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turnip_burrito t1_iuu9p7c wrote

Zero, basically. Think of it as similar to the chance of winning the lottery billions of times in a row. Even if you waited from the big bang until now, it wouldn't have happened even once.

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[deleted] t1_iuucd9f wrote

How small do you have to go for the odds of teleportation being 50/50 or happening often? Blood cells are a lot smaller than a person but the odds are much higher then why don't we hear people's blood being mixed or removed because of quantum physics?

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turnip_burrito t1_iuuey6g wrote

I don't know how small you'd have to go to see 50/50 odds. But I can suggest how a physicist would initially continue approaching the problem, if you're interested.

Blood cells are still too big to see these effects. Typically in labs you strive to measure these quantum effects with roughly atom-scale things: electrons, nuclei, and atoms are all less than 10^(-9) meters large. In contrast, red blood cellsare roughly 10^(-6) or 10^(-5) meters, so still at least 10 thousand or more times longer. Humans are larger still, order 1 meter. By volume, the difference is even larger. To have objects made of many objects tunnel, you need every particle inside it to tunnel. The chance of 1 particle tunneling is much higher than 10, and enormously higher than 100, etc.

If you're interested in learning how to calculate it though, here's a place to get started: you need to solve Schrodinger's equation for a particle of some given energy, and a potential wall. When you solve the equation, you get a wave function. The probability of seeing tunneling is given by integrating the squared amplitude of this complex-valued wavefunction over the region of space you want to see it in (other side of the wall) and dividing it by the integral of the squared magnitude of the wavefunction over all space.

The electric fields outside of your thing you want to see tunnel are responsible for producing the potential barriers. This could be things like liquids, vascular walls, other blood cells, objects in the liquid, etc. The larger the potential barriers are between where you are now and where you want to be, the exponetially lower the probability of tunneling across the barrier is.

For another reference, see this: https://physics.stackexchange.com/questions/223277/if-quantum-tunneling-is-possible-is-there-a-maximum-thickness-of-material-a-par

An introductory textbook to quantum mechanics like Griffiths' will also help.

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