General relativity and jet travel makes you fat?

[pletharoe]

Hi everyone!
I'm a pilot on a private jet, in conversation one of the crew mentioned that "You get younger when flying." Now I had to correct him saying that actually it's just that time slows down as you go faster. Unfortunately for the flight attendant, going faster also means that she puts on weight! So here's a conundrum for you guys:

At 500 knots (257 m/s) how much slower does time pass (relative to when we're stationary and how much more does my 50kg flight attendant weigh?

Yes, I know it's a ridiculous question, but I'm intrigued. Thanks for any answers!

 

[George Jones]

I think that your interested in effects due to special relativity. The appropriate factor is

$$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}},$$

where c is the speed of light. In this case, it is

1.000 000 000 000 37

There is a altitude effect due to general relativity.

 

[Drakkith]

From your frame of reference in the plane, you and your flight attendant have no increase in mass. When you slow down and land neither of you will have any more mass or wieght than you did when you first started.

 

[russ_watters]

I suppose you could relate the time dilation factor to the number of calories the flight attendant consumes/burns per year...

 

[pletharoe]

Hi Guys, thanks for the answers.
George:
I used your equation, if "V" is in meters per second, I get a square root of a minus number so I used a bit of poetic license to deduce that the "V" should be a factor relative to the speed of light (257 m/s / 299792458 m/s) is that right?
If so, the outcome of the equation is 1.00000000000037. Which sounds like a reasonable number (a very small factor). So am I right that the flight attendant is 1.00000000000037 times lighter relative to stationary people?
Do you have a similar equation for time? Since the process of ageing is only relative to her frame of reference, when she lands, she will have experienced slower ageing than the "stationary" world.

 

[nitsuj]

I suppose you could relate the time dilation factor to the number of calories the flight attendant consumes/burns per year...

Now that's clever ;)

 

[Buckleymanor]

From your frame of reference in the plane, you and your flight attendant have no increase in mass. When you slow down and land neither of you will have any more mass or wieght than you did when you first started.

How does that happen.Lets say you had an identical twin who was left behind.You both weighed the same at take off and you both wore the same type of watch set to the same time for demonstration purposes.
You on the plane ages less and your watch ticks at a slower rate.
When you land you and your watch have expended less energy than your identical twin on the ground you won't have any more mass than when you first started but you will have more mass than your twin.

 

[Drakkith]

How does that happen.Lets say you had an identical twin who was left behind.You both weighed the same at take off and you both wore the same type of watch set to the same time for demonstration purposes.
You on the plane ages less and your watch ticks at a slower rate.
When you land you and your watch have expended less energy than your identical twin on the ground you won't have any more mass than when you first started but you will have more mass than your twin.

You are correct. However there is no additional mass added to yourself after you stop and land. The only difference in mass would be because of time effects, not velocity.