We mark the progress of time by a thin line between past memories and no memories (the future). If time is actually flowing backwards or even standing still we would not know it. If memories are deleted one by one we would still remember a past and imagine a future so how can we be sure time is marching on?
First off, it's worth noting that if time moved "backwards," we would talk about it going "forwards" because our perceptions would shift. You would still have the question as to why time does not move "backwards."
Scientifically, the "forward" direction of time is the direction of increasing entropy in the universe.
Your question deals with perception, which may be one step beyond the simple scientific definition, if you believe that there is more to "everything" than just simple physics problems. I would answer your question with another question: would it make any difference if time flowed "backwards" instead of "forwards?" Would there be any perceptible differences, or moral implications? If not, then one can rest assured that the direction time flows is arbitrary and you may choose to view it in any direction you please. Just know that if you choose the "backwards" direction with respect to other people, they may get confused when you talk to them about past and future events due to lingusitics.
If there is a particular perceptive difference or implication which you see important, that might be a good start of another question tailored to that difference or implication.
We cannot. Furthermore we cannot even be sure there is such a thing as "time" in nature. "Time" is a bit of vocabulary that helps us coordinate our actions, i.e. communicate. It does not follow that there is a patch of nature that the term refers to. Relativity is way over my head, but I gather one point of it is that "time" is not absolute, not the same thing in all places and times - note the circularity involved in even talking about time.
"What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know." - Augustine.
For a thorough discussion by one of today's best philosophers see "Time's Arrow and Archimedes' point: New Directions for the physics of time" by Huw Price. Alas, I have not read it, but I know from his other writings that he knows what he's doing and he's very imaginative. For example he also addresses the nature of causality and suggests (my words here) that there is not necessarily any causality in nature, the concept is just a discursive device we invented to help ourselves cope and communicate more effectively.
Perhaps it is better to deconstruct the notion of time altogether. Neither the past nor the future actually exist. The past is what we call a collection of memories. The future is speculation upon what memories might be added to the existing pile. Both are mental constructs, and have no physical characteristics.
Time is simply the way we manage our pile of memories, and arrange them into a logical procession, a filing system and nothing more.
Remember that space IS time, and time IS space. It is equally correct to say that something is X miles long as it is to say it is Y seconds long. Time is an indication of movement. Time is how we make sense of movement. Movement produces the sensation/experience of time, not the other way around. Indeed, if a giant button was pressed that stopped all movement in the universe, would we not think that time had stopped as well? How could we confirm time's "flow" or even its very existence with a universe in which no movement occurred? Without motion, the ability to compare two different physical states, time loses all meaning.
That thin demarcation between the ideas of past and future is the present, and is the only thing that truly exists.
To answer your question then, "time" "moves forward" because it is an accretive process, an idea that is relative to an individuals experiences.
Time is measured by clocks. If your clock stops, there are two possibilities:
1) Change the batteries until the clock moves on again :-)
2) You yourself move with the speed of light. The latter is impossible as long as you are not a photon. That's a deep result of the Theory of Special Relativity. Photons do not experience time.
First of all we need to understand time. It is same as other dimension which we human has defined like we have length, speed, volume, weight, strength and many other.
So if we say that is something grows or we compare with other object then we can say that one this is longer or shorter than other or its same as other as we have created and defined that, in fact if we swap longer term with shorter then we will say totally opposite, so same is with time if its moving forward or its at a pause its all a perspective, as we try to compare our selves with the different time of past or what we want in future. but if you lost yourself in a jungle and live life free from any comparisons or desire then you will be at standstill.
So time is where it was but we being human think that we are in control of things and try to compare with other with respect to time which creates this illusion.
If time is not flowing forward, how exactly is that time? At the same time, if time is what allows for change, how can it move, including any sort of "flowing"? If it isn't moving, what is this forward and backward thing? This is just a vocabulary problem.
It is possible that the second law of thermodynamics is a side effect of the fact that human memory is an exothermic chemical reaction, rather than the other way around. It is further possible that not all beings that accumulate information are tied to the directionality of chemical processes in the same way. But that is not the same question.
Boltzmann at some point proposed that we experience time consistently because we are near an event of very low entropy, that we were being driven into higher entropy by falling away from a specific part of space. But even that somewhat lacks cohesion, in what way are we falling? It seems more consistent to assume that the accumulation of entropy continually reversed itself along some other dimension, but we can only remember the last time it moved forward for us.
Any other approach ties two dimensions up too tightly, which makes the physics of thermodynamics a little idiosyncratic to be realistic. Either time is the accumulation of entropy, or it is something else, or it is just coincidentally both, and we never needed to consider it as 'flowing' one direction or the other. But if it can only go forward or backward, it is just too special to be real.
The separation here makes some sense: if the last instant is not always the same copy of that point in "the other dimension of time", but our time has reversed back through it and come back forward, traversing some part of that 'other place', that leaves a convenient way to imagine a determinate, reversible, quantum mechanics that leads to superficial randomness.
In "The Elegant Universe" Green mentions predecessors to our current string theory that proposed five spatial dimensions and two temporal ones (which can be wound up into a single complex number, if one insists, as Stephen Hawking seems to). So this is not an entirely inane consideration.
But we need some way to think of what is or might be going on here as something other than time, or we need a broader conception of what a dimension is. (Otherwise, people will keep asking this same, silly question in this same silly form, which leads nowhere.)
I think there are two separate components to time:
The feeling we have of time flowing. This requires consciousness.
The objective existence of time. Event A happens before event B.
So when asking any question about time you should consider which of those elements you are discussing.
For your actual question you are asking about the subjective feeling that time flows in a certain direction. This is a question about our feelings and not about anything objective. So the simple answer is if we felt time was flowing backward then yes, we would feel time was flowing backwards.