One thing I’ve never understood about relativity is the seeming conflict between the following 2 statements:
[ol]
[li]Nothing can travel faster than light.[/li][li]There is no absolute reference frame.[/li][/ol]
If there’s no absolute reference frame, then there is no “absolute velocity” to any “thing”. So, statement 1 refers not to absolute velocity but relative velocity? Relative to what? Anything else? If so, is the correct version of statement 1:
Nothing can have a motion greater than the speed of light relative to any other thing in the universe.
???
Question 2:
Hubble’s law for the expansion of the universe is that the relative velocity between 2 galaxies is a linear relation given by v = ~75km/s/Mpc (kilometers per second per megaparsec). This means that each megaparsec (3.3 million light years) further away, galaxies at that distance will be receding at an additional 75km/sec. The speed of light is 300,000 km/sec. Simple division shows that galaxies further than 4000 Mpc should be receding at greater than the speed of light. How is this either possible or not possible?
[ol]
[li]There is no absolute reference frame.[/li][li]The speed of light is the same in every reference frame.[/li][/ol]
The resolution to that conflict is that velocities don’t transform the way you think they do between reference frames. In Newtonian mechanics, and common sense, if A sees B traveling at u (in a certain direction), and B sees C traveling at v in the same direction, we would conclude that A should see C traveling at u + v. Turns out that this is wrong.
In special relativity, we would conclude that A sees C traveling at (u+v)/(1+uv/c^2). if u and v are both much smaller than c, the denominator is very close to 1, and this is almost u+v. But if u and v are close to c, the answer is significantly different.
I won’t re-hash what leachimhas said, but the speed of light (in a vacuum) is c in all inertial (i.e. non-accelerated) reference frames. That means that our observer at rest in a particualr inertial reference frame will observe the speed of light to be c. If we change to another inertial reference frame, travelling with some non-zero velcoity relative to the first reference frame, an observer in that frame will alos measure the speed of light to be c. This is where time dilation and length contraction comes in: the distance and time between two events as measured by our two different observers will not be the same, which allows the speed of the same wave of light to be the same in both frames.
So-called recessional velocities can be greater than c as general relativity is a bit different tospecial relativity.It only predicts that the speed of light is ‘locally’ constant, which means that it is easy for very far away objects to have velcoities apparently greater than c.
As I understand it they are moving at less than the speed of light, but space is being created between us and them (dark energy?) so they appear to be moving faster. Don’t ask me for any further clarification as I don’t fully understand it either.
It’s not the speed they’re “moving” - they’re not moving through space at that speed. Rather, space itself is expanding, which can cause things to recede from us at greater than the universal speed limit.
They’re not breaking the speed limit because they aren’t actually moving away from us in the convention sense of an object moving through space. It’s just that more space is being inserted into the universe between them and us.
Let me add to the OP. It is not true that everything must travel below c. Massless particles not only may but travel at c. From what I have read, no law of physics forbids massy particles from traveling above c, but then they must always do so and adding energy to them slows them down! Nobody believes such particles exist (or they didn’t until last week), but if they do they are called tachyons (“tachy” from Greek means fast).
Now as must dopers will know, some researchers have recently claimed that neutrinos travel faster then c. Somewhere on these boards, someone calculated that had neutrinos traveled at the speed the researchers claimed, then the neutrinos from he 1987 supernova would have arrived 4 years before the light. But that supposes that the neutrinos from the supernova travel at the same speed as in the recent observation. But coming from the center of a giant supernova one might suspect that they were super-high energy and maybe traveling just barely above c.