On the deep meaning of the uncertainty principle and why it is necessary to move to the framework of quantum field theory
Quantum mechanics, as well as Newtonian mechanics, describes point particles, that is - every system is described by a set of discrete variables defined at specific points in space and time (hereafter - space-time). If there are N particles in the system, each particle will be described by two variables - its position in space-time and its momentum (in Newtonian mechanics momentum is equal to speed). The development of the system will be described by the dynamics of these N particles - that is, the development of the 2N discrete variables.
This is actually how all theories that are not field theories are built. Field theory is a theory that describes the development of fields, and not of a system of discrete variables. What, then, is a field? In our case, a field is a function that is defined at every point in space and time, that is, for every point in space and time the field will have some value. For example - the electric field. An electric charge will cause the formation of an electric field around it which will cause movement among other charges in the area.
An example of a field theory is Maxwell's electromagnetic theory (a non-quantum theory), which does not describe the development of point particles, but the development of the electric field and the magnetic field.
The equations of motion describe the development of those fields, and not of this or that particle. If we take, as an example, the case of two charged particles (for example - two electrons), the development of the system will be described by the development of the total electromagnetic field of these two particles at every point in space-time. In this simple case, the development of the system could be described by a set of 4 discrete variables, since there are two particles, but there are more complicated cases, in which this cannot be done. It should also be remembered that Maxwell's theory itself is a simple theory compared to modern theories, in which the problem arises even more strongly.
The meaning of a theory describing point particles is that if we look at a pointaccurate on timeEach particle will be located at a precise point in space. But it turns out that such a theory cannot correctly describe reality! That is why quantum theory "recruited" Heisenberg's uncertainty principle. The uncertainty principle states that it is not possible to accurately measure the position of the particle in space and at the same time also its momentum. There is always some uncertainty. A reasonable formulation is that it is not possible to look at exact times and at the same time measure exact energies - there is always uncertainty in the time and energy of a particle. Therefore it is not possible to look at an exact point in time! This is how quantum theory lays the foundation for the first sentence in this paragraph, that is, the ability to accurately describe the exact position of a particle at a given point in time.And so the uncertainty principle allows quantum theory to describe point particles without the need to place them at a specific point in space-time.
It can be said that the uncertainty principle casts a sort of "fog screen", or covers each and every particle with a tiny "fig leaf", so that we cannot look directly into the heart of physics. It is true that we can observe global, macroscopic phenomena, arising from the quantum nature of nature, but we cannot perform measurements at the microscopic level of matter. It must be understood that this is not a technological limitation, but a theoretical limitation built into quantum theory that does not allow us to do so. Alternatively, it is possible to come to the understanding that nature should not, and cannot, be described using point-particle-theory.
The reason why physical theory cannot correctly describe nature using point particles is that nature is physical, not mathematical, and therefore physical phenomena cannot be described using mathematical points, i.e. zero-dimensional entities. In contrast, field theories describe reality by defined fieldsat any pointIn space-time, that is, they are defined on a continuous and not discrete space, and therefore can constitute physical theories.
It can be said that point-particle-theory combined with the principle of uncertainty is "equivalent" in this respect to field theory.
Still, quantum theory has had many successes, that is, it has proved that nature behaves in a quantum way. Therefore, the obvious conclusion from this is that it is necessary to move to the framework of quantum field theory. This means that nature needs to be described using fields that behave quantumly, and not through point quantum particles.
The understanding that nature should be described by quantum field theories came from another place - when they tried to unite quantum theory with Einstein's special theory of relativity, they discovered that such a theory does not preserve causality. Causality means that if in a certain physical system event A occurred before event B, the same will happen in any other system moving relative to the first system. In any system, the time difference between event A and B will be different, but the causality will always be preserved, that is, event A will always precede event B.
Why should causality be preserved? Because if, for example, in a certain system Varda the hen laid an egg named Dobi, it is not possible that in another system the event of Dobi's laying will take place before Surda herself was previously laid by her mother. Quantum-relativistic theory does not preserve causality, and thus they had to move to the structure of quantum field theory in which relativity is built into (Manifest Relativistic Covariance) and it also preserves causality.
These are the reasons why all modern theories are quantum field theories.
epilogue
This article is not intended to argue against quantum theory, but to offer an interpretation of the meaning of the uncertainty principle and to explain, in retrospect, the reason for the transition to quantum field theories from this point of view, which holds that the world is physical and not mathematical, and for which it was possible to think from the beginning that particle-theory- Two points, like quantum theory, cannot describe reality correctly. But of course these lines are written retrospectively, and it is clear that without quantum theory it would not have been possible to move towards quantum field theory.
Just as it cannot be said about Newton's laws that they are "not true" (although in the world of electrons, for example, they are definitely not true), so it cannot be said about quantum theory. Each theory correctly describes nature in a certain area and as more researchers reach a deeper understanding of nature through more advanced theories, valid in wider areas.
53 תגובות
The smallest measure for a particle metric will always tend to 0. The smallest ideal measure that supposedly does not exist in reality is 0 (that is, a wave).
There is no doubt that the world of religion has recently achieved major successes in its successful and awe-inspiring war in science and secularism. Not only has it been proven that the theory of evolution is against a creator of the world who created everything in seven days, but recently it has been proven, beyond any doubt, that, among a crowd of religious believers, the phenomenon (not to say a "disease") of homosexuality has not spread, and is not spreading, and will not spread, mercifully .
fresh:
Well done.
Of course, your ability to decide on a subject that real scientists are dealing with without understanding their words and without understanding the words of a point is impressive.
By the way - I have to admit that I didn't read the words of a point until the end because the exaggerated interpretation of i made me jump right into a reaction. It is true that this is neither an ordinary wave nor an ordinary particle, but it has nothing to do with i and this follows immediately from the fact that when we talk about a particle in the macroscopic world then it is a particle and not a wave and when we talk about a wave in the macroscopic world then it is a wave and not a particle. This hybrid creature only exists in quantum theory, but, as mentioned, it has no macroscopic equivalent, and therefore the use of concepts from the macroscopic world is only an image in the first place.
As mentioned - this has nothing to do with i and it could be deduced directly from the two slits experiment (which was performed many times with different types of particles and has no flaw)
I think an interesting point has been made here.
It is possible that in the two-crack experiment there was a flaw that caused its non-intuitive result.
point:
What do I say and what will I speak?
Your words are simply not true but I have already said everything I have to say on the matter.
Michael there is a huge difference.
In quantum mechanics, the dynamics is carried out on i. And this is not for convenience, the equations cannot be rewritten into equations without the number i. I mean it's not for convenience.
In the normal waves we know, the dynamics are carried out on real values, and only for reasons of mathematical convenience the number i is sometimes used.
The number i is common in the world of mathematics, but in the physical world it is not possible to measure non-real numbers.
This is a very difficult problem, how is it that the physical laws are about imaginary and not real numbers. It seems like reality is simulated.
Just for the sake of accuracy - the wave that describes probability in quantum theory is not exactly the same wave that describes sound waves, but the *point* I wanted to make clear is that i enters here for one and only reason, which is that the wave formula described by it works...
point:
Here you are really wrong.
Calling i an imaginary number does not make it different from any other number.
Just as negative numbers were invented so that equations like X + 1 = 0 would have a solution, so i was invented so that the equation X squared equal to minus one would have a solution.
There is nothing imaginary about this number.
As the mathematical investigation expanded, they learned that waves can be described using imaginary exponents and indeed - even sound waves and waves in the guitar strings can be described in this way - even though they are very real and there is nothing probabilistic about them.
In quantum theory it turned out that the possible results of the experiments have a certain distribution that can be described as a wave and this is the only reason why i appears in the story.
It is still legitimate to ask what is the physical reality that causes this and we still do not have an answer to this question and maybe never will.
Not only that - if we discover the same physical reality it will not be illegitimate to ask what is the reason for the existence of this reality.
You are not dealing with the real problem. When there is something that is multiplied by the imaginary number i, it cannot be called either a wave or a particle, because these are real things. But its scalar magnitude is real and actually mathematically represents a probability wave of finding a particle (referring to a partial set of parameters describing a particle) at the moment of measurement.
fresh,
You were too quick to draw conclusions from the article, but nothing in quantum theory is simple...
Every particle is also a wave, including photons. The alternating use of the word particle or the word wave is done for reasons of convenience - after all, it is impossible to mention every time that every particle is also a wave.
In any case, the description of an electron that continuously emits and receives virtual photons as particles is of course equivalent to the description of an electron that continuously emits and receives photons which are themselves waves.
Therefore, the claim that a wave is made of particles is an attempt to describe a quantum phenomenon in classical terms (ie: there are waves and there are particles, and these are two different things), and it can never succeed
point:
The description you gave is close to reality but does not answer Raanan's question because it does not explain what the wave is made of.
In his response 42 you can see that this is not what he was looking for and you can understand his desire to see a wave as something physical and not a mathematical expression.
The number i is not a physical thing but a creation of the human brain, as are the complex numbers and the wave equations.
However, Ra'anan's response 42 also shows another thing and that is that he so wants to see waves as a collection of particles that nothing will convince him otherwise.
He ignores parts of the text he quotes - parts like
"The principle of summation over histories states that the particle will in fact pass through all possible trajectories simultaneously, so that in order to know what will happen to it in the end one must sum up (in a special way) all the possible histories of the particle, taking into account the probability of each history. We say that the history of the particle is a superposition of all its possible histories."
are not addressed because they show that the superposition - a word that appears in the quoted text already turns the particle into a...wave?
This wave is the mathematical function referred to by a point.
This wave is also the reason that in the experiment of the two slits the "particle" (which is a wave) struggles with itself.
fresh. I repeat. Shortcuts will not help here and your attempt to "sell" us theories that consist of quotes without context will not work.
To Noam 34
It turns out that a wave is indeed made of particles, the quote from the entry "Quantum Field Theory" in Wikipedia:
http://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A9%D7%93%D7%95%D7%AA_%D7%94%D7%A7%D7%95%D7%95%D7%A0%D7%98%D7%99%D7%AA
"Since every particle goes through a superposition of all the possible processes it can go through, it turns out that every electron continuously emits photons and swallows them back, after they "run" around it. Thus a kind of "halo" of photons is created around each electron; These photons are called virtual photons. When another electron passes through this "halo", it may swallow some of these photons, and thus an interaction is created between the two electrons - the photons that will pass between them will cause them to change their motion, which will be seen as the activation of an electromagnetic force between them. Therefore, this "halo" is actually an electromagnetic field, meaning an electric field and a magnetic field.
Before the development of quantum theory, classical physics dealt with fields like these as fundamental magnitudes that exist around electrons and other electrical charges. Quantum field theory explains what these fields are in terms of particles.
The opposite point of view is also legitimate: the field (like the electromagnetic field) can be treated as the basic quantity, and particles (like the photons) can be thought of as small, periodic changes in the field. We call such changes waves, as a sea wave is a small and cyclical change (approximately) in sea level. However, according to quantum mechanics, the waves in quantum theory behave differently from the waves we know in everyday life - they come in "packages", not continuously, and these packages are the particles.
All this is true for particles that are bosons (for example the photons). Several bosons of the same type can be found in the same place. A field corresponding to these particles is called a 'bosonic field', and as mentioned is a combination of many particles of the same type (the so-called coherent state)."
by anonymous user=dot
According to the Copenhagen interpretation, the wave means that it represents a probability that a certain measurement will cause a certain result. And this is basically the meaning of duality in quantum mechanics, there is a wave whose measurement will cause it to collapse into a particle.
This raises the important question, what exists in reality.
As I mentioned in another article, in quantum mechanics the wave consists of the imaginary number i. There is no direct access to this wave. Only to its absolute value in measurement (and then the product becomes real). So what exists in reality? It already depends on attitudes. And there is no one answer.
Don't know if the site is a suitable/correct way to learn, but it's definitely a fun way. If everything was known it wouldn't be fun.
fresh:
Very briefly: not all the questions you asked have clear answers.
One of the attempts to give answers is the string theory, but beyond the fact that this theory has not yet reached maturity and there is still no way to determine if it is correct, even after it is complete you can ask what the strings are made of.
In short, life is not simple. Correspondence with knowledge is not the right way even to learn everything that is known and certainly not suitable to learn what is unknown.
What is that quantum wave that according to certain interpretations can move faster than the speed of light? What is this wave made of? The definition in Wikipedia for a wave is: "A wave is the propagation of a disturbance in space" when emptiness is also considered space. What is that "disorder" and what does it come from? What is it made of?
A particle with a wavy nature is a particle that creates a "disturbance" in space?
Fresh (28):
Your words in this response are correct, but they are of no importance and I don't think that is what you meant at the beginning of the discussion.
When we have no possibility of knowing anything about the future or about parallel worlds, there is not much meaning to the claim of determinism that refers to everyone as a whole.
The fact is that you are on a given world line and even if your entire future is determined you have no way of knowing this and for any need the acts of splitting and drawing lots are completely reasonable.
In this sense the word lottery seems more useful to me because it represents what we experience. The claim that the world is deterministic can, in this situation, only mislead - this is not what the poet meant when he invented the word "determinism".
Regarding your question "what is a wave made of if not particles" you should know that in the quantum world there is no such clear separation. What you call "particles" (yes! even the electrons and protons) are also waves - it all depends on the nature of the experiment.
Therefore the claim that a wave is made of particles while the particles themselves are also waves is circular.
In short - quantum theory is the most complex and least intuitive theory in science and your attempt to approach it intuitively without studying the whole subject in depth is doomed to failure in advance.
fresh,
Of course I had to be precise and add that this is a wave in the quantum world.
In the quantum world, the ** single ** particle also has a wave character, and from this arises the uncertainty principle
Good question, and the answer: of course not particles!
a question? What is a wave made of? If not particles?
fresh,
The Uncertainty Principle stems directly from the wave nature of the particle.
It seems to me that you have decided to solve all the world's problems with the help of the "quantum nature of space-time", but in my humble opinion this is both incorrect and causes you to miss deeper meanings (as in the case of the Achilles and the tortoise paradox).
Raanan, you are confusing different concepts.
Where did you even get the concept of free choice? There is no connection.
And regarding quantum mechanics, you should read a few books before you think too much and develop misconceptions that will be difficult for you to get rid of.
The Uncertainty Principle is necessarily true because at one given moment (Planck time) all the particles are frozen in place and therefore they will not have momentum/momentum/velocity in a certain direction, because for a velocity to be defined and exist you need at least two Planck moments, and then you can see the path the particles took Between the two moments of time, only then does speed have meaning. Velocity has no existence when looking at one Planck time, therefore necessarily the uncertainty principle is true, and it was possible to hypothesize it even without an experiment. And so even if we would like to know only what is the speed of a particle in just one Planck time, it is impossible and all the more so since it is impossible to know both the speed and the position at a given moment. Of course, if we change the definition of the word moment to include two adjacent Planck moments, then it is possible to know both momentum and position (as in macroscopic objects) if we succeed in making the measurement (which is technically very difficult).
I did not understand why it is impossible to know the momentum + position of the particle at a given moment, the necessity means that there is free choice (or randomness understood in nature) and there is no determinism.
In my opinion, determinism can exist even if it is assumed that the principle of uncertainty is a true truth
Michael
You assume that time is constantly in the making and therefore you think it can split into all sorts of different scenarios. It is possible that this assumption is correct but not certain. According to Einstein's theory of special relativity there is no "simultaneity" and therefore some see this as the idea that the future, the past and the present exist exactly to the same extent, but for some unknown reason we cannot see them. If you imagine the time dimension in the form of a spatial surface with mountains and hills, it makes it easier to deal with the time dimension. You can imagine it in front of an existing space when there is fog and there is zero visibility or epsilon visibility that allows us to see only the present, even though the future and the past that we walked in and that we will walk in exist just like the present. Each parallel universe has a TIMELINE or such surfaces and it only travels on these surfaces in a deterministic way, we are in a deterministic parallel universe but cannot move to other parallel universes, where maybe our future develops differently. And so in my opinion the determinism of multiple worlds speaks of the determinism of both a given world line and the totality of universes.
fresh:
It is not wise to take anything out of context.
At the beginning of the chapter is written the definition of that CFD that in the sentence you quoted says what happens *if you neglect it*.
Counterfactual definiteness (CFD) is the ability to speak meaningfully about the definiteness of the results of measurements, even if they were not performed
By the way, the idea of multiple universes is a mechanism for cosmic evolution. Which solves the problem of the origin of the constants
"Abandoning CFD allows one to claim that violation of Bell's inequalities does not necessarily imply a violation of the locality principle"
http://en.wikipedia.org/wiki/Counterfactual_definiteness
Be that as it may, the determinism of the interpretation of the multiple worlds is not a determinism that speaks of a given world line but of the whole complex.
As soon as a given situation can split in several different ways it means that the behavior of such a world line is not deterministic.
point:
Ra'anan was not only talking about determinism.
He also talked about the existence of a location.
The multiple worlds interpretation does not solve this problem.
The difference between the probabilistic interpretation and the multiple worlds interpretation concerns what happens at the moment of collapse of the wave function and not what happened before it collapsed.
Michael, you have to be precise.
It is true that the popular interpretation of the Bell experiment dismisses what Raanan said.
But as far as I know there is another interpretation of multiple worlds, which still allows for a deterministic world
fresh:
What you say in section a is a theory that was proposed and disproved by Bell's theorem and Bell's experiment.
Of course, you are free to continue to hold this opinion, but you should know that it has been refuted.
What you say in section b is a baseless prophecy. You are of course welcome to create a basis for it by building such a theory (but one that does not contradict reality)
A. The fact that we do not know the position of a particle and its momentum at a given moment does not necessarily mean that it does not have a position and momentum at a given moment. Therefore the principle of uncertainty does not necessarily mean that there is understandable randomness in nature, in my opinion nature is completely deterministic as Einstein thought. The uncertainty is ours only and not nature's, and stems from our lack of technical ability and our understandable inability to know the position and momentum of the particle at a given moment.
b It is possible to build a physical theory that will be described by mathematics in which a point/quantum has a very small dimension but not zero, and thus the mathematics will faithfully represent the physical nature and at the same time will also be a point and discrete theory and not a continuous field theory.
This links to the paradox of Zeno and the tortoise.
Does all of the above imply that the connection between causality and our mass does not allow for time travel?
Yes, that's true.
If the difference between two events is time-like, that is, there cannot be a causal relationship between them (there cannot be an effect of one on the other), then there can be a reversal of the order of events between two different observers.
But if one observer sees a causal connection between the two events (that is, the difference is space-like), then every other observer will see the same.
And this is exactly the point of maintaining causality:
If causality exists - it exists for every observer, in every system.
If it does not exist - it does not exist in any system.
Laurie Cole,
In my opinion, it is possible, as I explained in my first response, on the condition that each of the viewers sees that the time difference between the events is such that one could not have an effect on the other because the distance between them is too great.
to Bella
It should be said "the laymen" and not as you claim "the laymen"
A typical mistake of laymen.
What is the relationship between system relativity and causality.
You will learn something in a thorough way Mr. Yedan.
Laymen conduct a scientific discourse (postmodernism at its best).
Uri Kol,
Did you just claim that Stav's mass is very large?
It is not nice.
for autumn,
In principle, yes, according to quantum theory not only can you be found anywhere in the room, but you can be found at any given moment anywhere in the universe.
Practically, the chance of this is zero for all intents and purposes.
This is because position uncertainties are very small relative to your size. For an electron, whose size is careful, the uncertainty is relatively large.
Alternatively, if we look at your wave function, we will find that your wavelength is very small, and this is because your mass is very large (wavelength is inversely proportional to mass). That's why you are most likely to find one specific point in space.
It is not possible for one observer to see event A before B, and another observer to see B before A.
Laurie Cole.
In your response to the words you actually confirmed them. I understand that was your intention. Right? I wrote my words because it was possible to understand something else from the article.
So actually, right now I can be found anywhere in the room?
A mathematician may say anything he pleases, but a physicist must be at least partially sane
In response to Michael
The relationship between the time difference and the distance should be such that causality is preserved, meaning that in any system event A will precede event B.
Conservation of causality is an axiom.
In response to Elon
When uncertainties in energy will aspire to infinity - uncertainties in time will aspire to zero, but it must be remembered that these are only limits, it is an aspiration to zero, and not an actual zero. Therefore, it is impossible to measure a physical size at a precise mathematical point in time.
This is exactly the point - in the world of physics there is no "infinity", but only an aspiration for infinity.
It is true that from the beginning the transition to field theory was related to causality, as I also wrote. Here I tried to describe another angle of observation, which in my opinion is a way of thinking and a touchstone in examining physical theories.
In the framework of private relativity, causality is not violated, except when a quanta is attempted.
Causality is not only the order of events but a connection between the time difference and the distance that allows one event to have an effect on another. When this relationship does not exist, it is possible to reverse the order between the events.
This is a conclusion that can be reached even without relying on the equations if you just remember that one of the well-known conclusions is the loss of "simultaneity" and understand that from considerations of symmetry, if two events A and B appear simultaneously to observer A and to observer B, it appears that A precedes B, then if we place an observer C. Under suitable conditions, he will actually see B occur before A
The claim is not true. It is possible to measure something in the exact time of a particle. The uncertainty in the energy will then be infinite. The transition to field theory is not a priori related to the physical or mathematical. It was in the first place related to the causal nature of nature, which caused a hole to occur only if they changed in the same place in space and time. in space That is, a wave in some field. Even Newton in his tremendous intuition realized that his theory of gravity is not final because it is not a field theory. What became necessary in Einstein's time because of the violation of the principle of causality (of direct effects at a distance - action at a distance) within the framework of special relativity and led to the first gravitational field theory - general relativity.
Mr. Point
My heart, my heart is with you one point.
Now you too feel what it is to be slandered.
I suggest that you show all the slanderers that you don't care about them, and change your name to "dotted"
::::::::::::::::
in a fraternity of friends
Sabdarmish Yehuda
What is this?
I disagree with all of the above.
Next time I will ask to consult with all concerned (me) before publishing such a slanderous article.
Thanks for the interesting article. I especially liked the explanation of causality and the need for it.
Challenging article.
I hope that those who need to understand what things are meant to understand have understood. I myself only got the (logical) impression that in a physical world it would not be correct to treat bodies as if their size were actually a point - as a point is defined in a mathematical world. Indeed, the statement makes sense and is called for in retrospect. It seems that just as Newton invented the differential calculus in order to explain his theory, so it is possible to develop one or another mathematical theories that can be applied to physics according to its needs. For example: since there are no bodies in nature whose size is a point, it is determined (currently arbitrarily) that the Planck distance is the shortest distance in nature between a point and a point and it cannot be divided into two and we contain this size as an indivisible group in our mathematics. Of course, the meaning is simply to try and explain phenomena that can be predicted according to quantum theory but are not consistent with observations.