# Higgs wave experiment?

Is the Higgs Boson like a wave made in the pool?

An electron is an excitation of the electron field. So when we observe a higgs boson that means we've excited the higgs field?

If particles are excitations what are their fields?

How the Higgs field exist if the Higgs boson is unstable?

What is the relationship between a gravitational wave and a graviton?

Now we know that the photon is the excitation of the EM field.

We know that the graviton is the excitation of the gravitational field.

We know that the EM wave consists of a herd of photons as per QM.

We know that the GW consists of a herd of gravitons as per QM.

The answers said that the Higgs boson is the excitation of the Higgs field.

But none of these answers were talking about the Higgs boson and if the Higgs boson, when in a herd, represents the Higgs wave or not as per QM.

Question:

1. Is there a Higgs wave (just like EM wave and GW)?

2. Is the Higgs wave (if exists) a herd of Higgs bosons, and is there any experiment where we try to detect Higgs waves?

• "We know that the graviton is the excitation of the gravitational field" - It's more like we have defined the graviton to be a quantized excitation of the gravitational field assuming that the gravitational field quantizes in the same way as the gauge fields. There is no theory involving gravitons that has any credible supporting evidence yet, and it could be that gravity simply works completely differently on that scale, in such a manner that a graviton might not even exist. – probably_someone Jul 3 '18 at 1:12
• You seem to be mixing the concepts of classical and quantum fields. The correct statements would be as follows. "Now we know that the photon is the excitation of the quantum EM field", and, "We know that the classical EM wave consists of a herd of photons as per QM" – safesphere Jul 3 '18 at 4:52

1.Is there a Higgs wave (just like EM wave and GW)?

Quantum field theory for particle physics, posits for all elementary particles in the table,

a field. This is a mathematical field, represented by the free particle wavefunctions of the corresponding particle in the table. An electron field, a photon field, a gluon field, a Higgs field, ... at each space time point. It is based on the postulates of quantum mechanics, a mathematical extension and tool.

It is like a Lorentz invariant version of a special aether for each particle, where measured particles with their fixed mass and quantum numbers are defined by creation and annihilation operators at each space time point. Thus a particle is like a disturbance on its corresponding field. Because the field is in all space time, and the free particle wavefunction covers the whole space time, to get a localized particle, an electron, one has to use the concept of wavepackets, but that is an other story.

The QFT model is very good because it allows the Feynman diagram representation for interactions and decays, and simplifies calculations of real numbers to be compared with experiment.

So the Higgs boson is an excitation on all spacetime permeating Higgs field, ( as with other particles and fields). The difference lies in the vacuum expectation value, VEV, of the Higgs field versus all the other particles, which is the mechanism that the Higgs field gives masses to the particles in the table. The Higgs field has a 246GeV VEV, whereas all other particles in the table have a zero VEV

The electromagnetic wave is a superposition of real photons, and the gravitational wave is a superposition of real gravitons ( if they exist) and is an emergent classical level from the underlying quantum mechanical, and should not be confused.

1. Is the Higgs wave (if exists) a herd of Higgs bosons, and is there any experiment where we try to detect Higgs waves?

No and no, as explained above. There is no Higgs wave , as the Higgs boson has a mass, in contrast to the photon and the graviton (if it exists). The Higgs boson is an excitation of the Higgs field, and its discovery is important because it validated the standard model of particle physics, which needs the Higgs field for the generation of masses.

Edit after comment by OP:

What makes me confused is when they say that an electron can behave like a wave. But the electron has rest mass. Is that just a mathematical description for the propagation of the electron that we call wave in that case? – Árpád Szendrei

Electromagnetic waves, and gravitational waves are classical models representing accurately what happens and is observed in experiments, down to sizes comensurate to $h$, i.e when sizes and velocities introduce the heisenberg uncertainty and quantum mechanical effects become dominant. These are an underlying level from which the classical has to emerge if our underlying theory is correct. By all the data and observations we have , the underlying level of all nature is quantum mechanical and the emergence from this of the classical fields, like the electric, etc can be demonstrated .

The quantum mechanical level is also modeled by wave equations., BUT, in contrast to the classical waves, it is not a wave of energy that is displayed in space time, but a probability wave . See my answer here on this. One needs many "events" with the same boundary conditions for the quantum mechanical equations , to build up the interference patterns predicted by the quantum mechanical wave equations.

Thus the electron "wave" behavior is a different manifestation than the classical electromagnetic or gravity waves, where there, it is the energy carried by the wave that is being transferred through a vacuum with velocity c, that is waving. Other waves, like acoustic and water waves, transfer the energy in a medium. A single electron can only be detected once at an (x,y,z,t) point and has a fixed four momentum vector.

So a Higgs boson, if it were long lived, would have left a point by its decay in a detector, and an accumulation of such points would show a wave nature, given similar boundary conditions as in the double slit experiments.

An electron beam can show collectively the patterns, thus in principle able to transfer energy in a medium, with wave properties, but this wave cannot be confused with the theoretical waves built up by zero mass gauge bosons macroscopically that do not need a medium to appear and transfer energy in spacetime.

• Thank you. Can you please tell me where you say "There is no Higgs wave , as the Higgs boson has a mass, in contrast to the photon and the graviton (if it exists)". Do you think that the wave can only be of a herd of massless bosons? – Árpád Szendrei Jul 3 '18 at 16:13
• Yes, if one wants to keep to the classical wave equations as they will emerge from the quantum mechanical. This blog post of of Motl . motls.blogspot.com/2011/11/… points out the mathematics. – anna v Jul 3 '18 at 18:16
• I understand. What makes me confused is when they say that an electron can behave like a wave. But the electron has rest mass. Is that just a mathematical description for the propagation of the electron that we call wave in that case? – Árpád Szendrei Jul 3 '18 at 23:45
• OK, I will address this in an edit. – anna v Jul 4 '18 at 3:16

Firstly, what is a wave? It is a field that propagates and oscillates. However, not all fields are waves. For instance, the static electric field around a charges particle is not a wave. The gravitational field around a star is also not a wave.

For a field to be a wave, it must satisfy a wave equation. For instance, in the case of an electromagnetic field, we have the Helmholtz equation. It contains no mass. However, we can also have the Klein-Gordon equation, which is a wave equation for a field with mass.

In the case of a quantum field, the wave describes the probability amplitude for a particle to be observed at any given location. The particle then serves as a single excitation of the entire field or wave.

One can observe wave-like phenomena for the quantum particle that are associated with such fields. Consider for instance the double slit experiment. We don't need `herds' of particle to define the wave. One particle is enough, because it represents the entire field. The problem is that we only see the wave-like phenomenon after we have performed the experiment several times with several particle to build up enough statistics.

In the case of the Higgs boson (which is not exactly the same as the Higgs field, BTW), we have an unstable particle. Once created, it decays very quickly to other particles. So, it is very difficult to observe such wave-like phenomena with the Higgs boson. However, being a massive scalar field, it obeys the Klein-Gordon equation, which is a wave equation. So, in principle, it can act as a wave, if only it were not so unstable.