James Fodor

speaker

3,084 appearances 4 recordings 1 series first heard Jun 2026 last heard 30 Aug

James Fodor’s voice in public audio — every appearance, attributed to the second.

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Recordings per month over the last 12 months — 4 in all, peaking in Aug 2026 with 2.

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The Science of Everything Podcast · Episode 164: Gauge Theory and the Higgs Boson · 30 Aug 2026 podcast

This this um So the physicist trying to work out what are the conditions that we have to impose uh like mathematically in order to make it so that this gauge symmetry doesn't change the experimental results.

There was an extra degree of freedom, so we need to impose extra structure in order to get the result not uh being dependent on the extra degree of freedom.

And they worked out that a very specific mathematical choice actually m meant that the any dependency on the on this internal degree of freedom is cancelled out and the results are always independent of of the choice of gauge.

So you can choose different gauges and and get the same answer.

So what was this mathematical trick that they needed to use?

Well, it turns out that's very interesting.

Remember I said earlier that an internal degree of freedom gives rise to a symmetry.

In this case, the extra phase that we have in the uh that's not measurable, the f the phase of the photon, form that by

A global transformation, so the same everywhere, like just add the same mass of the field everywhere throughout space and time, uh, then that gives that doesn't change the theory and that gives rise to the symmetry which is corresponds to the conservation of charge.

Well, it turns out that if we modify this symmetry to make it a local symmetry instead of a global symmetry, the result is actually that this gauge term is effectively cancelled out.

And so we can pick any gauge we like.

How does this work?

Well, uh so-called upgrading.

the symmetry from a global symmetry to a local symmetry means that instead of changing the field by a constant at every point in space and time, just like adding five to it, instead, now the transformation is a function of our coordinates, of our x-coordinates.

So the the transformation of the field is a function of x, where x is just space-time coordinate.

So this means that in one point in space-time we could increase the field by one, and in another point we could decrease it by two, and in another we could increase it by seven.

I'm just using arbitrary unity to illustrate the point, right?

Um so it's not that we're shifting the field by uh the phase rather by a constant amount, is that we're shifting it by different amounts.

Uh in fact an arbitrary function.

We like we don't specify specifically, we just write it as an arbitrary function.

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