- #51
digi99
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So finally my summary.
The formula I found in my first topic (already a problem in many forums) (1 - V/C) . t before Lorentz and γ . (1 - V/C) . t after Lorentz was correct, for a light wave. The meaning lies in the relativistic Doppler effect, but it does not mean it can be have a second explanation. You could think in frame A is the prediction for the time dilation (1 - V/C) . t, in reality it's a factor γ bigger. The formula Lorentz came with, is dificult to show in little pieces with a formula like mine, otherwise you could found 1 / γ too, with the math integration function. So even if you see in many little pieces (1 - ΔV/C) . Δt you will not find 1 / γ. So for an easier explanation for the time dilation, you may not use it in this way, but you may use the traveled path of the light wave 1 / γ. That the length of a piece of lightwave would be γ has not a special meaning, because it is the length of a moving object, not measured while standing still. You could say the coordinates c (as used by DaleSpam) go after transformation to γ . c. But the path of a traveled lightwave c . t goes to c . t', so the lightwave will going smaller in size like all other objects in frame B (B is moving in frame A), t' = 1 / γ . t and x' = 1 / γ . x.
When something moves it will not going smaller to 1 / γ (and lower time) for us, but for the moving object itselves in his rest frame. But we calculate that length and time dilation for corrections, the moving object itselves in this own rest frame is not aware of this changes. Some thinks, a time must be corrected (my confusion in the beginning) by Lorentz, yes that's
true but not the time we meassure in our frame for the moving object, but the time of the moving object in his own rest frame.
Now my reformulation to explain time dilation easier for others (I think) on my website or in fact exactly what it is (maybe still difficult, but a confusing drawing does not make it more simple). My goal is to understand (general) relativity and all related topics (parallel universa etc.) but to give it through to others in a simple way (e.g. when I die my knowledge is gone, what's the point of knowing that difficult knowlegde only for myself). Time dilation is the very basic term to understand first.
In my explanation on my website I will first start about light and relation (relative) time and distance etc. before I explain next:
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First an explanation for a normal object, different than light.
Consider a passing train. If you are standing still, count the meters train passing with a special device developed for it for e.g. about 5 seconds. Now walk with a constant speed in the driving direction of a train and count with that device again for the same period, so 5 seconds in this case. Because you are moving you will count lesser meters (in fact your own
movement lesser).
Light presents time and distance in the most exact way by nature. At any moment by nature traveled distance / time = always the lightspeed c, so just nature, nothing to understand only to accept. So light is the most exact clock existing, so the length of the path of a traveled light wave can be recalculated to time passed. Every clock can meassure time, but all clocks needs corrections, light is the onliest exact clock by nature (in fact it defines relative time).
Consider a passing light wave in mind as the passing (relative) time. If you are standing still, after the same 5 seconds as for the train, the passing light wave is in distance c . 5 meters further. Now walk with the same constant speed in the direction of the light wave, the light wave seems to go slower for you in mind but by nature at any moment the speed must be
the same c, so this will only be possible when time and traveled distance of the light wave is going smaller for you (light wave is going smaller). Compared to standing still, the light wave has traveled in the same 5 seconds, lesser distance while moving. So the lesser distance represents lesser time. So compared to standing still, the 5 seconds while moving takes lesser time. So while moving time is going slower, 1 second moving goes slower than 1 second standing still. A clock represents the same time, so a moving clock goes slower. The difference in time (expressed in time while standing still), is called time dilation. It's only to accept nature, nothing more. But you are not aware of the slowing going time. Like the light wave is going smaller, everything is going smaller for you while moving in the same ration. Again just nature. In physics by formula is the passing time t' while moving equal 1 / γ . t (t is the passing time while standing still, γ is a calculated constant factor but 1 / γ is always lesser 1).
Maybe not exactly true, but easy to remember :
See a passing light wave as the (relative) time passing, if you move in the direction of that light wave it goes slower for you, so (relative) time goes slower.
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Ok, some will say, turn the direction of the train. You may not compare this (and in fact, you use not the most difficult explanation) because a train has not the same speed at any moment while you are moving, that's something extra's. Some will say, turn the direction of the light wave, that will be exactly the same but more difficult to understand, a movement gives a time dilation, but the direction of a movement is not important only the positive value in meters of your movement, time can't be negative (maybe a time dilation can when a speed can be greater than c somewhere proved in the future, in that case you will be going faster older I guess but not going back in time).
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