Let us define a galactic empire as a political entity that encompasses at least a few percent of the habitable planets in our galaxy (not to be confused with an interstellar empire, which is one consisting simply of more than one solar system). What would be the chance of such a galactic empire arising? It would seem that there would be almost no chance of such a thing.
The main thing that would act against the creation of a galactic empire is simply a law of nature. According to Einstein's Special Theory of Relativity, nothing can travel faster than the speed of light. Such a limitation makes it virtually impossible for any planet to exert command and control over a region as large as even a thousandth (a tenth of a percent) of the size of a galaxy.
Consider the dimensions of our galaxy. It is between 100,000 and 120.000 light years in diameter, meaning that it takes between 100,000 and 120,000 years for light to travel from one end of the galaxy to the other end. To control even 1 percent of the galaxy, a galactic empire would have to control a unit of space at least a thousand light years in width.
Why would such a thing be most unlikely to occur? The reason is that when any planet started to make colonies on planets revolving around distant stars, the colonies would be too far away to be in the effective sphere of control of the parent planet.
Imagine if Earth were to create colonies on planets revolving around other stars. The nearest colony would be about 4.4 light years away. The colonists would know that if they went their own way and declared their independence, it would take 4.4 years for the news of such an announcement to reach Earth. It would then take at least another 4.4 years before a spaceship came from Earth to punish them for their disobedience (and probably many years longer, because of the near-impossibility of traveling at anything close to the speed of light). Such a colony would therefore not feel that it was under very strong political control by Earth.
Colonies that were farther away from Earth would feel even more free to do whatever they wanted. If an expedition from Earth established a colony on a planet revolving around a star that was fifty light years from Earth, then the inhabitants of that planet would know that they could declare their independence, and it would be at least 100 years before they would suffer any punishment – fifty years for the news to get to Earth, and at least fifty years for a punitive expedition to travel from Earth to the colony.
The farther the colony was from Earth, the more its inhabitants would feel that they could do whatever they wanted without suffering any ill effects. If a colony was established 500 light years from Earth, and then declared its independence, it would have no worries at all about some punishment from Earth that could not arrive in less than 1000 years (500 years for the independence announcement to reach Earth, and more than 500 years for a punitive expedition to travel from Earth).
I can illustrate this situation with a simple diagram, shown below.
The yellow dot at the center of this sphere represents the home solar system of a galactic empire, the center of imperial control (the dot has been enlarged from its actual size on this scale, to make the dot visible). The graph represents an area of space about 200 light-years wide. The different colors represent different degrees of control. There is no color indicating a strong level of control, because once a colony is established even 4 or 5 light years away from the home planet, the home planet's control over that colony would at best be only moderate. The farther you get from the home planet, the weaker the home planet's control. The home planet does not have any significant control over colonies established farther than 100 light years away from the home planet.
The rings and scale in this diagram are admittedly arbitrary, but I believe it is an accurate general depiction of the effective difficulties that any planet would have in maintaining control over distant colonies.
What about a galactic empire that holds together on a voluntary basis? The planets in the empire might be so persistently enthusiastic about maintaining the empire that it holds together, even though there is no practical way to sanction planets from ignoring the empire and going their own way.
There are cultural and historical factors that argue against such a possibility. Civilizations do not tend to stay in a fixed state for thousands of years. Below are some of the long-term factors that break up or change civilizations.
Cultural fission--the splitting up of one culture into two different cultures. An example is when the Roman Empire broke up into the Eastern and Western empires, with the Eastern Empire adopting a different ruler and a different religion. Another example is the American Revolution.
Cultural fusion – a case where one culture drastically changes after adopting characteristics of another culture, such as happened when the culture of Japan was radically changed after World War II.
Cultural adaption – a case when a culture radically changes because it adapts to its physical surroundings. An example might be the evolution of American cowboy and Wild West culture during the late 19th century.
Cultural dissipation – a case when a culture gradually loses interest or enthusiasm in some idea or tradition that once gripped it. An example might be the decline of Christianity in Western Europe, where church attendance has plummeted.
If a planet tried to establish a galactic empire, the planets that it colonized would be very subject to these cultural forces of fragmentation, particularly given the huge lengths of time needed for even a miniature galactic empire to form. Cultural fission would occur whenever a newly colonized planet split off from the empire to go its own way. Cultural fusion would occur when imperial colonizers came in contact with existing cultures in star systems they were trying to colonize. Cultural adaption would occur when imperial colonizers adapted their culture to be suitable for some strange new planet. Cultural dissipation would occur when distant colonies lost interest in the ideals or religion or traditions of some distant world that had originally tried to establish the galactic empire (and the farther the distance from the parent planet, the more cultural dissipation there would be).
Over the thousands of years needed to establish a galactic empire, these forces of fragmentation would act to split up an aspiring galactic empire into a smorgasbord of diverging cultures, diverging philosophies and religions, diverging interests, and diverging political systems. The collection of planets would end up being as divergent as the little fabric squares on a homemade quilt. It therefore would not be an empire in any cohesive sense.
The arguments above are based on the assumption that no ship can travel faster than the speed of light. There is always the possibility that nature has a gigantic gift waiting for us – some undiscovered twist of the laws of physics that may allow us to sidestep the speed limit set by the speed of light. Such a possibility is evoked by those who imagine warp drives and star gates allowing instantaneous travel. If it ever is possible to create a warp drive allowing faster than light travel, then the arguments above would not apply, and it would be much more likely for large-scale galactic empires to exist. But given the fact that warps drives and star gates are just speculative, we should for the time being assume that we will not be able to travel faster than the speed of light. If that is true, a large-scale galactic empire should be very unlikely to occur, for the reasons given above.