this post was submitted on 24 Jul 2023
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Astronomy
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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.
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
wheret
is the time elapsed on the clock, andx = 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, sox' != 0
(using'
for the moving frame), but the intervals
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!
Using the Lorenz transformation formula, here's what I get:
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:
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 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 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)
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.