
#199
Sep1811, 05:36 AM

P: 152

http://www.eduobservatory.org/physi...l#Twin_paradox which states that: "The socalled “twin paradox” occurs when two clocks are synchronized, separated, and rejoined. If one clock remains in an inertial frame, then the other must be accelerated sometime during its journey, and it displays less elapsed proper time than the inertial clock. This is a “paradox” only in that it appears to be inconsistent but is not. " Now if people keep saying acceleration has anything to do with the elapsed time, it will confuse people... I do not know if this is the case this time... The link is actually referencing to jour example: "“Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” " 



#200
Sep1811, 06:32 AM

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The acceleration does not directly affect time dilation. It only breaks the symmetry between the twins. There is nothing wrong with mentioning acceleration, because the broken symmetry is important (even though by itself it does not affect time dilation).




#201
Sep1811, 08:45 AM

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Two clocks set up to accelerate uniformly such from the view of the (e.g.) the back clock the distance between the clocks remains constant. There will be a clock rate difference proportional to the distance between the clocks and the acceleration, as if in a uniform gravitational field. However, in an inertial frame, the above requirements lead to observation that the clocks get closer together, do not have identical acceleration or velocity, and that the velocity difference accounts for the difference in clock rate. 



#202
Sep1811, 09:38 AM

P: 152





#203
Sep1811, 10:22 AM

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One key point is that if the distance remains constant from the point of view of the back clock, then length contraction demands that the two clocks get closer and closer in the inertial frame (as the back clock goes faster and faster). This requires that their speeds cannot be identical in the inertial frame. Thus two different explanations of the same observations: (pseudo)gravitational potential difference in the accelerating frame, simple difference in speed in the inertial frame. 



#204
Sep1811, 12:17 PM

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"Let's say this train accelerates further to c. Now SR predicts time stops and in my view there no longer is an angle that will allow the observer to point towards the spot on the wall. With time stopped it seems difficult to move, but in my view nothing changes." This is an incorrect understanding of SR. As I said earlier, no matter how much the train has accelerated, it still is just as far from c as before it started. SR makes no prediction that there is any condition in which time stops. Rather, it states that time will be completely normal for any train, it never slows down or speeds up or stops, no matter how it has accelerated in the past. 



#205
Sep1811, 03:11 PM

P: 19

[QUOTE=ghwellsjr;3508992 As I said earlier, no matter how much the train has accelerated, it still is just as far from c as before it started. SR makes no prediction that there is any condition in which time stops. Rather, it states that time will be completely normal for any train, it never slows down or speeds up or stops, no matter how it has accelerated in the past.[/QUOTE]
According to my starting FoR, which I didn't change, you are wrong. 



#206
Sep1811, 05:35 PM

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#207
Sep1811, 06:19 PM

P: 472

Well where do you draw the line, at which point do you decide where tidal(spagetiffication) forces and gravitational effects are distinct and apart. 



#208
Sep1811, 06:25 PM

P: 472

How do accelerate a sample without making it move. 



#209
Sep1811, 07:07 PM

P: 152

The acceleration goes as (v^2)/r. 



#210
Sep1811, 07:52 PM

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#211
Sep1911, 04:55 AM

P: 1,414

But let me try to think through this out loud. The general form of the Lorentz Factor, γ = (1  v^{2})^{1/2}, remains unchanged wrt acceleration. The value of the Lorentz Factor is directly affected only by the speed at which an oscillator is moving. So we can say that the period of an oscillator is directly affected only by the speed at which the oscillator is moving. The faster(slower) an oscillator is moving, the greater(lesser) its period, and the lesser(greater) its frequency. However, the speed at which an oscillator is moving is a direct effect of the oscillator's most recent acceleraton (assuming that the oscillator's speed hasn't remained constant throughout its entire history). That is, when the speed of an oscillator has changed during a certain interval, then we call the rate of change during that interval an acceleration. (Although an oscillator can presumably be accelerated, by changing its direction of motion, without in any way changing its speed, we're only concerned with the component of velocity that has to do with the oscillator's speed. And, a change in speed refers to, by definition, an acceleration.) I'm assuming that changes in either the rotational radius of the samples, or the RPMs of the samples isn't done on the fly. Otherwise, there are obvious accelerations involved. (Ie., if the arm is extended/retracted while keeping the RPMs constant, or if the RPMs are varied while keeping the rotational radius constant.) I agree that the experiments you mentioned do show that the general form of the Lorentz Factor is unaffected by acceleration. What I'm wondering about (with the understanding that the quantity of differential aging is a function of the time during which an oscillator is propagating at a certain speed), is when the change occurs wrt an oscillator whose frequency has been altered  as it seems obvious that it can't be occuring while the oscillator is propagating at a constant speed. It follows that the changes in oscillator frequency must be occuring during intervals of acceleration. Which means that speed accelerations/decelerations do directly affect (produce changes in) the periods of oscillators. Thus, acceleration (involving variations in speed) affects time measurement. 



#212
Sep1911, 05:32 AM

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#213
Sep1911, 12:52 PM

P: 1,414

Wrt differential time measurement, it's the accelerations that involve changes in speed that we're concerned with. But, again, a change in speed is, by definition, an acceleration. And time measurement depends on speed. Therefore it's incorrect to say that changes in the rate of time measurement don't depend on acceleration. It's just a semantic thing that needs clarification. By the way, thanks also for your feedback on my previous concern. Since I don't have a mechanistic theory of relativistic differential time measurement to refer to (the extant ether theories aren't quite what I had in mind), then I'm left with the geometric account. 



#214
Sep1911, 01:06 PM

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P: 4,521

Consider a traveling twin that doesn't just decelerate to a stop at the turnaround point and then accelerate back to the home twin but rather maintains a constant speed and makes a loop back to turn around. Now he has never changed speed but he has accelerated. Or consider Einstein's original introduction of the Twin Paradox in his 1905 paper in which one clock takes a circular path away from the inertial clock and every time it comes back, it has accumulated less time on it. 



#215
Sep1911, 03:44 PM

P: 133





#216
Sep1911, 05:04 PM

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P: 16,473

Do you know the difference between a partial derivative and a total derivative? When scientists say "X doesn't depend on Y" what they generally mean is [itex]\frac{\partial X}{\partial Y}=0[/itex]. Basically, this means that X does not change if you change Y without changing anything else. So if X is a function of Y and Z then the partial derivative of X wrt Y is obtained by keeping Z fixed. So, the type of centrifuge experiment described by Janus above is exactly the kind of experiment that would be used to investigate this type of dependence. That way you could change accelerations without changing speed and obtain [itex]\frac{\partial \gamma}{\partial a}=0[/itex] indicating that time dilation does not depend on acceleration, in the meaning intended by scientists. 


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