I see what you mean with the frame of reference(I hope) but shouldn’t the fastest it could take them be one second? Or am i just missing this. And is the .88 seconds from the ships frame of reference? because time moves slower for moving objects so in reality could it have actually taken them more than .88 seconds which in turn would explain it. As you can tell, slightly confused over here 
That is exactly what is accepted in physics. So what happened? How is it that they measure that it only took 0.88secs?
I’m not sure what you mean by that…? Did you mean that Science has observed the truth of that statement?
I am not disputing your statement. But the scenario in the OP is doable by Science principles… except for that nasty forbidding of an absolute frame. Otherwise, it works well with all know principles of Science.
Why 1 sec?
The reading of 0.88 came from one of the ship’s “travel clock” (running only during travel).
Fine. So how much longer and by what means of measure would you know?
Btw, the typical formula for calculating time (or length) dilation is;
df = 1 / (1-(v/c)[1]2[/size])[2]1/2[/size]
In case you can’t make that out;
dilation factor = 1 divided by the quantity of the square root of (1 minus the square of (sample_velocity divided by the speed of light))
Basically there relative speeds may appear to be x from their frame of reference but in fact it is not >c and the rule of composition of velocities applies. Looking at
we can use the lorentz transform thusly
The question is poorly phrased though as it would never be possible to measure a time difference that would give 2.27 times light, but that said basically relativistically speeds approaching c don’t add because of time dilation and space contraction effects.
This “problem” is entirely flawed from the beginning.
First, however, a note. Special relativity doesn’t simply say that there is no absolute reference frame. It assumes that changing the reference frame one uses does not change the fundamentals of physics and that the speed of light is the same in all reference frames. This means that for a large range of reference frames, we can choose whatever we want and we will get the same events happening according to the laws of physics. It also means that there is no absolute reference frame that is picked out by the events in physics; i.e., there is not one special frame where everything works out or where all the laws of physics have their true form.
OK, so now to the problems.
One thing that is a prerequisite to any discussion of physics is a reference frame for measurement. In non relativistic scenarios we can assume a vague reference frame, but in relativistic scenarios we need to understand what reference frame we are using because it matters to the calculations. In this case, we are not told the reference frames in which the “2 light-seconds (2Ls) apart” is given.
In this case, I could presume that both ships are at rest relative to one another and that the distance given is in a reference frame currently at rest with respect to the ships. However, this is information that should be supplied at the start.
We have to know what a “travel clock” is. Does this measure the travel against a given reference frame? The reference frame that should have been given above but wasn’t? And what was the speed relative to the given reference frame? Is it the measurement of how long the engine was firing?
The distance between each ship is not a constant thing, it is something that depends on the reference frame that we use to determine the distance. Through choice of reference frame, we can make the distance between the ships arbitrarily small.
I fear that in the above question there is a confusion between an absolute reference frame and a reference frame as an intellectual artifact. An absolute reference frame is a particular frame that is picked out by peculiar physical laws or phenomena; this is something that is effectively ruled out by special relativity. A reference frame is an intellectual artifact that we use to describe physical situations and always has been; this is something used by special relativity. In order to describe distances and use physics, we need a reference frame.
I am afraid that I simple do not understand what this is supposed to mean.
I’m glad I’m not the only one. Nice expansion Physbang.
Nice explanation.
The question itself is paradoxical though, therein lies the problem, if you understood special relativity you would never ask that particular question in that particular way. you’d maybe say 1.98x the speed of light, but 2.27 would break the laws of physics as we know them in the first place and would be out of kilter with all measurable scientific fact.
Right, what I’m saying is that the 0.88s thing doesn’t happen.
The second postulate of special relativity is: As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.
All entities involved in the example are inertial frames of reference, since two objects traveling at c towards each other are at a constant velocity, and any stationary observer would also be in an inertial frame. So, we are good to go. No violations here. It is that pesky bit in the denominator that normally gets ignored because, well, how often do we calculate velocity for things approaching c? It’s all about Einstein’s flashlight.
Now there is a surprising first statement from you. {{NOT!}}
You are given all of the information necessary to answer the question of what happened. The challenge is to do it without introducing an absolute frame which is by definition independent of the observers.
Exactly correct.
But the 0.88secs does happen. So explain how. 
Source?
Of?
James: maybe I can explain it using some different numbers. You’re near Earth in your spaceship, and I’m out near Alpha Centauri in mine. We’re pretty much at rest, and we agree that we’re separated by 3.96 light years. I now start heading towards you at .99c as measured by you. You calculate that it will be four years before I reach earth. I of course now measure distance and time rather differently. As far as I’m concerned, the distance from me to Earth looks length-contracted by a factor of 7 down to .57 light years. ( 1/√(1-v²/c²) → 1/√(1-.99²) = 1/√(1-.98) = √(.02) = 1/.1414 = 7 ). I’m also time-dilated by a factor of 7, so as far as I’m concerned it’ll be 4/7 or .57 years before I reach earth.
You now start heading towards me at .99c as measured by observers on earth. The velocity addition formula says I measure our closing speed s = (v + u) / (1 + vu/c²). This works out to be (.99 + .99) / ( 1 + .99 * .99) = 1.98 / 1.9801 = .99995c. That’s how fast I would say you were travelling if I considered myself to be at rest. But if I did, I’d also have to assert that the distance between the Earth and me is shortening. We crash into each other after .285 years subjective time, which is 2 years as measured by observers on Earth. At that instant the distance from me to Earth has shortened to .285 light years, and you’ve come across it at .99995c. This “shortening” is what’s missing from your scenario.
There is no length contraction except by the measurements of someone while they are traveling.
In my scenario, no measurement except time is being taken while any motion is taking place. Length contraction doesn’t apply.
And before anyone mentions it, relativity of simultaneity doesn’t apply either.
No problem re the length contraction James. The distance between here and Alpha Centauri doesn’t actually change when you travel at .99c. Your measurements of distances in the universe are altered by your motion through the universe, that’s all. Your measurements of the distance diminish as your speed increases. Some might say that this is “real”, but it’s no more real than the way measurements of size are diminished by distance. You can speed up and slow down and see a distance concertina-ing, just as you can move back and forth and see a size concertina-ing.
As for measuring time, a clock clocks up motion. When you measure time, what you’re actually measuring is cumulative local motion. Your measurements of this motion are altered by your motion through the universe.
Note that this doesn’t mean that special relativity is wrong. Just that the way people describe it is wrong, because they rely on a “mystical” non-explanation for the constant speed of light. See The Other Meaning of Special Relativity for the right way to describe it. We measure the speed of light to be the same because in simple terms, we’re made of it.
Right, so back to the question; “What happened such as to cause a measurement of 2.27c?” {{without introducing an absolute frame}}
The answer seems to be: “You wouldn’t get a measurement of 2.27c.”
Trust me enough to accept that there really is an answer that shows how easy those numbers would be real. It isn’t that complicated of a scenario. The challenge isn’t really how it could happen, but rather how it could happen without an absolute frame.
No I mean… you wouldn’t do the calculation by saying 2/.88
You are ignoring the fact that your clock would have been running slower the faster you moved… for one.
Those are the only measurements they have.
No. I am asking for you to “do the math” and show me how you do it without introducing an absolute frame.
The astronauts don’t believe the figure either.