Markus Hanke

Of course it does, but that effect is far too small to cause any measurable time dilation effects - unless of course you can show us some numbers proving otherwise, but then again, you appear to reject any maths, so obviously you are unable to. I should also remind you that the travelling twin's proper time dilation explicitly depends on the exact path it takes before returning to earth, including all maneuvers undertaken while far away from the stationary twin, i.e. far outside the range of any measurable gravitational interaction. Likewise, it is easy to show that the total proper time dilation experienced by the observer does not depend on their masses; if you were to substitute the twins with, say, muons, you would find that the particles' lifetime is dilated by the exact same amount as the much more massive spaceship would have been. Therefore it is obvious that the time dilation in this experiment is not the result of gravitational interactions between the observers.

News to me. Can you specify exactly what those "forces acting on him from escaping twin" would be, both qualitatively and quantitively. I was once present at the launch of a rocket carrying a satellite - what forces from the escaping rocket was I supposed to be feeling ? Please be very exact here, and provide a textbook reference to the force you are proposing.

It changes the arc length of the worldline connecting the same two events in space-time. In other words - the proper times as measured by the two twins will no longer agree, which is precisely what we wanted to explain in the first place. Too imprecise. The basic proposition is that both twins start off at rest in the same frame of reference, with synchronized clocks; one twin remains at rest, whereas the other twin makes a round trip of arbitrary distance and duration, and then returns to the stationary twin. In the end both twins are once again together at rest within the same frame. They then compare their clocks which each of them has been carrying, and find that the readings don't agree. There is no contradiction. The stationary twin feels no forces acting on him, so will always consider himself at rest. The travelling twin feels the forces of his own acceleration and deceleration during his round-trip journey, so he will always consider himself moving. These two frames are physically distinct, and not interchangeable, hence there is no contradiction, and the fact that their clocks don't agree at the end of the experiment is not a paradox because they know precisely who was moving and who was stationary at the end of the experiment. Mathematics is just simply a language to express physical ideas in concise form. You learn maths just as you learn any other foreign language. Dealing with physics and refusing to use maths is like living in China and refusing to use Mandarin; not only are you going to make your own life extremely difficult ( trust me, I've been there ), but you will also forego any chance of ever really understanding or appreciating what it really is you are dealing with. That is a simple truth of life. In this example, everything that has been so verbously elaborated on over the course of 18 pages can be mathematically expressed in just a handful of lines - if everyone here spoke the language of maths to the same standard, we would not have had to engage in this lengthy discussion. It is very easy to show mathematically that the proper times of the two twins cannot agree in this scenario, and more crucially also precisely why that is. Doing the same verbally on the other hand takes literally a wall of text to do it right; everyone needs to decide for him/herself which one they prefer.

They do have inertia, just like all bodies with non-vanishing rest mass. It is just that their gravitational interaction is extremely small. They are effected by Newton's laws. They are not different, both domains obey the same set of laws of mechanics, being quantum mechanics. It is just that for macroscopic objects, quantum effects become so vanishingly small as to be entirely negligible, thereby reducing the observable laws to standard Newtonian mechanics. In the microscopic domain that is not the case, so the laws "look" different at first glance. In other words - Newtonian mechanics is just a subset of quantum mechanics for systems where quantum effects are negligible. Difficulties arise once we leave the domain of applicability of Newtonian mechanics, namely once we get into the domain of General Relativity; this is because GR is most definitely not a subset of quantum mechanics, so there appears to be a contradiction here. For that reason, finding a self-consistent model of quantum gravity is one of the core areas of research in theoretical physics at present.

Why is this nonsense still in the science section ? The link provided by the OP is a crackpot site, and the idea of "gravity is electromagnetism" is a well known crackpot concept which has been done to death countless times on countless crank forums. This really shouldn't be in the main sections of the forum - at best this belongs in "Speculations".

I don't really follow you, to be honest...what exactly is the scenario you are considering, and what are the conclusions you draw ?

You are contradicting yourself here - first you say that it is not the acceleration, then you say that you need to match the accelerations to get the same result. So which one is it ? Regardless of the exact circumstances though, the difference - if there is one - in proper times arises because one of the frames is inertial, whereas the other one is not. If both frames where inertial, you could never get differences in proper times between the same two events; if one or both are non-inertial, then the result depends on the space-time geometry within those frames, in other words, the metric tensor. This is what I tried to demonstrate with the maths you quoted me on earlier.

I dream and think in English 95% of the time, even though that is not my first language. Mind you, it took a few years after I started to be exposed to English for that to happen. Good luck

In order to get the same result, you would need to match the net effects of the accelerations in both frames. Their proper times will then agree. But again, the "twin paradox" is a well defined scenario, where you compare an accelerated with an unaccelerated frame. If you alter that setup you can no longer call it "twin paradox", but some other experimental setup of your own making.

I'm fluent in both English and German, and have elementary knowledge of French, Spanish, Samoan, Mandarin ( written & spoken ), and conversational mathematics. Yes indeed - I consider mathematics a language in its own right.

You can do that of course ( "back and forth" equates to acceleration ), but then you have officially left the confines of the "twin paradox" scenario.

I'm in agreement with you, elfmotat. That is pretty much what I was saying anyway; it boils down to the fact that there is a difference in metric tensors between the observer at infinity and the observer inside the cavity, even though the actual values are not fixed and simply are a result of the boundary conditions imposed. Hence the time dilation. So I think we are all good

That's true, but you need to consider the boundary conditions of this problem as well. The metric inside the cavity needs to connect smoothly to the interior metric of the shell itself to ensure global differentiability, which then again needs to connect smoothly to the exterior Schwarzschild metric. It would be interesting to do the numbers here, but just by looking at it I don't think it will work if the metric in the cavity is Minkowskian. If that is the case we will get either a discontinuity at the boundary, or a hypersurface where the metric is smooth but not differentiable, both of which is unacceptable. I don't believe it is possible for the elements of the metric tensor inside the shell itself to be exactly +/-1 at any point including the boundary, since this would imply a Minkowskian vacuum with vanishing energy-momentum tensor; so, in order to maintain smoothness and differentiability at the boundary, the vacuum metric in the interior of the cavity cannot be +/-1 anywhere either, or else we have a boundary problem. But then again, that's just my two cents' worth from the point of view of differentiable manifolds, I might well be wrong. Has anyone got any references to a fully worked calculation for just such a case ? I couldn't find anything. I think here's the solution : locally the metric inside the cavity is Minkowskian; however, if we want a global coordinate system which asymptotically approaches Minkowski at infinity, then the cavity will be flat, but not Minkowskian. This takes care of the time dilation issue, and tallies nicely with Newton.

Having thought about it further, it would appear I made a serious mistake here, so I have to retract the above statement. We will indeed find a region of completely flat space-time, but not the Minkowski metric; instead, we will have a metric tensor the elements of which are all constants, but not equal to +/- 1. These constants will be some function of the shell mass and the cavity radius. Physically this means there is no gravitational field in the cavity, but a clock located there is still dilated compared to a clock located at rest infinitely far away. This tallies nicely with the Newtonian shell theorem, and in terms of classical mechanics, can be thought of as a non-vanishing gravitational potential inside the cavity. It should be noted that there are no potentials in GR, it is the metric tensor which is the source term for gravitational time dilation.

Take the first sentence for example : This is without any meaning.

I am afraid you are using too much non-standard terminology for me to give any meaningful reply; I quite simply have no idea what you are trying to say.

Yes, I agree, and that is currently our problem. The domain of quantum gravity is far beyond the reach of any experimental setup which we can conceive of. This may change in the future, but it's what we are up against right now.

So far as gravitational time dilation is concerned, the important term is the metric tensor. In the case of the cavity within the shell, we simply have the Minkowski tensor [math]\eta_{\mu \nu}[/math], which represents a completely flat region of space-time. Btw, the Newtonian potential of the gravitational field in the cavity is constant at all points, and equal to the potential at the surface of the shell. This represents an extremum of the potential energy function; the numerical value - and thus whether this is a minimum or a maximum - is simply a matter of convention. The important point is that a stationary observer inside the shell will, as compared to a stationary observer outside the shell, age faster, due to the fact that his region of space-time possesses no curvature. Observers outside the shell are in a region of curved space-time, and thus age more slowly due to gravitational time dilation.

Ha ha, this is brilliant !

This is an old idea, and trivially wrong. Gravity and electromagnetism do not behave in the same fashion, and cannot be described by the same laws. In fact they differ in pretty much all aspects, most notably that one of them is a vector field and the other one a tensor field, and that gravity is self-interacting whereas electromagnetism is not. While it is true that electromagnetic fields are one possible source of gravity, so too are all other forms of energy. All forms of energy are sources of the gravitational field, not just electromagnetism. Btw, the term "strong electromagnetic force" is physically meaningless. You have electromagnetism, and you have the strong interaction. They are physically distinct phenomena, and not the same thing. Again, these interactions behave in completely different ways. I should also remind you that this section is not the place to present personal theories; the moderators will probably not take kindly to that. I suggest you open your own thread on this in the appropriate section, but you will find that the idea is old and has long since been shown to be wrong.

The ability of GPS to triangulate positions is dependent on clock synchronisations. A GPS satellite in orbit and clocks on earth are subject to both relative velocity time dilation and gravitational time dilation. The latter is a result of GR, and induces a difference in proper times to the order of 35ms each day. The GPS system compensates for this effect - if it didn't, all positions determined by it would be off by roughly 10km each day, so accounting for GR effects is crucial in making GPS work. This compensation is built into the software on all GPS receivers, since the orbital parameters of the satellites are fixed and thus the amount of gravitational time dilation is always known. Space-time is modelled as a 4-dimensional pseudo-Riemannian manifold endowed with a metric and the Levi-Civita connection. How that model relates to physical reality is a largely philosophical question which I will not attempt to answer here. Suffice it to say that the predictions made by the model are in good agreement with experiment and observation, or else GR would not be part of mainstream science. Gravity is an intrinsic geometric property of aforementioned manifold; in classic GR this would be curvature, but there are other possibilities. We do not actually know the set of all possible solutions to this problem; LQG was just one example, and whether or not the finally accepted solution will fall into one of the two categories mentioned by yourself remains yet to be seen. All of this is, at this point in time, very much pure speculation. We quite simply don't know yet how to reconcile GR and QM.

You see, here's the problem - if you consider a spherical shell of mass surrounding a ( spherical ) cavity, then Birkhoff's theorem implies that the geometry of space-time in the interior of the shell is actually Minkowskian. What that means is that, if you sit inside a hollow space surrounded by a shell of mass, you experience no gravitational time dilation at all as compared to an observer at infinity.

I am not certain what you mean here. I only mentioned LQG as an example; truth is, at this point in time we simply don't know which of our current hypothesis, if any, will represent a valid model of quantum gravity. No, you are right of course. I should have said that the idea of LQG is that macroscopically it becomes indistinguishable from GR, I did not mean to imply that it is actually the case. You are right that the proof of this is, as per yet, still outstanding. Presently LQG is really just a hypothesis with many ends still be tied together. My apologies for any confusion, I should have been more precise.

LQG is scale dependent; on macroscopic scales it is indistinguishable from deterministic GR, whereas on microscopic scales it is probabilistic in nature. So it incorporates both models. This works because on a macroscopic level probabilistic effects are so small as to be negligible.

Yeah, that's the big question, isn't it. One such attempt is Loop Quantum Gravity; basically what it boils down to is that on large scales it should be indistinguishable from standard GR ( proof of this is pending though ! ), whereas on small scales space-time itself becomes quantized, inducing quantum effects. This would be one way to do it.