How much time passes on Earth?

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In summary: Question: The only way three million years could have passed on Earth is if he actually traveled 3 million light years (at 0.99999999875c), right? i.e. he would have had to loop around the core and back again, like, 57 times!Yes.
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DaveC426913
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TL;DR Summary
We sometimes talk about millions of years passing back on Earth during a relativistic journey but how is that possible without actually traveling 3 million light years?
The recent threads about relativity and the (ersatz) twin paradox got me flummoxed (again).

I referenced a story (A World Out of Time) where the man character came back to an Earth that was 3 million years older than when he left. The reason is that he journeyed to the galactic centre and back at very near light speed - the time dilation was such that only 150 years passed on board his ship - a factor of 20,000.

Question: The only way three million years could have passed on Earth is if he actually travelled 3 million light years (at 0.99999999875c), right? i.e. he would have had to loop around the core and back again, like, 57 times!

* there's mention of a trip around a black hole in the story but let's just ignore that for now and concentrate on a generic scenario
 
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  • #2
DaveC426913 said:
TL;DR Summary: We sometimes talk about millions of years passing back on Earth during a relativistic journey but how is that possible without actually traveling 3 million light years?

The recent threads about relativity and the (ersatz) twin paradox got me flummoxed (again).

I referenced a story (A World Out of Time) where the man character came back to an Earth that was 3 million years older than when he left. The reason is that he journeyed to the galactic centre and back at very near light speed - the time dilation was such that only 150 years passed on board his ship - a factor of 20,000.

Question: The only way three million years could have passed on Earth is if he actually travelled 3 million light years (at 0.99999999875c), right? i.e. he would have had to loop around the core and back again, like, 57 times!
Yes.
DaveC426913 said:
* there's mention of a trip around a black hole in the story but let's just ignore that for now and concentrate on a generic scenario
There was a thread about this a while ago. There is a minimum stable circular orbit around a non-spinning black hole, where the time dilation is not that large. In order to come back a lot younger, you have find some clever tricks, although I think a factor of 20,000 is probably unrealistic.
 
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In flat spacetime yes, he'd have to travel 3 million years as measured by Earth. The black hole could have a material effect depending what he did with it.
 
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DaveC426913 said:
there's mention of a trip around a black hole in the story but let's just ignore that for now
If the ship is capable of rocket thrust for a long enough period, it could hover close enough to the hole's horizon to achieve the required time dilation factor. But "close enough" is extremely close: 1.0000000025 times the horizon radius for a time dilation factor of 20,000, which for a 3 million solar mass black hole means about 22 meters above the horizon for a hole whose horizon radius is 9 million kilometers. You would want to be extremely confident in your navigation.
 
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PeterDonis said:
...about 22 meters above the horizon for a hole whose horizon radius is 9 million kilometers. You would want to be extremely confident in your navigation.
There would be detectable time dilation within the ship!

You could literally observe the twin paradox play out in real-time as your buddy walked* from the cockpit to the loo.

* fell. And died.
 
  • #6
PeterDonis said:
But "close enough" is extremely close: 1.0000000025 times the horizon radius for a time dilation factor of 20,000, which for a 3 million solar mass black hole means about 22 meters above the horizon for a hole whose horizon radius is 9 million kilometers.
At that distance the required acceleration would be enormous, too much for humans to bear.

For a large black hole and a short distance, we can approximate it using the Rindler horizon formula ##c^2/22##, about ##4 \times 10^{15} \text{ m/s}^2##.
 
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Depends what you mean by distance traveled. A rocket could never leave the solar system, yet when the traveler returns to earth, it is 3 million years ahead of when they left, while they are still alive. All you need to do is follow a circular loop e.g. between Jupiter and Saturn orbit, at sufficient speed.
 
  • #8
PAllen said:
Depends what you mean by distance traveled. A rocket could never leave the solar system, yet when the traveler returns to earth, it is 3 million years ahead of when they left, while they are still alive. All you need to do is follow a circular loop e.g. between Jupiter and Saturn orbit, at sufficient speed.
Yes. And that Jupiter-Saturn loop would have to cover 3 million light years.

I pointed this out in the OP - a loop around the core and back is "only" 52,000ly, so you'd have to do that loop about 57 times.
 
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DaveC426913 said:
Yes. And that Jupiter-Saturn loop would have to cover 3 million light years.

I pointed this out in the OP - a loop around the core and back is "only" 52,000ly, so you'd have to do that loop about 57 times.
Yeah, but the core central BH complicates things. Also, you wouldn’t cover 3 million ly from the traveler perspective. If, for example, the traveler only aged 50 years, then an odometer used by the traveler would show slightly less than 50 ly traveled. In the case of a loop within the solar system, earth and traveler would agree on number of loops, but would wildly disagree on distance around each loop.
 
  • #10
PAllen said:
odometer used by the traveler would show slightly less than 50 ly traveled
Measuring the movement of a hideously length-contracted and shape-shifting galaxy against his accelerating, but always at rest self.
 

Related to How much time passes on Earth?

1. How is time measured on Earth?

Time on Earth is measured using the international standard unit of time, the second, which is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. This measurement is maintained by atomic clocks and is used to determine the length of a day, year, and other units of time.

2. How long is a day on Earth?

A day on Earth is defined as the time it takes for the Earth to complete one rotation on its axis. This is approximately 24 hours, or 86,400 seconds. However, due to the Earth's elliptical orbit and the tilt of its axis, the length of a day can vary slightly throughout the year.

3. How long is a year on Earth?

A year on Earth is defined as the time it takes for the Earth to complete one orbit around the sun. This is approximately 365.24 days, or 31,557,600 seconds. However, to account for the extra fraction of a day, a leap year is added every four years, making the average length of a year 365.25 days.

4. Does time pass at the same rate everywhere on Earth?

No, time can pass at slightly different rates depending on factors such as altitude and velocity. This is due to the effects of gravity and the theory of relativity. For example, time passes slightly faster at higher altitudes and slightly slower at higher velocities. However, these differences are extremely small and only measurable with highly precise instruments.

5. Can time be affected by human activities?

Yes, human activities such as daylight saving time and time zones can affect the way time is observed and measured on Earth. These adjustments are made to better align time with the Earth's rotation and the position of the sun, and to accommodate for the varying lengths of days and years. Additionally, the use of calendars and timekeeping devices also plays a role in how time is perceived and managed by humans.

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