# Time dilation effects on a human being

1. Jul 29, 2013

### stawker

Hello everyone, long time lurker first time poster here.

Let's suppose a newborn baby is placed in a spaceship capable of traveling at 0.95c. The baby travels from Earth to a (theoretical) planet 95 light-years away which is at rest relative to Earth in the same frame of reference.
Assuming the baby stayed alive all this time and travelled at constant 0.95c speed, what would come out of the space ship at the end of the journey?

According to my calculations the journey time interval inside the ship is approximately 31.22 (Earth) years. but since I've never had any sort of actual teaching in relativity I might be way wrong.

So could anybody help me find out what would actually come out of the ship? A grey-haired old man? a ≈31-year-old man? a teenager? a toddler?

2. Jul 29, 2013

### Staff: Mentor

Show your work and we can tell you if it's right... FWIW, I came up with 29 years and change, but there is every chance that I fat-fingered the calculation somewhere.

3. Jul 29, 2013

### stawker

hi, thanks for your response. Here's what I did:

Δt= $\frac{Δt_{0}}{\sqrt{1-u^{2}/c^{2}}}$

Where $Δt_{0}$ is the time interval measured by the observer at rest (on Earth and the destination planet in this case).
And Δt is is the time interval measured by the observer moving with constant speed relative to the rest frame (The baby in my example).

So inserting the values I get Δt= $\frac{Δt_{0}}{\sqrt{1-(0.95c)^{2}/c^{2}}}$
Δt=$\frac{Δt_{0}}{\sqrt{0.0975}}$
$Δt_{0}$≈0.3122Δt and here's where I'm not quite sure what to do. We know it takes 100 years to travel 95 light-years at 0.95c so I just replace Δt with 100 and get $Δt_{0}$≈31.22 years

4. Jul 29, 2013

### Staff: Mentor

You're right.

5. Jul 29, 2013

### stawker

So an approx. 31 year-old would come out of the ship? that's insane!

6. Jul 29, 2013

### Staff: Mentor

It's not so much insane as it is completely at odds with our intuition about how the world works... But that intuition comes from a lifetime of experience with speeds that are small compared with the speed of light. You might try repeating the calculation with the spaceship moving at 10 kilometers a second - still much faster than any speed that we're familiar with. The relativistic effect will become insignificant, and our traveler will most certainly die of old age about when we on earth expect.

It's also a bit more plausible if you consider it from the point of view of the traveler, and allow for length contraction as well as time dilation. as far as the traveler is concerned, he's at rest, earth is moving away from him at .95c, and the destination star is approaching him at .95c. But because of length contraction the destination star is much closer than 95 light-years away - in fact, it is only 29.6 lightyears away, so moving towards him at .95c it only takes 31.22 years to reach him. It would be somewhat weird, from his point of view, for him to age any more than 31.22 years in that time.

These effects have been observed with particles called muons - there's a pointer to some of the experiments in the FAQ on experimental support for relativity at the top of this forum, and several good threads on the topic.

7. Jul 29, 2013

### Staff: Mentor

I don't think that this was done correctly. If Δt is the time interval measured by the observer moving with constant speed relative to the rest frame (The baby in this example), and $Δt_{0}$ is the time interval measured by the observer at rest (on Earth and the destination planet in this case), then the correct equation should read:

$$Δt_{0}=\frac{Δt}{\sqrt{1-(0.95c)^{2}/c^{2}}}$$

In this example, Δt0=100 years, which gives Δt = 31.22 years

The time interval measured by the observers in the earth-planet frame for the spaceship to traverse the distance is 100 years. The space traveler will be 31.22 years older when he reaches the planet.