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View Full Version : Is this at all a good analogy for special relatavistic time dilation?

WaxRubiks
2019-Jan-23, 01:23 AM
Is this anything like a good analogy for how special relativistic time dilation works?

Imagine a very wide, and long van, with the back compartment(say 20meters wide and 20 meters long) lacking a floor, and has large transparent perspex windows in the walls.

In this back compartment sits a guy on a motorbike, which is resting on the ground, like the van(say a salt flat somewhere in the world). This motorbike has Tron like abilities to just bounce(reflect) off the inner sides of the van.

The motorbike starts moving and quickly gets to 20kmp, its maximum speed.

The guy on the bike is charged with the task of going between the sides of the van in a short a time period as possible, so as the van is stationary he is travelling perpendicular with the walls of the side of the van.

Then the van starts to accelerate. and when it gets to 10kmp, the motorbike has to travel in a diagonal(45degrees), as seen by an observer(O) standing outside the, but is still moving perpendicular with the sides of the van according to the driver(D) of the van looking in his mirror.

and as the van keeps accelerating, the motorbike has to take an increasingly deeper diagonal path, according to O, but is still moving perpendicular to the sides of the van, by D.

As the van's speed increases, and the bike takes a deeper and deeper diagonal path according to O, the time it takes to get from side to side of the van increases.

And as the van gets to 17kmp, and then 18kmp, and then 19kmp, the bike is nearly travelling parallel to the van, and is taking a long time to get from side to side of the van.

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So if you compare the bike to the path of a photon, and take the bike and the walls of the van, as a clock that always keeps time according to the driver(D)......well something like that..!

If the driver measures 1 second as the time it takes to get from one wall to the other side, but the observer measures time according to the speed he sees the motorbike travel 20meters, then perhaps it shows that the driver is taking longer to measure one second, than the observer...

So is that at all a good analogy with special relativities time dilation?

If it is, I guess it is just a reworking of what I have read, to help me understand it....

WaxRubiks
2019-Jan-23, 01:31 AM
that leads me to ask where there is such a thing as length elongation under acceleration in SR?
If the van is accelerating, then the motorbike has to take a curved path to keep up with the van, and the path will measure longer for the observer(O), than the driver(D), which might be seen as length elongation(opposite of length contraction).....if the same applies to light...?

or maybe as the bike is travelling perpendicular to the walls, then it is a width elongation..?

edit: maybe I should have put this in Q&A...

edit2: oh, I think I get it.....is it a rotation as seen by O? I think I have read about SR rotation....

grant hutchison
2019-Jan-23, 09:15 AM
So, basically, you're trying to reproduce the "photon in a mirrored box" thought experiment using a motorcycle-in-a-van thought experiment instead of the swimmer-and-two-rafts thought experiment?
It seems ... elaborate.

Grant Hutchison

Swift
2019-Jan-23, 02:12 PM
Moved from OTB to S&T

Hornblower
2019-Jan-23, 04:35 PM
No, I don't think this is a good analogy to the high speed case with a photon where SR effects are significant. While it is true that the lateral component of the cyclist's motion slows down as the van goes faster, the observed change is the same for both O and D. In addition the van can go faster than the cyclist's top ground speed and simply leave him behind. All of this can be analyzed in Newtonian mechanics at these low speeds.