How do we know that Newton’s 2nd law holds true? Honestly, we don’t. We can’t prove it.1 But we strongly believe it does.
‘How vague!’, you might yell out loud. ‘In science, we shouldn’t “believe”, we should know!’
Sure. But we also can’t prove that gravity always works… Will you now start doubting gravity?
Of course not. Of some reason, you are – we all are – convinced that gravity works again tomorrow, even though no one can prove that. Drop your pen. What happens? It falls. Can you be sure it will also fall the next time you do it?
No, you can’t, you just strongly believe that it will – because it has always done so. You have never in your life seen a single counterexample – where the pen did not fall when dropped – so, you feel certain that ‘falling’ – that ‘gravity’ – truly is a universal always-working phenomenon.
Countless people over countless years in countless locations have made countless experiments, and never once have we seen a single result where Newton’s 2nd law didn’t hold true. (Actually, we have seen that at the nanoscopic size scale.2 Newton’s 2nd law is not fully universal, but universal within its own range of validity. Within this range, Newton’s 2nd law has never been shown wrong.) Had we seen just one counterexample, then we wouldn’t trust it to always hold true. A single counterexample can prove it false, whereas countless confirmations can’t prove it to be true. ‘The power of the counterexample’ or ‘disproof by counterexample’, we could say.
No amount of experimentation can ever prove me right; a single experiment can prove me wrong.Albert Einstein
Let’s call this method of proving that something most likely is true, by trying hard to prove it false: falsification.
- If we can falsify it, then it isn’t true.
- If we can’t falsify it, then it might be true.
- If countless people doing countless tests can’t falsify it, then it most likely is true.
Falsification is a method involved in several types of proofs. See an overview of different types of proofs in Resource: Types of proofs.
- ‘What is the proof of Newton’s second law of motion?’ (web page), Akshat Khare, Joe Gedge and others, Quora, 2016, www.quora.com/What-is-the-proof-of-Newtons-second-law-of-motion (accessed Sep. 27th, 2019)
- ‘Feynman’s Thesis — A New Approach to Quantum Theory’ (book), Laurie M Brown, World Scientific, August 2005, www.worldscientific.com/worldscibooks/10.1142/5852, ISBN 978-981-256-366-8, DOI 10.1142/5852
- ‘When Did Isaac Newton Finally Fail?’ (web page), Ethan Siegel, Forbes, 2016, www.forbes.com/sites/startswithabang/2016/05/20/when-did-isaac-newton-finally-fail (accessed Sep. 26th, 2019)
- ‘Relativistic Dynamics’ (web page), Michael Fowler, University of Virginia, 2014, galileo.phys.virginia.edu/classes/252/relativistic_mass.html (accessed Sep. 26th, 2019)
- ‘Relativity from the geometrization of Newtonian dynamics’ (article), Y. Friedman & T. Scarr, EPL (Europhysics Letters), vol. 125, issue 4, article 49001, 2019, stacks.iop.org/0295-5075/125/i=4/a=49001?key=crossref.2259c956996f20025c68ace6d440904e, DOI 10.1209/0295-5075/125/49001
- ‘Can a proof and a counterexample coexist? Students’ conceptions about the relationship between proof and refutation’ (article), Andreas J. Stylianides & Thabit Al-Murani, Research in Mathematics Education, vol. 12, issue 1, 2010, www.tandfonline.com/doi/abs/10.1080/14794800903569774, DOI 10.1080/14794800903569774, pages 21–36
- ‘What exactly is the scientific method and why do so many people get it wrong?’ (web page), Peter Ellerton, The Conversation, 2016, www.theconversation.com/what-exactly-is-the-scientific-method-and-why-do-so-many-people-get-it-wrong-65117 (accessed May 2nd, 2020)
- ‘Fraud and Scientific Culture’, Brent E. Turvey, Forensic Fraud, Elsevier, 2013, linkinghub.elsevier.com/retrieve/pii/B9780124080737000057, DOI 10.1016/B978-0-12-408073-7.00005-7, pages 67–95