4 ms·

It took a few tries, but I got Wolfram Alpha to compute its velocity compared to the speed of light[1]. I started with: sqrt(1-((1/(1+120 PeV / (neutrino

by thamer 2y ago

It took a few tries, but I got Wolfram Alpha to compute its velocity compared to the speed of light[1]. I started with: sqrt(1-((1/(1+120 PeV / (neutrino mass * c^2)))^2)) but it simply said "data not available". So I changed: 120 PeV to 120e15 * 1.602176634e-19 kg m^2 s^-2 neutrino mass to 1.25e-37kg speed of light to 299792458 m/s and finally it gave a numeric result: 0.999999999999999999999999999999999999829277971 (that's 36 nines in a row). Pasting it in Google says the value is "1", which is… not far off. If you want details about the way this is calculated, I dug up the formula from an article I'd written about particle velocities in the LHC, back in 2008[2]. For comparison, their 7 TeV protons were going at 0.999999991 × c. [1] https://www.wolframalpha.com/input?i=sqrt%281-%28%281%2F%281%2B%28120e15*1.602176634e-19+kg+m%5E2+s%5E-2%29+%2F+%281.25e-37kg++*+%28299792458+m%2Fs%29%5E2%29%29%29%5E2%29%29 https://www.wolframalpha.com/input?i=sqrt%281-%28%281%2F%281... [2] https://log.kv.io/post/2008/09/12/lhc-how-fast-do-these-protons-go https://log.kv.io/post/2008/09/12/lhc-how-fast-do-these-prot...

dr_dshiv 2y ago
That’s fast! But for how much energy? For comparison, the total energy from this one particle (0.0192 joules) is equivalent to keeping a 50 mW LED lit for a third of a second.
davrosthedalek 2y ago
We don't know the neutrino's masses, so this is a lower limit for v (since the mass you used is an upper limit)
wd776g5 2y ago
I can see it came from your source but why is the neutrino mass specified in kg instead of g? why not 1.25e-34g?
- thamer 2y ago
  The kilogram is the base unit of mass in the International System of Units (SI): https://en.wikipedia.org/wiki/SI_base_unit https://en.wikipedia.org/wiki/SI_base_unit Time is in seconds, length in meters, temperature in kelvin, etc. A unit of energy like a joule is then defined using these base units, so 1 joule is 1⋅kg⋅m^2⋅s^-2.
  - skissane 2y ago
    > The kilogram is the base unit of mass in the International System of Units (SI) Arguably, an ugly wart, but one we are stuck with for historical reasons. The base units of the original metric system (metre and gram) were poorly proportioned for practical use, resulting in the two main scientific/engineering systems of metric units both choosing to prefix one base unit - the centimetre-gram-second (cgs) system chose to prefix the metre, the metre-kilogram-second (mks) system chose to prefix the gram, and eventually mks won out over cgs and evolved into SI. Whatever warts SI has, they are nothing compared to the chaos of the Imperial/customary system
    - myrmidon 2y ago
      > The base units of the original metric system (metre and gram) were poorly proportioned for practical use What is the dealbreaker here though? Because we have plenty of "poorly proportioned" SI units anyway; e.g. it would be much more practical to have megapascal, microfarad and megajoule as base units from an engineering pov (particle physicists might disagree;).
      - skissane 2y ago
        Pascal, farad, joule aren't base units, they are derived units. Ideally, the base units should be prefixless. Except for kilogram, they all are. Imagine a system exactly the same as SI, except instead of the kilogram, it had the kram, where 1 kram = 1 kilogram... then the gram would be the millikram, the milligram would become microkram, the microgram would become the nanokram, etc... if you were starting from scratch, without any historical baggage, wouldn't such a system be superior? But of course, we aren't starting without historical baggage – almost everybody knows what a kilogram is, kram is a word I just now made up. I think some derived units being "poorly proportioned" is inevitable given the physics we have.
        jaybro867 2y ago
        [dead]
        2y ago
- l33tman 2y ago
  In particle physics you just use GeV (with varying powers) for most parameters :)

by thamer 2y ago

dr_dshiv 2y ago

That’s fast! But for how much energy? For comparison, the total energy from this one particle (0.0192 joules) is equivalent to keeping a 50 mW LED lit for a third of a second.

davrosthedalek 2y ago

We don't know the neutrino's masses, so this is a lower limit for v (since the mass you used is an upper limit)

wd776g5 2y ago

I can see it came from your source but why is the neutrino mass specified in kg instead of g? why not 1.25e-34g?

thamer 2y ago
The kilogram is the base unit of mass in the International System of Units (SI): https://en.wikipedia.org/wiki/SI_base_unit https://en.wikipedia.org/wiki/SI_base_unit Time is in seconds, length in meters, temperature in kelvin, etc. A unit of energy like a joule is then defined using these base units, so 1 joule is 1⋅kg⋅m^2⋅s^-2.
- skissane 2y ago
  > The kilogram is the base unit of mass in the International System of Units (SI) Arguably, an ugly wart, but one we are stuck with for historical reasons. The base units of the original metric system (metre and gram) were poorly proportioned for practical use, resulting in the two main scientific/engineering systems of metric units both choosing to prefix one base unit - the centimetre-gram-second (cgs) system chose to prefix the metre, the metre-kilogram-second (mks) system chose to prefix the gram, and eventually mks won out over cgs and evolved into SI. Whatever warts SI has, they are nothing compared to the chaos of the Imperial/customary system
  - myrmidon 2y ago
    > The base units of the original metric system (metre and gram) were poorly proportioned for practical use What is the dealbreaker here though? Because we have plenty of "poorly proportioned" SI units anyway; e.g. it would be much more practical to have megapascal, microfarad and megajoule as base units from an engineering pov (particle physicists might disagree;).
    - skissane 2y ago
      Pascal, farad, joule aren't base units, they are derived units. Ideally, the base units should be prefixless. Except for kilogram, they all are. Imagine a system exactly the same as SI, except instead of the kilogram, it had the kram, where 1 kram = 1 kilogram... then the gram would be the millikram, the milligram would become microkram, the microgram would become the nanokram, etc... if you were starting from scratch, without any historical baggage, wouldn't such a system be superior? But of course, we aren't starting without historical baggage – almost everybody knows what a kilogram is, kram is a word I just now made up. I think some derived units being "poorly proportioned" is inevitable given the physics we have.
      - jaybro867 2y ago
        [dead]
      - 2y ago
l33tman 2y ago
In particle physics you just use GeV (with varying powers) for most parameters :)