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Point Particles vs. String Theory

  1. Jun 27, 2009 #1


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    Up to now I have learned that matter particles (aka Leptons) were point particles with no physical size/extension. As a matter of fact, it appears that most (including many here based on responses to one of my earlier threads: https://www.physicsforums.com/showthread.php?t=301495") apparently cling to this concept.

    I have been recently reading about String Theory ("The Elegant Universe" - Brian Greene). Am I missing something, or are these two concepts (Point Particles and String Theory) in conflict with each other? String theory seems to indicate that strings are 1-dimensional objects with actual size, although I find it hard to understand how anything 1-dimensional can exist in a world with (at least) three spacial dimensions.

    It appears that String Theory looks pretty strong. If these two concepts are mutually exclusive, which is thought to be most correct??

    P.S. I would appreciate your responses not be too technical. I am not a college student, but just a housewife that likes to read. Thanks!

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  3. Jun 27, 2009 #2
    In the standard model of particle physics that is absolutely correct.

    This concept is a central part of the most well tested physical theories we have i.e. quantum physics + special relativity.

    In special relativity there can be no such thing as a perfectly rigid object, which rules out the idea that leptons are small rigid spheres.

    The presumption of point particles is equivalent to saying that the leptons don't have any internal structure, that they have no ways of storing energy internal (i.e. vibrating).

    The reason that our current point particle theories can be replaced by string theories is that the strings are so small, that at the distance scales we have probed so far we would expect these tiny strings to look just like point particles. To investigate shorter distances, we need a larger amount of energy.

    We know that our current theories are incomplete at extremely large energies; way beyond those currently accessible to experiment. The theories breakdown in the limit as energy goes to infinity, we need to use tricks to recover answers from these incomplete theories.

    String theory solves all the divergences that occur at very high energy, and in this sense it completes our detailed picture of physics at extremely high energies but still reduces to our familiar theories at the low energies we are familiar with.

    A simple way to think of it is that a point particle is too singular, so if you probe smaller and smaller distances by using greater and greater energies, then you get infinite results. If instead we move to higher energies and start to see that what looked like a point-particle was actually a vibrating 1-d string, then the physics of the string fills in the missing details that confused us.

    When you pluck a guitar string, the wave on the string moves with a certain speed. Imagine tuning the guitar string to a higher tension, then the waves on the string will move faster (and produce a higher pitch). Now imagine that you tuned the tension so high that the waves on the string began to move near or even at the speed of light. Then you would have a relativistic string.

    Therefore a key property of relativistic strings is that they are theoretically unbreakable, capable of withstanding enormous amounts of tension. One application of string theory would be to cosmic strings, if they exist. These are strings are enormous strings which have been stretched for billions of years by the expansion of the universe, so they are very nearly 1-dimensional and have nearly infinite tension, and so many calculations from string theory would apply to these.
  4. Jun 27, 2009 #3
    The notion of a point-like particle is illusory. It is easy to understand. Let me remind you that in Classical Mechanics one studies motion of point-like bodies which are not point-like - they have internal degrees of freedom. So any macroscopic body has its center of inertia coordinates (or center of gravity, whatever) and internal degrees of freedom. If such a compound system is affected by a long-range external force, like gravitational force, then one studies how the center of inertia (which stands for the whole body) moves in this field. In this case the three coordinates of CI are sufficient to get answers. But if you push such a compound system by another body (a collision), some part of the projectile energy and momentum is transferred to the CI and the other part increases internal motion of our "target". If the internal energy increases, such collisions are called inelastic.

    Now, when one tries to describe charged particles of the smallest charge (electrons, for example), one adds another hypothesis that the smallest charge is elementary and point-like. This hypothesis leads to huge difficulties. In particular, the charge interaction with the electromagnetic field is not well "guessed". In order to preserve the energy-momentum conservation law for such interactions, one introduces a "self-action" into equations. The self-action term leads to non-physical solutions and is eliminated later on by the so called mass and charge renormalizations. Sometimes it works, but such elimination does not work in many many cases. So they invented strings to avoid these difficulties. String theory exists since long ago but it does not work either.

    On the other hand we know that pushing an electron leads to radiation of electromagnetic waves (photons). This means that the electron and the electromagnetic field form a compound system, just like any macroscopic body. I called such a compound system an electronium. It contains the charge and the electromagnetic field oscillators. The latter describe the internal degrees of freedom in the system. Then there is no problem with the energy-momentum conservation and there is no self-action. The theory becomes a theory of potential interaction of compound (quantum mechanical) systems without difficulties.

    The charge in a compound system is always quantum mechanically smeared, just like negative charge in an atom (cloud of probability). Each elementary scattering off such a system changes the initial internal motion (excites internal degrees of freedom = photon oscillators) and excites them differently from one collision to another. But if one sums up all inelastic cross sections, one obtains an average (inclusive) picture which coincides with the Rutherford's cross section as if the target charge were point-like. In "poor" experiments one cannot distinguish different inelastic cross sections, one observes the inclusive cross section. This is the way how the notion of point-like charge "finds" the experimental support. As soon as one distinguishes differently broken compound target events, one never obtains a point-like picture. So the classical picture of point-like electron is a kind of cinematographic illusion where many different "frames" are added together.

    Last edited: Jun 27, 2009
  5. Jun 27, 2009 #4


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    I had never heard this before. :redface:

    1. Can you briefly explain why this is?

    2. Am I wrong to say that 1-D strings are rigid objects? And if so, why does this not violate your statement above?
  6. Jun 27, 2009 #5


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    Bob - Hello!

    I think I agree with you in the sense that I thought I had read that "point-like" meant that something was only a mathematical construct and had absolutely no spacial dimensional structure of any kind. I realize a "point-like" item can have characteristics like charge, spin, mass, energy,..., but these too are not real physical concepts either. Right? :confused:
  7. Jun 27, 2009 #6
    In Classical Mechanics the point-like body characteristics, like mass, energy, momentum, angular momentum - all belong to the center of inertia of the body. They are real physical concepts, no problem with it.

    In Quantum mechanics it is the same - any compound system has its center of inertia variables and internal degree variables. For simplicity consider first two point-like bodies connected with a spring. The system can move as a whole and at the same time the two body can oscillate due to spring (internal or relative motion). Each degree of freedom is independent: we write two separate equations for CI and relative (internal) motion. Each degree of freedom can take and give away energy-momentum, etc. So they are physical. Another thing is averaging over internal motion. Then nothing rests of internal motion. We write only one equation for the CI coordinates. But we should keep in mind that in the averaged picture we cannot predict positions of these two bound point-like bodies, OK?
    It is so even in Classical Mechanics.

    In Quantum Mechanics the positions of two "point-like" bodies is uncertain even without averaging - we have waves of probability instead of coordinates. So the negative charge in an atom is smeared quantum mechanically. The positive charge (from atomic nucleus) is also smeared but "localised" in smaller space. Both positive and negative charge clouds are described with atomic form-factors (see "Atom as a "dressed" nucleus" by Vladimir Kalitvianski at arXiv, for example).

    Pushing electron or nucleus in atom breaks their initial relative motion state - the atom gets excited. But both CI and relative motion have physical meaning as "subsystems" of a compound system.

    The same is valid for the "electronium". Pushing a charge excites internal degrees of freedom = photon oscillator excitations = photon creation.

    As I said, any degree of freedom (CI and relative ones) can receive and give away some energy, momentum, and angular momentum. The physical equations are just a bookkeeping of such exchanges. They are physical.

    Last edited: Jun 27, 2009
  8. Jun 27, 2009 #7
    Imagine a perfectly rigid ball sitting in front of you in three dimensions. Now using your left hand, push the left side of the ball, so that the ball begins to move rightward. Now freeze time at the instant that your left hand first makes contact with the ball. An instant later the entire ball will be moving, since it is not allowed to compress at the point you touched it. Therefore the right side of the ball instantaneously knows that the left side of the ball has been pushed, which violates relativity.

    If you pluck a relativistic string then the waves will spread outward from the point you plucked at the speed of light. In this sense a 1-d string is as flexible as could be.

    Now you might say, why not treat leptons as 3-d flexible blobs, instead of rigid ones? The real reason leptons are treated as 0-dimensional points is that 1-d strings, 2-d blobs (jargon = 2-branes), etc all have the property that they cannot exist in 3 space + 1 time dimension if we force them to be consistent with special relativity and quantum mechanics. Furthermore, objects which are higher dimensional than strings run into new problems that can only be solved by having 1-d strings around.

    This is not really true. If it were, then the interaction term between the two electrons in a helium atom would not be simply the Coloumb potential between point charges.

    [tex]V = \frac{q_1 q_2}{|\mathbf{r}_1 - \mathbf{r}_2|}[/tex]

    It can be confusing at first to combine quantum mechanics with intuition. The spread out nature of an electron wave function cannot be thought of as the electron itself being spread out. I will repeat that the standard model of particle physics absolutely treats leptons as point-particles, 0-dimensional objects with no spread or extent.
  9. Jun 27, 2009 #8


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    Special relativity says that no information can travel faster than the speed of light. If you had anything perfectly rigid, then information CAN travel faster than the speed of light which violates special relativity. For example, if you had a perfectly rigid rod - a light year long (just imagine) - then by pushing on one side of that rod, you can tell someone on the other side INSTANTLY that you are pushing on the rod. Everything in nature is deformable, so if you actually had a rod a light year long in the real world, it would take more than a year for the other side of the rod to move.
  10. Jun 27, 2009 #9
    Why appeal to the electron-electron potential in Helium? Take the electron-proton potential in Hydrogen. It is also the Coulomb one but it acts between de Broglie waves, not point-like particles: the equation is a wave equation, not Newton one. For an external observer both bound charges "look" smeared quantum mechanically. These two charged clouds are described with two atomic form-factors (see my publication with detailed pictures).

    The same is valid for the other "elementary" particles. For example, the electron is in permanent interaction with the quantized EMF, so they form a compound system. Neglecting this fact leads to divergences in calculations (see "Reformulation instead of Renormalizations" by Vladimir Kalitvianski).

    Yes, I agree, usually they teach that the elementary particles are point-like. But this notion has flaws I have just mentioned. It is better to recognize their permanently being bound and then the theory becomes much more physical.

  11. Jun 27, 2009 #10
    OK. I'm glad you made it clear that mainstream physics treats leptons as point-particles, and that what you are discussing is a personal theory that you argue improves on the standard model. I agree with you that there are problems with using point particles, but like most mainstream physicists I think that these problems are resolved by string theory.

    The electron-proton potential in the well-known exactly solvable Hamiltonian for the hydrogen atom is in fact the ordinary coulomb potential between two point charges.
  12. Jun 27, 2009 #11
    Any theory is somewhat personal. And mine is much simpler that the string theory - it does nor involve anything else but electrons and photons.
    Why then we use a wave equation if the charges are point-like?

    If you read my "Atom as a "dressed" nucleus" (I hope you are sufficiently literal to understand what a form-factor is), you will agree with me. (My work was published in the Central European Journal of Physics.)

  13. Jun 27, 2009 #12


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    Makes sense. I never thought of that. Of all the books I've read recently about Special Relativity and QM, this concept was never mentioned.

    Since a string is a 1-D object, could we not theoretically break a string into two 1-D pieces, and then even more smaller 1-D pieces? Everything that has spacial extent has to be made of something smaller. And if this "something" is "solid", then it would violate special relativity, no? Otherwise, a string would ultimately be a mathematical construct as well.

  14. Jun 27, 2009 #13
    The fundamental strings in string theory are indivisible, this comes with being a relativistic string.

    No, this is not necessarily true, although it may be argued that this concept is wired into our brains, there is nothing inherently contradictory about having a spatially extended object that is not made of smaller pieces.

    Just because something is made of one piece, it can still flex and vibrate in such a way as to obey special relativity. The allowed motions, however, are highly constrained and complicated and this is why string theory makes such specific predictions e.g. about the number of dimensions in spacetime.

    I'm not sure I understand. If strings were not consistent with special relativity, we would throw the entire theory in the trash can immediately (seriously, it's been known to happen to other approaches). One of the key inputs in developing string theory is the consistency with special relativity.

    Also, my attitude as a scientist and philosopher is that all of our physical theories are just mathematical models. To know the true nature of things is not allowed for us, but sometimes a certain fictive hypothesis will suffice to explain many phenomena i.e. strings, point-particles, whatever, I judge them all by how well they function as mathematical models.

    But surely there is a difference between the theories which are established over the course of thousands of peer-reviewed publications, and the theories which have been cited only a handful of times.

    Simplicity is good, but we can only simplify our theories up to the extent that they remain true. I have my own opinions about why simple solutions are unlikely to answer our outstanding questions, just as it is unlikely that elementary mathematics will be apart of the solution of the Reimann hypothesis. But this forum is a place to discuss mainstream physics, and my opinions are only relevant in this forum if they conform to established physics.

    It's called canonical quantization. Starting from the classical Hamiltonian we promote observables such as position and momentum to be operators. If you follow this simple procedure, you will see that the QM treatment of the hydrogen atom is given in terms of the coulomb interaction between point charges, this is what you get by following the rules of quantum mechanics.

    You have discussed brought up wave equations many times, but I think you might be confusing the wave function of an electron with the electron itself. The wave function of an electron is typically spread out in space, but the electron is a point particle.

    First, note the irony in you questioning my literacy by asking whether I was "sufficiently literal", when you meant to ask if I was sufficiently literate. This means nothing, however, and I sincerely applaud you if, as I suspect, you have learned english as a second language.

    Secondly, you'll be pleased to know that I have spent about ~1 hour reading your paper after you recommended it in another thread. To be honest, I did not find the paper sufficiently well-motivated, it seemed like an original approach towards the pre-Wilson problems with renormalization, but I did not find it compelling enough to think that it will replace the conventional approach.
  15. Jun 27, 2009 #14


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    Thanks, Civilized.

    But to me the term "point particles" means having NO spacial extent. Non-dimensional. So if something is 1-D, I don't see how it can be like a point particle. Unless by the term "look just like" you mean that for all practical purposes something of the size of the Plank Length or smaller might as well have no size because we cannot "see" things that small.

    But to me there is a difference. One has size - a string (however small), and one does not - a point particle. And string theory says (I think) that everything has a size, although very, very, very small (Plank Length).

    And is it not also true that string theory does away with what is called Quantum Foam, also a feature of the standard model? And this is because nothing can be smaller than the Plank Length, where Quantum Foam exists, and a "point particle" would definitely be smaller.
  16. Jun 27, 2009 #15
    You are thinking about the problem like a philosopher, but it is important to understand the complex relationship that these models, the standard model and string theory, have with reality.

    Any physicist must appreciate that the standard model is a is a very good model, from both a theoretical and an experimental point of view, it is a remarkable achievement. The standard model is at its essence a quantum field theory where excitations of the fields come in discrete lumps i.e. quanta or particles. The standard model agrees with all experimentally observed high-energy physics within an accuracy of a few percent, and in some experiments it agrees to 9 or 10 decimal places, which is like measuring the width of a hair on someone's head who is in San Fransico while you are in New York. These are the most precise measurements of anything that have ever been done, and they come from some very beautiful mathematics.

    In high energy physics the idea of an "effective field theory" is very precisely understood. In everyday terms, imagine that you wanted to describe the movements of a pendulum e.g. in a grandfather clock. Intuitively the motion of the micro-organisms on the bob of the pendulum etc would not be relevant for the physics of the pendulum.

    The gap between where the standard model has been tested and where it breaks down to be overtaken by string theory is more than a trillion times larger than the gap between micro-organism and macroscopic pendula. Therefore the standard model covers a lot of ground, and since the essence of this theory is based on truly 0-dimensional point particles with "NO size" this is a notion worth teaching.

    But as nice as the standard model is, it has major problems that make it theoretically incomplete beyond e.g. the planck length. String theory steps in to solve these problems and complete the model in the ultra small length scale / ultra high energy regime.

    Above I have been the stressing practicing physicist's shift in philosophical viewpoint, that the models do not describe ultimate reality, even though they do represent a deeper understanding then mere observation. Therefore it's not just a matter of practicality, but rather crafting better theories.
  17. Jun 28, 2009 #16
    Concerning the positive charge atomic form-factor, I published this work first in the USSR in 1993 and only recently in the West. It is a strict quantum mechanical result. It means any bound charge is smeared quantum mechanically. It can be tested and has already been tested experimentally. So there is no point-like particles, especially charged.
    In the standard QED there is nothing but electrons and photons. In my novel QED it is the same. The difference is in directly obtaining finite perturbative series due to starting from better initial approximation (electronium) rather than from "point-like" (non interacting) electron.
    Point-like particle notion failed in atomic physics. Canonical quantization of dynamical variables or writing a wave equation means change of this notion.
    Saying "the electron is a point particle" means the corresponding experimental support and a good working "point-like" theory. In reality the experiment and the theory support quantum mechanical smearing, not point-likeness.
    It is because the "mainstream" people speak more loudly (showing off) to get funding. It is they who have funding and who attract young researchers. However, they have not achieved a good description yet. On the other hand, I have some successful experience in reformulating problems and bypassing divergences. My works have been published in the USSR and recently I made some of them available at arXiv. They contain strict results, not just fantasy or irrelevant speculations.

    One hour of reading is not sufficient to get a gist, especially if you have a prejudice about point-likeness of leptons.

    Vladimir Kalitvianski.
    Last edited: Jun 28, 2009
  18. Jun 28, 2009 #17


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    Hey, Bob. :smile:

    Been reading some of your writings. Your paper was WAY over my head, as was most of your first post above. But that is not your fault.

    When you say "a point-like particle is illusory", I assume you are saying point-like is just a mathematical way of describing a quantum particle, and all of the characteristics of the particle. To me, point-like means "has no dimensional structure". So by illusory, do you mean (according to the standard model):

    1. Particle does exist - the particle DOES in fact have a physical dimensional structure and point like is only a mathematical way of representing the particle in equations
    2. Particle does NOT exist - the particle not only has NO physical dimensions, point like is only a mathematical way of explaining what we have experimentally observed happening with the particle

    I think with this statement you threw me off-track. I guess I find it hard to imagine the most basic form of physical structure being anything less than perfectly rigid. It just seems to me that if something were NOT perfectly rigid that something could be cut in half to make two of that something where each part is roughly half of the size of the original object. What theoretically keeps a string from being broken into two parts?
  19. Jun 28, 2009 #18
    Particles exist, of course. But one particle is always bound to, say, another particle. Let me explain in simple terms. When we look at the full Moon, we see a disk. Its center can be associated with the Moon itself, so we have three coordinates R to describe it. We obtain this R as an average position over the disk. In fact, the Moon consists of many particles. A couple of bound particles can oscillate. In quantum mechanics theses oscillations are quantized. A quantum oscillator can get excited (absorb energy of a photon) and get deactivated (give away its energy thus emitting a photon). So a bound couple can be observed with help of photons due to exchange with its internal degrees of freedom. This is how we observe the macroscopic bodies - with help of light = exchange of photons with the body.

    If we observe only one separate photon at once, for example with a photo plate (a slide), we will obtain a series of "frames" with different pictures, one point on a "frame" (low light intensity regime). Each such a picture does not resemble the Moon, but if we superimpose all the images, like in a movie, i.e., if we add them up, we will obtain the usual Moon image. This adding images up is called the inclusive picture.

    The same is valid for electron and other leptons. They are bound to the electromagnetic field, so they are "smeared" due to mutual oscillations. When we try to observe them with help of scattering of some energetic projectiles, we inevitably push the charge and change its, say, "position" with respect to the quantized electromagnetic field. The field gets excited - it takes some energy. Each particular scattering event looks like a point on a slide: they are different from one case to another. When we take a sum of different "pictures", we obtain the inclusive picture which looks as if we scattered our projectiles off a point-like particle situated at the center of inertia of the electron. In this sense it is illusory - the inclusive picture is a sum of different inelastic pictures, each signifies that the electron is not point-like and free but is a part of a compound system.

    If it is still vague, never mind. I wanted to say that the electron is real, it exists and it is in permanent coupling with its partner - the electromagnetic field. So it is "smeared" due to being always bound. It is not possible to liberate it from the electromagnetic field. In fact, creating the electromagnetic field is the main feature of any charge. The photons are emitted and absorbed in any process of observation, just like they help us to see the Moon. And averaging (=inclusive picture) helps us introduce only three coordinates for the average (simplified) description.

    Bob_for short.
  20. Jun 28, 2009 #19


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    Bob, Maybe I misunderstood the basic theories to begin with, and therefore the question I asked at the outset of this thread is invalid. I thought there were two predominant theories regarding QM. What I am asking here is about the those two theories - The Standard Model, and String Theory.

    Based on the Standard Model, it was my understanding that if one were small enough (to take a ridiculous example), and were to take a hammer the size of the Plank Length, and swing it at an electron (or where the electron should be), there would be nothing there to hit. The electron has no size at all, and therefore cannot be "hit". It is composed of nothing physical. This is what is called a point particle - no physical size. Is this wrong or right?

    Based on String Theory, the electron is composed of string(s), and if someone were to take a swing at an electron with that same miniscule hammer, that person would hit a String, which DOES have physical size (the Planck length) - it is NOT a point particle. It physically exists and is 1-diminsional. Is this right or wrong?

    Am I misunderstanding concepts of these two theories, or am I asking this question in a wrong way? Thanks for your patience. :redface:

  21. Jun 28, 2009 #20
    This is one of "problems" with the point-like particles: they have zero size and cannot collide, they should always miss each other. In order to avoid such a non-physical behaviour, in theory the particles are "furnished" with long-range or finite-range potentials. For example, the electron is supplied with infinitely "long hands" (Coulomb potential) to be able to interact at any distance. Any charge has a Coulomb potential to interact with other charges. A neutral particle has a finite-range potential that makes this particle to have effectively a finite size. So effectively there is no point-like neutral particles. Such particles would be non-observable.

    Another thing is the interaction potential r-dependence. If you are charged, the closer you are to the electron, the stronger is the potential. In classical mechanics is depends only on the relative distance: V(r)=q1q2/r. For non-pointlike charges the potential would be dependent on the charge forms. But anyway, "feeling" the electron at a finite distance is somewhat contradictory to its point-likeness.

    It is true that a point-like neutral particle (q=0) cannot interact with the electron. They do not "see" or "feel" each other. In reality any neutral particle has a magnetic moment or is not truly point-like so they interact but much more weakly than charges q1 and q2.

    In quantum electrodynamics the charges not only scatter from each other passing at long distances but also radiate inevitably photons. So there is no "free" point-like charges but compound systems where r1 stands for the center of inertia of a compound system. Each charge (electron) is a part of a compound system including electromagnetic field.

    I cannot reply for stringy people; I am not good at strings.

  22. Jun 28, 2009 #21


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    I thought that was one of the mysteries behind point-like particles in the standard model. They have zero size, but they do collide (actually their forces collide, like you stated above). I'm not sure I would call this a problem, but instead a mystery. I guess to physicists that is the same thing. :smile:

    Or are you using this "problem" as evidence that point-like particles do not exist?

  23. Jun 29, 2009 #22
    No, as I said, the point-likeness accompanied with long- or finite-range potential is kind of contradictory thing. It should be understood as a simple dependence of the interaction potential where only distances between centers of inertia of two compound systems are involved. Point-likeness associated with truly neutral particles is senseless.

    Anyway, the center of inertia of a compound system described as a point with three coordinates R makes sense - it describes the compound system as a whole. The center of inertia has some energy, momentum and the angular momentum. And it can exchange them in course of interactions. It behaves as a point-like body of the total mass M. It can say you where the body is. But it does not correspond to a particular elementary particle.
  24. Jul 1, 2009 #23
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