ask a physicist

[Landifarne]

Uh, yeah, I fully understand the magnitude of 10^120. That approximates the number of atoms in all of the galaxies in about 10^45 visible universes. One visible universe has about (~10^24 atoms/kg of matter)(10^30 kg of matter/star)(10^11stars/galaxy)(10^10galaxies in the visible universe) = 10^75 atoms in its galaxies. I can't comment on all the dark matter, but one of the pros can easily rectify that.

Despite that, not a single "Similar Earth" would have followed the same "path of Earth up to 3 weeks prior." To suggest that one would have done that is ludicrous, as the entropic variation in the positional states of the atoms of that single "Similar Earth" exceeds the 10^45 factor, alone.

 

[freyar]

Uh, yeah, I fully understand the magnitude of 10^120. That approximates the number of atoms in all of the galaxies in about 10^45 visible universes. One visible universe has about (~10^24 atoms/kg of matter)(10^30 kg of matter/star)(10^11stars/galaxy)(10^10galaxies in the visible universe) = 10^75 atoms in its galaxies. I can't comment on all the dark matter, but one of the pros can easily rectify that.

Despite that, not a single "Similar Earth" would have followed the same "path of Earth up to 3 weeks prior." To suggest that one would have done that is ludicrous, as the entropic variation in the positional states of the atoms of that single "Similar Earth" exceeds the 10^45 factor, alone.

I think I missed where the 10^120 came in. That's the factor between the cosmological constant and the Planck scale (roughly), but the size of the universe isn't related to that really. When people talk about duplicate earths, etc, they're generally talking about truly infinite universes.

 

[Umbran]

Uh, yeah, I fully understand the magnitude of 10^120.

As an aside, that's a bold claim. Generally speaking, when a number gets that large, humans *don't* really understand the magnitude. They are just numbers unless you make a lot of effort to set scales.

 

[AbdulAlhazred]

The least controversial category of multiverse in Tegmark's scheme is Level I, which describes distant spacetime events "in our own universe", but suggests that statistical analysis exploiting the anthropic principle provides an opportunity to test multiverse theories in some cases. If space is infinite, or sufficiently large and uniform, identical instances of the history of Earth's entire Hubble volume occur every so often, simply by chance. Tegmark calculated our nearest so-called doppelgänger, is 10^10^115 meters away from us (a double exponential function larger than a googolplex). In principle, it would be impossible to scientifically verify an identical Hubble volume. However, it does follow as a fairly straightforward consequence from otherwise unrelated scientific observations and theories.

https://en.wikipedia.org/wiki/Multiverse#Tegmark.27s_classification

There is this... and the original reference http://arxiv.org/abs/astro-ph/0302131, which references 10^10^29 meters.

Now, we don't know that the Universe spans 10^10^29th (let alone 10^10^115th) meters, but the point is even if it doesn't there could be Hubble Volumes almost indistinguishable from ours MUCH closer than that, etc.

My only point was that there are interestingly many ways to think about things like 'time travel'.

 

[Umbran]

My only point was that there are interestingly many ways to think about things like 'time travel'.

Well, time travel is still implicit. You are talking about reaching places outside the observable universe, which means outside Earth's light cone. That implies FTL travel, and thus time travel becomes possible.

 

[AbdulAlhazred]

Well, time travel is still implicit. You are talking about reaching places outside the observable universe, which means outside Earth's light cone. That implies FTL travel, and thus time travel becomes possible.

Well, that's a good question. What's the 'distance' to a point in space-time where we absolutely cannot measure? How 'fast' do you have to go to get there? Is it possible that even though FTL/time travel to areas which ARE causally connected to us is impossible (as the fact that it causes paradoxes and violations of conservation laws suggests), but travel to areas OUTSIDE that region might be technically 'legal'.

Not that I don't understand what you're getting at, nor that I necessarily disagree with you. Still, in an RPG you could still at least use it as a fig leaf

 

[freyar]

Well, that's a good question. What's the 'distance' to a point in space-time where we absolutely cannot measure? How 'fast' do you have to go to get there? Is it possible that even though FTL/time travel to areas which ARE causally connected to us is impossible (as the fact that it causes paradoxes and violations of conservation laws suggests), but travel to areas OUTSIDE that region might be technically 'legal'.

Not that I don't understand what you're getting at, nor that I necessarily disagree with you. Still, in an RPG you could still at least use it as a fig leaf

FTL travel by definition takes you from one spacetime point to another that's out of causal contact with the first one. That is, it takes you out of the future light cone of the first point.

 

[Umbran]

Well, that's a good question. What's the 'distance' to a point in space-time where we absolutely cannot measure?

I think you are conflating practical human limitations with physical reality. The fact that we cannot physically measure it does not imply that somehow the meaning of distance changes.

Consider, for example, that you can measure to the edge of the visible universe. If you go just a tad beyond that, you can then measure to the end of your new visible universe, and *add*. Lather, rinse, repeat, and you can stepwise measure any distance.

Is it possible that even though FTL/time travel to areas which ARE causally connected to us is impossible

As freyar mentioned - FTL travel is, by definition, travel to a place that is not causally connected with your origin. Causal connection is a thing of spacetime, not just space. The Sun is about 8 light minutes away. If I get to the Sun in six minutes, I'm at a point that is not causally connected with the point on Earth from which I left. And "point" in this case is "point in space *and* time".

 

[AbdulAlhazred]

I think you are conflating practical human limitations with physical reality. The fact that we cannot physically measure it does not imply that somehow the meaning of distance changes.

Consider, for example, that you can measure to the edge of the visible universe. If you go just a tad beyond that, you can then measure to the end of your new visible universe, and *add*. Lather, rinse, repeat, and you can stepwise measure any distance.

Except you CANNOT DO THAT, not even in principle. I think this reasoning is incorrect because its not 'human limitations' we're talking about here. It is limitations built into the rules by which the Universe fundamentally operates. Rules that operate at the same level as these various other rules like causality and thermodynamics. I'm not saying "your wrong", but I'm saying that there's a fundamental difference between say not being able to measure the distance to the Moon because we don't know how and not being able to measure the distance to a point outside our light cone because its fundamentally disallowed.

As freyar mentioned - FTL travel is, by definition, travel to a place that is not causally connected with your origin. Causal connection is a thing of spacetime, not just space. The Sun is about 8 light minutes away. If I get to the Sun in six minutes, I'm at a point that is not causally connected with the point on Earth from which I left. And "point" in this case is "point in space *and* time".

Yes, I understand this. There are however regions of space, presumably, which are 'causally disconnected' from us. They are FOREVER outside our light cone. If I travelled instantly to the Sun then in 8 minutes light from that location would arrive and there would be different inertial frames of reference in which causality, conservation of angular momentum, etc would be violated. If I travel instantly a googleplex lightyears from here, that will NEVER HAPPEN. So is such travel disallowed for the same reasons that travel 8 light minutes from here seems to be? I question that! Again, its a question, not a statement of some fact that I think I've uncovered or some crackpot theory that I insist must be true. It is really at this point more of a philosophical question almost than a science question, until some unforeseen time when we invent a way to do it.

Anyway, I feel like I'm moving the thread rather far from where it was intended to be, I don't want to derail it.

 

[Umbran]

Except you CANNOT DO THAT, not even in principle.

In the normal universe, yes.

But you're positing a universe where going there is possible. That possibility throws the principle out the window! We cannot measure the distance only because FTL travel is not possible - as soon as you allow FTL to the spacial location, then the measurement becomes possible in principle.

Which is to say, you cannot stand by the principle, and break the principle, in the same breath and remain consistent.

It is limitations built into the rules by which the Universe fundamentally operates.

Which the stipulated travel breaks.

There are however regions of space, presumably, which are 'causally disconnected' from us. They are FOREVER outside our light cone.

I think that, given the assumptions of Special and General Relativity (in which context we are talking about light cones), that the difference isn't relevant. So long as the space between is continuous, smooth, and the same rules of physics apply in all of it, then "forever outside" and "temporarily outside" are not fundamentally different. If those assumptions do not hold, then we have to hld the whole idea of the light cone as suspect.

Specifically, I believe you can construct the following scenario: Point A and Z in space are so far apart, that they never fall into each other's future light cone. There is a point M, between them, that is, at the time of your travel, is not in the light cone of either A or Z, but will eventually lie in the light cones of both. A stepping stone, so to speak, that allows the piecewise measurement. I think that you can always generate a string of such stepping stones, so long as the distance between A and Z is not *actually* infinite.