# Can a particle exceed the speed of light in water

## Homework Statement

Light travels through water at a speed of about 2.25e8 m/s. Is it possible for a particle to travel through water at a speed v greater than 2.25e8.

## Homework Equations

E=(Rest Energy)/sqrt(1-v^2/c^2)

## The Attempt at a Solution

I realize that light requires no medium to propogate through and is massless and therefore nothing can exceed this speed since it would require infinite energy to do this. However when light passes through a dense media it scatters and slows through different refractive indexes. So I would thinnk the answer would be yes it is possible but then again I look tat the equation I gave for finding total energy and no matter what the value of c is if your numerator in higher it will become imaginary so by that equation it fails no matter what so would the answer be no?

Thanks for the info and sorry for the grammatical errors all over the place. So by that article I assum the answer to the question would be yes but I am really stuck here because we havent cover Cherenkov Radiation yet, so I am confused uggg. I would have to say the overwelming response seems to be yes.

berkeman
Mentor

## Homework Statement

Light travels through water at a speed of about 2.25e8 m/s. Is it possible for a particle to travel through water at a speed v greater than 2.25e8.

## Homework Equations

E=(Rest Energy)/sqrt(1-v^2/c^2)

## The Attempt at a Solution

I realize that light requires no medium to propogate through and is massless and therefore nothing can exceed this speed since it would require infinite energy to do this. However when light passes through a dense media it scatters and slows through different refractive indexes. So I would thinnk the answer would be yes it is possible but then again I look tat the equation I gave for finding total energy and no matter what the value of c is if your numerator in higher it will become imaginary so by that equation it fails no matter what so would the answer be no?

Hint -- what particle can travel through the Earth at nearly the speed of light in a vacuum...?

The electron? Maybe I am sorry not trying to sound like a goober im seriously trying to understand this.

berkeman
Mentor
The electron? Maybe I am sorry not trying to sound like a goober im seriously trying to understand this.

No, an electron would be stopped as soon as it hit the atmosphere inbound to the Earth. There is a particle (the major local source is the Sun) that basically does not interact with matter at all. Do some Googling to see if you can figure out which particle it is...

The neutrino I would assume it was what I was going to say but I figured it wasnt the answer.

Ok so the answer to my question is then yes because in water the c constant slows down and the neutrino a particle which doesnt interact with matter can pass right through a very near the speed of light.

berkeman
Mentor
Ok so the answer to my question is then yes because in water the c constant slows down and the neutrino a particle which doesnt interact with matter can pass right through a very near the speed of light.

Sounds right to me 