  Intrinsic time is an example of an event-based conception of time, used to
analyze financial time series. Here, for the first time, we reveal the
connection between intrinsic time and physical time. In detail, we present an
analytic relationship which links the two different time paradigms. Central to
this discovery are the emergence of scaling laws. Indeed, a novel empirical
scaling law is presented, relating to the variability of what is know as
overshoots in the intrinsic time framework. To evaluate the validity of the
theoretically derived expressions, three time series are analyzed; in detail,
Brownian motion and two tick-by-tick empirical currency market data sets (one
crypto and one fiat). Finally, the time series analyzed in physical time can be
decomposed into their liquidity and volatility components, both only visible in
intrinsic time, further highlighting the utility of this temporal kinship.
