# Uncertainty Principle & W Boson Energy (Mass): Higgs Reconciled?

• nigelscott
In summary, the W boson get their energy by temporarily breaking the energy conservation laws in accordance with the Uncertainty principle. The W boson gets its mass through the Higgs mechanism.
nigelscott
I have read that W boson get their energy (mass) by temporarily breaking the energy conservation laws in accordance with the Uncertainty principle. I have also read that the W bosons get their mass through the Higgs mechanism. How are these two things reconciled? Is this the distinction between a virtual W and a real W?

nigelscott said:
I have read that W boson get their energy (mass) by temporarily breaking the energy conservation laws in accordance with the Uncertainty principle.
Where did you read that? It is completely wrong.
nigelscott said:
I have also read that the W bosons get their mass through the Higgs mechanism.
That is right.

That is a problematic way to try to put formulas into words.
Energy conservation is not violated. The W mass can be "wrong" (lower than the mass of a real W) for virtual particles. That is a violation of the energy/momentum relation, but both energy and momentum are conserved exactly and everywhere. They just don't match the properties a real W would have.

Note that he describes it as "apparent violation" (44:40), it is not an actual violation.

I think his comment is exaggerated.
There is no energy violation, and the energy is conserved in all vertices individually.
The virtual particle however is an off-shell particle, which means that its 4-momentum squared is not equal to the particle's rest mass. In formula what is violated is the equality : $E^2 - |p|^2 c^2 = m^2 c^4$.
The mass would have to be replaced by $s= q_w^\mu q_{w \mu} \ne m_W^2$.

If someone wants to use the Uncertainty principle to describle virtual particles he generally says that there can be fluctuations in energy $\Delta E$ within some time $\Delta t$, that obeys the $\Delta E \Delta t \sim \hbar$. This can help you get an insight about how the particle pops up into being. Of course it's not a real particle, meaning that you cannot observe it. In order to observe it you have to use higher energies and make it pop up into being real (that's a resonance)

OK, so the Higgs mechanism actually generates the mass and the Uncertainty Principle approach is not quite true but gives some insight as to what is going on. So in the case of neutron to proton decay, where a down quark switches to up and emits a W-, what actually happens at the vertex? The Higgs generates the mass and there is a charge transference (weak isospin/weak hypercharge) to the W-. Is this also through the Higgs field or a different mechanism?

The higgs mechanism gives the W boson its mass by letting it interact with the Higgs field's vev... The virtual particle doesn't have the W boson's mass although it's a W.

Also what do you mean by what happens at the vertex? That W boson which appears does not have 90GeV mass (that's impossible from the kinematics). So it should be lighter than 90GeV - should be virtual. What it does is to make the transition of the "quark" and also transfer some momentum.

OK, I think I am getting more confused. The Higgs gives mass to a real W correct? The virtual W has less mass and mediates the down to up quark transition. It has some mass. Where does that mass come from? Apologies in advance for my lack of understanding. I am a QM guy from years ago!

Nowhere, there is no fixed mass.. It's a whole spectrum. It can be any value and that depends on probabilities.
And it comes from the fact that the virtual particle carries some 4mommentum from the quarks to the electron/neutrino.

I believe you need to rethink your perception of what a virtual particle is. It is not something that you can measure. The mass of a field is what it is and is related to the pole of the propagator. Now, Feynman diagrams are a graphical representation of terms in a mathematical expression. They do not "mean" that a reaction occurs in that way, just as little as an electron goes through the left slit in a double slit experiment. What suppresses the terms for weak interactions is that the momentum in that term is way smaller than the value needed to be at the propagator pole, this is what we call an off shell propagator.

OK. I think I got it. Thanks for you help and patience.

## 1. What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, states that it is impossible to know the exact position and momentum of a particle at the same time. This means that the more precisely we know the position of a particle, the less we know about its momentum and vice versa.

## 2. What is the W Boson Energy (Mass)?

The W Boson is a subatomic particle that is responsible for the weak nuclear force. It has an energy or mass that contributes to the overall mass of an atom. Its energy is measured in electron volts (eV) and its mass is measured in GeV (Giga-electron volts).

## 3. How does the Higgs boson reconcile the Uncertainty Principle and W Boson Energy?

The Higgs boson, also known as the "God particle", is a subatomic particle that was theorized to exist in order to explain how other particles acquire mass. Its discovery in 2012 confirmed its existence and helped reconcile the Uncertainty Principle and W Boson Energy by providing a mechanism for particles to acquire mass without violating the Uncertainty Principle.

## 4. What is the relationship between the Higgs boson and the W Boson Energy (Mass)?

The Higgs boson is responsible for giving mass to particles, including the W Boson. Without the Higgs boson, particles would have no mass and the W Boson would not exist. This means that the Higgs boson and the W Boson Energy (Mass) are closely related and dependent on each other.

## 5. What implications does the reconciliation of the Uncertainty Principle and W Boson Energy have in the field of physics?

The reconciliation of these two principles has significant implications for our understanding of the fundamental laws of physics. It helps to explain how particles acquire mass and plays a crucial role in the Standard Model of particle physics. It also opens up new avenues for research and could potentially lead to discoveries of new particles and forces in the universe.

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