Edit: someone asked for a more detailed explanation, so here it is. Because of the equation in the article, it's impossible to see anything as moving faster than the speed of light in any reference frame; they just appear to asymptotically approach it. Both protons are moving at nearly the speed of light and perceive the other as moving at a speed that's slightly closer to the speed of light.
A key insight of Einstein's relativity is that the speed of time isn't fixed and absolute. Hence, "relativity".
I highly recommend Chris Lee's excellent 2012 article on the history of "the speed of light" at Ars Technica: https://arstechnica.com/science/2012/09/the-complicated-trut...
Isn't 'speed' defined with the use of 'time'? Doesn't that make an expression such as 'speed of time' kind of meaningless?
You can in fact express this in terms of "seconds/second", as in how many seconds pass in some other reference frame for each second in yours. In that sense, the "speed of time" can in fact be meaningful.
Relativity provides a more rigorous way of modeling this, treating spacetime as a four-dimensional manifold. When you move through the spatial dimensions relative to some reference frame, the rate of your motion through time is reduced relative to that same reference frame. This is commonly modeled on a spacetime diagram: https://en.wikipedia.org/wiki/Minkowski_diagram
Btw our atomic standard of length is defined with respect to the speed of light, making speed (he first derivative of space with respect to time) more fundamental than space itself. This isn’t just abstract theory.
Think of an object's "velocity" as a unit vector in a 2d circle. X axis is fraction of C(meter/second), Y axis is rate of time passage (seconds/second).
Every object no matter how slow moving has a velocity on the unit circle. An object that isn't moving is moving forward in time at the same rate as you, the observer. But an object that is moving very quickly moves much more slowly through time than you do as the observer.
So the key distinction is that time is not a fixed reference, it's subjective depending on who is watching.
General relativity basically starts with the assumption that everyone is moving through space-time at the speed of light. We sedentary material beings experience that mostly as moving through the dimension of time. Non material things like photons experience it as moving through space (because they lack inertia). When you accelerate to high speeds, you’re somewhere between the two extremes.
The issue is in your own frame (say if you're a muon or a person), unless you're accelerating, you're at rest with respect to your frame. Physics after Einstein's special relativity assigns to each reference frame a way to measure spatial differences and times (cute terms used in textbooks are rulers and a clock). Now, if another object is moving wrt you at a fast speed that you measure that is close to c, when you measure things that happen to it, it appears to happen slower as measured by your clock. So the reality is it appears slower to you in your frame. An good example of this is a particle like a muon will appear to have a longer lifetime if it were moving relativistically (near c). The converse is (sort of) true: for the moving object, in its frame, when accounting for the distances traveled, your clock also appears slower to it.
The reason framing it this way is important for me when I teach students is because it honors ones of the main points of special relativity that it did away with Newton's concept of a universal rest frame and made the important rest frame any inertial frame, and this helps demystify SR from being something esoteric but instead be based on simple logic: everyone is at rest in their own rest frame, so the physical laws in two frames moving respect to one another must be the same laws if you switch from one frame to the other. Since physics in any given rest frame seem to require light moves at c, certain other things must change in order to have both frames agree a light ray observed by both move at c.