NASA, ESA, and Johan Richard (Caltech, USA); Acknowledgements: Davide de Martin & James Long (ESA/Hubble)
This image illustrates a gravitational lensing effect due to the distortion of space by mass. This is one prediction where Einstein's theory of relativity gave the right answer where Newton's did not. But even with this, it's impossible to 'prove' Einstein right.
You've heard of our greatest scientific theories: the theory of evolution, the Big Bang theory, the theory of gravity. You've also heard of the concept of a proof, and the claims that certain pieces of evidence prove the validities of these theories. Fossils, genetic inheritance, and DNA prove the theory of evolution. The Hubble expansion of the Universe, the evolution of stars, galaxies, and heavy elements, and the existence of the cosmic microwave background prove the Big Bang theory. And falling objects, GPS clocks, planetary motion, and the deflection of starlight prove the theory of gravity.
Except that's a complete lie. While they provide very strong evidence for those theories, they aren't proof. In fact, when it comes to science, proving anything is an impossibility.
Art by Karen Teramura, UH IfA with James O’Donoghue and Luke Moore
In theory, the differing properties of Jupiter's great red spot, distinct from the rest of the atmosphere, could be related to thermal differences coming from below. Even if the evidence comes in to support this idea, it won't constitute scientific proof.
Reality is a complicated place. All we have to guide us, from an empirical point of view, are the quantities we can measure and observe. Even at that, those quantities are only as good as the tools and equipment we use to make those observations and measurements. Distances and sizes are only as good as the measuring sticks you have access to; brightness measurements are only as good as your ability to count and quantify photons; even time itself is only known as well as the clock you have to measure its passage. No matter how good our measurements and observations are, there's a limit to how good they are.
John D. Norton
A light-clock, formed by a photon bouncing between two mirrors, will define time for an observer. Even the theory of special relativity, with all the experimental evidence for it, can never be proven.
We also can't observe or measure everything. Even if the Universe weren't subject to the fundamental quantum rules that govern it, along with all its inherent uncertainty, it wouldn't be possible to measure every state of every particle under every condition all the time. At some point, we have to extrapolate. This is incredibly powerful and incredibly useful, but it's also incredibly limiting.
The curvature of space means that clocks that are deeper into a gravitational well -- and hence, in more severely curved space -- run at a different rate than ones in a shallower, less-curved portion of space. While our predictions for GPS satellites work extraordinarily well, even this cannot 'prove' that General Relativity is correct.
In order to come up with a model capable of predicting what will happen under a variety of conditions, we need to understand a few things.
What we're capable of measuring, and to what precision.
What's been measured thus far, under specific initial conditions.
What laws hold for these phenomena, i.e., what observed relationships exist between specific quantities.
And what the limits are for the things we presently know.
If you understand these things, you have the right ingredients to formulate a scientific theory: a framework for explaining what we already know happens as well as predicting what will happen under new, untested circumstances.
NASA / STScI / A. Felid
If you look farther and farther away, you also look farther and farther into the past. The farthest we can see back in time is 13.8 billion years: our estimate for the age of the Universe. It's the extrapolation back to the earliest times that led to the idea of the Big Bang. While everything we observe is consistent with the Big Bang framework, it's not something that can ever be proven.
Our best theories, like the aforementioned theory of evolution, the Big Bang theory, and Einstein's General Relativity, cover all of these bases. They have an underlying quantitative framework, enabling us to predict what will happen under a variety of situations, and to then go out and test those predictions empirically. So far, these theories have demonstrated themselves to be eminently valid. Where their predictions can be described by mathematical expressions, we can tell not only what should happen, but by how much. For these theories in particular, among many others, measurements and observations that have been performed to test these theories have been supremely successful.
But as validating as that is — and as powerful as it is to falsify alternatives — it's completely impossible to prove anything in science.
Paul Dawkins / Lamar University
A mathematical proof that the derivative of [f(x) - g(x)] equals the derivative of f(x) minus the derivative of g(x). In science, even mathematical proofs are less than 100% certain, as it's not 100% certain that the mathematical rules apply to your physical system.
In science, at its best, the process is very similar, but with a caveat: you never know when your postulates, rules, or logical steps will suddenly cease to describe the Universe. You never know when your assumptions will suddenly become invalid. And you never know whether the rules you successfully applied for situations A, B, and C will successfully apply for situation D.
Larry McNish of RASC Calgary Center
It isn't simply that galaxies are moving away from us that causes a redshift, but rather that the space between ourselves and the galaxy redshifts the light on its journey from that distant point to our eyes. Of course, this is predicated on an assumption whose validity we have no way of testing. If it's wrong, so may be all the conclusions we draw from this.
It's a leap of faith to assume that it will, and while these are often good leaps of faith, you cannot prove that these leaps are always valid. If the laws of nature change over time, or behave differently under different conditions, or in different directions or locations, or aren't applicable to the system you're dealing with, your predictions will be wrong. And that's why everything we do in science, no matter how well it gets tested, is always preliminary.
Thomas Gutierrez, who insists there is one 'sign error' in this equation
The Standard Model Lagrangian is a single equation encapsulating the particles and interactions of the Standard Model. It has five independent parts: the gluons (1), the weak bosons (2), how matter interacts with the weak force and the Higgs field (3), the ghost particles that subtract the Higgs-field redundancies (4), and the Fadeev-Popov ghosts, which affect the weak interaction redundancies (5). Neutrino masses are not included. Also, this is only what we know so far; it may not be the full Lagrangian describing 3 of the 4 fundamental forces.
Even in theoretical physics, the most mathematical of all the sciences, our "proofs" aren't on entirely solid ground. If the assumptions we make about the underlying physical theory (or its mathematical structure) no longer apply — if we step outside the theory's range of validity — we'll "prove" something that turns out not to be true. If someone tells you a scientific theory has been proven, you should ask what they mean by that. Normally, they mean "they've convinced themselves that this thing is true," or they have overwhelming evidence that a specific idea is valid over a specific range. But nothing in science can ever truly be proven. It's always subject to revision.
public domain work from Andreas Knecht
In the standard model, the neutron's electric dipole moment is predicted to be a factor of ten billion larger than our observational limits show. The only explanation is that somehow, something beyond the Standard Model is protecting this CP symmetry. We can demonstrate a lot of things in science, but proving that CP is conserved in the strong interactions can never be done.
This doesn't mean it's impossible to know anything at all. To the contrary, in many ways, scientific knowledge is the most "real" knowledge that we can possibly gain about the world. But in science, nothing is ever proven beyond a shadow of a doubt. AsEinstein himself once said:
The scientific theorist is not to be envied. For Nature, or more precisely experiment, is an inexorable and not very friendly judge of his work. It never says "Yes" to a theory. In the most favorable cases it says "Maybe," and in the great majority of cases simply "No." If an experiment agrees with a theory it means for the latter "Maybe," and if it does not agree it means "No." Probably every theory will someday experience its "No"—most theories, soon after conception.
The idea of unification holds that all three of the Standard Model forces, and perhaps even gravity at higher energies, are unified together in a single framework. This idea is powerful, has led to a great deal of research, but is a completely unproven conjecture. Nevertheless, many physicists are convinced this is an important approach to understanding nature.
So don't try to prove things; try to convince yourself. And be your own harshest critic and your own greatest skeptic. Every scientific theory will someday fail, and when it does, that will herald a new era of scientific inquiry and discovery. And of all the scientific theories we've ever come up with, the best ones succeed for the longest amounts of time and over the greatest ranges possible. In some sense, it's better than a proof: it's the most correct description of the physical world humanity has ever imagined.