What Happens to Communication at Light Speed?

[airbourne]

I first pondered this a number of years ago but I've never formally studied physics or known anyone who has, so I've had no one to ask and it falls into the back of my mind for years at a time before I revisit the thought.

I'm sure this is a question physics students deal with in some form and I am sure the answer is simple but it's been bugging me since I was young.

You have a spaceship with a radio receiver and transmitter.
Your friend, who is not coming for the ride also has a receiver and transmitter.

You board your spaceship, and start broadcasting to your friend "Hello, I'm in the ship, preparing for takeoff".

Your friend replies "Good to hear. Bla bla".

You launch and accelerate rapidly into the vacuum of space, towards the speed of light while reading your speed to your friend (and casually conversing).

"50 000 kilometers per second…we are accelerating quite quickly"
"100 000 kilometers per second…the weather is cold and dark out here"
"200 000 kilometers per second…we're heading for the nearest pulsar"
"299 000 kilometers per second…almost…there"
"We have reached the speed of light"

Lets say that took 5 minutes.

Cruising at light speed, you continue to make small talk to your friend, in fact you talk for a VERY long time.


My questions:

1) Say your friend just listens and doesn't say anything. What does he hear?

2) You and your friend have a continual conversation about an array of subjects. What does each of you hear?

3) (answers to the first two may cover this) let's say you make a round trip for 50 years, talking all the while, and return to visit your friend. What now?

 

[Passionflower]

The speed wrt the stationary observer can never reach the speed of light.

 

[airbourne]

I can fathom that, but what happens to your communication, which essentially occurs at the speed of light which is constant and does not depend on an observer? If the person moving speaks for the 5 minutes it takes them to reach reach the speed of light, what does the observer hear?

I feel like I'm overlooking something simple but that bit has got me.

 

[Passionflower]

I can fathom that, but what happens to your communication, which essentially occurs at the speed of light which is constant and does not depend on an observer? If the person moving speaks for the 5 minutes it takes them to reach reach the speed of light, what does the observer hear?

I feel like I'm overlooking something simple but that bit has got me.

Well if the spaceship is moving with constant velocity away from the stationary observer communications will obviously slow down, think of the relativistic Doppler effect here (e.g. (c-v)/(c+v) ).

 

[yuiop]

Lets say that took 5 minutes.

In relativity you have to state who measures 5 minutes. In an extreme case 5 minutes in a accelerating rocket could be years as measured on Earth.

Here are some numbers for a rocket with constant proper acceleration of 9.8 m/s^2. I am using years rather than minutes because it makes the numbers easier to handle:$$\begin{matrix}<br /> \text{Traveller Years (T)} & 1 & 2 & 3 & 4 & 5\\ <br /> \text{Earth Years (t)} & 1.19 & 3.75 & 10.67 & 29.96 & 84.00\\ <br /> \text{Distance lyrs (d)} & 0.56 & 2.90 & 9.74 & 29.00 & 83.04\\ <br /> \text{Message time} & 1.75 & 6.65 & 20.41 & 58.96 & 167.04\\ <br /> \end{matrix}$$

In this example with fairly mild acceleration, 5 years on the rocket equates to 84 years of Earth time. The message time is the elapsed Earth time, plus the light travel time for the signal to return to Earth. For example, after one year the traveller sends a greeting message which is equivalent to 1.19 Earth years. In that time the rocket has traveled a distance of 0.56 light years from Earth so the first anniversary signal arrives back at Earth after 1.19 + 0.56 = 1.75 years. It is easy to see from the table that the time between messages received on Earth gets progressively longer. After about 4 years into your journey almost everyone you knew back on Earth will have died of old age by the time you turned around and returned.

There is also significant Doppler shift of the messages and they get slower and deeper on the outward trip and it will be necessary to record the messages and play them back speeded up to understand them. (The opposite effect happens on the way back. The messages sound speeded up and high pitched and have to be played back slow to understand them.) Small talk ain't going to be easy. There could be many years between asking "What's the weather like today?" and receiving the reply "Did you mean my today when I got the message or your today when you asked the question?".

 

[airbourne]

Thanks for the replies everyone (especially yuiop). This is much clearer now and I can put to rest something that has been bugging me (in the back of my mind) for a long while.

 

[John232]

He probably wouldn't hear anything over the radio. The doppler shift would contract or expand the radio waves where the radio would no longer properly function.