Einestien train example

[ahmeeeeeeeeeed]

hello

 

About Einestien's train example

 

 

 

I can't get what it really does with the constancy of the speed of light , what would be the difference if , instead of two bolts , we have two balls thrown at the same angle ?!

 

the observer in the train would still see the front ball first

 

Or we are using light because it is what determines simultaneity in our eyes , which means when I see two balls passing by me at different times , I don't have to conclude they weren't thrown simultaneously but when I see Light doing that I will ?

 

I need basically to know what difference does the constancy of the speed of light make here

 

thanks in advance ;

[derek w]

If the train was travelling at 120 mph,then the passenger would be travelling at 120 mph.A ball travelling from front of train to passenger(at middle of train) at 50 mph would have a speed of 120 - 50 mph = 70 mph.The passenger in effect would be travelling towards the ball at 50 mph.A ball travelling from back of train to passenger at 50 mph would be travelling at 120 + 50 mph = 170 mph in effect the ball would be travelling towards the passenger at 50 mph.

 

Light would travel at the speed of light (c ) irrelevant of the speed of the train.

[Melissa Mika]

If the train "stops" in the middle of a 30 km/h, an adequate new session transforms. Until it stops, you can only measure weigth in time and space, like a flash or something.

[Janus]

hello

 

About Einestien's train example

 

 

 

I can't get what it really does with the constancy of the speed of light , what would be the difference if , instead of two bolts , we have two balls thrown at the same angle ?!

 

the observer in the train would still see the front ball first

 

Or we are using light because it is what determines simultaneity in our eyes , which means when I see two balls passing by me at different times , I don't have to conclude they weren't thrown simultaneously but when I see Light doing that I will ?

 

I need basically to know what difference does the constancy of the speed of light make here

 

thanks in advance ;

 

If you replaced the light with balls you would conclude the same thing as you do with light, it just takes a bit more explaining as to why.

 

First consider how you would determine when the balls were thrown. You would take the speed of the ball with respect to you and the distance to the point is that they were thrown from. For example, if the ball is moving at 50 m/s relative to you and it was thrown from 50 meter away, you know that it was thrown 1 sec ago.

 

Thus if you were on the embankment and you knew that both balls were thrown at the same speed and from the same distance from you, you would know that they were thrown at the same time.

 

For the train, it becomes a little harder. For him, the speed of each ball is the result of both the ball's speed with respect to the ground, and his speed with respect to the ground. The ball coming from the front will be moving faster than the one coming from the rear. Again, since they were thrown when the ends of the train were next to the origin point, from the train observer's perspective, they were thrown from equal distances from him.

 

From this, it is easy to see that just the fact that the balls arrive at his location at different times is not enough to conclude that they were thrown at different times. Instead, we have to do some calculation. We have to determine how long it took for each ball to make the trip and then compare that to the difference in arrival times. Thus if the ball from the back arrives 1 sec later than the ball from the front, but took 1 sec longer to make the trip, we can conclude that they were thrown at the same time. However, if the difference in arrival time is different than the time of flight, we have to conclude that the balls were thrown at different times.

 

Now here is where things start to become a little complicated.

 

Let's say that the ground observer notes that the two ball reach the train observer 1 sec apart. Since the train is moving, then it undergoes time dilation. So, for example, if the speed of the train is 0.6 c, in that 1 sec, the train only measures 0.8 sec. This is the time difference that the train observer will note between the ball arrivals.

 

The other thing to note is is how you add velocities in SR. We can't use the straight forward velocity addition used a couple of post ago, because that is not how velocities really add (Though at the speeds used in the post the correct answers come out to be very very very close to the answers given.) Velocities add by the rule of:

 

[math]W = \frac{u+v}{1+\frac{uv}{c^2}}[/math]

 

So for example, if the balls were moving at 0.5c relative to the ground and the train was moving at 0.6 c. Then the speed of the ball coming from the front would be 0.846c according to the train observer, and the one from the rear at 0.077c.

 

Now, if you were to take these speeds, the length of the train and the 0.8 sec difference in arrival times, you would end up concluding that the balls, according to the train observer, were thrown at different times, just like you do when you use light.

 

We use light in the example because it is much more straight forward. If you plug c in for one of the velocities in the formula, you always get an answer of c. The train observer measures the light coming from the front and rear as traveling at the same speed and from the same distance and thus the time of flight is the same for both, and if they arrive at different times this can only be because they left at different times. You don't have to go to all the trouble of computing time dilation, length contraction, different arrival times and different times of flight like you do with the balls, only to come to the same final conclusion.

[derek w]

'Janus'.For the balls to be travelling at a speed relative to the ground,they would have to be outside the train.

Edited November 7, 2012 by derek w

[swansont]

'Janus'.For the balls to be travelling at a speed relative to the ground,they would have to be outside the train.

No, That's not true. Any object inside the train has a speed relative to the ground.

[derek w]

Ok.I will re-state the point I was trying to make.

There are 2 frames of reference in this example,(1) is the passenger on the train,(2) is the observer by the side of track,which includes the lightning strikes to the rear and front of train.

To replace the example of light travelling in these 2 frames of reference,with balls,you must have 1 set in the first frame of reference(1) travelling from front and rear of train arriving at the passenger at the same time,and a 2nd set in the frame of reference(2) travelling from front and rear of train to the observer also arriving at same time.

[phyti]

So for example, if the balls were moving at 0.5c relative to the ground and the train was moving at 0.6 c. Then the speed of the ball coming from the front would be 0.846c according to the train observer, and the one from the rear at 0.077c.

 

The rear ball speed relative to the passenger is -.143, i.e. it's moving away.

The ball can't catch up to the passenger!

 

You must have been interrupted by the cat, or something. You usually have to the point responses, and great animations.

 

If a passenger in a static capsule points a laser vertically, it reflects from the ceiling vertically.If the capsule is moving at .5c, the laser is still supposed to reflect in the same manner per the 1st postulate of SR. The posts I've read say the beam moves at an angle to accomplish this, as viewed by a static observer. I've never seen an explanation as to what causes the angular deflection in terms of physics. As the op says, it is contrary to constant independent light speed, which has much experimental verification.