There are a bunch of different ideas in this thread about what the modern era is supposed to represent. Based on some information present in comments in the game files, it looks like firaxis was assuming the modern era should start around ~1880. There are a number of features of this time period that can distinguish it from the earlier industrial era. The industrial revolution was a major shift in the production and agricultural practices of nations. Pre-industrial nations usually have about 90% of the population involved in Agriculture in some way- either growing, herding, transporting or selling food. This was necessary to sustain the population. Industrialization saw many technologies that increased this productivity...
Specifically, the collection of technologies that changed everything about human society was the application of artificial power to Everything people did. Water power, animal power, and wind power had been harnessed for centuries, but it was all limited: water only falls so fast, wind only blows so hard, and there is an Upper Limit beyond which it is more destructive than helpful (no one ever tried to use a windmill in a Hurricane, or a waterwheel in a Tsunami!). Steam Power was unlimited, because you could keep improving the technology and build bigger, more powerful steam engines and apply them both to stationary power and mobile power: factory machinery and railroads. These changed everything about how people lived and perceived the world.
First, the railroad made it possible to do almost anything, anywhere. Want a city in the desert? Use the railroad to bring in materials, people and food from Anywhere Else the railroad runs, and the piping to bring in water. The only limit is where the railroad runs. In game terms, every city connected by a railroad now has a City Radius that extends the length of the railroad. In a nutshell, before the railroad no human being had ever gone faster than 40 miles and hour unless he was falling off a cliff - after railroads, Anyone with the price of a ticket could go further, faster than any King of Kings before the railroad.
Second, the steam-powered factory allowed not only massive increase in productivity, but also required massive concentrations of people to tend the machines, and this was possible because the railroad could feed them wherever you decided to put the factory. Result: the majority of people within a few generations were living in greater (urban) concentrations rather than next to the food sources. In addition, people's daily personal schedules changed. Since before Homo Erectus, the day was the daylight. With the requirements of the machinery-driven industry and the consequent development of artificial light, that definition changed. People's lives no longer ran according to seasons, planting, harvesting or husbandry, they ran according to the Time Clock (No coincidence that the first clocks and watches in the 17th [pre-Industrial] century had no Minute Hands - there was no requirement to be that precise. After Steam Powered Industry started in, Minute Hands and Second Sweeps became common, because the interlocking workings of machines require precision)
As a result of the cascading changes started by the application of the steam engine, people's jobs, schedules, and lives all changed. As a consequence of great concentrations of people being more susceptible to epidemic diseases (always true: ancient Rome averaged an epidemic every 10 - 15 years) medicine went looking for Remedies, produced Germ Theory and Anticsepsis, and in every industrializing nation the population surged in numbers - and flocked to the cities.
All the changes since then have just been More Of The Same: more power (electrical, internal combustion, nuclear), more speed, more precision. The same watches that had to develop second hands in the Industrial Era now track individual heart beats, but the Massive Change was from tracking days and seasons to tracking Minutes.
An analogy is that the industrial revolution is puberty and the modern era is adulthood.
Or, the Industrial Era is Puberty, with all its massive changes in your personal perceptions, wants and needs, and the Modern Era is Adultery, when you think you can satisfy all the wants, needs, and desires all at once...
As in other Eras, the Industrial Era starts at different times in different Civilizations, because it starts whenever that Civ starts using Artificial Power. Historically, this started with steam engines, but some 'third world' nations in the 20th and 21st centuries have gone straight from Animal/Wind/Water power to Internal Combustion and even more advanced power sources.
Two points I want to make, though:
1. The Industrial Era is probably second only to the discovery of Fire or Tools in the changes it made to how humans live. IF you must have Eras, it is absolutely necessary to include some form of the Industrial Era.
2. The Industrial Era was Massively Disruptive. People do not like to change everything about the way they live. Result: Luddites, the Liberal Revolutions of 1830 and 1848, Karl Marx, and reactionary Fundamentalism of all kinds - people pining for the Good Old Days, which weren't. Hobbes' observation that a person's life was 'nasty, brutish, and short' is Pre-Industrial Era, and not inaccurate for 90+% of the population then.
That means, in Game Terms, the discovery and application of Steam Power should be followed by Factories, a change in the definition of City Radius, huge population increases, and recurring Unhappiness unless specific Social/Civic Policies are adopted: the extreme capitalism that came in with Factories always led to great increases in wealth and productivity, and greater concentration of wealth in fewer hands - those that controlled the Factories. That in turn has always led to either Revolution or Reform. The Industrial Era changes both Technologies and Civics requirements, and the game should reflect that.