[Jim Marsh]

Jim Marsh asked the Naked Scientists:
   
Hi, I love your podcast.
 
I learned a while back that time slows down for an object that is being accelerated. I was reading an article on the internet about centripetal force and it stated that the object being swung around is in constant acceleration. If someone was in a spinning centrifuge would time be slightly slower for that person compared to a person standing outside the centrifuge?
 
Thanks
Jim Marsh
San Antonio, Texas, USA

What do you think?

[wolfekeeper]

The answer is yes, according to special relativity, the person in the centrifugal is ageing fractionally slower; because they're moving.

The equation for the slowdown is:

1/sqrt(1-v^2/c^2)

where v is the speed in metres per second and c is the speed of light (299,792,458 m/s).

If you plug some numbers in though, you'll find that the slowdown is really, really tiny.

[LeeE]

I recently worked out the degree of time dilation for a 10 m turbine spinning at 60 rpm (much higher than you'd get in a human centrifuge^*) for 30 years, and assuming I did the maths right it amounted to 0.00000524520874023438 (5.25E-006) seconds.

Edit: ^*Actually, now that I've thought about it a little more, I think I'm just about 100% wrong there; a 10 m rotor spinning at 60 rpm is probably quite close to a human centrifuge.

[Don_1]

The answer is yes, according to special relativity, the person in the centrifugal is ageing fractionally slower; because they're moving.

Just as well nobody told M Jackson about that!

[lyner]

Also slower for someone on the Earth's surface, compared with his bro at the top a a skyscraper (or even a bijou semi det).

[WylieE]

Hi Sophie,
 Will you elaborate on that? 
At first glance it seems like the person up high would be traveling faster ... maybe I am thinking about it backwards?

[LeeE]

Weelll...  The person at the top of the tower will be stationary relative to the person at the bottom of the tower, so there'd be no relative speed difference between them.  To a person stationary, out in space, and not rotating with the Earth at all, both people would be running slow, and at different rates too.

However, the person at the bottom of the tower would be in a stronger gravitational gradient than the person at the top of the tower and this results in time passing more slowly for them [the person at the bottom].

It's very important to be clear on where you're looking at things from (the observer's frame of reference) as it makes a huge difference.

[Bored chemist]

"It's very important to be clear on where you're looking at things from (the observer's frame of reference) as it makes a huge difference."
Huge in the sense of 5 microseconds in 30 years.

[lyner]

Hi Sophie,
 Will you elaborate on that? 
At first glance it seems like the person up high would be traveling faster ... maybe I am thinking about it backwards?

I was doing the smartarse thing and  bringing in the additional effect of gravity on the rate that time passes.

[LeeE]

"It's very important to be clear on where you're looking at things from (the observer's frame of reference) as it makes a huge difference."
Huge in the sense of 5 microseconds in 30 years.

"Time is an illusion, lunch time doubly so"  D.N.A.

[lyner]

Before the Railway timetable, no one assumed that time was the same everywhere. Noon was Noon - but trains had to go at different speeds when going East or West to keep to the timetable. But then they introduced GMT for all.

[LeeE]

Having railway clocks all keeping the same time also reduced the number of collisions in the very early days of railways before block-working was introduced.  Until then trains were just sent off on a time interval basis and relied upon the driver to spot stopped or failed trains ahead []  Fortunately, trains were a lot slower and lighter then, but on the other hand, breakdowns were much more common too.

Recommended reading on this subject is 'Red For Danger' by L.T.C. Rolt.  It's considered essential reading for those working on the railways and is written in such a style as to make it entertaining reading for the non-railway enthusiast too.

[WylieE]

Thanks LeeE, BC, & Sophie,
 I think I understand now (at least relatively so).