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user81619
user81619

You will get a better answer than this but, assuming all you want is a rough analogy compared to your chair idea, here goes.

For a local gauge symmetry analogy, forget the chair.

Imagine you are building a house on rough surface, with the ground sloping all over the place. Obviously you want the floor to be level, no matter how uneven the ground is.

So you have to take into account how to get a level line between two points, say the corners of the building.

A local symmetry has to allow for changes in the ground to keep the line level, so its going to be a function/transformation that does this. We need independent transformations at each point to keep the line level, this is the connection field.

With this connection field come the forces, such as the photons associated with the electromagnetic field, for example.

Compare this to a global symmetry, which as you say, means you've changed nothing that can be measured.

A global symmetry is basically an overall phase factor, it is a trivial symmeterysymmetry, whereas a local symmetry has to preserve properties across a wide range of "uneven ground".

You will get a better answer than this but, assuming all you want is a rough analogy compared to your chair idea, here goes.

For a local symmetry analogy, forget the chair.

Imagine you are building a house on rough surface, with the ground sloping all over the place. Obviously you want the floor to be level, no matter how uneven the ground is.

So you have to take into account how to get a level line between two points, say the corners of the building.

A local symmetry has to allow for changes in the ground to keep the line level, so its going to be a function/transformation that does this. We need independent transformations at each point to keep the line level, this is the connection field.

With this connection field come the forces, such as the photons associated with the electromagnetic field, for example.

Compare this to a global symmetry, which as you say, means you've changed nothing that can be measured.

A global symmetry is basically an overall phase factor, it is a trivial symmetery, whereas a local symmetry has to preserve properties across a wide range of "uneven ground".

You will get a better answer than this but, assuming all you want is a rough analogy compared to your chair idea, here goes.

For a local gauge symmetry analogy, forget the chair.

Imagine you are building a house on rough surface, with the ground sloping all over the place. Obviously you want the floor to be level, no matter how uneven the ground is.

So you have to take into account how to get a level line between two points, say the corners of the building.

A local symmetry has to allow for changes in the ground to keep the line level, so its going to be a function/transformation that does this. We need independent transformations at each point to keep the line level, this is the connection field.

With this connection field come the forces, such as the photons associated with the electromagnetic field, for example.

Compare this to a global symmetry, which as you say, means you've changed nothing that can be measured.

A global symmetry is basically an overall phase factor, it is a trivial symmetry, whereas a local symmetry has to preserve properties across a wide range of "uneven ground".

Source Link
user81619
user81619

You will get a better answer than this but, assuming all you want is a rough analogy compared to your chair idea, here goes.

For a local symmetry analogy, forget the chair.

Imagine you are building a house on rough surface, with the ground sloping all over the place. Obviously you want the floor to be level, no matter how uneven the ground is.

So you have to take into account how to get a level line between two points, say the corners of the building.

A local symmetry has to allow for changes in the ground to keep the line level, so its going to be a function/transformation that does this. We need independent transformations at each point to keep the line level, this is the connection field.

With this connection field come the forces, such as the photons associated with the electromagnetic field, for example.

Compare this to a global symmetry, which as you say, means you've changed nothing that can be measured.

A global symmetry is basically an overall phase factor, it is a trivial symmetery, whereas a local symmetry has to preserve properties across a wide range of "uneven ground".