If time is relative, how could time pass?

Question

EDIT: I appreciate people who answered below. But it does not answer the question, so I will clarify my questions:

-It seems like everyone is saying that time passing is actualized by physical process happening. But wouldn't that mean that photon can never change, as no physical process could happen to it? Then how could photon be absorbed, and whatever other thing that could happen to it.

-We start with this spacetime. At the present moment, I am at a point in spacetime. Which other part of this spacetime constitute "universe at present time"? And if I perceive something happen (say an explosion on a star), what allow me to determine whether it happens at the present, or X amount of time ago?

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Original question: I was just starting to have a look of general relativity, which have an assumption that basically say that time itself is relative. As I was reading this article: What Do You Mean, The Universe Is Flat? (Part I)

I saw the sentences "So here is one natural notion of the universe: all of three-dimensional space at the present time. Call it the nowverse." Now this strucks me as odd. We knew for a long time that there are no absolute space: it makes no sense to say that an object stay at the "same place". Then what does that means to say "present time". In a more general term, what does it mean for time to pass for an object? 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? Since there are no global time coordinate, we can't just take the time coordinates of these 2 events and find the differences. 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, since the metric tensor is an even more abstract object.

(the "How can time be relative?" question is about discrepancy between intuition and physics, while this question already assume the physics is correct; in particular, that question does not explain how can people say "the universe at present time")

Answer 1

Time might be relative, aging (time passing) is absolute.

Run around, jump into a rocket, speed up and circle a few times around a black hole, and do whatever else you fancy, all observers will agree how much you have aged in the process. Here, for 'aging' you can read 'proper time': the time that has passed according to your wristwatch.

Answer 2

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.

Answer 3

To add to Johannes's succinct answer: there are two other things about time that we believe to be absolute:

1. The topology of any web of causal links between events in space time and
2. The direction in time of causal links.

If we postulate that a cause-effect relationship can only propagate at a maximum speed of $c$, then if a cause comes before an effect in one reference frame, it comes before the effect in all reference frames. Geometrically, a vector $\vec{AB}$ drawn from an event $A$ such the head $B$ is inside the forward (or backward) pointing light cone with apex at $A$ is transformed by any orthochronous[1] Lorentz transformation such that the image of $B$ is still confined to the same light cone.

Indeed this property of the Lorentz transformation is what leads us to postulate that $c$ is a speed limit. If we heed this speed limit, then our everyday notion of causality - that causes always come before effects - is unchanged. This is one of the most remarkable things about relativity: even though proper times of different paths through spacetime between points can be shrunken or stretched a bit in twin paradoxes and so forth, most of our everyday intuitions about time - namely those to do with causality - are altogether unchanged by the notion of relative time that relativity describes.

[1]. An "orthochronous" Lorentz transformation is one that is the composition of any finite number of finite rapidity boosts (transformations between inertial frames of reference) and rotations.