This is a mistake. There is actually a two-electron state in the OP. (And there is no assumption ‘that they are independently and individually real.’ The claim is merely that the two-electron state is real.)
The current deepest level of understanding of physics is quantum field theory, and according to that theory there are no such things as particles, fundamentally. The only thing that exists are quantum fields. (Except gravity, but I will ignore that huge problem for now, because I don’t think it is important for this discussion.)
The two particle state belongs to the Fock space formulation, that you get when tailor expanding quantum fields. This is not to say that the two particle space is not a real possibility. To my mest understanding of the math involved, there is a quantum field configuration that is exactly the two electron state. But the two electrons here are NOT two separate objects.
The philosophers mistake is not about whether two objects can be proven to be exactly identical. The philosophers mistake is in thinking that two electrons are different objects. From now on I will steel man the philosopher a bit and assume that what he ment was “fundamental objects” and not “electrons”. He was just not up to date with the latest ontology and though though that “electron” was an example of “fundamental object”, but has now updated his statement to be about actual things, and not mare emergent phenomena such as individual particles.
All the quantum fields in the standard model clearly have different properties. Different charges, different mas, etc. But it is not inconceivable, with in this model, to have two identical, but separate objects. There are probably quantum fields that has not yet been detected, because of week charge and/or high mas. It is possible that in the future we will find two new quantum fields, that, to the limit of our technology, are identical. Maybe later when we discover that all the quantum fields are just aspects of some deeper level, then we might be able to prove that those two quantum fields are identical. But in the same stroke we will also find that these fields are not actually separate objects.
In the end the philosopher will still be correct.
What ever your deepest level of understanding is, you will always have to go one level deeper before you can prove that two “different objects” are identical in every way. ”different objects” = things that appear to be different object at the previews deepest level of understanding.
One could argue that the philosopher is wrong if there are no bottom level of physics, because by talking about fundamental objects he kind of assumes that there exist such things. If the problem of physics i bottomless then that assumption is wrong. However, I see no reason to believe that physics is bottomless.
This is a mistake. There is actually a two-electron state in the OP. (And there is no assumption ‘that they are independently and individually real.’ The claim is merely that the two-electron state is real.)
I am with pudge on this.
The current deepest level of understanding of physics is quantum field theory, and according to that theory there are no such things as particles, fundamentally. The only thing that exists are quantum fields. (Except gravity, but I will ignore that huge problem for now, because I don’t think it is important for this discussion.)
The two particle state belongs to the Fock space formulation, that you get when tailor expanding quantum fields. This is not to say that the two particle space is not a real possibility. To my mest understanding of the math involved, there is a quantum field configuration that is exactly the two electron state. But the two electrons here are NOT two separate objects.
The philosophers mistake is not about whether two objects can be proven to be exactly identical. The philosophers mistake is in thinking that two electrons are different objects. From now on I will steel man the philosopher a bit and assume that what he ment was “fundamental objects” and not “electrons”. He was just not up to date with the latest ontology and though though that “electron” was an example of “fundamental object”, but has now updated his statement to be about actual things, and not mare emergent phenomena such as individual particles.
All the quantum fields in the standard model clearly have different properties. Different charges, different mas, etc. But it is not inconceivable, with in this model, to have two identical, but separate objects. There are probably quantum fields that has not yet been detected, because of week charge and/or high mas. It is possible that in the future we will find two new quantum fields, that, to the limit of our technology, are identical. Maybe later when we discover that all the quantum fields are just aspects of some deeper level, then we might be able to prove that those two quantum fields are identical. But in the same stroke we will also find that these fields are not actually separate objects.
In the end the philosopher will still be correct.
What ever your deepest level of understanding is, you will always have to go one level deeper before you can prove that two “different objects” are identical in every way.
”different objects” = things that appear to be different object at the previews deepest level of understanding.
One could argue that the philosopher is wrong if there are no bottom level of physics, because by talking about fundamental objects he kind of assumes that there exist such things. If the problem of physics i bottomless then that assumption is wrong. However, I see no reason to believe that physics is bottomless.