# In Interstellar, why isn't the signal affected by relativity?

The planet Miller is close enough to the black hole to be affected by relativity, so that one hour on the surface is equivalent to 7 years in the real world. Earth has received a signal from Miller saying the planet is hospitable for human life, but it turns out that Dr. Miller died shortly after arriving and the message has been repeating.

But my understanding of relativity would suggest that the signal would be enormously speeded up when received in the real world because of time dilation. Instead of being a radio signal the frequency would be over 60,000 times higher (24 hours * 365 days * 7 years = 61320). If we assume they're using the Ka band then a 23 GHz signal would end up as 375 KHz, in the medium frequency radio range.

Update: Hypnosifl pointed out I'd got this the wrong way round.

• By "the real world" I assume you mean Earth? I don't think a planet becomes unreal just because it is relativistic. – SethMMorton Dec 30 '14 at 21:41

In the movie, the initial Twelve are described as only being able to send a "very simple signal, yes or no". (Disclaimer: I saw the movie six weeks ago and may be misremembering the exact quote.)

It's possible that this "very simple signal" was transmitted on a variety of frequencies, one of which redshifted down to another one, or at least close enough that they picked it up.

The transmission could also be non-electromagnetic - for example, the transmission could be simply a neutrino generator, where on = habitable and off = non-habitable. Neutrinos are...complicated and I'm not sure how climbing out of a gravity well affects them.

Time is running slower on Miller's world relative to distant observers approximately at rest relative to the black hole, so the signal would be slowed down (redshifted), not speeded up (blueshifted). This matches with what's said in the "Important points to stress" section of the Gravitational redshift wiki article:

The receiving end of the light transmission must be located at a higher gravitational potential in order for gravitational redshift to be observed. In other words, the observer must be standing "uphill" from the source. If the observer is at a lower gravitational potential than the source, a gravitational blueshift can be observed instead.

• Are you saying that this redshifting is detectable on earth ? So they knew the signal came from a planet where time goes much much slower ? So they knew they received a signal that had been emitted for only 5 real minutes ? Are those questions "question worthy" or not ? – Kalissar Dec 23 '14 at 11:57
• Yes, the amount of redshift as the signal climbs out of the gravity well should be the same as the redshift seen by arbitrarily distant observers, so unless the wormhole further adjusts the frequency significantly (which I suspect it wouldn't since it doesn't have intense gravity), this should be the same redshift seen on Earth. Whether they would know the time dilation factor would depend on whether Dr. Miller had only one available frequency to transmit at, or if she could pick a higher transmitter frequency based on knowledge of the redshift factor. – Hypnosifl Dec 23 '14 at 13:10
• What I meant was that the received the message. But the message was dilated (redshifted), right ? In my mind, instead of receiving "good planet, ping" they receive something like "gooooood plaaaaneeeeeeet, piiiiiiing" so they must realize there is something wrong. Because their transmitter can't make the adjustment automatically, right ? – Kalissar Dec 23 '14 at 13:58
• I'm just saying we don't know what the transmitter can do--seems quite possible that it can both adjust the frequency and the speed at which 1's and 0's making up the message are sent. – Hypnosifl Dec 23 '14 at 14:08
• Yes, but if it does so, it would be ridiculous if the NASA couldn't detect it. I mean from an engineer point of view, having some device take some liberty (like automatically adjusting a signal) without warning you seems dumb. That's why I find it hard to believe the NASA couldn't detect that this planet was in a time dilated environment. – Kalissar Dec 23 '14 at 14:13