It is a Christian belief that Jesus came back from the dead (McGrew & McGrew, or as I will refer to the article, ). Some claim that the resurrection has significant historical evidence, great enough to compel a rational person to accept it as an historical fact. If something is an historical fact, then it happened physically, at some time and in some location. Maybe Jesus’s resurrection is not an historical fact, but rather a religious fact or some mystical experience. We can figure out the probability of it being an historical fact, but not of it being a mystical experience.
Let’s consider the physical resurrection. How unlikely is it? It’s hard to say with great precision, but an estimate can be made about how likely it is for a person to come back from the dead by known natural causes. It’s possible. A person is, physically speaking, the sum total of his atoms in a particular arrangement. Let’s say that each atom or molecule in this person’s body has nine indendent degrees of freedom (3 vibrational/velocity-components, 3 rotational, 3 translational). When he dies, let’s say some large fraction of his body is reduced to what can be approximated as an ideal gas. Let’s say molecules.
The simplest approximation to be made involves calculating the difference in probability function between an ideal gas and a person, and we can do this via Boltzmann’s entropy equation for entropy, considering the entropy of a dead person compared to the entropy of a live person:
Where is the number of microstates that correspond to the “macrostate” of “being alive” or “being dead”. For the ideal gas, we can use the Sackur-Tetrode equation, assuming the volume of, say, a sealed tomb near the first temple period. I’ll approximate the volume as . We also take for the internal energy (assuming equipartition for the gas) and is Boltzmann’s constant:
where is the average molecular mass, taken here to be the mass of a water molecule and is Planck’s constant. We will assume that the temperature in the room is about 300 K. Our approximation for the entropy of a dead person is about . will be crudely approximated by approximating the number of microstates that corresponds to “being alive” as , and so , at least compared to the value of . So:
And the probability is then:
But this is only for one attempt, one roll of the dice. We can roll the dice a whole bunch of times, over and over. Let’s say that the molecules completely re-arrange themselves over the average time it takes a molecule of the dead person to get from one end of the tomb to the other, assuming random diffusion. The diffusion equation is:
Which can be solved by taking the size of the room as the scale length, and is the time it takes for the system to get rearranged:
And so for a diffusion coefficient for oygen-air , the time-scale to reset is about , or faster if warmer (although the entropy also increases in such a case).
In order for this to be likely to happen by the known laws of nature, we would have to wait times longer than the age of the universe.
Virtually any explanation is more likely than that Jesus came back from the dead through the known laws of nature. This means that, among other possibilities, there are either unknown laws of nature that make it more likely for people to return from the dead, or some supernatural force or entity has the capability and desire to raise at least one person from the dead. Since there is no good evidence* for either of these alternatives, it seems best to conclude that the resurrection of Jesus is at most a spiritual resurrection, and not a physical resurrection.
EDITED TO ADD:
We can do a very simplistic Bayesian analysis, given my prior and using the hand-wavy probabilities of . We find that the probability for a miraculous resurrection () vs. no miraculous resurrection (), given the facts of the matter, , and background information, :
The probability for the resurrection is effectively completely unchanged by the available evidence, as unlikely as it is to have happened by chance.
*What does this “no good evidence” even mean?
All I mean by this is that I personally am not aware of any other value to set my priors, because I don’t know what other mechanism to use in order to estimate these priors. How likely should I think it is that someone resurrects before I look at the evidence? It seems best to compare to the physical principles that we know now, and treat the resurrection as a thermodynamic miracle that requires evidence. Even if someone thought that all physical events are enacted by God, this would suggest that God’s behavior is so orderly that him deviating from this order would be just as likely as a thermodynamic miracle.
The alternatives, new physics and divine free action, are difficult to incorporate into any Bayesian analysis. How do I include new physics? What processes should I invoke to estimate my probabilities? How do I include divine free action? By what method do I estimate the chance that God will decide to resurrect people? Stan says he came back from the dead and that he’s the son of God. Because of his special relationship with God, he claims it’s more likely he came back from the dead already. How do I determine the prior probability that Stan came back from the dead, before looking at the evidence? Do I assume his claim is true? If I assume it’s true, then why bother claiming that the resurrection is decisive evidence for the claim? If I assume at the beginning that his claim is likely false, then I’m back with the calculation above. Besides, why would God want to kill his own son? How am I going to psychoanalyze the Creator of the Universe?