Amrit:
Actually, Dr. Barbour is perfectly wrong. He's wrong on so many points that it takes up most of a chapter of a book that I have now in proposal form on the nature of time. However, I will leave the discussion of his ideas for a later time and probably a new paper that I will post at scientificblogging.com. In the meantime, however, allow me to deconstruct your statements which followed.
"The universe is in a continuous change."
If this is true, then time is real. Time is the dimension where events take place. In Barbour speak, time is that arrangement of Now slices that he talks about but is, by his own admission, incapable of slicing down to any minimal measurement. If you have change, then you have time, but it is wrong to believe that change equals time, because it doesn't.
"A change n gets transformed into a change n+1, the change n+1 into a change n+2 and so on."
If there is no time, then there is no transformations because those transformations, i.e. "changes" take time to take place. No time, no change.
"Clocks measure a frequency, velocity and numerical order of change. Changes do not occur in time, changes occur in space only."
Wrong. It's called a "space-time" continuum for a reason. Time and space are connected but serve different purposes. Space is where things go - tables, pizza, the moon, whatever. At 1 PM I can have an empty table by a window. At 9 PM I can have a pizza on that table and a view of the moon through that same window. The table and the window never moved yet things changed around them. Why did those things change? Because events took place over time to change them. If you take away time, you have nothing for change to take place in. No time, no change.
"Time is not a part of space. Space is timeless".
Again, "space-time continuum". Minkowski - "from this point on, time and space are inextricably connected". There is zero credible evidence to the contrary.
"In the space there is no past and no future. Past and future belong to the inner time that is a result of neuronal activity of the brain."
Really? If that were true we would not be able to view anything in space. The light reaching us from the sun takes time to get here from the moment of its radiance. Black holes in distant galaxies that we see might not even exist anymore because the light that we observe is millions of years old. Our entire view of the universe consists of looking into the past, a past that your statement says doesn't exist. Well, as Einstein pointed out, time is not absolute and our now, with that light from the black hole, is in the black hole's past from its view point, if it still exists.
Time is real. It is misunderstood, maligned, misrepresented, and denied. None of that changes the fact that time is real and none of that passes vigorous scrutiny, once it is applied.