I know that nothing can exceed the speed of light, but

[1977ub]

But isn't that precisely how relativity was figured out? It's not like Einstein took data points and worked backwards.

Classic Galilean "relativity" existed before Einstein. The Michelson-Morley experiment had heads scratching before Einstein developed relativity.

http://en.wikipedia.org/wiki/Michelson–Morley_experiment#Fallout

Lorentz transformations predate relativity.

http://en.wikipedia.org/wiki/History_of_Lorentz_transformations

"Talent hits a target no one else can hit; Genius hits a target no one else can see." ~ Arthur Schopenhauer

 

[1977ub]

it is theoretically possible to increase the velocity of a spaceship until the velocity is well beyond the speed of light when compared to some initial velocity?

There are different ways to look at how this is impossible. If the traveler uses classical calculations to determine that he can use a certain amount of energy to get to 51% of c relative to the rest frame, and then plans that he'll just do it again from that 51% bringing him above c, when he actually executes that project, people in the RF find his clocks are quite slowed down once he executes his first thrust and he is not even all the way to his projected 51%, and his speed up from the 2nd thrust just doesn't take him beyond c. The more energy he puts out, the more his clock is slowed down, and it just can never happen.

Some explanations refer to how the ship becomes "heavier" and this requires more and more energy as measures from the rest frame.

It turns out that it takes infinite fuel/energy to get up to [what the rest frame calls] c (let alone beyond).

A lot of descriptions of this out there - you might enjoy reading a few.

http://www.edge.org/3rd_culture/hillis/hillis_p3.html

 

[Agerhell]

hmmm...

Looking at this again, brings up another question in my head.

If you had a train that circled the globe at the equator traveling at 2m/s, with another train riding on top of that train traveling at 2 m/s, a stationary observer would view the top train as traveling at 3.99999999982224 m/s, both coming and going.

Does that sound right?

And with a equitorial circumferance of ≈40,000,000 meters, the lower train would make the trip in 20,000,000 seconds. The upper train would do this in 10,000,000.00044 seconds, or ~4.4 tenth thousandths of a second longer than it should.

Does that sound right also?

Well, as the Earth is spinning at a velocity of 40000km/24 hours at the equator eastwards it matters if the train(s) are going east or west. When the trains are going east the rotation of the Earth has the same direction as the trains. Therefore the clocks onboard the trains will tick slower than an earthbound clock and the upper train will move slower than 4m/s as seen from an earthbound observer.

However, if the trains are going west the clocks onboard the trains will tick faster than that of an earthbound observer and the upper train will move faster than 4m/s as seen from the earthbound observer.

 

[jalsck]

Thanks for the replies. I understand that the ship cannot be observed to be traveling at or faster than c. All observes are on the ship and they can measure the acceleration of the ship. Is it true to say that after a period of measured acceleration (measured by the observers in the ship) the observers cannot conclude that their speed has changed?

 

[HallsofIvy]

What speed are you talking about? If there is a non-zero acceleration, then the observers on the ship would determined that some outside objects speed, relative to them, has increased. Of course, the ship's speed, relative to observers on the ship, is always 0.

Of course, if at some time, the speed of an object outside the ship is .9c relative to observers on the ship, and the ship accelerates, yes, the observers will see that speed increase to, say, .99c. Then later, it might increase to .999c, constantly increasing but always slightly less than c.

 

[Nugatory]

Thanks for the replies. I understand that the ship cannot be observed to be traveling at or faster than c. All observes are on the ship and they can measure the acceleration of the ship. Is it true to say that after a period of measured acceleration (measured by the observers in the ship) the observers cannot conclude that their speed has changed?

When you say "their speed has changed", I have to ask you what that speed is relative to.

If all the observers are in the ship and they have no outside reference point, then for all they know they are at rest the whole time and using their rocket engines to hover in a powerful gravitational field.

 

[jalsck]

When you say "their speed has changed", I have to ask you what that speed is relative to.

If all the observers are in the ship and they have no outside reference point, then for all they know they are at rest the whole time and using their rocket engines to hover in a powerful gravitational field.

Instrumentation on the ship would enable the observers to measure any distortions in space/time . For the thought experiment we could say there is only the ship and uniform space/time. I'm not attempting to argue that there is something wrong with relativity. The only observers are on the ship.

 

[jalsck]

I think the cause of some people's confusion is the phrase "nothing can travel faster than the speed of light". We see this statement in the media now and then. I believe it would be better to say "matter cannot be observed to be traveling at or faster than the speed of light".

An unmanned spaceship could potentially travel to a star 100 light years away and return in a matter of weeks (measuring elapsed time on the ship itself). If people were traveling on the spaceship and they could survive 2 G's of acceleration then the round trip would take just over 10 years (as measured by the people on the ship). They would have to accelerate at 2 G's until they were half-way there and then decelerate at 2 G's until they arrived at the star. Same heading home. A little over 202 years would have passed on Earth by the time they were home.

Disclosure: I'm not an expert on the subject. I'm learning... slowly.