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## Main Question or Discussion Point

**Local Gauge Symmetry ??**

Trying to understand local gauge symmetry

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I have an undergraduate degree in physics, so I know basic quantum mechanics, but that's all.

Still, I'm trying to understannd the concept of local gauge symmetry.

I would appreciate if someone could tell me what's wrong with my point of view.

So here is my understanding of it:

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As an example, consider the classical Newtonian equation for the gravitational force between masses m1 and m2 at position x1 and x2 on the x-axis.

It is F = G m1 m2 / (x2 - x1)^2 .

Now if we replace x1 and x2 with x1+k and x2+k, we get the same equation and the same force F.

So here we have a global gauge symmetry.

What are the physically real value of x1 and x2 ?

They don't have physically real values, cause they are not measurable.

So let's go one step further and replace x1 and x2 with x1+k1 and x2+k2.

We now have a local gauge symmetry.

That's fine except now we don't get the same equation, nor the same force.

So let's add a new field or force to compensate for that.

But that new field is arbitrary, since it is function of the arbitrary values for k1 and k2.

And that new field has no physical reality, it is not measurable (how could it be, since it is arbitrary?)

So how can we switch to local gauge symmetry if it changes measurable values?

How does postulating a new compensating field help anything?

I don't understand what is gained by doing this.

All this doesn't make sense to me.

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