Can you build a relativistic clock?

Question

Is it possible to build a clock that will be immune to relativistic effects on the passage of time? Can a clock exist that will always display the time of the place in which it was set? For instance, if we built the clock on Earth, then put it on a spaceship which accelerated away from the Earth at a significant fraction of the speed of light, the clock would continue to display the time on Earth. To observers on the ship the clock would appear to run faster and faster as the ship accelerated.

Additionally, strong gravitational fields can change the flow of time. If our ship entered orbit around a black hole our clock would still compensate and display the real time on far-away Earth.

The clock must be self-contained. It can't communicate with other clocks or otherwise observe the universe outside of it, but it can be as big and complex as necessary.

EDIT: To clarify the capabilities of this clock: A clock that meets my specifications that was sent on a journey should display the same time as a clock left on Earth when it is returned to Earth.

Further EDIT: This clock should match a clock left on Earth at all times and places. If the starship travelers want to celebrate Christmas on the same day as their families on Earth they should be able to using this clock.

Answer 1

No.

In General (and indeed Special) Relativity, there is actually no such thing as "the time on Earth" from the point of view of a distant observer. There is also no such thing as "the place it was set".

Relativistically speaking, the only things that make sense are events - which in non-relativistic terms, can be thought of as a combination of a time and a place together. The relationship between events depends on whether they are timelike, spacelike or null separated:

• Two events are timelike separated if a massive object (such as a spaceship) can get from one event to the other without resorting to exotic things like wormholes or warp drive.
• Two events are null separated events if only a massless particle (e.g. a photon) can get from one to the other.
• Two spacelike separated events can't be experienced by the same particle or object even if it can travel at the speed of light. You can't send a signal between two spacelike separated events.

A pair of timelike or null separated events always happen in a particular order, and everyone agrees on what order they happen in. So everyone can agree that event A happens before event B, no matter where they are or how fast they are going.

However, people might disagree on the order in which two spacelike events happen. In fact, it doesn't really make sense to say that event A happens 'before' event B if they are spacelike separated.

This means that if you leave Earth in a spaceship tomorrow, and you want a clock that tells you what the time is on Earth, you are out of luck! The 'time on Earth now' isn't a well defined concept. What you could potentially do is have a clock that tells you, for example, what the earliest time it could be on Earth when a signal you emit reaches home: the sending and receiving events are null separated, so you don't have a problem. You could also have a clock that tells you the time on Earth that you would observe if you looked back at a clock on Earth with an enormous telescope.

Answer 2

Yes.

Though it's not immune, it's just informed. Luckily you have no limit on complexity or size, because it's not going to be simple or small. This isn't any kind of shielding, the time is simply adjusted given proper inputs. In the same way we would be able to calculate the effects from time dilation given the proper information about the system, like acceleration and gravity for each frame of reference, we could do that in 'real time' for a clock. If the clock is provided (or internally measures) the requisite information, it can calculate, within the precision of the information it's given, the time in a different reference frame.

EDIT: BrettFromLA brings up a good point, intentionally or not, that measuring gravity and acceleration will muss with the velocity (with respect to Earth) measurements. The velocity would normally be measured by integrating the ship's acceleration with respect to time, but the acceleration due to gravity would be superimposed on those measurements. To account for that, careful measurement of all forces acting on the ship would be required. By tracking engine output, micrometeor impacts, radiation, etc; the acceleration adding to the velocity with respect to Earth's reference frame could be measured. In this way the clock, being allowed any size or complexity, could be considered as a gaussian surface around the entire ship. The measurements required would be only forces acting on the ship/clock. Clearly this is more complex than simply looking at an external reference, but it is still possible.

Answer 3

If you are in a spaceship that constantly maintains a line of sight to our solar system, you could monitor the red/blue shift of our sun, as seen from your ship. From that you can infer what kind of time dilation you are experiencing with regards to the Earth and correct the clock's time as you go along.

This gives you the time of our solar system, as it appears to you. Then add to that time a year for every light-year that you have travelled.

EDIT: I'll try to briefly explain red/blue shifting, because probably not everybody is familiar with these terms. The speed of light is constant, so when you move towards/away from an object, the light coming from it to you does not seem to change its speed relative to you. But it seems to change its wavelength in a predictable way in relation to the relative speed. When you split light coming from a star into a spectrum (like a prism splits it into a rainbow), there are gaps in the spectrum, which are characteristic of every star. By tracking how these gaps move towards the red or blue end of the spectrum, you can find out how much the light has shifted.

Answer 4

Would you be happy with something pseudo-scientific?

Quantum entangled oscillator

Similarly to how a quartz crystal's oscillation will provide a time signal for a modern watch, you could have some kind of quantum particle suspended in a field that causes it to oscillate at a very well-defined frequency.

Then you'd need some mechanism to entangle a 'receiver' with the oscillating particle. This means that measuring the state of the 'receiver' gives you the state of the oscillator.

Entanglement seems to allow instantaneous communication - meaning that the 'receiver' will oscillate at the same observed frequency as on Earth - meaning, it will get faster as the ship accelerates away from Earth. (although, I don't remember reading anything involving entanglement and accelerating frames of reference).

It might even be possible to have multiple entanglements.

This is actually probably not at all different to various ansible mechanisms that have appeared in other works.

Answer 5

A Broken Clock and a Black Hole

Take a clock and throw out the battery. Now throw a black hole at the earth. Now time on earth is frozen, as time does not pass in a black hole. The time on the clock will match the time on earth.

This solution, though it may require a lot of mass, is not very complicated. I suppose the criteria "If the starship travelers want to celebrate Christmas on the same day as their families on Earth they should be able to using this clock" is fulfilled vacuously now.