What is the Relationship Between Track Growth and Universe Expansion?

[Treval]

referring to:


0:59

factors:

- you are on a 100 meter track
- person A walks towards you
- person A takes a 1 meter step every second
- track grows longer as person A walks
- track grows 1 meter for every 100 meters every second
- after 10 seconds, the walker has taken 10 steps, but the remaining 89 meters has grown so that he still has 98 meters from you
- another 10 seconds and he still is almost 97 meters away
- It will take him 460 seconds to reach you; during this time, the track is stretched so that it's now 10000 meters long.

My questions are:

- I don't understand how he becomes the result '98 meters away from you'. In my reasoning, track grows up to 101 meters because the track itself is already 100 meters.
Perhaps I'm wrong?

- What exactly does he mean by "the track grows 1 meter for every 100 meters every second"?

- How does he conclude that person A needs 460 seconds to reach me?

- How does he conclude that the track has grown 10000 meters long?


Many thanks for your cooperation.

Regards,
Treval

 

[Orion84]

The track grows 1 meter for every 100 meters every second means that for every second that passes during Person A's walk, the track stretches by 1 meter for every 100 meters of existing track. So if we were to start with a 500 meter track, after one second the track would stretch 5 meters, so it would be 505 meters. One meter for every hundred meters. Once the track reaches 600 meters, it will then be stretching at a rate of 6m/s. Unfortunately I royally suck at math, so I can't help with question 2 or 3.

Hopefully that helped.

Chris

 

[Chalnoth]

The primary answer is that the track is stretching the entire time, so you basically have to use calculus to compute how the rate of movement of the person is impacted by the rate of expansion of the track.

 

[Chronos]

You might be interested in a paper by Lineweaver and Davis:
"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe"
http://arxiv.org/abs/astro-ph/0310808