This may be a bit pedantic, but I don't like the framing "its 'timeframe' slows down" which is similar to an often used phrase "when you go close to the speed of light, your clock runs slower" because it gets the situation backwards and actually misses Einstein's key insight about relativity.
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.
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.