What if there is no rebirth?

The final goal in Buddhism is to overcome rebirth, as all misery (old age, sickness, company of people you do not like, parting from loved ones) starts with birth as explained in the Dhammacakkappavattana Sutta.

Once you reach full liberation you have no more rebirths.

I will try to rescue the question from speculative paths.

It's not a stretch to see the Dalai Lama's words expressing the buddhist original commitment to what is real. But the question underneath is about how one's faith (or the faith of a community) is confronted with a different reality. Yet, the canon has quite a few teachings and warnings about faith (of the "kind" talked about here), and the insistent plea for direct knowledge.

The discovery of false claims no doubt diminish our trust in the texts and may interfere with our commitment to try its suggestions. But it is worth noting that the tone of these texts is not "take it as I say", but of "come and try [and at this point, here is what I expect you to have seen]" -- exercises followed by a map, with evaluation cues.

Buddhism, in its original form, is not alone in its careful attitude towards foreign propositions not tasted by one's mouth. Science has similar flavor (though much more loose in regard to one's direct experience, and much more strict in regard to communication and "observability"), with a community reasonably aware of its stance. Thus, one could reasonably argue that what ultimately survive from both science and buddhism (in its essence) are not the factual assertions made therein (they may as well be discovered to be otherwise). However, its goal, its method and its evaluation strategies are something to preserve.

Maybe the map is wrong. In science, often it is. Yet, trained scientists cherish the system above any temporary result. The system reinforces how to approach itself.

A buddhist could say exactly the same thing about the canon. "why are you clinging to beliefs you did not investigate and could cause you misery?" it asks directly of the reader.

Lets say science proves that there's no rebirth. What does scientific proof really mean to you? It means you are putting your faith on the scientists who supposedly prove it. It is not your direct knowledge. Rebirth is already proven within the Buddhist community. Proven by Lord Buddha and the Ariya Sangha who can see the past and future lives. Even a non-Buddhist who attains the knowledge of seeing past births through perfecting the Jhanas sees the process of rebirth. So Buddhists don't have a problem in accepting rebirth on faith. Because we take refuge in the Buddha, Dhamma and Sangha instead of scientists. Furthermore, what is proven in Buddhism can be known by direct knowledge. Scientific proof is not known by direct knowledge. It's always a hypothesis. Otherwise, it can't change from time to time.

"If this is definitely proven" is the key phrase in what Dalai Lama has said. Proven according to science or proven according to Buddhism? In other words, proven by hypothesis(which again may change in the future) or proven by direct knowledge? Such sayings are typically targeted at audiences with materialistic views. If it gets them to be more interested in the practice of Dhamma, it serves the purpose.

If science were to prove literal rebirth wrong, then Buddhists would have to accept the fact that literal rebirth does not exist, and begin to examine the possibility that the Buddha meant moment to moment rebirth and we were interpreting the teaching incorrectly. I don’t know how science would do this but since the practice asks you to look and see for yourself, if you were to somehow discover this truth (that rebirth was not literal) the practice would dictate that you acknowledge it.

If there is no rebirth, then there is no rebirth, the point with the Buddha's teachings is that they are useful not only for the next life, but for this one! That is exactly why there are many debates about Buddhism being a religion or a way of life, that is also why Buddhism can be used by people from other religions.

If you practice the Buddha's teachings at least you will leave good things behind (in case there is no rebirth).

I suggest you don't put to much focus on your next life, your focus should remain here and now. In the practice!

Sometimes an apparently well-formed question can suffer from a "category error", such as in "Is the present King of France bald?" or "What noise would the programming language Pascal make if you dropped it on the floor?" In such cases, an appropriate way to "answer" the question is to point out the category error, instead of just saying, for example in the previous examples, "No" and "'CLANG!' (although some authorities argue "SPLAT!" is more accurate)". This Buddhism question isn't completely prone to this problem, but one aspect of it might be. So I'm going to attempt that kind of answer.

First, I'm with the Dalai Lama in that if science proves something in Buddhism to be wrong, then Buddhism would have to adjust. However, it's important to understand that there are certain kinds of true things that science simply cannot prove wrong. That's not because, as with many things in the past, our science just isn't advanced enough yet. It's because the scope of science doesn't cover everything important we might want to say. This goes against the modern prevailing view, sometimes called, often by its detractors, "scientism", which is really a modern version of positivism. However, it is not difficult to see that such scientism isn't obviously true.++

As an example, take the law of gravity, and in particular the component that says that "the gravitational force between two masses varies inversely with the square of the distance between them". That is very deeply established in science, and has been for centuries. If it were proved wrong, it would shake things up a lot. But science could indeed prove it wrong. In fact, there is already some evidence, surprising though it is, that in certain situations, the inverse square law isn't exact.

But now take the proposition "2+2=4". Philosophers would refer to that as a "necessary" truth. Science cannot ever prove that statement wrong because science relies on that statement and, more to the point, science does not deal with such truths. They are important truths that lie outside of science (in fact the existence of such statements doesn't break positivism which is broader than scientism, but it does constitute something that science cannot disprove).

Another one: "people typically experience redness when looking at tomatoes". Now science could certainly show that the frequency of light reflected off tomatoes corresponds not with red light but with blue light, but that doesn't change the fact that we experience redness. Science would probably come up with a theory as to why we experience redness when exposed to blue light (for example, perhaps we'd discover that tomatoes emit a certain gas that confuses our brain's color recognition system, leading us to experience redness instead of blueness), but as I say that would explain why, it would not disprove that we experience redness.

So, what about something like "there is no rebirth". Well to me that is clearly a statement that lies outside the scope of science, certainly of science as we usually use the word. To be a "scientific" statement typically means in practice that we can construct some kind of experiment capable of allowing us to make observations confirming the statement's truth and, even more important, observations confirming the statement's falsehood. But scientific observations are observations of the natural world and it's not clear that "rebirth" is posited as a phenomenon within the natural world. Now it's possible to argue, or at least to claim, that there is nothing but the natural world, but that's just begging the whole question. A claim that "natural science is all there is" is itself not a statement of natural science, so where does that leave it?

This doesn't mean, of course, that there's nothing in Buddhism that science couldn't disprove, but it does exclude a whole bunch of things from being disproven in that way. For example, I'd say that the entirety of the Four Noble Truths lies outside the scope of science. I'm not saying that they are necessarily true, nor that they couldn't be shown to be false. But science cannot do that, any more than gardening or cookery can.

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++ Note that I'm not saying that scientism argues that science can know everything. Even the scientistic view allows that some things may simply never be known. I'm making the point that scientism typically argues that if something is knowable, science will eventually, in principle, figure it out; and that if science cannot eventually, in principle, figure something out, then nothing else will.