I Are All Electrons Truly Identical?

[Sciencelad2798]

TL;DR Summary

If so how, and why?

I'm just confused on whether not all electrons are identical and if they are, how they are.

 

[Henryk]

Yes, they are
Same mass, same charge, same spin, same magnetic moment, all of their properties are the same.

 

[Sciencelad2798]

Yes, they are
Same mass, same charge, same spin, same magnetic moment, all of their properties are the same.

How is it possible theyre all identical though?

 

[Dale]

This question makes no sense to me. Why would being the same be impossible? Why would being different be impossible? What does sameness have to do with possibility?

I just don’t see any connection at all between the two concepts

 

[symbolipoint]

Summary:: If so how, and why?

I'm just confused on whether not all electrons are identical and if they are, how they are.

BECAUSE THEY LIKE THAT!Good luck with the question. One images no progress will be made in the discussion. The physicists can check some properties; maybe they know all the possible properties, and maybe they as yet do not. For now, just accept that all electrons are identical.

 

[symbolipoint]

I just can't resist this:

What one electron said to another electron - "Stay away from me! I can't tolerate you crowding my space!"

 

[Baluncore]

Are all electrons identical?

Yes.
You see an electron in many different places, at many different times.
How do you know there is more than one electron ?
If you cannot tell the difference between two electrons, how can they not be identical ?

 

[vanhees71]

I think the problem is to use of the word "identical". One should rather use "indistinguishable". Besides this linguistic quibble the question is definitely in the wrong forum, because it's a specific quantum-theoritical issue. In classical physics point particles are always distinguishable by their trajectories in phase space, and if it comes to statistical mechanics this apparently obvious property is a problem rather than a feature. It's one of the first examples in the history of science, which indicated that incompleteness of the classical description of matter!

 

[Herman Trivilino]

How is it possible theyre all identical though?

Because they are fundamental particles. They have no internal structure.

 

[vanhees71]

I think the problem is to use of the word "identical". One should rather use "indistinguishable". Besides this linguistic quibble the question is definitely in the wrong forum, because it's a specific quantum-theoritical issue. In classical physics point particles are always distinguishable by their trajectories in phase space.

 

[Drakkith]

How is it possible theyre all identical though?

Put a dozen electrons in a dozen different boxes, each labeled 1 through 12. Then get a bigger box and empty all the smaller boxes into it. Now close the box and shake it around. Then open it, reach in, and grab an electron. You will not be able to tell which box the electron originally came from because there is no way to distinguish it from its brothers and sisters. It has the same mass, charge, spin, and other observable properties. That's what we mean when we say that they are identical.

 

[Sciencelad2798]

Put a dozen electrons in a dozen different boxes, each labeled 1 through 12. Then get a bigger box and empty all the smaller boxes into it. Now close the box and shake it around. Then open it, reach in, and grab an electron. You will not be able to tell which box the electron originally came from because there is no way to distinguish it from its brothers and sisters. It has the same mass, charge, spin, and other observable properties. That's what we mean when we say that they are identical.

I'm still kinda confused on why they're all indistinguishable. Like I still don't get how it's possible for all electrons to have the same exact mass

 

[Dale]

Like I still don't get how it's possible for all electrons to have the same exact mass

You still have not explained why you think the concept of electrons being the same is at all related to their possibility of existing. Why should being identical or being non-identical have anything to do with they possibility or impossibility of their existence.

They are completely independent concepts that have no bearing on each other as far as I can see. What connection do you see?

 

[Sciencelad2798]

You still have not explained why you think the concept of electrons being the same is at all related to their possibility of existing. Why should being identical or being non-identical have anything to do with they possibility or impossibility of their existence.

They are completely independent concepts that have no bearing on each other as far as I can see. What connection do you see?

I guess I think that the fact they're all identical, shows some fine tuning in the universe

 

[Gaussian97]

I'm still kinda confused on why they're all indistinguishable. Like I still don't get how it's possible for all electrons to have the same exact mass

On a more fundamental level, there exists what we call an 'electron field' (really, it's a combination of 4 fields that are intimately related). What we observe as an electron is either an excitation of the field or just some interaction of this field that affects our measurement devices in some way.

Then the properties of these electrons can have two sources, is that property arising by the particular form of the excitation? Or is it arising due to fundamental properties of the field?
The first kind of properties are, of course, exclusive to each 'individual electron', such properties may be the position of the electron, the velocity of the electron or its energy.
The second kind of properties, because are properties of the field itself and doesn't depend on the details of the excitation, must be shared for any excitation, i.e must be exactly the same for all the electrons. Examples of such properties are spin, charge and, as you may guess, mass.

So, in short, all electrons have the same mass (and other properties like charge, etc) and we call them indistinguishable because they are just manifestations of the same fundamental object, the field.

 

[Sciencelad2798]

On a more fundamental level, there exists what we call an 'electron field' (really, it's a combination of 4 fields that are intimately related). What we observe as an electron is either an excitation of the field or just some interaction of this field that affects our measurement devices in some way.

Then the properties of these electrons can have two sources, is that property arising by the particular form of the excitation? Or is it arising due to fundamental properties of the field?
The first kind of properties are, of course, exclusive to each 'individual electron', such properties may be the position of the electron, the velocity of the electron or its energy.
The second kind of properties, because are properties of the field itself and doesn't depend on the details of the excitation, must be shared for any excitation, i.e must be exactly the same for all the electrons. Examples of such properties are spin, charge and, as you may guess, mass.

So, in short, all electrons have the same mass (and other properties like charge, etc) and we call them indistinguishable because they are just manifestations of the same fundamental object, the field.

Ah that makes sense, thank you

 

[Dale]

I guess I think that the fact they're all identical, shows some fine tuning in the universe

That is an unjustified conclusion, but even if you think something required fine tuning what would be impossible with a fine tuned universe?

The point is that it is clearly possible since we observe the fact. So any thought that you have that makes it impossible is clearly incorrect. Such a thought is contradicted by observation.

 

[hutchphd]

This question makes no sense to me. Why would being the same be impossible? Why would being different be impossible? What does sameness have to do with possibility?

I think in classical mechanics the notion of identical particles is fraught. The question naturally arises "how much identical ?" The identity of a particle is in principle capable of ascertainment from careful historical tracing of that particle. In QM the answer is more clear cut.

And (for the OP) neither forms an existence proof for an almighty being.

 

[PeterDonis]

Moderator's note: Moved thread to Quantum Physics forum.

 

[PeterDonis]

I think in classical mechanics the notion of identical particles is fraught.

Indeed. And we already know electrons are not classical particles anyway, and the question of why all electrons are identical requires quantum mechanics to answer (more precisely, quantum field theory, per the answer @Gaussian97 gave in post #15) . Hence, I have moved this thread to the quantum physics forum.

 

[PeterDonis]

You see an electron in many different places, at many different times.
How do you know there is more than one electron ?

This is a different question from the OP's question. Saying that all electrons are identical is not the same as saying there is only one of them. The latter is a much stronger claim (and one which no physicist thinks is true--the one historical attempt at such a theory, based on a speculation by Wheeler, did not work out).

 

[vanhees71]

That's why I said above "identical" is not a good name for the discussed issue. It's better to call it indistinguishability.

The modern approach to the description of (elementary) particles is relativistic quantum field theory and the use of symmetry principles, which finally lead to the Standard Model of particle physics.

One starts with the Poincare symmetry of the relativistic spacetime model, Minkowski space and the fundamental principles of quantum theory (QT), according to which Lie symmetries are represented by unitary ray representations of the corresponding symmetry group. In the case of the Poincare group all irreducible ray representations can be lifted to unitary irreducible representations of the covering group, where the Lorentz subgroup of the Poincare group is substituted by $\mathrm{SL}(2,\mathbb{C})$.

The classification of these representations together with the demand to have "microcausality", i.e., that the operators that represent local observables commute at space-like separated arguments, leads to representations which physically either represent massive or massless "particles". The mass squared is a Casimir operator of the Poincare group, leading to the energy-momentum relation, $p_{\mu} p^{\mu}=m^2 c^2$.

The massive representations are further characterized by the spin of the corresponding field, which takes the values $0,1/2,1,3/2,\ldots$. It tells you the representation of rotations (and angular momentum as it's generators) in the rest frame of the particle. One should note that it is convenient and standard convention to represent all quantities that refer to intrinsic properties of a massive particle (i.e., not referring to the state of motion like energy, momentum) in the rest frame of this particle.

The massive representations are also characterized by a "spin", but there's of course no rest frame, and the only way to define the intrinsic spin-like properties of massless particles is to look at the helicity, i.e., the projection of the angular momentum to the direction of the momentum of the massless particle (which cannot be "at rest", because it moves with the speed of light wrt. any inertial reference frame). These can always take only two values $\pm s$ (with $s \in \{0,1/2,1,3/2,\ldots \}$).

Further it is clear that particles can only be distinguished by their intrinsic properties. In our yet pretty rough characterization by the irreducible representations of the Poincare group that's just mass and spin. In general it's impossible to distinguish individual particles by trajectories in phase space as in classical physics, due to the Heisenberg uncertainty relation between position and momentum (for massive particles; massless particles don't even admit the definition of a proper position observable at all, at least if they have $s \geq 1$). In 3 (or more) spatial dimensions this leaves only the possibility of particles to be either fermions or bosons, i.e., two many-body states where only two indistinguishable are interchanged are in fact the same state, and the corresponding state vector either stays the same (bosons) or is multiplied by (-1) (fermions), i.e., the states are either symmetric (bosons) or antisymmetric (fermions) under exchange of any pair of indistiguishable particle.

Together with the microcausality condition of relativistic QFT and the demand that the energy should be bounded from below, so that a stable ground state exists, one concludes that (a) for each particle there's always a corresponding antiparticle of the same mass (it can also be that particle and antiparticle are the same particle, which is then called a "strictly neutral particle", as becomes clear as soon as one considers interactions), and (b) particles with integer spin must be bosons; particles with half-integer sspin must be fermions.

Of course, the classification of the particles must be extended concerning the various charges which describe which interactions each particle participates in, and this leads to all the charges of the standard model (color for the strong interaction, flavor and electric charge (or hypercharge) for the electroweak interaction), but that doesn't change the fundamental point of the indistinguishability, it just adds "intrinsic quantum numbers" that make the different particle sorts distinguishable, but if two particles carry the same intrinsic quantum numbers, they are indistinguishable, i.e., they are either bosons or fermions, characterized by the behavior of their many-body state vectors under exchange of two indistinguishable particles (either symmetric for bosons or antisymmetric for fermions).

 

[ohwilleke]

Summary:: If so how, and why?

I'm just confused on whether not all electrons are identical and if they are, how they are.

Mostly. Electrons can differ in parity, location, and momentum.

 

[PeterDonis]

Why are the charges of protons and electrons even?

Because that's how things work out in the Standard Model of particle physics.

 

[Sciencelad2798]

Because that's how things work out in the Standard Model of particle physics.

I know this is theoretical, but that's quite the coincidence, no?

 

[Baluncore]

Some history and light reading on the subject.
https://en.wikipedia.org/wiki/One-electron_universe
https://en.wikipedia.org/wiki/Identical_particles

 

[PeterDonis]

I know this is theoretical, but that's quite the coincidence, no?

No.

Your question has been answered. Thread closed.