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What's between particles

  1. Jul 7, 2005 #1
    There are bundles and bundles of information about particles to be found on the web and on this forum as well (many thanks to marlon).
    However, when you want to think about what's connecting these particles, what's between particles, things get rather blurry..

    So, a couple of blurry questions:

    1) It's physically possible to break an apple in half, and thus break the bounds between the two halves. It's physically possible to break a crystal in half, and thus have a deformed crystal with broken bounds.
    Now, when I look deeper, I notice that less and less people are talking about bounds, and more and more people talk about interactions. So, at the level of electrons floating around an atom, or at the level of atoms being made up out of quarks, is it still possible to imagine a physical operation that 'breaks' the bounds? Or will it always be one of two things:

    - the broken bits are unstable stuff and decay immediately
    - the broken bits find each other instantly and recombine

    In other words, is there some way to shield off one bit from the other?

    2) Are such bounds physical things? I mean, can you give certain physical properties to what's between particles, and you can have different bounds with different properties thus making surrounding particles behave differently?
    You can describe particle physics by looking at the particles and describing their interactions according to certain rules - but is it also possible to make a dual description by looking at the bounds and describing the rules of the 'nodes' interconnecting them?
  2. jcsd
  3. Jul 7, 2005 #2

    I really think the essence of your post is about semantics here. At the atomic scale we indeed talk about interactions but they have the same physical 'use and signifcance' as the bounds between atoms that constitute a crystal. When you split a crystal in two parts you are breaking up the bonds or interactions between the atoms. The result will be a surface with its defects like trapped charges or dangling bonds. A bond in this case really is nothing else as an inter atomic interaction of some kind. There are different interactions ofcourse that yield Van der Waals bounds, covalent bounds, ionic bounds, etc but the clue is that the underlying interaction has something to do with electrons/polarizations... So a bound is a result of some interaction going on.

    For example the three constituent quarks inside a proton are 'bound' together by the strong force mediated by gluons. Now, ofcourse, this is different with respect to the previous example because quarks do not form something like a covalent bound by each sharing a gluon. So, although the interactions are very different in nature, the concept of a bound is always the same. It is a direct consequence of those interactions...

    Last edited: Jul 7, 2005
  4. Jul 7, 2005 #3
    Besides, keep in mind that you cannot just break up the 'bonding' between quarks because of asymptotic freedom. The strong force reduces its strength when the quarks have high kinetic energy...but indeed you cannot just chop then all up into little pieces, even if you had a very small knife. The reason for this is the different nature of the strong force, which does not work with actual covalent bounds...This is the case for a crystal (among other possible bounds ofcourse), so when a bound is made by sharing matter-particles, you can break them up mechanically. But gluons/photons/vectorbosons are NOT matter particles, they are force-mediators and ofcourse they are totally different in nature

  5. Jul 8, 2005 #4
    But also we don't know the behaviour of the strong force if we could muster up enough energy to separate two quarks (and avoid phenomena such as gluon flux tube breaking etc). Interesting theory to be done there.
  6. Jul 8, 2005 #5
    which bring the question what is energy!
  7. Jul 9, 2005 #6
    How are you gonna avoid the breaking up of the gluon flux tube ?

    Ps, keep in mind you are using a terminology here that does not completely describes the quark confinement bahaviour. But nevertheless, i ask you what theory is there to be done here ?

  8. Jul 9, 2005 #7
    Maybe he's talking about hadronization models?
  9. Aug 20, 2005 #8
    Yeah, asymptotic freedom really turns this question on its head. I think it's the weirdest part of all QM - weirder than randomnes, Pauli exlusion violations, and nonlocality... weirder than everything.

    But then here's this New Scientist article that says someone has exposed the "naked quark" and I can't access it because I don't have a subscription! Perhaps it changes the answer to this question?

  10. Aug 20, 2005 #9
    A question, has the gluons and quarks have an associated wave motion like electrons ?
  11. Aug 20, 2005 #10
    No, gluons and quarks are excitations of fields that obey certain equations with specific local symmetry properties.

    To be short, think of a mattress that you jump on, the excitation is just the vibration of the mattress because you jump on it. The transition from one vibrational mode to another corresponds to a change in energy. Via the Einstein relation for energy, we know that E and m are equivalent and hence, this energy-change corresponds to a 'mass' (ie the particle).

  12. Aug 20, 2005 #11
    To Marlon,

    Just so I understand, are you saying that QM predicts that the pions (a quark+antiquark pair) do not have a wavefunction that can be solved via Schrodinger equation ? It was my understanding that de Broglie showed that QM dissolved the matter/field distinction and showed that everything is made of one substance (what Herbert calls "quantumstuff"), which has the ability to combine wave and particle if one uses Schrodinger mathematical approach to QM. As explained by Herbert, after 1925 at least four different theories were put forward to explain the new QM view: (1) Heisenberg matrix mechanics, (2) Schrodinger wave mechanics, (3) Dirac's rotating arrow transformation theory, and finally (4) Feynman's sum over history theory. According to Herbert, all four of the above are correct interpretations of QM--that is, Feynman's approach can never falsify Heisenberg's approach, etc.

    Thus, my point is that if QM is a valid theory, then quarks must be able to be described via Schrodinger wave mechanics--or we must conclude that quarks do not follow rules of QM--as they say, we cannot have our cake and eat it too--at least this is my understanding and I welcome corrections on my thinking.
  13. Aug 20, 2005 #12
    Quarks are described by QCD (quantum chromo dynamics) which is a quantum field theory. So yes, QM is valid when it comes to quarks but you need to be aware of the fact that QFT is different in nature when compared to QM. The big 'difference' is that the QM wavefunction has creation and annihilation operators in QFT. So a wavefunction really is a field in QFT in which particles are created and annihilated by distrubing this field (ie making the mattress vibrate). But ofcourse the QM principles are totally incorporated in QFT. The Schrodinger equation really is an equation that expresses conservation of total energy and this law is also respected in QCD, as it should be. The same goes for momentum conservation.

    Ofcourse quarks cannot be described by the ordinary schrodinger equation because quarks have certain symmetries (ie the local SU(3)-symmetry) that needs to be incorporated in the physical theory that describes quarks. This local SU(3) symmetry has 8 generators, which correspond to the gluons that mediate the quark interactions (ie the strong force).

  14. Aug 20, 2005 #13
    Marlon, thank you for this lesson--I see the Schrodinger equation used so much in modern papers on nuclear physics I just assumed it applied to the level of quarks--but apparently not. But one more question just so I am clear, if Schrodinger equation cannot be used to describe quarks, then neither can: (1) Heisenberg matrix mechanics, (3) Dirac's rotating arrow transformation theory, and (3) Feynman's sum over history theory. Would this be a correct interpretation of "quantum field theory" in 2005.
  15. Aug 20, 2005 #14
    it is not because the SE does not describe quarks that the formalism of QM cannot be adopted in QFT, as a matter of fact IT IS and hence YOU CAN use the techniques you mentioned. For example, the path integral formalism is widely used in all QFT theories.

    Your mistake is the argumentation that if quarks are not described by SE, than QM does not apply in QFT. THAT IS INCORRECT as i have outlined before. Generally, one starts from a Largangian which exhibits the imposed gauge symmetry and than you can apply the variational principle to derive the physics, or you can chose the path integral formalism or you can chose the canonical second quantization formalism...

  16. Aug 20, 2005 #15
    As an addendum : i suggest you compare how the Schrodinger equation and the QCD Lagrangian are 'built' and applied to describe the physics at hand...It is important to realize that the QM Schrodinger eq. is NOT a field equation...the 'field equation-variant' of the SE is the Dirac equation, which describes the dynamics of fermions in field theory (ie fermions that arise as fluctuations of antisymmetric fields)...

    Last edited: Aug 20, 2005
  17. Aug 20, 2005 #16
    OK, please correct me if I error, but I think what you are saying is that QM is in fact adopted in QFT--but just not the form of QM described by the Schrodinger equation (which would allow the quark itself to have a wavefunction). But now I have another confusion, because on p. 42 of Nick Herbert's book "Quantum Reality" I read :...Dirac was able to show that both the Heisenberg's and Schrodinger's theories were special cases of his own rotating-arrow version of quantum theory. Dirac's arrow looks like a cluster of matrices or a wave, depending on what coordinate system you select...

    So, if as you stated a few posts back to a question from "dimitrimikhalinos" that quarks do NOT have an associated wave motion like electrons, then I do not see how this meshes with finding of Dirac that quark would be predicted to show wave function if that was the coordinate system you selected to observe the quark ? :confused:
  18. Aug 20, 2005 #17
    Ok, again, the Dirac equation is NOt the same as the SE. It is the relativistic generalization of the SE and it applies to spin 1/2 particles. In relativistic QM, this equation indeed works with wavefunctions but in QFT, the wavefunctions are replaced by fields. However, in QFT, you first start from a Lagrangian and than by applying the Euler Lagrange equations of motion and variation with respect to the fields, you will acquire the actual Dirac equation.

    Now, if you wanna describe quarks you will also start from a certain Lagrangian and come to the actual equation of motion by varying the fields (these are the variables). Again, the resulting equation of this variation will yields an analoguous Dirac equation BUT for quarks.

    My point is that the quark-Lagrangian you start from is different than the Lagrangian you start from if you wanna calculate the actual Dirac equation. It is different because of symmetry, as i outlined in previous posts (ie the local SU(3)-symmetry)...

    You missed my point. In QFT electrons are also described in terms of fields, just like every other particle. In QM you use wavefunctions to describe electrons via the SE, that is true but this will not work in the quark-case because they 'behave' totally different from electrons in an atom for example. this different behaviour is incorporated in the symmetry of the equations. Again, you need fields to describe quarks, otherwise it will not work.

    Something else, you cannot observe a single quark because of asymptotic freedom, which states that the strong force (ie the interaction between quarks) gets stronger when energy lowers. So to see a single quark (ie not interacting with other quarks) you will need to make sure it has a tremendous amount of energy.

  19. Aug 21, 2005 #18
    Marlon, I did not understand why Dirac equation could not be used to describe quark structure, so I ran the question by Dr. Chris Oakley, who works in field theory. Here is what he had to say (in italics) :

    Quarks *are* described by the Dirac equation, so I don't quite understand this:

    "My point is that the quark-Lagrangian you start from is different than the Lagrangian you start from if you wanna calculate the actual Dirac equation. It is different because of symmetry, as I outlined in previous posts (ie the local SU(3)-symmetry)..."

    The Lagrangian is the sum of Dirac terms, one for each colour and flavour of quark, plus terms for the interactions. An approximate SU(3) symmetry results from the approximate invariance upon mixing up quarks of different flavours, and an exact SU(3) symmetry is a consequence of invariance when quarks of the same flavour but different colour are mixed up amongst themselves. The extension of the latter to local symmetry leads to non-Abelian gauge theories, of which QCD is an example.

    So, I seem to be back to my initial problem--since quarks can be described by the Dirac equation directly (at least as stated above by Dr. Oakley), and Dirac showed that his equation and the relativistic Schrodinger equation are one and the same, then I do not see why you need "field theory" to describe the motion dynamic equations (e.g., Lagrangian) for a quark--it seems that all you need is the Lagrangian that is the sum of the Dirac terms for the quark, then transpose into the wavefunction equation of Schrodinger. Thus, the initial question posted awhile back:

    Originally Posted by dimitrimikhalinos
    ...do the gluons and quarks have an associated wave motion like electrons ?

    should be yes, at least for quarks ? :confused: :confused:
  20. Aug 22, 2005 #19
    I am very sorry but have you not read my previous posts ?

    I told you that quarks are described by a 'Dirac like' equation but the differemce was the extra terms you need to add the the Dirac Lagrangian in order to describe quarks, which obey the symmetry of the strong force. That is also what Oakley is saying.

    Theclue is in the Lagrangian being different for quarks, as it is different for he weak force, the EM-intercation,...

    In all these cases, fields are used to describe the particles because of the QFT formalism...ie the quantum mattress story...

    again, you cannot describe quarks in terms of an ordinary wavefunction and a Schrodinger equation because gauge symmetry needs to b respected and mathematically you need fields to do so...

    ps have you read the 'why do we need fields in physics'-entry of my journal ? I have explained the need of fields there.

    check out https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=7 [Broken]
    Last edited by a moderator: May 2, 2017
  21. Aug 31, 2005 #20


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    The particles of free field theory have Schrodiger's wave FUNCTIONAL, a functional of the field functions (wave functions in the 1st quantization), which are now (in the 2nd quantization) operators and can be taken as basis for FOCK space. Those wave functional do satisfy Schrodinger functional equation, basicaly QM WITH DERIVATIVES WITH RESPECT TO X-COORDINATES CHANGED TO DERIVATIVES WITH RESPECT TO FIELD FUNCTIONS. You can do the same in interacting field theories if you work in the so-called Schodinger representation (FOCK space's basis are time independent). Here you go, you got your quarks wave function.
  22. Sep 1, 2005 #21
    No they are not wavefunctions, they are field operators. This is the whole point of this thread.

  23. Sep 1, 2005 #22


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    The field operators, or operator-valued distributions to be precise, need a wave function to act on, "they don't just play with the kids in the back garden".
    Have you heard about [in> & [out> states? Do you know any thing about the FOCK SPACE in quantum field theory? elements of this space are wave functions for the quantum fields.These subjects are well presented in the book;
    "Quantum field theory of point particles & strings" (chapter11) 1992, Addison Wesley, frontiers in physics. have a look at it if you have good mathematical background.
  24. Sep 2, 2005 #23
    field operators act upon fields, not wavefunctions. You are missing the difference between QFT and QM (and i am not talking about special relativity here :wink: )

    Yes i have, how do you think these are described ?

    fields arise from wavefunctions. i never said this was not he case. as a matter of fact, i have mentioned this several times when trying to outline the difference between them.

    In QFT, particles are described by field-excitations, which does not occur in QM. This Fock example (in QFT) is no exception to this.

    Besides, would you describe quarks in terms of Fock space ? I do not think you would be using gluons in that case...

  25. Sep 2, 2005 #24


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    This is for marlon; I am sorry sir, I think you need to do alot of reading & studding. Try BRAIAN HATFIELD's BOOK (THE ONE I MENTIONED BEFORE) it is avery good book.
    or the all time classic on QFT; introduction to the theory of quantized fields, by
  26. Sep 3, 2005 #25
    I will do the reading, but what is "studding"

    i know this book very well and whatever you say about wavefunctions versus fields is not in there.

    This is a bit ironic, since i have been explaining this stuff many times here. Then, up comes a new dude with totally different (read : wrong) ideas on this...But anyway, i suggest you read entry nr 40 on https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=7 [Broken] in the link.


    ps or read QFT in a Nutshell by Zee, or read Peskin, Weinberg,...
    Last edited by a moderator: May 2, 2017
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