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Throwing a tennis ball through a wall

  1. Mar 13, 2006 #1
    I was having an argument with my sister last night about the limits of scientific knowledge (her beliefs encompass a more "spiritual" world view than mine) and she brought up quantum mechanics as an example of how weird things are possible (as peddlers of hocus-pocus love doing).

    Leaving aside the point that just because QM looks weird to us, doesn't mean the whole world is inherently "weird", and certainly shouldn't be used to try and pass off any mumbo-jumbo idea as worthy of credence...

    The example she brought up was that of, "if you threw a tennis ball at a wall for long enough, eventually it would pass straight through the wall". This is something I remember being said from my school days, I think to illustrate the principle of quantum tunnelling.

    Now I know it's dangerous to extrapolate quantum weirdness to the macroscopic world, and my scientific spidey sense is telling me that this is one of those times when a metaphor used to explain quantum weirdness to a layman is taken literally.

    So, what's the score? Assuming that I threw a tennis ball against a brick wall from now until infinity, and assuming neither ball nor wall were damaged nor deteriorated over time, would it just so happen that one time the ball would pass through the wall?

    Is it physically possible (and just very, very unlikely), or is it completely physically impossible?
  2. jcsd
  3. Mar 13, 2006 #2
    I think what you said here is probably closest to the truth. Imagine a book sitting on a table, since it is in contact with the table it has more of a chance to (tunnel?) through the table than a ball that only contacts a wall briefly. I don't think there has ever been a book fall through a table yet, or anything even remotly like that.

    It would be far easier, and more likely, that part of the book would pass through part of the table. Then we would be able to observe that part of the book is stuck in the table, but there again I don't think there is any evidence of that ever happening.

    Considering all the things that touch each other, just here on earth, there seems to be a great potential for things to tunnel into one another, but as I said I don't see any evidence of it happening.
  4. Mar 13, 2006 #3


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    There are several issues that need to be considered here:

    1. A "ball" is not a quantum particle.

    2. An object that can exhibit such a behavior has every part of it in coherence with each other. A ball doesn't. the atom in one part of the ball cannot be described via a coherent wavefunction with another part of it, especially at ordinary room temperature. So different parts of the ball have different probability of tunneling through a potential barrier. But you also can't have parts of the ball going through while another part bouncing back, because you have to overcome the ball's cohesive forces also.

    3. You have no ability to throw a ball exactly in the identical manner each time, so you are not repeating the identical situation. So the statistics doesn't quite work here.

    4. We have never, ever observed a ball tunneling through a wall. This is where experiments (or lack of it) trump all claims that this can happen. In physics, a claim must be backed by empirical evidence, or else it isn't physics, but String Theory. <ZapperZ runs and hides>

  5. Mar 13, 2006 #4

    I would guess that there have been millions of particles from a book that have tunnelled through a table. Just because one of the particles did doesn't mean that the whole book has to. Maybe I am wrong with this assumption. Correct me if I am.

    Paden Roder
  6. Mar 13, 2006 #5


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    I got the impression that QM says it really is possible for the ball to pass through the wall, or the book to fall through the table... it's just that that would be such a statistically rare event that it quite likely that a similar event has never happened in the history of the universe.

    But, the point is that it's an analogy for what "can" happen in the microscopic world, where the statistics are actually favorable, as opposed to being so tremendously lopsided against.
  7. Mar 14, 2006 #6
    So the consensus is that it is possible (i.e. is allowed by the laws of physics as we know them), just astronomically impossible.

    Bugger, I was hoping for a definitive no!

    For the entire ball to tunnel through the wall, would a particular amount of energy be required? I understand that in quantum tunnelling, particles "borrow" energy from the vaccuum to "jump" infinitesimal barriers. How much energy would all the particles in a tennis ball need to borrow to jump a six inch wall?
  8. Mar 14, 2006 #7


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    The answer to your question is in fact, a matter of opinion. Quantum theory SAYS that there is an (indeed astronomically small) probability for the ball to tunnel through the wall. For that to be true, however, quantum theory must be a VALID theory on the macroscopic level (in other words, macroscopic objects must be describable by quantum theory). This is perfectly possible. It leads (again!) to a view on quantum theory which is a "many worlds" interpretation.
    However, there's another view on quantum theory, which says that it DOES NOT describe macroscopic objects - which are strictly classical, but only microscopic objects, and that there is a kind of mysterious transition between them, called a "measurement process". This is the Copenhagen interpretation (the historical view on the matter). Personally, I don't like it, but it exists.

    Now, the difficulty (and the reason why it is just a matter of opinion) is that the predictions of both viewpoints are essentially identical.
    If you calculate that you have a chance of 10^(-23451234) to 1 to have your ball tunnel through the wall (quantum prediction), and you say that you've never seen it happening (and you've tried maybe, 10^(12345) times only), then there is PERFECT AGREEMENT between prediction and experiment so far. So the pure quantum prediction is verified.
    If you take on the Copenhagen view and you say that, given that the ball is a macroscopic, and hence, classical object, it CANNOT tunnel through the wall, and you've tested that 10^(12345) times, then you ALSO conclude, that this is experimentally verified.

    However, an argument in favor of the quantum case is that each time that there COULD have been a difference in prediction between the quantum and the classical case, the quantum case won. Albeit for much "smaller" systems than tennis balls. Still, it is a huge extrapolation, and it remains, as for now, still a matter of opinion to decide whether quantum theory is, or is not, valid for macroscopic objects. I like to think that it is, just for the economy of concept. But others are entitled to other opinions.
  9. Mar 14, 2006 #8


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    And since vanesch has tried to introduce his pet point of view into this, there's no reason why I can't do the same. :)

    The big question here is why isn't a tennis ball, or any of our familiar object, a "quantum object". While the consituents of the tennis balls (i.e. the atoms) are governed by quantum mechanics, the ball itself isn't. You can measure very accurately the position of the ball and its momentum simultaneously, and follow the trajectory of the ball every single step of the way. These are physical behavior that you cannot do with a quantum object.

    So already we can clearly see that the ball obeys one set of rules, while the constituents of the ball obey a different set of rules. But what is causing such a difference, and do they actually converge into one another at some scale? Strangely enough, you get all kinds of answer when you ask that, mainly because (i) it is still an active research area i.e. the area of mesoscopic physics and (ii) we have no means of computing a gazillion interactions.

    In putting together a gazillion atoms to make a tennis ball, you have produced an "emergent" object. This is where you do not have the ability to predict large, macroscopic phenomena simply by looking at the interactions at the microscopic scale. The atoms have no ability to mimick the behavior of the tennis balls, even as you try to include more and more interactions to account for the tennis balls, the same way one cannot derive superconductivity simply by writing down all the interactions of each individual electrons.

    So for condensed matter physicists, there is a "discontinuity" in our knowledge in going from one scale to the next. To the atoms in the ball, the ball itself is an emergent object. All the interactions, plus the decoherence, plus the interactions with large degree of freedom with the surrounding, etc.. all produced the tennis ball. And according to Bob Laughlin, this emergent properties are what produced newton's physics and newton's objects.

  10. Mar 14, 2006 #9
    as you say that the quantum theory does not describe the macroscopic object tive. but a macroscopic object are compose of the "quantum" particles.there must be a relationship between them. there must be a possibility that it will tunnel through the wall is we can give the ball a motion so that all particles of the ball will become a "wave-particle" with that energy(if i wrong please correct me).
    i have a question here. is it possible that if a particle (electron) were accelerated to near the speed of light. it can become a wave?:confused:
  11. Mar 14, 2006 #10


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    Here we go again :biggrin:

    Well, a quantum ball could be put in a quantum state of which the errors in position and momentum are well within what is experimentally possible with a classical ball. I think that there is no clash here. The "no trajectory" is only clearly valid for microscopic objects. The larger the object, the more a "trajectory" is quantum-mechanically possible (within certain errors which are tiny as compared to what can actually be measured).

    My point was that it does not HAVE to follow different rules. Of course, its behaviour is compatible with different rules, but - what I called the economy of concepts - if we can do it all with the SAME set of rules, isn't that nicer ?

    That's an unproven assertion! Although you are right that *up to now* nobody has been able to do all of the math to show it, nobody has been able to derive a contradiction either, in that he could prove that, when taking into account all the interactions, one cannot derive superconductivity. This is like, before Wiles, claiming that Fermat's last theorem was FALSE because nobody had succeeded in finding a proof.

    So the honest statement, as of now, is that there are emergent properties that nobody has ever been able to derive from ab initio principles of an underlying theory - as there are emergent properties that people HAVE been able to derive in such a way. As far as I know, however, there is no proof that any of these emergent properties are UNDERIVABLE from the ab initio principles. As such, IT IS AN OPEN QUESTION of whether they are, or are not, an emergent property that is NOT accounted for by the underlying theory. On open questions, one has the right to have opinions, but they are not more than that.

    Reductionists, like me, like to cherish the opinion that all emergent properties are accounted for by underlying principles (although it is sometimes such a hard mathematical problem that nobody has ever succeed yet in doing so explicitly). Holists like to think that this is not the case. But, again, it is a matter of opinion, and the reductionist viewpoint has not yet been *proved to be false* as far as I know.
  12. Mar 14, 2006 #11
    Prove it!

    Whether you prefer reductionism or emergence; whether quantum mechanics is valid on the macroscopic level (which it seems to me it obviously is) - regardless of any of these things, the fact stands that no one has ever used quantum mechanics and quantum particles to produce a working model of a tennis ball - or anything remotely like it.

    So how do you know what quantum theory says about the way a tennis ball behaves? Are we really to assume that there exists anywhere near the same behaviour on a macroscopic scale, even within the framework of quantum mechanics?
  13. Mar 14, 2006 #12


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    I blame you for starting it. :)

    That isn't true. I could have a "macroscopic" object yet it still behaves quantum mechanically. The supercurrent in the SQUID experiments consists of 10^11 electrons. These are HUGE when compare to the typical quantum objects. Yet, they behave quantum mechanically.

    And note, while emergent properties can produce newton objects, they can also produce quantum mechanical objects. The issue here isn't just particle-particle interactions within the constituents of the object, but the coupling to the environment, what most people consider as decoherence. So the emergent phenomena is due to many different forms and causes. If you produce a lot of interactions, but still isolate it from external decoherence, you get a macroscopic object that is also a quantum object.

    And my point is that you do not HAVE to follow many-worlds rules to get the same thing.

  14. Mar 14, 2006 #13


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    And I really tried to be moderate so as not to trigger a reaction :cry:

    Yes, but that should have been MY argument! That's to me one more reason to claim that quantum theory is universal (even if we can't prove it rigorously for things such as a tennis ball).

    I couldn't agree more...

    Well, if you claim that quantum theory is *universally valid* (which is, to me - although for sure unproven - the most *economical* hypothesis), you end up giving a hilbert space of states to everything, including yourself. I do not see how you get out of that without some flavor of MWI...

    The only issue out of it (and I thought you took it) was to claim that quantum theory is NOT universally valid. Then the burden is to show where it FAILS to be valid, and how this fits into a more encompassing view. As far as I know, it has never been SHOWN to fail. This is the point I tried to make.

    That said, it is entirely possible to be of the opinion that quantum theory is somehow not universally valid - such a viewpoint is ALSO compatible with experimental observation as of now. I just find that a less economic viewpoint, and there is no strict NEED for that. So - again - it is all matter of taste and opinion.
  15. Mar 14, 2006 #14


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    Nor has anyone ever produced a working classical model of ALL ASPECTS of a tennis ball. So if we are allowed to MAKE APPROXIMATIONS to build a more or less realistic PHENOMENOLOGICAL MODEL of a tennis ball, I CAN give you some quantum model of it. The simplest one is a point particle with mass = mass of the tennis ball + degrees of freedom of rotation (and if you want to, vibration), some hamiltonian describing the elastic interactions of the tennis ball (which will give you its spatial extention and the correct "bouncing" of the ball off walls). A wall can be phenomenologically represented by some or other potential barrier, and here we go!

    If you find this too crude, and you want me to descend down to nucleae, electrons and all that, then I go back to my previous remark: no such CLASSICAL model for a tennis ball exists either !
  16. Mar 14, 2006 #15
    Are you suggesting that some particles broke from their bonds in the book and travled through the table? Where are those particles now? They are no longer part of a book at this point. Electrons may be exchanged between the table and the book, and some may actually tunnel to their position, but I don't think a complete molecule (or group of molecules) would.

    My point was that it is more likely that a massive object would begin to tunnel through another massive object, under the right conditions, but very quickly those conditions would change, and any further tunneling would be halted by the fact that it's such a small probability in the first place. This would leave the two massive objects entangled to some degree (in a classical sense). I just don't see any evidence that massive objects become entangled in this way.
  17. Mar 14, 2006 #16
    If the tennis ball were radioactive, wouldn't bits of it be more likely to tunnel through the wall?
  18. Mar 14, 2006 #17


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    Just a thought, regarding scale. If you look at a graph of the function pi(x) (the one producing the number of primes less than, or equal to x) close up, it doesn't look like it is following a pattern. But as you zoom out enough it almost becomes a smooth line. I saw this in this page:
    At the quantum mechanical level, there may not be much certainty regarding a particles position and momentum, but as you zoom out, if the particles belong to a whole, as a tennis ball, then the differences between the position and momentum of each constituent particle become too small relatively to the current scale, and so variables such as position and momentum might emerge as being the "average" of the constituent particles. Small deviations from the average by a few constituent particles are not enough to change the average, so we might see the tennis ball as having a definite position and momentum. Not that this "average" doesn't change, but that it doesn't change enough to be noticeable at this scale.
    So i think, the Copenhagen view that i just heard Zapperz mention does seem reasonable, in my opinion.
    If the 3D world we live in were just a graph of various functions, then we might notice similar behavior as the graph of the function pi(x).
    Last edited: Mar 14, 2006
  19. Mar 14, 2006 #18
    It seems to me that the issue isn't whether quantum theory is universally valid as a predictor of experimental probabilities. There's every reason to believe that it is.

    But to adopt MWI requires that one take quantum theory as a complete description of an underlying reality --- and there's no particular reason to believe that it is.

    The viewpoint that quantum theory doesn't completely define an underlying reality is why there is a measurement problem in the first place. So, while solving the measurement problem by assuming that quantum theory is a complete description might seem economical, it isn't necessarily the most reasonable approach to take.

    Thus, Bohmian Mechanics for example is a more reasonable approach to the measurement problem because it is a hidden variable theory of underlying processes, which MWI (as well as quantum theory according to the standard interpretation) isn't.

    In saying that it's all, at least for now, a matter of taste and opinion, you've hit upon the most economical viewpoint which is that all of the alternative formulations-interpretations of quantum theory are models, ie. fictions, and there really is no physical basis for choosing one over the other --- which brings you right back to conventional quantum theory (at least until there is some compelling reason to adopt a different formulation).

    Then there's Bell's (vis ttn) two-part argument for nonlocality. If this argument is indeed sound, then relativity's prohibition on superluminal causation is just wrong and the ONLY approach that then makes sense is something along the lines of Bohmian Mechanics.

    But under no formulation is there any physical meaning to the notion that a tennis ball can tunnel through, say, a brick wall.
  20. Mar 14, 2006 #19


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    I want to propose a question here.

    On the Beyond the Standard Model forum, several well-trained physicists have posted the opinion that "Planck scale physics" can have nothing to do (some say "cannot" others "is extremely unlikely to") with phenomena like the scattering of W particle on each other. This is the reverse hierarchy problem.

    If this is true, then the success of quantum theory in accounting for such scattering, and by extension its successes in all current and past experiments, can have nothing to do with supporting such a statement as "Quantum uncertainty is a deep principle of the universe", and ditto for superpositon, entanglement and the rest.

    How say ye all to this?
  21. Mar 17, 2006 #20
    Quantum theory is valid at the level of instrumental phenomena. Since this is as deep as knowledge of the universe goes, then, in that sense, the principles of quantum theory are deep.

    However, whether these principles describe a level of reality beyond or underlying instrumental phenomena is an open question.

    As a student of quantum theory, I get sort of mixed signals from the theory itself regarding how it might be related to an underlying quantum world.

    As to your specific question, I agree with what the well-trained physicists say :smile: --- at least until I become one myself, which at my current pace will require that I live well beyond the normal human life span.

    Consider this post a boink to see what some of the well-trained physicists who frequent this forum have to say about it.
    Last edited: Mar 17, 2006
  22. Mar 17, 2006 #21


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    Yes, but that's about the only argument. It doesn't seem "reasonable" ; it is "just too crazy". As I repeated zillions of times, quantum theory is no better than any other scientific theory, and can, as such, be falsified. When that happens, all what goes with it as "picture of the world" can of course go down the drain, and it is up to the new queen in town to say what's now the new picture. This ephemere nature of things is inherent in any scientific endeveour. So if you ask me if quantum theory "really" describes the world, as with all scientific knowledge, I put this caveat. However, quantum theory is NO LESS a scientific theory than any other. Given its empirical success, I don't see why it should be a LESSER theory than any other scientific theory. I don't see why quantum theory should receive that dubious stature of "complete description of outcome of experiment" together with "it is of course NOT a DESCRIPTION of an underlying reality". Why not ? What's so terrible about quantum theory as a scientific theory, that others don't have ? Why should we take the 4-dim space-time manifold of GR somehow as a "description of underlying physical reality" but the wavefunction of quantum theory not - apart from the usual caveat about scientific theories, namely that one day, they can be falsified ? Isn't this similar to accepting natural evolution for animals, and even as an empirically complete theory for humans, except of course that it is "not reasonable" to say that our far ancestors were apes ?

    There are serious conceptual problems with Bohmian mechanics too, because of the mixture between epistemological and ontological concepts. In essence the "quantum equilibrium condition" - the requirement that our INITIAL KNOWLEDGE of the state of the system, as a probability distribution, corresponds to |psi|^2 of the ONTOLOGICAL state (the wavefunction, with all its parallel worlds, is as much part of the ontology of Bohmian mechanics as it is in MWI - the only thing we have extra is a "token" (the particle positions) which indicate which branch we're supposed to collectively experience). So if you say that, in Bohmian mechanics, the subjective experience is only derived from the particle positions, and not from the wavefunction (both are part of the "state of the world"), then there's no way of requiring that our knowledge of the particle positions of our body should not be more precise than what's allowed by the HUP and the wavefunction (and if you do that, Bohmian mechanics breaks down). It is only in the particular case when our subjective knowledge of our own bodystate corresponds to particle positions with a probability distribution given by the wavefunction, that Bohmian mechanics can save the HUP. But this means that the particle positions, by themselves are NOT the thing that determines (as in classical physics), our subjective perception: the wavefunction is just as much part of it. And in Bohmian mechanics, the wavefunction is exactly the same one as in MWI (no collapse) - with all its parallel branches and all that.
    So the relationship between subjective experience, knowledge, particle positions and wavefunctions is just as involved in Bohmian mechanics as it is in MWI. On top of that, Bohmian mechanics is not compatible with the minkowski spacetime view of SR. So I'd say that Bohmian mechanics has its own interpretational issues, and is not as clear as Newtonian mechanics in any case.

    This is not entirely true. Ether theory also works for special relativity. Does that mean that special relativity has no ontology ?

    I would like to point out that ttn agrees that the *other* way out is MWI - but considers it "just too crazy".

    I think it is of the same order as the physical meaning of all life on earth dying, because all air molecules suddenly end up in a big lump on top of Antarctica.

    My impression of the entire interpretational debate of quantum theory is that we've been inventing all of this "empirically complete but ontologically meaningless" positivist babble because we simply refuse to make the mental step which the quantum formalism cries out, and that is: the wavefunction describes reality - with the usual scientific caveat of the possibility of being falsified one day. Just as one could refuse the mental step that his great great great old dad was something close to a chimp, or that the sun doesn't turn around the earth, or that the earth isn't flat, or that organic chemistry is like any chemistry... I agree that the mental shock is greater. The entire speculation, and the "matter of opinion" resides in fact in speculation of how quantum theory will be falsified.
    For instance, according to Bohr, quantum theory does NOT describe macroscopic objects, but classical physics does. This means that certain quantum interference experiments, with large enough objects, will *falsify* quantum theory.
    But this is an odd way of thinking! Never before, in the interpretation of a new theory, we started by speculating on how it was going to FAIL ! Newton didn't say that his theory of matter points in Euclidean space was probably just an approximation to a field theory ! Einstein never said that the 4-dim spacetime manifold was probably an erroneous concept which gave good empirical results, but which was probably going to be shown to be wrong ! So this is what I don't understand: people thinking about quantum theory seem to START with the assumption that it must be somehow fundamentally flawed, and base their view of things on that. Strange...
  23. Mar 18, 2006 #22
    it is possible for the the ball to tunnel through the wall or the brick.but the probability of that to happen is 1 out of 10^34 times.
    so please don't try this at home.otherwise you will have to do this almost up to infinity. but these probability is only true if take the points into consideration given by zapperZ
  24. Mar 18, 2006 #23
    see theoritically it is possible. the chances of transmission of a particle (or group) is expressed as the transmission coefficient T

    T= 16E/U [1-E/U] exp -2kx where k is
    k=2PI(2m(U-E)^1/2 / h

    so, T increases with particle mass and with barrier energy (ball width). so there are chances but really REALLY small, probably that's why you don't fall through the floor to the other side of the earth.
  25. Mar 18, 2006 #24
    But wait, the tennis ball is not a single particle. Instead it is about ~10^23 particles all interacting with each other.
  26. Mar 18, 2006 #25

    1. You try to disprove this statement in a later post, in a sense when you say, 'That isn't true. I could have a "macroscopic" object yet it still behaves quantum mechanically. The supercurrent in the SQUID experiments consists of 10^11 electrons. These are HUGE when compare to the typical quantum objects. Yet, they behave quantum mechanically.' CAn you give a link to this experiment, I'd be curious to learn about it, ty.

    2. Irrespective of the fact that different parts of the tennis ball have different wave functions and therefore different probabilities of tunnelling through the wall, it is still possible for every one of these parts to tunnel through the wall simultaneously. So you are wrong there (at least in the 'theory' of tunnelling), but experimentally we just don't know.

    3. This is just nitpicking to the nth degree, forshame.

    In a later post you said, 'The big question here is why isn't a tennis ball, or any of our familiar object, a "quantum object". While the consituents of the tennis balls (i.e. the atoms) are governed by quantum mechanics, the ball itself isn't. You can measure very accurately the position of the ball and its momentum simultaneously, and follow the trajectory of the ball every single step of the way. These are physical behavior that you cannot do with a quantum object.'

    This is just a silly argument. 'Quantum objects' are limited to the Uncertainty Principle because of the limitations of Rayleigh's Criterion and the particle(s) needed to 'probe' them. Inelastic scattering and the interference patterns observed from particle collision experiments are limited by the wavelengths of the particles used (the higher their energies the lower their wavelengths) and not some deeply rooted property of the Universe that gives us the Uncertainty Principle.

    The reason you can easily measure a tennis ball's momentum and position simultaneosly is because you measure it with visible light (~500 nm wavelength) which under Rayleigh's Criterion, can EASILY resolve the position of the tennis ball (a ~100,000,000 nm diameter object!!). AND this visible light imparts such a NEGLIBIBLE amount of energy onto the ball that its momentum is virtually unchanged.
    So using the Uncertainty Principle to question why a tennis ball isn't a 'quantum object' while its particle constituents are, makes entirely no sense.:smile:Zzz
    Last edited: Mar 18, 2006
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