Uniqeness of elemental particles

[mark noble]

No two atoms can be identical. Though performing seemingly identical tasks, each individual atom is either side (isotopically) of the definitive elemental. May I therefore assume that, theoretically, every atom in existence could be lined up end to end? I would be grateful if you could confirm this because it has massive implications for my theory of 'Omniparticle-residue'.
Thank you
Mark...

 

[humanino]

This is a more than century old achievement from Mendeleev : two atoms with the same mass and charge are identical, they are impossible to distinguish, it does not matter whether they were formed billions of years ago or just a few nanoseconds ago.

According to Wilczek, he once asked Dyson what is the most important lesson from quantum field theory which one does not know using quantum mechanics and special relativity separately. Dyson answer "why, that electrons are the same, of course !".

 

[fermi]

... According to Wilczek, he once asked Dyson what is the most important lesson from quantum field theory which one does not know using quantum mechanics and special relativity separately. Dyson answer "why, that electrons are the same, of course !".

Well, "electrons are the same" even in quantum mechanics, not just in QFT. If two electrons can be different, the Pauli exclusion principle makes no sense at all. We don't need to anti-symmetrize multi-particle wave functions, if you can tell the difference between two electrons. Try calculating Lithium atom ground state assuming the electrons can be distinguished. It gives an answer badly off target. So, even though I fully agree with your answer to the original question, I disagree that you need QFT to get there. QM alone is enough. (I guess I just disagreed with Dyson, so I deserve to get ten lashes...)

 

[humanino]

That's why we call it the Pauli exclusion "principle" and not "theorem". You can prove the identity of two electrons in QFT, you do not need to postulate it (this just stems from the (anti)commutator of the creation/annihilation operator for (fermions) bosons).

 

[Vanadium 50]

There's also evidence from thermo that this is so: the Gibbs paradox.

 

[DrChinese]

No two atoms can be identical. Though performing seemingly identical tasks, each individual atom is either side (isotopically) of the definitive elemental. May I therefore assume that, theoretically, every atom in existence could be lined up end to end? I would be grateful if you could confirm this because it has massive implications for my theory of 'Omniparticle-residue'.
Thank you
Mark...

I hope you have walked away with the idea that the above cannot be considered correct in any meaningful way. There are many nuances to these concepts as well.

 

[mark noble]

The only way two separate particles can be integrally identical is if they are one particle in two different places : The fact that one particle can be in two different places is, in itself, ridiculous. Any object, whether galactic or subatomic, must, by its alternate environment, be, no matter how miniscule, different to the other... No two objects in this or any realm of physicality can, due to alternate location in relative time and space, be identical.
If, indeed, the Electron is absolutely invariable then it must, no matter how impossible it may seem, be a singular event : A constant, unfluctuating energy particle, that is everywhere at once.

 

[SpectraCat]

The only way two separate particles can be integrally identical is if they are one particle in two different places : The fact that one particle can be in two different places is, in itself, ridiculous. Any object, whether galactic or subatomic, must, by its alternate environment, be, no matter how miniscule, different to the other... No two objects in this or any realm of physicality can, due to alternate location in relative time and space, be identical.
If, indeed, the Electron is absolutely invariable then it must, no matter how impossible it may seem, be a singular event : A constant, unfluctuating energy particle, that is everywhere at once.

Except we know from quantum mechanics that what you have written above is not correct, at least not in any way that is physically meaningful. There are consistent experimental and theoretical demonstrations that prove the fundamental indistinguishability of particles, for example the Pauli exclusion principle, the heat capacities of homonuclear diatomic gases, the spectroscopy of multi-electron atoms and molecules. All of these are example of cases where the physical results show that we cannot tell the difference between one particle and another.

Your point is only valid in the macroscopic world, where when facing two identical things, we can point at one and say, "I call that one 'Charlie', and the other one 'Sam'", so I can tell them apart. Of course, if you turned your back and someone swapped them, you would not be able to tell when you turned around. If all you had to identify them was their spatial positions (and/or velocities) you could not be sure that 'Charlie' had not been swapped with 'Sam'. In physics we call this property 'symmetry', and the 'swapping of identical particles is called a 'permutation'. These are fundamental concepts with deep physical significance.

The upshot of all this is that when dealing with the microscopic world, to use the above analogy, our back is always turned. Our measurements do not generally have the resolution to allow us to name electrons 'Charlie' and 'Sam', and so we must always account for the possibility that they have been swapped when making quantum mechanical calculations .. this is often called 'exchange'.

So, while what you have written may resonate with you philosophically, that is as far as it goes. In physics, we have to deal with symmetry, permutation and exchange, which arise from the fundamental indistinguishability of sub-atomic particles and atoms.

 

[Redbelly98]

The only way two separate particles can be integrally identical is if they are one particle in two different places

This is not true.
There has never been observed any measurable difference in the properties (mass, charge, etc.) of, for example:

• different atoms of Carbon 12
• different electrons
• etc.

...my theory of 'Omniparticle-residue'...

What you don't realize is that such discussions are off-limits at Physics Forums. Our main purpose is to teach and discuss the current state of science, math, and technology. Get your theory accepted and published in a peer-reviewed scientific journal first, then (and only then) can you offer it up for discussion, critique, whatever at our forum.

 

[PTM19]

This is a somewhat tricky subject. Even though all electrons are considered identical in physics they can still have different energy, different momentum, different spin, different position, different past, and different future.

It is therefore at least partly due to the way physicists abstracted physical reality into separate concepts that they consider all electrons the same. Momentum for example is not a defining feature of an electron which differentiates it from other electrons but rather a temporary property of electrons.

Alternative abstractions are also possible - one could for example say that each electron with a different momentum is actually a different object. Such definition would be perfectly valid if used consistently but it would be less useful for a number of reasons. The main are that momentum often changes and that it is applicable to many more entities besides electrons so it's better to abstract it as a separate concept.

So whether entities are considered identical or not is at least partly a matter of semantics.

 

[SpectraCat]

This is a somewhat tricky subject. Even though all electrons are considered identical in physics they can still have different energy, different momentum, different spin, different position, different past, and different future.

It is therefore at least partly due to the way physicists abstracted physical reality into separate concepts that they consider all electrons the same. Momentum for example is not a defining feature of an electron which differentiates it from other electrons but rather a temporary property of electrons.

Alternative abstractions are also possible - one could for example say that each electron with a different momentum is actually a different object. Such definition would be perfectly valid if used consistently but it would be less useful for a number of reasons. The main are that momentum often changes and that it is applicable to many more entities besides electrons so it's better to abstract it as a separate concept.

So whether entities are considered identical or not is at least partly a matter of semantics.

No, because your analysis does not consider the effects of electron exchange. Consider an excited helium atom in the 1s¹2p¹ configuration, the electron in the 2p orbital has a different energy,momentum and angular momentum than the one in the 1s orbital. So, by your definition they should be distinguishable. However, we know that this is not true, because if we do not allow for exchange of the electrons, we simply cannot calculate the correct energy for the excited state. Furthermore, if the electrons were distinguishable, then there would be no need for the Pauli exclusion principle, which is one of the most fundamental concepts in quantum mechanics.

My point here is that this a fundamental issue, not a semantic one, and it has deep significance in quantum physics.

 

[PTM19]

No, because your analysis does not consider the effects of electron exchange. Consider an excited helium atom in the 1s¹2p¹ configuration, the electron in the 2p orbital has a different energy,momentum and angular momentum than the one in the 1s orbital. So, by your definition they should be distinguishable. However, we know that this is not true, because if we do not allow for exchange of the electrons, we simply cannot calculate the correct energy for the excited state. Furthermore, if the electrons were distinguishable, then there would be no need for the Pauli exclusion principle, which is one of the most fundamental concepts in quantum mechanics.

As I said it is a tricky subject.

Although by convention distinguishability is tied to exchange it does not have to be. We could distinguish electrons and still allow them to be exchanged.

For example imagine two pool balls which look so similar that you can't tell them apart. From the point of view of pool rules they are indistinguishable - since you can exchange them and the game will remain unaltered. But that is only a convention, in reality we can distinguish them for example by their position on the table, by their momentary speed, by their history and so on.

Physics considers particles in the same way the pool rules consider balls - if their exchange doesn't alter physical picture they are called indistinguishable. But just as with pool balls we can use additional information to distinguish particles, for example electrons in my monitor are distinguishable (in conventional sense) from those in my eye. I can specifically alter the state of electrons in my monitor by turning it off and since electrons in my eye are not affected in the same way they have to differ somehow - there have to exist information which distinguishes them from those in my monitor. So this shows that electrons in my eye and those in my monitor are distinguishable in the conventional meaning of the word.

My point here is that this a fundamental issue, not a semantic one, and it has deep significance in quantum physics.

Well, my point is that semantics does play a significant role.

As another example consider bubble chamber - the case of the atom you mentioned is not a good illustration due to uncertainty principle and measurement problem - I don't want to argue what really happens in the atom.

So imagine we have a picture of tracks of two electrons with very different momentum curving in magnetic field, high momentum one in top part of the picture and low momentum one in bottom part of the picture, their tracks obviously differ by the amount they curve. Now according to conventional definition electrons are indistinguishable because if we exchange electrons - put electron from the top in the place of the one at the bottom and vice-versa then all else being the same - the picture won't change.

That's true but it's more a consequence of the way we defined our concepts then anything fundamental. Specifically it's because unlike charge or mass we don't consider momentum a defining property of an electron (and for good practical reasons) so when we exchange electrons we leave momentum where it was. But as I said that is not the only possibility, if we were using different definitions ones in which momentum is a defining property of electrons on the same footing as charge and mass then we would have to exchange electrons together with their momentum and then the picture would of course change - the track which were more curved before would now be less curved and vice-versa.

So as you can see a change in semantics changes the conclusion.

 

[Vanadium 50]

I don't think the pool balls are a good analogy. The Gibbs paradox tells us that. If I swap two pool balls, I have two different states that look the same. If I swap two electrons, I have the same state.

 

[mark noble]

Hello,
I just want to know, without having to spend the rest of my current existence studying relative equations, is it inconceivable that, although generating similar energy forces, obliging apparent physical mannerisms and performing seemingly identical functions, can ANY object in your particular field of expertise be IDENTICAL to another.
Thank you and goodnight.

 

[SpectraCat]

Hello,
I just want to know, without having to spend the rest of my current existence studying relative equations, is it inconceivable that, although generating similar energy forces, obliging apparent physical mannerisms and performing seemingly identical functions, can ANY object in your particular field of expertise be IDENTICAL to another.
Thank you and goodnight.

And I'd like you to know that you have no idea what you are talking about, for the reasons explained in some detail in this thread. Furthermore, unless you take the time to study the subject matter, you should probably avoid making strong declarative statements about someone else's field. You have not been able to refute anyone of the points in the explanations given to you, nor have you provided evidence to support your position, other than your OPINION. Shouting it from the rooftops or making "dramatic exit" type posts doesn't make it any more correct or convincing.

 

[Vanadium 50]

Asked and answered.