1. Consider two observers moving in the x direction with respect to a stationary reference frame. The worldline of one observer is given by x1 = (1/3)t while that of the other is given by x2 = (1/18)t^2.
(a) Determine the event at which the two observers meet after leaving the origin.
(b) Determine the proper time measured by both observers between the origin and the point found in part (a).

I'll assume that we are using units such that c=1. The two world lines are given by:

x1 = t/3

x2 = t^2/18

Here the "18" must carry the units of time used. So, we'll just assume that some units are chosen and the numbers that come out for times/distances are given in terms of that unit.

The time when the observers meet follows from equating x1 to x2:

x1 = x2 -->

t = 0 and t = 6.

At t = 6, x1 = x2 = 2.

The event where they meet again is thus the event t = 6, x = 2.

Now, you know from elementary special relativity that the relation between proper time tau and coordinate time t is:

tau = t/gamma

where gamma = 1/sqrt[1-v^2]

But you must be very careful about applying equations from special relativity derived for inertial observers to accelerating observers. So, let's apply this equation to observer 1 and then I'll show how you deal with the general case. Observer 1 moves ...

Solution Summary

A detailed solution is given. The expert determines the event at which the two observers meet after leaving the origin. The proper time measured by both observers between the origin and the points found are determined.

... Ø I have the skills to make proper judgement at the time of a problem. ... I have the skills to make proper judgement at the time of a problem. ...

... Directors and Team Manager will meet three times a week ... come in over budget and not on time due to ...Proper risk management techniques can help avoid the project ...

... How does this help us to solve the problem? ... is, by definition, the invariant distance the clock travels in the time direction (aka proper time). ...

... a similar manner, I encountered a situation in the past where I faced problems while handling ...Time management: The aspect of proper time management is ...

... to ensure that overtime is available at other times employees operated ... new technology because of receiving a proper salary ... but I must also take the time to hear ...

... perhaps even prototyped, to assure proper alignment with ... increased production uptime, reduced production cycle times,. ... PAT can also speed time to market for new ...

... Some of the defects:- Poor knowledge base of representatives Lack of time due to overwork Inability to understand problem Lack of proper nfrastructure Less ...

... But I have other places to put my study time. ... in order communicate clearly and with the proper tone, you ... you provide an example of such a problem that happened ...

... Write your final answers using mixed numbers, proper fractions, or whole ... Multiply your answer to question 4 times to find out how much time you will need ...

... test is identified in each equation eith proper reasoning. ... is 7.74 which means that if time is zero ... year then In (Visual Field) will decrease by 0.03492 times. ...