Tortoise and Hare Race

[arkain101]

Here I ponder a paradox in special relativity.

 

I will make it short.

 

We have two ships.

 

One is the (turtle) and it has a maximum speed of 100,000mph

 

The second ship (the hare) has a maximum speed of 0.99 C

 

They are flying to a distant planet, 1 light years in distance.

 

The slow ship will be experiencing very little time dialation so, the surrounding world will remain pretty much the same as it tugs along through space.

 

The fast ship will experience the sensation of itself experiencing slower time than the rest of the universe or the universe simply just going through time fast. Now if a clock will literally act faster in time dialation, then so will matter as a whole. So even though the fast ship is covering more miles per hour than the slower ship, it is infact losing time according to SR.

 

The problem here is, and I wish I could make the correct calculations. How can the ships arrive at the distant planet at very much different times in the sense that the fast ship will leave the slower ship in the dust and arrive there before. Yet with all the time dialation occuring, it should create a problem that because time was speeding along for the faster traveler, the slow ship will actually speed up. Now I dont know the exact numbers, but the problem here is they should overall arrive to the planet in generally the same time zone even though according to the slow ship, the fast ship got there much sooner.

 

I look at this in two extreme cases.

First a case in slow speeds, where the destination is person C. and the travelers are persons A and B. A going 100mph and B going 1000mph. Person C will shake B's hand before A's Hand.

Now for high speed travel, if A is going 100,000mph and B is going nearly the same speed as light, the time dialations will create a problem for C to decide who got there first. :) :hihi:

[Erasmus00]

The fast ship will experience the sensation of itself experiencing slower time than the rest of the universe or the universe simply just going through time fast.

 

To the people on the ship, the universe is moving. It appears as if the universe's clock runs slow, not fast.

-Will

[arkain101]

? I thought the high speed traveler was the one to "travel into the future" so to speak.

 

hmm.

[InfiniteNow]

? I thought the high speed traveler was the one to "travel into the future" so to speak.

 

hmm.

As seen by the folks left behind (not moving as quickly) it would appear so.

 

The good sir, Erasmus00, is correct...

 

 

The ship's travelers see everything else move more slowly.

Those watching the ship see them move very quickly.

 

 

The twin paradox sums it up well.

 

Two twins, one stays behind on earth, the other rocket's away at near the speed of light to a distant star. The one in the ship returns after what he experienced as 1 year, however, to his twin who remained, much more time (even millenia) has passed.

[arkain101]

The ship's travelers see everything else move more slowly.

Those watching the ship see them move very quickly.

What about the clocks?

 

The one in the ship returns after what he experienced as 1 year, however, to his twin who remained, much more time (even millenia) has passed.

 

 

How can the traveler think that time has moved ahead unless the surrounding physically does move ahead?

 

Besides, I was not refering to the twin paradox, I was talking about a slow ship and a fast ship racing towards a planet. If the fast ship was going to get to the planet years and years later, then his higher speed travel was not effective in getting there any sooner. The slower ship althought takes a longer time for himself, the surrounding time remains generally the same so the time it takes to get there will be the time that passes aswell at the destonation (at rest). So who really wins?

[InfiniteNow]

What about the clocks?

They would behave no differently than anything else on the fast moving ship. Relative to an observer in a stationary (or nearly stationary... slower moving) frame of reference, the clocks time expereinces the exact same thing. Anything in the system... clock, astronaut, vegetation, your computer helper HAL... will be part of the spacetime of that system and will be subject to the dilation.

 

 

How can the traveler think that time has moved ahead unless the surrounding physically does move ahead?

:eek2: They would not experience any changes different from what they would if they were standing still. All contextual cues around them would be experiencing the same dilation effect, and hence, it would all appear as normal. They would not know that their time was being any differently than someone else who is stationary.

 

When you're travelling on an airplane, you are experiencing (a very very very minute amount of) time dilation... but you don't notice it. Same with the traveller on the fast ship... the effect is just greater.

 

 

Besides, I was not refering to the twin paradox, I was talking about a slow ship and a fast ship racing towards a planet. If the fast ship was going to get to the planet years and years later, then his higher speed travel was not effective in getting there any sooner. The slower ship althought takes a longer time for himself, the surrounding time remains generally the same so the time it takes to get there will be the time that passes aswell at the destonation (at rest). So who really wins?

I know what you're trying to say, but your interpretation is off. I am no expert myself, and readily admit that, but I am rather certain this is not how it happens. If I'm wrong, then please accept my apologies, but think the above shows there is some more understanding from which you would benefit.

 

 

Cheers. :)