Is it possible to completely void space, and if we can would photons travel at an infinite velocity? After many talks with my physics professor over the span of a few weeks last semester he told me about what he called "the sea of space."  He explained to me that space isn't really a vacuum but instead filled with tons of "imaginary" particles that we can't directly observe but we can easily interact with and bring into the observable universe.  
I assume anyone answering this question already know about that, so I'll jump to the chase. 
In the observable universe we can create a "vacuum" by removing particles from any given volume.  By doing so we can observe light traveling at "the speed of light," however, that speed is limited by the unobservable particles in the universe.  Could we possible remove the unobservable particles from space to create a true vacuum and if so, would light travel instantaneously across this perfect medium. 
 A: It is not possible to completely void space.  In fact, if you and your friend each have a Geiger counter (a particle detector) and yours doesn't go off (so you see a vacuum) and your friend accelerates with their Geiger counter then  their device will go off, i.e. they won't see a vacuum.  And if you adjust your space so that your friend's device doesn't go off (so they think there is a vacuum) then your device will go off, so you won't think there is a vacuum.  This is the Unruh effect, it has a similar basis as Hawking Radiation from black holes (accelerations are similar to gravity).
So two observers that are accelerating differently will disagree about whether there is a vacuum, they won't both see a vacuum.
And even if you could make a super vacuum, it would not make light go faster. It is in the nature of light to go at speed $c.$  The vacuum is just what allows things to move the way they naturally move, and light naturally moves at speed $c.$
But what if you tried to find something other than light that moved at a faster speed?  It turns out that if you could alter the properties of space to allow something (even pure information) to travel faster than $c,$ that you could use this method to send information backwards in time.
Literally you could read the stock prices tomorrow and send the information back to today.  I know it isn't super obvious, but we've done the physics to know that if we could do a faster than $c$ transmission we could send information back in time.
It is similar to those different observers disagreeing on whether there is a vacuum, except this time they just need relative velocity and don't need relative acceleration.  You carve out space between here (and tomorrow) and some distant place and someone else carves out space between here (and today) and that same distant place.  But if those people are moving relative to each other, their disagreements about motion means that when something faster than $c$ from their point of  view, the thing is moving just right to  go from here-tomorrow out to the distant place and then to turn around and come back to here-today.  The whole idea that the universe all experiences time the same way died over a hundred years ago.
Again, you'd have to study relativity to see how to figure out which paths and how fast those people need to move and in which direction.  But that's how bad it would be if something went faster than $c.$
So even making a theory where things move faster than $c$ is hard because your theory then allows time travel, which makes it hard to do experiments if future things can affect your experiments.  So we don't even have a theory that allows such things, because we don't even know how to do that. We have actual experiments showing that time behaves differently for different observers, and the experiments are quite detailed and don't allow much room to wiggle.
So even if something experimentally looks like it might be going faster than $c$ we look for every possible other explanation first.  And we've always found another explanation.  
So you can't make a super vacuum. And a super vacuum wouldn't make light go faster.  And trying to make anything go faster than $c$ would be as hard as making a time machine.  Time itself behaves differently rather than allow things to go faster than $c$.
For instance you might think that shooting a laser on a high speed train might make the light go faster $c,$ but time itself will pass more slowly on the train to prevent it.  I want you to know how big a claim/ask/discovery you are talking about.
A: The vacuum is, by definition, the state with no particles (or any other kind of excitation of a field). This is good, because a vacuum that actually had particles and antiparticles jumping in and out of existence would not be Lorentz covariant (that is, it would not respect relativity).
Instead, what people mean by this "sea" of virtual particles is that if one were to measure the value of some quantum field, like the electromagnetic field, in some volume, the result would not necessarily be zero, even in a vacuum. Instead the results would be randomly distributed around a mean of zero (well, except for the Higgs field, which has a non-zero vacuum expectation value, but that's another story) - this is just a manifestation of the uncertainty principle.
The point I am making is that the vacuum is a constant, steady state with no particle content, so there is nothing for you to remove and no way of "speeding up" your photons. I know this post has taken a somewhat indirect route to answering your question, but your fundamental misunderstanding is in the nature of the vacuum in quantum field theory, so it seemed important to correct that and hopefully allow you to see why your suggestion cannot work.
