My paradox, dead or not according to different observers

[ppppppp]

My paradox, dead or not according to different observers!

1. Suppose, a fast moving train (600,000 km long) circling on track (radius is 600,000 km, radius can be even more, this is just convenience reason) at speed 0.999c. A stands at center of the track.
2. B stands in center of train. C stands at end of train. D stands in head of train.
3. Now B flash a lights. According to B, the lights reaches C, D same time (in one second). According to A, the light reaches C first, then (22 seconds later) reaches D.
4. Now suppose, as soon as light reaches C, C shoot a super fast bullet (at speed 100,000 km per second) at A. And D shoots a laser beam (to destroy) C's bullet as soon as light reaches D
Now I ask, will A die or not! According to A's reference frame, he is dead! Because the bullet travel time travel from C to A is only 6 seconds, D's laser is fired only 22 seconds later, too late to save A. (we can even suppose bullet travels evern faster, so fewer seconds, but for convenience, I set up as 6 seconds, radius 10m km/1m km speed of bullet.)

But according to B or C, D (all on the train). A is saved. Because when light reaches C, D same time. D's shoot laser it takes less than 2 seconds, less than 2 seconds in A’s reference frame as well for laser light intercept the bullet. (2 seconds is very simple geometry, you can check out with pencil & paper)Please find out the problem or solve this of my paradox.

 

[ppppppp]

jess, can you check?

 

[Dale]

a super fast bullet (at speed 1 million km per second).

http://en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds
Better luck on your next "paradox".

 

[ppppppp]

http://en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds
Better luck on your next "paradox".

yes, I corrected. Can you solve the paradox? Do you understand the essence of questions! if you can answer, share your answer!

otherwise, just stay aside!

 

[Dale]

Work the math, you will see that all frames agree on whether or not A dies. None of these things that you have posted are paradoxes, they are just sloppy conclusions assuming the answer you want rather than doing the math.

 

[ppppppp]

Work the math, you will see that all frames agree on whether or not A dies. None of these things that you have posted are paradoxes, they are just sloppy conclusions assuming the answer rather than doing the math.

then share your answer with math! otherwise, please do not pretend you know the answer.

 

[DaveC426913]

Okay, the track has a radius of 100,000km and the train is 600,000km long.

Thus, C and D are right next to each other. Light reaches them both at virtually the same time.



And pppppp: be courteous. you're coming across a bit rude.

 

[Dale]

then share your answer with math! otherwise, please do not pretend you know the answer.

I know the answer, but you won't learn unless you at least make an attempt to work the problem. Don't be lazy, it's your question, at least attempt to answer it rigorously.

 

[ppppppp]

Okay, the track has a radius of 100,000km and the train is 600,000km long.

C and D are right next to each other. Light reaches them both at virtually the same time.



And pppppp: be courteous. you're coming across a bit rude.

I can easily make radius few times longer. I will make you feel comfortable if this works

 

[DaveC426913]

Also, are you accounting for the fact that, at .999c the train will be length-contracted by a factor of 22?

 

[DaveC426913]

I can easily make radius few times longer. I will make you feel comfortable if this works

That will completely change all your numbers and locations of passengers and transit times of signals.

A 600,000 km long train on a 600,000 km track will put C and D right next to each other.


As you can see, it is easy to create paradoxen if you start with poorly defined scenarios.

 

[JesseM]

1. Suppose, a fast moving train (600,000 km long) circling on track (radius is 100,000 km) at speed 0.999c. A stands at center of the track.

2. B stands in center of train. C stands at end of train. D stands in head of train. [/quote]
Do you understand that the various rules of SR, such as the time dilation equation and the idea that light always has a coordinate speed of c, only apply in inertial frames? In your example, B C and D are moving in a circle, therefore they are not moving inertially and do not have their own inertial rest frame.

3. Now B flash a lights. According to B, the lights reaches C, D same time (in one second).

Since B does not have an inertial rest frame, "according to B" cannot mean "in B's inertial rest frame". So what does it mean? Are you talking about what would happen in a non-inertial rotating coordinate system where B is at rest? But in such a coordinate system light would not travel at the same speed in both directions, so you can't say that the "the lights reaches C, D same time" if you're talking about "same time" in such a coordinate system.

I'll wait for your answers to these questions before looking at the rest, I suspect you just didn't realize that B & C & D were non-inertial, or else didn't realize that light doesn't necessarily move at c in a non-inertial frame.

 

[Dale]

Start by assigning coordinates to all of the important events and worldlines in B's frame, then transform to A's frame. Or vice versa. Once you have the coordinates in one frame, it is easy to determine everything in the other frame.

EDIT: As JesseM points out B's frame is non-inertial so it will probably be easiest to start with A.

 

[ppppppp]

Hi, i just changed the radius, please check if there is still problem.

Also for lorenz factor, i can set up train speed 0.999c or even faster to a factor of millions. (did with lorentz transformation formula 1/(1-0.999^2)^0.5 = 22..)

 

[JesseM]

Hi, i just changed the radius, please check if there is still problem.

Circular motion is always non-inertial, regardless of the radius. Can you reformulate your problem with a train moving on a straight track rather than a circular track?

 

[ppppppp]

Hi, i mean train circling at constant speed 0.999c on the track. In side the train frame, lights reach both end and head of train same time, as it is on constant speed. not right?

 

[DaveC426913]

Hi, i mean train circling at constant speed 0.999c on the track. In side the train frame, lights reach both end and head of train same time, as it is on constant speed. not right?

Why would light reach C and D at the same time? In the time it takes light to travel to the observers, they have both moved a significant distance. One toward the source and one away from the source.

 

[ppppppp]

Circular motion is always non-inertial, regardless of the radius. Can you reformulate your problem with a train moving on a straight track rather than a circular track?

Please let me know if train circling at constant speed 0.999(...)c is causing lights not reaching both ends of train same time, in the reference frame of inside train, ie. B, C, D?

2nd, if I change to straight line. Can you check/digest the paradox in straight line scenario?

 

[JesseM]

Hi, i mean train circling at constant speed 0.999c on the track. In side the train frame, lights reach both end and head of train same time, as it is on constant speed. not right?

No, inertial motion means constant speed and direction relative to all other inertial frames, the train is constantly changing direction relative to the inertial frame of A at the center. And observers on the train know they're not moving inertially because they feel G-forces, in this case the centrifugal force felt by anyone moving in a circle. So observers on the train do not have an inertial rest frame, and therefore have no reason to predict light should reach the front and back of the train at the same moment.

 

[ppppppp]

Why would light reach C and D at the same time? In the time it takes light to travel to the observers, they have both moved a significant distance. One toward the source and one away from the source.

i think for A it is not. But for B, C, D inside the train, in their reference frames, the train is traveling at constant speed (although on a large circle), so lights reaches C, D same time.

 

[JesseM]

Please let me know if train circling at constant speed 0.999(...)c is causing lights not reaching both ends of train same time, in the reference frame of inside train, ie. B, C, D?

Again, there is no inertial rest frame for the inside of the train because B, C, D are moving non-inertially. Only in an inertial frame is light necessarily predicted to move at the same speed in all directions.

2nd, if I change to straight line. Can you check/digest the paradox in straight line scenario?

I don't know what aspects of the scenario you would have to change if the train was moving in a straight line (for example A could no longer be at the "center", so would you want A at any special position, or just anywhere at rest relative to the tracks?) Please copy and paste your original scenario and then change whatever you think needs to be changed to make it a straight-line scenario, then I'll look it over.

 

[ppppppp]

No, inertial motion means constant speed and direction relative to all other inertial frames, the train is constantly changing direction relative to the inertial frame of A at the center. And observers on the train know they're not moving inertially because they feel G-forces, in this case the centrifugal force felt by anyone moving in a circle. So observers on the train do not have an inertial rest frame, and therefore have no reason to predict light should reach the front and back of the train at the same moment.

Let's just say in straight line case, the paradox still not solved.

(although i am not sure if centrifugal force can minimize the significant lorent factor, the lz factor can arbitrary set as higher as millions/billions seconds later according to A's reference frame.

 

[JesseM]

Let's just say in straight line case, the paradox still not solved.

Again, please actually give the full details of what is supposed to be going on in the "straight line case", even if that just means copying and pasting the original description of the circular case and changing a few words.

(although i am not sure if centrifugal force can minimize the significant lorent factor.

I didn't say anything about "centrifugal force minimizing the Lorentz factor", that seems like a completely meaningless claim. The Lorentz factor can only be defined relative to an inertial frame, for example the train still has a high Lorentz factor in the inertial rest frame of A at the center of the track. My point was just that B, C, D don't have their own inertial rest frame if they're moving in a circle, because circular motion is by definition non-inertial.

 

[Ashwin_Kumar]

This is crazy. You have not considered that the train would appear shorter! And because of that, A will live or die in every case!

 

[nitsuj]

This is crazy.

I like this answer the most.

 

[dimension10]

1. Suppose, a fast moving train (600,000 km long) circling on track (radius is 600,000 km, radius can be even more, this is just convenience reason) at speed 0.999c. A stands at center of the track.
2. B stands in center of train. C stands at end of train. D stands in head of train.
3. Now B flash a lights. According to B, the lights reaches C, D same time (in one second). According to A, the light reaches C first, then (22 seconds later) reaches D.
4. Now suppose, as soon as light reaches C, C shoot a super fast bullet (at speed 100,000 km per second) at A. And D shoots a laser beam (to destroy) C's bullet as soon as light reaches D
Now I ask, will A die or not! According to A's reference frame, he is dead! Because the bullet travel time travel from C to A is only 6 seconds, D's laser is fired only 22 seconds later, too late to save A. (we can even suppose bullet travels evern faster, so fewer seconds, but for convenience, I set up as 6 seconds, radius 10m km/1m km speed of bullet.)

But according to B or C, D (all on the train). A is saved. Because when light reaches C, D same time. D's shoot laser it takes less than 2 seconds, less than 2 seconds in A’s reference frame as well for laser light intercept the bullet. (2 seconds is very simple geometry, you can check out with pencil & paper)


Please find out the problem or solve this of my paradox.

The premises are flawed. Special rlativity contradicts it.

 

[peterpang1994]

I have tried to calculate, and I assume that the train is traveling along a straight line and B flash a light when B passes A. If you consider the speed of the bullet, the distance between C and A, the distance between D and A, you will find that A must die.
P.S. The train is traveling with 0.999c and I use the principle of "motion is relative" to simplify the question.