Time when talking on the phone...? A few days ago I noticed (I'm sure we all know this) that when talking on the phone you receive the messages a few seconds after it is said by the sender.
So person A says "hello" to person B.
In person A's time frame they now finished saying "hello" and it has started traveling down the telephone wires/3G to a tower to the other persons phone and it arrives (let's just say) a second later. To person A, they must wait for their message to send (1s) and return (1s). (1s is the signal propagation time for each person to get the others message)
In person B's time frame they say nothing, until they hear "Hello". So they wait 1s and hear "Hello". Then they respond back with "Hello Person A", which takes 1s to get there. 
So why do telephone conversations feel like they are happening in real-time? (I know this is common sense, but I want to see it spelled out; i.e. I know the sky is blue, but why?)
Are person A and B talking NOW but the actual information exchange is happen 2*propagation time later?
 A: Whether or not a telephone conversation with latency above, say, 150 ms "feels" like "happening in real-time", differs for different people. In the following graph you'll see that more and more people start to get dissatisfied as the latency increases. (I assume that (very) satisfied means that one doesn't "really" notice, but there is room for different interpretations.)



Source: ITU-T Recommendation G.114
NB: There are several elements to latency, not just distance. See the link in my first sentence.
A: It is very simple, you are overestimating the propagation time. The signal travels with speed in the order of the speed of light. Suppose the information travels with $0.1c$, and you have a conversation over 1000 km, then the propagation time would be $10^6/(0.1\times 3\times 10^8)$, which would be approximately 30 ms, this is the reason you barely notice anything.
A: *

*You overestimate the lag. Yes, your phone buffers some sound before sending a network packet. Yes, the signal has to go through a number of wireless, optical and galvanic lines. Possibly some repeaters that have an internal buffer too. But the total roundtrip lag is typically below 200ms. These lines are optimized for low latency. 

*Human brains are also slow. In a face to face conversation, you are used to delays in the reaction of people. (Some only get a joke after several minutes). And this delay varies all the time. So, in a phone call you don't notice the extra lag.
A: When you speak into your phone, your sound waves are converted into electric signals which then travel to the other end through the electric cable at the speed of light. So, with a rough calculation, it would take about 20 miliseconds to cross the entire US. That's why it feels instant.
