Relativity question: near-light speeds and perception in different reference frames

[RaynorWolfcastle]

OK, my phys. prof. asked an interesting relativity question which I don't know how to explain. Could someone give me a hand? Now this is only special relativity so the math is easy.

Bob is in a 360m spaceship traveling at .99c toward a barn in which Joe is standing. The barn is 120m long.

Q1: From Joe's point of view, will the spaceship ever be completely contained in the barn?
A1:yes, because of length contraction

Q2:From Bob's point of view, will the spaceship ever be completely contained in the barn?
A2:no, because of length contraction.

Q3: How do you explain this?
A3: ?????

From analyzing the length contraction equation I concluded that someone going infinitely near the speed of light would see in his reference frame that he spans an infinite length while maintaining a correct height. For the people outside the ship, the ship is infinitely thin and is essentially a vertical line.

While this makes sense mathematically, doesn't this create a paradox? I.E. People in different frames see different events. Can someone help me understand how this works?

-Ice

 

[Stealth1024]

Paradox related to near light speed travel? Wouldn't be the first time...

The effects of acceleration on time leads to the very interesting twin paradox. Let there be two twins each of identical age. Let one twin stay on earth and the other board a theoretical spaceship capable of near light speeds. The twin in the spaceship then proceeds to travel at near light speed for several hours while the twin on earth remains stationary. Upon returning to earth, the twin on the spaceship would observe that several years have passed on earth, while from his perspective in the spaceship, only several hours have passed. While traveling at near light speeds, the twin in the space ship does not notice any anomalies in time. Time, as does the speed of light, always moves at a constant rate as observed by an individual, but time relative to two individuals may vary. Logically applying previously discussed theories, yields the statement that movement through space creates distortions in space that are felt as gravity, and thus gravity slows down time.


Consider a spaceship with a bubble of light outward from the ship in all directions. All possible futures are depicted by what the light sphere encompasses. Since one cannot travel faster than the speed of light, as far as one is concerned, there exists nothing outside of the light bubble, or at least one cannot travel there. As the spaceship nears a black hole, the light bubble becomes completely biased in the direction of the black hole by the extreme. One?s future is now completely biased towards this massive object and one has no possible future but to continue toward the center of the black hole. Time has been converted into a direction in space by gravity.

 

[Sohcan]

The paradox can be explained through the relativity of simultaneity....events that occur at the same time in one frame can happen out of order in a different frame. The classic example is a light bulb in the middle of a railroad car that emits two pulses of light, one towards the front of the car and the back. In the stationary frame, the two pulses hit the front and the back at the same time...these are the two events that happen simultaneously. In the lab frame, if the railroad car is moving forward at velocity v, a stationary observer sees the pulse hit the back of the car before the other pulse hits the front of the car, due to the finite speed of light. Thus the two events have occured in a different order in different frames. This principle has to obey causality, though....if the two events are spacelike, such that in the stationary frame they are seperated by a distance that is greater than the time it takes light to traverse that distance, the events cannot happen out of order. For example, if I were to shoot a target with a bullet in the stationary frame, there is no other frame such that the bullet strikes the target before the gun is shot....that would imply the bullet travelled faster than light and/or moved backwards in time.

So back to the barn paradox, let's say the barn is 5m long and a guy is running towards it carrying a pole that is 10m long. Let's say he's running at a velocity such that, due to length contraction, an observer in the lab frame sees the pole as 5m long. Gamma = Lp/L = 10/5 = 2, so v = .866c. At some instant, the stationary observer sees the entire pole inside the bard....these are the two events that happen at the same time: the front of the pole exits the front of the barn at the same instant the back of the pole enters the back of the barn.

From the runner's point of view, the barn has a length L = Lp/gamma = 2.5m, compared to his 10m pole. The difference now is that the two events described above don't happen at the same time, due to the relativity of simultaneity...you can't assume that the clocks are synchronized. If you draw the world line graphs (it's kind of hard to describe them), it's pretty easy to see that the events of the front and back of the pole entering and leaving the barn happen in the order and at the times the runner would expect.

Do you have a modern physics or relativity textbook? A good one should explain the paradox pretty well (probably a lot better than I did ), as well as the relativity of simultaneity and world line graphs.

 

[RaynorWolfcastle]

Well, this class is really just an introduction to relativity and modern physics. The book I have (Tipler, if that helps) really contains a in introduction to pretty much everything in physics. I also have Feynman's "Six-not-so-easy-pieces". I understand that both events do not occur simultaneously, I just don't understand how 2 people can see two different realities because of high speeds (Joe sees the rocket contained in the barn, whereas Bob will never see the rocket contained in the barn). Could you possibly explain that to me?

-Ice

 

[LordMagnusKain]

Could you possibly explain that to me?

yes:

it's all a matter of perception!, light bounced offof stuf diferently when it goes fast.

the ship will never RILLY fit in the barn, it'll just look that way.

verry simple, stop confusing yourself with relotivistic volocitys, and super-string theories ofthe unification of fealds; just apply a little comon scence, to your mound of knowledge.


-----------
how's THAT for highly techinical?

 

[Sohcan]

Well, you just have to convince yourself that, because of the relativity of simultaneity as I explained above, the paradox doesn't exist...you can't really apply your intuition when events in different frames are happening at different times and in different orders. I know it's a horrible explanation, but I normally don't have to teach this stuff.

 

[RaynorWolfcastle]

Sohcan, so what you're saying is that there is no absolute reality i.e. we cannot say that "the pole was completely in the barn but was obseved otherwise by observer X". We can only say " in observer X's reference frame the pole is never completely in the barn, but in observer Y's reference frame the pole is completely in the barn for time t." Is this a correct way of stating things?

-Ice

 

[Sohcan]

<< so what you're saying is that there is no absolute reality >>

Essentially, yes....time is not a constant, causality is. Because events can happen in different orders and at different times in different reference frames, I guess you can't make assumptions about certain aspects of a system...such as if an object should or should not appear to be completely contained in the barn in all reference frames. Certain quantities are invariant across all frames, such as the spacetime interval ( s^2 = (ct^2) - x^2) and invariant mass ( E^2 = (mc^2)^2 -(pc)^2), which can be very handy when solving special relativity problems.

You said you have a book by Tipler? If you have the third of edition of Modern Physics by Tipler and Llewellyn, check out page p. 53 for the Barn paradox, p. 26 for spacetime diagrams, and p. 41 for the spacetime interval. For a more formal four-vector approach to special relativity, check out these notes, though it doesn't really give many examples as in Tipler....