@UtkarshPKumar said in #24:
at Akbar2thegreat (in #6): yes you are correct till certain extent, we have found out that the universe is expanding faster than light which means it might end in "big RIP" (thats a whole lot of another story) but don't forget motion is relative. It happens so, That our
galaxy is moving and the galaxy we are observing is also moving in the opposite direction so if you see it this way both of these bodies are moving 1/2C but we perceive the galaxy we are observing is moving apart at speed of light (because we think we are stationary).
That's not quite the reason we observe galaxies which seem to move away from us at c. I might be misunderstanding you here. I'm under the impression that you're arguing that we see a distant galaxy moving away from us at c because both our galaxy and the distant galaxy are moving through space at c/2 (relative to the Hubble flow), but in opposite directions, their relative velocity therefore adding up to c/2 + c/2 = c. That's not the case.
There are (to my knowledge) no galaxies with peculiar velocities (velocity relative to the Hubble flow) near c/2. Galaxies are not moving through space that fast. Typical peculiar velocities are in the hundreds of km/s, maybe in the low thousands of km/s in highly dynamic galaxy clusters (source: https://en.wikipedia.org/wiki/Peculiar_velocity#Cosmology). Nowhere near c/2 ≈ 150,000 km/s.
Even if there were, this model could not account for the observational fact that we see galaxies with apparent recession velocities in excess of the speed of light all around us. Our Milky Way galaxy cannot move at c/2 in two opposite directions at the same time (that's a contradiction).
Even if it could, you just cannot add relativistic velocities the way you add slow velocities in Newtonian mechanics. In special relativity the relative velocity u is given by u = (v + u')/(1 + (v*u')/c^2), not by u = v + u' (as in Newtonian mechanics), where v and u' are the individual velocities measured in an external inertial frame.
See: https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity
Adding velocities in special relativity can therefore never produce a velocity greater than c.
In your example of two objects moving away from each other at v = c/2 and u' = c/2 respectively (as measured in an inertial frame external to both objects), their relative velocity measured in this inertial frame would be: u = (4/5)c = 0.8c
This is only 80% of the speed of light.
Even if we increase both velocities to 99% of the speed of light, we will obtain a relative velocity lower than c (instead of the classically expected 1.98*c):
u = (0.99c + 0.99c)/(1 + (0.99c0.99c)/c^2)
u = (1.98c)/(1 + (0.9801c^2)/c^2)
u = (1.98c)/(1.9801)
u = (19800/19801)c
u ≈ 0.9999495c
The relative velocity would only be about 99.995% of the speed of light, even though the individual velocities were both already 99% of the speed of light. This is a direct consequence of the fundamental postulate of special relativity that the speed of light is always measured to be exactly c = 299,792,458 m/s regardless of the motion of the emitter relative to the observer ("The principle of invariant light speed").
The above treatment of velocity composition concerned velocities through space.
However, the recession velocity of distant galaxy is not (significantly) due to a motion of the galaxy through space (such a peculiar motion usually occurs at much less than 1% of the speed of light). It's due to the metric expansion of space between that distant galaxy and our galaxy. None of the two galaxies is travelling through space anywhere near the speed of light, the relative velocity just appears to exceed c because all of those billions of light years of space between them are slowly being stretched out.
Oh and also due to this motion of celestial bodies faster than C (in relative context) the observable universe will loose all its stars except for our local cluster and the space will be alone except of milkdromedia galaxy which our future generation would see dw we might find ways to go to other galaxies but thats for another story again.
Mind-boggling. And absolutely correct!
Dont see ahead if you want to be in peace...
To conclude things very nicely un-confusingly neutrino can travel faster than light... i guess you might Have figured that out of from the end of the video. Lemme eaze out things its still under debate.
You're probably referring to this: https://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly
The experiment had limited accuracy. I quote:
"On July 12, 2012, OPERA updated their paper by including the new sources of errors in their calculations. They found agreement of neutrino speed with the speed of light."
So this doesn't look like a likely candidate for disproving Einstein's relativity. Neutrinos probably cannot travel faster than light. It has since been discovered that they actually have nonzero mass:
https://en.wikipedia.org/wiki/Neutrino_oscillation
They are so light that they are usually ultra-relativistic particles (travelling very near the speed of light). But special relativity predicts that they will not be able to reach the speed of light.
@UtkarshPKumar said in #24:
> at Akbar2thegreat (in #6): yes you are correct till certain extent, we have found out that the universe is expanding faster than light which means it might end in "big RIP" (thats a whole lot of another story) but don't forget motion is relative. It happens so, That our
> galaxy is moving and the galaxy we are observing is also moving in the opposite direction so if you see it this way both of these bodies are moving 1/2C but we perceive the galaxy we are observing is moving apart at speed of light (because we think we are stationary).
That's not quite the reason we observe galaxies which seem to move away from us at c. I might be misunderstanding you here. I'm under the impression that you're arguing that we see a distant galaxy moving away from us at c because both our galaxy and the distant galaxy are moving through space at c/2 (relative to the Hubble flow), but in opposite directions, their relative velocity therefore adding up to c/2 + c/2 = c. That's not the case.
There are (to my knowledge) no galaxies with peculiar velocities (velocity relative to the Hubble flow) near c/2. Galaxies are not moving through space that fast. Typical peculiar velocities are in the hundreds of km/s, maybe in the low thousands of km/s in highly dynamic galaxy clusters (source: https://en.wikipedia.org/wiki/Peculiar_velocity#Cosmology). Nowhere near c/2 ≈ 150,000 km/s.
Even if there were, this model could not account for the observational fact that we see galaxies with apparent recession velocities in excess of the speed of light all around us. Our Milky Way galaxy cannot move at c/2 in two opposite directions at the same time (that's a contradiction).
Even if it could, you just cannot add relativistic velocities the way you add slow velocities in Newtonian mechanics. In special relativity the relative velocity u is given by u = (v + u')/(1 + (v*u')/c^2), not by u = v + u' (as in Newtonian mechanics), where v and u' are the individual velocities measured in an external inertial frame.
See: https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity
Adding velocities in special relativity can therefore never produce a velocity greater than c.
In your example of two objects moving away from each other at v = c/2 and u' = c/2 respectively (as measured in an inertial frame external to both objects), their relative velocity measured in this inertial frame would be: u = (4/5)*c = 0.8*c
This is only 80% of the speed of light.
Even if we increase both velocities to 99% of the speed of light, we will obtain a relative velocity lower than c (instead of the classically expected 1.98*c):
u = (0.99*c + 0.99*c)/(1 + (0.99*c*0.99*c)/c^2)
u = (1.98*c)/(1 + (0.9801*c^2)/c^2)
u = (1.98*c)/(1.9801)
u = (19800/19801)*c
u ≈ 0.9999495*c
The relative velocity would only be about 99.995% of the speed of light, even though the individual velocities were both already 99% of the speed of light. This is a direct consequence of the fundamental postulate of special relativity that the speed of light is always measured to be exactly c = 299,792,458 m/s regardless of the motion of the emitter relative to the observer ("The principle of invariant light speed").
The above treatment of velocity composition concerned velocities through space.
However, the recession velocity of distant galaxy is not (significantly) due to a motion of the galaxy through space (such a peculiar motion usually occurs at much less than 1% of the speed of light). It's due to the metric expansion of space between that distant galaxy and our galaxy. None of the two galaxies is travelling through space anywhere near the speed of light, the relative velocity just appears to exceed c because all of those billions of light years of space between them are slowly being stretched out.
> Oh and also due to this motion of celestial bodies faster than C (in relative context) the observable universe will loose all its stars except for our local cluster and the space will be alone except of milkdromedia galaxy which our future generation would see dw we might find ways to go to other galaxies but thats for another story again.
Mind-boggling. And absolutely correct!
> Dont see ahead if you want to be in peace...
> To conclude things very nicely un-confusingly neutrino can travel faster than light... i guess you might Have figured that out of from the end of the video. Lemme eaze out things its still under debate.
You're probably referring to this: https://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly
The experiment had limited accuracy. I quote:
"On July 12, 2012, OPERA updated their paper by including the new sources of errors in their calculations. They found agreement of neutrino speed with the speed of light."
So this doesn't look like a likely candidate for disproving Einstein's relativity. Neutrinos probably cannot travel faster than light. It has since been discovered that they actually have nonzero mass:
https://en.wikipedia.org/wiki/Neutrino_oscillation
They are so light that they are usually ultra-relativistic particles (travelling very near the speed of light). But special relativity predicts that they will not be able to reach the speed of light.