/delta t = (g_{uv} dx^{u}/dt dx^{v}/dt)^{1} (Eq. (3.5.1)) No explicit force terms in sight. No second derivatives (the metric tensor is first derivatives), so no acceleration terms, so no force terms in hiding, expressed as acceleration. Thus, force does not contribute to gravitational time dilation. QED. 
#109




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Rather than asking for cites, tackle my objections to the prescriptiveness of your statement directly. Posting cites that don't actually disagree with what I've said doesn't acheive this. Quote:
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Firstly, the fact that the equation uses the ordinary derivative should alert you as to its coordinate dependent nature. Seocndly if what you'd said was actually true and there was a totally valid general method for nonarbitarily defining gravitational time dilation in an arbitary gravitational field, then the relationship between gravaitonal time dialtion and gravaitional potnetial must be very weak. This is as the gravaitional potnetial cannot be defined (satisfactorily) for an arbitary gravitational field. The arbitariness in Weinberg's equation lies in the fact that choices of the cooridinate basisare arbitary. If we had an exact prescription for deciding the components of the metric at an event then it wouldn't be arbitary, but we don't, so they are. Even if we limit the possible cooridnate bases by imposing restricitions so as to make them 'physically sensible' we can still end up with being able to define multiple different coorindate bases or even worst none at all! E.g. Schwarzchild cooridnates are only a cooridnate patch in Schwarzchild spacetime as opposed to a global coorinate system as they fail to cover the region of spacetime bounded by the event horizon. So you cannot use Schwarzchild compoents to define the time dilation factor of an object inside the event horizon (this may seem sensible, but on the other hand using a cooridnate system thta does cover the inside of the event horizon you could). Consequently different chocies of the cooridnate bases in the above equation will result in different time dilation factors. Of course gravaitonal time dialtion is also an empirical phenemona, but this comes from being able to compare a particular spacetime or region of spacetime with a flat sapcetime either because it is asymptoically flat or a region of it can be viewed as a peturbation of the flat metric. Quote:



#110




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#113




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You can make all the handwaving arguments you want, they don't prove anything. 
#114




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More smoke and mirrors. You asked "Where in the equations representing the Lorentz transformation do you see a term for mass? Actually deriving socalled 'mass increase' from the Lorentz transformation is actually quite complicated. Also note that when you define mass in this manner you actually get two types of mass: transverse and longitudinal." You said that that their masses did not alter. L mass and T mass are old expressions which became relativistic mass, which definitely does alter with velocity when viewed from a different FR. More smoke and mirrors. You said there was no Lorentz equation for mass increase, and yet in the next sentence said that deriving socalled mass increase fom the Lorentz equations is quite complicated. If there is no term for mass how can you derive it  complicated or not. Quote from Albert Einstein "It is not good to introduce the concept of the mass M = m/sqrt( 1(v/c)^2)) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m." Quote from Wikepedia (which I assume that we all trust as we all quote it). "So, according to Lorentz's theory no body can reach the speed of light because the mass becomes infinitely large at this velocity." 


#115




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You seem to be saying that the equivalence principle implies that the time dilation between us in both cases is the same; but this isn't so, as can easily be seen (and as These are my own pants has tried to point out). Obviously, in the second case, the dilation is constant, equal to t_{m} = t_{y}*sqrt(1  2*g*r/c^{2}) = t_{y}*sqrt(1  2*G*M/r*c^{2}), where t_{m} is my time, and t_{y} is yours  you observe my clock ticking slower by a fixed factor. But in the first case, things are different  at any moment in time, my clock appears to you slowed by the factor sqrt(1  v^{2}/c^{2}). However, I am accelerating, and thus, my speed is not constant  it increases. Thus, the factor by which you observe my clock ticking slower is not constant, either  it increases, as well. The two situations thus are quite different, even though in both cases, I experience an acceleration of 1g; thus, it doesn't suffice to state the acceleration to work out the time dilation. Nevertheless, this situation is quite consistent with the equivalence principle. The reason is that it is only valid locally  I either in my spaceship or hovering in the Schwarzschild spacetime can't tell the difference. Quote:
Perhaps a better, if also flawed, intuitive explanation is that you move at the speed of light all the time (the magnitude of the fourvelocity is c), just that the bulk of this movement is through time; thus, as you move through space faster and faster, you move through time slower and slower, and going arbitrarily close to c means basically not moving through time at all. Last edited by Half Man Half Wit; 11052011 at 12:19 PM. 
#116




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The actual force terms appear in the coordinate system itself, for example nonvanishing Christoffel symbols at an event will tell you at that point there's an equivalnce between the coordinate basis and an accelerated observer's local cooridnates. As I pointed out earlier the equation that you posted results in a nontensor quantity and so depends purely on the chocie of cooridnate systems and nothing else. 
#117




Blah blah blah. I'm done here.

#118




...and with that departure, the tone of civility returns to polite.

#119




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It's been years since I studied general relativity, but I was introduced to the concept via examples that did not include forces, but did include potential (the elevator example for example), and while I find papers such as this one in Nature http://www.nature.com/nature/journal...ture08776.html (which states "One of the central predictions of metric theories of gravity, such as general relativity, is that a clock in a gravitational potential U will run more slowly by a factor of 1 + U/c2, where c is the velocity of light, as compared to a similar clock outside the potential") about the use of potential in gravitational time dilation calculations, I haven't found anything helpful about force. Please give me some more information. Thanks. 


#120




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#121




The problem is precisely that general relatvity is a metric theory of gravity.
Take the stressenergy tensor, this is a rank2 tensor field which among other things describes the (nongravitational) enegry of spacetime. In a vacuum this vanishes, which is precisely what we'd expect as a vacuum is a region that contains no nongravitational energy. So far no problems, but let's imagine what sort of object could describe the gravaitional potential energy. By the equivalance principle, you can always choose a local frame (descrbing an observer in free fall) so that spacetime appears locally flat. Now a flat spacetime is one without an sort of gravitational energy, so locally the gravitational energy must also vanish. I.e. in gravitational energy, should it exist in general relatvity cannot be a local property of spacetime as it can be made to vanish locally just like the stressenergy tensor vanishes when describing a region containing no energy. Already we're at odds with the idea of gravitational potential energy, because the precise point of GPE is to give gravitational energy a local definition on par with other kinds of energy. So you cannot derive a cocnept of gravitational potential energy purely from the general relativstic description of gravity, you need either explicitly or implicitly add something else such as a preferred frame of reference or a decompostion of the metric in to a gravitational part and a background part (this is driectly paraphrased from Wald's General Relativity). There are what are known as pseudotensor fields which can be defined on spacetime to allow us to find some sort of expression the total energy/energy flux (including graviational energy) of some arbitary volume of space, but that's still not the same as GPE as they can be made to vanish locally (whereas in Newtonian gravity GPE does not vanish). I believe the statement that time dialtion due to GPE is a central prediction of metric theories of gravity comes from MWT's Gravity where it is shown that in the limit relativistic theories of gravity must reduce to a certain metric described by the Newtonian potential, from which graviational time dialtion can easily be related to gravitational potnetial. The reason I think it's too prescriptive to rule out the role of force is that in general relatvity terms forcelike terns appear as Christoffel symbols related to some coordinate system and I think it's just as easy to see time dialtion as a result of the aggregate effect they have on the transport of vectors in spacetime. 
#122




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#123




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Yes, graviational time dilation is an effect that comes from essentially not local. However; no, picking a local frame will not fix the frame at some other point, that I guess would be equivalent to saying that defining a local basis defines a tetrad basis for the whole of spacetime, which is not true and I'm not sure that there's any sensible conditions you could impose on a tetrad bsis to make it true. Quote:
The issue you've brought up is gauge arbitariness and that's not really the issue here. I feel a bit over my head discussing gauge theory aspects of general relativity, but the problem is not fixing a gauge for GPE (i.e. in particualr fixing a zero point) Perhaps the best way to understand it is to compare to an elctrostatic field in general relativity. In an electrovacuum (i.e. a 'vacuum' containing only an elctromagnetic field), the stressenergy tensor does not vanish, unlike a 'true vacuum' in general relativity (i.e. one not containing any gravitational sources, though it still may contain a gravitational field) where it does vanish identically. Your just never goign to get a definition of graviational potential energy in general relativity where there's a basic equivalnce it and for example electrical potential energy. Electromagentic energy exists locally in general relatvity, graviataional energy does not. Quote:

#124




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Last edited by Andy L; 11062011 at 03:54 PM. Reason: Edited to fix the quotes 


#125




Hi, sorry for my enforced absence, I'm joining in again.
I got so carried away with the ongoing arguments about 1G gravity versus 1G acceleration that I forgot my original mission. I was wrong in pursuing the argument about the 1G accelerated frame not going out of sync with the reference clock as I had the wrong parameters. Here are the correct parameters, and why I have been keen to establish the time connection between 1G gravity and 1G acceleration. There is a closed chest resting on the surface of the Earth. Naturally the man inside experiences 1G. During the course of this experiment he is not allowed outside the chest. There is a closed chest with a man inside in a rocket ship which is about to be accelerated at 1G. During the course of this experiment he is not allowed outside the chest. The Earth and the rocket to be accelerated are both placed in intergalactic space, far away from any other bodies so there are no reference points except each other. They are aware of each other, and know they are eg 1 million Km apart. Their clocks are synchronised and the rocket motor is fired up. The distance between the two then rapidly increases at 9.8m/s^2. The man in the rocket (he does not know he is in a rocket remember) experiences 1G, and time for him passes normally  ie he cannot detect any change in the passage of time. He can also conduct experiments which tell him he is experiencing 1G, and all experiments he conducts behave normally, just as they did when he performed them on Earth before this experiment began. The man in the chest on Earth experiences 1G and for him the passage of time is "normal" also. He can also conduct experiments which tell him he is experiencing 1G, and all experiments he conducts behave normally, just as they did previously on Earth before this experiment began. After 2,191.5 hours by the clock on the rocket, the motor on the rocket is cut, the rocket is rotated round 180 degrees, and the motor restarted. The man in the chest on board does not know this, all he knows is that he was weightless for 60 seconds, then all was normal again. Unknown to the man in the rocket, 2,191.5 hours after that period of weightlessness, the rocket very briefly (almost instantaneously) stops (relative to Earth) and starts accelerating back. 4,383 hours after the first period of weightlessness, the procedure is repeated. All he knows is he was weightless again for 60 seconds. Another 2,191.5 hours passes, and the Earth and the rocket are adjacent to each other again. One year has passed on the rocket. The experiment has now ended, they are back again to the 1 million Km apart. The rocket cuts its motor and the clocks are compared. Note that the man in the chest on Earth did not undergo two 60 seconds periods of weightlessness, and this will cause a disparity between the clocks of 0.00008 seconds, a trifling amount. With the above scenario, any GR effects are present in both FRs, and therefore cancel each other out. Are the clocks in sync to within a few seconds. If not, which clock is slow, and why? We have here of course the twin paradox, as each man can justifiably say that he was the one who was stationary, and the other was moving. Their only reference was each other. They both experienced 1G for one year (except for one man who experienced 0G for 120 seconds, wich will not affect the outcome. It can be arranged for the man in the chest on Earth to be weightless also for 2 periods of 60 seconds, by having him suspended and dropped, but the experiment is simpler as laid out here, and just as accurate. 
#126




at one time (haha) Einstein said that there were only half a dozen people who understood his theories. are there more than that now?

#127




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#129




Einstein didn't say that. It was written about him in a newspaper article. It wasn't true at the time or since.



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#131




The article does make an unsourced claim that Einstein said it to his publishers, but there's no evidence for it. And he would certainly know it wasn't true.
Although he did have an odd sense of humor... 
#132




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#133




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What's clear is that the time dilation 'suffered' by the rocket ship observer massively outweighs the tiny peturbation caused by general relativstic effects and the rocket ship observer will experince much less time between the start and the end of their journey than is measured on the Earth bound observer's clock. 
#134




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But it's easy to see that of course, the travelling clock will show less time elapsed than the stationary clock on Earth. As I said, after 2191.5 hours at 1g acceleration, the rocket is going at roughly 0.25c, meaning a gamma factor of roughly 1.03  small, but noticeable. By contrast, the equivalent factor for the observer in the gravity well, giving the slowing down of his time relatively to a 'far away' observer, is roughly 1.0000000007, utterly negligible in comparison. As These are my own pants said, we can thus just think of this as the familiar twin problem, where of course less time passes for the moving observer. 


#135




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At no point does the rocket instantaneously go from .25c to 0. The instantaneous point where the rocket changes from moving away from Earth to moving towards Earth won't be felt at all in the rocket, because it is accelerating smoothly at 1g the whole time. 
#136




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There's also the issue of him considering 0.000008 s to be a trifling amount when doing GR calculations for 1G. 
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#138




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One thing to note is that I didn't calculate the amount of time the rocket ship twin experinced,so when I said he will experince much less time that was a slight exaggeration (though to make iso its no exaggeration a all we need to do is to extend the time that the rocket accelerates) , however it is still painfully clear that the special relativstic twin effect dwarves the peturbation due to the Earth's gravity. 
#139




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#140




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Okay we can both agree the question of which one "moved" is totally subjective and metaphysical, however the question we want to ask is what interval of time does each one measure between events which, whilst in the scenario you've set up there is an elemtn of subjectivity (which we will ignore), is an objective physical question Quote:
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As has been pointed out the rocket twin changes direction. In the special relativistic version, changing direction breaks the symmetry between the two twins and remember that special relativity is just a special case of GR. However, try this scenario: after a period the twin on Earth drops through a hole which goes directly through the Earth's centre and where he comes out the other side and stops. This exactly simulates what the rocket bound twin feels when they stop and then turnaround and whilst it may have a significant effect on the GR correction, whatever effect it does have will still be much smaller than the time dilation effect from the standard twin paradox. We can alos adjust the setup in other ways. So now we do have two apparently symmetrical situations, however there will still be a time dilation like effect between the two twins. The reason is that there is a global asymmetry is in the spacetime which both twins occupy. Compare to the cosmological twin paradox of GR. In this both twins start and finish at the same spot and neither twin is subject to acceleration and the spacetime they occupy is (or at least can be made) very symmetric, yet there is a significant time dilation effect due to the asymmetry introduced by something as esoteric as them having different winding numbers in spacetime. 
#141




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The questions, which one moved and which one was stationary? and what do the clocks show when compared? still have not been answered. 
#142




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In answer to your second question: sorry, but if your going to create a reasonably complciated setup like you have don't expect others to take the time (and it would be timeconsuming especially if we were to include general relativistic effects) to solve it for you. I've already told you the qualitive answer which is easy to arrive at with some straight forward arguments. 
#143




[QUOTE=These are my own pants;14466574]it's not an argument, it's a fact. If the twins are truly symmetric their cannot be a time dilation effect between them as that would indicate an asymmetry. I'm pointing out where the asymmetry comes from in this situation
And there we have the crux of the problem. In SRT, the twins are truly symmetrical as they carry on travelling for ever away from each other so the experiment is not falsifiable. They have to be brought together again for the clocks to be compared, and this is where the adherants say the assymmetry comes from, as acceleration was used to turn one around. By using FRs of 1G, there is symmetry. 
#144




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Last edited by Andy L; 11162011 at 03:08 PM. Reason: Fixed quote 


#145




Yes  you're right.

#146




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While I am answering objections, here is another Quote:Originally Posted by naita (I think) What's clear is that the time dilation 'suffered' by the rocket ship observer massively outweighs the tiny peturbation caused by general relativstic effects and the rocket ship observer will experince much less time between the start and the end of their journey than is measured on the Earth bound observer's clock. The tiny pertubations caused by GR effects in fact add up to 8.72 hours over the year. I asume this time dilation (suffered by the rocket ship observer) is caused by SRT, and that is what this posting is really about. Gravity and acceleration cause clocks to run slower when increased, and run faster when decreased. Actually that is not quite true, as a pendulum clock does exactly the opposite, but we'll leave that for now. It is SRT's prediction of time dilation and length contraction that I have an issue with. I shall now refer you to an address to the Prussian Acamedy of Sciences in 1921 given by A Einstein. In the paragraph starting "Sub specie aeterni" he recants. Recall that both Poincare and Lorentz believed in a "real" time. It is to be found at : http://www.relativitycalculator.com/...ience_1921.pdf 
#147




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#148




I have already pointed out how the other FR can undergo the same accelerations.

#149




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The brightest physicists etc are all earning their wages on the back of relativity, they are hardly likely to renounce it. It takes a brave man like Professor Dingle to admit there is something wrong with the theory. None of the so called tests of SRT have actually proved it, they have merely failed to disprove it, which is entirely different. For instance, GPS satelites are time corrected by using relativity. Note that this is vague. The relativity used to correct these satelites is in fact not SRT but LET, which is Lorentian relativity, and all satelites are synchronised with the Earth clock. Tom Van Flandern was involved in the development of GPS, read what he has to say on the subject : http://metaresearch.org/cosmology/gravity/gpstwins.asp 


#150




See post 147 for my discussion of why the other FR will not undergo the same acceleration.

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