Ask Ethan #17: The Burden of Proof

"Never waste your time trying to explain who you are to people who are committed to misunderstanding you." -Dream Hampton

Perhaps no word in the English language generates as much misunderstanding as the word theory. In scientific circles, this word has a very specific meaning that's different from everyday use, and -- as a theoretical astrophysicist myself -- I feel it's my duty to help explain exactly what we mean when we use it. In this week’s Ask Ethan column, I'm pleased to pull out of our question/suggestion box the question of Ripley, who asks:

I often see that because there is no "100% proof" to something, especially in relation to theories, it cannot be possible. So I ask, would it be wrong to say that "just because we lack 100% proof doesn't mean it can't be true/real?"

Of course, there's always the short answer.

Image credit: NASA / Cosmos Studies. Image credit: NASA / Cosmos Studies.

Which is not to say that all things ought to be taken as true, even in the absence of evidence.

What this sentiment echoes -- from a scientific perspective -- is that if you want to validate or invalidate a theory, you have to put the explicit-and-unique predictions arising from that hypothesis to the test.

But let's back up a little more and define what I mean by theory, because when I use that word, I mean something very particular, and it's likely different from what you think of when you use it.

Image credit: Wikimedia Commons user Aeddub. Image credit: Wikimedia Commons user Aeddub.

At the very beginning of knowledge, you have straightforward facts about our reality. If I set up a system in a particular way, make a certain measurement using a specific method and/or set of tools, I will get a result. If I repeat that experiment many times, I'll get a set of results. And if I look at the results of similar phenomena, experiments and/or natural occurrences as they've occurred many times, I'll have an even more valuable set of data.

That's the beginning of knowledge.

Image credit: Kassaw and Frugoli, Plant Methods, 2012, 8:38. Image credit: Kassaw and Frugoli, Plant Methods, 2012, 8:38.

And then we apply our minds to that raw data, and we notice things.

When you take a sealed balloon filled with air and you submerge it deep underwater, its volume decreases. But it decreases in a particularly quantitative way: if you double the pressure around it, the volume it takes up halves. Noticing those types of relationships -- or the empirical correlations between different parameters-and-variables in a system -- is what leads to a slightly more advanced state of scientific knowledge, the formulation of scientific laws.

Image credit: Open Water Diver Manual, via Image credit: Open Water Diver Manual, via

Scientific laws can tell you what's going to happen under certain conditions, but they haven't yet advanced to the point of a scientific theory. You see, a scientific theory is even more advanced than this, and posits an explanation and/or a mechanism from which scientific laws arise. And that's where science can really show off its true power.

Image credit: Leonard Eisenberg, 2008, via Image credit: Leonard Eisenberg, 2008, via

You see, as the generations pass, living organisms give rise to subsequent generations of living organisms; that's data.

Those organisms are different in measurable ways from their predecessors; that's the scientific law of evolution.

But the mechanism behind it -- that organisms have the information for their traits encoded in their DNA, that DNA mutates and (in the case of sexually reproducing organisms) combines from two parents to form an offspring's genetic makeup, and that the least fit organisms for survival are selected against, naturally -- that's a scientific theory.

Image credit: Rensselaer Polytechnic Institute. Image credit: Rensselaer Polytechnic Institute.

Scientific theories are the deepest and most powerful explanations of how a scientific process takes place. The germ theory of disease is a theory; biological evolution is a theory; the atomic (and subatomic) theory of matter is a theory; and the theory of gravity is a theory.

To address your question, there never is 100% proof of a theory. Even a hundred million successful tests and observations cannot prove a theory; they can validate a theory, they can demonstrate the robustness of a theory, but a single irreconcilable, reproducible observation is enough to show that a theory is not correct in all regimes, everywhere. This is likely true of all theories, by the way: that they have a range-of-validity, and outside of that range their validity breaks down.

Image credit: NASA / Norbert Bartel, from "Testing Einstein's Universe". Image credit: NASA / Norbert Bartel, from "Testing Einstein's Universe".

Newton's laws of gravitation are fantastic over a huge range of applications, but their validity ends when confronted with very large gravitational fields, very small distances and speeds very close to the speed of light. As is often the case, it was superseded by an even better theory: Einstein's theory of General Relativity, which both includes Newton's range of validity and extends it to these special cases. (Although Einstein's theory, too, has limits.) Attempts to extend Einstein's theory are currently active areas of research, although it would be better for us all if we correctly called these attempts hypotheses right now, and only promote them to theories if they are, in fact, validated by experiments and observations.

But that does not mean everything posing as a scientific theory has validity behind it, or is worth considering seriously.

Image (dis)credit: International Metaphysical University, via Image (dis)credit: International Metaphysical University, via

You need the data to support the foundations of your reasoning. You need the laws and correlations to build your theoretical framework atop them. You need a hypothesis or an idea of how it all fits together and can be explained by (relatively) simple principles. And finally, only if you have multiple lines of evidence and multiple tests and confirmed predictions, can you begin to rightly call your idea a theory.

Image credit: Dave Reneke of Image credit: Dave Reneke of

Of course it's wrong to say "just because we lack 100% proof doesn't mean it can't be true or real." Some of the best theories we have today have outstanding predictions that have yet to be confirmed: the theory of General Relativity predicts gravitational waves, which we haven't directly detected (yet); the theory of Dark Matter predicts the existence of new particles in the Universe, which we have not detected in terrestrial laboratory experiments (yet); the theory of abiogenesis predicts that life originates from non-life, although we have never once created life from non-life ourselves.

The burden of proof for an idea to get promoted to a scientific theory is tremendous, as even the vaunted Supersymmetry (and, in connection with it, String Theory) should be rightly referred to as a hypothesis and not a theory, as the evidence, successful tests and confirmed predictions still have not arrived.

Image credit: DESY at Hamburg. Image credit: DESY at Hamburg.

So although it's true that absence of evidence is not evidence of absence, there is a burden of proof that must be met before we're willing to promote an idea or hypothesis to the status of scientific theory. Once we're there, however, we take the predictions of that theory very seriously, and are willing to consider not only the possibility but the probability that those new predictions -- even the ones for which we do not yet have evidence -- might be correct, no matter how assumption-challenging they may be.

So thanks, Ripley, for a great question for this week's Ask Ethan column, and if any of you have a question or suggestion for a topic, ask away!

Further recommended reading:

More like this

Ethan, this is one of your BEST articles ever.
I've been reading your blog for years now, and you've had many beautiful articles on so many themes. But this one is about a PRINCIPLE and you have managed to clearly present it in so simple words. Beautiful!

Great article, although I disagree about this statement :

"At the very beginning of knowledge, you have straightforward facts about our reality."

ALL observations are theory laden. We need a theory, even if it is a basic one, to interpret and make sense of even the images we see on our retina.

Dear Ethan,
I am new to your blog and I can only say CONGRATULATIONS!!! for this article. As physicist and research scientist, I would wish everyone would read this article at least once in their life.
Best, Daniel

By Daniel Huertas… (not verified) on 27 Dec 2013 #permalink

absence of *proof* is not proof of absence. but use the word "evidence" instead of "proof" and you're suddenly incorrect.

when you've lost your damn car keys (again), do you look through your coat pockets over and over, or after failing to find them there, do you move on to another place that was moderately less likely to hide the keys than your coat was?

i would offer that "proof" is misused more frequently, and more severely, than "theory", by the way.

By misanthropope (not verified) on 27 Dec 2013 #permalink

I doubt Sagan ever said anything like "Absence of evidence is not evidence of absence," since it's patently false. When Earl Warren testified to Congress about a suspected "fifth column" of Japanese saboteurs, he claimed the absence of evidence only increased his suspicion that they were planning something big. But of course, no matter what the probability that the fifth column existed and did nothing, the probability must be higher that the *lack* of a fifth column would produce no evidence of its activities.

By Mike Stay (not verified) on 27 Dec 2013 #permalink

Nice article Ethan. I was pleased you mentioned supersymmetry and string theory and pointed out that these were hypotheses. But you also said the theory of Dark Matter predicts the existence of new particles. That's a hypothesis. There's unequivocal evidence in the guise of flat galactic rotation curves and anomalous gravitational lensing, but it isn't actually evidence for dark matter particles. You could equally say it's evidence for a non-constant Lambda.

By the way, the word "atom" should perhaps be "from" in this sentence:

"You need the laws and correlations to build your theoretical framework atom them".

By John Duffield (not verified) on 27 Dec 2013 #permalink

If may be more helpful to frame the opening/closing quote as: The absence of evidence is not evidence of absence, unless said evidence was expected to be found, yet wasn't.

I'm new to this blog, having been directed to it by the blog Physics Week in Review on Scientific American. Now that I know it exists, I'll be reading it often. Excellent work.

By David Cummings (not verified) on 28 Dec 2013 #permalink

"But you also said the theory of Dark Matter predicts the existence of new particles. That’s a hypothesis"

No, there is a dark matter theory and there are many hypothetical definitions of what that dark matter is.

But Dark Matter theory is a theory. Not a hypothesis.

Proposing micro black holes as dark matter is a hypothesis. One that currently doesn't fit observations.

"i would offer that “proof” is misused more frequently"

Well, there's the old meaning for prove, which was basically "test to destruction".

Which makes "The exception proves the rule" far more sensible: an exception shows the rule does not hold - it is broken, not proven right.

"ALL observations are theory laden."

Yeah, but some axioms must be made or else you're Alice. Neo. Or Arthur Dent.

If your observations are unreliable and no other observations can be trusted to be more reliable, then you have a chaos, not cosmos, and there's no point to existing because you don't know if you do.

Well, "proof" actually is a mathematical term and is of course 100%, or else it's not a proof. So, if you read carefully Ethan's article, there is no such thing as a "proven" theory, since there is no 100% valid theory.
We can only have (more or less) good experimental evidence for a theory to be valid.
And, when I come upon terms like "ether theory" or "string theory" (they have something in common, you see) it is at least to me clear that they are not theories, but hypotheses. String theorists may be excellent matematicians and profound thinkers, but the stuff they are working on is not a theory.
Excellent article and again, thank you Ethan!

Mike Stay (#5) claims

I doubt Sagan ever said anything like “Absence of evidence is not evidence of absence,”

Have you checked "The Demon-Haunted World," chapter 12, page 221?

By Michael Richmond (not verified) on 28 Dec 2013 #permalink

More commonly misused words
About Language
Some words have different meanings in common practice, science, philosophy, and religion. The heritage of scientific language is philosophy where everyday words are used.
Theoryis the ultimate of our understanding in science. Philosophical and propaganda usage often says ``Its only a theory’’ to imply it has little value compared to some ``explanation’’ and has little value in describing ``reality’’. In science, a theory has been tested by predicting. ``Predicting’’ is not a requirement for other word usages. To make the situation worse, when dealing with the public, scientists often call their proposed model a theory before the scientific criteria are met. For example, ``string theory’’ is currently a speculation because a hypothesis of a prediction has not been formulated much less tested.
ExplanationThe common usage means to be self-consistent with all thoughts. Although scientists use this term, its use in cosmology is declining because of the confusion with low or no predictability thoughts. Terms that are replacing ``explain’’ are ``consistent with’’, ``suggest’’, and ``account’’.
BeliefIn religion “belief” is taken to be an absolute, unquestionable truth. In common practice “belief” is an uncertain statement such as ``I believe he is coming at 5 PM (but I am not sure).’’ In science “belief” means the predominant (sometimes only majority) opinion (not a hypothesis or theory) or ``there is no evidence that directly contradicts my opinion.’’
“We know that...” Never true in science. When you see this in a paper, discount the paper’s credibility by at least 50%.
“Scientific findings support ...” tests only reject or not reject. Unfortunately, this is said too often as means to assert scientific authority.
True or iscommon, philosophical means “reality”, “in absolute truth”, invariable, etc. In cosmology “true” or “is” means a logical statement. For example, If 1+2=0, then 2+1=0. Does this mean 2+1=0 is true? Yes, under the assumptions included in the “if” statement. That this uses a common number system is also understood. But, that the number system is not decimal should be stated. By the way, this is a trinary number system used in initial computers designed in the USSR – the US went binary. In science, there are always many assumptions implied in statements.

Measurement accuracy – (see Measurement in the appendix) –
Our principle reference frame is ourselves such as our heart rate combined with our perception of the intuitive concept of how our reference frame acts. Our principle perception is sight. We design instruments for measuring the physical behavior beyond our senses. The use of instruments depends on our model how the instrument behaves relative to some standard. Our scientific understanding depends heavily on these models. The interpretation of the physical universe depends on the accuracy of both the models and the instruments. Accuracy of our measurement is a concept formed by Kepler and is expressed as a range of instrument and observation error (±) – see the measurement section in the appendix. See the “collapse of the wave function” in the Modern – the small section for a discussion of measurement philosophy. The common understanding of “accuracy” is that the reality is within the measurement error. The Scientific meaning of accuracy is the observational and instrument error relative to a model. For example, below is listed the calculated distance with the accuracy statement to the LMC according to various models. The RR Lyrae method quotes a measurement considerable outside the range of the other methods. Yet, it is a scientifically correct statement. That is, the RR Lyrae and the other models were derived from triangulation method of star distance that also has error of up to 10%. The error listed below is only of the particular measurement assuming the triangulation model has no error. We don’t know the reality of the “true” distance to the LMC. The other models are used to calculate greater distances. These in turn are used to calculate the “Hubble constant” that is fundamental to the Big Bang model of the expansion of the universe. Research is continuing to determine the distance to the LMC. If this distance is significantly different than 50 kpc, the Big Bang model is in trouble.

LMC (Large Magellanic Cloud)
Measurement modelDistance/kpc

Main sequence fitting50±5
RR Lyrae44±2
SN1987a time delay52±3
SN1987a Baade-Wesselink 55±5

I think the writer's query has more to do with the notions of "proof" and "truth" as they're used in science than it does with the idea of a "theory". Because a scientific truth that's beyond all challenge and 100% certain in all known and unknown circumstances just isn't possible, every scientific explanation is called a "theory". It's a "theory" because the possibility always exists, no matter how remote, that one day an exception to it will be found.

Science doesn't deal with absolute ontological truth. If a scientific theory is testable and predictive, if it's self-consistent and consistent with other scientific theories, falsifiable but never falsified, then that's considered "true enough" and the theory is accepted.

By dr_mabeuse (not verified) on 28 Dec 2013 #permalink

"Yeah, but some axioms must be made or else you’re Alice. Neo. Or Arthur Dent."

You mean the axioms of logic? Yes of course, but is this what was meant by" basic facts "?


Axioms such as "there is a reality out there that is independent of your observation and it is consistent", Chris.

If you cannot expect that everyone observing something coming to agreement on that observation, facts become merely meaningless hallucinations with no underlying reason.

" For example, “string theory’’ is currently a speculation because a hypothesis of a prediction has not been formulated much less tested."

It would be more correct to call it a model.

Fluid motions of a gas in bulk is a model. There is no continuous bulk. There is no "entropy" or "temperature" in its reality, but in the model we use it has meaning and makes predictions.

There's the "string theory model", as in it is a model of reality where the theory is that everything is an excitation of a string from which all other phenomena arise.

It's more than a hypothesis, far more than a guess but not a theory as strong as, say, Russell's "atomic nucleus theory".

There's a gradation. As with many things.

And this could be argued as a weakly tested theory or a strongly supported hypothesis.

But whichever it is, it's a model of reality. Whether it's useful is the only undecided thing at the moment.

@ Wow

"If you cannot expect that everyone observing something coming to agreement on that observation, facts become merely meaningless hallucinations with no underlying reason."

But isn't Relativity in it's broadest sense a contradiction of this? Not about there being an underlying reason, but that everyone will observe different things?

By Sinisa Lazarek (not verified) on 29 Dec 2013 #permalink

"But isn’t Relativity in it’s broadest sense a contradiction of this?"


It's about how everyone will observe the same thing.

If SR did not hold and light speed were not consistent, then a collision would be near or impossible depending on where the observer of the collision was standing.


By Sinisa Lazarek (not verified) on 29 Dec 2013 #permalink

mind giving a shot at my question under questions/suggestions?

By Sinisa Lazarek (not verified) on 29 Dec 2013 #permalink

I would suggest looking at ray tracing, since this is probably the cause of the shadow.

Try changing the angle below the glass surface the light is.

The light was sunligh coming through the window. Tried to achieve perspective in the illustration, so it might have not been clear.

Sunlight was coming thorough the window. The top shadow is no mystery, but the bottom one.. I have never seen something like that before. I know it must be due to reflection from table-top... just don't know how it works. Can't figure the angles. Also, from QM point... was looking to find out what interference or amplification causes the double shadow to appear.

I know raytracing from graphics and 3d. Not sure how that relates to double shadow.

By Sinisa Lazarek (not verified) on 29 Dec 2013 #permalink

A model, yes. But of reality?

A very enjoyable post! Thank you!

The way I use these and related terms (as a layperson):

Fact: a measurement that's repeatable by others.

Data: a collection of facts that bear upon a hypothesis.

Hypothesis: a prediction about facts that will be observed under specified conditions. Hypotheses are either falsified or supported by observations, but not "proven." The degree of support required for a hypothesis ranges from p .00001 or greater in the hard physical sciences.

Proof: a mathematical or logical statement of truth that is 100% correct with no uncertainty. Does not apply to empirical facts and empirical hypotheses, which are always subject to a (usually specified statistically) degree of uncertainty.

Theory: a statement that consists in part of supported hypotheses and in part of predictions that follow from those hypotheses, that generates further testable hypotheses. The power of theories is that they encompass wide ranges of observations and predictions.

Model: an analogy that may be used to gain insight into a given phenomenon in order to formulate hypotheses. For example much of AI uses models of cognition that are arguably different to theories of cognition. (Though, the Standard Model in physics is obviously not a "model" in this sense, it's more like a collection of theories. So it's apparent that physicists use the term "model" differently.)

Belief: a set of working assumptions that may be composed of facts, hypotheses, theories, and various subjective content that may or may not be empirically or logically supported.

Speculation: a prediction that does not yet rise to the level of a testable hypothesis.


Feel free to tear the above to shreds and suggest improvements.

"A model, yes. But of reality?"


Why? What else would you call it then? Unreal?

G, put hypothesis next to and just before theory.

"I know it must be due to reflection from table-top"

I would suggest that ray tracing would determine if that is the only possibility.

The light from underneath has two surfaces to refract through: the top and bottom of the glass.

So check that first.


As posted: "The degree of support required for a hypothesis ranges from p .00001 or greater in the hard physical sciences."

As written (and mangled by whatever software is used here):

"The degree of support required for a hypothesis ranges from p (symbol for "smaller than") .05 in the social sciences to p (symbol for "smaller than") .00001 or greater in the hard physical sciences."

We need a "preview/edit" button.


If I owned a physics ray tracing computational software and knew how to use it, I wouldn't post a question here. I appreciate the answer that the calculations itself are done through raytracing, but still that doesn't give me an answer about what's going on. Thought that this is a more or less usual behavior and would be easily explainable.

By Sinisa Lazarek (not verified) on 29 Dec 2013 #permalink

You can raytrace yourself, SL. Protractor, pencil, ruler and a calculator if you don't particularly want to divide by a six or more digit number in your head.

It's not going to be necessary to use QM to explain it any more than it is needed to explain glycolosis.

G, expanding on your differentials between hypothesis and theory, it may be worth thinking of this distinction between them.

Hypothesis: "If THIS then THAT should happen".

Theory: A set of self-sustaining and self-supporting hypothesis that hang together.

Or, more cynically: Hypothesis: someone else's theory you don't think is true.

PS POVRay is open source, SL, and fit for the task if you want to raytrace by computer.

Interesting article. It would be nice if Ethan would write about some of the pitfalls of scientific theory or models of yesteryear, like epicycles. You can learn much by studying previous failures, especially learning to being skeptical of sloppy terminology, reasoning, methodology. If you can keep mucking about with your theory or model endlessly to fit new data but call your model by the same name, it can be made to seem as if your model/theory is predictive when in fact you just keep changing your story (moving goalposts). In software design you must keep careful track of exactly which version of a particular program (i.e. v1.0030, v1.0120) you are working with in order to test, service, or update correctly. It would be nice if such a stringent standard would migrate to the sciences, it would cut down on the intentional and unintentional confusion created by so many different versions of various models with the same name being bandied about and being used interchangeably (blackbody, darkstar, neutron star, black hole, collapsed singularity, etc.).

@ Wow
"You can raytrace yourself, SL. Protractor, pencil, ruler and a calculator if you don’t particularly want to divide by a six or more digit number in your head."

Like I said before, if I knew how, and why and where the rays are coming and how they are reflected, I wouldn't be here asking for an explanation of the effect. Not interested in numbers nor do I know the equations. Was looking for an explanation in plain language. Not in formula.

As for QM. I know that almost all optical effects can be explained in plain geometry terms and trigonometry. But also, that all of them are fundamentally QM processes, since there is no actual reflections and refractions. Instead photons are absorbed and emitted along the way. Some interfere some don't. So I want to know what's going on.

By Sinisa Lazarek (not verified) on 30 Dec 2013 #permalink

@Sinisa: I wish that you and Wow had kept your discussion where it originated, instead of hijacking this blog topic :-( With regards to your #38 and previous -- you don't need any "QM processes" to deal with geometric optics. Natural light is an incoherent mixture of many different frequencies, and does not present quantum coherence effects.

Wow is correct. You don't need any equations to do simple geometric ray tracing. If your light source is the Sun, then you draw parallel rays from the direction of the Sun. From air to glass, the index of refraction is 4/3, which is what you use to get the ratio of the sines of the angles to the normal (big angle in air, small angle in glass); for this you need a calculator to get it precise. At each glass-air surface, you will get two rays: one refracted through the glass, and one reflected back (equal angles, like a mirror). For normal, thick glass, there won't be any observable interference effects.

By Michael Kelsey (not verified) on 30 Dec 2013 #permalink

"Like I said before, if I knew how, and why and where the rays are coming and how they are reflected,"

This lack of knowing how or why didn't stop you claiming some QM effect, did it?

And Michael is right.

One would think that the world wide flood of Noah would have left lots of physical evidence. In this case, absence of evidence is fairly convincing evidence of absence.

By Jim Thomerson (not verified) on 08 Jan 2014 #permalink

Dark matter and abiogenesis are hypotheses, not theories.