Universe without a fixed universal speed limit What would a universe without a fixed universal speed limit (like $c$ in the actual universe) look like? Would it be paradoxical? Would time travel into the past become possible?
 A: No special relativity effects would probably lead to completely different laws of physics compared to these we are so used to. And it's not all about gravity...
For example, quantum mechanics based on de Broglie wavelength wouldn't be possible, since the de Broglie relation probably wouldn't be effective in this case (see de Broglie waves). In a similar fashion, no electromagnetism with its wavelike behavior, nor other quantum effects which our material world is based on won't be probable. No atoms, no familiar electrons, protons, quarks... Nevertheless, some entities might exist, but surely in completely different proportions of their fundamental properties. Furthermore, mass and time are somehow deeply connected in our universe, while in my opinion the speed of light and time are basically two sides of the same underlying effect $-$ if there wasn't the finite speed of light, the time wouldn't flow as we experience it, nor it would be the 4-dimensional space-time. Just a guess, though :)
So, no $-$ this wouldn't be a Newtonian universe with the matter we know and are built of.
After all, the universe like that wouldn't develop at all in the way our did $-$ the instantaneous propagation of gravitational forces probably wouldn't allow expansion of the universe in an event like the Big Bang (probably) was. Of course, we may imagine a universe like that with a consistent set of laws that holds up, but he has had a reason for setting the universal speed limit...
A: A universe without a speed limit would look just like our universe, except it would be far simpler.
Having a finite speed of light/speed limit leads to things like the theory of relativity.  Without a universal speed limit, then the universe behaves according to newtonian mechanics.  There aren't any paradoxes, because without a universal speed limit, there is no time dilation, and none of the other effects which come out of relativity.
If we then assume that light itself travels at an infinite speed, things become more interesting.  This means that you see exactly what something looks like, no matter how far away it is.  The night sky would be brighter, because you could now see all the stars (you wouldn't have to wait for light to reach us).
In addition, radio signals would travel instantaneously.  While this does not sound like something very important, it means that pretty much every device that humans have built for determining location or distance would not work.  Systems like GPS work by measuring the difference in time between satellites (i.e. by measuring the time difference, and then working out the position based on the speed of light)  In addition, systems like RADAR or LIDAR would be affected.
In addition, many of the heavier elements on the periodic table have electrons that are travelling at a significant portion of the speed of light, and relativity plays a part in determining how they bond with other elements.  So, without a finite speed of light, some of the bonds in heavier chemicals could change as well.
