No. Spacetime is an abstract dimension. Space-time merely references the relative position and change of relative position (motion) of matter.
Time measures change, You would only need a unit of time is you were expressing / measuring power change rate.
Causality is precisely the empirical evidence that proves what nonsense the block universe ‘theory’ is.
The past changes to become the present, which changes again to become the future.
The very essential, inherent meanings of these words, past (was) present (is) and future (will be), screams what a nonsense the block universe is.
No dimension is tangible.
It is one of the most frustrating aspects of science, the fact that otherwise eminent academics have allowed the word dimension to be so badly misused. (And, yes, Einstein must take some of the blame – but mostly I blame those who came after him)
Dimension means measurement.
A dimension is a measurement framework that we overlay an aspect of reality to calibrate and reference that aspect of reality.
Example – Temperature is the dimension of heat. Temperature is how we calibrate and index heat. Temperature is abstract, heat is real.
Space and Time are both words with multiple meanings. Both have a context as dimensions.
In the context of dimensions, Space is the dimension of (relative) static position, hence xyz-axis. The dimension of Space is how we measure relative static position, using standard units. It is static relative position because, by definition, it excludes Time.
The dimension of Time is how we measure, calibrate, index change. For instance, changing position (motion) is calibrated in, say, miles per hour. The per hour bit is time calibrating the rate of change.
So merge Time, the dimension of change, and Space, the dimension of relative position, and we get Spacetime, the dimension of relative changing position (motion) (in fact relative constant motion, as dimensions are reference-frame specific).
So, in answer to you question, the fourth dimension, like all dimensions, is NOT tangible.
Obviously Yes; abstract nouns, are outside the space-time continuum. Mathematics, justice, fashion, arts, science, religion…all abstract nouns that only exist in our mind.
But are you sure you know what the Space-time continuum actually is??
Space (in this context) is the dimension of (relative) position (hence xyz-axis)
Time (in this context) is the dimension of change (hence ‘rate’).
Spacetime is hence the merged dimension of changing position aka, motion.
So anything that is a ‘concrete noun’ (as opposed to an abstract noun) i.e. has a tangible reality – like a quark, or a table or a solar system – has a physical ()relative) position, and probably incurs change. And mostly will include change of (relative) position…most things in the universe (maybe all things) are experiencing motion, and all experiences relative motion (dimensions being reference-frame specific).
So anything with a physical presence will always be within the space-time continuum as you call it.