We do. That's good enough.
And it's not so much that we can't reach the speed of light in a vaccum. More that we cannot reach C. Which just happens to be the same value as that of the speed of light in a vaccum.
And... light DOES have a fixed speed. Its just that when you move that fast the rest of the universe shrinks to a very thin slice in the direction you're traveling (imaging a beach ball being flattened like a pancake). Therefore it doesn't take you long to go the distance because the distance...
Well, in your previous example, although it only takes you 16 days everyone else sees it take you about 10 years. So when you think about light in the same way you'll realize that the light travels everywhere in no time at all, but we see it take distance/C time. The same as everyone else saw...
To measure the the length of something you have to record the positions of the front and rear ends at the SAME TIME. Therefore it makes no sense to compare lengths across frames. The object can appear shrunken to one observer and unshrunken to another because their experiences of time will be...
There is, as someone has already mentioned, a limit to the speed at which information can be transfered. In this case "reality" is affected by this limit too. "Reality" is what we can measure or observe. If we can't measure it then it doesn't exist. So the universal speed limit directly affects...
What the guy above said...
If the front clock was 1 ls ahead then when he swaps the same clock (now at the rear) will stay 1 ls ahead. The clocks will only swap the 1 ls difference, eventually, if they were moving ahead away from the bloke who swapped them.
Look at "relativity of simultaneity" on wikipedia. Check out the explanation of the light hitting each end of the train simultaneously in one frame and not so in another. Then apply that phenomena to this situation.
As one person slows (accelerates) the agreement of what is considered...
Just to clarify: While the two are moving inertially they WILL both will see the other aging less when taking their own frame as being static. This is not an illusion or anything. Both are ageing quicker RELATIVE to the other when considered static.
When one turns round though this symetry...
A line of simultaneity just links more than one event that are considered simultaneous according to the observer. So on a spacetime diagram they'll be horizontal lines all along the time axis.
Usually they are used to show differences in simultaneity between 2 different observers moving...
I feel compelled to point out, for anyone who hasn't realized yet :rolleyes:, that Mr Bentley is fully aware that there cannot be an actual working ansible. He proposed the idea as a way to make it clear that he is giving his explanations of events having already accounted for, and removed...
I think the idea is that one person can see the invading fleet deliberating a potential invasion. He's watching; waiting to discover his fate.
Meanwhile some other bloke moving relatively has already seen the aliens decide on war and launch the fleet.
The first guy is deciding what course...
That's the old alien invasion from alpha centauri "paradox"?
Lack of simultaneity is the reason of course, but i think that the main cause of "concern" regarding this scenario is implications regarding determinism, fate, free will, and all that stuff.
Actually I'm not quite sure if I'm right here. I know it to be the case and i know that the changing orientation of the simultaneity lines "fixes" the "paradox". But I'm not sure if I'm correct in saying that the lines show the clock running slower. It doesn't matter. It's besides the point.
Look at this diagram:
The shows something that could be the two twins. Alice at home and Bob moving. It shows the situation of Alice's viewpoint. Her time and space axes are in white.
The diagram also shows Bob's time and space axes in bold blue. They are skewed, as expected, because he is...