Mathematical Quantum Field Theory -- Equations? So what?

[John1945]

<< Mentor note -- posts broken off from an Insights comment thread >> [/color]

Typo in proof of example 2.23: "hatv".

Ok, this is where I show my ignorance, but all this is theoretical and why I get lost with these academia discussions. Time is just a mathmatical construct to measure the motion of two or more objects relative to each other. What is the so what here? We can write an equation to describe anything but it does not make it true or part of our world.

 

[Nugatory]

What is the so what here? We can write an equation to describe anything but it does not make it true or part of our world.

The "so what" here is that quantum field theory is one of the most accurate mathematical descriptions of how our world works that humanity has discovered. You are right that not all equations and mathematical structures are "true or part of our world", but the stuff that Schreiber is describing here is part of our fundamental understanding of the universe that we live in.

[Edit: After I wrote this post, the Mentors moved the entire discussion into a new thread, so the part below about starting a new thread is irrelevant - it's already happened, and you're reading the new thread right now]
If you want further discussion of why quantum field theory is relevant, it would be best to start your own thread in the "General Physics" section, as this thread is for people who already understand its relevance and what to understand the theory itself more deeply. But please be mindful of the Physics Forums mission statement:

Our mission is to provide a place for people (whether students, professional scientists, or others interested in science) to learn and discuss science as it is currently generally understood and practiced by the professional scientific community.​

 

[Dale]

Time is just a mathmatical construct to measure the motion

This is a self contradiction. Mathematical constructs cannot measure physical quantities.

 

[strangerep]

We can write an equation to describe anything but it does not make it true or part of our world.

The stunning revelation in theoretical physics comes after you crunch away at the math, find it predicts a hitherto-unknown phenomenon, which is subsequently confirmed by careful experiments in the real world.

 

[Urs Schreiber]

Ok, this is where I show my ignorance, but all this is theoretical and why I get lost with these academia discussions. Time is just a mathmatical construct to measure the motion of two or more objects relative to each other. What is the so what here? We can write an equation to describe anything but it does nfo ot make it true or part of our world.

Just got back from a short off-line vacation with family. I gather your comment is about the series A first Idea of Quantum Field Theory. I am not sure what the exact question is, but I sense that you are finding the mathematics too abstract for your liking.

Me, too, I am enamoured with simplicity and elegance in the foundations of physics, and if anyone points out where my exposition is more complicated than necessary, I will try to improve on it. But not to throw out the baby with the bathwater, one must beware not to make it simpler than possible, and not to mistake concepts appealing to everyday intuition with simplicity in the structure of foundational physics, which is far remote from what our senses evolved to grasp. If there is simplicity to be found in fundamental physics, then it is economy of mathematical concepts:

Philosophy [ meaning natural philosophy, i.e. physics ] is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics [...] without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.

 

[bhobba]

We can write an equation to describe anything but it does not make it true or part of our world.

I am, going to give a slightly different answer than others.

First you need to be clear what is 'true' and what is 'part of our world'. You will not find that easy. Philosophers have been arguing about it for centuries.

In physics its simple - what does it predict and can it be tested. If the test is in accord with the theory its a good theory - otherwise down the gurgler it goes. What Urs is writing about has well and truly passed that test. It's described in quite advanced math - but nobody ever said natures secrets were easy to describe.

Thanks
Bill

 

[zonde]

In physics its simple - what does it predict and can it be tested. If the test is in accord with the theory its a good theory - otherwise down the gurgler it goes.

My guess about OP question is along the same line. I would say the question is about connection of math to experimental observations. But then it would be nice to hear from OP if it's so.

 

[Urs Schreiber]

I would say the question is about connection of math to experimental observations.

By the way, in the philosophy of physics, the technical term for this connection is "coordination".