Exploring Relativity: Bert's Trip to Alpha Centauri

[zambi]

Hello! I have looked at this forum a number of times but haven't been quite able to understand something. I took intro physics in college and although I accept the theories of general and special relativity, I never quite understood *why* some aspects of it work.

Please bear with me--I'll use an example similar to some that I've read.

Suppose Bert is traveling toward Alpha Centauri at near the speed of light (c). Let's say his velocity is 0.999c. Bert's friend Ernie is waiting back at Earth for Bert's return. Alpha Centauri is about 4.37 light years from Earth. So, from Ernie's perspective, it takes Bert nearly 8.75 years to travel to and from Alpha Centauri. However, from Bert's perspective, the trip only takes less than 5 months.

I understand and believe that this is true, but I have a question. If Bert is traveling at 0.999c, how does he travel that distance (8.269X10^13 km) in less than 5 months? Does the distance change from Bert's perspective? If not, I don't understand how he travels that distance in that time. I know it must be something simple that I am missing, but I can’t figure it out on my own.

Any help understanding this or directing me toward a good book or website would be much appreciated. A friend has offered a book by Nigel Calder, I think called "Einstein's Universe"... has anyone read this?

Thanks!

Zambi

 

[dx]

I understand and believe that this is true, but I have a question. If Bert is traveling at 0.999c, how does he travel that distance (8.269X10^13 km) in less than 5 months? Does the distance change from Bert's perspective?

Yes the distance does change in Bert's perspective. It is the phenomenon usually called "length contraction".

 

[bapowell]

I understand and believe that this is true, but I have a question. If Bert is traveling at 0.999c, how does he travel that distance (8.269X10^13 km) in less than 5 months? Does the distance change from Bert's perspective? If not, I don't understand how he travels that distance in that time. I know it must be something simple that I am missing, but I can’t figure it out on my own.

Right. Given the distance (8.269X10^13 km) and speed (0.999c), one finds that the trip should take 8.75 years. That's according to Ernie. However, in relativity, we learn that measurements of time and space depend on the observer's state of motion! The 1st rule is that moving clocks run slow; this is known as time dilation. This means that Bert's clock, moving relative to Ernie, runs slow according to Ernie. It registers that only 5 months have elapsed, in disagreement with Ernie's measurement. The second rule is that moving rods shrink; this is known as length contraction, and applies to any dimension along the direction of motion. Bert is moving relative to the space between himself and his destination, and hence, perceives this distance to be shorter than Ernie would measure it to be. Therefore, all is consistent -- according to Bert, it took only 5 months, but he only traveled 8.269X10^10 km!

 

[zambi]

Thank you all very much. I've wondered about this from time to time but unfortunately always when I'm otherwise occupied and couldn't research it (i.e. while driving, or trying to fall asleep, etc.)

This has been very helpful--I appreciate it!

Zambi

P.S. I teach middle school math (you'll probably all be glad to know I don't teach science). I have a few very bright students who I anticipate will be interested in a discussion of this one of these days after class hours.