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But a photon has no charge either, right? So both particles have little or no mass, travel close to or at the speed of light, have no charge, but the photon has an electromagnetic field whereas the neutrino doesn't. I understand the particle-wave duality but, from the particle perspective, how does a particle without a charge have an electromagnetic field? I mean, other than by definition, or perhaps that's what it is -- a defined particle to make the mathematics work.

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Photons *are* electromagnetic fields, or rather waves in the electromagnetic fields ...

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Neutrinos interact only via the weak interaction. Photons interact via the electromagnetic interaction. The weak interaction is much weaker than the electromagnetic interaction.

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I understand the particle-wave duality but, from the particle perspective, how does a particle without a charge have an electromagnetic field? I mean, other than by definition, or perhaps that's what it is -- a defined particle to make the mathematics work.

It is a difference between waves and waves, all waves do not carry same information.

How a particle without charge has an electromagnetic field you will probably learn in a class in electrodynamics.

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It is a difference between waves and waves, all waves do not carry same information.

OK, so how do you distinguish between waves?

so if I give you a wave function (as in a map from R^4 to C) how can you tell

if this corresponds to a photon, or a neutrino...or the entire universe for that matter.

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The photon wave carries the density of E and B, and the Neutrino the corresponding density for the weak force (roughly speaking).

A photon, in quantum field language, is the quanta of the electromagnetic field - a vector field (spin 1). A Neutrino is a quanta of a fermion field (spin 1/2). So the photon and the neutrino has many differences mathematically, but this you will learn later in school.

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mathematically one can not, but physics also deal with quantities and units.

what! what calculations can you do in "physics" that you can't do mathematically.

The photon wave carries the density of E and B, and the Neutrino the corresponding density for the weak force (roughly speaking).

A photon, in quantum field language, is the quanta of the electromagnetic field - a vector field (spin 1). A Neutrino is a quanta of a fermion field (spin 1/2). ...

you are really mixing all sorts of objects here. Let's restrict to the "scalar" case

(R^4 to C). We can deal wil spin 1/2, spin 1,... independantly. For example for

spin 1/2 : how do you distinguish between any two maps R^4 to C^2. That aside,

I think I know what you're trying to say as far the photon "carrying em field" and

a neutrino "corresponding to weak force density" so let's fix the gauge group to

be the electroweak SU(2)xU and let's look at the right handed neutrino which is

a scalar...how do you distinguish between two scalar functions in this setting?...

So the photon and the neutrino has many differences mathematically, but this you will learn later in school.

followed by many more years of unlearning

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You are trying to describe particle physics with inappropriate language, you must to it in quantum field theory. You are trying to describe it with wave-equations.

Let us instead do the comparison between ultra relativistic electrons and neutrinos, both which are fermions. Electrons have interactions which are both weak and EM, neutrinos only weak - hence electrons which moves at same speed as neutrinos will be absorbed more easily than the neutrinos. Just have a look at the Standard Model Lagrangian and derive all possible interactions.

It is not true that neutrinos travels close to light speed, that is a reference dependent statement! You can find a frame of reference where the neutrino is non-relativistic, so you can't logically say that since it has no charge and travel close to light speed it should interact similar as the photon does. So logically your argument fails there, since the neutrino speed is a reference dependent statement and interactions are frame independent.

You derive what interactions particle has by inspecting the SM - Lagrangian interaction terms, not by looking at particle speeds in some reference frame.

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a + b = c

where a,b and c are real numbers.

in physics, a, b and c must have the same units:

1kg + 5m = what?

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Malawi is right. This is not even a "high-energy physics" question. Take the x-component of the magnetic as a function of y, and take the temperature as a function of time. Those are two real function of a single real variable. How do you distinguish ?how do you distinguish between two scalar functions in this setting?

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Thanks for all the replies. I understand this a lot better now.

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Malawi is right. This is not even a "high-energy physics" question. Take the x-component of the magnetic as a function of y, and take the temperature as a function of time. Those are two real function of a single real variable. How do you distinguish ?

Actually both of you are way off...we probably

speak different languages and a lot is being lost in the translation...

let's leave it at that.

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OK, so how do you distinguish between waves?

so if I give you a wave function (as in a map from R^4 to C) how can you tell

if this corresponds to a photon, or a neutrino...or the entire universe for that matter.

the wavefunction just tells you the probability density to detect a particle at a certain position with a certain momentum - it has nothing to do with interactions. Quantum Mechanics is not enough to describe particle physics, you need quantum field theory.

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the wavefunction just tells you the probability density to detect a particle at a certain position with a certain momentum - it has nothing to do with interactions. Quantum Mechanics is not enough to describe particle physics, you need quantum field theory.

Actually, this raises another question I’ve had, related to time dependence of the wave function.

Say I generate a single photon from a laser with the laser pointed along the x direction at a known time. I realize QM says that there is uncertainty on the photon’s position over time, as described by the probability density of the wave function. Does the wave function itself evolve over time, or does it remain the same as it was when the photon was generated?

Not sure if this is the correct way of thinking about it, but I’m thinking of the photon’s wavefunction traveling in the x direction and its probability density being spread along the y-z plane centered along the x-axis with a certain variance. With this thought, my question is, does this density function continue along the x-axis but with increasing variance along the y-z plane? Or does its variance remain the same as it was at the beginning?

The reason for my question is that if the wave function expands with time, it seems that the photon would have a higher probability of being absorbed by nearby matter over time or, if not absorbed, in the end it could be just about anywhere in the universe.

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