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Implications of the statement Acceleration is not relative 
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#253
Feb2413, 01:39 PM

P: 221

When I throw a ball in SR, its motion is indeed determined purely by its mass and the force I apply. It does not return. It continues to move forever at some constant speed. That is how it seems to me. I don't really have the right to speak on the matter because I do not know anything about Christoffel symbols, and therefore cannot understand the line of reasoning taken by DaleSpam. It is much better for me to leave this alone for the time being. I only mentioned it in my summary because it is an outstanding issue that must eventually be addressed. 


#254
Feb2413, 02:10 PM

Physics
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P: 6,274

The laws in question are the simple laws of flat spacetime. You already know them in an inertial frame. The talk about a "gravitational field" that appears when you choose noninertial coordinates, or about the movement of the Earth and stars being caused by the choice of coordinates, is just a way of describing the fact that noninertial coordinates make the laws look more complicated. This is one way that trying to choose a frame in which you are always at rest, when your motion is noninertial, makes the laws of physics look more complicated: the laws of physics now have to include the possibility of "motions" that violate the usual rules of causality. The example Einstein used was rotation: if I consider myself, sitting here on the surface of the Earth, to be "at rest", then the stars must be moving around me faster than the speed of light. But nothing can move faster than light! you say. Correct: but the "motion" of the stars due to my rotation is not a "real motion" that is subject to that law. The complete laws of physics in my "rest frame" now have to include the possibility of "fictitious motions" like the motion of the stars around me, or the motion of the stars in response to you firing your rocket engine, which can be faster than the speed of light and which can stop and start "instantly" if I change my state of motion, even though that "violates" causality. Once more, you can't have it both ways. If you want simple, intuitive laws of physics, where there are no "fictitious motions" or "fictitious forces", you have to pick a reference frame that allows the laws to look that simple. If you insist on picking a frame where you are always at rest, even when you move noninertially, the laws will not look simple in that frame. You can't avoid that tradeoff. 


#255
Feb2413, 03:40 PM

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P: 17,569

However, what we can do with current tecnhology is to take modern clocks and make them so incredibly stable and accurate that we can measure relativistic effects with ordinary velocities. I.e. whether or not a velocity is "relativistic" or not depends on your sensitivity, and modern clocks are so exquisitely sensitive that we can measure relativistic effects at walking speeds. 


#256
Feb2413, 04:10 PM

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#257
Feb2413, 10:54 PM

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P: 2,215

[itex]m \dfrac{dV^\mu}{d \tau} = F^\mu[/itex] where [itex]V^\mu[/itex] is the 4velocity. When you use noninertial or curvilinear coordinates, the relationship between applied force and coordinate acceleration is more complicated: [itex]m \dfrac{dV^\mu}{d \tau} +[/itex]fictitious force terms [itex]= F^\mu[/itex] So even when the applied force [itex]F^\mu[/itex] is zero, the coordinate acceleration [itex]\dfrac{dV^\mu}{d \tau}[/itex] can be nonzero due to "fictitious force" terms. Examples of such fictitious forces are the "g forces" due to acceleration, the "centrifugal force" and the "coriolis force". These "forces" are not due to any kind of physical interaction, but are artifacts of your choice of coordinate systems. 


#258
Feb2513, 02:12 AM

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#259
Feb2513, 02:19 AM

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#260
Feb2513, 02:34 AM

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#261
Feb2513, 03:04 AM

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#262
Feb2513, 06:34 AM

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P: 17,569

Yes, SR does predict that. According to SR the proper acceleration is:[tex]a^{\mu}=\frac{d^2x^{\mu}}{d\tau^2}[/tex]Where x is the worldline in an inertial frame and τ is the proper time along that worldline. That quantity is nonzero. 


#263
Feb2513, 06:40 AM

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#264
Feb2513, 06:56 AM

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#265
Feb2513, 07:01 AM

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#266
Feb2513, 07:15 AM

P: 3,188

Promised thread started here: http://www.physicsforums.com/showthread.php?p=4284966 


#267
Feb2513, 07:25 AM

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#268
Feb2513, 07:30 AM

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#269
Feb2513, 12:43 PM

P: 24




#270
Feb2613, 03:21 AM

P: 3,188

 http://en.wikisource.org/wiki/The_Fo...itypostulate. 


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