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What does the Lorentz factor actually mean? 
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#19
Nov612, 05:51 PM

P: 181

I suppose we can extend my definition a bit more and say:
This includes the possibility that the velocity is 0, in which case, the Lorentz factor will be 1. Does that sound more like it? 


#20
Nov612, 05:59 PM

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P: 4,781

It's between one observer and one reference frame. Please go back and read my posts. 


#21
Nov612, 09:44 PM

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If I were going to talk about the meaning of the Lorentz factor as something different from its definition then I would talk about its derivation, not its applications. 


#22
Nov712, 12:29 AM

P: 181

Let me know where specifically you are disagreeing on this. 


#23
Nov712, 01:22 AM

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#24
Nov712, 02:23 AM

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P: 4,781

Do you see that the Proper Time for each observer can be easily calculated from the formula no matter what the speed is? And do you see that a coordinate frame does not require any observer to be stationary nor does it require any particular number of observers, not even one? Finally, do you see that if you use a definition for the Proper Time (or for time dilation) that does not include a specified coordinate frame, but rather is just between two observers, then it won't work because whatever you say about the passage of time for one of them with respect to the other one can also be said about the two observers if you interchange them and that would create a dichotomy. You can't say that the ratio of the times between A and B is the same as the ratio of the times between B and A unless both ratios are one. 


#25
Nov712, 02:40 AM

P: 181




#26
Nov712, 03:01 AM

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#27
Nov712, 04:33 PM

P: 181




#28
Nov812, 12:59 PM

P: 421

In the U frame of reference, one unit of time is defined as the distance light moves from the origin to a mirror m located perpendicular to the x axis and return. If the light source is not moving, the distance is 2d for 1 time unit. Observer A moves a distance (a) while a light wave composed of multiple photons, moves from the origin a distance d. Because light speed c is constant and independent of the source, the Aclock photon must have an x component equal to (a) to compensate for A's motion. The p component becomes the active part of the Aclock. Since p is less than d, the photon will move a greater distance to reach m, resulting in a tick rate less than that for U. The clock photon for B will have a greater compensating component b, and thus a smaller active component q, resulting in a tick rate less than that for A. The tick rate is a nonlinear function of (clock speed)/(light speed), or v/c, with each observer clocking a different photon. The observer is not aware of his slow clock rate, because all processes involving photon interaction, including biological/(chemical) are also ocurring at the same rate, i.e. his perception is altered. Gamma(the Lorentz factor) equals d/(the vertical component) with v/c substituted for (the x component)/d. Gamma for A = d/p with v/c substituted for a/d. The 't' factor has been omitted, because it is common to each vaiable and d, and to emphasize that the clock is in fact counting distances. Attachment 52787 


#29
Nov812, 01:43 PM

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P: 4,781

Your diagram and explanation are very difficult to follow.
I think what you have discovered is that if we plot the reciprocal of gamma as a function of normalized speed, we get a quarter of a circle. I made a similar plot some time ago to show the normalized age of the traveling twin (compared to the stationary twin) as a function of normalized speed (beta): This was discussed in this thread, as well as others. Although your plot might also describe the relationship of 1/gamma to speed, it is not labeled as such and has no discernable connection to a light clock, at least as far as I can understand. Maybe you could explain it some more and show how it relates to your diagram. 


#30
Nov812, 03:10 PM

P: 848




#31
Nov812, 07:47 PM

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What, no picture?



#32
Nov812, 09:40 PM

P: 848




#33
Nov1212, 11:30 AM

P: 421

This post is intended to explain gamma/(the Lorentz factor) in terms of physical
processes and minimal math instead of theoretical statements. The light clock consists of an integrated light emitter/detector, and a mirror, separated by a rod of length r. The clock counts a unit of time (t=1 tick) when a photon moves the length of the rod to the mirror, and returns to the detector. There are two observers, U who is not moving, and A who is moving at .6c relative to U on the Ux axis. Each has a copy of the clock with the rod oriented perpendicular to the x axis. Since the outbound path equals the inbound path, we only need to consider the first path. With U and A at the origin, each clock emits multiple photons (shown as a blue quarter circle because object motion is restricted to the +x axis.) For U the photon moves a distance r (.5 tick). For A the intersection of the circular arc and rod determine which photon becomes part of the clock. [1]The photon path ct can be resolved into the vt component which compensates for the motion of A and the st component which is the active part of the clock. When a photon arrives at the U mirror, the A clock photon has not reached the mirror because the photon speed relative to the rod is s. If r' equals the path length to the mirror for the A photon, then t'/t = r'/r = c/s = gamma. [1] A vector can be expressed in components suitable for the situation. Attachment 52882 


#34
Nov1212, 12:15 PM

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P: 4,781

Your problem is that you claim that there is something significant when a photon hits the moving rod at the 80% mark. In fact, there are photons hitting both rods all along their trips to their respective mirrors. So what? There is no significance to the fact that a photon hits a rod at any particular time. What matters is when a photon hits the moving mirror, which you don't show. If you would continue the diagonal line up to the location of where the mirror would be when it hits it and then measure the time it takes for the photon to hit the mirror, you would see that it take 1.25 times as long as it takes for the photon to hit the stationary mirror which gives the correct illustration "in terms of physical processes". 


#35
Nov1412, 01:41 PM

P: 421

a greater speed, a greater angle and a lesser s. The drawing is intended to show why 1 tick for the A clock is longer than 1 tick for the U clock for the general case, which it does. The reason is the constant and independent speed of light. The degree of dilation is a function of v/c. If the path is extended, it will not show anything new. Gamma is still the ratio c/s or (A time)/(U time). 


#36
Nov1412, 04:42 PM

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