## Comments about the article in Nature: Special relativity validated by neutrino's

Following is a discussion about this "News & Views" article in Nature Vol 560 16 August 2018, by Matthew Mewes
To read the article select: https://www.nature.com/articles/d41586-018-05931-2
• The text in italics is copied from the article
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
Neutrinos are tiny, ghost-like particles that habitually change identity. A measurement of the rate of change in high-energy neutrinos racing through Earth provides a record-breaking test of Einstein’s special theory of relativity.
The result is apperently that no such rate of change was detected. It would IMO be much more physical interesting if such a change was detected.
Writing in Nature Physics, the IceCube Collaborationnow uses neutrinos, etc, to scrutinize another cornerstone of physics: Lorentz Invariance.
See: https://en.wikipedia.org/wiki/Lorentz_covariance and: https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation The second url is 'better'
This principle states that the laws of physics are independent of the speed and orientation of the experimenter's frame of reference
and serves as the mathematical foundation for Albert Einstein's special theory of relativity.
The first question to answer is: what are the laws of physics.
Why not write: All physical processes are independent of the speed and orientation of the experimenter's reference frame?
The question is how do you demonstrate this? and more important what is the physical relevance.
Physicists generally assume that Lorentz invariance holds exactly.
That seems to me the simplest assumption.
However in the late 1990's the principle began to be systematically challenged, largely because of the possibility that is was broken, etc, such as string theory.
That only makes sense if you can demonstrate that string theory is correct.
Over the past decades researchers have tested Lorentz invariance in objects ranging from photons to the Moon.
See https://arxiv.org/abs/0801.0287v11. That document discusses a "Standard Sun-centered inertial reference frame".
That is interesting because a Sun-centered reference frame is only inertial or free-floating by approximation because it also circulates around our Galaxy. This is specific important if you want to investigate the movement of the planet Mercury.

#### Figure 1 Propagation of neutrinos through the earth

Figure 1 shows the earth with at the North pole two points marked as a and b. At the south pole there is a detector. At each point a and b a Muon neutrino enters the earth crust and travels through the earth and is detected at the South pole. Both Muon neutrinos are at the point a and b depicted as two waves in phase. The behaviour of both is different.
• the Muon neutrino particle at point a is detected as a Tau neutrino particle. In Figure 1 this is depicted that the in phase wave changes slowly into an out of phase wave.
• the Muon neutrino particle at point b is detected as a Muon neutrino particle. In Figure 1 this is depicted that the in phase wave stays in phase.
What Figure 1 indirectly shows is that the South pole detector can detect both Tau neutrinos and Muon neutrinos.
If a principle known as Lorentz invariance were violated, these waves could travel at different speeds through Earth’s interior and be detected in the out-of-phase tau-neutrino state.
A different way of describing this situation is (my wording):
• If Muon neutrinos are stable only Muon neutrinos should be detected at the South Pole
• If Muon neutrinos are instable a mixture of Muon and Tau neutrinos should be detected at the South Pole.
No such instabilities are detected,
constraining the extent to which Lorentz invariance could be detected.
The question is if such an instability is a demonstration of Lorentz violation and is a 'problem' for SR.

However in its test of Lorentz invariance the collaboration studied more abundant neutrinos that are generated when fast-moving charged particles from space collide with Earth's atmosphere.
(1)
Such changes stem from the fact that electron, muon and tau neutrinos are not particles in the usual sense.
What means usual sense?
They are actually quantum combinations of three ‘real’ particles — µ1, µ2 and µ3 — that have tiny but different masses.
(2)
IMO as such there are 3 combinations: (µ1,µ2), (µ1,µ3) and (µ2,µ3).
In a simple approximation relevant to the IceCube experiment, the birth of a muon neutrino in the atmosphere can be thought of as the simultaneous production of two quantum-mechanical waves: one for µ2 and one for µ3 (Fig. 1).
I hope we do not make the issue too simple.
These waves are observed as a muon neutrino only because they are in phase, which means the peaks of the two waves are seen at the same time.
More information is required. The question is this more an mathematical assumption or or can it also be demonstrated.
By contrast, a tau neutrino results from out-of-phase waves, whereby the peak of one wave arrives with the valley of the other.
More or less the same as above. The question is this more an mathematical assumption or or can it also be demonstrated.
The issue is because there are three real particles µ1, µ2 and µ3, than there are 6 types of neutrinos possible:
1 and 2: µ1 and µ2 in phase and out of phase
3 and 4: µ2 and µ3 in phase and out of phase
5 and 6: µ1 and µ3 in phase and out of phase
If neutrinos were massless and Lorentz invariance held exactly, the two waves would simply travel in unison, always maintaining the in-phase muon-neutrino state.
(3)
This is a typical case where neutrino physics, waves and SR are discussed in one sense.
Reflection 1 - Overall evaluation
However, small differences in the masses of µ2 and µ3 or broken Lorentz invariance could cause the waves to travel at slightly different speeds, leading to a gradual shift from the muon-neutrino state to the out-of-phase tau-neutrino state.
Again neutrino physics, waves and SR are discussed in one sense.
Oscillations resulting from mass differences are expected to be negligible at the neutrino energies considered in the authors’ analysis, so the observation of an oscillation would signal a possible breakdown of special relativity.
(4)
This is a mixture of physics versus SR.
Reflection 1 - Overall evaluation
The IceCube Collaboration saw no sign of oscillations, and therefore inferred that the peaks of the waves associated with µ2and µ3 are shifted by no more than this distance after travelling the diameter of Earth.
It is very interesting to know more precise what they saw. It is also very interesting to know if there are experiments which show oscillations in almost similar experiments.
The problem is when you don't detect anything (i.e. oscillations) you don't know if the cause is in the process itself or in the apparatus you use to measure or detect the phenomena or in all the physical assumptions.
To be more precise you do not know if Figure 1 makes any sense.
(5)
Consequently, the speeds of the waves differ by no more than a few parts per 10^28 — a result that is one of the most precise speed comparisons in history.
See reflection 4 - Figure 1

### Reflection 1 - Overall evaluation.

The article tries to discus three subjects:
1. The physics of neutrino's. That there are three types of neutrinos: electron, muon and tau, their physical behaviour and how they interact.
2. That particles con be treated as waves. See https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality
3. The explanation of the realation of this physical behaviour versus Lorentz violation and SR.
The problem is that the article does not make a clear distinction between the three subjects. First everything related to the physics of neutrinos should be discussed. Including the results of the experiments. Next how the different types of neutrino's can be understood. Specific the difference tau en muon neutrino should be considered. How do we know that in one the waves are in phase and in the other not? The same should be discussed electron neutrino. Finally the relation between the results of the experiments and SR and Lorentz violation. For eample: see the text near the notes (1) , (3) and (4) which is a mixture of both.

The IceCube Collaboration saw no sign of oscillations. My interpretation is that no Tau neutrino particles were detected at the South Pole.
If that is case how valid is the interpretation that this is an experiment in favour of SR?
SR says something about the speed of light. This experiment does not say anything about the speed of light.
Only if you make the link that particles are waves it says something about the relation quantum mechanics and waves.

### Reflection 2 - IceCube Collaboration.

A much better reading is: https://arxiv.org/pdf/1805.11112.pdf Opening a New Window onto the Universe with IceCube
This document explains is much larger detail the physics involved with neutrinos etc. The document does not mention the words Relativity and Lorentz. Strange?

### Reflection 3 - Mass

What exactly is mass? How easy(?) is it to measure the small differences in mass mentioned in (2)
IMO everything related to mass is a subject of Newton's Law or General Relativity and not of Special Relativity.
Newton's Law also uses masses, but they are an inbetween parameter. I mean by that mass is calculated by using Newton's Law. The mass is calculated by observing the positions of a closed set of objects, during a certain time period, at regular intervals. Anyway that is the idea or the ideal. With that data as input and with Newton's Law the masses of the objects are be calculated. In fact you try to find the closests fit (smallest error) with all observations. That is difficult.
The next step is to predict the future. That is relatif easy. In that

### Reflection 4 - Figure 1

Figure 1 shows in some sense a very simple physical situtuation.
• You have one Muon neutrino who starts in phase and arrives in phase. That is neutrino b
• You have one Muon neutrino who starts in phase and arrives out of phase and becomes a Tau neutrino. That is neutrino a
However and that is the problem: This phase change continues slowly along the whole path that neutrino a follows. How can this be explained? It seems much more logical that such a state change happens at a specific position along its path during a specific event.
Using the same logic the same could happen: a Tau neutrino changes into a Muon neutrino.
A Tau neutrino changes into an electron neutrino or an electrom neutrino into a Tau neutrino etc.

If that is true the importance of wave concept becomes tricky including any link towards SR. (Your writer is not an expert on this)
See (5)

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Created: 5 September 2018