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At first, I know the question sounds ambiguous and maybe pseudo-scientific, but it's a thing I've been arguing about with my colleage for quite some time and while neither of us knows much about quantum mechanics besides the popular statements you see in internet, it has been bugging me to finally end the argument.

Here's the point: let's say there's a coin lying on the ground. He says, that there is a very small chance, but still a chance, that the coin isn't really there, but, say, 5 meters away. That's because there's a probability of finding an electron 5 meters away and thus, a probability of finding all of the object's particles 5 meters away. I'm not really sure if there IS a probability of finding an electron that far away, since I've always imagined the electron cloud as something existing around the nucleus but certainly not reaching infinity. Bet even so, doesn't the fact that I SEE the coin determine that the coin is in fact there? I'll never know the exact position of all the particles, but the uncertainty is small, for sure not as big as 5 meters.

I'm sorry if I offended anyone by this question that probably seems stupid to many, that wasn't my intent.

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  • $\begingroup$ Do not push uncertainty principle too far, especially when discussing things like coins etc. that are macroscopic. $\endgroup$ – mcodesmart Sep 2 '14 at 19:36
  • $\begingroup$ My keys are not where I think they are at least half the time. $\endgroup$ – WillO Jul 26 '17 at 5:02
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First, note that this comes from the Heisenberg uncertainty principle, $$ \Delta x\Delta p\geq \frac\hbar2 $$ where $\hbar\approx10^{-34}$ J$\cdot$s (i.e., a very small number). This is a constraint on the simultaneous measurements of momentum and position. If you know the position of the coin, then it can't actually be anywhere else because it's measured to be there.

Next, I quote Sean Carroll:

Quantum mechanics features a "classical limit" in which objects behave just as they would had Newton been right all along, and that limit includes all of our everyday experiences. For objects such as cats that are macroscopic in size, we never find them in superpositions of the form "75 percent here, 25 percent there"; it's always "99.9999999 percent (or much more) here, 0.0000001 percent (or much less) there." Classical mechanics is an approximation to how the macroscopic world operates, but a very good one. The real world runs by the rules of quantum mechanics, but classical mechanics is more than good enough to get us through everyday life. It's only when we start to consider atoms and elementary particles that the full consequences of quantum mechanics simply can't be avoided.

For your coin, we can describe it correctly by classical mechanics (meaning we can measure its position and momentum simultaneously), so there is no need to invoke quantum mechanics in regards to this thought experiment.

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    $\begingroup$ but then it could be five meters away just seconds after observation, right? $\endgroup$ – John Dvorak Sep 2 '14 at 19:05
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    $\begingroup$ The real question is whether a macroscopic object can be described by a (linear superposition of) quantum states, not the behaviour of a quantum state. This answer would be fine it the question were about e.g. an electron, but it's about a coin. $\endgroup$ – innisfree Sep 2 '14 at 19:09
  • $\begingroup$ @innisfree: Hmm, I do see that aspect. I'll update my answer to reflect this in just a moment. $\endgroup$ – Kyle Kanos Sep 2 '14 at 19:13
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    $\begingroup$ Having observed it at location x with velocity v, you can safely say that the probability of it appearing 5 m away due to quantum effects is zero. But an earthquake might do it. It certainly has a MUCH greater probability. Or your cat knocks it. Or... Etc. $\endgroup$ – Floris Sep 2 '14 at 20:19
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It's not a stupid question. In fact, a common physics problem is the quantum jailbreak. It explores a prisoner that runs at the wall of his cell once every second. The student is asked to calculate the expectation of how long it will take for the prisoner to "get lucky" and quantum tunnel through the wall.

The only thing stupid about it is how vanishingly small the probabilities actually are. They are very stupid odds. This is definitely one of those times where the house always wins.

A key phrasing change is required, however. We can't say "a coin is lying on the ground." This is phrased as a statement of truth. If this statement is true, then the coin is lying on the ground, and quantum physics can't do a thing about it.

However, we can say something like "we have observed that a coin is lying on the ground. 1 second later, what is the probability that the coin is 5m to the left?" Now we have an observation and then a period for quantum effects to possibly affect the outcome.

As it turns out, there is a possibility that the coin will actually be 5m to the left a second later. However, that probability is so tiny it's not worth calculating. A rough estimate would be a 0.0000{hundreds of zeros}001% chance. It's that small. But it is there.

The bigger issue is the other things that might happen. It's actually far more likely that the particles in the coin will all tunnel to different places, and you will end up with no coins. There's no guarantee that every particle in the coin will "try" to tunnel in the same direction at the same time.

And, to that end, it's also similarly likely that a bowl of petunias and a large sperm whale will pop into existence high in the atmosphere above your head. The probabilities are there, but don't hold your breath.

And don't ask me to calculate the probabilities that the bowl of petunias will think "oh no, not again!" before it hits the ground. Some things should not be calculated.

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Physicist Michio Kaku Builder String Theory Says that once the possibility of a single world is allowed, we open the door to the possibility of possible and infinite worlds. For quantum mechanics, the electron is not in a specific place but in all possible places around the nucleus of the atom. But the universe was smaller than the electron (at the beginning of the Big Bang that made up the universe), and if we applied quantum mechanics to the universe as a whole, The result is that the universe exists in all the many different and possible situations simultaneously. These possible and different situations are only the many universes. Hence, Kaku concludes that it is inevitable to recognize the possibility of possible universes. These universes are not galaxies in our world, but galaxies are part of our own real world. The possible universes may resemble our world and may differ from them, and some of these possible universes differ in their natural laws, facts and phenomena from other possible universes and our world in which we live.

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  • $\begingroup$ Why did you refuse the answer that I gave about Multiverse? The electrons of your coin, my friend, are in our universe by more probability; at the same time it exist in other universes with lower possibilities; but in another form according to the laws of this other universe. $\endgroup$ – Benzian Jul 25 '17 at 23:44

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