Wikipedia:Reference desk/Archives/Science/2024 August 14

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August 14

Indeed measuring the neutrino's restmass is regarded to be extremely problematic (or hard), but why can't the following simple experiment solve the problem?

In Cowan–Reines neutrino experiment, anti-neutrinos created in a nuclear reactor by beta decay, reacted with protons to produce neutrons and positrons, by the following reaction:

ν
_e +
p⁺
→
n⁰
+
e⁺

Now I suggest the following calculation:

1. Both the proton's restmass, the neutron's restmass, and the positron's restmass, are already known.

2. Hence, by the mass-energy equivalence, along with the kinetic energies in that experiment, both the proton's energy - the neutron's energy - and the positron's energy, are already known.

3. Hence, by the (quasi-)equation
ν
_e +
p⁺
→
n⁰
+
e⁺
, along with the conservation of energy, we receive the anti-neutrino's energy.

4. Hence, by the mass-energy equivalence, along with the anti-neutrino's kinetic energy in that experiment, we receive the anti-neutrino's restmass.

Where is the wrong stage? Maybe I'm not allowed to assume the conservation of energy? HOTmag (talk) 07:01, 14 August 2024 (UTC)

The neutrino speed is unknown.  --Lambiam 08:44, 14 August 2024 (UTC)

Unknown yet, but once we discover the anti-neutino's speed, the experiment I've suggested may simply solve the problem of measuring the anti-neutrino's restmass, right?

Additionally, even without measuring the anti-neutrino's velocity, still the quasi-equation
ν
_e +
p⁺
→
n⁰
+
e⁺
, along with the conservation of energy, and with the mass-energy equivalence, do determine the anti-neutrino's relativistic mass, right? HOTmag (talk) 09:39, 14 August 2024 (UTC)

The speed of a neutrino or anti-neutrino is not a physical constant. One may hope to measure it, but should then be aware that it varies with the frame of reference of the observer. In some frames of reference the (anti-)neutrino is at rest.  --Lambiam 22:42, 15 August 2024 (UTC)

I've never said this speed is constant. You said it was unknwon - you referring to the neutrino's varying speed, so I answered it was unknown yet - me referring to the neutrino's varying speed. Anyway, my previous comments still hold. HOTmag (talk) 08:07, 16 August 2024 (UTC)

You cannot measure its speed after it has disappeared in the interaction. If you succeed in measuring a neutrino's speed before the interaction with the positron has taken place, you thereby will have changed its speed. Moreover, how can you know that the particle whose speed you measured is the same particle that disappeared a few nanoseconds later? You can hardly tag it.  --Lambiam 01:30, 17 August 2024 (UTC)

Your first postulate is simply false, per Amble below. Remsense ‥ 诉 09:47, 16 August 2024 (UTC)

Your current indent is simply false, because you're responding to my response to a user other than the one you indicated. By "my previous comments", I referred to my comments to the user I was responding to. HOTmag (talk) 11:01, 16 August 2024 (UTC)

It's false regardless of who you were replying to. Remsense ‥ 诉 11:05, 16 August 2024 (UTC)

What's false? My first postulate? So again, also your indent was false. HOTmag (talk) 11:07, 16 August 2024 (UTC)

The first statement is not "false". Those masses are known, just not with sufficient precision to make HOTmag's proposal a viable way for measuring neutrino masses.--Wrongfilter (talk) 11:33, 16 August 2024 (UTC)

They asked where the flaw in their reasoning was, and if one had to pick a spot, it's that the first point is not the case. Apologies for coming off more pedantic about it than it sounded in my head. Remsense ‥ 诉 11:49, 16 August 2024 (UTC)

Besides the difficulty in measuring the small difference between the neutrino's speed and the speed of light, there's the problem that the neutrino's mass is small compared to the uncertainty on the masses of the other particles. For example, the standard uncertainty on the proton mass is 0.29 eV [1] and the standard uncertainty on the neutron mass is 0.48 eV [2]. These are very small errors in fractional terms, but the neutrino mass is even smaller: the sum of the three neutrino masses is below 0.120 eV (Neutrino#cite_note-Mertens-2016-mν-1). On the whole, an endpoint experiment like KATRIN can achieve much better sensitivity to the neutrino mass. --Amble (talk) 16:04, 14 August 2024 (UTC)

To put it another way, it's not a logic puzzle where each item is either "known" or "unknown". We know all of these things to within some level of uncertainty. In absolute terms, we know the neutrino mass better than we know the neutron or proton mass, or the difference between the two. Therefore, your procedure wouldn't improve our knowledge of the neutrino mass, it would (if anything) improve our knowledge of the proton-neutron mass difference, using our current knowledge of the neutrino mass as a "known" input. --Amble (talk) 16:52, 14 August 2024 (UTC)

In short, OP has proposed a purely logical solution for what remains a purely empirical problem. Remsense ‥ 诉 23:07, 15 August 2024 (UTC)

Yes, in the same vein I could measure the mass of a table tennis ball by throwing it at a known speed at a large wrecking ball and measuring how far the wrecking ball is deflected. Other ways might work better. NadVolum (talk) 10:09, 17 August 2024 (UTC)