Undergrad Quantum interpretation and classical-quantum distinction

[PeroK]

Your answer appears to be:I disagree. It is perfectly logically consistent to have two sets of laws of physics for different domains, with some kind of rule about what happens at the boundary. It might not suit your expectations, and it might not be what you believe, but that's not the same as it being logically inconsistent. Logical inconsistency is an extremely strong claim.

Niels Bohr certainly tied himself in knots to establish the consistency of the CI! It was never really satisfactory to exclude macroscopic measuring devices. Whether that's truly logically inconsistent is perhaps debatable.

 

[PeterDonis]

Niels Bohr certainly tied himself in knots to establish the consistency of the CI!

I would say he tied himself in knots trying to convince other physicists that the CI was physically reasonable (and in many cases he failed, which is one reason why we still have debates about QM interpretations now, a century later). But "physically unreasonable" is still a long way from "logically inconsistent".

 

[DesertFox]

@PeterDonis, tell me, please.

Given the following:

· there are so many objects in the world (visible with the naked eye: from a grain of sand to a ping pong ball and so on);

· so many people have lived on the Earth and so many are are living up to now,

and if (for the sake of the context of my question) we imagine that the Universe functions (the way it does it now) for eternity and won’t cease to exist (in other words: if we somehow, by means of the imagination, manage to ignore the second law of thermodynamics),

do you think that somebody will see quantum tunnelling of a visible object for sure?

Or maybe that already has happened in spite of the very, very, very small probability?

Please, share some personal thoughts on that imaginary question!

 

[CoolMint]

What is a 'visible object"? A particle of dust might have tunneled through a thin barrier somewhere given the 13 billion year life span of the Universe.
A golf ball? No. A rock - no.
Why is this important? You will never ever see anything like this in 100 lifetimes.
Get below 5 nm and it will be a daily routine.
Quantum rules apply to quantum scales.

 

[DesertFox]

What is a 'visible object"? A particle of dust might have tunneled through a thin barrier somewhere given the 13 billion year life span of the Universe.
A golf ball? No. A rock - no.
Why is this important? You will never ever see anything like this in 100 lifetimes.
Get below 5 nm and it will be a daily routine.
Quantum rules apply to quantum scales.

What further clarification does the phrase "visible with the naked eye" need? It's that which every healthy person can see with his eyes.

 

[Motore]

Check out this:
https://physics.stackexchange.com/questions/16296/chance-of-macro-tunneling

Or maybe that already has happened in spite of the very, very, very small probability?

Very, very, very small probability is a very, very, very big understatement. The probability is still too close to zero for that. As per the response from the link above:

I'm going to trust that Alexander's interpretation is good and say that the probability is arbitrary as T depends on unknown parameters. The important part is that the double exponent you need to raise T to to get the transmission probability of all of the particles will make any probability less than exactly 1 vanishingly small. If T were 1 in 10, T^10^23 would be 1 in 1 followed by 100 sextillion zeroes. That's a number so gobsmackingly large it gives me a headache to think about it.

 

[DesertFox]

Very, very, very small probability is a very, very, very big understatement. The probability is still too close to zero for that.

It's not "very, very, very big understatement", but a turn of speech which is specially designed for the context.

 

[PeterDonis]

do you think that somebody will see quantum tunnelling of a visible object for sure?

Or maybe that already has happened in spite of the very, very, very small probability?

No and no. The responses you have been getting about this are correct. The evidence is that we have not observed quantum tunnelling of an object large enough for a human to see with the naked eye. However, this evidence tells us nothing useful either way about whether QM is valid for such objects; there are not enough such objects and we have not been observing for long enough for the probability QM predicts for such an event to be large enough to make the fact that we have not observed such an event significant evidence against QM. And "not enough" means not enough by many, many, many orders of magnitude; it's not even close.

 

[DesertFox]

It is somehow natural to consider the wavefunction as a reflection of our knowledge of the system (not as a description of the system itself). As far as I know, that view was held by Einstein. He suggested that quantum mechanics is incomplete, since it gives us only an instrumental recipe for calculating the probabilities of outcomes, rather than a description of the underlying state of the system that gives rise to those probabilities. However, it was later "proved" that it is impossible to construct such a description of the underlying state. What exactly is that proof? Can somebody explicate it, please?

 

[DesertFox]

there are not enough such objects

It is amazing how we can take that for granted without even bothering to do the numbers.

In other words: Very bold claim; but i don't find it well-grounded at all.

 

[PeterDonis]

It is amazing how we can take that for granted without even bothering to do the numbers.

The people who responded to you have done the numbers. Have you? If so, please show your work.

 

[DesertFox]

The people who responded to you have done the numbers. Have you? If so, please show your work.

These people did the numbers regarding all the visible objects that the humankind have had the chance to see tunneling? Please, show me a comment containing such calculation.

All of the answers so far consider what is the very small probability for, let's say, a grain of sand to quantum tunnel and nothing more. That's very different from ALL the visible objects that humankind have seen and that eventually have had any miserable probability to tunnel.

 

[PeroK]

The people who responded to you have done the numbers. Have you? If so, please show your work.

Although it's not the tunnelling calculation, a tennis ball typically has a mass of $0.05 \ kg$ and if we say that the uncertainty in its speed is $10 \ m/s$, then according to the Heisenberg UP, the uncertainty in its position is approximately $10^{-34} \ m$. We can compare this with the diameter of the hydrogen nucleus at about $1.7 \times 10^{-15} \ m$.

Not only is this calculation absurd, in a way, but anyone who demands such a calculation has shown that their grasp of the scale at which QM applies is non-existent.

 

[PeterDonis]

These people did the numbers regarding all the visible objects that the humankind have had the chance to see tunneling?

No, they gave you the numbers for one visible object, and the probability for that is so vanishingly small that even multiplying it by the most generous upper bound imaginable for the number of all the visible objects humans have had the chance to see tunnelling still leaves a probability that is much too tiny to matter. You should be able to calculate that for yourself. It is not incumbent on people responding to you to spoon feed you every single piece of information.

If you think the numbers are different, the burden is on you to show your own calculation. Either do that or your thread will be closed since without you showing your own work, or giving a reference to some similar calculation in the literature that supports your claims, your claims are baseless.

 

[DesertFox]

even multiplying it by the most generous upper bound imaginable for the number of all the visible objects humans have had the chance to see tunnelling

It is THAT number that NOBODY considered it in any well-grounded way.

And i don't say if the numbers are DIFFERENT or the SAME. I just claim that nobody focused on that crazy big number. That's all I said. Of course, I can't give reference in the literature for such a claim.

And if closing the thread will give some base to your claims: fine, i am ok with that. However, it will be sad, cause I really like that place.

 

[PeroK]

The other relevant point is that quantum tunneling tends to take place over barriers in the region of a few nanometres ($10^{-9} \ m$). If the potential barrier were the width of a house brick, say, then even electrons would be unable to tunnel. There's no basis at all on which to scale that up and conclude that a tennis ball could tunnel through a wall, say.

Any tunnelling would be part of the interaction between the surface of the ball and surface of the wall at the molecular level. QM effects would take place on that scale and govern the microscopic interactions. Even those effects have vanishingly small probabilites above molecular scales.

This is why quantum tunneling and quantum uncertainty are just not a thing when it comes to the behaviour of a tennis ball.

 

[PeterDonis]

It is THAT number that NOBODY considered it in any well-grounded way.

Then you need to give your number and show how it was calculated and why that calculation makes sense. You have not done so. I told you what would happen in that case, and it has now happened.

Of course, I can't give reference in the literature for such a claim.

In other words, you can't support your claim. Then closing the thread is obviously appropriate.

if closing the thread will give some base to your claims

Closing the thread has nothing to do with anyone's claims in this thread except your own, which you have failed to provide support for despite being asked explicitly.

This thread is closed.