The Arrow of Time

A Philosophical Interpretation of Positive and Negative Time

Jim Redgewell
28 October 2026

Abstract

This paper explores the arrow of time using the philosophical principle of Presentism, which holds that only the present exists. It proposes a simple interpretation of negative and positive time without requiring time to run backwards.

1. The Present

Presentism maintains that the past no longer exists, the future has yet to occur, and only the present is physically real.

We therefore define the present moment as:

t = 0

All events are described relative to this moment.

2. Negative and Positive Time

Consider three events:

• t = −5 minutes: An event that occurred five minutes ago.

• t = 0: The present moment.

• t = +5 minutes: An event expected five minutes into the future.

Negative time does not represent time travelling backwards. It simply identifies an event that occurred before the present.

Similarly, positive time identifies an event that lies ahead of the present.

3. The Arrow of Time

The arrow of time always points from the past towards the future.

As time progresses, future events become present events, and present events become past events.

The reference point t = 0 continually advances with the present.

This description requires no reversal of time and no physical existence of past or future events.

4. Could Positive and Negative Time Cancel?

One interpretation might be that negative time and positive time cancel.

For example:

−5 + 5 = 0

This suggests the possibility that opposing temporal quantities balance at the present moment.

However, mathematical cancellation of time coordinates does not establish physical cancellation. Whether such a balance represents a genuine physical process remains an open hypothesis.

5. Physical Interpretation

The distinction between negative and positive time is mathematical. The additional claim that only the present exists is philosophical.

This interpretation is compatible with ordinary time-coordinate conventions, although Presentism itself raises unresolved questions concerning relativity and the nature of simultaneity.

6. Conclusion

Time does not need to run backwards for negative time to have meaning.

Negative time represents the past, zero represents the present, and positive time represents the future.

The arrow of time describes the continuous progression of events in one direction.

One possibility worth investigating is whether positive and negative temporal contributions could cancel, leaving the present as the only physically existing moment.

The central philosophical proposition remains:

Only the present exists. The past has ceased to exist, and the future has yet to occur.