Electromagnetic waves, whether gamma ray, microwave, radio or visible light frequencies, travel through vacuum at the speed of—well, uhm—light.
When on Earth, this means communication is pretty much instant. If the distance travelled in one second by a photon, a light particle, were a string, it would wrap around the Earth almost five times.
You will notice that if your call goes via satellite, there is a small time lag. This is because your voice has to travel all the way up to the satellite in Earth orbit, and back down again. Communication satellites generally reside in geostationary orbit, at 35,000km above the Earth** so there is still a small, but noticeable time lag.
This time lag becomes larger the further you go.
If you were to call someone on the Moon, at 380,000km from Earth, your voice would take a bit over a second to get there.
Travelling time for a signal from Earth to the planets, travelling outwards:
Mars 19 minutes
Jupiter, 47 minutes
Saturn 74 minutes
Uranus 174 minutes
Neptune 258 minutes
Pluto 271 minutes
We say that Mars is 19 light minutes from Earth. Note that a light minute, like a light year, is a unit of distance, not time. A light minute is sixty seconds times 300,000 kilometres, which is the distance traveled by light in one second.
That’s right. If you were on the outer edge of the solar system, a radio signal would take at least four hours to get back to Earth, and another four hours to get a reply, presuming the receiving party doesn’t have to think about the response for too long. At this point in time, barring magic and wormholes, this is the fastest possible travel between these points. Immediate communication by radio between Earth and even Mars is physically impossible. This is an important point to consider if you write space-based Science Fiction
Think of the consequences:
You’d have to think very carefully about what you say. Your questions would have to be very detailed, efficient and concise. No chit-chat.
If there was an emergency, you’d have to figure things out by yourself.
If you were facing a hostile alien army, you would not have the time to ask a base on Earth if it was OK to attack, because by the time you got a reply, you might have been shot to bits.
On top of this, the strength of a radio signal is directly related to the square of the distance from the signal. Double the distance between transmitter and receiver, and the signal is reduced to a quarter of the strength. This would severely limit your options to communicate if you were talking to someone in the outer reaches of the solar system.
There might well be political consequences for your made-up solar system-wide human empire. They would suffer a lack of communication reminiscent of that which existed in the early days of European colonisation. They had no radio and letters took months to get to their destination. Lack of efficient communication may well have contributed to the fact that those new colonies went their own way within a generation, even if they were nominally still within the formal colonial structure. Eventually, wordwide communication problems were solved by radio and the telephone.
That won’t happen so easily to distances from here to the outer planets. Unless we find faster-than-light communication, which physics tells us is impossible, even the solar system will probably be too big for a connected human empire. For coherence of a human society, communication is essential.
**Geostationary orbit is the altitude at which an object orbiting the equator of a planet or moon travels at the same speed as the rotating body. In this way, the orbiting object is always in the same position over the surface of the planet or moon.