Why does a clock appear to run slower on a space probe moving away from Earth?

[Mu naught]

Probably not but I'm too dumb to figure it out. I'll describe the scenario as clearly and concisely as I can:

Suppose a space probe is sent out into space moving away from Earth at a relatively high velocity, but not high enough that there are any significant time dilation effects.

Without worrying about the details, suppose on this probe there is a video camera which is focused on a clock that is set to keep Earth time. The probe sends back an uninterrupted video feed of this clock, so someone on Earth can continually observe the time the clock reads on board the space probe.

As the probe goes out further and further into space, the time it takes for the radio signal it is transmitting back to Earth gets longer and longer, causing a greater and greater delay between the probe and earth. After traveling for a long time, suppose the probe is 4 light hours away from earth.

The observer on Earth must see the clock as running 4 hours behind because that is the time delay between he and the probe. Yet, suppose he has been watching the clock the whole time the probe has been traveling out into space. When it began its journey, the time was accurate, but now he sees it as running 4 hours behind.

How can this be? If the clock is slowing down on the space craft, then he would see it ticking slower from the video feed, but the clock isn't slowing down, it's keeping perfect time with earth. And the video feed being transmitted is constantly sending back signals at a constant rate - say 30 transmissions per second. Where does the time delay come from?

 

[Curl]

The time between the transmissions is 1/30th of a sec from the probe's perspective, but it is a bit longer from the Earth's perspective.

After some time (like 1 year), this time difference adds up to a noticeable amount and will create lag, so what you see on the clock is an old time (it's not real-time feed).

This is a pretty cool question. Took me about 40sec of thinking to figure it out, which is actually a long time to think (for me), no joke.

 

[rcgldr]

Essentially it's a doppler effect without special relativity issues. The frequency of the received lightwaves on Earth would be slightly longer, for the same reason.

 

[Taturana]

Sorry for my noob answer but what I understand is:

The signals will be transmitted at constant rate but the larger is the distance between the probe and the Earth the longer will be the "distance" between the signals. So the distance between the signals will keep increasing, so the frequency that the Earth receives the signals will be smaller and smaller (because the interval between them is longer and longer and the light speed is constant)...

Am I right?

 

[Jim1138]

If the spacecraft and receiver (Earth) are traveling at a constant velocity, the frequency received would be constant. Wikipedia Doppler Effect: http://en.wikipedia.org/wiki/Doppler_effect

 

[Curl]

This question is not about the Doppler effect, so I don't know why you're all bringing it up.

 

[1MileCrash]

This question is not about the Doppler effect, so I don't know why you're all bringing it up.

Yes it is.

"And the video feed being transmitted is constantly sending back signals at a constant rate - say 30 transmissions per second."

It started out as 30 transmissions per second, and as the probe travels away from Earth this becomes less and less transmissions per second due to the doppler effect. That is where the time delay comes from.

[PLAIN]http://img163.imageshack.us/img163/3936/doppler.png

Suppose I have a paintball gun in space and I start shooting at 30 balls per second at a probe in front of me. The probe gets hit with 30 paintballs per second when it's stationary. Now it starts moving; Even though I am still shooting 30 balls per second, the probe is not getting hit 30 times per second because each paintball has to travel further than the one before it due to the probe's motion away from the paintball gun.

That's my answer.

If the spacecraft and receiver (Earth) are traveling at a constant velocity, the frequency received would be constant.

Only if they are traveling at both the same direction and constant velocity; which is basically not moving at all in reference to once another. I could be wrong but I thought the doppler effect applied as long as they are moving at all within reference to one another.

 

[Born2bwire]

Basically it is going to come about from an increasing latency in the signal. For simplicity, let's assume that the bandwidth of the signal is high enough that we can broadcast an entire frame well before the next frame is taken and so we can think of the data as being transmitted in bursts of packets.

So what happens is that the time it takes for a packet to arrive on Earth will be longer than 1/30th of a second. If the travel time is instantaneous then each 1/30th of a second we get a packet of data containing the frame. But now that the craft is moving at a constant velocity away from Earth, each successive packet has to cover an extra unit of distance than the last packet. So each packet has to travel, let's say, 10 feet before it reaches the point where the last packet was broadcasted. Thus, there is an extra (and constant) delay between each packet or frame associated with the time it takes to travel 10 feet.

Thus, the received video will not be 30 frames per second. Instead, it must be something like 29.999990 frames per second or so. So the viewed video, if watched without any synchronization techniques, will run slower than real time. In reality, the extra delay between the frames will probably mean that the video feed will freeze every now and then to remain in sync with the desired 30 frames per second.

So yes, it can be likened to that of the Doppler effect if we think of the frequency of a wave as being the the rate in which we receive a frame of video (but the video information need not be constantly sent, it is easier to visualize it as a small packet of data that occupies a short space of time).