Let's start this first talk of the two that we are going to do, this week and next. In this one I'll try to make you see that in science things are not always black or white, they are not always as clear as we tend to think. Sometimes we tend to think that science has the last word of most problems, and quite often this is not the case.
Even the exact sciences, those which are considered most mathematics, most rigorous. . .
, even physics, which is perhaps the most accurate of the natural sciences, has aspects that we still do not quite understand, that are under discussion, that it is not clear how they should be interpreted. Not everything is mathematically defined. The most paradigmatic example is quantum mechanics, and we'll see here some examples that illustrate why this is so.
In fact, thanks to this there is still a role for scientists, because if science were a purely mathematical thing, probably a powerful computer, entering the necessary equations and making the appropriate programs, could solve any problem. But things are not like that simple: there are many problems in which a certain intuition is needed, something more than a pure mathematical development. Let's see that quantum theory very nicely illustrates this.
Looking at my son's high-school physics book I remember that there was a chapter about "modern physics". I leafed through it and saw that it was aptly called "modern physics. " It included some notions of quantum physics and relativity.
I think it was properly named, because in physics there is a clear frontier in 1900. I already told you in the classroom that in 1900 Planck posed a hypothesis that was the seed of quantum theory, and that it took still many years to develop the theory -25 years- but that's when it all started. Curiously, very soon after -in 1905- Einstein raised the theory of restricted relativity, which is also a tremendous revolution in the previous ideas of physics.
So I think that the two strongest revolutions that have taken place, both originated by the early 20th century. At the end of the 19th century many physicists considered that physics was, if not finished, almost. There were some sets of laws that fitted very well: Newton's laws for mechanics; Maxwell's laws, that summarized electromagnetism; they had connected electric and magnetic fields in a single theory, but not only that, optics was also seen to be a part of electromagnetism, which brought together two important areas of physics.
There was thermodynamics, statistical mechanics to connect it to the microscopic world. . .
and there were some details that did not fit into this scheme, this puzzle, but it was thought that it would be just a matter of time to find the way to tackle those problems, to properly apply the laws and solve the corresponding equations. As an example I put here a couple of references: Albert Michelson was the first American to won a Nobel Prize in physics -in 1907- and, according to a book on the history of physics, in 1899 -just before Planck's hypothesis- he made this statement: "the most fundamental aspects of the physical laws have already been discovered, and these laws are so firmly established that it is very unlikely that they can be replaced in the future by other laws. " Curiously, just the year before Planck hypothesis.
The second quote shows that quantum mechanics was far from trivial, so if you find it hard to understand that is because it IS hard to understand. The proof is that Planck himself, who had put the first seed of the theory, still didn't believe in it in 1913, 13 years after. He took many years to think that he had really discovered something important.
He was convinced that things could not be that way, that the world could not be quantum. A proof of this is that when the main physical scientists of Germany at that time presented Einstein to enter the Prussian Academy -the most prestigious scientific academy at that time- they had to make a cover letter in which they praised his great discoveries, and it included an interesting comment saying that the fact that he had ever speculated, the fact that he had sometimes "tried to be clever" by proposing crazy ideas has not to be held against him, because it is clear that one has to be risky and launch wild ideas in order to make new discoveries. And they were referring to the quantum nature of light, something that nowadays is universally accepted.
That is, most of the main physicists at the time, still didn't accept the theory, because, as we shall see, it's really weird in some respects. But I'm going to start by trying to convince you that the theory has been verified as few theories have ever been. The coincidence with the experimental results is amazing.
For example, the electron g factor, as you know, gives an idea of the size of the intrinsic magnetic moment -the spin- of the electron, that behaves like a tiny magnet. The value of the g factor is this. It has been measured with an extraordinary precision: with all these digits.
Its relative error is 2. 6 x 10 to -13, and it has been theoretically predicted with the same degree of accuracy. For several years there has been a kind of race, between theorists and experimentalists: if the experimentalists got one more digit, few months later the theorists refined their calculations and reproduced that figure, and vice versa.
And all the figures agree perfectly. There are few cases of physical constants that have been theoretically predicted and experimentally verified so accurately. Let's give you an idea: if I measure the length of a one-meter-long table and I make an error similar to that of this constant, the error would be 2.
6 x 10 to -13 meters. This is one 400th of the diameter of a hydrogen atom. Namely, to measure this length with that precision I would have to refine to that point; it is really amazing the accuracy of that value.
Quantum theory applies from the scale of fundamental particles to cosmology: nowadays the evolution of the universe cannot be understood without using -for explaining the evolution of the stars, for example- quantum theory. There has not been found any experimental fact contradicting the theory at none of those scales. The predictions of the theory are countless, and there is such a conviction that the theory works, that it won't fail, that whatever prediction it has made is believed blindly.
Even if it hasn't been checked experimentally, it's always thought that it will be verified soon or later; if the theory predicts it it must be true. There have been many examples such as antimatter: when Dirac joined quantum theory with relativity he concluded that, in addition to the electrons, there should exist particles -that have been called positrons- which are the antiparticle of electrons, and that an electron and a positron could be canceled out to produce radiation, energy. Antimatter was discovered because it was searched for; because the theory had predicted it.
In 1916 Einstein predicted induced emission, a mechanism of radiation emission different from the standard mechanism in nature, which is spontaneous emission. Since then it was intuited that someday lasers would be made. The first laser was made in 1960, but already in 1916 the theory that explained how lasers should be made was there.
Let's finish with a curious example: the Bose-Einstein condensate, a state of matter -at very low temperature- with very peculiar properties that was predicted by Bose and Einstein in 1924 and has not been realized experimentally in a laboratory until 1995, 71 years later. Well, no one doubted that, sooner or later, a Bose Einstein condensate would be obtained. It had to be at very low temperatures, it was technically complicated, but everyone was convinced that it should exist.
And like this there is plenty of things, some of great technological interest, such as the high density discs of any computer, flash memories, nanotechnology, semiconductor electronics, chemical reactivity, spectroscopy. . .
, none of this can be understood without quantum mechanics. And more curious applications such as inviolable signal transmission -in fact, rather than inviolable we mean that if someone cracks or captures the signal we can positively know it- and things like that, things that sound like science fiction, such as teleportation, quantum computing, weak measurements etc. I will give you an example that shows to what extent these applications can be technologically interesting: weak measurements.
In 1964 two physicists -Aharonov and another one- published a paper in a journal which deals with philosophical ant interpretative aspects of physics. Until a few years ago, physicists considered that these discussions about interpretation and such were not physical, were not serious, that this was more the domain of philosophy than of physics, and therefore those things were seldom published in the most prestigious journals. In 1988, these same authors realized that, on the base of what was explained in that article, peculiar measurements systems could be devised -which they called weak measurements- that could have important practical applications: they would allow to reach high levels of accuracy.
In 2009 this was put into practice, and the first devices to implement this measurement system were made. Based on this angles have been measured with errors of 4 x 10 to -13 radians. As usual, this has to be illustrated with an example, since otherwise it is difficult to get an idea of what this means.
If you take a laser, focus it towards the moon and move it this angle the ray will move on the moon about the width of a human hair. This is an angle of 4 x 10 to -13 radians. Length measurements with an accuracy of 2 x 10 to -14 meters: this is the diameter of a uranium nucleus.
A moment ago I spoke about the diameter of the hydrogen atom, but a nucleus is about 10,000 times smaller than an atom. If we could see an atom we would see an empty space with some small dots flying around -the electrons- and a small dot in the middle, almost invisible at the atomic scale, that would be the nucleus. Well this is the precision that has been achieved in lengths based on a consequence of theoretical considerations that, at first, were raised as a curiosity.
Eventually those curiosities almost always end up having a use. Measurements of time: in 2014 a type of atomic clock was designed -the optical lattice clock- with a precision of one second in 5 x 10 to 9 years. The age of the universe is 14 x 10 to 9 years, so that we are talking about times of the size of the age of the universe.
That is to say, during the whole evolution of the universe that clock would delay or advance a second. This could have important technical applications. For example, the gps: the main limiting factor in the precision they give when getting our position is the accuracy in the measurement of time.
Time measurement is very important for getting the position. Already in the middle ages, the British admiralty gave a prize to the one who managed to measure time with a certain accuracy, which was essential for the ships to get their location when sailing in the open ocean. It was won by a watchmaker with a windup clock; an ordinary clock, that he improved very much.
The same happens nowadays with the gps: to get a good position they need a very precise measurement of time, and they use atomic clocks with an error of ≈50 ns per day. And they give a precision in the meter range for an object well located relative to the gps satellites. Well, that's a second in 6 x 10 to 13.
Compared with this the optical lattice clock has an accuracy 4 orders of magnitude higher. Of course, these clocks are nowadays too sophisticated, too complicated, to be put on a satellite, but if we neglect other sources of error -considering only time- changing those clocks for these new ones we could theoretically specify the position with an error in the range of tenths of a millimeter. Anyway, everything ends up having a use.
And yet, this theory so verified, so accurate, so reliable, is amazing, and it breaks in many respects the patterns of the intuition we had until the twentieth century. - For example, the first one is what has given its name to the theory: there are properties that were thought to change continuously and they vary discontinuously, they are "quantized": the energy of an atom, and many others that you already know. - Determinism: according to Newton's laws -and to any other fundamental law of classical physics- given some causes we could, in principle, solve certain mathematical equations to find what is going to happen.
Quantum theory tells us that this is not so: even if we perfectly know the state a system -its "wave function", that contains all the information about the system- we can't predict, in general, what will be obtained if we measure some property; it is intrinsically indeterministic. - In classical physics the differentiation between particles and waves -say, electromagnetic waves- was very clear. In quantum mechanics it turns out that light has sometimes a particle-like behavior -actually it is considered as a flow of photons- and matter can interfere just like waves do.
Hence, the border has become completely blurred. - In classical mechanics the measurement of the position and the measurement of the speed -or the momentum- can be done independently with arbitrary precision, at least in principle. Quantum mechanics tells us that this is not so, that there's a relationship between the indeterminacies of one and the other, and, for that reason, we can't, for example, define accurately the trajectories of the particles, and we have to resort to something much more abstract: a wave function, which is part of a mathematical Hilbert space, something much more difficult to visualize.
- The observer in science was always considered someone external who just sees the system behavior, and it turns out that in quantum mechanics the observer unavoidably affects, in general, the observed system; so, there is a certain degree of subjectivity in the measurements, in the observations. - In classical mechanics and, in general, in any physical theory whenever we want to study a problem we try to isolate it from the rest of the universe, so as to simplify things. Well, there is a feature of quantum mechanics that we have not dealt with in the subject, but that will be commented later on: "non-locality".
What we do in some point in space may affect other particles no matter how far and isolated they are and, in addition, this effect is essentially instantaneous. This is one of the most surprising aspects of the theory which gives rise to what is called "entanglement", a quite subtle concept that has applications such as the famous "teleportation". - Identical particles were distinguishable in classical theories, while they are indistinguishable in quantum theory, etc.
I want to highlight three of these features, because, curiously enough, they are related, with three main pillars of modern science. Why did Newton come up with a mathematical equation for describing the effect of gravity? It is said he was inspired by watching an apple falling from a tree.
I don't know if it's true, but, if it were, he would have verified that given the initial state of the apple -its position, height, etc. - what happened to it when it was dropped was reproducible, that it always followed well-defined rules. If each time he dropped the apple the fall-time changed and the results of different measurements were inconsistent he would not have bothered to seek for a physical law.
The reproducibility, the fact that for fixed causes the effects are determined, is basic for the human being to have ever come up with searching for laws to describe nature. And precisely the cause-effect relationship is (partially) denied by quantum mechanics. There seems to be a certain degree of indeterminism in nature.
Another of the pillars of science is that it describes something that is out there, that can be observed, but happens regardless of whether we observe it or not. The observer is someone objective who tries to affect the system as little as possible. But quantum theory tells us that the observer is, in a certain way, creating part of reality; that is, what you observe is affected by what you measure and, therefore, is not always something that is there regardless of the existence or not of an observer.
Observation becomes something much more subjective than in pre-quantum theories. And, well, the fact that we can't isolate a system, that we can have a system in a lead chamber to avoid radiation and whatever external interaction, and there may be mysterious connections with other parts that are very far away, this also breaks the schemes upon which science has developed. But keep calm, because, despite all this, the rules of quantum mechanics are very clear.
To pass the exam you have to know how to apply them, and the recipe is as clear as day. Another thing is that when we we try to imagine, to visualize how the microcosmos looks like we run into trouble, but when you have to solve a problem and you have to apply the laws, the way to do it is very clear. Still, there are quotes that reflect that .
. . For example, Bohr once said that anyone who is not surprised, shocked by quantum mechanics is that he has not understood it.
He comes to say: anyone who thinks he understands it perfectly has not understood it, because there are things that nobody understands. And Feynman, who was one of the greatest quantum physicists of the mid- 20th century, once said he believed for sure that nobody understands quantum mechanics, at least in some respects. Today we are going to treat one of these and the next day we will talk about some other.
But, in a way, that's the fun of quantum mechanics, despite the fact that it was developed almost 100 years ago, is still giving us surprises, applications that no one had thought of before. There are aspects that are so counterintuitive that only by following strictly the mathematical laws of the theory we can arrive at them, we can predict them. Thanks to that, new consequences -such as teleportation and quantum computing- are still being discovered.
Nobody had imagined them before, and I'm sure that it will lead to new technology and new developments for many more years to come. That is, somehow, the beauty of this theory. Let's start with quantization.
Quantization is what gave the name to the theory: there are properties that -classically- we thought they were continuous, and quantum theory has revealed that they are not. But hey, this is not that serious. An harmonic oscillator -say a pendulum- seems to be able to oscillate with any energy, with any amplitude.
According to quantum theory, it can oscillate with a certain energy with another greater one, with another greater one, . . .
but there are no intermediate energies. What happens is that these energies are so close together in a macroscopic pendulum that their discontinuity is completely imperceptible, the jumps of energy are imperceptible. Therefore if they exist but are so small that we can't see them why not believe it?
This is not hard to understand. It happened likewise with the pyramids of Egypt: when a westerner arrived for the first time and saw them from a distance, he saw a perfect thing, with beautiful straight lines. But when he approached them he saw that, in fact, those seemingly straight lines were steps the size of a human being.
It seemed a continuous line and it was a broken line. Water looks like a continuous fluid and you perfectly know that it's made of individual molecules, so small that we can't see them or feel them. The same also happens with light: if we are told that it's a jet of photons that go so close together that they appear something continuous, why not believe it?
There are many examples of things that seem continuous and are discontinuous. Therefore quantization, is not an issue that should worry us too much. Indeterminism is somewhat more curious.
Let's consider an example: you have a barrier of potential -it could be a plane with a little mountain- and you throw marbles from there towards the little mountain. According to classical mechanics, if the kinetic energy you give to the marble is less than the potential energy necessary to climb up here, the marble will turn back, and if you give it an energy greater than that potential energy it will pass by. No more mystery.
Quantum mechanics says that particles having lower energy sometimes pass (tunnelling effect), and those with higher energy sometimes bounce. That is, at least for energies near the height of the barrier (and very light particles) things are not so "black or white". And, in addition, it says that we can not predict, what will a particle will do in each individual experiment.
This a typical instance of indeterminism, and there are very important examples. You know that a radioactive nucleus can emit an alpha particle, but we can not predict when it will released it. This is because the alpha particle has to traverse an energy barrier by tunnelling effect, and so there is a certain probability per unit of time that it passes through it, but it is impossible to predict, for an individual nucleus, when it will disintegrate.
In classical mechanics there are indeterminate problems: if you throw the dice you do not know what will come out, but the indeterminism appearing in classical theories is not "authentic". You'll probably think: well, when I throw the dice I don't know what will come out because it is impossible to know exactly how I threw them, how I put my hand, at what height, what speed I gave them, what's the exact shape of the die, the table . .
. If I had all this data I could surely calculate the exact path of the die and know what will come out. By solving Newton's equations we would have the solution.
That is to say, classical indeterminism is always associated with a lack of information about the initial conditions. There are examples -but I'm not going into them- of other classic problems that also present indeterminism, but quantum indeterminism seems to be something much deeper much more unavoidable. Notice that, in fact, it is very interesting that the world is apparently indeterministic.
If quantum theory is true, it seems to imply that the world is, indeed, indeterministic. If it were deterministic, if we were governed by laws -like Newton's and Maxwell's- totally precise, I would mean that each of the particles that compose us moves according to a plan foreseen since the universe was created. Of course it is impossible to calculate it: there are so many particles in a human being and in the universe that there would be no way -even with the most powerful computers- of calculating what will happen to each of those particles, but there would exist a perfectly determined future from the origin of the universe.
And the feeling we have of "free will", of being able to say: well now I decide to take this and throw it; and I've just decided it right now. . .
that freedom of doing what we want -within certain limits- would be a pure fallacy, a pure illusion. Quantum mechanics, by telling us that the world is indeterministic, opens the door to a possible explanation, perhaps, of the free-will feeling we have. This is not obvious, the connection is not clear, but it is an interesting consequence of indeterminism.
In what remains of today's talk we will analyze this topic in more detail and we'll see that a consequence of it is that, according to quantum mechanics, an object seems to be able to be in several places at the same time. Let's get to it. We are going to perform a slightly modified experiment of the particle crossing a barrier.
I have not a particle but a beam of particles reaching a potential barrier. Let's assume that, when they arrive here, they have say 50% probability of passing by and 50% of bouncing. If they pass I make them collide here and deviate towards a screen where each particle leaves a mark.
Then I count how many particles reach each point of the screen. The particle beam is not perfectly collimated, they do not travel exactly in parallel, so not all of them reach the center; there is rather a certain distribution of arrivals. This curve gives the number of particles that arrive per millimeter -for example- of the screen.
It will have a maximum here in the middle, and then decay quickly. This is in the case that only the particles having crossed the barrier are allowed to pass. I could have done the other way round: I could have intercepted the particles that go through the barrier and leave open only the path of those having bounced.
Since 50% bounce, I'll get a similar pattern: a maximum here in the middle and a distribution curve of arrival positions decaying quickly to 0. What will happen if I don't put any barrier and leave the two paths free? What would you expect?
Well, as they now arrive this way and this way, the spot should be more intense, but it should have a similar shape; the curve should be the sum of these two. Well, if you do this experiment with elementary particles you will find a much stranger thing, much odder: a series of maxima and minima. At the minima no particle arrives, then there are zones at which many particles arrive.
Well, here I have drawn it with peaks, but it should be more or less rounded. A series of zones at which many particles arrive separated by zones at which none arrives. This is not that rare actually, because this pattern is quite similar of what -in wave physics- it's called an interference pattern.
If you let the light pass through two close enough slits, interferences are produced leading to a similar pattern: illuminated areas followed by dark areas, illuminated-dark. . .
, in a plane somewhat away from the slits. And this is a very easy to understand: I bet some of you have ever surfed or, al least, have seen surfers on the beach and, at least here in the Mediterranean, their main activity is to wait riding on the table. Why?
Well, because the waves can be considered as superposition of wave trains more or less sinusoidal with different wavelengths, and if you take -for example- two sinusoidal waves like these up here: a the green one with a wavelength slightly shorter than that of the gray one, there will be times when the two add and a much more deep ripple results -it has twice the amplitude- and times when they get out of fase -when one is at a maximum and the other at a minimum- and then the result is almost no ripples. That is, two waves can interfere constructively or destructively. And, if instead of only 2 we put together many waves constructive interferences are much less frequent but much more intense.
And, since in the Mediterranean the waves are usually small, surfers have to wait until a significant constructive interference occurs and the typical set of 3 big waves, much higher than the rest, appears. And the rest of the time. .
. waiting for a new set to come. Thus, interference phenomena were well understood long before the 20th century.
However, it is relatively easy to understand that one wave cancels with another one, but that two particles may cancel each other out. . .
. at least to me it is much much harder to accept. There are points -for example this zone of the screen- at which many particles arrived when only the upper path was open: all these.
When only those going downwards passed many arrived also, but when both paths are open, no one arrives. Do the particles cancel each other out? Let's try to understand this.
Let's find some explanation for this phenomenon. I might be that the particles interact in some way: since they come through two different paths, when they get to the screen. .
. well, if they were electrons, their repulsion would make the curve no longer equal to the sum of the curves that were obtained when there was only one beam or the other. There may be collisions, or any type of interaction that makes the problem more complicated than it looks at first glance.
This is a possible hypothesis; is there any way to check it? Is there any way to avoid this interaction between them? There is one: to send them one at a time.
I send a particle and when it has arrived I send the next one, and the same for the next and the next, and with patience, I gather the marks of a great many. . .
and what we get is exactly the same. That is, the explanation of possible interactions between particles does not work. Any other idea?
Who said that the particles are indivisible? We don't know what's happening inside the barrier. May be they are split into two parts, in two halves, and those two halves, each one has its charge or whatever, they interact and who know what it happens.
Well, we could also try to check this; we could put well separated detectors in both possible trajectories and see what they register: when launching a particle both give a signal it would mean that that particle has split into two pieces, has been divided into two parts. Let see what is obtained in this case. Moreover, this would give us the key to what's happening in between.
The mystery is in the way from the barrier to the screen, it is not clear how they travel it. Well, detectors will give us the solution. What is found?
Well, what comes about is something typical of quantum mechanics: when we try to spy the system out and try to get information about the fuzzy zone, that area where we don't understand what is happening, the process of obtaining this information -the detection- modifies the system in such a way that those strange quantum phenomena -the interferences- disappear. If I put detectors I know where every particle has gone through, but the interference disappears and the curve becomes the sum of those two. Quantum theory -or we should rather say nature- seems to keep for itself its strange behaviors, and when an observer tries to spy and see what's happening it quickly behaves correctly, stops doing weird things, and dissimulates, so that its secret, better kept than Coca-Cola formula, is not discovered.
It behaves in an essentially classical way. It could be argued that, since the detectors are macroscopic devices, they interact with the particle in a complicated way, changing completely the experimental conditions. But we can know the trajectory even with a single detector and, then, the particles that take the lower path -and therefore never interact with the detector- would not know that there is a detector and they should generate some kind of interference, something different should be seen.
. . Well, it is not.
Even though there is only one detector, if a particle is launched and it is not detected -and the detector is reliable and works properly- we know that it hasn't taken the upper path, that it has gone down. And quantum mechanics states that if we get information about the system its state collapses and, in our case, one of the two trajectories becomes defined. The mystery about how a particle going through the lower path knows whether the upper one is open or not so as to produce interferences or not, disappears.
Well, we still can imagine other possible explanations. We don't know everything about the electrons. They are so small that there is no way to see how they are.
Who knows? May be they have eyes and, if they go through the upper path they find out if the down-side barrier is put or not, and they are very skilled and think: "look! since the barrier is set, I'll go to the center.
" And, otherwise, if they see that the barrier is not set they do strange things, they go here or there so as to be distributed according to the interference pattern. Well, we can't rule out any hypothesis. But, can we verify this one?
Well, not exactly with this experiment, but with other variants -that will be seen next day- it can verified that, if the decision of putting or not the barrier it is taken at the very last moment, at a time when not even light can travel from the barrier to an electron in the other path -and according to relativity if light can't travel no signal can travel, because the speed of light is the maximum speed of propagation of signals, of information- then, even if the particle had eyes to see if the other path is also open or not, it would not have time to adapt his trajectory, to decide if it has to go to the center or to do such weird things as the interference pattern. Thus, even that hypothesis is discarded. Who knows?
. . .
Maybe the particles have telepathy with the scientist who is doing the experiment, and they read his mind. They say: "Ah! Look!
He hasn't done anything yet but he is going to put the barrier, I know it because I've read his mind, and although he hasn't put it yet I'll adapt my trajectory to the case in which there is a barrier". And exactly the same if the scientist has decided not to put it on. Well, this is another possibility, but even this one has been excluded.
The decision to put or not the barrier can be taken not beforehand by a scientist, but by a random system, and nowadays there are random systems based on the indeterminism of quantum mechanics that are authentically indeterminate; that is to say, it is impossible to predict in each experiment, for each particle, what will happen: if the barrier will be there or not. Then it is physically impossible for any object to obtain information about whether or not there will be a barrier. Conclusion: it seems that the particles, when we do not observe what happens there in the middle, if they follow one path they somehow find out what happens in the other.
It is as if they were on both paths at the same time. This makes us doubt that a particle is something with a well-defined position in space: when we detect it we find a definite position; before detecting it the quantum state that describes the particle is what is called a "superposition" of two states corresponding to two different trajectories, and it seems that the particles can be in both places at the same time. If both paths are open, they know it somehow when the particles arrive here, Returning to a more technical topic related to the course subject, it's like when an object is in a state that is not an eigenstate of the Hamiltonian and, therefore, does not have a well-defined energy.
If you measure the energy it becomes perfectly defined, but before measuring it you can't assign an energy to the object. The same thing happens here: you measure the position with a detector and you know that the particle has gone this way; if you do not measure it the particle can be anywhere or, rather, it seems to be in both trajectories at the same time. In a way, then, it seems that the particles -in some respects- can't be considered as localized entities, such as the image we have of something very small.
Some people think that they are not, that everything has to be interpreted as fields . . .
But I am not going to get into the odd consequences of this interpretation. Let's see what happens when we go to larger scales, because it is clear that when you play with billiard balls these weird things do not happen. These interference experiments have been made with elementary particles and also with bigger things: for example, molecules as big as fullerenes: 70 carbon atoms with their electrons; that is, hundreds of particles.
Devices such as the "SQUIDs" -electrical circuits through which an electrical current circulates (although they are intercepted at two points)- can be in states in which electrons circulate in one direction and in the other at the same time. It's not that some electrons go to one side and others go to the other; even if there was a single electron its state would be a superposition of a state of the electron spinning in one direction and a state of the electron spinning in the opposite direction. They have an important technological interest: these devices allow to measure very weak magnetic fields with great precision; and they are macroscopic objects -very small but visible to the naked eye- that can be prepared in superposition states of electrical currents flowing in different directions.
In 2010 an article was published about an oscillator -a tiny metal tongue, the size of a human hair- that could also be prepared in superposition states, with different energies; different oscillation amplitudes. That is, it has neither one amplitude nor the other, it is in some superposition of both states. And where is the limit?
Nowadays attempts are being made to get superposition states with viruses; a virus is already on the frontier of living beings, and, if we keep increasing the size . . .
why not with cats? And this is where the famous Schrödinger cat comes in. Schrödinger, that was one of the fathers of quantum theory, never believed it.
He always thought that things could not be that way, and he proposed the following example: imagine a box in which we have a radioactive substance that after 1 hour has, say, 50% probability of having emitted an alpha particle. That particle is captured by a detector that moves a mechanism that drops a hammer. The hammer breaks a bottle of poison and the cat, poor thing!
dies. The point is that, according to quantum mechanics, while the box is closed and there have been no observations the alpha particle has, after one hour, a 50% chance of having been issued and 50% of having not, and its quantum state is a superposition of particle inside and particle outside the nucleus. That means that the state of the hammer is a superposition of hammer up and hammer down, and that cat is in a superposition of live and dead.
The poor schizophrenic cat in here would not be dead nor alive, but in a superposition of both states. This has led to a long-standing controversy: is the cat an observer? Can it cause the state collapse?
Are only human-beings observers? We should ask the cat with a microphone and tell him to explain what it is seeing, but this is not easy . .
. Besides quantum superposition states are very fragile; to keep them we often need systems at temperatures very close to absolute zero, isolated from any external influence, and it is obvious that the poor cat, if we put it at absolute zero and isolated from any source of light and heat it will be more dead than alive for a while now. This is a caricature of the quantum mechanics interpretation problem I have raised, but gives a first idea of why this so-precise theory is something about which -about the interpretation of which- there is still a strong controversy, there is not yet a universally accepted consensus.
In science, not everything is black or white, rather some things are much more subtle. We leave it here so you have time to go to the lab sessions, and next Wednesday we will talk about an interesting topic that is an extension of this, and that will raise an interesting question: can we change history? We will see that quantum mechanics, allows, in a way, to change history.
See you next day.
