Light speed and cosmological constant

[Stu21]

E=mc² gives us the cosmological constant, which later was found to be the maximum speed at which light can travel. i also understand that when accelerating particles such as they do at CERN, it requires more and more energy the faster u want to go, the mass/speed issue. so i think i understand why photons can move at the speed of light while the rest of matter(for the most part) can't reach those speeds, photons have no mass while other particles do. I've also come across several articles claiming that they have, also at CERN, found neutrinos that may be moving faster than light can travel. my questions are; if both photons and neutrinos have no mass then that's not why photons can't reach the speeds of neutrinos. could it have something to do with matter interaction? also, now I am no mathmatician, but if the c in e=mc² was found to be the speed of light, and we know the equation holds true since its been put to the test countless times. why is it squared. what's the square doing to the speed of light?

 

[ZapperZ]

E=mc² gives us the cosmological constant, which later was found to be the maximum speed at which light can travel.

This is incorrect. That equation doesn't give such a thing. The speed of light being a constant is a POSTULATE that has been verified via experiments.

I've also come across several articles claiming that they have, also at CERN, found neutrinos that may be moving faster than light can travel.

This is out-of-date. The OPERA experiment has been corrected by the recent results (even by them), and neutrinos have been found NOT to travel faster than light.

my questions are; if both photons and neutrinos have no mass then that's not why photons can't reach the speeds of neutrinos.

This is incorrect. Neutrinos have mass, and this has been shown experimentally in many different measurements of the neutrino mixing angles.

Zz.

 

[Mark M]

E=mc² gives us the cosmological constant,

No, Einstein's field equation gives us the cosmological constant. The cosmological constant is a negative pressure vacuum energy that accelerates the expansion of the universe. I doesn't have anything to do with special relativity.

which later was found to be the maximum speed at which light can travel.

Light doesn't have a maximum speed, as it only has one speed, c. The constant speed of light was implied by electromagnetism, and was taken as a postulate by Einstein for special relativity.

I've also come across several articles claiming that they have, also at CERN, found neutrinos that may be moving faster than light can travel.

This was an error caused by a loose cable. They move slightly slower than light.

if both photons and neutrinos have no mass then that's not why photons can't reach the speeds of neutrinos.

Neutrinos move slightly less than the speed of light. They have a very small mass.

what's the square doing to the speed of light?

It shows up during the derivation. Since E = pc for photons, and p = mc, then it follows that E = mc².

 

[Ibix]

I think you are confused about a number of things. E=mc² is not an equation related to the cosmological constant, usually denoted \Lambda.

The famous E=mc² is a part of Einstein's Special Relativity theory, which only applies where you can ignore gravity. It is the "rest mass-energy" of a particle of mass m - the amount of energy you can realize by annihilating the particle. It accurately describes the energy released by nuclear reactions, where some of the mass of the radioactive material is converted into energy.

The cosmological constant is a factor in Einstein's General Relativity theory. Einstein introduced it (with little justification, if I understand aright) when someone realized that the equations of General Relativity implied the existence of a Big Bang. Adding in the cosmological constant and setting it to the right value allows you to avoid a Big Bang. Einstein later described the venture as the largest mistake of his life. It was subsequently revived because the maths isn't wrong, just the justification. It describes the way in which the expansion of the universe is accelerating just a little bit - ascribed to Dark Energy by some.

The neutrino experiment at CERN was found to be an error - a loose fiber optic cable was delaying one of the timing measurements by just enough that the neutrinos appeared to be exceeding the speed of light. Had it not been an error, that would have been revolutionary because, as you correctly state, only massless particles can travel at the speed of light, and neutrinos are not massless. As others have noted, by the way, the speed of light is the only speed at which massless particles may travel, not the maximum. Edit: arguably, I suppose, that makes it both a maximum and a minimum speed, but that's just confusing terminology.

Regarding the square in E=mc², that's just the way it is. The formula can be derived from Einstein's original postulates (the speed of light is a constant, and physics is the same everywhere, loosely), as I understand it, so is a direct consequence of those claims. That's really all there is in the way of a "why".

Does that help?