B Does Time Pass at Different Rates on Other Planets?

[mathewmcgill]

I hope this appropriate place. I'm just an average guy asking a question. Does time pass at different rates on other planets in our solar system?
In fact, if we were able to reach another solar system with an earth like planet orbiting a much larger sun, would the inhabitants of that planet age at a different rate than us?

 

[phinds]

I hope this appropriate place. I'm just an average guy asking a question. Does time pass at different rates on other planets in our solar system?
In fact, if we were able to reach another solar system with an earth like planet orbiting a much larger sun, would the inhabitants of that planet age at a different rate than us?

Aging rate could be a function of their biology, but their clocks would tick at one second per second just like ours.

 

[PeroK]

I hope this appropriate place. I'm just an average guy asking a question. Does time pass at different rates on other planets in our solar system?
In fact, if we were able to reach another solar system with an earth like planet orbiting a much larger sun, would the inhabitants of that planet age at a different rate than us?

Time, by definition, is measured in the same way everywhere. E.g. by a caesium atomic clock.

An important question, however, is whether natural processes have the same frequency everywhere. One example of this is the
frequency/wavelength of the spectrum of various atoms and molecules. The evidence from spectroscopy of distant stars is that they do. For example, the spectrum of a Sun-like star is the same everywhere in the observable universe.

 

[Filip Larsen]

if we were able to reach another solar system with an earth like planet orbiting a much larger sun, would the inhabitants of that planet age at a different rate than us?

Just in case you have heard about this as an effect of relativity let me add a bit about that since it hasn't been mentioned yet.

Assuming an Earth-sized planet that orbits a star many times more massive than the Sun, but still at the same distance as Earth is from the Sun, then there would indeed be a tiny difference in gravitional time dilation due to the difference of mass between the two stars. This would mean that the exact same process happening on the surface of the two planets (e.g. two identical build atomic clocks ticking away) if averaged over a long enough time (by any observer, as far as I understand it) would show that the process around the massive star ticks slower compared to that around the less massive star. Given any two specific planets around any two specific stars (or same star for that matter) one can in principle make a calculation and determine the average relative clock rate between the two planetary surfaces. Note however the effect is very tiny, perhaps in the order of around 1 second per human life span, so it would probably be almost impossible to measure the effect even if we one day somehow from Earth could observe a well-known natural process on the surface of an exoplanet around a massive star.

 

[Ibix]

Does time pass at different rates on other planets in our solar system?

In the sense that if you dropped a clock on one of them and watched it through a telescope, it would tick at a different rate to a clock beside your telescope, yes. If you brought the clock back to Earth (after waiting a long enough time that effects from the journey itself were negligible) it would tick at the same rate as your telescope clock, but would show a different time. This is roughly speaking due to gravitational time dilation from the Sun being different at different planets, the gravitational time dilation from the planets themselves being different at their surfaces, and kinematic time dilation from the different orbital speeds of the planets. (Note: this explanation isn't quite true for technical reasons, but the result is correct and the errors if you did a calculation on the basis of this explanation would be small.)

In fact, if we were able to reach another solar system with an earth like planet orbiting a much larger sun, would the inhabitants of that planet age at a different rate than us?

If you actually travelled there your clocks would tick the same as the locals' clocks, which might well mean your clocks tick at a different rate to clocks left on Earth. "Aging" is a rather imprecise term, so the answer to that depends a bit what you mean. I would guess you were meaning it asa metaphor for the rate of passage of time, in which case the answer is no, they would experience the same passage of time as them while we were there.

 

[phinds]

would show that the process around the massive star ticks slower compared to that around the less massive star.

COMPARED, yes but keep in mind that ALL clocks, whatever their depth in a gravitation field and whatever their relative velocity, tick away at one second per second, locally. Gravitational time dilation, which is what you are thinking of, is real and your two observers WOULD see each other's clocks ticking at different rates (this is the "comparison" you mention), but each clock, locally, in its own rest frame will tick at one second per second.

 

[Hornbein]

On the surface of a neutron star the gravity is so great that time would pass at 2/3 the rate of here on Earth.

 

[phinds]

On the surface of a neutron star the gravity is so great that time would pass at 2/3 the rate of here on Earth.

But locally, the clocks would still be ticking at the same one second per second as our clocks. This is a point that many people miss, which is why I keep emphasizing it.

 

[Filip Larsen]

COMPARED, yes but keep in mind that ALL clocks, whatever their depth in a gravitation field and whatever their relative velocity, tick away at one second per second, locally.

I was almost about to include a similar clarification, but choose to wait until the OP in a reply would indicate actual confusion about this point. But I guess since it's such a common fallacy I should probably have mentioned it anyway in order to keep everyone happy (But I do now wonder if threads on length contraction also have to spend effort to explain that 1 meter in local flat space always is 1 meter?)

 

[OmCheeto]

But locally, the clocks would still be ticking at the same one second per second as our clocks. This is a point that many people miss, which is why I keep emphasizing it.

Plotted on a log-log scale, if I were to be standing next to 'yo mama', and her wrist watch was transmitting our conversation to my cousins on Pluto, would they notice anything odd about our voices?

 

[Ibix]

Plotted on a log-log scale, if I were to be standing next to 'yo mama', and her wrist watch was transmitting our conversation to my cousins on Pluto, would they notice anything odd about our voices?

No. The Schwarzschild radius of the Sun is about 3km, and we're about 150 million kilometres away so the time dilation factor between Earth and interstellar space is of the order $1+10^{-8}$, so you would see about 10ns (give or take - I did not do a precise calculation...) difference in elapsed time per second. You need an atomic clock to be aware of that kind of difference - one of the cheap ones that come in on the order of a few $100k would do I think.

 

[phinds]

Plotted on a log-log scale, if I were to be standing next to 'yo mama', and her wrist watch was transmitting our conversation to my cousins on Pluto, would they notice anything odd about our voices?

I think so, since we are in a noticeably higher gravity well than the surface of Pluto (Pluto is 63% of Earth's gravity). I haven't done any calcs, so not sure how MUCH difference there would be, but seems to me there would be some measurable difference.

Hm ... according to Google, there would be a measurable difference but NOT enough to make any noteable change in voices, I think

To determine the gravitational time dilation between Earth's surface and a point with 63% of its gravity, we must first calculate the altitude where that reduced gravity is experienced
. For every year that passes on Earth's surface, a clock at the higher altitude would gain approximately 32 minutes and 46 seconds.

 

[Ibix]

Hm ... according to Google, there would be a measurable difference but NOT enough to make any noteable change in voices, I think

The figure you're quoting is way too high. The gravitational time dilation depends on potential difference, and the time dilation factor between $r$ and infinity is approximately $1+\dfrac 12\dfrac{r_s}r$. For the Earth, that's about $1+10^{-9}$, which works out to about 3s per century difference.

 

[mathewmcgill]

Thank you all. I want to write a sci-fi novel and wondered about that. What I'm gathering is that the dilation is insignificant like for instance, between the Earth and Mars. You see I was even wondering what would be the dilation between a person standing on the ground as opposed to a person suspended in a fictional anti-gravitational bubble. Specifically speaking of a person in the middle of a spherical area where gravity has been attenuated to the degree where he or she would float some distance above ground. Again, I gather that it wouldn't be worth considering or mentioning.

 

[Ibix]

What I'm gathering is that the dilation isn't great at all, speaking between the Earth and Mars.

Totally negligible, correct.

You see I was even wondering what would be the dilation between a person standing on the ground as opposed to a person suspended in a fictional anti-gravitational bubble.

There's no scientific basis for such a thing, so you can give it any properties you like.

 

[PeroK]

Specifically speaking of a person in the middle of a spherical area where gravity has been attenuated to the degree where he or she would float some distance above ground.

Like a helicopter?

 

[jbriggs444]

I think so, since we are in a noticeably higher gravity well than the surface of Pluto (Pluto is 63% of Earth's gravity)

It is not gravitational field strength (local gravity) that matters. What matters is gravitational potential. Or, almost equivalently, escape velocity. If one works through the math, the escape energy from a planet is the product of surface gravity times planetary radius.

Both Earth and Pluto sit within the gravitational potential well of the sun. The escape velocity from Earth is around 11 km/s. To escape from the sun starting at the position of Earth's orbit is about 42 km/s.

Meanwhile, the escape energy from Pluto is only about 1.2 km/s. The escape velocity from the sun starting at Pluto's orbit is around 1 km/s if I've done the math correctly.

Edit: After a moment's thought, that 63 percent figure sounded quite high. Pluto would be much smaller than Earth and would likely not have an iron core. A surface gravity that high is implausible. So I checked. It is not 63 percent. It is 0.62 meters per second. Or about 6.3 percent.

 

[Filip Larsen]

What matters is gravitational potential.

And speed too. E.g. the clock rate on the Earth surface is equal to the clock rate when in circular orbit at around an altitude of half the Earths radius (~3200 km).

 

[jbriggs444]

Specifically speaking of a person in the middle of a spherical area where gravity has been attenuated to the degree where he or she would float some distance above ground.

We might imagine achieving this by counter-balancing local gravity with an implausibly massive awning suspended overhead.

The gravitational potential beneath the awning would be the same (to a good approximation) as the gravitational potential nearby. So zero effect on time dilation. For a stationary body, it is gravitational potential that matters. Not the local acceleration of gravity.

One easy example would be an implausible spherical hollow somehow created at the center of the Earth. The local acceleration of gravity would be zero throughout the hollow. But the time dilation would be somewhat greater than at the Earth's surface. Still rather negligible.

Again, I gather that it wouldn't be worth considering or mentioning.

Yes. Negligible.

 

[256bits]

Thank you all. I want to write a sci-fi novel and wondered about that. What I'm gathering is that the dilation is insignificant like for instance, between the Earth and Mars. You see I was even wondering what would be the dilation between a person standing on the ground as opposed to a person suspended in a fictional anti-gravitational bubble. Specifically speaking of a person in the middle of a spherical area where gravity has been attenuated to the degree where he or she would float some distance above ground. Again, I gather that it wouldn't be worth considering or mentioning.

As for 'aging', yes. the gravitational time dilation is insignificant, for say Earth-Mars.

But hold on.
GPS has to take the 'insignificant' time dilation ( both relative velocity and gravitational ) into account so as to pinpoint locations on earth's surface to reasonable accuracy. If that was not done, the error of wanted location and calculated location from GPS would be out by 100's of meters.

If errors of time measurement on the order of nanoseconds doesn't look like much in the manner of time keeping, the error accumulation over longer durations of time becomes problematic. In addition, the 30 cm distance travelled by light in 1 ns, accumulates as well. The moon has a time differential with that of the earth of .6 nanosecond/second, an error of only 18 cm distance wise. Over a day the accumulation of error, results in a 56 microsecond difference between earth-moon time keeping, and location differentials of 17 km per day. The insignificant becomes significant, depending upon whose clock one uses, the one on the earth or the one on the moon, for something such as space traffic control, whenever spaceships travel between the earth and the moon becomes a part of the projected possibilities of the future.

Note that the gravitation of Jupiter, a large mass similar to the umbrella analogy of your anti-gravitational bubble, has an affect counteracting and reinforcing that of the sun. For the earth-moon system, the effects on both bodies are similar to a degree. For Earth-Mars navigation in the future the ns accumulation should be accounted for the Mars-Earth space traffic control.

A write-up of what they call a messy problem can be seen at
https://eos.org/articles/the-relatively-messy-problem-with-lunar-clocks

The GPS time keeping problem should be able to be found on internet search.