Proper time Definition and 155 Threads

We know that the proper time between two events is the shortest possible time between those two events that can be measured in any frame. This follows from the idea that moving clocks run slow-- a stationary clock at rest in S' which moves relative to S at a constant speed v will be time dilated...

In general relativity, we have a gravitational time dilation of: \frac{d\tau}{dt} = \frac{1}{\sqrt{1 - \frac{2GM}{rc^2}}} The term - \frac{2GM}{rc^2} appears to be based on the fact that gravity is attractive. If I understand correctly, if the curvature of space-time leads to attraction, then...

Hello everyone. I understand how to figure out the paths of the free particles following the principle of extremal proper time, but... where does it come from? I mean, how it's derived that particles follow a path of extremal proper time in space-time? I know that for example in flat space-time...

Consider the Schwarzschild line element for radial motion only: c^2 d\tau^2 = \left(1-\frac{2GM}{rc^2}\right) c^2 dt^2 - \frac{dr^2}{ \left(1-\frac{2GM}{rc^2}\right)} Solve for d\tau^2/dt^2: \frac{d\tau^2}{dt^2} = \left(1-\frac{2GM}{rc^2}\right) - \frac{dr^2/dt^2}{...

Please explain me how to find the proper time taken by one twin to travel around a massive body while his other twin stays on the Earth in Schwarzschild space?

If one clock is moving with constant velocity. The other clock moving with constant acceleration , both with respect to Earth . And both clocks travel the same distance in the same time with respect to earth. distance/rate = [2d/a]1/2 Gamma is given for velocity clock. Would you expect the...

Homework Statement 3 clocks at to A clock on Earth B clock above Earth 4.66 * 1014 meters C clock above Earth 3.30 * 1013 meters B accelerates to .6 c and arrives at Earth when Earth clock reads 2.6 *106 sec = 30 days With velocity 1.8 *10^8 m/sec with gamma = .8 B clock reads 2.07 *...

On several homework questions I have encountered the following type of scenario: Two clocks are perfectly synchronized. One is placed in a spaceship, and the other is left on the ground. The spaceship flies to some distant location at some high speed, and then returns to earth. When the...

In relativity, proper time along a world-line is be defined by d\tau^{2} = ds^{2} / c^{2} However, proper time can also be understood as the time lapsed by an observer who carries a clock along the world-line. In special relativity, this can easily be proven: The line element in special...

I am using the schwartzchild metric given as ds^2 = (1 - \frac{2M}{r})dt^2 - (1 - \frac{2M}{r})^{-1} dr^2 , where I assume the angular coordinates are constant for simplicity. So if a beam of light travels from radius r0 to smaller radius r1, hits a mirror, and travels back to r0, I am...

Someone posted this animation in a previous discussion and I just 'rediscovered' it in my notes: http://www.adamtoons.de/physics/gravitation.swf Do you experts think it accurate, and if so, wouldn't this be a nice tool to display coordinate time versus proper time?? [Is it worth...

Hello, So, I have just started studying relativity, and I am confused about some basic concepts in relativity. So, the book we use says that that time has three different kinds, proper or path time, coordinate time and spacetime intervals. I understand that coordinate time is the same as...

Homework Statement A satellite is in circular polar orbit radius r around Earth (radius R, mass M). Clocks C on satellite and C0 on south pole of earth. Show the ratio of the rate of C to C0 is approximately 1 +\dfrac{GM}{Rc^2} - \dfrac{3GM}{2rc^2} Homework Equations d\tau =...

Hi, I am trying to show that timelike geodesics reach the Rindler horizon (X=0) in a finite proper time. The spacetime line element is ds^{2} = -\frac{g^{2}}{c^{2}}X^{2}dT^{2}+dX^{2}+dY^{2}+dZ^{2} Ive found something helpful here...

Homework Statement How fast must a meter stick be moving if its length is observed to shrink to 0.5 m? The Attempt at a Solution A meter stick moving at speed V to a stationary observer is the same thing as a stationary meter stick and an observer moving at speed V. Lproper = Lp = 1 meter...

Homework Statement Alpha Centauri, the closest star to Earth, is 4.3x10^6 m away. How long would it take a spaceship to reach the star if it were traveling at 0.999c? Homework Equations I did get the answer as 0.2a...and the textbook also said it would take about 2 months, I do not...

Hi everyone! Let's take two events P_1,P_2 in a Minkowsky spacetime, and let's choose them both lying on the \omega axis, separated by a certain distance. Now, I want to calculate the world line of the particle which experiences the least proper time during its trip between the two points...

It has REALLY been bugging me lately. I'm studying Einstein's Special Rel and am finding it annoying to determine who observes the proper length and time in the following conditions: An electron accelerator is 4km long and can accelerate electrons up to speeds of .9999995c. So when asked...

I'm having trouble getting my head around the idea of 'proper time'. I've been thinking of this situation and I can't seem to understand what exactly the proper time is. Say we have a planet 'A' and a rocket B moving towards this planet. From the perspective of A, B is moving towards A. If an...

The idea of proper time has been confusing me. Say for example we have a spaceship with John in it traveling past the Earth, towards a planet called NEC. Ann is on Earth and starts her timer as John travels past the Earth, towards NEC. Ann notes that it takes 2 years for John to arrive at NEC...

Hello, Can anyone help me with that? It's a problem taken from Wald book on General Relativity,in the section of Schwarzschild solution Thanks Show that any particle (not necessarily in geodesic motion) in region II (r < 2M ) of the extended Schwarzschild spacetime, Figure 6.9, must...

General relativity states that all free falling bodies follow spacetime geodesics. A geodesic is a path of extremal proper time. My intuition tells me that extremal proper time is the maximum amount of real time. So does this mean that all objects will take the path of most time to get from...

Howdy! I'm new to Physics Forum and glad to be part of the community. I just finished reading Einstein's Special Theory of Relativity and cannot understand the term 'proper time'. What does it specifically mean? When deriving the equation for length contraction, the author of Giancoli Sixth...

This is a continuation of the thread Derivation of proper time of acceleration in SR We have definitions for proper time, proper speed, proper acceleration, coordinate speed, coordinate time, and coordinate acceleration. 1) What is the definition ofproper distance? 2) If proper...

To yuiop: Consider an object of mass m0 which, subjected to a constant force, accelerates at a0 initially. Initially, the velocity of this mass is zero but then picks up as this force is applied. By the relativistic momentum equation, a = dv/dt = a0\sqrt{(1 - v^2/c^2)}...

I have tried to derive the formula for the proper time from the two equations of the Lorentz Transformation. The formula is as follows (see Wikipedia: http://nl.wikipedia.org/wiki/Eigentijd): tau = t*sqrt (1 - v**2/c**2) The two equations of the Lorentz Transformation are as follows...

Le K_0 and K_1 be two inertial frames moving relative to each other with velocity v, from Lorentz transfromation we have that a watch(t') at the origin of K_1 is slow(proper time contraction) acording to dt'=dt/gamma=(1-(v/c)^2)^{1/2}dt where v is the velocity of the watch. My question...

1. Homework Statement [/b] Just need some help getting started on what looks like a rather simple problem! A rocket travels to a star 5 light years distant, observers on the star time the journey at 6years. I need to find the time recorded on a clock aboard the rocket and the distance to the...

A very basic question, perhaps, but I am starting from basics and checking all my understanding. In Relativity is τ (tau), the proper time experienced by an observer adjacent to a clock in an inertial frame of reference, an invariant quantity? And if not, in what way can it vary?

Is this the correct way to calculate the proper time that has passed for an object under constant acceleration over the time interval [0,t1]? I just downloaded and started teaching myself how to use LaTex today so bear with me here. I can get the output PDF file but I don't know how to insert...

Quick question: Suppose I hold two initially synchronized clocks on Earth and throw one up and catch it when it comes back down. Now my (small amount of) knowledge of GR tells me that the proper time on the thrown clock should be maximized since it was on a geodesic. However, this seems like...

Homework Statement A spaceship leaves earth, travels to Pluto (which os 5 hours of distance away at the time), and then returns to Earth in exactyly 11 hours later. assume the spaceships acceleration time is very short so it is always traveling at a constant speed. also assume that Earth and...

I've been trying to learn GR and I've been back and forth through Schutz's first course book. I think I understand the basic principals, but one thing still eludes me: a traveler in free fall travels along the geodesic, the path of longest proper time. If the path between two points passes...

is proper time invariant? proof? thanks...

Homework Statement I have the trajectories of a particle in the space-time: \tau(\sigma) = \frac{1}{a}senh(\sigma) x(\sigma) = \frac{1}{a}cosh(\sigma) How can I write this equations depending on proper time t of the particle? Homework Equations The Attempt at a...

A particle has a constant acceleration in a laboratory from 0 to 0.5c in 3 seconds. What time elapses for the particle (i.e. what is the proper time for the particle)? Hint: (you will have to integrate the proper time of the particle over the 3 seconds as measured in the laboratory frame)...

The question is: A rocket has a constant acceleration in a rest frame that is 0 to 0.8c in 4s. What is its proper time? This question I found, I guess I'll have to use integration but don't have a clue where to start off. Could you give me some ideas please?

In Tipler & Mosca: Physics for Scientists and Engineers, e5, extended edition (page R-14 of the supplementary section on special relativity), there is a question: “You are standing on a corner and a friend is driving past in an automobile. Each of you is wearing a wrist watch. Both of you...

What role does proper time play in quantum theory? Does proper time have any meaning in QM? By quantum theory I should perhaps say "relativistic quantum mechanics" since I don't know enought QFT to ask a proper question. If there were a proper time \tau parameter or dynamical variable...

I can understand the logic from some arguments as to why proper time in a photon's "frame of reference" is zero. I cannot understand how this follows from the argument that (SPACE)2 - (TIME) 2 = 0. This to me says that the SPACE-TIME interval for the photon is zero (null interval) and SPACE =...

Hey guys, Can someone please explain to me this image: http://www.astro.ucla.edu/~wright/omega0.gif from the page http://www.astro.ucla.edu/~wright/cosmo_02.htm What i do understand: I understand the concept of light cones I understand that the units used for the axes means the lines...

Doran/Lasenby define a proper interval as: \delta \tau = \int \sqrt{\frac{dx}{d\lambda} \cdot \frac{dx}{d\lambda}} d\lambda (c=1, x= (t,x1,x2,x3) is a spacetime event, and the dot product has a +,-,-,- signature) and say that this is called the proper time. I can see that this...

Foster and Nightingale give an equation for the proper time of a radially falling clock between any two distances. (Short Course in General Relativity, 1979, p. 128.) As they state, the equation is the "same as its Newtonian counterpart." So there are no factors representing any slowing of the...

Homework Statement A particle has a constant acceleration in a laboratory from 0 to 0.5c in 2 seconds. What time elapses for the particle (i.e. what is the proper time for the particle)? Hint You will have to integrate the proper time of the particle over the two seconds as measured in the...

In other threads the topic of how the proper time of a clock under acceleration has come up a number of times so I have decided to analyse this subject in a little more detail. For this analysis we have these conditions: a)Two clocks are initially at rest separated by a distance L_o along...

Homework Statement If the spacetime interval (delta S)^2 > 0, show that delta t=deltaS/c is the proper time between the two events. Homework Equations Can anyone please explain to me how I should be approaching this problem. I have been working on it for a while with no success. I was...

Homework Statement A plane flies with a constant velocity of 208 m/s. The clocks on the plane show that it takes exactly 2.00 hours to travel a certain distance. Calculate how much longer or shorter than 2.00 h this flight will last, according to clocks on the ground. ________s Homework...

do you kinow a simple and convincing argument for the fact that proper time is a relativistic invariant?

i find in the literature in different textbooks the term proper time Thomas A. Moore, Six Ideas that Shaped Physics (McGraw-Hill) 1998 and the term proper time interval Yuan Zhong Zhang, Special Rekativity and its Fundamental Foundations, (World scientific ) I consider that the first is...

How do you calculate the proper time and the proper distance for an object free falling into a black hole from the event horizon to the singularity?