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Implications of the statement Acceleration is not relative 
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#235
Feb2213, 02:48 PM

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#236
Feb2213, 08:22 PM

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#237
Feb2213, 09:06 PM

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I pointed out that earthbound experiments and specifically comparison of orbit versus hovering at an approximately constant distance from sun, and approximately constant distance from earth's center really are immune to substantial gravitational time dilation effects. The theoretical justification (nearly constant gravitational potential) need not be known to observe this fact. A stellar flyby is not so immune. I do think the idea of bounding this, and swamping it with very long 'near inertial' travel is valid. However, the flyby, taken by itself, is actually very substantially affected by gravitational time dilation, because you have rapid change of potential. For highly elliptical orbits, gravitational time dilation swamps SR kinematic effects. 


#238
Feb2213, 09:27 PM

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I am not making a claim that SR is inapplicable in every scenario where there is any gravity present. It is inapplicable in the twin paradox, for the reasons I stated above. 


#239
Feb2213, 10:40 PM

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I was only saying that that does not allow us, today, knowing that the kind of theory of gravity he was thinking of is *not* consistently possible, to say that his version of the twin paradox, with the traveling twin not feeling acceleration, can be explained "just by using SR". He thought it could, but today we know it can't. 


#240
Feb2313, 10:34 AM

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But this much I believe to be undeniably true of a purely SR treatment of a scenario in which two bodies, one inertial and the other noninertial, separate from each other and then approach to reunion: the noninertial body must experience unbalanced force at the transition from separation to approach. There is no other way for the period of separation to end. Therefore I agree with DaleSpam's statement in [my] bold, above. I think I understand the point that even if one posits that the noninertial twin reverses direction by "swinging around" a star, there must still be an unbalanced forcea nonzero reading on an accelerometer. The unbalanced force is due to the change of gravitational potential during the flyby. However, at this time I am unable to verify my understanding by calculation, so I have no actual opinion in the matter. I'm about ready to sign off this thread, as the question in the OP has been answered to the extent possible with my current knowledge. My response to George's concerns will be in a new thread, as it pertains specifically to the explanation of the twin paradox, rather than to the more general question of the relativity of acceleration. What have I learned? 1. Coordinate acceleration is relative; proper acceleration is not. 2. Proper acceleration may be experienced while at rest in a coordinate system. (This follows from 1.) 3. Loosely speaking, the experience of proper acceleration corresponds to the experience of an unbalanced force. I think this is in agreement with the definition of proper acceleration as the phenomenon that occurs when there is a nonzero reading on an accelerometer. However, I personally am not a fan of a definition of a fundamental physical phenomenon that requires the use of a mechanism. It seems to me that this leads to getting bogged down in the details of the design of the mechanism. I'd rather talk about the underlying phenomenon that the mechanism is intended to measure. In engineering, we are constantly aware of the difference between theory (the ideal) and practice (the inability to make actual conditions to correspond to the ideal). Defining proper acceleration as the reading on an instrument blurs that distinction, in my opinion. 4. Formally, proper acceleration is the derivative of proper velocity with respect to proper time. I have no idea how proper acceleration can ever be nonzero, because I cannot understand how proper velocity can ever be nonzero, if one defines proper time as the interval between two events at the same location. However, at this point in my education I am content to let this alone (for now). 5. From 3, only noninertial bodies experience proper acceleration. 6. In the twin paradox, only the rocket twin is noninertial. Therefore, the earth twin must have a straight world line in a spacetime diagram, and the rocket twin must have a bent worldline. By spacetime diagram I mean a diagram that charts the coordinate (Lorentz) transformation between inertial frames. I believe this is the same thing as saying Minkowski diagram. The design of the diagram does not allow a noninertial body to be represented by a straight worldline, nor does it allow an inertial body to be represented by a bent worldline. 7. Also from 5, and illustrated in 6, the rocket twin must experience less elapsed proper time than the earth twin; there is no treatment of the episode in SR that can result in the earth twin being younger than the rocket twin. 8. From all the foregoing (with special emphasis on 2), the "absoluteness" of proper acceleration does not contradict the claim of the rocket twin to be at rest throughout the episode. Therefore, the statement that proper acceleration is absolute does not have any "shocking" implications with respect to the general principle of relativity. 9. The case of the rocket twin at rest is treated in the Minkowski diagram. The typical explanation of the twin paradox does not draw attention to this fact, leaving some goodfaith objectors unsatisfied with the conclusion that the earth twin cannot be younger than the rocket twin. Further elaboration on this point will be given in the new thread that I intend to open; this will also be my response to George's concerns. 10. The discussion above is limited to the kinematics of SR. The essentially dynamic state of being noninertial is recognized in the solution of the problem, but it is not analyzed with respect to the laws of dynamics. 11. [edited for clarity] In my mind, 10 leads to a question. In the intuitive understanding of the universe, the Earth is absolutely at rest. The Earth, as it were, is anchored in place. The impression one gets from popular books on relativity is that the intuitive understanding of the universe may legitimately be claimed by any observer: Every observer may consider himself to be anchored in place. What are the implications of the rocket twin being anchored in place? Simply this: How is it that a force applied to the rocket causes the Earth and all the stars to move? Einstein's proposal is that a gravitational field is the cause. Granting that point for the sake of discussion, one must still ask how the rocket produces enough energy to accelerate the immense mass of the Earth and stars at the observed rate. [Side note: This objection was alluded to by harrylin at one point in this discussion. I believe it is at the root of his claim that few physicists these days accept the idea that the rocket is "really in rest". I find it interesting in this regard (without drawing any conclusions) that DaleSpam says that most physicists these days tend to leave the question of the gravitational field in SR alone.] Please understand that I am making no claim regarding the validity of the principle of relativity. I am merely stating the question that I wish to be able to answer, and wish (eventually) to be able to verify by calculation. 


#241
Feb2413, 07:39 AM

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Here is a link on covariant derivatives: http://en.wikipedia.org/wiki/Covaria...ve_along_curve It is closely related to the concept of parallel transport: http://en.wikipedia.org/wiki/Parallel_transport And the concept of a connection: http://en.wikipedia.org/wiki/LeviCivita_connection Sorry about the hardtodigest math. It is the price you pay for getting rid of the accelerometer definition. It doesn't add anything new (so feel free to skip it until you are ready for GR); it just defines it mathematically instead of physically. Personally, I prefer the accelerometer one for precisely reasons that you find objectionable. One problem with defining terms in general is that since there are always a finite number of terms you must always either wind up having circular definitions or undefined terms. In physics, we get around that by defining some terms experimentally. Proper time is the thing measured by a clock, distance is the thing measured by a rod, proper acceleration is the thing measured by an acclerometer. That accomplishes two things, first, it makes the link between the mathematical theory and the physical world more clear, and second it avoids the problem of leaving those things undefined. So, I personally prefer those kinds of "measurement based" definitions of fundamental quantities, but I recongnize that is a personal preference and alternative equivalent definitions are possible which hide the problem by pushing the measurements further away or embrace the problem by leaving some things completely undefined. So what does cause the Earth to move? The answer is that specific choice of noninertial coordinates. That choice of coordinates implies that the Earth moves, regardless of the presence or absence of any rockets with any forces. Every time you use that choice of coordinates the Earth moves. So the choice of coordinates causes the Earth to move, not the rocket. 


#242
Feb2413, 09:11 AM

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My initial reaction is: Nonsense. I'm sitting at rest in my rocket the whole time. Don't tell me about choosing coordinate framesthere is only one coordinate frame that matters: mine. (Isn't that the meaning of "absolute space", or "anchored in place"?) When I throw a ball, its acceleration (with respect to the only coordinate system that matters) is determined by its mass and the magnitude of the applied force. When the earth and the stars move, the same law should apply. {Edit: Not exactly the same law. I realize that gravity will cause coordinate acceleration without applied force. But the moving Earth and stars have acquired kinetic energy with respect to the rocket. That energy must have come from somewhere.} A secondary (and less emotional) reaction is to ask the original question in a more precise way. What causes the spacial displacement between the rocket and the Earth to change? 


#243
Feb2413, 09:35 AM

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It seems to me you guys are just playing with words  proper, real, coordinate. Try defining them before hitting one another on the head with them! I always thought position was x,y,z  whatever they are, they are relative. And velocity is their first differential with respect to time  so is relative. And acceleration is the second differential of relative things  so is also relative. Yes you can invent a special acceleration and use the word "proper" for it. But how can you MEASURE it in an experiment? As for "force" it can never be applied to anything without that thing witstanding it (unless it fractures) Hence "action and reaction are equal and opposite" whether acceleration results or not. So the net force at an SURFACE sums to zero! As for the idea of force "applied at the centre of an object" there is no way to measure it except by the ASSUMPTION that force is mass times "acceleration" When I stand here on the floor, my acceleration is 32 ft/sec^2 and it is as simple as that! No need to dream up "force" at all. All we need is the upward acceleration required to cancel my downward acceleration. Fortunately my brain is well used to providing this acceleration. 


#244
Feb2413, 09:49 AM

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#245
Feb2413, 09:55 AM

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#246
Feb2413, 11:30 AM

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In relativity, the primary thing is not a position, but an event, a point in space and time. So "the top of the Eiffel tower when Michelle Obama went up it" is an event, and it's absolute. But if I try to describe it using 4 numbers, for example, (latitude, longitude, altitude in meters, time in seconds since 1900), its description is relative to a coordinate system. A spacetime path, giving the events that a traveler passes through, as a function of the time on his watch, is an absolute thing, because each event is absolute. But to describe the path as a set of 4 functions [itex]x(\tau), y(\tau), z(\tau), t(\tau)[/itex] is relative to a choice of a coordinate system. The proper velocity of a path is again an absolute thing, while the components of the proper velocity are relative to a coordinate system. Proper acceleration is an absolute thing, while its components are relative to a coordinate system. 


#247
Feb2413, 12:11 PM

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#248
Feb2413, 12:35 PM

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#249
Feb2413, 12:38 PM

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The earth is a 3D object, while space is 4D in the modern way of looking at it. 


#250
Feb2413, 12:42 PM

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You give away the problem with the position you are trying to take when you say "not exactly the same law". That's just the point: if you want "the laws of physics" to be "the same" in all reference frames, so that you can always view yourself "at rest", then the laws of physics have to include counterintuitive things like the Earth and the stars changing direction and speed just because you fired your rocket engine. If you want the laws of physics to always look simple, then you have to restrict yourself to frames in which they look simple (because all the counterintuitive stuff cancels out in those frames). You can't have it both ways; you can't have both simplelooking laws *and* a free choice of frames; your choice of frames determines how simple the laws look in the frames you choose. 


#251
Feb2413, 01:00 PM

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Furthermore, I believe that the rocket twin will deny what you say about "path", and all that follows from it. See below. At each iteration of my clock, I place a monument. I inscribe on the monument the time as read from my clock. I also consult my accelerometer to determine (some calculation is necessary) the change in my orientation since the previous iteration. I inscribe the differential change in orientation on the monument that was placed at the previous iteration. The change in orientation is necessarily expressed as rotations about the axes of the arbitrarily chosen coordinate system. Finally, I take my measuring rod and place its end against the previously placed monument; I then read directly the distance traveled since the previous iteration. I write that distance on the previous monument. Thus, my friend can follow my path without a map (coordinate system) if he starts at the first monument, adjusts his orientation as directed, and travels the distance indicated. At each monument, he repeats the process. All of that is well and good, if one accepts the premise that I am moving through space. But, if you will recall, I am that very obstinate occupant of the rocket who insists that he is not moving at all. In my world, there is only one monument, and my orientation does not change. 


#252
Feb2413, 01:24 PM

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On a piece of paper, you draw a dot. That dot is a unique location on the piece of paper. You don't need coordinates to know that it's unique. You don't need coordinates to know whether the dot is at the same location as the X that someone else drew on the paper. A path through spacetime is a 4D analogue of a curve drawn a piece of paper. An event in spacetime corresponds to a point on the paper. A velocity of a path corresponds to the slope of the tangent line drawn through a curve. Now, you can certainly choose a coordinate system so that the spatial coordinates of the second event are the same as the spatial coordinates of the first event. But there is no way to choose coordinates so that all coordinates are the same. There is no way to avoid having motion in spacetime. 


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