Kevin's Watch

This question was asked by someone at the Real Life Forums - I've been puzzling over it for a while, but can't seem to work it out.

Say that starship Doohickey left point A with half the speed a radio-signal.

The ship would then receive a constant feed of radio-signals from Earth. With music. And talk. Radio and TV and such.

In theory... what will happen if they travel HALF the speed of the radio-signal AWAY from the source of the signal?

I've thought about it, and the only two effects I can think of is

A: The feed sounds slow and garbled. (Half the original speed, for instance.)

B: The feed sounds lagged. (Like an underbuffered server.)

I WANT TO KNOW WHAT HAPPENS!!!

Okay, so the question was intended in simple terms, but because it was asked about a ship moving half the speed of light, I started trying to work it out in relativistic terms - but I can't do it. All I've got in my lecture notes are the Lorentz tranformations. Anyone have any ideas?

I think that there would be no difference.
Starship Doohickey is traveling 1/2 the speed of the radio-signal away from the source.
However, the signal is still traveling at 100%, or, 1/2 speed faster still than Starship Doohickey.

Idea to ponder yet -
What if the starship is traveling at the exact same speed as the signal?
Will it receive only that moment of the broadcast?

Don't radio waves travel at the speed of light? In which case, no ship can travel at the exact same speed as the signal. And any ship travelling at any other speed will measure the speed of the radio signal the same. Radio signals are not subject to the Doppler Effect, are they?

Since light is subject to the Doppler effect (see: evidence for expanson of the universe), I'd suggest that radio signals also are.

Oy, I said that about as badly as it could possibly have been said! Partly because I wasn't thinking at all clearly, partly because I worded it poorly. Let's try this: Would the sound your radio produces from the radio waves it receives be subject to DE because the waves themselves were? Or would there be silent parts? Or what?

Well, the effect produces a shift in wavelength, not content. The thing I'm puzzling about is whether this shift would manifest as a distortion in the sound - since the quanta are arriving at slightly larger intervals, would it sound slow? Perhaps a greater knowledge of how radio works would help.

But hasn't such a thing been tested? Simple enough to do, so I figured it's been tried. Drive or fly away from a radio transmitter reeeeeeeeaaaaaaally fast. I wonder if such tests are discussed on some site(s). Does Barry Gibb suddenly sound like Barry White?

I think the speeds required in this particular case are purely theoretical, but you're probably right thatsome kind of similar test will have been done. I'll try and look something up.

I think I get it now. The equations are different for something at 0.5c, but the frequency of the wave will still get lower. In numbers, a ship travelling 0.5c would get a signal with frequency 0.577 times the transmitted frequency.

All I need to know is what happens when you lower the frequency of a radio signal then convert it back to sound. I sucpect it'll be a change in the speed, as was suggested - it'll sound slower and deeper.

depends whether it's amplitude modulated or frequency modulated.

Yeah, and as far as I can tell looking around, the only types of broadcast which use FM are audio-only, so I'd assume the signal in question was AM. And considering that FM is based on variation in frequency, I'd guess FM would sound the same as long as your reciever was tuned in right. AM, again guessing, would be slowed down because the information would be arriving at a lower rate.

Sounds about right to me.


Another one for you:

If you move an object at .5c in one direction and another in the opposite direction at .5c can people inside the objects see each other?

Any light emitted by one object would still appear to the other to travel toward it with velocity c. So, yes, they would see each other.
However, I don't think the situation is possible, since each object would appear to the other to have no length, infinite mass, and appear to take an inifinite time to move any distance.

Nathan wrote:Sounds about right to me.


Another one for you:

If you move an object at .5c in one direction and another in the opposite direction at .5c can people inside the objects see each other?

Yes, the addition of velocity is non-linear when the speed approaches c. The exact equation, called the Lorentz Transformation, goes like this:

V=(U+W)/(1+UW/(c squared))

Where U and W are .5 and c is 1. In this case, V=.8. To the observers on the first ship, the second appears to be moving away at .8c.

What's W?

Fist and Faith wrote:What's W?

U is the velocity of the first ship. W is the velocity of the second ship. V is the apparant velocity of one ship as seen from the other. They are usually written V sub 1, 2, and 3, but I can't write a subscript here.

So then I guess you meant to write U and W are .5 and c is 1? The math works out that way. Not picking, just trying to make sure I understand. I've never been able to understand relativity, despite several attempts at it. It would be nice to at least know the formulas, even if I can't understand how they came about.

Yes, that's what he meant.

Interesting, I've not heard of that equation before, I guess A-level physics doesn't cover this.

I didn't do anything on relativity until just this term at uni - I just finished 'Special Relativity I' last week. Most of the module was on using the Lorentz transformations.

Murrin wrote:Yeah, and as far as I can tell looking around, the only types of broadcast which use FM are audio-only, so I'd assume the signal in question was AM. And considering that FM is based on variation in frequency, I'd guess FM would sound the same as long as your reciever was tuned in right. AM, again guessing, would be slowed down because the information would be arriving at a lower rate.

(Long delayed response to my kind of question)
Even if your receiver could handle the red-shift of the radio waves, you still couldn't hear the broadcast like the people on the planet would.
Since the planet is moving away from you at 0.5c, time would be passing on the planet at only 87% of the rate that time flows on the ship. And in addition, the transit time for the signal is becoming longer as the planet moves away. So, after ten of your years, the planet is 5 light years away and has transmitted 8.7 years of signal. The last of that signal is going to take another 5 years to reach you, so you end up getting 8.7 years of planet-time signal in 15 ship years. So, if you were watching someone's web cam of their private life, they'd seem to be moving at 58% of normal speed.