Bluetooth Latency Considering Bluetooth uses EMR, and EMR requires x amount of time to travel any distance.  Does this mean the farther my Bluetooth headphones get from my phone, the gaps between each byte of music increase (while moving away)?  If so, why is this not noticed as I am walking away from my host machine?
 A: Light travels $300,000,000 m/s$ or $30 cm$ per nanosecond. From earth to the moon takes light less than $1.5s$. Your walking speed is about $5 km/h$, or about $140\times10^{-9} cm/ns $. That should give you an idea how slow your walking speed is, compared to light. Any time difference caused by your speed or distance will be so small that it is completely unnoticeable.
You would certainly notice a problem if you could move anywhere near light speed. GPS satellites in orbit around the world travel so fast that they need to make allowances for their speed, to make sure the receivers on the ground can compute their position accurately.
A: The speed of light is so fast that the human ear will not be able to detect any latency between separate data packets.
If you have a friend who can press play on the phone, and you are say $5$ meters away from your phone, the time it takes to receive data is $t=\frac 5c=1.6\times 10^{-8}\ s$. If you then move to a distance of $10$ meters and do the same, the time it takes would be twice this, or $3.2\times 10^{-8}\ s$.
The difference in reception time between these two intervals is therefore in the order of fractions of a nanosecond.
So if you were moving away from the phone, any "gaps" would be way too small to notice. Of course if you could move away at very high speeds, this changes things. But also note that the distance standard Bluetooth can travel is ~$20$ or so meters and maybe much more with no obstructions. So even if you could move relativistically, you would be out of range in an instant.
