# B Can a "Cat paradox" exist inside a nucleus?

#### Andrew Wright

Hi,

A cat cannot be alive and dead at the same time. Is it possible for particles in a nucleus to be both protons and neutrons at the same time? How could you tell whether this is happening?

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#### mfb

Mentor
As all protons are exactly identical and all neutrons are exactly identical, it doesn't make sense to talk about "this particle". You cannot even ask the question in a physical meaningful way.

#### Andrew Wright

I didn't see that one coming. I feel cheated by nature!

#### Andrew Wright

So my question is all wrong. All protons are identical and all neutrons are identical. A particle cannot become one and then the other or be in a superposition of both. You can't track a single particle's identity through a series of changes. There are simply a certain number of neutrons and protons in a nucleus at fuzzy locations, which have no individual identity.

So, if there were beta decay (for example) could you then say that a particular neutron became a proton and emitted an electron?

#### mfb

Mentor
You can say "a neutron in this energy state" (different energy states are different), but not "neutron #5" (because there is no neutron #5).

#### Andrew Wright

Thanks. It's a funny universe we live in.

#### PeroK

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Thanks. It's a funny universe we live in.
There are a lot of posts on here than presume that if things on the smallest scales (elementary particles etc.) are different from everyday objects, then that is strange or weird. But, in my opinion, it is almost impossible to imagine elementary particles having the properties of everyday objects and this is a case in point.

First, all protons must be exactly the same. If they had fundamental differences like different masses, then we'd have two different types of particle. Second, there is no way to identify a particular proton by changing it permanently in some way. You can't put a serial number on it. To change it you either take something away (in which case you have to split the particle and you no longer have a proton) or you add something, like an electron, and you have a hydrogen atom. Neither uniquely identifies your original proton.

Everyday objects are distinguishable either because they are not physically identical (dollar bills have serial numbers) or, if they are (practically) physically identical, you can mark them, write on them or put a label on them. And, critically, not change what they are: a bowling ball with your initials on it is still a bowling ball.

To turn your question round: how could you have a universe where the protons were all distinguishable from one another? How could you possibly distinguish them? That would be strange.

#### Andrew Wright

I read that protons have anti-symmetric wave functions and that this tells us something profound about what they are.

#### PeroK

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I read that protons have anti-symmetric wave functions and that this tells us something profound about what they are.
Protons, like electrons, are fermions and this means that must have anti-symmetric wave functions. One significant consequence of this is the Pauli Exclusion Principle. Applied to electrons this is what determines the limit on the number of electrons in each shell of an atom.

#### Andrew Wright

Are there shells inside a nucleus?

#### PeroK

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Are there shells inside a nucleus?
Ah well, if you don't know that, we've probably taken this thread beyond your ability to understand what is being said. There must be loads online about the structure of the atoms, electron shells and identical particles. If you are interested, start reading about the structure of the atom.

#### mfb

Mentor
The electron shells? No. And they are not places anyway, they are energy levels.

#### Andrew Wright

So I think protons and neutrons have seperate shells?

#### Andrew Wright

Are there shells inside a nucleus?
Read as "Are there shells for protons and neutrons (particles that exist in the nucleus)."

#### e.bar.goum

Read as "Are there shells for protons and neutrons (particles that exist in the nucleus)."
Yes! The shell structure of nuclei was first suggested by Maria Goppert-Mayer, and it is necessary for explaining many nuclear properties. For example, like nobel gasses in atoms, nuclei have closed shells of increased stability- for example, 208Pb and 40Ca - these are called "magic" nuclei. When both the neutrons and proton shells are full, we call these "doubly magic". This is why physicists shouldn't name things.

This is a pretty good introduction. http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html

#### Andrew Wright

Electrons in atoms are said to (mostly) come in pairs with opposite spins. So do you get entangled pairs of protons that have the same energy but opposite spins?

#### Andrew Wright

....in the nucleus.

#### mfb

Mentor
Yes, energy levels always have two protons or two neutrons with opposite spin in them - apart from the highest occupied energy level which has just one if the total number of protons or neutrons is odd.

#### Andrew Wright

One reason why I was hoping to find my "cat" in a nucleus is because real cats cannot be in a superposition but subatomic particles can.

I realise that this question might be wrong but I want to ask it anyway.

If neutrons entangle with each other in the nucleus, do they also entangle with the protons there?

#### Andrew Wright

read "cat", "cat paradox" etc. as an object being two different things at once.

edit: or however you make sense of that thought experiment if it is done on a proton not a cat.

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#### mfb

Mentor
If you want entanglement, use electrons or photons. Much easier.

#### Andrew Wright

Is there an experiment that demonstrates electrons entangled with photons or do we only have photon-photon and electron-electron experiments?

#### mfb

Mentor
Many.
This is one
Here is another one
Two more
...

Every experiment with Rabi oscillations produces entanglement between electron energy levels and light, even if it does not use it directly.

#### nikkkom

One reason why I was hoping to find my "cat" in a nucleus is because real cats cannot be in a superposition but subatomic particles can.
Not everybody agrees that cats can't be in a superposition. I, for one, understand the experiment as *requiring* the cat to be in a superposition of "dead" and "alive" as long as it is entangled with the unstable atom and is not disturbed (observed) by the rest of the Universe.

"Can a "Cat paradox" exist inside a nucleus?"

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