This question may be nonsensical, but I have to ask. I'm a noob to relativity so please bear with me. All observers measure the same speed of light, correct? We also know that there is no favored frame of reference. So... what is to stop an object from accelerating to 0.95c, taking a measurement of the speed of light within this reference frame, and then accelerating to the "new" 0.95c from that reference frame? Would this not qualify as exceeding light speed according to some arbitrary frame of reference? Conceivably, the object could continue to this forever unless a fixed frame is defined... Perhaps I am missing the point, but it seems as if there must either be a true rest frame in the universe or special relativity is self-contradictory. Any thoughts? I think I am misunderstanding because I haven't taken a crack at the maths. Maybe this turns into an exponential function of some sort at which the speeds are not additive but are bottle-necked by some limiting formula... Perhaps the arbitrary point will only see fractional increases?
Good guess! Here's how to add velocities that are given in different reference frames. In your example, v=0.95 in the original frame u=0.95 in the frame already moving with v=0.95 w=0.9987 resulting velocity in the original frame It's easier with rapidity: v=1.83 u=1.83 w=3.66
Thanks, Ich! The implications of this are astounding. Who is to say that according to some observer, we are not already moving at 0.999999999c and just playing around in a very small margin of spacetime. I suppose this means that light "speed" is more of a relationship between reference frames, and not exactly as we would picture "speed" in the concrete sense.
Forget this "small margin". It is completely irrelevant whether or not you're moving with .999999999999999999999999 c relative to some observer. It is one of the postulates of SR that this doesn't matter. Maybe it helps if you use - for a start - a definition of speed that behaves more like speeds in Galilean times: rapidity. Even if you have a large rapidity relative to something, you can still increase it infinitely. It is without bound. You can translate from rapidity to speed with a (relatively) easy formula, and it is only then that you map the infinite range of rapidities to the ]-c;c[ interval. c is special as the corresponding rapidity is infinite. You can say that c plays the part of an infinitely great velocity. Maybe that helps to understand why many formulas yield infinities at the speed of light.
I understand that it is irrelevant to us. I am thinking philosophically. I mean, we are bound to this inertial reference frame for the most part and perfectly happy measuring everything in earth time, earth speed, and light speed derived from the earth meter and second, etc. The point I was making is that on some scale our universe could be expanding at a rate beyond anything we can possibly conceive of, and all the changes in the universe that we observe would appear to someone "outside" of the expansion (knowing that this is a completely different argument) to be quantum-scale changes. All of this makes spacetime seem very dynamic. I am trying to picture the difference between time inside of our galactic orbit and time in a place where there is comparatively little gravitational influence or magnitude of velocity. I am assuming that in such a place, time would approach infinity relative to us... that by some stretch, our galactic supermassive black hole could be that which regulates our clock, our ruler, and basically our total reference point. Not only are we within a gravitational field at all times, but also in motion at all times. It seems to me that our knowledge may be limited due to a self-referencing issue... that we really do not know just how "deep" the stillness can be outside of our present position. Have we really ever dealt with any values outside of our constant galactic velocity? It seems that matter and motion must create time as Stephen Hawking sort of touched on when he talked about the expanding universe being one of the possible drives of time. I am wondering if relativity skews our perception of the "billions of years" it takes light from distant galaxies to reach us. After all, the light must travel through this comparative void where time, speed, and distance could be FAR different than we can conceive of. It seems to me that the "speed" of light as measured by us could take on a whole new meaning outside of our galaxy... speaking relative to us of course. I also understand what you mean about light being an infinitely great velocity. When time dilation is possible, covering extraordinary distances with very little elapsed time is possible (at least in someone's frame of reference).
Same question is bothering me, kamikaze762 I posted a topic with a thought experiment on the issue and you may take a look at it: https://www.physicsforums.com/showthread.php?t=391423
You're drifting off into philosophy. To address two points which seem reasonably concerned with physics: These theories are named after "Relativity", which is the guiding principle behind them. Gravitational potential as well as velocity are relative concepts. You can't tell where things are slowest or potential is highest (except in artificial toy models). That's not a matter of lacking knowledge. Both absolute velocity and absolute potential don't exist, so how could we know their values? You bet! You can gain an understanding of these things if you study GR. You have the metric there as a basis (well, at least after finding a solution to the field equations), and all these concepts like distance, time, velocity, and potential have to be drawn from it. There are are usually infinitely many way of doing this, and you get a feeling how much these concepts are relative.
Thanks again, Ich. I think I will peek at the field equations. I just wish I had as great an interest in math as I do in concepts, lol.
We ARE already moving at .999999999c relative to an infinite set of inertial reference frames! Of course assuming we're practically at rest relative to the "fixed" stars, there might be no actual observer at rest in any of those frames. But who knows?