# Here's why your statement doesn't work..

by Walrus (no login)

To make it easy, lets work with kilometers instead of miles. So, if I understand you correctly, you're saying that if a small train (lets say 4 km, with the passenger sitting right in the middle) is going 50% the speed of light, the light from the lightning near the back is going to move so quickly it won't be noticeable to the passenger, however if you increase the train's speed to nearly the speed of light while keeping the size of the train (which in this example corresponds to the distance between strikes) to 4 km, then eventually you reach a speed where it becomes noticeable to the passenger. This however, is untrue.

The reason that doesn't work is because you have a law of diminishing returns working against you. Lets say you're moving at 99.99% the speed of light. Well at that speed it only takes the light from the second flash of lighning .1 "earth second" to reach the passenger (at a distance of little over 2 km), so instead let's say the passenger is moving at the incredible speed of 99.9999% the speed of light. Now it takes 10 "earth seconds" for the passenger to see the second lightning strike, which is a very noticeable amount of time, except for one thing. That's time relative to the earth, but the passenger is moving so quickly his time is a lot slower. In passenger time, those 10 seconds are a mere .14 seconds. Faster you say? Ok, let's say the passenger is moving at 99.99999% the speed of light. It now takes 100 "earth seconds" for light from the second lightning bolt to reach him, which corresponds to .0447 "passenger seconds".

It's obvious that increasing speed from here on out is just going to warp the passenger's sense of time so much that no matter how many "earth seconds" it takes for the light to reach him, he'll never notice the difference. There is obviously a peak in there somewhere though. I don't know what it would be (it may be interesting to calculate what it would be though), but I'd be surprised if you could find a speed where "passenger time" would be greater than 1 second, which, if you found a speed that would allow a 1 second gap between flashes, that'd certainly qualify as "noticeable", but by increasing the distance between flashes, the gap in times can become much greater than 1 second (minutes, hours, days), while increasing speed causes the time difference to peak and then start to decrease again.

Posted on May 4, 2005, 3:40 PM

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 Response Title Author and Date * note, this is all assuming i'm calculating correctly :-) Walrus on May 4 by the way, here's the calculation i'm using to determine the amount of change in time Walrus on May 4 Well, to me, the peak seems to be the highest possible value. Am I doing something wrong? Michael Calkins on May 4 Re: Well, to me, the peak seems to be the highest possible value. Am I doing something wrong? Walrus on May 4 Thanks for the help. I made improvements, but something still seems wrong. Michael Calkins on May 5 Re: Thanks for the help. I made improvements, but something still seems wrong. Walrus on May 7 *ok Michael Calkins on May 7

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