The Scientific Meaning Of Impossibility Statements

"Unless a man can quantify or measure what he’s talking about, he’s not talking about anything."

- Lord Kelvin

Through the years, at dozens of lectures that I've given, I've invariably been asked whether this or that event or entity is "impossible". Are 3-eyed aliens possible or impossible? Are miracles impossible? Is an asteroid strike that kills everything on Earth possible or impossible? Is reversing global warming impossible? Is nuclear fusion possible or  impossible? The list seemingly goes on and on.

What I've had to make clear to all these inquirers is that there are such things as "impossibility statements" in science and they have far more generality and validity than possibility statements. But one must understand what this means.

One of the most famous and oft-cited impossibility statements in all of physics is the Clausius statement associated with the 2nd law of thermodynamics. This statement reads:

"It is impossible to construct a cyclical machine that produces no other effect than to transfer heat continuously from one body to another at higher temperature."

This is a statement of impossibility because it violates the well observed property of heat transfer whereby the temperature gradient is always such that heat flows from hotter to colder bodies, not the converse. Hence, it is preposterous that one can continuously pump heat from a colder body- say from a large block of ice - to a hot metal container.

Or consider the principle behind a refrigerator, the reverse of the heat engine, i.e.. 


 The engine absorbs heat Q₁ from the low temperature (T₁) or cold reservoir and expels heat Q₂ to the hot (T₂)  reservoir.  In practice heat will flow from colder  to hotter body only if work is done on the system.

 If this were the slightest bit invalid, all our machines, computers, etc. would cease to function in nanoseconds. The slightest heat built up from the working components would be enough to shut down the overall function once a critical temperature was reached. This is the next aspect, that impossibility statements are predicated on real world observations....not from claims made in ancient books or out of the mouths of ignorant people who opine on matters they don't understand. Say like the biology of the SARS- Cov-2 virus.

Another impossibility statement is:

"It is impossible to construct a machine that works with 100% efficiency"

In other words, the way our universe is constituted - given its laws as manifest - one cannot make or engineer a machine that is capable of operating continuously with no loss of energy. It simply can't happen.

Now, in science, the applicable terms that usually replace "impossibility" are what we call "laws of permission" and "laws of denial". The first detail all the actions that are allowed based on the laws of physics; the latter detail all the actions disallowed.

The laws of denial are predicated on such foundational physical laws as: the laws of conservation of mass-energy, momentum and electric charge. All these assure us that NO action can take place in a closed system in which the total energy, momentum and electric charge are not conserved.

I cannot take a 2 oz. bite out of an 8 oz. apple and come back and find it weighs 10 oz.! I cannot put 8 gal. of gas into my tank, and know my car only gets a max. of 20 miles/gallon - drive one hundred miles and find 7 gallons of gas left! I cannot bring out a loaf of bread and one fish and magically multiply them to become five hundred loaves and one thousand fish! I can't do that because it violates a basic law of mass-energy conservation. Nor do I find such violations anywhere in the natural world, or in the cosmos (as far as large scale plasma and astrophysical processes go)

I can't put an electric charge of 5 Coulombs on a polythene surface, then come back two minutes later and find 10 Coulombs - assuming the system was closed to external influences.  Thus, certain things really are impossible! There is no getting round it, and it's definitely scientific! What is blatantly unscientific and unsupported, is to claim certain events are not only possible but probable - but they violate specific physical laws or principles.

Thus, "perpetual motion machines"  (e.g. a pendulum that never ceases its oscillations) are also denied  or "impossible".  They not only violate conservation of energy, but also specific laws of thermodynamics, e.g. the 2nd or entropy law. Closed systems such as dead biological ones (no longer open to radiant energy or changes in chemical potential- since no food is taken in) also cannot be "brought back to life"- because this would violate the same law as perpetual motion machines. What stands for the latter, also applies to any proposed claims for the former. They are all impossible, full stop.

There are also detailed biologic - genetic laws that prescribe what can and can't develop - and in conjunction with physical laws, detail what can be allowed. Thus, given planet Earth's properties of gravity, mass, density etc., NO flying elephants can ever develop since there is NO basis in the genome for the species to acquire the ability of flight via "wings" on a planet with g = 9.8 m/sec/sec.. (Apart from the fact that enormous wings would be required to support a 2 ton creature!) Neither is there any capacity in the chicken genome to acquire lips. Both of these may sound like plausible or cute examples, but they fall flat (like perpetual motion machines) when closely scrutinized. Of course, one must have adequate scientific background to do this, and education! Hence, neither flying elephants nor chickens with lips "could happen". They are foreclosed by the laws of denial.

Meanwhile, an intelligent race of green aliens with immense brain in proportion to body and bulbous eyes with nictating membranes - MIGHT be so. To assert such aliens (or any advanced aliens) are "impossible" is to make a claim for total knowledge of every last solar system in the universe. This is foolhardy since, first, the claimant has not been to all those places so cannot know - at the very least he's constrained to say "I don't know" -nothing more, and second we know from spectroscopic analysis that the same chemical elements we find in Earth labs also exist on other worlds. Thus, the same chemical compounds we have on Earth exist there, and hence there is no reason a priori the same physico-chemical laws that incepted evolution here, can't do it there.

Now, one might aver that “I don’t personally believe green aliens or any aliens are possible”,  but that’s a rationally self-contained and subjective statement of one’s personal beliefs – not an objective claim. Unless one has actual scientific evidence, he is not allowed to make any statements of impossibility on the issue of advanced green aliens with large craniums. If he does, he is merely talking beyond his mental frame or jurisdiction with no basis or validity.

Now, this is not to say that a specific statement of denial cannot be made in respect to aliens existing in a specific place! But that specific statement is contingent on specific information known about X, Y or Z planet. Hence, once one lists the composition of the atmosphere being considered, the planet's surface gravity, its temperature ranges, and whether any magnetosphere ( to protect against high energy particles, etc.) he may at least offer a limited statement of denial contingent on THOSE conditions. But he's not permitted to make a general statement applicable to ALL conditions and planets in the universe!

All events in the cosmos also obey Lorentz invariance, meaning that NO object, energy or mass or information can propagate faster than the speed of light (c = 300,000 km/s). A particle or rocket ship can approach this limiting velocity, but can't exceed it. (Einstein's basic equation for mass in special relativity shows that if a particle were to travel at light speed, its inertia would be infinite- another way of asserting it's impossible).

What about miracles?  

In his essay collection Unweaving the Rainbow biologist Richard Dawkins, Britain's most prominent atheist, chose to examine the Fatima miracle of 1917, where 70,000 people "reportedly saw the sun move", to apply Hume's principle: As Dawkins observed:

"On the one hand, we are asked to believe in a mass hallucination, a trick of the light, or mass lie involving 70,000 people," Dawkins writes. "This is admittedly improbable. But it is LESS improbable than the alternative: that the sun really did move...If the sun had moved in truth, but the event was seen only by the people of Fatima, an even greater miracle would have been perpetrated: an illusion of NON-movement had to be staged for all the millions of witnesses not in Fatima."

The dual –tandem improbability associated with this is less than getting a royal flush in poker 6.5 million times in succession. It is actually less than the proverbial monkey on a typewriter re-typing Hamlet in its entirety, and with no errors.

As another example of applying the Hume principle, consider the claim of the miracle of "Jesus “walking on water”.  Clearly, it is impossible because the "law of gravity" - which dictates all objects on Earth fall toward its center unless supported - would be violated. 

Prof. Hugh Schonfeld (The Passover Plot) has a simple explanation for this: a mistranslation of the Hebrew word “al” which can mean “by” or “on” from the relevant biblical passage. So, when a scribe supposedly wrote “walking by the water” it was translated to “walking on the water”. Now let us apply the Hume test: Is the Schonfeld claim of mistranslation MORE or LESS miraculous than a man actually violating the law of gravity and walking on water? 

It doesn’t require a lot of thought or effort to see that the mistranslation of a passage of the New Testament is LESS miraculous (or if you prefer, less improbable) than that a man actually, literally walked on water.  Thus, applying Hume's principle, one opts for the less dramatic explanation, and the more conservative in terms of preserving natural principles.

Now, what about the "miracles of the loaves and fishes".  Again, same principles apply.  If one claims, therefore, that a "miracle" occurred such that thousands of loaves and fishes were produced from only a few (a clear violation of the law of conservation of mass-energy) he needs to show how or where there are ANY single exemptions in the cosmos. No one I know has ever, EVER proven any!

Indeed, if we did not expect these (physical) laws to hold everywhere and at all times then anything could happen! One minute this keyboard could be here on my desk, and the next it could rise up and vanish! This is the sort of haphazard universe one gets when physical laws are treated frivolously and with total disdain for their inherent predictability and repeatability. It is also a common treatment I have found from people who have never taken even a basic high school physics course.

Physical laws may be suitably modified or extended, however, should there be sufficient observational and empirical data to warrant it. This is exactly what was done to Newton's law of gravitation by Albert Einstein. This has resulted in a new law of gravitation which applies to the entire universe (i.e. taking into account its shape or curvature) instead of just a small region like the solar system

Once one understands what constitutes "impossibility" in terms of the laws of permission and denial then one can argue on the basis of what is impossible or not. When one doesn't understand these limits - or perhaps isn't even familiar with physical laws on the whole, then "anything goes" and worse, anything can be believed- even that a man survived three days in a whale's stomach despite the presence of hydrochloric acid, that would have reduced him to bones and less in that time,  according to our chemical laws.  

Is a thing or claim possible or impossible?  Always examine its behavior or the underlying claim in terms of known physical laws, then apply a dollop of reason as well. 

"But what about unknown physical laws that might be at work?"

Well, we simply patiently await their elucidation and articulation, preferably in quantitative form (see Lord Kelvin's apt statement at the top)

What we don't do is jump ahead to claim a law that hasn't yet been proven or demonstrated.