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How is local causality possible?

  1. Apr 26, 2010 #1
    So much hay is made out of the fact that quantum theory—and its associated experiments—violates the principle of local causality, as canonically developed by the classical (Newtonian) and relativistic (Einsteinian) models. But no one ever really asks about what these models are 'truly' saying about physical reality. That is, in all of these theories, it is axiomatically assumed that material bodies, in the elemental sense, come in the forms of geometric points. But there is a major difference between the following two ideas:

    1) points as the solutions to linear, analytical equations
    2) points as 'really existing' physical objects

    In fact, it is my thesis that the desire to satisfy idea #1—at least within the community of mainstream academic physics—has always overshadowed the question that idea #2 is constantly begging. And this question is:

    "If the form of physical bodies, in the most elementary sense, is not that of the geometric point, then what is it?"

    But before we even demand from ourselves a [hypothetical] answer to this question, let us return to the original question: How is local causality possible?

    That is, we will assume the existence of two elementary bodies that come in the form of geometric points, and for the sake of simplicity, we will consider a one-dimensional space. Now, just like those 'cars approaching each other from opposite directions' questions, we will consider our particles, A and B, to be involved in the same kind of collision course.

    So A and B are now approaching each other with some arbitrary relative speed (it makes no difference what the individual velocities might be in a given frame of reference). So, A and B get closer and closer until something happens. My question is simply this:

    "What is the nature of this 'something' when we say that two physical bodies, in the form of points, have 'interacted'?"

    And I ask this because of this difficulty: the only way that we can say that two points are not different is when they are, in fact, the same point. So here are the choices that we have left:

    1) The two points are not interacting precisely because they are different—i.e. there is some amount of space between them.
    2) It is senseless to say that interaction exists precisely because there is only a single point in existence.

    Anybody have any comments about this difficulty?
     
  2. jcsd
  3. Apr 26, 2010 #2
    Probability density. There are fields in spacetime which have some value. From these fields you can derive position, mass and other properties of what we call particles. Value of the fields itself appears to us as the probability of finding a particle at specific point.

    I strongly believe that the spacetime itself is composed of points. In other words: it is Riemann manifold and position operators do exist and commute. However, we don't know what future theories would be. Maybe they will not have concept of spacetime points, i.e. the spacetime would be quantized or position operators would not commute.

    All classical theories have one common drawback: they assume that particle count is constant. No classical theory can explain how particles annihilate, pop up or change. So it is impossible to tell this using only concept of point.

    In quantum physics, however one field can continuously transform into some another.
    Suppose we have two fields: "a" and "b". In the beginning, field "a" has probability 1 and "b" is 0. Then, the probability of "a" starts to decrease and "b" goes up, so that the sum of probabilities remains 1.

    There is no one moment of "interaction". It's just high possibility of seeing substrates before "collision" and high chance of seeing products after. You can say that probability flows from one field to another.
     
  4. Apr 26, 2010 #3
    Okay, those are some good, textbook answers. However, I was asking about the form of physical bodies and not of spacetime. Your reply was:

    "I strongly believe that the spacetime itself is composed of points."

    Are you saying that 'physical bodies' and 'spacetime' are one and the same concept?
     
  5. Apr 26, 2010 #4
    define "physical".... you will see that this is ambiguous
     
  6. Apr 26, 2010 #5
    Good point, ansgar. The conclusion being that the discipline known as 'physics' is ambiguous. Should we attempt to set the record straight here and now?
     
  7. Apr 26, 2010 #6
    You brought it up, what do you mean by "physical"?
     
  8. Apr 26, 2010 #7
    I was not saying this here, but indeed, I do believe that spacetime and matter is the same thing.

    "Physical body" is an illusion that we mere humans see when we dare to look at quantum fields. Quantum fields are defined on (I believe) absolute space. Then math follows.
     
  9. Apr 26, 2010 #8
    I guess this definition off of the top of my head would suffice:

    "Of or related to the objects of experience"

    Satisfied?
     
  10. Apr 26, 2010 #9
    My main concern with theoretical physics is with 'scare quotey' language just like this. On the one hand, we want to use (i.e. be inspired by) certain images that are related to our every day experiences (e.g. watching an apple fall from a tree).

    But when pressed, the typical theoretical physicist will say that these are only analogies, and that the formalism is the thing that really counts. What I want is to come up with an idea of theoretical physics that no longer plays such games.

    Can anyone help me?
     
  11. Apr 26, 2010 #10
    my experience and all data suggest that there are point particles preserving local causality..

    What are you really after?

    are you a curious physics student? a professional physicists or physics layman?

    There are many people out there having hard to comprehend the concept of "points"
     
  12. Apr 26, 2010 #11
    I am helping you. You just yet have to accept it.

    By "interaction" and "collision" enclosed in dreaded quotes i meant classical interaction and collision. Classical electron and positon approach, then they classicaly collide, a tiny thunder smites and two photons pop out. This is the classical view of interaction.

    In reality, there is no such thing. Quantum interaction (not quoted) is about changing relative probabilites of fields. Also, quantum fields are not point particles, so there is no concept of collision.

    If you do not like this view of physical world, it's not my fault. You should however stick to some "realistic" interpretation of QM, which is necessarily non-local.

    Reality is about maths, not falling apples. You should not believe that there is a tiny falling apple inside each atom. There are lot of quantum fields, though.
     
  13. Apr 26, 2010 #12
    Or is it your experience rather that there are three-dimensional bodies that always seem to be where you expect them to be? I guess what I'm really trying to get at is the huge disconnect between this kind of everyday experience and the theoretical difficulty that I presented in the first post.

    Ah... 'reality.' That's a tough one!

    None of the above, but we can get to that in due time!
     
  14. Apr 26, 2010 #13

    DrChinese

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    Me too! I want to stop these games. Gimme something I can touch.

    And after the physicists, let's go after the philosophers!!

    :biggrin:
     
  15. Apr 26, 2010 #14
    well, one should be more modest.. Quantum Fields are "just" theory/model... but everything else in your post is fine.
     
  16. Apr 26, 2010 #15
    A model far more closer to reality than the concept of solid point-like particles everyone in this world has printed into his head before birth.
     
  17. Apr 26, 2010 #16
    welcome to the world of QM... and special relativity, which is not taking place at everyday life basis hence our brains have no intuitive sense for such phenomenon except for what we can deduce from our logical and analytical "brain-spot" (i.e. making up theories based on math and ways to test them)

    why should even human beings be able to understand reality as "it is" in the first place, what kind of premise is that?

    You seem to limit yourself quite a bit if you want to feel everything.. have you ever felt the moon by your hands? have you felt a single atom? have to touched a galaxy? once? maybe twice?

    Why should theoretical physics adapt to you? The reason for why choosing maths to formulate science is that it is unambiguous!
     
  18. Apr 26, 2010 #17
    well maybe, the more modest and humble answer would be that QFT fits to data over a larger range of energy scales than other models.
     
  19. Apr 26, 2010 #18
    I should probably stress that it is a difference in trying to DESCRIBE reality and KNOWING what reality is. The first task is physicists task, the other one touches upon methaphysics.. which is NOT the forum we are at this very moment..
     
  20. Apr 26, 2010 #19
    Yes, you are helping, and I am accepting your help. I'm just trying to understand, is all.

    My point in the OP is that there is no such thing as a theoretically complete notion of classical locally-caused interaction.

    If you can't provide a good definition of classical interaction, then I don't know what I'm supposed to make of the idea of quantum interaction. That is, the very concept of interaction (i.e. causality) is what is at issue.

    My point is that QM, in its purely formal understanding, has nothing to do with a "view of [the] physical world." That is, nothing is being viewed. It's pure mathematics, and we should stop speaking of it as if there is a connection to physical reality.

    What I'm trying to say is that 'reality is just reality' and 'mathematics is just mathematics.' In my view, the question that theoretical physics should come to grips with is the way in which these distinct concepts can possibly relate to one another.
     
  21. Apr 26, 2010 #20
    You can touch a Riemannian manifold.
     
  22. Apr 26, 2010 #21
    No, many theoretical physicsts would say that even the term 'description' is too strong. That is, according to the standard, Bohr/Bell notion of QM, the only thing involved is the prediction of the results of a given experimental arrangement over an infinite number of trials.
     
  23. Apr 26, 2010 #22
    Yeah, there is not.

    Locality and causality on a quantum level come from the fact that the probability current may not flow as it wants, but must obey some laws.
    Imagine quantum fields as some kind of gas or liquid. This liquid may not disappear, appear out of nowhere and it must satisfy local continuity. From this law come some observed facts, i.e. that nothing can travel faster than light, bodies can not suddenly disappear and apples fall from trees.

    Is this what you wanted to understand?

    No, mathematics is the reality. What we see with our eyes is not. If maths says something you think is wrong, then you are wrong, not maths.

    Quantum physics is connected to real world. Our senses are not, they are just tricks the evolution gave to chimps so they can eat more bananas. Maths is our only way to explore reality, even if it gives us answers an average chimp would not believe.
     
  24. Apr 26, 2010 #23
    Why would one need a "way to test a theory"? Isn't a theory supposed to be the proof of those empirical observations that are otherwise just going to remain random collections of "events"?

    Hmm... ask the first guys in ancient Greece why they started pondering in such ways, only to infect us all, two-plus millenia later with that damn virus that is known as "trying to understand reality"!

    Is there any difference between feeling the moon and being affected by its gravitational pull? Why must we always reduce things to the base sensation of touch?

    Do you know how many mathematicians would disagree with that statement? It is true, that to non-mathematicians, everything that mathematicians devise/prove is carved in stone. But let me assure you, there is a huge amount of interpretation that goes on in that field!
     
  25. Apr 26, 2010 #24
    How about we just put it like this:

    Mathematics deals with mathematical reality and physics deals with physical reality. I think that the project of theoretical physics is to find a way to marry these two forms of reality. To me, no one has been very successful in showing how these two realities are related. I think it is a very interesting question.
     
  26. Apr 26, 2010 #25
    Physical reality is a subset of mathematical reality.

    What you are calling (physical) reality here is just an illusion created by your senses. Quantum physics describe true physical reality. And why can you not relate physical reality with what you see? The answer is simple: your mind is fooling you. No further explanation needed.

    Now, forget that the world is what you see with your eyes. Wake up from Matrix. Maths is the only true world and it always was.
     
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