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Comment by bigdubs | Hacker News Reader

Something I never understood. If velocity (?) affects time, wouldn't time operate a different speed at different parts of the universe / solar system?

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I always thought it would be an interesting physics exam question to ask: "If a clock were landed on Halley's comet, and retrieved on its next orbit, what would be the expected difference in time relative to an earth bound clock?" It's tricky because all orbiting bodies experience a range of velocities as they orbit their star. But I gather Halley's comet has a particularly eccentric orbit (0.9) with a rapid perihelion of around 70km/sec, an aphelion of about 1km/sec, and about 75 years for a single orbit (ΔT' = ΔT / sqrt(1 - (v²/c²)))

That would be one hell of an exam question.

Best method I can think of is to measure the proper time of both the trajectory of the earth and the trajectory of Halley's comet, and compare, but with the combined effects of gravity and a changing speed that could be quite challenging.

It's even worse if you insist on using geodesics instead of elliptical orbits, or if you decide to include the rotation of the earth in your calculations.

The movie Interstellar does a decent job demonstrating this (well the gravity piece anyway with the proximity to black holes).

I also think satellite clocks have to take time relativity it into account (both due to distance from earth's gravity and their speed).

Randall Munroe has a pretty entertaining write up that does a decent job giving a high level overview in pretty easy to understand terms: http://www.newyorker.com/tech/elements/the-space-doctors-big...

Absolute velocity does not affect time, simply because there is no such thing as absolute velocity. Relative velocity, though, does. For instance, if you look at a clock on a GPS satellite, moving fast relative to you, you can see it run slower than the one on your wrist. Similarly, someone stationary on the surface of the sun would see us here on earth moving in slow motion.

However, someone moving on the satellite would see the clock on the satellite move normally, and us on earth moving in slow motion, because they are on the same frame of reference of the satellite.

So no, time does not operate differently on different parts of the universe per se. It all depends on how it's moving relative to the observer.

The velocity-time relationship is explained by Special Relativity (SR).

The Sun example is a bit more complicated, because there's the velocity-time effect due to SR, but also the fact that you're deep in a big gravity well, which has effects on your measured time due to General Relativity (GR).

SR says that "moving clocks run slow", but deep in the Sun's gravity well, we should also be running slow relative to the Earth. Not sure what the relative size of the two effects is.

EDIT> I assume the SR effect is larger than the GR effect, simply because SR was obvious before GR.

> For instance, if you look at a clock on a GPS satellite, moving fast relative to you, you can see it run slower than the one on your wrist.

Actually, the general relativity effects of weaker gravitational field dominate the special relativity effects of velocity[1]. So the GPS satellite clock actually runs faster, not slower.

[1] http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....

There's a really neat thing about this, the relationship balances out at a certain orbital height, before it flips over so there's an orbit where your chronologically in synch with the ground.

Hadn't thought about it that way, but you are right.

That's only true with respect to a given locus of points on the ground, not the full surface. I.E., the relative velocity of the SV isn't the same for all points that may be measuring.

In practice the GR effect is compensated by the satellite at manufacturing, the SR effect is treated in the receiver - for just that reason.

Yes, time is slower/faster in different parts of the solar system. Atomic clocks on the GPS satellites ticks 38 microseconds faster than on the surface of earth each day (which they correct for).

It does. There is no such thing as "now" unless you also include a "here". Everyone experiences a different time. Even us, who live in different points on the surface of the planet experience time differently.

Yep, that's relativity.

I am not a physicist but I believe the answer is yes as time is affected by acceleration.

Both velocity and gravity (distance from the nearest planet/star) affect time.

It does, but the difference is negligible unless we're talking about the surface of a neutron star.

The difference is not negligible if we are talking about applications like GPS etc.

This is based on my limited physics education, but I believe there are two things at play:

1) Velocity doesn't affect time, acceleration does. So if your twin flies to Mars and back, you age more quickly. But if your twin flies to Mars, and you join him after a year (following the same trajectory), you age the same. This is special relativity.

2) Acceleration due to gravity doesn't count. In fact, the opposite is true -- by standing on the ground, you are accelerating up at 32 feet per second squared. This is general relativity.

So, to answer your question. On the one hand, yes, if I am accelerating (not counting gravity), then I observe time pass more slowly. On the other hand, most of the universe is dominated by gravitational forces, so most systems wouldn't notice these effects.

The fascinating thing is that both (1) and (2) happen because of a very basic physics principle: if I can't use an experiment to tell two frames of reference apart, then the physics in the two frames of reference are identical.

For (1), I observe the same speed of light as someone moving at velocity v relative to me. Einstein used this simple axiom to derive special relativity. For (2), I can't tell the difference between free fall and being at rest (alternatively, I can't tell the difference between being on Earth and being in an elevator in space). This is because the inertial mass equals gravitational mass, a "coincidence" that dates back to Newton's law of gravitation. From this (and a lot of math) Einstein derived general relativity. Beautiful!

That's not really correct, if you sit at the center of a large object you don't accelerate, but you experience time dilation.

Further, as you dig deeper your acceleration decreases but time dilation continues to increase.

That's incorrect as well. You are mixing two relativistic effects: from the velocity of something relative to an observer, and from the gravity on that spot of the universe (which is what I assume you mean by acceleration).

Also wrong, as you dig deeper into a planet you experience less gravity, not more.

Velocity and acceleration are different things and Talking about less or more gravity is a poor descriptor.

At the center of the moon you would 'float' aka no acceleration relative to the moon. You would still be orbiting the earth, sun, etc.

However by being at the bottom of a gravity well you get time dilation relative to someone in the same orbit on the other side of the earth.

However, it's important to note LEO means high orbital velocity which counters being higher in the gravity field. Similarly, standing on the surface of the earth you have time dilation from the earths rotation which you would not have at the center.

PS: On way to think about it is at the center space time is pulled by all the mass around you which is a stronger pull than standing beside a planet. However the pull is in balance, like a tug of war game nobody is winning.

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