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I have read this question:

Neutrinos vs. Photons: Who wins the race across the galaxy?

https://en.wikipedia.org/wiki/Neutrino

And it made me curious.

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The wiki article says that neutrinos travel at 0.99c, but they do not say whether neutrinos are affected by gravity.

I do not know if there has been any experiment since that would prove if neutrinos are affected by gravity.

So I wanted to know that due to the Shapiro delay, EM waves travel slower (when viewed from Earth) then c, and if this would decide a race between a bent photon and a straight path neutrino.

For this race, since the neutrino only interacts weakly, it would just pass through the sun (I do not know if the Sun would slow it down or not since I do not know if gravity affects it or not), but for the sake of the argument let's make it simpler for the neutrino to pass through the Sun.

  1. Imagine that the Sun is not rotating.

  2. It also has a tunnel throughout its body exactly through the core. Please disregard any other effect then gravity.

  3. From a far away point A (far from the Sun) I would shoot two particles, one neutrino through the tunnel, and a photon a little bit next to the Sun (so just to pass next to the Sun). Point B is so that the line from point A to point B is on a straight (in 3D) line through the tunnel.

I am making the race so that both particles will pass through both point A and B. (given GR/SR bending effects, the photon's path will be bent just right to pass through point B.)

Now it becomes interesting because neutrinos are traveling at 0.99c already, and seen from Earth, a photon would travel (around the Sun) maybe slower then that according to the Shapiro effect.

Questions:

  1. Which particle would according to GR/SR arrive at point B first?
  2. My question's answer could sound at first obvious, but considering that the neutrino's gravitational interaction is not clear, and it traveling inside the tunnel would be affected by gravity too, the answer is not obvious.
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    $\begingroup$ Neutrinos have mass, and as such they're not required to travel at any particular speed. Practically, all of the neutrinos we see must be sufficiently energetic to detect, and that energy is high enough with current technology that they basically move at the speed of light. But it's not impossible for neutrinos to be at rest. $\endgroup$ – probably_someone Jun 13 '18 at 19:32
  • $\begingroup$ Also, the article doesn't say that neutrinos travel at $0.99c$. It says that a particular set of neutrinos, produced with a particular energy, travels at a speed of at least $0.999976c$. So, practically, even over long distances, high-energy neutrinos will travel the same speed as light. $\endgroup$ – probably_someone Jun 13 '18 at 19:35
  • $\begingroup$ I thought that since according to general relativity space-time is curved, all particles are affected by gravity. Even photons are affected by gravity, right? $\endgroup$ – Samuel Weir Jun 13 '18 at 19:35
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    $\begingroup$ @SamuelWeir Photons are indeed affected by gravity, as they follow the geodesics of spacetime. This is why gravitational lensing happens. Neutrinos are also affected by gravity, as they also live in spacetime. $\endgroup$ – probably_someone Jun 13 '18 at 19:37
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    $\begingroup$ "due to the Shapiro delay, EM waves travel slower (when viewed from Earth) then c," Shapiro delay is caused by the photon taking a detour, not by it going a a speed smaller than c. Surely, neutrinos are affected by Shapiro delay as well. $\endgroup$ – my2cts Jun 13 '18 at 21:22

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