Electrons, how do they work?

[ALine]

How can a electron, being a single point in space, have mass? If it has an infinitely small volume while having a certain mass then wouldn't that mean that it would have infinite density? I don't know I am probably wrong, maybe missing something.

[studiot]

46 minutes ago, ALine said:

How can a electron, being a single point in space, have mass? If it has an infinitely small volume while having a certain mass then wouldn't that mean that it would have infinite density? I don't know I am probably wrong, maybe missing something.

Not a point in space in the way you are thinking of it.

 

For many purposes an electron can be considered as what is called a 'point particle'.

This is defined to be a lump of 'stuff' small enough for its dimensions to be insignificant compared to the other dimensions in consideration.

 

For instance when considering the orbits of the planets, they are considered as 'point particles' in comparison to their distance from the Sun.

 

An electron has actual dimensions around a million times smaller than the atom for instance, whilst the Earth's radius is less than 30,000 smaller than its orbital radius.

[ALine]

Ohhh ok that makes sence. Thanks for the help

[MigL]

How does an electron work ?
Exactly how the math suggests it should.

[Markus Hanke]

It should also be remembered that mass arises from a quantum field’s interaction with the Higgs field, so in some sense it isn’t actually an intrinsic, isolated property at all. Prior to electroweak symmetry breaking, all elementary particles were massless.

[pavelcherepan]

1 hour ago, Markus Hanke said:

It should also be remembered that mass arises from a quantum field’s interaction with the Higgs field, so in some sense it isn’t actually an intrinsic, isolated property at all. Prior to electroweak symmetry breaking, all elementary particles were massless.

Are you certain that electrons interact with Higgs field? I thought it was mostly for gauge bosons.

[swansont]

11 hours ago, studiot said:

 An electron has actual dimensions around a million times smaller than the atom for instance, whilst the Earth's radius is less than 30,000 smaller than its orbital radius.

Nobody has measure a definite finite radius for an electron. They are consistent with zero.

[studiot]

3 minutes ago, swansont said:

Nobody has measure a definite finite radius for an electron. They are consistent with zero.

Indeed, which is why I based my figure smack in the middle of the range that can can currently be found.
This range is very large, larger than the range of atomic sizes for instance.

 

Furthermore zero is a finite number.

Edited July 28, 2018 by studiot

[swansont]

8 minutes ago, studiot said:

Indeed, which is why I based my figure smack in the middle of the range that can can currently be found.
This range is very large, larger than the range of atomic sizes for instance.

 

Furthermore zero is a finite number.

Finite is often used to mean a non-zero number

https://en.wikipedia.org/wiki/Finite_number

"In mathematical parlance, a value other than infinite or infinitesimal values and distinct from the value 0"

[Markus Hanke]

2 hours ago, pavelcherepan said:

Are you certain that electrons interact with Higgs field? I thought it was mostly for gauge bosons.

Unless my understanding of this is badly flawed somewhere (which I can never entirely rule out), then the answer is yes, fermions interact with the Higgs in a manner similar to gauge bosons. From what I remember this is implemented in the (unbroken) Lagrangian via a Yukawa coupling term between the fields. When you break the symmetry, this leaves behind mass terms in the new Langrangian.

[studiot]

1 hour ago, swansont said:

Finite is often used to mean a non-zero number

https://en.wikipedia.org/wiki/Finite_number

"In mathematical parlance, a value other than infinite or infinitesimal values and distinct from the value 0"

Since further discussion about this is offtopic I have started a new thread for folks to express their opinions.

https://www.scienceforums.net/topic/115450-is-zero-finite/