Build a Time Dilation Clock for 8th Grade Science Project

[Dc2LightTech]

A science teacher ask if I could help one of her students build a "Time Dilation Clock"
so, at launch the Ships chronometer and the local time are in sync. with a 3g continuous thrust, at some point the time, the time at the launch site will be going twice as fast as the ships chronometer.
so the build will consist of the Ships Chronometer, velocity as a % of the speed of light
time difference from the ships clock to the time at the launch site.

what would be the function of T(microseconds) to Velocity as a function of %c?

 

[Ibix]

A clock traveling at $v$ with respect to you will tick once for every $1/\sqrt{1-v^2/c^2}$ times an identical clock at rest with respect to you ticks. To get a 1% difference you'll need the clock to be doing 14% of light speed, around 43,000km/s (compare to high velocity rifle ammunition, doing around 1km/s). Alternatively you need to travel at highway speeds and get a clock that is stable to around one part in 1000 million million. Cheap atomic clocks start in the thousands of dollars, and you need a good one not a cheap one.

This kind of experiment is probably out of reach of school students, I'm afraid.

Note that you also seem to have a few misconceptions about how relativity works, from your phrasing of the description. Even if the equipment could be procured you would need to think very carefully about the experimental design - it wouldn't be enough to just bung a clock on a rocket and hope.

 

[Dc2LightTech]

I actually have two 10MHz Rubidium Frequency Standards, one I built into a Nixie Tube clock. I will try to upload my infinity astronical clock I made with NeoPixels.
So the clock will be a regular clock:
(AM/PM) HH:MM:SS
Flight Time DDH:MM
ship acceleration setting (+3g,0,-3g )
V(%c) display 0.999999
time offset from launch side:
DDH:MM:SS:MMM:UUU
and it will need to have a DNS switch

https://www.adafruit.com/category/275​

 

[Dc2LightTech]

this is my NiePixel Astronomical clock.
outer ring is Seconds (Green), Minutes, (Red)
Inner ring is Hours (Red), position of sun in sky (bright Yellow), position of moon in sky (Aquamarine), the yellow band is hours of daylight for that week of the year, based on latitude for that week

 

[Dc2LightTech]

now its is an infinity clock

 

[Dc2LightTech]

 

[anorlunda]

It sounds like you are trying to duplicate this experiment:
https://en.wikipedia.org/wiki/Hafele–Keating_experiment

Make sure your clocks can measure differences in their times to the nearest nanosecond.

 

[Dc2LightTech]

A clock traveling at $v$ with respect to you will tick once for every $1/\sqrt{1-v^2/c^2}$ times an identical clock at rest with respect to you ticks. To get a 1% difference you'll need the clock to be doing 14% of light speed, around 43,000km/s (compare to high velocity rifle ammunition, doing around 1km/s). Alternatively you need to travel at highway speeds and get a clock that is stable to around one part in 1000 million million. Cheap atomic clocks start in the thousands of dollars, and you need a good one not a cheap one.

This kind of experiment is probably out of reach of school students, I'm afraid.

Note that you also seem to have a few misconceptions about how relativity works, from your phrasing of the description. Even if the equipment could be procured you would need to think very carefully about the experimental design - it wouldn't be enough to just bung a clock on a rocket and hope.

A clock traveling at $v$ with respect to you will tick once for every $1/\sqrt{1-v^2/c^2}$ times an identical clock at rest with respect to you ticks. To get a 1% difference you'll need the clock to be doing 14% of light speed, around 43,000km/s (compare to high velocity rifle ammunition, doing around 1km/s). Alternatively you need to travel at highway speeds and get a clock that is stable to around one part in 1000 million million. Cheap atomic clocks start in the thousands of dollars, and you need a good one not a cheap one.

This kind of experiment is probably out of reach of school students, I'm afraid.

Note that you also seem to have a few misconceptions about how relativity works, from your phrasing of the description. Even if the equipment could be procured you would need to think very carefully about the experimental design - it wouldn't be enough to just bung a clock on a rocket and hope.

thanks for the equation, that should do what I need.
Philip

 

[PeterDonis]

thanks for the equation, that should do what I need.

How? How do you propose to measure the $v$ that appears in the equation? You have a clock, not an inertial navigation system.

 

[Vanadium 50]

What is the question here? I can't connect the original question to the (albeit pretty) homemade clock.

As mentioned, one can get chip scale atomic clocks (CSACs) good to about 10^-11. That's good enough to measure time dilation at the one mile per second level. You need to do about 100x better to repeat Haefle-Keating. Those are considerably more expensive.

 

[Dc2LightTech]

How? How do you propose to measure the $v$ that appears in the equation? You have a clock, not an inertial navigation system.

the V will be simulated! so a continuous acceleration of 3g on the good ship Molly Brown will at some point have a measurable dt. set V to 0 then set the V switch to 3g. With that acceleration how long till the dt is 1 second. I will have to put that into Labview to do the math. velocity will increase but not past c, I need to come up with 1/x function for v so it does not go past c.

 

[Vanadium 50]

If this is simulated, what is the purpose of the pretty clocks? I don't have a clear ideaof what you want to do.

 

[Dc2LightTech]

I want the 8th grader to get 1st place is the science fair! so he is going to build a 3d printed clock and have a volicty to time dilation clock. he will have to explain all the math and programming.

 

[PeterDonis]

the V will be simulated!

If everything is simulated, you could just have the same computer that is doing the simulation do the calculation of the time dilation factor and simulate the clock display as well as everything else.

With that acceleration how long till the dt is 1 second.

The math you need is the relativistic rocket equation. See this Usenet Physics FAQ article:

https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

 

[PeterDonis]

The math you need is the relativistic rocket equation.

Note, though, that all of the math in the article I linked to assumes you are using the simultaneity convention of the Earth frame (or whatever inertial frame your starting point is at rest in). That will not be the same as any "natural" simultaneity convention for the rocket itself. So the simplest interpretation of the output based on that math will be that it gives you the readouts on the display in "Houston" (or wherever Mission Control is on Earth) of Earth time and of "ship's clock time" at the same time as the displayed Earth time.

The ship itself can of course adopt the same simultaneity convention even thought it is not the "natural" one for the ship; and there might even be good practical reasons to do so (for example, if the ship is traveling to a distant planet that is at rest relative to the Earth and whose clocks are synchronized with Earth clocks). But you should be aware of the simultaneity convention being used.

 

[Dc2LightTech]

wow you gave me some stuff to chew on, thanks. we will have to see if an Arduino has the math libs :)
Philip

 

[Vanadium 50]

I want the 8th grader to get 1st place is the science fair

This is difficult with pure simulation. What's the actual science?

You might want to rethink this a bit.

 

[Dc2LightTech]

This is difficult with pure simulation. What's the actual science?

You might want to rethink this a bit.

have you ever seen 8th grade science projects?

 

[Dc2LightTech]

I would like to keep this at an 8 grade programming level ;)
first, his ship under continuous acceleration can not indicate a velocity grater than the speed of light.
therefore the acceleration will drop to 0 as a function of %c.
Indicated time at the launch site will go faster as a function of v ( I need to find the equation stated earlier).
That is it.
He will have time clock his mother can read.
perhaps he will have:
time from launch (T+)
Current velocity m/s
current time at the launch site (going faster and faster) (delta t)

 

[Vanadium 50]

have you ever seen 8th grade science projects?

Seen 'em, judged 'em.

This is at the level of "which light bulb lasts the longest" - i.e. won't be #1.

 

[Mister T]

have you ever seen 8th grade science projects?

I'll chime in here, too, since I've also judged (and therefore of course seen) many. If you're doing a pure simulation then hopefully the science fair has a separate competition for programming or the like. If so, you may do well in that category depending on the quality of the sim and the clarity of the exhibit, you could possibly win first place. In a general science fair competition it's very unlikely that he would win first place.

As a veteran educator it bothers me that you are setting goals for the student. It's supposed to be the student's project, not yours or anyone else's.

But to answer your question, let's start with a simple case of the ship moving at a constant velocity relative to Earth. The equation you'd use for the sim is $t=\gamma \tau$ where $\gamma=\frac{1}{\sqrt{1-(v/c)^2}}$, $\tau$ is the so-called proper time, and $t$ is the coordinate time. If a clock is at rest relative to an observer then that clock is measuring $\tau$ and if the clock is in motion relative to an observer then that clock is measuring $t$. That's a good place to start the student off. See how much help is going to be needed!

 

[phinds]

his ship under continuous acceleration can not indicate a velocity grater than the speed of light.
therefore the acceleration will drop to 0 as a function of %c.

Why? You can accelerate forever and never reach c. If the simulation says otherwise, it is a crappy simulation and will be recognized as such.

 

[jbriggs444]

Why? You can accelerate forever and never reach c. If the simulation says otherwise, it is a crappy simulation and will be recognized as such.

Proper acceleration (measured based on the apparent force experienced by the astronaut pushing him down into his seat) can be maintained forever according to the astronaut's wrist watch.

The associated coordinate acceleration (the rate of increase in velocity measured against the original rest frame according to clocks at rest and synchronized in the original rest frame) will decrease asymptotically to zero as the coordinate velocity approaches but never exceeds c.

Before writing a correct simulation, one needs to figure out what scenario is being simulated.

If one decides to simulate a fixed coordinate acceleration (and an asymptotically increasing proper acceleration to go with it), one can do so. But there will be a hard stop when the speed of light is reached and no amount of proper acceleration can suffice to continue the process.

 

[cianfa72]

The equation you'd use for the sim is $t=\gamma \tau$ where $\gamma=\frac{1}{\sqrt{1-(v/c)^2}}$, $\tau$ is the so-called proper time, and $t$ is the coordinate time. If a clock is at rest relative to an observer then that clock is measuring $\tau$ and if the clock is in motion relative to an observer then that clock is measuring $t$.

What does the last claim physically mean ? In the context of SR (flat spacetime) assume the given observer is moving inertially and suppose to "disseminate" identical clocks at rest w.r.t. the given observer synchronized with it using Einstein's synchronization procedure. The coordinate time defined such way is actually the proper time as measured from a clock at rest w.r.t. the given observer.

Take now a moving clock with velocity $v$ w.r.t. the given observer (i.e. w.r.t the inertial rest frame of the given observer as defined above). Suppose the moving clock shows the time $t_1$ at the event 1 for which the spatially-colocated stationary clock shows the (coordinate time) $\tau_1$ and the time $t_2$ at the event 2 for which the spatially-colocated stationary clock shows the (coordinate time) $\tau_2$.

Then for the moving clock $\Delta t = t_2 - t_1 = \gamma (\tau_2 - \tau_1) = \gamma \Delta \tau$.

 

[Mister T]

What does the last claim physically mean ?

It means that to the Earth-based observer the ship's time will be dilated. And vice-versa, of course.

Then for the moving clock Δt=t2−t1=γ(τ2−τ1)=γΔτ.

I agree that it's better expressed as $\Delta t=\gamma \Delta \tau$.

 

[cianfa72]

It means that to the Earth-based observer the ship's time will be dilated. And vice-versa, of course.

Yes, my point was that Earth-based observer must use light signals emitted from the ship's clock at fixed time intervals (according to the ship's clock) to compare it against his own clock and evaluate the difference. In principle this is the same as evaluating the difference in coordinate time as shown by Einstein's synchronizated clocks at rest w.r.t. the Earth-based observer (i.e. at rest in the Earth's observer rest inertial frame) spatially-colocated with the ship's clock at regular intervals.