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In real life, for a tennis ball to go through a wall, does it have to completely prevent the particles from interacting? What would happen if we tried infinitely in the real world, where the interaction of particles could not be completely prevented? Because of quantum coherence, will the ball not pass through the wall even if it tries infinitely?

Nunes
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    It will eventually go through. The potential coming from "the particles" might be hard to model but that doesn't matter. The only thing that makes tunnelling impossible is a potential of infinite strength. – Connor Behan Jun 14 '22 at 17:24
  • But in the real world, don't tennis balls constantly interact with the environment? If quantum decoherence continues, how can we get through it? – Nunes Jun 14 '22 at 17:36
  • The ball, the wall and the environment will go from being separately coherent to entangled. Their Hilbert space includes states with the ball bounding off, going through, breaking apart, ending up on the moon, etc. Computing the probabilities of them is a many-body nightmare but none of them can vanish for realistic interactions. – Connor Behan Jun 14 '22 at 17:46
  • The reason we have the properties of particles rather than waves is because we interact with the environment. So we know that our bodies and objects have the properties of particles. Don't we have wavefunction collapse every moment? Isn't quantum tunneling possible only when we exist as wavefunctions? – Nunes Jun 15 '22 at 01:57
  • If you believe there is a poorly understood phenomenon which constantly intervenes to prevent the predictions of quantum mechanics from being realized, then sure. "Big" objects will never tunnel. But that framework is not quantum mechanics. Collapse is a crutch which we don't need even though 1900s era physicists thought we did. See https://physics.stackexchange.com/questions/713459/why-arent-macroscopic-objects-or-really-the-entire-universe-coherent – Connor Behan Jun 15 '22 at 02:34
  • Doesn't the real world constantly maintain quantum decoherence to large objects? Is this true? I don't think it will happen even if I try infinitely, because in the real world, quantum decoherence is maintained. I think that for such a phenomenon to be possible, it is only possible to prevent the particles from interacting. What do you think about this? – Nunes Jun 15 '22 at 03:25
  • About quantum tennis balls: https://physics.stackexchange.com/questions/669910/will-tennis-ball-produce-same-interference-pattern-in-double-slit-experiment-if/669927#669927 – Roger V. Jun 15 '22 at 08:40
  • As I've said here and in the linked post... I think the opposite. Separate wavefunctions with the purpose of "choosing" one of their values when they interact do not exist. A single wavefunction which becomes ever more entangled exists. If you want to blend quantum and classical physics, you need to specify the precise blend before it makes sense to ask what phenomena from purely quantum physics can still happen. – Connor Behan Jun 15 '22 at 11:05
  • Roger Vadim Thank you It helped me understand this Thank you – Nunes Jun 15 '22 at 16:25

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The problem is the tension here between "real life" and "infinitely". In "real life" we cannot do an experiment infinitely many times, and if we tried other factors like the erosion of the ball and wall for unrelated reasons would mess up the result.

The in-theory answer is of course that the ball can tunnel through the wall with a finite probability. We can estimate it (see equation 7.7.29 here), but the answer turns out to be vanishingly small. The relevant wavelength of the tennis ball wave packet is $1/\beta \approx h/mv = 2\cdot 10^{-34} $m for a tennis ball moving 50 m/s, making the transmission probability way smaller than $e^{-2\beta L}$; for a 10 cm wall I get something like $10^{-10^{32}}$. That is astronomically small: if you tried this every second until proton decay in $10^{36}$ years time, you will still almost certainly not see it happen.

Anders Sandberg
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  • I know there was a probability. However, in the macro world, quantum decoherence continues to occur, so even if you throw a tennis ball an infinite number of times, tunneling does not occur, right? – Nunes Jun 15 '22 at 08:51
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    @Nunes - Decoherence will make the formulas much messier, since now the wall and ball are not separate things, and even defining a "ball has tunneled" state becomes complex. But tunneling does not require a coherent state. – Anders Sandberg Jun 15 '22 at 10:07
  • In order for a tennis ball to tunnel, shouldn't it be possible to prevent it from interacting with the environment? When electrons interact with the environment, they can't tunnel, right? Am I not understanding? I'm sorry I misunderstood, but can you explain a little bit more? – Nunes Jun 15 '22 at 16:30
  • Wrong. Fire an electron at a potential barrier such that it interacts along the way. Project the joint wavefunction of the electron and everything it has interacted with onto your favourite state which includes the position of the electron being on the other side. The result will not be zero. – Connor Behan Jun 15 '22 at 17:00
  • Does it mean that a thrown tennis ball is in a state of quantum coherence and interacts with the environment before hitting the wall, causing wavefunction collapse and passing through the wall? – Nunes Jun 16 '22 at 00:38
  • @ConnorBehan https://physics.stackexchange.com/q/92534 In the real world, even if you throw a tennis ball an infinite number of times, I don't think it will happen. This is because in the real world, particles interact continuously. What do you think about this? – Nunes Jun 16 '22 at 19:28
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    If the measurement you perform is infinitely strong and infinitely frequent then a ball known to have not tunelled yet will never tunnel. You seem to think that tunelling is some idealized situation that breaks down after the slightest perturbation but it's the opposite. The infinities needed to prevent tunelling are the finely tuned concepts. Real life measurements performed in a realistic way might make tunelling even less likely than it already is but they will not eliminate the possibility. – Connor Behan Jun 16 '22 at 20:35
  • Even if interactions are frequent in real life, there is a chance that the particle waves of all tennis balls will diffuse and interact. So the probability is not 0, so it happens if you try infinitely, right? – Nunes Jun 17 '22 at 10:04
  • @ConnorBehan Thank you for your kind replies so far. What I wanted to say was this.https://physics.stackexchange.com/q/57404 – Nunes Jun 19 '22 at 19:07
  • Yes. I think "immediately decohere" in that answer should be "very quickly decohere". – Connor Behan Jun 19 '22 at 23:27
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    @ConnorBehan The amount of time it takes for quantum decoherence to occur https://www.theatlantic.com/science/archive/2018/10/beyond-weird-decoherence-quantum-weirdness-schrodingers-cat/573448/ – Nunes Jul 12 '22 at 18:35