Just because time is relative does not mean time is subjective. Time is a fundamental objective part of reality, and time and distance relativity is probably less weird than you think it is. There …
I’m not an astrophysicist nor a relativity theorist, but this makes absolutely no sense… The article writes,
When we say that the Earth is 4.5 billion years old, technically we mean 4.5 billion years is the maximum amount of relative time any thing could have experienced since the Earth was formed.
If by “Earth is 4.5 billion years old” it means the time lapse as experienced on earth – in other words, as measured by a clock on earth, then the clock is in the rest frame and therefore measures the shortest possible time duration among all clocks in other (moving) inertial frames, not “the maximum amount of relative time” (special relativity). I think the author is confusing this with the twin paradox where the traveling twin ages slower. The talk of
There is a maximum amount of relative time that can be experienced between any two points in time (no time dilation). There is a maximum relative distance between any two points in space (no length contraction)
is also troublesome – what is even “two points in time (no time dilation)”? One should instead be talking about two events and their space-time coordinates
If by “Earth is 4.5 billion years old” it means the time lapse as experienced on earth
Nope. It means that 4.5 billion years is the roughly the MAXIMUM amount of relative time anything anywhere in the universe in any frame of reference could have experienced since the creation of the Earth. Now obviously it is true that Earth’s reference frame is close enough to that maximum such that the difference is a rounding error of the 4.5 billion years figure. But there is literally nothing in the universe that could have experienced 5 billion years of time since the creation of the Earth, although it is certainly possible to experience only 4 billion years. It is also true that 13.8 billion years is the maximum amount of relative time anything in the observable universe in any frame of reference could have experienced since the big bang.
I think the author is confusing this with the twin paradox where the traveling twin ages slower.
I think the author means exactly what he said. Experiencing 5 billion years (more than the maximum) since the Earth’s formation would be impossible in all frames of reference - but experiencing 4 billion (less than the maximum) is possible.
“what is even two points in time”
You don’t understand what a point in time means? It is well understood by astrophysicists that there is a maximum amount of relative time that can be experienced between any 2 points in time, just as there is a maximum amount of relative distance that can be experienced between any 2 points in space (no length contraction). It is impossible for time dilation and/or length contraction to be negative.
One should instead be talking about two events and their space-time coordinates
You can talk about that if you want. But then you probably won’t learn anything new. This article talks about the implications of the well understood facts by astrophysicists that there exists a maximum relative length between any 2 points in space and also between any 2 points in time and how length contraction is related to time dilation.
It means that 4.5 billion years is the roughly the MAXIMUM amount of relative time anything anywhere in the universe in any frame of reference could have experienced since the creation of the Earth.
Another confusing thing is that NO ONE calculates the age of the Earth this way. People do things like measure isotopes and radioactive decay rates, which gives you the Earth’s age in its own reference frame. No one is messing about with measuring the CMB or calculating galactic flow rates or some such.
True, for the Earth “the difference is a rounding error”. But imagine if the Earth formed 10 billion years ago, then between age 500 million and 1000 million years some alien pranksters accelerated Earth to near lightspeed and took it on a joy ride around the universe for 6 billion years, then put it back here. All our measurements would still show the Earth is 4.5 billion years old, yet by the article’s calculation it would be 10 billion years old, disproving the article’s entire point!
I think the author just got confused. The only context where the “maximum amount of relative time” concept comes up is in calculating the age of the universe. It is objectively 13.8GY. There we do look at the CMB to make corrections for our relative speed! This way all observers will agree on that number regardless of their speed, even if their own clocks show less. But the author heard that, got excited, and started trying to apply it to the age of Earth, where it doesn’t serve any use.
But imagine if the Earth formed 10 billion years ago, then between age 500 million and 1000 million years some alien pranksters accelerated Earth to near lightspeed and took it on a joy ride around the universe for 6 billion years, then put it back here.
But we know that did not happen. Sure you could always make outlandish scenarios and say that the CMB could have been put in place to fool us and therefore the elapsed time since the big bang might have actually been 20 billion years.
I think the author just got confused.
The author did not get confused. The author knows that aliens did not kidnap the Earth, move it around at light speed without Earth being ripped apart, and then put it back to prank us. The difference between the time that elapsed on Earth and the maximum since the Earth’s creation is a rounding error relative to the 4.5 billion year duration figure. And that is how the author is certain that there is no frame of reference anywhere in the observable universe in which 5.0 billion years elapsed since the creation of the Earth.
The only context where the “maximum amount of relative time” concept comes up is in calculating the age of the universe. It is objectively 13.8GY.
That may be the only situation where it comes up for yourself. But the concept of the “maximum amount of relative time” can apply to literally anything just as the “maximum relative distance between two objects in space” can apply to literally anything. You do not have to calculate or to know what the maximum amount of relative time is to know that it exists, and to realize the implications that time is objectively a fundemental part of the universe. The important thing is that there IS a maximum, not whether it is trivial to calculate so you can throw it into your favorite equations.
People do things like measure isotopes and radioactive decay rates, which gives you the Earth’s age in its own reference frame.
That is irrelevant though. It is perfectly fine to start with a figure calculating Earth’s age of about ~4.5 billion in its own reference frame. And then it is perfectly fine to take that figure and calculate a 2nd figure where the estimated time dilation is factored in, and notice the difference is a rounding error and therefore the figures for both Earth’s frame and the maximum are ~4.5 billion years. By calculating first the Earth frame figure and then the maximum figure, we know for certain that there is no frame of reference that can exceed approximately 4.5 billion years.
You are also missing the larger picture which is that generally, time flow rates can be recalculated from one frame of reference to another. To whatever extent we can accurately estimate time dilation figures, we can also estimate time flow rates as a percent of the maximum rate. Then we can use that maximum time flow rate to track a ‘universal time’ outside of our local reference frames. Ideally a space ship computer could be programmed to tell you not only what the travel speed is, but also what the ship’s time flow rate is as a percent of the maximum (both total rate and current rate) and make it easy to sync up time measurements later. No need to check the clocks of 2 space ships when they get together if the computers have it all figured out beforehand.
Then we can use that maximum time flow rate to track a ‘universal time’ outside of our local reference frames.
I still disagree.
In deep space you encounter an alien spaceship from Zebulon 5, a planet that is 100 light years away and is travelling at 10% lightspeed towards Earth (it’ll miss and pass by, no biggie). You need to synchronize your shipboard clock with Zebulonians. You tell them:
“We should use Earth’s time, which happens to be the universal time, as it flows the fastest, because Earth is nearly still! The clocks on your Zebulon tick much slower because of your speed.”
But the Zebulonians reply:
“No, you should use Zebulonian time! YOUR Earth is moving towards Zebulon, and YOUR Earth clocks tick much slower. Zebulon 5 clocks are the ones that tick the fastest, and our ship clock is synchronized to them. Synchronize your clocks to ours!”
Now, without reference to the CMB or some CMB proxy like the “average speed of all stars in the galaxy and nearby galaxies”, how would you resolve this dispute? Whose clock is actually faster?
“We should use Earth’s time, which happens to be the universal time,
Earth time is not universal time. Maximum time is universal time. No local reference frame can achieve maximum time.
Zebulon 5 clocks are the ones that tick the fastest
They won’t be ticking at maximum time either. No local reference frame can achieve maximum time.
how would you resolve this dispute? Whose clock is actually faster?
Neither clock is as fast as the maximum time flow. Planet Earth calculates it’s percent of the maximum. Planet Zebu also calculate their percent of the maximum. To convert you could go from Earth time to maximum time to Zebu time, although I suspect they would already be very close in their percentages. For this purpose you can ignore speed and calculate time dilation using gravitational time dilation + acceleration time dilation. Neither planet is going to be accelerating towards the other. Time dilation due to non-accelerating motion is more optics than real time dilation, because maximum time does not require you to wait for light from another source to travel towards you.
Time dilation due to non-accelerating motion is more optics than real time dilation
I’m afraid it’s both… Just to be clear, you are aware that relativistic time dilation is very much real, right? There is the doppler component AND the relativistic component, the latter of which you can’t get rid of regardless of the correction for perspective. That was the whole weird part with the special relativity, want to be sure we agree here.
For this purpose you can ignore speed and calculate time dilation using gravitational time dilation
Hold on, let’s not ignore the speed! I agree that for gravitational time dilation there is a time rate that is the maximum rate possible, which is as far away from any massive bodies as possible - away from planets, away from stars, even away from galaxies, and certainly away from any supermassive black holes. But you haven’t been talking about gravitational time dilation all this time, have you? I was about to suggest doing the opposite: for this purpose let’s ignore the mass of Earth and Zebulon for now as that is negligible, and just focus on the speed, which is very much not! Zebulonians are saying that for every hour on Zebulon 5, only 59 minutes 42 seconds pass on earth! (3600 * (1-0.1**2)**.5) This is way more than some microseconds per year that you accumulate from being in the Earth’s gravity well.
you are aware that relativistic time dilation is very much real, right?
I do not agree that 2 objects can both have time flow rates faster or slower than the other. That is impossible, so it is really optics. If 2 objects each think the other is moving towards them at a faster or slower time flow rate, you can ignore that. Because neither has a time flow rate faster than the other even if they both think they do. What matters is (1) time dilation due to acceleration and (2) gravitational time dilation. We do not age faster/slower just because another planet exists. And they would not age faster/slower just because we exist.
Look at this article below. Your scenario is #1 (2 objects moving past each other) Author says that time APPEARS to pass more slower for the other object. My scenario is #2 (gravitational time dilation). It says your head AGES FASTER than your feet.
[Time dilation has now been shown to apply in three separate instances. (1). When two objects pass each other at high speeds, each one sees the other as having their clocks dilated, and time appears to pass more slowly for the other, even though each experiences time as normal. (2). When two objects are in different gravitational fields, the one that’s deeper in a gravitational field experiences time passing more slowly than the one in a shallower field, and as a result, your head ages faster than your feet when you stand on Earth. (3). And cosmologically, when a local observer sees a signal emitted from an object across the distant Universe, the expansion of the Universe will both stretch the wavelength of that signal and also stretch it out, in time, when we observe it.]
For purposes of determining what your time dilation is as a percent of the maximum, you never need to directly compare 2 reference frames and “observe events” or observe light traveling over long distances from another object. You ignore the other planet and compute your percent of the maximum by adding your gravitational time dilation with your time dilation due to acceleration. The other planet does the same. Since neither planet accelerates, it comes down to how big the planets are and the gravitational time dilation that they generate. Since this affect is very small, both planets time flow rates will be very close to the maximum. Let’s say that Earth’s percent is 99.999% of the maximum. Zebu is a bigger planet, so their time flow rate is only 99.998% of the maximum. You simply sync the time by computation. On earth, you add 1 second to every 99,999 seconds to track the maximum. If you then want to go to Zebu’s time flow rate from the maximum, you would then subtract 2 seconds for every 100,000 “maximum time” seconds.
! I agree that for gravitational time dilation there is a time rate that is the maximum rate possible, which is as far away from any massive bodies as possible - away from planets, away from stars, even away from galaxies, and certainly away from any supermassive black holes.
Actually this is not the case. Even a single atom would generate its own gravity field. That is why no matter can ever obtain the “maximum” time flow rate.
Zebulonians are saying that for every hour on Zebulon 5, only 59 minutes 42 seconds pass on earth!
That is because they are observing our light moving over large distances, which they don’t need to do. They don’t need to observe us to know what their own time dilation is. They do not age faster or slower just because we exist. And we do not age faster or slower just because they exist. They should be ignoring our planet completely and computing their own time dilation as a percent of the maximum, based on gravitational time dilation.
I do not agree that 2 objects can both have time flow rates faster or slower than the other. That is impossible, so it is really optics.
Great! I’m glad we found your core mistaken belief and this conversation has been productive! The 2 objects do indeed each have time flow rates faster than the other. As to how that impossible paradox is resolved they teach that in a special relativity class or textbook. If you don’t believe me you could post in ask science with “Is special relativity time dilation real or just optics?” and others will confirm.
Hey, you seem to have a better understanding of the stuff, so perhaps you could point me in the right direction? Here’s my confusion: Let’s say at the inception of the earth, a clock started ticking (event 1), and let’s count earth’s age as up to the moment I made the post right next to that same clock (event 2). By special relativity (so obviously ignoring gravity etc), the interval between the two events is s^2 = t^2 - x^2 where t is the time elapsed on the clock, and x = 0 is the distance traveled by the clock in its own frame (earth’s frame), which is zero. For an observer moving at a constant speed relative to earth, the clock has moved, so x' != 0 (using ' for the moving frame), but the interval s is the same in both frames, so the time elapsed in the moving observer’s frame, between the same two events, must be greater than on the earth clock, t'^2 = s^2 + x'^2 > s^2 = t^2. In other words earth appears older (as measured by the relative time between the said two events) to the moving observer than to someone living on earth. This is where my comment about “two points in time” come from: without the spatial information, I wouldn’t be able to compare different relative times and pick its maximum.
I’m obviously not an astrophysicist and not familiar with the “well understood facts by astrophysicists” of maximum relative time/space. I suspect from your comment that my interpretation of “relative time” is wrong, but if you could point me to some accessible references, that would be very much appreciated!
I think your problem was you forgot the γ factor, which is still present even when using natural units. Or as the wiki describes it: “As illustrated in Fig 2-3, the boosted and unboosted spacetime axes will in general have unequal unit lengths.”
Edit: oh wait, you would still be upset that t’ = γT > T = t. Ok then! So using this diagram for example, two time units pass between O and P along the Earth’s red time axis, but 3 time units pass along the spaceship’s green prime time axis, and this is in conflict with the article’s claim that the Earth’s frame is the frame with the maximum rate of time.
I think the author meant to say you should calculate the time elapsed along the path that ends up back at the same point. If the spaceship were to turn around and return, 6 time units will have elapsed for it here, but 7 time units on earth. I.e. we are in the Twin’s Paradox/relativity of simultaneity territory here, but the important thing is that there is no path for the spaceship where you would see 7 or more time units elapsed, other than staying on Earth.
Thanks, I think we are actually in agreement here: if you account for the fact that \gamma>1 in general, then your calculation showed that T' = \gamma T > T, that is, the moving observer in general registers a longer duration T' between the two events than the clock at rest (T). I was just taking a shortcut when I said this should follow from X' != 0 (the -\gamma v T in your calculation).
Also, thanks for the imagery of aliens taking earth for a joy ride. This might be how we are saved when the sun dies.
Edit: I think we agree on both accounts as the twin paradox is also the only way I can rationalize the original claim (even said so in my first reply)
twin paradox is also the only way I can rationalize the original claim
The fact that there is a maximum amount of relative time that can elapse between any 2 “events” does not rely on the twin paradox in any way. It doesn’t even depend on movement at all since there is gravitational time dilation and the 2 events don’t even need to be “witnessed” for time to have a particular relative duration between the events. Whichever of 2 different inertial frames of reference has the least amount of gravitational time dilation has the faster time flow rate and is closest to the maximum rate.
If a piece of matter had no gravitational time dilation at all (which admittedly is impossible) what would be the time flow rate for the object? For simplicity let’s assume it is not accelerating or even moving at all (except for expansion of universe). How would we know it is not moving? Let’s assume (call it a thought experiment) that the universe has a center and boundaries, and that the distance and direction to the center is not changing. This object would have no time dilation, the maximum time flow rate, and experience the longest possible duration of time across any arbitrary points in time.
In other words earth appears older (as measured by the relative time between the said two events) to the moving observer than to someone living on earth.
It’s fine and to be expected that time passes differently with different levels of time dilation. You might have Reference Frame A where the time flow rate is 99.999% of the maximum and Frame B where the time flow rate is 99.998% of the maximum. The time flow rate in Frame A is faster than B, because A is closer to the maximum rate than B.
This is where my comment about “two points in time” come from:
Think of “two points in time” as 2 events in time, and (for simplicity) at the same fixed point in space in your frame of reference (A) and another person’s frame of reference (B). Whichever frame is under the greater influence of gravitational time dilation, will have a slower time flow rate than the other frame. But there is also a maximum amount of time between the 2 events that neither of those 2 frames (or any other frame of reference) can exceed.
without the spatial information, I wouldn’t be able to compare different relative times and pick its maximum.
Figuring out the maximum time flow rate between any 2 events or points in time would not be a simple thing at all. You would have to calculate the entire amount of gravitational time dilation of every gravity field in range of your object, and add to that the total amount of time dilation due to acceleration of your object. But just because the total amount of time dilation is not a simple thing to calculate and add to your equations, does not mean that “zero time dilation” == “maximum time flow rate” does not exist nor that there is not a maximum amount of relative time duration between any 2 events/point in time. I assume you agree that there is a maximum amount of relative distance between any 2 objects/points in space right? There is also a maximum amount of relative duration between any 2 events/points in time. And the length contraction that shrinks distance length is related to the time dilation that shrinks time duration.
but if you could point me to some accessible references that would be very much appreciated!
I hate to mention reddit here but this reddit comment explains it better than I can.
[It’s likely based on the proper time of a comoving observer in simplified cosmological solutions of general relativity. A comoving observer is an observer whose ‘motion’ is due to the expansion of the universe, not any motion with respect to the comoving frame. The cosmological solutions are also isotropic and homogenous, so there are no clumps of matter like black holes to influence time - the comoving proper time is the same everywhere and can be considered a maximum time.]
I’m not an astrophysicist nor a relativity theorist, but this makes absolutely no sense… The article writes,
If by “Earth is 4.5 billion years old” it means the time lapse as experienced on earth – in other words, as measured by a clock on earth, then the clock is in the rest frame and therefore measures the shortest possible time duration among all clocks in other (moving) inertial frames, not “the maximum amount of relative time” (special relativity). I think the author is confusing this with the twin paradox where the traveling twin ages slower. The talk of
is also troublesome – what is even “two points in time (no time dilation)”? One should instead be talking about two events and their space-time coordinates
Nope. It means that 4.5 billion years is the roughly the MAXIMUM amount of relative time anything anywhere in the universe in any frame of reference could have experienced since the creation of the Earth. Now obviously it is true that Earth’s reference frame is close enough to that maximum such that the difference is a rounding error of the 4.5 billion years figure. But there is literally nothing in the universe that could have experienced 5 billion years of time since the creation of the Earth, although it is certainly possible to experience only 4 billion years. It is also true that 13.8 billion years is the maximum amount of relative time anything in the observable universe in any frame of reference could have experienced since the big bang.
I think the author means exactly what he said. Experiencing 5 billion years (more than the maximum) since the Earth’s formation would be impossible in all frames of reference - but experiencing 4 billion (less than the maximum) is possible.
You don’t understand what a point in time means? It is well understood by astrophysicists that there is a maximum amount of relative time that can be experienced between any 2 points in time, just as there is a maximum amount of relative distance that can be experienced between any 2 points in space (no length contraction). It is impossible for time dilation and/or length contraction to be negative.
You can talk about that if you want. But then you probably won’t learn anything new. This article talks about the implications of the well understood facts by astrophysicists that there exists a maximum relative length between any 2 points in space and also between any 2 points in time and how length contraction is related to time dilation.
Another confusing thing is that NO ONE calculates the age of the Earth this way. People do things like measure isotopes and radioactive decay rates, which gives you the Earth’s age in its own reference frame. No one is messing about with measuring the CMB or calculating galactic flow rates or some such.
True, for the Earth “the difference is a rounding error”. But imagine if the Earth formed 10 billion years ago, then between age 500 million and 1000 million years some alien pranksters accelerated Earth to near lightspeed and took it on a joy ride around the universe for 6 billion years, then put it back here. All our measurements would still show the Earth is 4.5 billion years old, yet by the article’s calculation it would be 10 billion years old, disproving the article’s entire point!
I think the author just got confused. The only context where the “maximum amount of relative time” concept comes up is in calculating the age of the universe. It is objectively 13.8GY. There we do look at the CMB to make corrections for our relative speed! This way all observers will agree on that number regardless of their speed, even if their own clocks show less. But the author heard that, got excited, and started trying to apply it to the age of Earth, where it doesn’t serve any use.
But we know that did not happen. Sure you could always make outlandish scenarios and say that the CMB could have been put in place to fool us and therefore the elapsed time since the big bang might have actually been 20 billion years.
The author did not get confused. The author knows that aliens did not kidnap the Earth, move it around at light speed without Earth being ripped apart, and then put it back to prank us. The difference between the time that elapsed on Earth and the maximum since the Earth’s creation is a rounding error relative to the 4.5 billion year duration figure. And that is how the author is certain that there is no frame of reference anywhere in the observable universe in which 5.0 billion years elapsed since the creation of the Earth.
That may be the only situation where it comes up for yourself. But the concept of the “maximum amount of relative time” can apply to literally anything just as the “maximum relative distance between two objects in space” can apply to literally anything. You do not have to calculate or to know what the maximum amount of relative time is to know that it exists, and to realize the implications that time is objectively a fundemental part of the universe. The important thing is that there IS a maximum, not whether it is trivial to calculate so you can throw it into your favorite equations.
That is irrelevant though. It is perfectly fine to start with a figure calculating Earth’s age of about ~4.5 billion in its own reference frame. And then it is perfectly fine to take that figure and calculate a 2nd figure where the estimated time dilation is factored in, and notice the difference is a rounding error and therefore the figures for both Earth’s frame and the maximum are ~4.5 billion years. By calculating first the Earth frame figure and then the maximum figure, we know for certain that there is no frame of reference that can exceed approximately 4.5 billion years.
You are also missing the larger picture which is that generally, time flow rates can be recalculated from one frame of reference to another. To whatever extent we can accurately estimate time dilation figures, we can also estimate time flow rates as a percent of the maximum rate. Then we can use that maximum time flow rate to track a ‘universal time’ outside of our local reference frames. Ideally a space ship computer could be programmed to tell you not only what the travel speed is, but also what the ship’s time flow rate is as a percent of the maximum (both total rate and current rate) and make it easy to sync up time measurements later. No need to check the clocks of 2 space ships when they get together if the computers have it all figured out beforehand.
I still disagree.
In deep space you encounter an alien spaceship from Zebulon 5, a planet that is 100 light years away and is travelling at 10% lightspeed towards Earth (it’ll miss and pass by, no biggie). You need to synchronize your shipboard clock with Zebulonians. You tell them:
But the Zebulonians reply:
Now, without reference to the CMB or some CMB proxy like the “average speed of all stars in the galaxy and nearby galaxies”, how would you resolve this dispute? Whose clock is actually faster?
Earth time is not universal time. Maximum time is universal time. No local reference frame can achieve maximum time.
They won’t be ticking at maximum time either. No local reference frame can achieve maximum time.
Neither clock is as fast as the maximum time flow. Planet Earth calculates it’s percent of the maximum. Planet Zebu also calculate their percent of the maximum. To convert you could go from Earth time to maximum time to Zebu time, although I suspect they would already be very close in their percentages. For this purpose you can ignore speed and calculate time dilation using gravitational time dilation + acceleration time dilation. Neither planet is going to be accelerating towards the other. Time dilation due to non-accelerating motion is more optics than real time dilation, because maximum time does not require you to wait for light from another source to travel towards you.
I’m afraid it’s both… Just to be clear, you are aware that relativistic time dilation is very much real, right? There is the doppler component AND the relativistic component, the latter of which you can’t get rid of regardless of the correction for perspective. That was the whole weird part with the special relativity, want to be sure we agree here.
Hold on, let’s not ignore the speed! I agree that for gravitational time dilation there is a time rate that is the maximum rate possible, which is as far away from any massive bodies as possible - away from planets, away from stars, even away from galaxies, and certainly away from any supermassive black holes. But you haven’t been talking about gravitational time dilation all this time, have you? I was about to suggest doing the opposite: for this purpose let’s ignore the mass of Earth and Zebulon for now as that is negligible, and just focus on the speed, which is very much not! Zebulonians are saying that for every hour on Zebulon 5, only 59 minutes 42 seconds pass on earth!
(3600 * (1-0.1**2)**.5)This is way more than some microseconds per year that you accumulate from being in the Earth’s gravity well.What’s that?
I do not agree that 2 objects can both have time flow rates faster or slower than the other. That is impossible, so it is really optics. If 2 objects each think the other is moving towards them at a faster or slower time flow rate, you can ignore that. Because neither has a time flow rate faster than the other even if they both think they do. What matters is (1) time dilation due to acceleration and (2) gravitational time dilation. We do not age faster/slower just because another planet exists. And they would not age faster/slower just because we exist.
Look at this article below. Your scenario is #1 (2 objects moving past each other) Author says that time APPEARS to pass more slower for the other object. My scenario is #2 (gravitational time dilation). It says your head AGES FASTER than your feet.
https://bigthink.com/starts-with-a-bang/time-run-slow-early-universe/
[Time dilation has now been shown to apply in three separate instances. (1). When two objects pass each other at high speeds, each one sees the other as having their clocks dilated, and time appears to pass more slowly for the other, even though each experiences time as normal. (2). When two objects are in different gravitational fields, the one that’s deeper in a gravitational field experiences time passing more slowly than the one in a shallower field, and as a result, your head ages faster than your feet when you stand on Earth. (3). And cosmologically, when a local observer sees a signal emitted from an object across the distant Universe, the expansion of the Universe will both stretch the wavelength of that signal and also stretch it out, in time, when we observe it.]
For purposes of determining what your time dilation is as a percent of the maximum, you never need to directly compare 2 reference frames and “observe events” or observe light traveling over long distances from another object. You ignore the other planet and compute your percent of the maximum by adding your gravitational time dilation with your time dilation due to acceleration. The other planet does the same. Since neither planet accelerates, it comes down to how big the planets are and the gravitational time dilation that they generate. Since this affect is very small, both planets time flow rates will be very close to the maximum. Let’s say that Earth’s percent is 99.999% of the maximum. Zebu is a bigger planet, so their time flow rate is only 99.998% of the maximum. You simply sync the time by computation. On earth, you add 1 second to every 99,999 seconds to track the maximum. If you then want to go to Zebu’s time flow rate from the maximum, you would then subtract 2 seconds for every 100,000 “maximum time” seconds.
Actually this is not the case. Even a single atom would generate its own gravity field. That is why no matter can ever obtain the “maximum” time flow rate.
That is because they are observing our light moving over large distances, which they don’t need to do. They don’t need to observe us to know what their own time dilation is. They do not age faster or slower just because we exist. And we do not age faster or slower just because they exist. They should be ignoring our planet completely and computing their own time dilation as a percent of the maximum, based on gravitational time dilation.
Great! I’m glad we found your core mistaken belief and this conversation has been productive! The 2 objects do indeed each have time flow rates faster than the other. As to how that impossible paradox is resolved they teach that in a special relativity class or textbook. If you don’t believe me you could post in ask science with “Is special relativity time dilation real or just optics?” and others will confirm.
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Hey, you seem to have a better understanding of the stuff, so perhaps you could point me in the right direction? Here’s my confusion: Let’s say at the inception of the earth, a clock started ticking (event 1), and let’s count earth’s age as up to the moment I made the post right next to that same clock (event 2). By special relativity (so obviously ignoring gravity etc), the interval between the two events is
s^2 = t^2 - x^2wheretis the time elapsed on the clock, andx = 0is the distance traveled by the clock in its own frame (earth’s frame), which is zero. For an observer moving at a constant speed relative to earth, the clock has moved, sox' != 0(using'for the moving frame), but the intervalsis the same in both frames, so the time elapsed in the moving observer’s frame, between the same two events, must be greater than on the earth clock,t'^2 = s^2 + x'^2 > s^2 = t^2. In other words earth appears older (as measured by the relative time between the said two events) to the moving observer than to someone living on earth. This is where my comment about “two points in time” come from: without the spatial information, I wouldn’t be able to compare different relative times and pick its maximum.I’m obviously not an astrophysicist and not familiar with the “well understood facts by astrophysicists” of maximum relative time/space. I suspect from your comment that my interpretation of “relative time” is wrong, but if you could point me to some accessible references, that would be very much appreciated!
Using the Lorenz transformation formula, here’s what I get:
γ = 1/sqrt(1 - (v/c)^2) Δs^2 = (cΔt)^2 - Δx^2 ct' = γ (ct - (v/c)x) x' = γ (x - vt)In the Earth’s reference frame, the planet starts at (t=0,x=0) and just stays still for time T (say 4.5 billion years):
In the spaceship’s prime frame, we get:
p_i' = (0,0) p_f' = (γT, -γvT) s'^2 = (cγT)^2 - (-γvT)^2 = γ^2 T^2 (c^2 - v^2) = T^2 (c^2 - v^2) / (1 - v^2/c^2) = T^2 (c^2 - v^2) / (c^2 - v^2) * c^2 = (cT)^2I think your problem was you forgot the γ factor, which is still present even when using natural units. Or as the wiki describes it: “As illustrated in Fig 2-3, the boosted and unboosted spacetime axes will in general have unequal unit lengths.”
Edit: oh wait, you would still be upset that t’ = γT > T = t. Ok then! So using this diagram for example, two time units pass between O and P along the Earth’s red time axis, but 3 time units pass along the spaceship’s green prime time axis, and this is in conflict with the article’s claim that the Earth’s frame is the frame with the maximum rate of time.
I think the author meant to say you should calculate the time elapsed along the path that ends up back at the same point. If the spaceship were to turn around and return, 6 time units will have elapsed for it here, but 7 time units on earth. I.e. we are in the Twin’s Paradox/relativity of simultaneity territory here, but the important thing is that there is no path for the spaceship where you would see 7 or more time units elapsed, other than staying on Earth.
Thanks, I think we are actually in agreement here: if you account for the fact that
\gamma > 1in general, then your calculation showed thatT' = \gamma T > T, that is, the moving observer in general registers a longer durationT'between the two events than the clock at rest (T). I was just taking a shortcut when I said this should follow fromX' != 0(the-\gamma v Tin your calculation).Also, thanks for the imagery of aliens taking earth for a joy ride. This might be how we are saved when the sun dies.
Edit: I think we agree on both accounts as the twin paradox is also the only way I can rationalize the original claim (even said so in my first reply)
The fact that there is a maximum amount of relative time that can elapse between any 2 “events” does not rely on the twin paradox in any way. It doesn’t even depend on movement at all since there is gravitational time dilation and the 2 events don’t even need to be “witnessed” for time to have a particular relative duration between the events. Whichever of 2 different inertial frames of reference has the least amount of gravitational time dilation has the faster time flow rate and is closest to the maximum rate.
If a piece of matter had no gravitational time dilation at all (which admittedly is impossible) what would be the time flow rate for the object? For simplicity let’s assume it is not accelerating or even moving at all (except for expansion of universe). How would we know it is not moving? Let’s assume (call it a thought experiment) that the universe has a center and boundaries, and that the distance and direction to the center is not changing. This object would have no time dilation, the maximum time flow rate, and experience the longest possible duration of time across any arbitrary points in time.
That was exactly the point, although I think there are also other ways to prove it. Thanks for expressing this better than I.
It’s fine and to be expected that time passes differently with different levels of time dilation. You might have Reference Frame A where the time flow rate is 99.999% of the maximum and Frame B where the time flow rate is 99.998% of the maximum. The time flow rate in Frame A is faster than B, because A is closer to the maximum rate than B.
Think of “two points in time” as 2 events in time, and (for simplicity) at the same fixed point in space in your frame of reference (A) and another person’s frame of reference (B). Whichever frame is under the greater influence of gravitational time dilation, will have a slower time flow rate than the other frame. But there is also a maximum amount of time between the 2 events that neither of those 2 frames (or any other frame of reference) can exceed.
Figuring out the maximum time flow rate between any 2 events or points in time would not be a simple thing at all. You would have to calculate the entire amount of gravitational time dilation of every gravity field in range of your object, and add to that the total amount of time dilation due to acceleration of your object. But just because the total amount of time dilation is not a simple thing to calculate and add to your equations, does not mean that “zero time dilation” == “maximum time flow rate” does not exist nor that there is not a maximum amount of relative time duration between any 2 events/point in time. I assume you agree that there is a maximum amount of relative distance between any 2 objects/points in space right? There is also a maximum amount of relative duration between any 2 events/points in time. And the length contraction that shrinks distance length is related to the time dilation that shrinks time duration.
I hate to mention reddit here but this reddit comment explains it better than I can.
https://www.reddit.com/r/cosmology/comments/14dg7yf/saying_that_the_universe_is_138_billion_years_old/joq3n5i/
[It’s likely based on the proper time of a comoving observer in simplified cosmological solutions of general relativity. A comoving observer is an observer whose ‘motion’ is due to the expansion of the universe, not any motion with respect to the comoving frame. The cosmological solutions are also isotropic and homogenous, so there are no clumps of matter like black holes to influence time - the comoving proper time is the same everywhere and can be considered a maximum time.]