If time is relative, how could time pass?

It doesn't really pass. That's just a figure of speech. Footballers pass. Buses pass. But there is no physical thing called time that actually passes. Instead things move. Things like light and planets and planes and people and hearts and blood and electrochemical signals in your brain. And pendulums and cogs and piezo-electric crystals in those things called clocks. That's not to say that time does not exist, as you might think from the blurb for A World without Time: The Forgotten Legacy of Gödel and Einstein . It's more like time exists like heat exists. And a hundred years will kill you just as surely as a hundred degrees C.

Now this struck me as odd. We knew for a long time that there are no absolute space

Actually, there is a kind of absolute space defined by the CMB reference frame. See this question. The CMB reference frame isn't an absolute reference frame in the strict sense, but it's the reference frame of the universe, and that's as absolute as it gets.

Then what does that means to say "present time"

It refers to where everything is, rather than to where it was or will be.

In a more general term, what does it mean for time to pass for an object?

It means how much local motion has occurred. If you send a clock on a fast out-and-back trip, less local motion occurs inside it because of the macroscopic external motion. Because the total motion is c. Because of the wave nature of matter.

Specifically, if an object perceive event A followed by event B, what does it means to say X amount of time elapsed between the 2 events?

It's how much local motion occurred. A clock doesn't literally measure the flow of time like some cosmic gas meter. It "clocks up" some kind of regular cyclical motion and shows you a cumulative result that you call the time.

And I am looking for an answer that tie the concept of time pass to actual physical phenomenon, so "length of the object's world line" won't work

Leaving gravity out of it for now, what you want is the length of the light path. A light year is a distance, and if you had a parallel-mirror light clock, you would call it a time too. But it all comes back to motion really. Einstein gave us the equations of motion, not the equations of curved spacetime. Search the Einstein digital papers for equations of motion and there's plenty of hits. Search on curved spacetime and it's no results found.

The metric tensor is an even more abstract object.

It is. It's all to do with your measurements of distance and time, typically made with light and light clocks.

How can time be relative?

Because motion is relative. Your time is your cumulative measure of local motion. So when you move relative to me, your time is relative too.

If time is relative, how could time pass?

It doesn't really pass. That's just a figure of speech. Footballers pass. Buses pass. But there is no physical thing called time that actually passes. Instead things move. Things like light and planets and planes and people and hearts and blood and electrochemical signals in your brain. And pendulums and cogs and piezo-electric crystals in those things called clocks. That's not to say that time does not exist, as you might think from the blurb for A World without Time: The Forgotten Legacy of Gödel and Einstein . It's more like time exists like heat exists. And a hundred years will kill you just as surely as a hundred degrees C.

Now this struck me as odd. We knew for a long time that there are no absolute space

Actually, there is a kind of absolute space defined by the CMB reference frame. See this question. The CMB reference frame isn't an absolute reference frame in the strict sense, but it's the reference frame of the universe, and that's as absolute as it gets.

Then what does that means to say "present time"

It refers to where everything is, rather than to where it was or will be.

In a more general term, what does it mean for time to pass for an object?

It means how much local motion has occurred. If you send a clock on a fast out-and-back trip, less local motion occurs inside it because of the macroscopic external motion. Because the total motion is c. Because of the wave nature of matter.

Specifically, if an object perceive event A followed by event B, what does it means to say X amount of time elapsed between the 2 events?

It's how much local motion occurred. A clock doesn't literally measure the flow of time like some cosmic gas meter. It "clocks up" some kind of regular cyclical motion and shows you a cumulative result that you call the time.

And I am looking for an answer that tie the concept of time pass to actual physical phenomenon, so "length of the object's world line" won't work

Leaving gravity out of it for now, what you want is the length of the light path. A light year is a distance, and if you had a parallel-mirror light clock, you would call it a time too. But it all comes back to motion really. Einstein gave us the equations of motion, not the equations of curved spacetime. Search the Einstein digital papers for equations of motion and there's plenty of hits. Search on curved spacetime and it's no results found.

The metric tensor is an even more abstract object.

It is. It's all to do with your measurements of distance and time, typically made with light and light clocks.

How can time be relative?

Because motion is relative. Your time is your cumulative measure of local motion. So when you move relative to me, your time is relative too.

If time is relative, how could time pass?

It doesn't really pass. That's just a figure of speech. Footballers pass. Buses pass. But there is no physical thing called time that actually passes. Instead things move. Things like light and planets and planes and people and hearts and blood and electrochemical signals in your brain. And pendulums and cogs and piezo-electric crystals in those things called clocks. That's not to say that time does not exist, as you might think from the blurb for A World without Time: The Forgotten Legacy of Gödel and Einstein . It's more like time exists like heat exists. And a hundred years will kill you just as surely as a hundred degrees C.

Now this struck me as odd. We knew for a long time that there are no absolute space

Actually, there is a kind of absolute space defined by the CMB reference frame. See this question. The CMB reference frame isn't an absolute reference frame in the strict sense, but it's the reference frame of the universe, and that's as absolute as it gets.

Then what does that means to say "present time"

It refers to where everything is, rather than to where it was or will be.

In a more general term, what does it mean for time to pass for an object?

It means how much local motion has occurred. If you send a clock on a fast out-and-back trip, less local motion occurs because the total motion is c, because of the wave nature of matter.

Specifically, if an object perceive event A followed by event B, what does it means to say X amount of time elapsed between the 2 events?

It's how much local motion occurred. A clock doesn't literally measure the flow of time like some cosmic gas meter. It "clocks up" some kind of regular cyclical motion and shows you a cumulative result that you call the time.

And I am looking for an answer that tie the concept of time pass to actual physical phenomenon, so "length of the object's world line" won't work

Let's leave gravity out of it. What you want is the length of the light path. A light year is a distance, and if you had a parallel-mirror light clock, you would call it a time too.

The metric tensor is an even more abstract object.

It is. It's all to do with your measurements of distance and time, typically made with light and light clocks.

How can time be relative?

Because motion is relative. Your time is your cumulative measure of local motion. So when you move relative to me, your time is relative too.

If time is relative, how could time pass?

It doesn't really pass. That's just a figure of speech. Footballers pass. Buses pass. But there is no physical thing called time that actually passes. Instead things move. Things like light and planets and planes and people and hearts and blood and electrochemical signals in your brain. And pendulums and cogs and piezo-electric crystals in those things called clocks. That's not to say that time does not exist, as you might think from the blurb for A World without Time: The Forgotten Legacy of Gödel and Einstein . It's more like time exists like heat exists. And a hundred years will kill you just as surely as a hundred degrees C.

Now this struck me as odd. We knew for a long time that there are no absolute space

Actually, there is a kind of absolute space defined by the CMB reference frame. See this question. The CMB reference frame isn't an absolute reference frame in the strict sense, but it's the reference frame of the universe, and that's as absolute as it gets.

Then what does that means to say "present time"

It refers to where everything is, rather than to where it was or will be.

In a more general term, what does it mean for time to pass for an object?

It means how much local motion has occurred. If you send a clock on a fast out-and-back trip, less local motion occurs inside it because of the macroscopic external motion. Because the total motion is c. Because of the wave nature of matter.

Specifically, if an object perceive event A followed by event B, what does it means to say X amount of time elapsed between the 2 events?

It's how much local motion occurred. A clock doesn't literally measure the flow of time like some cosmic gas meter. It "clocks up" some kind of regular cyclical motion and shows you a cumulative result that you call the time.

And I am looking for an answer that tie the concept of time pass to actual physical phenomenon, so "length of the object's world line" won't work

Leaving gravity out of it for now, what you want is the length of the light path. A light year is a distance, and if you had a parallel-mirror light clock, you would call it a time too. But it all comes back to motion really. Einstein gave us the equations of motion, not the equations of curved spacetime. Search the Einstein digital papers for equations of motion and there's plenty of hits. Search on curved spacetime and it's no results found.

The metric tensor is an even more abstract object.

It is. It's all to do with your measurements of distance and time, typically made with light and light clocks.

How can time be relative?

Because motion is relative. Your time is your cumulative measure of local motion. So when you move relative to me, your time is relative too.