If the future influenced the past, that would be retrocausality. As Victor Bhaura puts it,

Retrocausality means that, when an experimenter chooses the measurement setting with which to measure a particle, that decision can influence the properties of that particle (or another one) in the past, even before the experimenter made their choice. In other words, a decision made in the present can influence something in the past.

Victor Bhaura, “Retrocausality — Future Influences Past Information Before Occurrence Of An Event” at Medium (June 8, 2022)

Bhaura reminds us of a limerick called “Relativity” from 1923:

There was a young lady named Bright
Whose speed was far faster than light;
She set out one day
In a relative way
And returned on the previous night.

Now, if Bright was exceeding the speed of light, she was already violating the laws of physics for entities as large as ourselves — and she could well end up going backward in time, according to philosopher of mathematics Sam Baron.

But, as Bhaura has noted, quantum particles do not follow such rules. In 2019, scientists showed that time travel is theoretically possible by sending a simulated particle back in time via a quantum computer. A quantum computer doesn’t use 1’s and 0’s (bits) but rather qubits, which are simultaneously 1’s and 0’s. That’s much faster. Yes, quantum systems can do that. It’s why Albert Einstein called them “spooky.”

Since quantum mechanics is about probability (not certainty), success was no guarantee. However, in a two-qubit quantum computer, the algorithm managed a time jump an impressive 85 percent of the time. When it was upped to three qubits, the success rate dropped to about 50 percent, which the authors attributed to imperfections in current quantum computers.

Kevin Dickinson, “Researchers successfully sent a simulated elementary particle back in time” at Big Think The paper is open access. (May 13, 2019)

The particle was “simulated” because the amount of force required to send an actual particle back in time exceeded natural capabilities:

This experiment also shows us that sending even a simulated particle back in time requires serious outside manipulation. To create such an external force to manipulate even one physical particle’s quantum waves is well beyond our abilities.

“We demonstrate that time-reversing even ONE quantum particle is an unsurmountable task for nature alone,” study author Vinokur wrote to the New York Times in an email [emphasis original]. “The system comprising two particles is even more irreversible, let alone the eggs — comprising billions of particles — we break to prepare an omelet.”

Kevin Dickinson, “Researchers successfully sent a simulated elementary particle back in time” at Big Think (May 13, 2019) The paper is open access. (May 13, 2019)

That’s the reason that time travel into the past, as in H. G. Wells’s The Time Machine, is impractical. It may also be futile if the object is to change anything because that is unlikely to be possible.

Meanwhile, in 2021, another team of physicists offered calculations proposing that quantum particles can move forward as well as backward in time — again because of quantum superposition:

According to the principle of quantum superposition, individual units ( for instance, of light) can exist in two states at once, both as waves and particles, manifesting as one or the other depending on what you’re testing. Rubino’s team looked at a quantum superposition with a state that evolves both backward and forward in time. Measurements showed that more often than not, the system ended up moving forward in time. But for small entropy changes, the system could actually continue to evolve both forward and backward in time.

The paper is open access.

Stav Dimitropoulos, “Time Can Actually Flow Backward, Physicists Say” at Popular Mechanics (April 22, 2022)

Team leader Giulia Rubio stresses, that still wouldn’t move us. But there may be another way, as we shall see… Christian apologist C.S. Lewis (1898–1963), who read and wrote science fiction, pointed out that the present and future can change the past. If we assume that God exists and God is not in time, an action taken now could influence an event in the past. He offers an illustration:

When we are praying about the result, say, of a battle or a medical consultation the thought will often cross our minds that (if only we knew it) the event is already decided one way or the other. I believe this to be no good reason for ceasing our prayers. The event certainly has been decided— in a sense it was decided ‘before all worlds’. But one of the things taken into account in deciding it, and therefore one of the things that really cause it to happen, may be this very prayer that we are now offering.

Thus, shocking as it may sound, I conclude that we can at noon become part causes of an event occurring at ten o’clock. (Some scientists would find this easier than popular thought does.) The imagination will, no doubt, try to play all sorts of tricks on us at this point. It will ask, ‘Then if I stop praying can God go back and alter what has already happened?’ No. The event has already happened and one of its causes has been the fact that you are asking such questions instead of praying. It will ask, ‘Then if I begin to pray can God go back and alter what has already happened?’ No. The event has already happened and one of its causes is your present prayer. Thus something does really depend on my choice. My free act contributes to the cosmic shape. That contribution is made in eternity or ‘before all worlds’; but my consciousness of contributing reaches me at a particular point in the time-series.

Lewis, Clive Staples. Miracles (p. 163). Kindle Edition.

There is another way in which the present can change the past. Suppose a woman has made rather a mess of her life and reaches a crisis point. Two possibilities: 1. She gives up and sinks further into misery and despair. 2. She decides to seek help and, on getting it, turns her life around — becoming, in time, a support to others.

As she looks back on her life in the first scenario, she will see a bleak, grim “born to lose” picture, punctuated by disasters, the worst of which was perhaps that crisis point, after which she just gave up…

In the second scenario, looking back from some years’ distance, she sees a very different past: That crisis point “is the moment I decided, I to do whatever it takes to free myself!” All the other events of note are now remembered as steps, forward or backward, on a journey to a more meaningful life.

Perhaps that’s one of the roles that free will plays in our lives. It changes the past — not by changing the events but by making them mean different things. And after all, the main reason we care about the past is its meaning. So there is a sense — this sense — in which we can really travel back and change the past, by changing its meaning.

You may also wish to read:

A form of time travel that might be possible… In world of entropy, time runs in one direction and reversing it would create impossible contradictions, physicists say. The time travel that is likely to be possible would be like having a very good four-dimensional memory — it recreates events but it doesn’t change them.