question in relativity?

Question

1.A space probe is sent to the vicinity of the star Capella,which is 42.2 light years from earth.A light year is the distance traveled by light in a year.The probe travels with a speed of 0.9910c. An astronaut recruit on board is 19 years old when the probe leaves earth.What is her biological age when the probe reaches capella?

2.Two events are observed in a frame of reference S to occur at the same space point,the second occurring 1.80s after the first.In a second frame S' moving relative to S,the second event is observed to occur 2.35s after the first.What is the difference between the position of the two events as measured in S'?

Please help me solve this....i really appreciate your help

thanks

Answer 1

To compute the first, you need the Lorentz contracton factor

γ = 1 / sqrt ( 1 - v^2 / c^2 )

Compute this for v = .9910 c.

From the Earth's point of view, time will have slowed for the traveling astronaut by this factor (time dilation). From the astronaut's point of view, the distance to Capella is reduced by this factor (length contraction). Either way, the astronaut ages much less than 42 years.

Answer 2

The time dilation factor is given by:

gamma = sqrt (1 / 1 - (v/c)^2)

To an outside observer, the trip takes a time
t = distance / velocity

To the astronaut, though, the proper time ellapsed is
tau = t / gamma
= d * sqrt (1 - (v/c)^2) / v

They give you the distance and velocity. They are nice enough to give both the distance and velocity in multiples of c, so c cancels nicely. Plugnchug.

Note that gamma is a number greater than one, so the proper time is less than the earth time.

2) The interval between any two events is invariant

(ct)^2 - d^2 is the same for any observer.

(ct1)^2 - d1^2 = (ct2)^2 - d2^2

So the difference in distance in the second reference frame is
d2 = sqrt (d1^2 -(c t1)^2 + (ct2)^2)

They give you the times t1 and t2 and tell you that d1 is zero. Plugnchug.

d2 = c sqrt (t2^2 - t1^2)

Answer 3

The answer that the person ages less in space travel is not accrurate. It is based on time not being constant.

Albert had to deal with the constant nature of time. If Albert can remove the universal constant time, he can eliminate the conflict between the law of the propagation of light in vacuo and the principle of relativity developed in Section VII of his paper.

1) Newton's concept of universal time (time is the same in all reference frames)
2) Einstein's concept that time has no meaning ( Every reference-body has it’s own time)

If Newton’s concept (1) is correct, then Albert’s concept (2) is wrong and
If Albert’s concept (2) is correct, then Newton’s concept (1) is wrong.

In Albert’s thought experiment of the man on the moving train observing simultaneous lightning strikes, there are certain givens. We all know that the observer at mid point M between the two simultaneous lightning strikes will observe the events as simultaneous. We also know that the observer at the moving point M+Distance on the train will not observe the two simultaneous as being simultaneous because that observer is closer to one lightning strike.

However; Albert says: “Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.”

Albert further says: “Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.”

Although Albert knows M+Distance is closer to one of the two simultaneous lightning strikes, he specifically requires the reader to ignore that known information. Albert knows the difference but he says for all of us to forget the known difference. Albert claims to have eliminated the significance of time because he wants us to forget that the M+Distance observer should not observe simultaneous lightning strikes as being simultaneous.
As a result Newton's constant time remains but Albert meaningless time falls. Further the conflict between the law of the propagation of light in vacuo and the principle of relativity developed in Section VII of his paper remains.

That is but one part of the proof I provide in my paper that Albert is wrong.

Some people think a train does not move but the track does. Read about it at http://www.complexrelativity.com

The truth is out. Any theory based on knowingly excluding relevant data can not survive forever. Now, when people think of relativity, they will also think about known missing information to facilitate a false conclusion.