Massei — Bamidbar-Numbers 35
Whoever kills a person, based on the testimony of witnesses, he shall slay the murderer. A single witness may not testify against a person so that he should die.
In this verse, the Torah states that a murderer can only be convicted based on testimony of live witnesses. Contrary to common law jurisprudence in the US and the UK, and civil law jurisprudence of most other western countries, circumstantial evidence cannot be used alone to convict according to the Torah law. (It may, however, be used to interrogate witnesses in order to ascertain their truthfulness or to acquit the accused.) The only basis for a Torah conviction is eye-witness testimony. This seems strange, though. Why, for example, may fingerprints or DNA evidence, which is, surely, incontrovertible, not be used to convict a criminal?
When a person is accused of committing a crime, before he is either proven guilty or acquitted, he is in a state of superposition of two states – innocence and guilt. In other words, from our perspective, his state is in doubt. He might be said to be 50% innocent and 50% guilty. Sounds familiar? Does it sound like a Schrödinger Cat? Of course it does! (If you wish to revisit Schrödinger’s cat, see for example my post On the Age of the Universe in the Many-Worlds Interpretation of Quantum Mechanics.) Until the wavefunction of the accused is collapsed, he is in a blurred state. To be precise, he is neither innocent, nor guilty, nor both, nor neither; rather he is in a unique quantum-mechanical state of linear superposition of two states: innocent and guilty.
As I discussed at length in my essay, Towards Reconciliation of Biblical and Cosmological Ages of the Universe, according to the Copenhagen interpretation of quantum mechanics as it was understood by such physicists as John Von Neumann, a Nobel Laureate, Eugene Wigner and John Wheeler; only a human being can collapse the wavefunction. Perhaps this is why the Torah requires eye-witnesses to convict an accused criminal. Only a live witness can collapse the wavefunction of the accused by testifying about his crime.
An interesting question is, why does the Torah requires at least two witnesses to convict a criminal? Wouldn’t one person be enough to collapse the wavefunction? It seems as if it would, at least from a quantum-mechanical point of view. One observer is enough to collapse the wavefunction of the Schrödinger Cat! What makes our situation different from the gedanken experiment with the cat?
The problem here is that we don’t necessarily know who is the “cat” and who is the observer. If a single witness comes and testifies in court that he saw ploni ben ploni (so and so) committing a crime, what stops the accused from turning the tables on the witness and testifying that the so-called witness was the one who actually committed the crime and now is trying to pin it on him, but he – an innocent bystander – is actually the witness to the crime and can testify to this fact? As we see, this situation is untenable. Therefore, the Torah requiresthat at least two witnesses, who are unrelated to each other, who both saw the crime (and each other), testify about the event in precise detail and not contradict each other in any of the minute details.
To further support this proposition, let us recall that when the point in question doesn’t involve a human being, one witness is enough. For example, if one witness testifies that that the piece of meat on the table was treif (not kosher) and two witnesses testify that they saw the man eating this piece of meat, it is enough to convict him for a violation of the Biblical prohibition to eat treif, which makes him liable to receive malkot – lashes. (See Rambam Laws of Sanhedrin Chapter 16.) Why is it enough for one witness to testify that the meat was not kosher but we require no less than two to testify to the person eating it? Because the situation is not symmetric – the meat cannot turn around and claim that it is really the witness who is “not kosher”. The person accused of eating this meat, however, can easily turn the tables on the witness and claim that it was the witness who actually ate the meat and is now trying to pin this sin on him. We wouldn’t know who the “cat” is and who is the “observer.” Therefore, in situations which are not symmetric the Torah requires only one witness, but in symmetric situations where the roles can be swapped, it requires two.
Can you relate this to the concept of creation? Gd opened Adam’s eyes and Adam observed the world, effectively collapsing the wave function and bringing into existence and out of superpostion the universe. Can you more thoroughly explain why the universe was aged when it came into existence and why the cat would similarly have been decayed if the Schrodinger had opened the box after a certain amount of time? If something is in the state of superposition, it would seem to me to be unaffected by time. What does the half life of plutonium, a relative rate of decay, have to do with the cat?
The collapse of the wavefunction has no place in the Schrödinger equation. It is something that we know happens as a result of a measurement. That’s why it is called “the Measurement Problem.” Before the collapse, the wavefunction evolves in time. Schrödinger equation is the equation that describes the evolution of the wavefunction with time the same way the Second Law of Newton described the evolution of position and velocity of a particle with time. The collapse of the wavefunction reveals the value of the observable (say, position or momentum of a particle) at the time of the measurement, which caused the collapse. This value is the result of the evolution of the wavefunction (whose square amplitude is the probability of funding this value) with time. That is why, when the wavefunction collapses, it brings with it the entire history of its evolution in time.
Consequently, when we open the door to observe the Schrödinger cat, if we find the cat alive, it will be a hungry cat. But if we find it dead, we find a smelly cat. It is easier to visualize in the Many Worlds interpretation of quantum mechanics. In one world the cat is alive and is getting hungrier by the minute. In the other world, the cat is dead and is decomposing. When we open the box, we randomly chose one of these two worlds. In either world the cat will have evolved in time according to its fate – either getting hungrier or smellier.
Similarly, when Adam collapsed the wavefunction of the Universe, he brought this world into a tangible existence but he did not create the world anew – the world he brought into tangible existence was as old as it took from its original creation (say, from the Big Bang) till the moment when Adam collapsed the wavefunction of the Universe.