A logical approach to
Quantum mechanics
Aristotle, who first formulated logic.
Logic is a system in which we rewrite and combine statements, beginning from axioms. Such an axiom can be a fact of which you are sure. The statements should be clear and there should be no multiple interpretation of each statement. Rewriting the statements can lead you to new conclusions. For example, take statements a = b and b = c. We can combine and rewrite these two statements to the statement a = c. We can call a = c a logical conclusion from the axioms. If we would be insane, and we would conclude a <> c from these axioms, that would be an illogical conclusion: it would contradict the combination of axioms. If we choose axioms that don't contradict each other, in the whole logical system that follows there will also be no contradictions. A special form of logic is mathematics (which was - earlier than logic - first formulated in Babylon and Egypt). Logic and Mathematics can be applied to physics.
When it comes to quantum mechanics however, there are two persistent illogical claims. One claim is that quantum mechanics would be a contradiction in itself, and would show that physics wouldn't follow the rules of logic. The other claim is that quantum mechanics would imply that a particle could exists and not exist at the same time, an illogical claim also known as fuzzy logic. In this article I will argue against both claims.
QUANTUM MECHANICS AS A CONTRADICTION
Sometimes you hear people say that there is a contradiction in the science of physics. The contradiction would be that radiation would have both a particle-character (like matter consisting of little particles) and a wave-character (like consisting of waves). They are two models describing the state of the energy of radiation. In classical physics it was assumed that only one of both theories could be true.
But instead, science proved both theories to be true. I do not at all think this is a contradiction or a surprise. If you look for instance at the surf of the coast-line, you can see that the surf is consisting of water. This water can behave clearly like a wave. At the same time it is possible that the water consists of water-particles (molecules H2O, salt and some other minerals). There is no logic contradiction. Both could occur at the same time.
Later it is assumed by the way, following Louis de Broglie, that also all matter has both a particle-character and a wave-character as well. The smallest parts of which matter would exist, electrons and protons, would behave according to both models.
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The fact that we only have probability, and not certainty, of the existence of the electron on a certain moment is not a matter of ignorance. One could assume that, at some point in future, we would be able to have exact knowledge of where the electron would be next at a certain time and place. But the uncertainty principle of Heisenberg says that it is impossible to know where the electron actually is on a certain time, because we cannot know at the same time the position and the momentum (and thus the speed) of the electron. The uncertainty principle claims that we can only determine the position or the momentum of an electron (or any other particle like a photon) by means of shining at least one quant of light on it. The photon's that are fired at the electron when doing this alter the place and the momentum of the electron however in an unknown way. You could think that, like playing pool, you could determine the total outcome. But on this small scale this is mathematically impossible. Therefore the probability is fundamental in quantum mechanics. We have no certainty on this small scale of physics, but the theory is not at all in contradiction.
FUZZY LOGIC.
A very interesting phenomenon that has to be explained by quantum mechanics is shown in the following experiment. We have a non-transparant slide with two parallel slits. When we shine light on it, the light will go through both of the slits. Behind the slide the light will form interference of the light waves. The light going through the left split interferes with the light going through the right slit. In the experiment we fire one single photon to the slide. Then we measure through which slit the photon goes. Will the photon take the left or the right slit? We measure it, and sometimes the electron is found to take the left one and sometimes the right one. We can also measure that if he takes the left one, he does not also take the right one at the same time. But what is very interesting is that there is interference behind the slide, suggesting that the light wave has gone through both slits. Since it is only one photon, the single photon interferes with itself.
One (unfortunately very popular) solution to explain this phenomenon is the Copenhagen Interpretation (by Max Born and
Werner Heisenberg). The assumption of the Copenhagen Interpretation is that when the photon goes towards the slide, it is in a superposition in which it is not decided which slit it will take. At the point of the measurement, it can appear that the photon is found left, or right. At this moment one could say that the photon made a choice between left and right, and is not anymore in a superposition. There is a probability that the photon goes left, or that the photon goes right. And then something very mysterious is added to the theory: The existence or non-existence of the electron (or photon) at a certain place, just before the measurement, would both be even as true. The existence of the electron on a certain place would be half-true. Or in other words, if we don't measure, the photon stays in a superposition, and it would be half true that he goes right and half true that it goes left. Only during the measuring the existence of the electron (or photon) at a certain place would become really true (or false). But as long as we don't measure, both options would remain half true. The photon in for example the left slit, would half exist there and half not (as long as we don't measure).
Born and Heisenberg adopt fuzzy logic, and claim that the existence of the electron is both half true and half untrue (until the measurement has been taken place). The theory is that when making a measurement, the wave collapses into a particle at a certain place. It is also interesting that the measurement is done by shining at least one quant of light on the particle. When a wave would collapse into one particle, it is assumed that at the moment that the waves collapses the interference with another wave would stop - because the wave has collapsed.
But this would not to be the case when I just fire one photon (or more) into the wave. The shining of one quant of light on a wave would not make the wave to collapse. But when we make an actual measurement there is a particle found or not, and the Copenhagen Interpretation says that this - the measurement itself - would make the wave collapse. In the experiment with the slide, only when measuring through which slit the photon goes, this causes (according to the Copenhagen Interpretation) the wave to collapse, but directly after the slide the wave is yet restored. So there are two very mystical claims in the ideas that where formulated by the Copenhagen Interpretation:
- a particle can be in a fuzzy state, in which it half exists and half not
- a measurement can cause the end of this fuzzy state and causes a choice for a particle whether or not to exists at a certain place.
Notice that claim 1 is very explicit. It is not the assumption that there are entities in a superposition from which there is a probability that a particle comes into existence of not. It is very explicit that the particle in the superposition is there, which is half-true, and is there not, which is also half-true.
The two claims do not only refer to this experiment, which I only mention to illustrate the Copenhagen Interpretation more understandable. But in fact, it is assumed that this applies to all waves and particles in general. So every electron of every atom is in a fuzzy state, of which the place is not yet determined. Only when measuring it, the wave collapses as a result of the measurement - resulting in a determined place of the electron. Born and Heisenberg based the Copenhagen Interpretation on works of Erwin Schrödinger. But it was actually this same Schrödinger that thought that these two mystical claims are absurd and illogical.
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The Copenhagen Interpretation predicts that also radioactive decay will follow the wave-model of probability. Now you could assume that the chance for a radioactive source would be exactly thus, that to decay in an hour would be for instance 50%. So after one hour there is 50% chance that the radioactive source has decayed and 50% that it didn't. The moment before we measure, both possibilities would be even as true (in the Copenhagen Interpretation). So if one hour passed by and we are just about to make a measurement, it is even as true that the radioactive source would be decayed as that it didn't. Only when the measurement is done, we know which one of the two became the result.
If the source then decayed, the cat dies. If the source didn't decay, then the cat stays alive. If we open the box to see how the cat is doing, then that is a measurement. We then can see if the cat is still alive. But if we didn't open the box yet to check on the cat, and the hour has passed by, it would be even as true that the cat would be dead as that it would still be alive. Before we measure (read open the box), it would be even as true that the cat would be alive as that it was dead. If after an hour we didn't open the box, the cat would be even as dead as alive, it would be in a fuzzy state in which it is even as true that the cat is alive as that it is dead. Until we open the box. No sooner than the moment that we open the box it is decided whether the cat is dead or alive. So if we open it after an hour and a minute, it is decided if the cat is alive or dead. But if we wait for 10 more minutes, it still remains undecided... According to Schrödinger this would show the absurdity of the Copenhagen Interpretation.
The physician Paul Wigner goes even further than this, and claims that our consciousness determines whether the cat is still alive. On the moment that the observer gets conscious of the situation, the confusing state of the cat ends and then it is determined what happens to the cat. A lot of physicians, like Born, don't worry about the philosophy of the whole, and are only concerned with the mathematical formulas.
I totally agree with Schrödinger. The cat is either dead or alive. A situation in which the cat is even as dead as alive is illogical. It is simply a contradiction. The cat has a continuous live from its birth until its death, it cannot be that a half truth is valid about the cat being alive and at the same time dead.
Besides the argument of Schrödinger, I also think that the idea that a measurement causes something is absurd. I think that the reality is independent of what I think of it. It there is a plant behind the curtain where I cannot see it, I do not hold that the plant doesn't exists simply because I would not see it at that very moment. Only a very small child would think that when the curtain closes, the plant disappears. But with the development of the brains we learn at young age that the object (in this case the plant) is there even if we cannot see it. And the same goes for a particle. It is not the measurement as such that causes something to be or not to be.
This also goes for Schrödinger's cat. There is a certain chance that the radioactive source decais after an hour. But it is also possible that it doesn't. The wave model is maybe a good statistic to predict this. There is a certain chance that the source will decay. If the cat is lucky, the source didn't decay, and then the cat will stay alive. If the cat is unlucky, the source did decay after an hour and then the cat dies. It is one thing or the other. If we open the box after an hour, the cat is dead or it is alive. But if we didn't open the box, the cat is also dead or alive after an hour. It doesn't depend on the opening or not opening of the box.
Of course it is possible to do an experiment in which the measurement influences the experiment, like shining light on an electron. But then the experiment causes a disturbance (instead of that the source changes as a result of our expectations). Maybe if I open the box, the bottle would fall, break, and kill the cat. Then the measurement disturbs the reality that we want to measure. But this is clearly not what was meant by Paul Wigner. Here the measurement was correct, and then there is a claim that this measurement, without disturbing the inside of the box otherwise then measuring it, would cause the cat to be either dead or alive (while before that it would be in a fuzzy state between live and death). I would rather say that there is a chance that the radioactive source is decayed, and this would mean that the cat simply died as a result of the toxic gas.
It is ridiculous to adopt a complex theory on particles being in a fuzzy state between existing and non-existing. The so-called fuzzy logic, in which the cat is in an in-between state between existence and non-existence, is in contradiction with the very nature of existence. Existence is an absolute. Your existence (of everyone who reads this) can be derived from the statement "I think and therefore I am", as it was stated first by Descartes. It proves that you, the person thinking this, are existing regardless of whether we can see you. And your existence is also an absolute regardless of the experiment of Schrödinger. If I would put you, my reader, into the box instead of the cat, it would be possible in fuzzy logic that you could be in a fuzzy state between existence and non-existence so long as we do not open the box. So if after an hour I would still wait ten minutes with opening the box, and in these 10 minutes you would think "I am and therefore I exist"; Your thought would prove that you would still exist - even if I cannot see you, even if I do not open the box. Would it be an option that in these 10 minutes it would partly be true that you were thinking "I am and therefore I exist" and that at the same time it would also be partly true that you couldn't think this thought because you would be dead? Could both be half-true? I wouldn't think so. Either you could think this and exist, or you couldn't think this and would be dead. It is not a possibility that you are existing a little bit.
The insight of Descartes is a more fundamental insight than that of Born and Heisenberg, and it implies that fuzzy logic concerning the existence of someone is a bad concept. With that, also the fuzzy logic concerning an object is a bad concept, because the existence of an object is independent of the fact whether or not it has self-consciousness. The idea that existence can be depending on the consciousness of someone else, like Paul Wigner stated, is absurd for the same reason. I exist, even if you cannot see me.
Having said all this, surely I should come up with an alternative for the Copenhagen Interpretation. And there was also something not explained at all so far: if the photon goes through the left slit, and not through the right slit, how can it interfere with itself? The only consistent theory so far is the Many Worlds Theory (first postulated by Hugh Everett as the relative state formulation). With every probability that exists, the universe splits in two (or more) universes. In one universe happens A and in the other universe happens B. A superposition then is not a state of fuzzy logic, but a particle that exists in two or more universes having different behavior. The particles of different worlds can interfere with each other. So in universe A the photon goes left, in universe B it goes right. But although being in different universes they can and will interfere, and this is what we measure. In universe A the cat lives. In universe B the cat dies. Interesting articles on this topic, some in which Henry Sturman defends a variant on the Many Worlds Theory, are:
Quantum theory: spooky action at distance?
Book Review: The Fabric of Reality, by David Deutsch
The Parallel Universes of David Deutsch - a Critique
Physics: Quantum all the way, by Philip Ball
I am not sure whether the Many Worlds Theory is right. It is a very complex solution to a problem raised by very weird experiments. But Many Worlds doesn't have the mystical elements of the Copenhagen Interpretation. I would say that it is the best theory we have at this point in time (actually Many Worlds it is the only group of theories because the Copenhagen Interpretation is not logical and therefore it is not actually a theory at all). So we should accept Many Worlds until a better theory comes along.
Some people give an interpretation to the Many Worlds Theory as if everything that happens, happens differently in another world. I do not agree with this interpretation, because I think that this splitting into several worlds happens only when there is a probability - a chance that something happens or not. And with particles this occurs frequently, but in the macro world not (except for the rare cases where the macro world is made dependent on the micro world, like Schrödinger's cat). My choice for instance to walk to the left or to walk to the right is not a probability, as I explain in the article:
· RELIGION, BELIEVES AND CONCIOUSNESS
This is all simply cause and effect without chances and probability. It is the same as throwing dice. There is in reality not a probability that I will through a 6 or a 5. This is all determined by the force and the direction I use when I throw the dice, the resistance of the table, etc. So I do not believe that in universe A I walk to the left and in B I walk to the right. Or that in Universe A I get a 6 when throwing dice and in universe B I get a 5. In all universes happens exactly the same in the macro world (except for special cases like Schrödinger's cat), but the small particles do behave differently in the different universes.