Can a "Cat paradox" exist inside a nucleus?

In summary: The conversation revolves around the topic of particles in a nucleus and how they cannot be individually identified or distinguished from one another. The concept of identical particles and their anti-symmetric wave functions is discussed, along with the Pauli Exclusion Principle and the concept of energy levels in a nucleus. The idea of entanglement between particles is also brought up, with examples of experiments involving electrons and photons given. The conversation ends with a mention of the Schrödinger's cat thought experiment and the possibility of cats being in a superposition. In summary, the conversation explores the unique properties of particles in a nucleus and how they differ from everyday objects.
  • #1
Andrew Wright
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19
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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  • #2
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.
 
  • #3
I didn't see that one coming. I feel cheated by nature!
 
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  • #4
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?
 
  • #5
You can say "a neutron in this energy state" (different energy states are different), but not "neutron #5" (because there is no neutron #5).
 
  • #6
Thanks. It's a funny universe we live in.
 
  • #7
Andrew Wright said:
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.
 
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  • #8
I read that protons have anti-symmetric wave functions and that this tells us something profound about what they are.
 
  • #9
Andrew Wright said:
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.
 
  • #10
Are there shells inside a nucleus?
 
  • #11
Andrew Wright said:
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.
 
  • #12
The electron shells? No. And they are not places anyway, they are energy levels.
 
  • #14
So I think protons and neutrons have separate shells?
 
  • #15
Andrew Wright said:
Are there shells inside a nucleus?

Read as "Are there shells for protons and neutrons (particles that exist in the nucleus)."
 
  • #16
Andrew Wright said:
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. o0)

This is a pretty good introduction. http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html
 
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  • #17
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?
 
  • #18
...in the nucleus.
 
  • #19
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.
 
  • #20
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 realize 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?
 
  • #21
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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  • #22
If you want entanglement, use electrons or photons. Much easier.
 
  • #23
Is there an experiment that demonstrates electrons entangled with photons or do we only have photon-photon and electron-electron experiments?
 
  • #25
Andrew Wright said:
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.
 
  • #26
Is that your personal belief or is it an established thing?
 
  • #27
nikkkom said:
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.
Andrew Wright said:
Is that your personal belief or is it an established thing?

Any attempt to make a boundary between quantum and classical introduces new physics for which there is no evidence.

e.g. The Heisenberg cut:

Below the cut everything is governed by the wave function; above the cut a classical description is used.[1] The Heisenberg cut is a theoretical construct; it is not known whether actual Heisenberg cuts exist, where they might be found, or how they could be detected experimentally. However, the concept is useful for analysis...
In this situation it follows automatically that, in a mathematical treatment of the process, a dividing line must be drawn between, on the one hand, the apparatus which we use as an aid in putting the question and thus, in a way, treat as part of ourselves, and on the other hand, the physical systems we wish to investigate.
 
  • #28
Carrock said:
Any attempt to make a boundary between quantum and classical introduces new physics for which there is no evidence.
No evidence, and also no need. Many-worlds doesn't have such a cut.
 
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1. Can a "Cat Paradox" exist inside a nucleus?

The concept of a "Cat Paradox" is based on the famous thought experiment in quantum mechanics called "Schrödinger's Cat." This thought experiment involves a hypothetical situation where a cat inside a sealed box can be both alive and dead at the same time. However, this paradox cannot exist inside a nucleus as it is not a macroscopic object like a cat. In quantum mechanics, the principles of superposition and entanglement only apply to subatomic particles, not larger objects like cats or nuclei.

2. What is a nucleus?

A nucleus is the central part of an atom that contains protons and neutrons. These subatomic particles are held together by strong nuclear forces. The nucleus is responsible for the mass of the atom and determines its chemical properties. It is surrounded by a cloud of electrons, which orbit around the nucleus.

3. Can a nucleus be in two places at once?

In quantum mechanics, subatomic particles can exist in multiple places at the same time due to the principle of superposition. However, this does not apply to larger objects like nuclei. The size and complexity of a nucleus make it impossible for it to exist in multiple places simultaneously.

4. How does quantum mechanics apply to nuclei?

Quantum mechanics is the branch of physics that explains the behavior of subatomic particles. It is the most accurate and fundamental theory we have to describe the universe at the subatomic level. Therefore, it applies to the behavior of nuclei and their constituent particles.

5. Can a nucleus be observed without changing its state?

In quantum mechanics, the act of observation or measurement can affect the state of a subatomic particle. This is known as the observer effect. However, for larger objects like nuclei, the observer effect is negligible. Nuclei can be observed without significantly changing their state, making it possible to study their properties and behavior.

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