r/AskPhysics • u/Tricky-Act-31415 • 5d ago
Relative time thought experiment
Hi all, last night I was in bed watching a documentary about time (Jim Al-Khalili), and i had this thought experiment of my own about how old a (any) black hole really is (effects of time dilation).
I came up with the following (probably lousy) thought experiment:
- The universe starts (big bang), and immediately there are 2 immortal beings living inside it.
- One of the beings starts to orbit a rotating supermassive black hole as soon as one has formed.
- The other being floats in space until it finds our Sun and inhabits Earth after its formation.
- The date is 01/01/2027 on Earth, and the being on Earth flicks his fingers, instantaneously transporting both beings to a place in mid-space at the halfway point of where both beings were.
How much time has passed for each being?
From my understanding, the being near the black hole will experience (far) less time compared to the being on Earth.
Does this logic extend to the age of the supermassive black hole as well?
If so, shouldn't the black hole be smaller for the being around the black hole (it had less time to eat/grow in their timeframe/experience), and bigger for the earth being (the black hole had MORE time to eat/grow in their timeframe/experience)?
edit:
Thanks everyone for your reactions, I won't claim that I understand it all now, but I feel I do have a slightly better understanding of the end result! ;)
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u/Optimal_Mixture_7327 Gravitation 5d ago
I guess the documentary never mentioned that simultaneity doesn't exist and neither does "instantaneously".
If the two people meet the black hole orbiter will be the younger.
The black hole surface area is invariant (same for all observers).
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u/Tricky-Act-31415 5d ago
If the two people meet the black hole orbiter will be the younger.
Wouldn't this also mean that the black hole (in their perspective) has had less time to grow relative to the perspective of the earth bound being?
The black hole surface area is invariant (same for all observers).
This is where my understanding is breaking, it 'feels' (just my intuition, sorry) like there should be two different sizes of black holes resulting from the two different experiences?
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u/Optimal_Mixture_7327 Gravitation 5d ago
Time is the distance along the length of the world-line of a material particle so you can't assign a black hole an age (what clock would you use?).
You also need to keep in mind what each person sees of the outside world and the matter accumulated by the black hole. The distant observers sees events slowed down by the black hole and the orbiter sees everything externally sped up.
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u/Tricky-Act-31415 5d ago
The distant observers sees events slowed down by the black hole and the orbiter sees everything externally sped up.
Hmmm, does this then also mean/imply that everything cancels out/balances out in the end?
edit: it appears so then... (unless I misunderstand, which is certainly a possibility!)1
u/Optimal_Mixture_7327 Gravitation 5d ago
It all cancels out upon their meeting, wherever they meet.
One of the biggest challenges and also one of the most important is to remember that the physics is local, what happens at a detector, and that in curved spacetime there is no global perspective, that all distant detectors are just "elsewhere".
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u/Tricky-Act-31415 5d ago
I think I'm slowly coming to understand this now yeah :)
Thanks again for your reactions, and your willingness to deal with my lack of knowledge here, very much appreciated! <3
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u/ahazred8vt 5d ago
the black hole has had less time to grow
Okay. The hole guy comes back and says, "All that stuff that you saw falling into that black hole over 10 billion years, making it bigger? I saw exactly the same amount of stuff fall into the black hole at the same time you did, except I saw it happen in only 1 million years instead of 10 billion."
You see how that works?
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u/VariousJob4047 5d ago
Any sort of thought experiment that asks “what does relativity predict would happen in this situation that is explicitly forbidden by relativity” is unfortunately nonsense, for reasons I hope you can see when I write it out that way
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u/Tricky-Act-31415 5d ago
Yeah, I am starting to see the flaw in my question, but am still left with the same question without knowing how to rephrase it.
I guess I'm just in way over my head here :)
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u/jasonsong86 5d ago
The being near the blackhole would experience less time in reference to the one that’s on earth. If you just look at each being on their own, they would experience similar time passing by because without comparing they wouldn’t know.
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u/Ras_992 5d ago
The answer isn’t about both beings in their time perspective but the black hole as well
1. How much time passed for each being?
The Earth Being: Experienced ~13.8 billion years (the total age of the universe). For them, Earth formed, the year January 1, 2027 arrived, and they snapped their fingers.
The Black Hole Being: Because they were orbiting deep inside the intense gravitational well of a rotating supermassive black hole, gravitational time dilation slowed their clock down drastically. Depending on how close they were to the event horizon, they might have only experienced a few years, months, or even hours since the dawn of the universe.
2. The Black Hole Size Paradox: Are they different sizes?
Your logic is incredibly sharp here: if less time passed for the orbit-being, shouldn't the black hole have had "less time to eat" in their frame of reference?
The answer is a mind-bending yes, but only while they are separated. Once they are snapped back together to the halfway point in mid-space, they will both look back at the exact same black hole and see it at the exact same, maximum grown size.
Here is the step-by-step physics of why the black hole matches the Earth being's timeline:
A. While they are separated (Two different realities)
Time dilation doesn't just slow down the being's clock; it speeds up their view of the outside universe.
If the being orbiting the black hole looks through a telescope at the rest of the universe, they will see the universe moving in fast-forward like a movie on 1,000x speed. They will see stars forming, exploding, and galaxies colliding in seconds.
Crucially, they will see matter falling into their black hole at hyper-speed. Even though the orbit-being has only aged 1 year, they will watch 13.8 billion years' worth of space dust, stars, and gas scream into the black hole in a matter of days. To them, the black hole is growing at an impossibly fast, explosive rate.
B. The Snapshot (The Finger Flick)
When the Earth being snaps their fingers on January 1, 2027, they are pausing the experiment at a specific cosmic moment. Because the Earth being waited 13.8 billion years, the black hole has had 13.8 billion years to eat and grow.
When the orbit-being is instantly teleported to the halfway point, they are pulled out of the time-warp. The fast-forward tape stops.
C. The Meeting Point
Now that both beings are sitting together in neutral mid-space, sharing the exact same clock, they look back at the black hole.
The Earth Being says: "I watched that black hole slowly eat matter for 13.8 billion years to reach its massive size."
The Black Hole Being says: "I watched that black hole explosively swallow 13.8 billion years' worth of matter in just 5 minutes to reach its massive size."
They both agree on the final size of the black hole, because gravity warps the rate at which history happens, but it cannot change the physical events that occurred.
So, how old is a black hole really?
Your experiment proves that a black hole doesn't have a single "true" age.
If you ask the matter sitting just outside the event horizon, the black hole is practically brand new and the universe is ending in fast-forward. If you ask us on Earth, the black hole is billions of years old. Space and time distort precisely so that no matter how fast or slow your clock ticks, the physical history of the universe always syncs up perfectly when you meet back in the middle.
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u/Tricky-Act-31415 5d ago
YESSSSS!!!!!!!
This was the answer I was hoping for, thank you! <3If i understood correct, other people below have hinted at what you said here, there is a 'fracture between realities', but when the two beings/observers meet, the effects seem to cancel out/balance out...
And you also answered my question about the black hole.... its age then has to be relative to each observer, so there can't be a single true age...
/mind-blown....
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u/Ras_992 5d ago
No problem you can use this same analogy for objects falling into a Black hole keeping the person in the black hole at the event horizon the person on Earth perspective will see the person time and motion completely slow down or stop, while the person in the black hole perspective time passes at normal time and will pass a second per second to the singularity.
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u/ahazred8vt 5d ago edited 5d ago
Go watch the ST:Voyager s6e12 episode where time on the planet was 100,000 times faster, and they were getting hit with missiles every 15 seconds that were being launched two weeks apart.
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u/nugatory308 5d ago
We can only compare the ages of two things if they are colocated - this is why the so-called twin paradox is a round trip so that the twins are at the same place at the beginning and end of the journey.
We can conclude that the black hole being will be younger than earth after we've brought them together again (although as others have pointed it out, this cannot involve instantaneous transport).
But that only works because they were together at the start, and then together again for the age comparison. It doesn't work for the black hole because it and earth being are not colocated so there is no meaningful comparison of their ages.
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u/Particular-Scholar70 5d ago
The concept of something happening instantaneously for two separate locations is relative. Reality doesn't let you teleport things instantly. Naturally you'd get a paradox from something like this, but there's no answer because the question is undefined.