<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>You are not over-simplifying you are misconstruing. Even in classical mechanics a change in velocity requires an application of force over a period of time. It is not a matter of force alone or of time alone. Force gives an acceleration to a given mass, and after time that acceleration is reflected in a change of speed. Any positive amount of force increases speed, but it takes some time to realize that increase. Special relativity does not talk to acceleration. To talk about acceleration you need the machinery of general relativity. And there one proceeds as in Newton's mechanics and looks at the effect of force in changing momentum, only you need to expand your notion of momentum so as to apply it in a 4-dimensional space-time.Don't worry too much about the compound interest. By the time you get back from a long trip at relativistic speeds the debt will have been written off and your accounts will have long ago been appropriated by either the state or your heirs. But if you could avoid that then the key would be to leave a small amount in a savings account. I once did a calculation of what the $26 what was used to buy Manhattan would be worth if it had been put into a savings account at 6% interest on the day of the purchase. If the Indians had done that they could buy Manhattan back, with change. <br />Posted by DrRocket</DIV></p><p>Ok, I think I can see what you are getting at here. All right, I send my rocket off with enough fuel to take it up to 187,000 miles per second (I stay home and watch). The crew sets the controls to accelerate at a comfortable 1G. Once the ship gets up to 161325.2 (86.6% light speed) there is a Relativity Change Factor (RCF) of 2 (see the relativity calculator from a previous post). At this RCF 1 second on the spaceship = 2 seconds for me. Now (forgetting all that stuff about the weight ship decreasing as they burn up the fuel) if they are burning up a gallon of fuel per second to maintain 1G and one of THEIR seconds is now 2 seconds for me, it appears to me that they are burning up 1/2 gallon per second. At a RCF of 8 it appears that they are only burning up a pint per second. The closer they get to C the more they seem to close down the throttle. Those slackers have totally failed me! I gave them plenty of fuel to start with and they are using less and less of it! It's going to take them FOREVER to get to the speed of light!!!</p><p> Ill show them... Now I shrink the ship down (don't ask me how) and pop it into a particle accelerator, flip the switch and off they go. It seems like I've got the RCF working for me this time. At a RCF of 2 it's like 2 seconds worth of energy from the accelerator is pushed into 1 second on the ship. As the ship increases speed more and more energy is pushing it each second. Now the poor crew isn't accelerating at a comfortable 1G. The G forces are climbing at a exponential (?) rate. It's as if they are getting Heaver..and....HeAvER! From my control room it seems that the spaceship is still accelerating but at a slower rate as it gets closer to C due to the increase in inertia. It STILL seems like it will take forever to get it up to the speed of light! </p><p>Ok, I really want to see these guys go faster than the speed of light sometime before the end of the universe so I... (I know what your thinking... "Don't do it!") simply turn up the power on the accelerator to offset the effect of inertia. Inside the space ship their Tridimensional chess sets have long since clattered to the floor, their volley ball exploded. Now the exponential increase in G forces is increasing exponentially! (I think there is a term for this...some sort of function maybe? Honestly, I'm a blacksmith, I shoe horses. I'm not too good with the math part) I can tell that I'm going to have to turn the accelerator up way past eleven. Lights dim from Luxembourg to Sarajevo as it works to overcome the ever increasing enertia of the spaceship. It becomes apparent that I'm going to quickly need to turn it up to infinity! I abandon the smoldering ruins of the accelerator and skip town befor the electric bill arrives in the mail. </p><p><br /><br /> </p>
Basic Error: The accelerating Universe conclusion - reason
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