While there is an almost constant stream of small advancements in physics, few things really constitute a leap. Only discoveries such as gravity, relativity, and atomic structures are given this lofty place in physics. The next leap in physics must be one with implications that will affect the course of history. Great leaps in any area of science can affect civilization. With physics however, advancements of this magnitude will certainly have implications in space flight. There are three such advancements that would be considered a leap: manipulation of gravity, far more efficient and abundant production of anti-matter, and matter-energy conversion.
Let’s start with manipulation of gravity. This, like the others, is a big one when it comes to space exploration, specifically beyond our solar system. When most people think of the idea of gravity manipulation, they have visions of flying cars or anti-gravity belts. Gravity manipulation actually goes in both directions, positive and negative. It would not only make putting materials and people into space far easier via anti-gravity, but also provide artificial gravity once in space.
This is important to space travel due to the deleterious effects of zero gravity for extended periods of time. This is minor when considering a two week shuttle mission, but becomes a much more serious concern when in the context of a journey of several months or years. Another application of gravity manipulation is for space craft propulsion. Through the creation of an artificial gravitational field, it would be possible to propel, or rather pull, a spacecraft.
Given a gravitational field equal to that of Earth, the spacecraft would then proceed to accelerate at approx 32 ft/s/s. For the layman, this means that the speed of the spacecraft would increase by 32 ft/s every second. Given that there is no medium in space (such as air) to impede this acceleration, the spacecraft would never achieve a terminal velocity and would therefore continue to accelerate until the gravity field is shut down (or until the craft hits a speed limit, such as light speed).
After three months (given an average of 2,628,000 seconds per month), a spacecraft with such a propulsion method would reach a speed of 76,897,382.4 m/s (over 18,000 times the theoretical maximum velocity of a chemical rocket, or 5 km/s), or approximately 30% of the speed of light. Note that this corresponds to an increase in velocity of approximately 10% per month while the gravitational field is in operation.
We all know that gravity is generated by mass. No matter how the creation of artificial gravity is achieved, the fact is that it would inherently require an enormous amount of power (given a mass to energy ratio based on E=mc^2). This type of energy is beyond anything we can currently generate, and is absolutely ludicrous compared to anything we can currently generate aboard a spacecraft.
This is where anti-matter comes in. If we can find a way to reliably and efficiently produce anti-matter (currently, we as a people produce perhaps a few thousand atoms per year) and be able to harness it for energy production, we would have more than enough energy. In addition to interstellar travel, it would mean an end to not only our dependence on fossil fuels, but on every other type of energy production as well.
The final leap is that of matter-energy conversion. This is important for spaceflight, but not as important as it would be for society in general. If we were able to convert energy into matter and control not only the type of matter produced but the configuration of that matter, we would be able to make anything at the touch of a button. Whether it is food, clothing, building materials, or manufactured goods, it could be made from energy.
This could do many things for our civilization, not the least of which would be ending hunger and eliminating the concept of wealth. For spaceflight however, having a sufficient power source on board would mean mission planners would not have to take supplies into account. All food, clothing and other supplies could be made on board. The system could also work in the other direction, turning matter back into energy (even if not terribly efficient, it would still be highly useful). All spent supplies, dirty clothes/dishes, and trash could be recycled by the system. This would also mean an end to landfills and trash for us back home.
If all of these leaps came into being, our society would change drastically. However if even one of these were to be realized, the ramifications would be extreme, to say the least.