The distance to the nearest identical Hubble volume in light years?

[Vanadium 50]

Is there any science to this? Or are we arguing philosophy? Is a world identical to ours except that you asked for a cheesebrurger last week "close enough"? This seems more like a topic for late-night undergraduate musings than something subject to scientific inquiry.

 

[PeterDonis]

Can you address the part about quantum repeats? Is the wavefunction of particle positions supposed to be infinite, and, if so, even in an infinite universe, can every possibility truly repeat in that case?

Remember we are talking about repeats of our observable universe, which is finite in size. Any "wave functions" we use in a quantum model would be restricted to that finite volume. And in that finite volume there are only a finite number of possible quantum states. That is the basis for the "repeat" claim.

it is true that odds are you'd probably encounter countless numbers of different Earths with alternate histories on the way to finding the identical Earth.

I don't know that anyone has actually calculated this, but it seems plausible.

Well, to be an identical Earth, it would have to send an explorer out searching for an identical Earth in the same way you went out searching. Does that mean you'd cross paths?

No, because the identical explorer to you from "repeat Earth" would be going away from you. You are setting off from Earth towards repeat Earth. The repeat Earth explorer would be setting off from repeat Earth towards repeat repeat Earth, in the opposite direction from Earth.

And does that mean the path to and from each Earth would be mirror images?

No, because that would mean the explorer was not from repeat Earth, but from a different almost-copy of Earth where he set out in the opposite direction, towards Earth instead of towards repeat repeat Earth.

 

[syfry]

This seems more like a topic for late-night undergraduate musings than something subject to scientific inquiry.

Was thinking how this sounds like a vsauce episode

 

[syfry]

Doesn't a particle have a chance to be found at any distance toward infinity? So if the universe is infinite, and no matter how infinitely large, any particle on a repeat Earth can instead be found at the boundaries of infinity, so that a certain exact match could be mathematically impossible. Perhaps.

 

[Jaime Rudas]

any particle on a repeat Earth can instead be found at the boundaries of infinity

The boundaries of infinity is an oxymoron.

 

[syfry]

The boundaries of infinity is an oxymoron.

Of course, but all I'm saying is that whatever size area we choose as possible for Earth to repeat, any of its particles can appear beyond that area.

So the problem with any absolute replication down to the particle layer is that any of the components can be found outside of the replication, to the farthest reaches of infinity.

If I understand correctly the probability of where to find any particle.

 

[PeroK]

No, because that would mean the explorer was not from repeat Earth, but from a different almost-copy of Earth where he set out in the opposite direction, towards Earth instead of towards repeat repeat Earth.

This is where, IMO, the repeat Earth theory loses touch with the pure mathematics on which it relies. All you can do is find a planet that is identical to Earth in every respect at a given point in time. But, such a planet will immediately (almost certainly) diverge from Earth as microscopic interactions produce different outcomes from the same initial conditions. And, you don't know which repeat Earth will still be a repeat Earth one second later.

To put in mathematical terms. The following statement is false:$$\exists \ P: \forall t: \Psi_P(t) = \Psi_E(t)$$Where $E$ is planet Earth and $P$ is some planet. But, the following statement could be true:$$\forall t, \exists \ P: \Psi_P(t) = \Psi_E(t)$$Or, to put it another way, there is no time-independent identical Earth:$$\forall P, \exists t: \Psi_P(t) \ne \Psi_E(t)$$In general, if we want to invoke the paradoxes of infinite sequence, we cannot pick and choose the subtlties of infinite sequences that suit some narrative.

To go back to the original calculation. What that says is that for a given $t$ we would expect to find an identical Earth (let's stick to Earth rather than an entire Hubble volume!) within a distance $d$. But, the probability that the "identical" Earth is still identical one second later is practically zero. Instead, if you believe the theory, another planet within that distance that was previously nearly identical to Earth is now identical to Earth. The key point is that the planets identified as identical Earths are changing all the time.

That said, the whole thing is fantasy rather than real physics. All of this is completely untestable.

 

[KobiashiBooBoo]

Maybe it's easier to understand if one stated there are an infinite amount of Earths exactly like our own at all times of history and evolution. (In which case it is conjecture and risks the thread being closed.)

 

[PeterDonis]

All you can do is find a planet that is identical to Earth in every respect at a given point in time.

You will find that, yes, but in a spatially infinite universe, if you look further, you will find, not just an Earth, but an entire observable universe, that matches ours through its entire history. (I'm not clear on whether Tegmark also claims that the entire future will be the same.)

 

[PeterDonis]

All of this is completely untestable.

Agreed.

 

[PeterDonis]

Doesn't a particle have a chance to be found at any distance toward infinity?

No. Here you are using a very simple concept of a wave function in non-relativistic QM. But the cosmological models being used in the argument discussed in this thread are based on relativistic quantum field theory, where the statement you are making can't even be formulated as you state it. Non-relativistic QM doesn't even cover this domain. The key statement in QFT for the argument is that, within a finite volume, there are only a finite number of possible states. AFAIK that statement is valid in QFT.

 

[Jaime Rudas]

You will find that, yes, but in a spatially infinite universe, if you look further, you will find, not just an Earth, but an entire observable universe, that matches ours through its entire history.

And this would be valid for any given moment in the future.

 

[KobiashiBooBoo]

And this would be valid for any given moment in the future.

Everything could be exactly the same except a blade of grass is missing from the Browns/Steelers game (non-scientific, I know, sorry)

 

[256bits]

The Wiki gives a reference to the Tegmark estimate paper,

1. Tegmark, Max (2003). "Parallel Universes". Scientific American. 288 (5): 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329.

from the PDF, Tegmark's words are,

Just an estimate using the Pauli exclusion principle.
Low balled, and not repeatable, ie one doesn't find another 'earth ' every set of this distance - could be less, could be more depending again upon chance. [ ie there could be an exact earth in the sphere just outside our own - whose to know ]

 

[Quarker]

Just as a hypothetical, in order to be charge neutral, any universe that contains both matter and antimatter would have to be linked to an identical, antimatter version of itself, in which case an identical but oppositely charged you exists on the other side of what ever it is that separates the two universes.

 

[weirdoguy]

any universe that contains both matter and antimatter would have to be linked to an identical, antimatter version of itself, in which case an identical but oppositely charged you exists on the other side of what ever it is that separates the two universes.

And where did you get that from?

 

[Vanadium 50]

nd where did you get that from?

Wasn't that an episode of Star Treek?

 

[Quarker]

Wasn't that an episode of Star Treek?

No, those two universes were different for dramatic purposes. Charge neutral universes would have to be identical in every way.

 

[Quarker]

No, those two universes were different for dramatic purposes. Charge neutral universes would have to be identical in every way.

Except charge, of course.