Has it ever occurred to you that the universe behaves in a systematic, profound, orderly way? It’s as if it subconsciously follows a hidden set of rules, privy to none other than itself. It becomes the job of the scientist then, to probe into nature and try find these little nuggets of truth. To accomplish this, a scientist makes observations, conducts experiments, and uses perhaps the greatest probing tool ever: mathematics. When scientists do discover these hidden truths of the universe they hand out names such as laws, principles, theorems, theories, etc. to these general behaviors of the universe. We get terms such “laws of physics”.
I personally didn’t give much thought to these matters until one day when I was watching one of Professor Lewin’s lectures on YouTube and he said, “We can never prove Newton’s laws of motion, but we believe in them because they are consistent with our experiments”.
I thought, “That’s weird! Laws of physics ought to be proved. Right?”
Like most maniacs who have 50 tabs open on their computer at the same time, I quickly googled to see whether Mr. Lewin was right. And what I found surprised me:
I realized not only are we unable to prove Newton’s laws, we are actually incapable of proving any law in physics.
Why didn’t anyone tell me this in high school?
In this article
This is the objective of this article. To try to make sense of the term law as it is used in physics, and to understand why such “laws of physics” cannot be proven. It is more of a personal opinion than a dogma; feel free to engage with me (respectfully) in the comments.
How laws of physics emerge
Physics is a practical science. We observe our physical world, carry out experiments, take note of the results, develop a hypothesis to explain our results and with luck, generalize the results to a wider field. It is the last step that is embarrassing: “generalizing results to a wider field”. It is at this point that terms like “law”, “principles” and “theories” pop up.
Think of this scenario.
The ancient Greeks had long known that the mineral Loadstone had the property of attracting small bits of iron. Today we know that Loadstone is a magnetized form of a commonly occurring iron oxide mineral by the name of Magnetite. Now picture yourself as a stonemason in the 13th Century working with Loadstones trying to shape them into rectangular slabs. You discover, quite accidentally, that the magnetic effect of your rectangular Loadstones was strongest at their two opposite directed points of the rectangle. You go ahead and name these points the “poles of the loadstone”. When you messed around with your rectangular stones much further, you discover another interesting property: similar poles repel each other and opposite poles attract each other.
You are finally confident enough, to state the following:
- All rectangular Loadstones have two poles
- Like poles of all rectangular Loadstones repel one another while unlike poles attract one another.
When someone asks how you came to that conclusion, you’ll simply tell them. “That’s how rectangular Loadstones behave, here try for yourself”. And you proceed to hand them over your Loadstones so that they can replicate the experiments themselves and check your conclusions. The skeptical ones even carve out their own rectangular Loadstones and carry out their own independent experiments. When they do arrive at the same conclusion as you, they would probably say, “Hey! Andrew was right. Like poles of a Loadstone repel and unlike poles attract. It’s pretty cool. Let’s call it the ‘Andrew Effect’”
By doing so they wouldn’t have proved your statements in the technical sense, they would have simply shown them to be true within their limits of experiments. For example, neither you nor your friends could guarantee that magnets behave the same way on the Moon or in interstellar space as these locations are outside the limits of your experiments.
As such, all laws in physics are, in essence, temporary. They aren’t cast in stone like the ten commandments; one experiment can rip the whole thing apart. Back when there was controversy regarding Einstein’s theory of relativity, here what Einstein himself had to say about it, “No amount of experimentation can ever prove me right; a single experiment can prove me wrong”.
What does “proof” mean?
“Proof” is essentially a mathematical concept that for some reason found its way into the physical sciences.
A long time ago, mathematics along with other physical sciences (physics, chemistry, biology, and geography) were grouped together under the same umbrella of natural philosophy. Students studying “natural philosophy” had to take all those subjects together. As a result, terms were used interchangeably in between disciplines. It made sense at the time but had unintended consequences down the line. The concept of “proof” is one of those unintended confusions.
In its technical sense, to prove something simply means to deduce a given statement or equation from fundamental principles. It means to establish that an idea is absolutely true, beyond any shadow of a doubt. This is done through a stepwise logical deduction practice that begins with a fundamental statement(s) that are assumed true. To establish this idea, let us go through a few examples.
Example 1: A mathematics problem
A common mathematical prank is a problem such as the one in the figure.
This problem lacks a solution because in general, the sum of three odd numbers cannot give an even number. Which begs the question, how can you prove it?
As stated earlier, in order to prove a statement, we have to refer to a more fundamental statement or statements that are assumed to be true at all times. In this case, the fundamental statements are the definitions of odd numbers and even numbers. For simplicity, we will alter the definitions a little, without changing the actual meanings.
Odd number: whole numbers starting from 1 that cannot be divisible by 2. Such as 1, 3, 5, 7, 9, etc. The general formula is 2n – 1. Where n = 1, 2, 3, 4, 5, etc.
Even numbers: whole numbers starting from 1 that are divisible by 2. Such as 2, 4, 6, 8, etc. The general sequence is 2n. Where n = 1, 2, 3, 4, etc.
These are the fundamental statements. We don’t need to nor can we prove them; we take them as they are. Think of them as our starting assumptions, or in this case, starting definitions (the study of numbers has to start somewhere right?). The question is whether we can use these two fundamental statements to prove our conjecture.
Let’s see.
Since we have three random odd numbers, we may represent them as follows.
Number 1: 2n-1
Number 2: 2m-1
Number 3: 2s-1
Here m, n and s are any whole numbers starting from 1. i.e. 1, 2, 3, 4…
The sum of these three numbers, that is, (Number 1) + (Number 2) + (Number 3), may be represented in the general sequence as follows: (2n-1) + (2m-1) + (2s-1).
This gives a result of (2n + 2m + 2s) – 3
= 2(n + m + s) – 3 = 2(n + m + s -1) – 1.
Since 2(n + m + s -1) is always an even number (.i.e. it is divisible by 2), then 2(n + m + s -1) -1 cannot be an even number because deducting one from an even number always gives an odd number.
That is: Even number – 1 = Odd number
This concludes our proof.
Note that we needed to have at least one fundamental statement, taken to be true and proceed from there. The fundamental statements themselves do not need (or require) proofs; they are the most basic starting assumptions.
For instance, in our example, by defining even numbers as those that are divisible by two effectively eliminates any need for proof. That statement alone classifies as a fundamental statement from which we build our theory of numbers.
It’s pretty much like saying, “single people are unmarried”. It’s a definition and that’s that.
You can use the same fundamental statements to prove that the sum of any two consecutive integers is always an odd number.
Thus, fundamental statements (or in our case, definitions) cannot be proven.
Example 2: Are you alive?
Here is another situation that you may find relatable if math’s isn’t your cup.
Here is a statement that you probably already know.
“Humans need air, food, and water in order to stay alive”
This statement is based purely on obvious experience and observation. It is not one of those fundamental statements as it is not absolutely proof-sealed, but it’s close enough.
For starters, it would be nonsense if someone were to ask for proof of it. The appropriate reply for them would probably be, “Why don’t you go a day without breathing and see how that works for you!”
When someone dies due to lack of food, air, water, or a combination of those; that’s not proof in its strict sense, it just means that the statement has been supported by observation. There is no guarantee that future human beings would evolve to survive without air, or water, or even food. Think of a future in which humans can hibernate for months on end during severe winter seasons as a result of the Sun losing its heating power. In this scenario, an argument can be made that those evolved humans won’t always need food and water to stay alive. So our conjecture that food, air, and water are indispensable for survival isn’t exactly proof-sealed, but for the moment let us assume that it’s absolutely true under all circumstances present and future.
We can then use our “law” to make proofs.
Here is an example,
“Donald Trump is alive”. Prove it.
Here is how we would systematically proceed.
We recall our fundamental statement that we take to be true in all conditions; “all human beings need food, air, and water to stay alive”. We observe Donald Trump and we note that he is breathing. After an hour or so, we note that he eats and drinks some water. Over time, we would effectively establish that Mr. Donald Trump cannot survive without food, air, and water.
Ergo Donald Trump is alive as per our “law”. Q.E.D
You can use the same law to prove that stones aren’t alive.
Here is another example,
“Humans cannot survive on the Moon” prove it.
We refer back to our law, “Humans need air, food, and water in order to stay alive”
So we ask, “does the Moon have water, air, and food”. When we firmly establish that the Moon lacks either or a combination of food, air, and water. We conclude that humans cannot survive on the Moon because if they do, then our “law” would be disobeyed. And that cannot happen because it’s true in all circumstances present and future.
This is somewhat rusty proof but my point is; “proofs” are mostly talked about in mathematics. They are abstract in nature and based on deductive reasoning. We systematically go backward until we establish without a shadow of a doubt that a given conjecture is true. And once it is true, then it is true forever.
Euclid developed the basic laws of plane geometry over 200 years BC; those statements (called axioms) are true today – over 2000 years later. And they will be true 2000 years later.
But for physical laws, we can’t be so sure. For example, we can’t guarantee that future humans would need food, air, and water for survival. Nor can we guarantee that the like poles of a magnet will always repel one another. But we are sure that the founding axioms of plane geometry would remain the same forever, otherwise, it wouldn’t plane geometry as we know it. Much like changing the rules of basketball, changes the entire game completely.
Conclusion: Laws of physics are not proven.
The laws of physics aren’t proven, nor are they meant to be proven. They simply generalize a particular behavior of the universe in a certain field. In fact, contemporary physicists avoid using the word “law” nowadays. They rather use the term “theory” or “postulates” in place of laws. The term “law” usually means an existing condition which is binding and immutable (cannot be changed), which isn’t the case here.
Laws (and theories alike) are supported (or falsified) by evidence. Our confidence in a theory or a physical law increases when it is repeatedly confirmed by the evidence upon evidence. An incredible amount of evidence in favor of a theory isn’t proof, nor does it warrant that the theory may now be regarded as a “law”. A common misconception among many is that theories are upgraded to laws upon proof. So we get questions such as, “why is it still called the theory of relativity even though it’s been proven many times”. The concept of proof in its technical sense is irrelevant here since we can never guarantee that all future evidence will be in favor of the theory or law.
(I have digressed a bit, going back and forth between law and theory but I hope I’ve made sense).
