# Why do quantum effects arise due to microscopic size?

• B
First, in quantum mechanics, space is not quantized. So, you can have particles of any size. It's not like the minimum size should be a space quantum. If there's no absolute 'huge' and no absolute 'microscopic', just relative sizes, then there should be no reason to assume that we follow general relativity while electrons follow quantum mechanics.
My question is: Do quantum effects arise due to the difference in relative sizes of the observer and what is being observed? Considering space is not quantized, and you can divide it as much as you want, then there can be a particle whose size is microscopic relative to an electron and there can be living creatures for which Earth is of microscopic size. So, for those creatures, will Earth show quantum effects?

## Answers and Replies

Demystifier
Science Advisor
Gold Member
The crucial quantum feature is uncertainty. According to quantum mechanics, the product of momentum and position uncertainties is
$$\Delta p \Delta x \approx \hbar$$
The quantum effects are important when the uncertainties are big, i.e. comparable to the average values. In other words, when
$$\Delta p \Delta x \approx \langle p\rangle \langle x\rangle$$
Therefore quantum effects are important when
$$\langle p\rangle \langle x\rangle\approx \hbar$$
The Planck constant ##\hbar## is small, meaning that the quantum effects are important when ##\langle p\rangle \langle x\rangle## is small. Usually, this quantity is small for microscopic objects, not for macroscopic ones.

vanhees71
Science Advisor
Gold Member
There's no known limit of validity of the natural laws expressed by quantum theory (it's only not completely understood how to describe gravity by quantum theory, but that's not so relevant for your question). Given the atomistic structure of matter, one of the most frequent quantum properties of matter around us is its stability. The very fact that I'm sitting on a chair and not falling freely in space is a quantum phenomenon (Pauli principle of the electrons in the atoms of the chair and myself), typing this posting into a laptop (with chips based on the laws of quantum theory describing semicondutors).

The crucial quantum feature is uncertainty. According to quantum mechanics, the product of momentum and position uncertainties is
$$\Delta p \Delta x \approx \hbar$$
The quantum effects are important when the uncertainties are big, i.e. comparable to the average values. In other words, when
$$\Delta p \Delta x \approx \langle p\rangle \langle x\rangle$$
Therefore quantum effects are important when
$$\langle p\rangle \langle x\rangle\approx \hbar$$
The Planck constant ##\hbar## is small, meaning that the quantum effects are important when ##\langle p\rangle \langle x\rangle## is small. Usually, this quantity is small for microscopic objects, not for macroscopic ones.
If Plank's constant changed with relative size of observers and what is observed then......................

vanhees71
Science Advisor
Gold Member
According to our present knowledge ##\hbar## is just a conversion factor between arbitrarily chosen units, i.e., a fundamental constant of nature. It doesn't change with the size of observers.

Demystifier
Science Advisor
Gold Member
If Plank's constant changed with relative size of observers and what is observed then......................
I don't understand what do you mean. Planck constant doesn't change, that's why it is called constant.

I don't understand what do you mean. Planck constant doesn't change, that's why it is called constant.
Maybe it's value is larger for living beings of the size 10^32 times that of Earth (I'm not saying they exist, but if they existed) who are observing the Earth with a planet microscope. Maybe Earth has uncertain position and momentum for them. A relativistic Plank's constant,.....no wait, plank variable

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Demystifier
Science Advisor
Gold Member
Do quantum effects arise due to the difference in relative sizes of the observer and what is being observed?
No they don't.

Dale
Mentor
2020 Award
Maybe it's value is larger for living beings of the size 10^32 times that of Earth (I'm not saying they exist, but if they existed) who are observing the Earth with a planet microscope. Maybe Earth has uncertain position and momentum for them. A relativistic Plank's constant,.....no wait, plank variable
Do you have a scientific reference for this? If not, then please review the PF rules on personal speculation.

If you have such a reference then send me a PM. Until then the thread is closed.

vanhees71