I could start this with a lot of boring stuff like "synthetic" is big molecules built up from small ones. Or, that polyalphaolefin (PAO) starts as a simple two-carbon molecule and is built up to a 10 carbon molecule.
However, I have been asked my opinion of synthetic vs. conventional oils, so I will just explain my view on this subject. My opinion does not go to the laboratory, but rather to the inside of the motor. Granted, the synthetics are more stable, flow at a lower temperature, and are less susceptible to oxidation. But I do not care for their use in older cars. These cars were built before the invention of synthetics and should remain on conventional oil and have that oil changed at regular intervals. The exception to this would be that racing motor you just built with new racing parts. Synthetics would work for these.
For new cars with all, or mostly all, aluminum motors I would use synthetics after a wear-in period, if the motor was started with conventional oil. If your motor was started with synthetic, I would definitely stay with it.
Is the benefit of synthetics worth the cost? In new cars, the answer would be yes. In older cars, you could go to a semi-synthetic and chang the oil at the regular interval.
Can you switch back and forth? Most all oil companies do not recommend mixing or switching back and forth. Synthetics are fully compatible with each other and with conventional oils. The early synthetics had high levels of ester. This did cause discoloration and thinning of the oil and in my opinion the loss of protection.
As to the question of the use of special oil filters or special disposal techniques for those who change their own oil. The answer is that you can use the same recommended oil filter and follow the same disposal procedures that you use with conventional oil.
Lastly, does synthetic oil produce horsepower? In every study or car and the dyno, the answer is yes. Less friction - less heat - produces horsepower.
There you have my opinion on this subject. If you are in a fully committed relationship with the car of your dreams, then step up and protect it, but don't overdo it. Just remember the by-product of the combustion engine is still there no matter what oil you use. So whatever you use - Change It!