Over the past century or so, we’ve seen some pretty revolutionary changes in the world of physics. Newtonian mechanics held the crown as the best explanation for a long time, but in fairly rapid succession, relativity and quantum mechanics came along to oust it from the top job. It is now pretty much universally acknowledged that Newton was wrong about several important things, and that the modern theories do a much better job of explaining the physical universe.
Why, then, are Newton’s formulae still taught in schools? Because, in a broad sense, Newton wasn’t wrong - he just wasn’t quite specific enough. If you are calculating the motion of an apple falling in Earth gravity, to the kinds of tolerances required for such a task, Newton’s equations are perfectly fine to use. It’s only when you want to describe things with immense gravitational fields, things that are moving extremely fast, or things on a subatomic scale, that Newton falls apart. Now, don’t fall into the trap of treating these things as separate magisteria; if you use relativistic equations to calculate the motion of the apple you will get the correct result - to a much greater degree of accuracy than you will with Newtonian mechanics.
But since your methods of measuring the strength of gravity, the weight of the apple, and the time it takes are probably going to be pretty crude, and rounded to whatever decimal place you decide upon; and since it’s not moving fast enough, or in a strong enough gravitational field for relativity to make much of a difference, you can get away with using Newton. And in fact, you are absolutely better off using Newton in this case, it’s not just laziness - it would take you a hell of a lot more of your precious time to use relativity, and since your results are only as good as your least-accurate measurement, it’s unlikely to give you a better result anyway.
So, for the kinds of medium-sized, slow-moving objects we encounter day-to-day, Newton is still useful. This kind of near-enough-is-good-enough approach to science jars a bit at first; it seems antithetical to science’s spirit, the search for absolute truths. People often have this idea that there are these golden equations hidden in the base code of the universe, and that science is trying to discover what they are. But science isn’t really like that. Science isn’t about discovering a pre-existing set of equations that run the show, it’s about making equations that describe the way things happen, with varying degrees of accuracy. It is very much a results-oriented enterprise.
As an aside, none of this means we should get complacent, or that the things we’re learning now aren’t useful. There’s still so much we don’t know, and the applications of the things we learn from these small-scale studies into the nature of matter do have an effect on the everyday world. For example, if you’ve ever used a hard drive, you’ve benefited from humankind’s knowledge of quantum mechanics.
But nonetheless, for everyday-scale problems, Newtonian mechanics are a useful tool. “Right” and “wrong” aren’t really salient concepts here - quantum mechanics may be more “right” than Newtonian mechanics, but on a quantum scale, the interactions are too complex for us to get meaningful macroscopic answers very easily. So Newton, while “wrong”, is a useful abstraction.
In philosophy of late, there has been an ongoing debate between two camps. On the one hand, you have Free Will, which says that I am the author of my own actions, I have control over my life, and the phrase “I could have done X, but I didn’t” has meaning. On the other hand, you have Determinism, which is generally formulated as a denial of traditional notions of Free Will - we are just atomic machines, and our actions are the consequences of the electrochemistry in our brains; it’s all just atoms interacting with each other, so to say “I could have done X, but I didn’t” is false; since it’s simple cause-and-effect, you couldn’t have done anything but what you ended up doing.
And using these formulations, if you look at everything we know about the physical universe, let’s be blunt - Determinism is right, and Free Will is wrong. The human mind is inseparable from the human brain; states of consciousness are states of biology; if you go down the line, biology is chemistry, and chemistry is physics; it really is a causal chain of interacting quarks.
People don’t like this because it conflicts with a sense of Self that is still very much rooted in dualism. Even atheists, and other people who don’t really believe in souls in a traditional sense, still tend to think like this - like their consciousness is a computer program, for instance. And, certainly, it may be possible in the (relatively) near future for us to “download” our minds into a computer and live there - but this would not really be a download, it’d be a port. You can’t separate the self from the physical structures that underpin it, like you can with a program on a hard drive, because the Self is the structure. You can probably create a reasonable facsimile of that Self on a hard drive; it’s just important to remember that it’s a facsimile and not the thing itself.
The other main reason this answer doesn’t satisfy people is because it doesn’t answer any of the accompanying questions; we want to know whether we have Free Will for a reason, we want to use that information to answer other questions. We want to know whether it’s right to punish people for their actions. We want to know whether or not to fall into nihilism; whether what we think, feel and will actually matter. We want to know if morality can have any coherent purpose, through our will to act. And Determinism, while correct, doesn’t really answer these questions.
Free Will, however does. Much like Newtonian mechanics, it’s not so much a literal, accurate truth as it is a useful abstraction. Yes, your consciousness is the product of nearly 4 billion years of evolution, of the society you were brought up in, of the input of your family and friends, of every experience you’ve ever had; and therefore any act you perform can in some way be attributed to these causes. But the causal links are so mind-bogglingly complex, so incomprehensibly tangled, that it’s simpler to just call the whole Black Box “You”.
People get quite uppity about the notion of Determinism; as though the rejection of the idea “I am the author of my own actions” means that someone else is the author of their actions. As though the things your subconscious does are somehow separable from “you”. As though there can be any definition of “you” that does not include your biological urges, your upbringing, your experiences. These unique characteristics are what make you “you”, and we should not be so keen to bin them as Other.
In any case, this clearer positioning of Free Will as an abstraction - an abstraction we know the underlying truth about - allows us to answer those nagging questions. Is it right to punish someone for their actions? We can see that the focus needs to be on results; yes, that person may have been caused - or at least predisposed - to commit a particular crime by their upbringing, which is a causal force. But our punishment for this crime can also be a causal force; we can make this person see the error of their ways. In this light, it becomes clear that while it is certainly right and desirable to “punish” someone in a broad sense, it should not be punishment so much as rehabilitation. The focus should be on behavioural change in the offender, not on revenge.
Further, do our decisions matter? Does morality have any relevance; do our moral choices count? The answer to this one is clear: absolutely. People sometimes forget that introspection, reading new things, having discussions, and just plain thinking, are extremely powerful causal forces, of the same order as biology and cultural upbringing. Biology and acculturation are certainly important factors but they are by no means the last word - deliberate learning and willpower are much more important, if properly exercised.
Now, okay - the impetus for a particular thought might come from reading this article, or from reading what someone else has to say on Free Will; but the information you receive is going to be filtered through so many of your cognitive algorithms that what comes out the other side is definitely going to be a product of “you”. Furthermore, our brains have the capacity to self-modify, so whatever thinking you do will actually change the way that thinking is done (not just the data it thinks about). So yes, thinking matters; if we’re concerned about morality, if we ponder the big questions, it will affect our actions, and those actions do have an effect on the world. This formulation gives us the sense of agency that makes self-improvement possible under a Deterministic model; "I" may be the result of many preceding causes, but whatever "I" am, "I" have the power to act.
When comparing Newtonian mechanics with quantum mechanics, “right” and “wrong” aren’t really important concepts - what matters is what gives useful results in a particular situation. The same applies to Free Will and Determinism - and to answer the big questions of life, a notion of Free Will built on the facts of Determinism is by far the most useful.