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If the speed of light is constant no matter the speed of the source, shouldn't we be able to know the direction and exact speed we are going relative to the absolute 0 in speed? If a photon is sent in the direction we are going and one at the opposite, one of them should appear to go slower then the other because of our current speed, we would travel at some part of his speed, so from our perspective it wouldn't go at $c$/light speed and that difference would be our current speed no? All this assuming $c$ is constant and I still don't know why we believe in that.

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    $\begingroup$ You probably need to read up on this en.wikipedia.org/wiki/Special_relativity at least before we can give you sensible answers here. The speed of light is the same for all inertial reference frames but the direction of a light beam is observer dependent. So sometimes the invariance is incorrectly rendered "invariant light velocity". The invariance of $c$ is well motivated experimentally, by the Michelson Morley experiment and dependence of metastable particle lifetimes on their relative speed to the observer. $\endgroup$ – WetSavannaAnimal May 13 '15 at 8:44
  • $\begingroup$ Hi, thks for the reply. Can you tell me the expected result of the experiment i described? 2 photons sent from a moving source going in opposite directions aligned in the direction of the source? What velocity would we measure for each of them? $\endgroup$ – Nuno Figueiredo Barata May 13 '15 at 9:11
  • $\begingroup$ Each photon would move at $c$ in its respective direction of motion. There is no need to say "relative to..." while describing the motion of light because it will be the same for everyone. $\endgroup$ – SystematicDisintegration May 13 '15 at 9:39
  • $\begingroup$ And from one of the photons point of view the other is too moving at c? But from our point of view they are at c*c diference? $\endgroup$ – Nuno Figueiredo Barata May 13 '15 at 10:45
  • $\begingroup$ I mean 2c, c+c... $\endgroup$ – Nuno Figueiredo Barata May 13 '15 at 17:01
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It does not matter what your velocity is relative to a photon - the photon will always move at a fixed speed from your point of view.

This is the 2nd postulate of special relativity - the speed of light in a vacuum has the same value (it's invariant) for all non-accelerating observers (in a medium of uniform density, the speed would be different from its value in a vacuum, but it will still be invariant for all inertial observers in the medium). If someone were to flash a beam of light from the Earth in a direction perpendicular to the surface and if someone else were to chase the beam in a hypothetical rocket which can accelerate from rest to 200,000,000 m/s almost instantaneously, the person on the Earth's surface would measure the light to be moving away from him/her at $c$ (assuming that the speed of light in air is almost the same as that in a vacuum) and the rocket at the value stated above. However, the person inside the rocket that is chasing the light beam would also see the light beam move away at $c$ , not at ($c$ -200,000,000) m/s , while the Earth would appear to recede at 200,000,000 m/s. This is non-intuitive and cannot be reconciled with the observation made on Earth using Galilean relativity. The fact that speed is dependent on distance and time means that to ensure the constancy of $c$ in all inertial (non-accelerating) frames of reference, distance and time must differ for different observers in relative motion (length contraction and time dilation). You can then go ahead and derive the velocity addition formula. If two objects are moving in opposite directions with respect to someone in between at velocities $u$ and $w$ respectively, then the velocity of one of these objects relative to the other is given by $$\frac{u+w}{1+\frac{uw}{c^2}}$$ which reduces to the intuitive $u+w$ value when $|u|<<c$ and $|w|<<c$ .

The source of confusion with the postulate often arises due to the peculiar property of light - the fact that it can propagate without a medium. When we say sound waves move at approximately 330 m/s at room temperature, we mean relative to air (the medium in this case). No such analogy can be derived for light moving in a vacuum - after all, the speed $c$ is relative to what?

Only two conclusions can be drawn:

1) There is a medium spread all across the vacuum and the universe (aether) in which light moves ($c$ relative to the aether).

2) There is no aether and the speed of light is $c$ for all inertial observers.

The Michelson-Morley experiment strongly suggested that the latter is the actual case, and hence number 2 was incorporated into special relativity as a postulate. Since then, numerous experiments have added weight to this conclusion, and very little doubt (if it all any) remains about the true nature of the speed of light.

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  • $\begingroup$ "in a medium of uniform density, the speed will be lower than its value in a vacuum, but it will still be invariant for all inertial observers in the medium." I don't think so. A particle can move faster than the speed of light in a medium, then for this particle the speed of the light in that medium would be negative. And actually, the (signal) speed of light in the medium is $c$, only the phase or group velocity can have other values (even values greater than $c$). $\endgroup$ – Sebastian Riese May 13 '15 at 10:08
  • $\begingroup$ I did not wish to explore group, signal and phase velocities in my answer to keep it on track. No meaningful information can be transmitted faster than $c$ , and according to the Maxwell-equation derived formula, light in any medium with an electric permittivity or magnetic permeability greater than that of a vaccum will move at a velocity lower than $c$. To avoid complicating the matter with an issue which is altogether different, it is best to leave it here. $\endgroup$ – SystematicDisintegration May 13 '15 at 10:20
  • $\begingroup$ This was not my main critcism, I could be wrong, but I believe the (phase, group) velocity of the light in the medium will not be invariant for the observers. $\endgroup$ – Sebastian Riese May 13 '15 at 10:24
  • $\begingroup$ Hi thks for the reply, but we too are moving through space without a medium and at a measurable/comparable velocity. Some slower, some faster, some closer to c then others but they all respect the addictive vector speed without measurable loss, but light doesn't do this. $\endgroup$ – Nuno Figueiredo Barata May 13 '15 at 10:49
  • $\begingroup$ @NunoFigueiredoBarata I don't get your point. Velocities are measured relative to other objects. You can be at rest with respect to the Earth's surface and still be moving at 99.99% of the speed of light with respect to a particle in the LHC. Light will move at the same velocity relative to anything and everything. If you plug in $c$ for $u$ and $w$ in the velocity addition formula, you get $c$ as the resultant velocity. $\endgroup$ – SystematicDisintegration May 13 '15 at 11:02
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Einstein's postulate is that the relative speed between the observer and the source does not affect the speed the observer sees the photon moving, as long as the observer isn't accelerating, that is.

This basically means there is no such thing as absolute 0 speed. Speed of light is your new and only constant friend.

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  • $\begingroup$ Hi, thks for the reply. What i take from those postulates is that the photons sent in the same direction as the source would be always travelling at c and c is constant x m/s, so either the source must be at 0 m/s or we are travelling in a different space/time then light is... $\endgroup$ – Nuno Figueiredo Barata May 13 '15 at 9:32
  • $\begingroup$ No, the world is different than our everyday experiences at low velocities! Look up the velocity addition formula in relativistics. Regular Galilei transformation is just a low velocity approximation of the correct Lorentz transformation (which respects the speed-of-light limit). $\endgroup$ – Sebastian Riese May 13 '15 at 10:11
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If the speed of light is constant no matter the speed of the source

Actually, the speed of light isn't constant. It varies with gravitational potential, see Einstein talking about that here. However in gravity-free space the speed of light is constant. In addition you measure it to be constant regardless of your motion through space. That's because of the wave nature of matter. When you're made of waves along with everyting else, you calibrate your rods and clocks using the motion of waves. You define your seconds and metres using the motion of waves, and you then use them to measure the motion of waves. Magueijo and Moffat talked about the tautology in http://arxiv.org/abs/0705.4507. See The Other Meaning of Special Relativity by Robert Close for more.

shouldn't we be able to know the direction and exact speed we are going relative to the absolute 0 in speed?

Kind of, but we don't see the speed of light varying with direction, instead we see redshift and blueshift varying with direction. See the CMBR dipole anisotropy on Wikipedia: "From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 627±22 km/s relative to the reference frame of the CMB". You can gauge your motion through the universe from this. It isn't technically an absolute frame, but the universe is as absolute as it gets.

If a photon is sent in the direction we are going and one at the opposite, one of them should appear to go slower then the other because of our current speed

That isn't what happens. Again it's because of the wave nature of matter. It's like you can't detect any change in the speed of sound if you're made out of sound.

All this assuming c is constant and I still don't know why we believe in that.

It isn't constant. Einstein said it repeatedly, and the evidence makes it clear: optical clocks go slower when they're lower. Not because time goes slower, but because light goes slower. Unfortunately people tend to be taught that the speed of light is absolutely constant, and they never seem to do their own research. See this Baez/PhysicsFAQ article for more:

Einstein talked about the speed of light changing in his new theory. In the English translation of his 1920 book "Relativity: the special and general theory" he wrote: "according to the general theory of relativity, the law of the constancy of the velocity [Einstein clearly means speed here, since velocity (a vector) is not in keeping with the rest of his sentence] of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [speed] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers.

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