Periodic Reporting for period 2 - FLQuant (Fundamental Limits of Quantum Mechanics and Physical Laws in a Non-deterministic World)
Periodo di rendicontazione: 2023-04-01 al 2024-09-30
The basic laws of quantum mechanics, the theory that describes the behaviour of microscopic particles – atoms, molecules, sub-atomic particles, etc. – have been discovered over one hundred years ago. And it is the most successful of our theories of Nature. It has explained (within our computational power) virtually all known phenomena, except gravity. However, despite all this, it is generally accepted that no one really understands quantum mechanics. The behaviour of microscopic particles is so different – in fundamental ways – from the way in which ordinary “big” objects that surround us in our daily life behave, that nothing has prepared us to intuitively understand them. Very often, surprising, even seemingly paradoxical, new quantum effects are discovered; being surprised is the clearest sign that we do not have a deep intuition on what is going on. The aim of this project is to make progress in deepening our understanding of the fundamental aspects of quantum mechanics.
The present project has at its core a simple observation. Quantum mechanics is fundamentally different from all that came before in almost every aspect. But, as far as I can see now, there is one property that stands above all when we try to understand what quantum mechanics is all about: quantum mechanics is our first theory of Nature that is non-deterministic at a fundamental level. Repeat an experiment in identical conditions and the result may turn out to be completely different. Importantly, this has nothing to do with imprecisions in performing the experiment: no matter how much we improve the experiment, we cannot reduce the uncertainty of its result.
Long considered an unpleasant aspect, non-determinism is anything but: Non-determinism enables new freedoms. Phenomena that could not occur in deterministic theories because they would violate some basic laws of nature become possible in non-deterministic theories, under the cover of randomness.
A famous example is nonlocality, with well-known applications such as quantum teleportation, quantum computation and quantum cryptography. In a deterministic world, if something acting in one place would instantaneously produce effects somewhere else, it would violate relativity; non-determinism allows it. Following intensive research on the subject, in recent years nonlocality (deriving from the so-called quantum entanglement) came to be viewed as one of the main aspects of nature. However, because its existence implies non-determinism but not vice-versa, non-determinism itself was seen as secondary.
But non-determinism allows many more freedoms, beyond nonlocality. The vision of this project is to change the paradigm and put non-determinism at the core. The aim is to go well beyond the insights gained from nonlocality and focus on other freedoms.
The present project has at its core a simple observation. Quantum mechanics is fundamentally different from all that came before in almost every aspect. But, as far as I can see now, there is one property that stands above all when we try to understand what quantum mechanics is all about: quantum mechanics is our first theory of Nature that is non-deterministic at a fundamental level. Repeat an experiment in identical conditions and the result may turn out to be completely different. Importantly, this has nothing to do with imprecisions in performing the experiment: no matter how much we improve the experiment, we cannot reduce the uncertainty of its result.
Long considered an unpleasant aspect, non-determinism is anything but: Non-determinism enables new freedoms. Phenomena that could not occur in deterministic theories because they would violate some basic laws of nature become possible in non-deterministic theories, under the cover of randomness.
A famous example is nonlocality, with well-known applications such as quantum teleportation, quantum computation and quantum cryptography. In a deterministic world, if something acting in one place would instantaneously produce effects somewhere else, it would violate relativity; non-determinism allows it. Following intensive research on the subject, in recent years nonlocality (deriving from the so-called quantum entanglement) came to be viewed as one of the main aspects of nature. However, because its existence implies non-determinism but not vice-versa, non-determinism itself was seen as secondary.
But non-determinism allows many more freedoms, beyond nonlocality. The vision of this project is to change the paradigm and put non-determinism at the core. The aim is to go well beyond the insights gained from nonlocality and focus on other freedoms.
As envisaged, the project has evolved in a few inter-related directions. Arguably, the most important results that we obtained so far relate to the so called “conservation laws”. It has been long known that when we keep a system isolated from its environment, there exist various quantities that characterise it which do not change during its evolution. That is, if one measures them at the beginning of a process and then again at the end of it, they have the same value. In this sense, these quantities are “conserved”. A famous example is that of energy: If we don’t act with external forces and let a system evolve by itself, energy is conserved. And there are a few other such conserved quantities.
The existence of conservation laws is one of the fundamental aspects of Nature. Not only do they establish that some quantities are conserved in isolated systems and that changing them requires external intervention - hence they have extremely important practical consequences - but their very existence points to even deeper properties of Nature: They stem from, and imply, fundamental symmetries. For example, energy conservation is related to the fact that the laws of nature do not change in time.
The conservation laws description above however was made considering the behaviour of everyday objects, which is deterministic: repeat the experiment in identical conditions and you will get the same answer. This is not the case for microscopic particles. Repeating the experiment in identical conditions may yield different values for a conserved quantity. We thus may not know initial value. We also could not simply measure it, since quantum mechanically a measurement disturbed the evolution and the system will no longer evolve as it would were it not measured. Given this, a “statistical” version of the conservation laws was devised for quantum mechanics, which only takes into account averages over many repeated experiments, but cannot tell anything about what happens in an individual experiment. More than this, it was even thought that quantum mechanically conservation simply doesn’t apply to individual cases.
While this standard, “statistical” version of quantum conservation laws is valid, and extremely useful, we found that it in fact conservation does apply to individual cases (at least in a very large class of situations), changing thus the established view of a fundamental law of quantum mechanics.
The existence of conservation laws is one of the fundamental aspects of Nature. Not only do they establish that some quantities are conserved in isolated systems and that changing them requires external intervention - hence they have extremely important practical consequences - but their very existence points to even deeper properties of Nature: They stem from, and imply, fundamental symmetries. For example, energy conservation is related to the fact that the laws of nature do not change in time.
The conservation laws description above however was made considering the behaviour of everyday objects, which is deterministic: repeat the experiment in identical conditions and you will get the same answer. This is not the case for microscopic particles. Repeating the experiment in identical conditions may yield different values for a conserved quantity. We thus may not know initial value. We also could not simply measure it, since quantum mechanically a measurement disturbed the evolution and the system will no longer evolve as it would were it not measured. Given this, a “statistical” version of the conservation laws was devised for quantum mechanics, which only takes into account averages over many repeated experiments, but cannot tell anything about what happens in an individual experiment. More than this, it was even thought that quantum mechanically conservation simply doesn’t apply to individual cases.
While this standard, “statistical” version of quantum conservation laws is valid, and extremely useful, we found that it in fact conservation does apply to individual cases (at least in a very large class of situations), changing thus the established view of a fundamental law of quantum mechanics.
In my opinion, our results on conservation laws constitute a major breakthrough in fundamental quantum mechanics. Conservation laws, such as those for energy, momentum, and angular momentum, are among the most fundamental laws of nature. Stemming from the fundamental symmetries of nature, they are present in all our physics theories, non-relativistic and relativistic, classical and quantum.
Our results imply that the accepted definition of quantum conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended. Specifically, the standard definition of conservation laws in quantum mechanics is statistical; it refers to averages over a large number of repeated experiments but not to each individual case separately. We have showed that it is possible -at least in very large classes of situations - to go beyond this statistical definition and have conservation in each individual case.
What results do I expect to obtain by the end of the project? The nature of this research, which is purely theoretical and focused on fundamental questions, is very different from that of experimental work. Doing experiments takes many years and a lot of planning. On the other hand, if I would be able to say what I will discover in a few years time, I would deem the project too timid. Clearly, I do expect steady and significant progress in the objectives we have formulated at the beginning, including quantum frames of reference, Bell-type and dynamic non-locality, and the foundations of thermodynamics. We have already obtained important results in these areas in the first half of the project. However, from past experience I expect that the most important results of this project will be in new directions, completely unplanned and impossible to be anticipated. There is no better example than our progress in understanding conservation laws. We have discovered the paradox which is at the core of this breakthrough about three decades ago. It was about a strange case of energy conservation. We have frequently returned to it every since studying it from many different points of view, always learning more about it, but not being yet happy with what we understood. The breakthrough occurred now by asking an inspired question, in a totally unexpected direction. Once this occurred an entire new domain of research opened and we have concentrated our focus on it.
Our results imply that the accepted definition of quantum conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended. Specifically, the standard definition of conservation laws in quantum mechanics is statistical; it refers to averages over a large number of repeated experiments but not to each individual case separately. We have showed that it is possible -at least in very large classes of situations - to go beyond this statistical definition and have conservation in each individual case.
What results do I expect to obtain by the end of the project? The nature of this research, which is purely theoretical and focused on fundamental questions, is very different from that of experimental work. Doing experiments takes many years and a lot of planning. On the other hand, if I would be able to say what I will discover in a few years time, I would deem the project too timid. Clearly, I do expect steady and significant progress in the objectives we have formulated at the beginning, including quantum frames of reference, Bell-type and dynamic non-locality, and the foundations of thermodynamics. We have already obtained important results in these areas in the first half of the project. However, from past experience I expect that the most important results of this project will be in new directions, completely unplanned and impossible to be anticipated. There is no better example than our progress in understanding conservation laws. We have discovered the paradox which is at the core of this breakthrough about three decades ago. It was about a strange case of energy conservation. We have frequently returned to it every since studying it from many different points of view, always learning more about it, but not being yet happy with what we understood. The breakthrough occurred now by asking an inspired question, in a totally unexpected direction. Once this occurred an entire new domain of research opened and we have concentrated our focus on it.