Does time flow?

Many philosophers have argued that time itself is an illusion.
Consider this: time consists of past, present and future. Even
though we have records of the past and memories of certain events
that have taken place, it can no longer be considered to exist. The
future on the other hand has yet to unfold and therefore does
not exist either. This leaves the present which is defined as the
dividing line between past and future. Surely the ‘here and now’
exists. But although we ‘feel’ that this line is steadily sweeping
through time gobbling up the future and converting it into past, it
is nevertheless just a line and as such does not have any thickness.
The present, therefore, is of zero duration and cannot have a real existence either. And if all three components of time do not exist
then time itself is an illusion!
You may, as I do, take such clever philosophical arguments
with a pinch of salt. What is much harder to justify, however, is
the notion that time ‘flows’; that time goes by. It is hard to deny the
feeling that this is what happens, but having a ‘gut’ feeling about
something, however strong that feeling is, is not enough in science.
In our everyday language we say that ‘time passes’, ‘the time will
arrive’, ‘the moment has gone’ and so on. But if you think about
it, all motion and change must, by definition, be judged against
time. This is how we define change. When we wish to describe
the rate of a certain process we either count the number of events
in a unit of time, such as the number of heart beats per minute, or
the amount of change in a unit of time, such as how much weight
a baby has put on in one month. But it becomes nonsensical to try
and measure the rate at which time itself changes since we cannot
compare it with itself. People often jokingly state that time flows
at a rate of one second per second. This is clearly a meaningless
statement since we are using time to measure itself. To clarify
this, how would we know if time were to suddenly speed up?
Since we exist within time and measure the duration of intervals
of time using clocks which, like our internal biological clocks, must
presumably speed up also, we would never be aware of it. The
only way to talk about the flow of (our) time is to judge it against
some external, more fundamental, time.
But if an external time against which we could measure the
rate of flow of our own time did exist then we would only be
pushing the problem further back rather than resolving it. Surely
if time by its nature flows, then why should this external time not
flow also? In which case we are back to the problem of needing
a further, even more fundamental, time scale against which to
measure the rate of flow of external time, and so on in a neverending
hierarchy.
Just because we are unable to talk about a rate of flow of time
does not mean that time does not flow at all. Or maybe time is
standing still while we (our consciousness) are moving along it
(we are moving towards the future rather than the future coming towards us). When you look out of the window of a moving train
and observe fields rushing by you ‘know’ that they are standing
still and that it is the train that is moving. Likewise, we have the
strong subjective impression that the present moment (what we
call now) and an event in our future (say next Christmas) move
closer together. The time interval separating the two moments
shrinks. Whether we say that next Christmas is moving closer to
us or that we are moving closer to next Christmas amounts to the
same thing: we feel that something is changing. So how come
most physicists argue that even this idea is not valid?
Strange as this may sound, the laws of physics say nothing
about the flow of time. They tell us how things like atoms, pulleys,
levers, clocks, rockets and stars behave when subjected to different
forces at certain instants in time, and if given the status of a system
at a particular moment the laws of physics provide us with the
rules for computing its likely state at some future time. Nowhere,
however, do they contain a hint of flowing time. The notion
that time passes, or moves in some way, is completely missing in
physics. We find that, like space, time simply exists; it just is.
Clearly, say most physicists, the feeling we have that time flows is
just that: a feeling, however real it may seem to us.
What science is unable to provide at the moment is an
explanation for where this strong sense we have of passing time
and a changing present moment comes from. Some physicists and
philosophers are convinced that there is something missing in the
laws of physics. I will not go as far as to say that I subscribe to this
view, but I do believe we will only make progress when we have
a better understanding of how our own consciousness works, and
hence why we feel the passage of time.
I should mention that no less an authority than Einstein
himself held the view that the flow of time is illusory and even
expressed it when trying to console the bereaved widow of a close
friend of his, stating that she should take comfort in the knowledge
that the present moment is no more special than any other in the
past or the future; all times exist together.