Does Absolute Velocity Exist?
Yes it does.
It seems everyone is on the same page about there being no "absolute velocity" due to the fact that everything is relativistic.
I'm a "relativist", but I'm not on that page. Because of the CMBR. Google on CMBR reference frame and check out the CMBR dipole anisotropy. It isn't an absolute frame in the strict sense of the word. But you can use it to gauge your speed through the universe. And the universe is as absolute as it gets.
However, this leaves me confused. This seems to be disconnected with the concept that the speed of light is in fact an unchanging constant.
I'm afraid it isn't. Check out Is The Speed of Light Everywhere the Same? on the PhysicsFAQ website:
"Does the speed of light change in air or water? Yes. Light is slowed down in transparent media such as air, water and glass."
"These gyroscopes send light around a closed loop, and if the loop rotates, an observer riding on the loop will measure light to travel more slowly when it traverses the loop in one direction than when it traverses the loop in the opposite direction."
"In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the not-quite-well-defined "speed" of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers."
The answer is no. The speed of light is not everywhere the same. But you measure the local speed of light to be the same because you define our seconds and your metres using light. So when you use them to measure the speed of that light, you always get the same answer. See
Comments on "Note on varying speed of light theories" by Joao Magueijo and John Moffat.
But to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer".
Speed exists. It might be relative to something else, even if that something is the universe. But even though it's only relative, that's no reason to say it doesn't exist. A bullet is just a harmless lump of lead that you can weigh in your hand. But a speeding bullet will kill you dead. Think about how that sits with "speed does not exist, but is only relative to an observer".
But yet, the speed of light is a calculable constant that never changes. How then, can we say, there is no such thing as absolute speed?
We can't. We can say there's no such thing as an absolute reference frame, such that you won't find your experimental results in your sealed box are affected by the speed of that box. But like I said, the universe is as absolute as it gets, and you can measure your speed relative to the universe.
If I throw a flashlight in space that is turned on 50mph, does the speed of the emitted light from the flashlight increase by 50 miles per hour in the direction I threw it? Of course not. We know this.
Correct. Because light has an E=hf wave nature. The speed of a wave depends on the medium it's passing through, not on the speed of the emitter.
But if this is truly the case, how then can there not be an absolute velocity which could be calculated by determining the speed of light in relevance to the object we're measuring (since the speed of light is constant)? Please help because this is bothering me.
It's simpler than you think. Look at the definition of the second and the definition of the metre:
The SI definition of second is the duration of 9 192 631 770 periods of the radiation...
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.
You measure the local speed of light to be constant because of the way you define your seconds and your metres, and because of the wave nature of matter. Check out things like pair production and electron diffraction. Ask yourself this: if you and your rods and clocks were made out of sound waves, such that you defined your metres and second using the motion of sound waves, how would you ever measure the local speed of sound to be anything other than 340 m/s?
Edit 14/09/2017:
To check out what I said above, see this in the Einstein digital papers dating from 1920:
"As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable. From this it follows that the entire conceptual system of the theory of special relativity can claim rigorous validity only for those space-time domains where gravitational fields (under appropriately chosen coordinate systems) are absent."
The speed of light in vacuo varies. Also see this PSE answer which quotes professor Douglas Scott:
"However, the crucial assumption of Einstein's theory is not that there are no special frames, but that there are no special frames where the laws of physics are different. There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe. But for doing any physics experiment, any other frame is as good as this one. So the only difference is that in the CMB rest frame you measure no velocity with respect to the CMB photons, but that does not imply any fundamental difference in the laws of physics."
Special relativity pre-dated the CMBR. Also see this in the Einstein digital papers, again from 1920:
"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether".
See Wikipedia and above for the definition of the second and the definition of the metre. They are both defined using light.