I held off on my comment, but your first line is valid,imo.+1

equations explode towards what? let me rephrase : as the speed of a particle goes nearer to the speed of light, then the size of the universe goes nearer to what ? EDIT: you already answered, the size goes towards zero

@Manu de Hanoi: So you're asking about what happens as the speed of light is approached. That's rather different, and there, the equations do make sense. In that case, yes, you're right: length contraction goes to zero.

a reference frame is virtual, I can make it travel at the speed I want

@Manu de Hanoi: You can command it like that? That's rather funny. I get the image of you standing up and barking orders at those reference frames for some reason :) "I demand you travel at $c$!" heh. But actually no, it has to make sense physically, and it's the Lorentz transformations that allow you to make sense of a reference frame of a moving particle that's physically sensible, and they crap out when you make speed equal to $c$.

@Manu de Hanoi: But if you are asking about the approach case then yeah, that does make sense and can be analyzed. But it'd be a good idea to rewrite the question then if that's what you really mean.

"a reference frame is virtual, I can make it travel at the speed I want" is false, it's experimentally proven wrong: see for example the experiment of Michelson and Morley. It can be empirically proven that there is no rest frame for photons and that's it, the end of the argument.

@GennaroTedesco Michelson and Morley didnt deal with reference frames at the speed of light... and that it.

@mike4ty4 I dont have to reframe my question, it is perfectly valid. Lorentz or Einstein not having an answer to it doesnt mean the question is absurd

@ManudeHanoi Michelson and Morley proved that if light travels at $c$ in one reference frame, then it travels at $c$ any other reference frame. Therefore even if you sit on a photon, you will still see the photon travelling at $c$, hence by definition such reference frame would not be a rest frame, and that's it.

@GennaroTedesco Michelson and Morley didnt experiment with any relativistic refence frame. You are over extending the scope of their results.

@ManudeHanoi There is no such thing as "relativistic reference frame": there are inertial reference frames moving at some speed with respect to each other and non-inertial reference frames.

@GennaroTedesco I hoped you'd understand i was meaning reference frames moving at the speed of light

Oh, no, not again! There is a long standing sticky misconception, that nothing can move at the speed of light. Well, light does. With Lorentz-boosts, you can only show that nothing traveling below this speed can accelerate to it, nor anything traveling at or above that speed can de-accelerate. And beside, when we are talking about the speed of light, we are most often really talking about the limit-speed from Lorentz.-boosts. Maybe a future close examination might turn out that, like neutrinos, photons would be only damned close to the limit speed.

@ManudeHanoi It seems you didn't understand any of the comments above: whether something moves at the speed of light or not, as long as it is an inertial reference frame (i. e. moving at constant speed, even if $c$, with respect to some other already inertial frame) then the result of Michelson and Morley applies. Ergo, even if on a photon, as the reference frame is still inertial, the speed of light must be the same.

Don't you just hate when dividing by zero causes spacetime to collapse?

@ManudeHanoi Did you at least read one of the comments above?

I did, it's you who keep bringing "Michelson and Morley" when I told you you were overextending the scope of their results. You are confusing the scope of their experiement with the scope of the theory. They were testing for aether in as much as aether was affecting the speed of light. They found the speed of light was independant of the experiments. AGAIN that doesnt mean they experimented for aether going at the speed of light.

@ManudeHanoi "They found the speed of light was independant of the experiments. AGAIN that doesnt mean they experimented for aether going at the speed of light" this makes zero sense. Why would a reference with the speed of light be singled out of that experiment? As long as it is inertial, it falls into the scope. Unless you want to ad hoc say it doesn't, but it that case you are ad hoc stating that the universe must behave differently, for some unknown reason.