A central element of quantum mechanics is the uncertainty principle. To formulate it in a crude, qualitative way, the principle expresses the limitation of the precision with which physical properties of particles can be determined. The physicist who formulated (discovered) it, Werner Heisenberg, noted that a particle can be described by its position and its momentum, the first revealing where the particle is, the second how it is (one of the factors of momentum is mass) and how it moves (the other factor is speed). The product of uncertainties of the two cannot be smaller than a certain limiting value. Then, if we strive toward limitless precision in describing the momentum, we lose all ability to determine the position.
Rationalized at first as limitation in measuring, because of inherent imprecision of the methods and instruments used, particularly because the operation of measuring disturbs the measured object, the uncertainty was found to be inherent to wavelike systems, in which, as quantum mechanics has shown, particles are included.
The idea was for some scientists hard to accept. Albert Einstein spent a sizeable effort trying to shoot it down. His proposals of experiments that would disprove the principle and their corresponding refutation by his colleagues are interesting not only from a scientific viewpoint. For example, to a medieval man, the idea that there are limitations to human knowledge seemed natural. To a man educated in the spirit of the “Enlightenment,” such limitations are hard to accept. Heisenberg did not have such problems. It is worth noting that he was a deeply religious man.
There are such correlated properties in other things or phenomena. For example, in sound waves, the pair is frequency and time: the longer a musical note is sustained, the more precisely is its frequency known. A clever use of this limitation, affecting radio waves, benefits many patients in MRI tests. In magnetic resonance experiments, atomic nuclei are irradiated and absorb energy at various frequencies depending upon molecular structure and environment. Accuracy in measuring those absorptions requires that enough time is spent on each of them, say one second per hertz scanned. If the signals are spread over several thousands of hertz, a scan would last for hours. Moreover, most of the time is spent scanning regions where is no signal. In this manner, the method is practically useless, especially because to achieve adequate intensity several scans have to be run and added up. To make it practical, the entire range has to be excited at once. For this purpose, a very strong sharp pulse is sent through the sample at a precise frequency in the center of the range of interest, for an extremely short time (microseconds). Because of the uncertainty principle, the radiation actually produced is tens of thousands hertz wide, thus covering the whole range. Then, instead of measuring the energy absorbed, the signals emitted by the excited nuclei when they relax, at the same frequencies as those absorbed, are recorded simultaneously. The recording process is conducted over a sufficiently long period (seconds), so the frequency of each signal is determined precisely. The processing of these signals may produce the image of a kidney, showing whether it contains a stone or a tumor.
Of interest for the present discussion is the application of the uncertainty principle to chemical reactions. To undergo a chemical transformation, a molecule absorbs energy, usually by collision with other molecules. Part of the energy is distributed among the atoms and bonds within the molecule. The process is reversible, as the excited molecule loses energy in other collisions. When the energy content reaches a certain value (“passes a barrier”), the molecule can undergo a chemical reaction and the deactivation through collisions gives the reaction product. At any moment there is a distribution of the energy content and of positions. In some rare, special cases, the variability in position of atoms in the starting compound may bring the atoms in the arrangement existing in the product, even though the energy is lower than the barrier. Deactivation through collisions leads then to the reaction product. It is said that the molecules “tunnel” through the barrier, instead of crossing over it.
An interesting parallel can be found between quantum mechanical tunneling and modern theology.
It has been well understood from apostolic times that salvation requires:
– Faith and baptism. (“The man who believes . . . and accepts baptism will be saved; the man who refuses to believe . . . will be condemned.”). The Fathers of the church summarized the elements of faith in the Creed. The Law of the Old Testament (The Ten Commandments) is an element of Faith as well.
– Reception of the Holy Eucharist, the true body and blood of Christ, not some symbol of it. From the beginning. and to this day, this revelation has been a stumbling block for many. The manner in which this mystery is accomplished and the manner in which the power to effect it is transmitted have also been revealed, such as to assure Christ’s presence among His people to the end of time (“usque ad consummationem sæculi”).
The requirements received and transmitted by the Apostles are exclusionary. Those who do not fulfill them will not be saved. Also exclusionary (and detailed) are the commandments of purity.
This non systematic and summary enumeration is meant to reemphasize what Christ pointed out: the path to salvation is neither smooth nor easy.
A thesis opposite to the New Testaments and the Fathers of the Church has been put forward in the last century, essentially opening the Heaven for everybody. As an example, heard about ten years ago in a homily at a church on Long Island’s North Shore, Hindus recognize a supreme spirit and even consider the incarnation of that spirit; as we know that such characteristics describe only Christ, the Hindus, implicitly, are somehow Christian-like. The same theology is reflected in measures of the French episcopate of about thirty years ago. Before the Muslims reached a critical mass in France and became intolerant and violent, some dioceses and religious orders turned over to them churches to be transformed into mosques.
More recently, Jorge Bergoglio has promised salvation to atheists, constant adulterers, and men who lie with men. The development is natural coming from a bishop who espouses what I would call the theology of the belly, in which God’s plan for man is the satisfaction of man’s telluric needs and urges.
These positions remind us of quantum chemistry: one can acquire salvation either by climbing the (sometimes arduous) path of faith, sacraments, and actions, or “tunneling” under the barrier without those requirements.
Like in chemical reactions, the Church has always maintained that there are special cases in which someone might acquire salvation without formally belonging. I would think that those people did in some form fulfill the requirements laid down by Christ, undergoing at least a spiritual conversion, just we don’t know it.
Both for chemistry and eternal salvation, the “alternative” path is extremely rare. As a consequence, there is no reaction for which a chemical engineer would design a process and an installation based on tunneling. Likewise, telling someone that he can count on salvation foregoing faith, baptism, and sacraments, is cruelly misleading him. Christ’s commands cannot be altered by some sophist-cum-theologian, nor by some assembly of clerics.
Alternatively, if tunneling were a widely accessible pathway, no molecules would react by activation to cross a barrier and no one would run processes requiring high temperatures and pressures. Likewise, if people could tunnel wholesale into Heaven, the Vatican should close shop.
For if being a good Hindu or an upright Zoroastrian could assure inheritance in the kingdom of God, the incarnation of the Son of God would have been superfluous and His sacrifice on the cross — an absurdity.
Werner Heisenberg, Naturwissenschaftliche und religioese Wahrheit, Frankfurter Allgemeine Zeitung, 24 Maerz 1973, pp. 7-8. (Speech before the Catholic Academy of Bavaria, on acceptance of the Guardini Prize, 23 March 1973); http://2012daily.com/?q=node/52
 Mk, 16, 16; also, Mt, 28, 19,20; Jn, 3, 5, 18, 36.
 Jn, 6, 48-58.
 Jn, 6, 66-69.
 1Cor, 6, 9: “neither fornicators, nor idolaters, nor adulterers, nor the effeminate, nor liers with mankind . . . shall possess the kingdom of God “ (Taken from the Douay Rheims edition, checked with the two Romanian translations that I possess: (a) Bp. Ioan Bălan, Noul Testament, Lugoj, 1938; (b) Gala Galaction, Biblia, Bucureşti, 1939. The translation of the New American Bible, CCD, Washington, 1970, is imprecise.)
 Mt, 7, 13-14; Lk 13, 23-25.
 (a) https://www.yahoo.com/lifestyle/heartsick-boy-asks-atheist-dad-193340202.html; (b) Laura Rodriguez, Pope Francis suggests it’s better to be an atheist than a hypocritical Christian, Chicago Tribune, Feb. 26, 2018; (c) Jorge Mario Bergoglio, Abraham Skorka, On Heaven and Earth. Pope Francis on Faith, Family, and the Church in the Twenty-First Century, 2013
 See, among many others:
 (a) https://www.theguardian.com/world/2018/may/20/pope-juan-carlos-cruz?CMP=share_btn_tw;
(b) Francis X. Rocca, The Catholic Church’s Looming Fight Over Same-Sex Blessings, Wall Street Journal, May 24, 2018.