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My idea of explaining time dilation to others (average people) was : see a light wave as the time, person A standing still sees the time (light wave) passing, person B moving sees lesser time passing when going in the direction of the light wave (while "looking" to the light wave) because he is moving.

Ok, you can tell this but you have to proove if you are right.

So, I started my topic, https://www.physicsforums.com/showthread.php?t=536987" , consider only answer #11 with picture, answer #18 (ignore formula Lorenz, was wrong), and last answers from #39 (rest is nonsense because of mistakes).

So I show person A was predicting a time dilation without Lorenz (by measure the total length of the passing light wave in his rest frame, ΔXa_light, for himself and thinking for person B, ΔXb_light).

Person A calculated the next formulas :

ΔXb_light = ΔXa_light . (1 - V/C).

ΔTb_light = ΔTa_light . (1 - V/C).

Let's see how formula's are after Lorenz, by making an equation for the lightspeed in the rest frame of B (only the line c can be converted from restframe A to B, no other speedlines, than Lorenz goes wrong).

I found : (no mistakes this time)

ΔXb_light = γ . (ΔXa_light - V/C . ΔXb_seen_from_a).

ΔTb_light = γ . (ΔTa_light - V/C2 . ΔXb_seen_from_a) ... or ... ΔTb_light = γ . ΔTa_light . (1 - V2/C2)

In both formula's is clear to see that the length of the passing light wave (and time) is depended from ΔXb_seen_from_a (movement person B) in a way liking on person A it saw (so the prediction by A was right).

Question: have I now the facts to explain time dilation in this way ?

Ok, you can tell this but you have to proove if you are right.

So, I started my topic, https://www.physicsforums.com/showthread.php?t=536987" , consider only answer #11 with picture, answer #18 (ignore formula Lorenz, was wrong), and last answers from #39 (rest is nonsense because of mistakes).

So I show person A was predicting a time dilation without Lorenz (by measure the total length of the passing light wave in his rest frame, ΔXa_light, for himself and thinking for person B, ΔXb_light).

Person A calculated the next formulas :

ΔXb_light = ΔXa_light . (1 - V/C).

ΔTb_light = ΔTa_light . (1 - V/C).

Let's see how formula's are after Lorenz, by making an equation for the lightspeed in the rest frame of B (only the line c can be converted from restframe A to B, no other speedlines, than Lorenz goes wrong).

I found : (no mistakes this time)

ΔXb_light = γ . (ΔXa_light - V/C . ΔXb_seen_from_a).

ΔTb_light = γ . (ΔTa_light - V/C2 . ΔXb_seen_from_a) ... or ... ΔTb_light = γ . ΔTa_light . (1 - V2/C2)

In both formula's is clear to see that the length of the passing light wave (and time) is depended from ΔXb_seen_from_a (movement person B) in a way liking on person A it saw (so the prediction by A was right).

Question: have I now the facts to explain time dilation in this way ?

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