Spacetime interval question involving a Pendulum in a Space Ship

[Chenkel]

Hello everyone, I was working on a thought experiment and came upon an inconsistent result that I thought maybe I could get some help with.

Firstly I am using natural units (c = unitless 1 i.e 1 light second per second) and I chose v = 3/5 to make gamma come out nicely (gamma equals 5/4 when v equals 3/5)

So the spaceship traveling at 3/5 light seconds per second has a pendulum at rest inside it with a period of 1 hertz (1 cycle per second) so I calculated the spacetime interval to be the squared distance between events minus the squared distance light travels between the events occurring, so that means the spacetime interval is equal to 0 - 1 = -1 light seconds.

In one second the spaceship travels 3/5 light seconds so relative to earth there is now a distance between the event of the pendulum coming back to its initial position of 3/5 light seconds.

So to discover the period of the pendulum relative to earth I solve the equation $-1 = (\frac 3 5)^2 - (\Delta t)^2$ So that means $(\Delta t)^2 = \frac {9} {25} + \frac {25} {25} = \frac {34}{25}$ so I have $\Delta t = \sqrt {\frac {34} {25}}= 1.16$

So if the period of the pendulum in the spaceship is 1 second then the period of the pendulum that's on the spaceship relative to earth would be 1.16 seconds using my spacetime interval equations.

If I take the period of the pendulum on the spaceship (1 second) and multiply by gamma I should get the period of the pendulum on the spaceship relative to someone on earth which should be gamma, but gamma equals 1.25 using the time dilation formula, so these results seem inconsistent.

Any help would be appreciated, thanks in advance!

 

[PeroK]

A pendulum won't work on a spaceship! It relies on gravity.

 

[Ibix]

In the Earth frame, $\Delta x$ is not $v\times 1$, it's $v\Delta t$.

 

[Chenkel]

A pendulum won't work on a spaceship! It relies on gravity.

Can't a pendulum be made with springs?

 

[PeterDonis]

Can't a pendulum be made with springs?

A simple harmonic oscillator can be made with springs, but I don't think anyone would call it a "pendulum". "Pendulum" is a special case of "simple harmonic oscillator", not the other way around.

 

[PeterDonis]

I was working on a thought experiment

Which looks just like all the other thought experiments you have already posted multiple threads on. Your basic issue in every single one has been the same: you still haven't grasped how to correctly transform between inertial frames. Your question here has nothing specifically to do with pendulums or springs or oscillators, and could be posed just as easily with light clocks--if you hadn't already posted a thread on light clocks.

Enough is enough. It is pointless to keep repeating the same explanations that you have already been given multilple times in multiple prior threads. If it didn't work with you then, it's not going to work with you now. You will have to somehow figure this out on your own. We have done all that we can to help you.

Thread closed.

 

[Dale]

A simple harmonic oscillator can be made with springs, but I don't think anyone would call it a "pendulum". "Pendulum" is a special case of "simple harmonic oscillator", not the other way around.

There are torsion pendulum clocks

https://en.m.wikipedia.org/wiki/Torsion_pendulum_clock

 

[PeterDonis]

There are torsion pendulum clocks

Hm, yes, I wasn't thinking of a torsion spring, but it does qualify as a spring.

However, the basic point I made in post #6 remains the same.