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I was thinking of a situation with humans finding a solar system, in which entropy decreases over time instead of increasing over time. In this solar system heat would flow from a cooler planet to the hotter star. Shattered rocks sometimes spontaneously unshatter before rising back to the top of a cliff. Sand will sometimes spontaneously fill a crater before a meteor rises up and goes into interplanetary space.

Could humans colonize some of the planets of this solar system?

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    $\begingroup$ Time flowing backwards can be thought of as playing a film backwards. Humans would still remember the past, except the past is the future, and humans would not be the wiser. So if we're assuming time flows backwards, you should probably specify what doesn't flow backwards.. Perhaps beings from a place where time flows normally would be out of place in a solar system where time flows backwards? $\endgroup$ – Neil Jun 1 '17 at 6:24
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    $\begingroup$ Can you elaborate on "time flows backwards"? What would this look like to an outside observer? If I enter this system or land on one of the planets, does time flow backwards for me? $\endgroup$ – frodoskywalker Jun 1 '17 at 6:30
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    $\begingroup$ I agree you are not specifying the concept well enough for an answer. See this Q, and read the novel The Arrows of Time for a detailed description of a visit! $\endgroup$ – JDługosz Jun 1 '17 at 8:08
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    $\begingroup$ Is this system enclosed in some way? If not, how do these aberrations not affect the rest of the universe? If it is, how do you detect it,much less enter? $\endgroup$ – nzaman Jun 1 '17 at 9:47
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    $\begingroup$ @AndersGustafson you should edit the question to address concerns raised in the comments. Don't (just) answer with another comment! $\endgroup$ – JDługosz Jun 1 '17 at 10:42
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No. It would be too dangerous. The danger doesn't arise from coping with dual causality situations on any of the planets. Matter existing backwards in time is antimatter.

As everybody knows when matter and antimatter meet a lot of gamma radiation happens very quickly. This will be fatal.

Potential colonists will soon be dispersed in the form of rapidly expanding plasma accompanied by large amounts of gamma radiation. This means colonization will be impossible.

There is a good chance no-one will realize the solar system is a place where time flows backwards because all the matter in this solar system will be antimatter. It will be classified as an antimatter solar system.

ADDENDUM:

The relationship between antimatter and time reversal is established by a derivation of the CPT Theorem. (Vide the Wikipedia entry linked above.)

This defines a CPT transformation if we adopt the Feynman-Stueckelberg interpretation of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight analytic continuation, which is well-defined only under the following assumptions:

The theory is Lorentz invariant;
The vacuum is Lorentz invariant;
The energy is bounded below.

In words, matter moving backwards in time will be antimatter. Therefore, if there is a solar system where time flows backwards its matter will be antimatter.

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    $\begingroup$ "Matter existing backwards in time is antimatter." source? $\endgroup$ – Miguel Bartelsman Jun 1 '17 at 7:13
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    $\begingroup$ @MiguelBartelsman Dear me! What is physics education coming to these days? It's only time symmetry. OK. I'll mooch off and find a source. $\endgroup$ – a4android Jun 1 '17 at 7:17
  • $\begingroup$ @MiguelBartelsman I've done my mooching and a source has been provided. Richard Feynman came up with this concept back in the 1940s. Really a nice idea. $\endgroup$ – a4android Jun 1 '17 at 7:28
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    $\begingroup$ We don't actually know that anti-matter is time-reversed regular matter, but its pretty well accepted that the two are pretty much indistinguishable. "Feynman Diagrams were constructed using Ernst Stueckelberg's interpretation of the positron as if it were an electron moving backward in time. Thus, antiparticles are represented as moving backward along the time axis in Feynman diagrams." Doess't mean its true, but it works. $\endgroup$ – Draco18s Jun 1 '17 at 15:23
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    $\begingroup$ @Draco18s Your point was a good one. So I appreciated it. I included the three Stueckelberg assumptions in my quote from Wikipedia to indicate science isn't absolute truth. It may be better than other kinds of knowledge, but that isn't everything. Models and reality in science is always a vexed issue. I thought it was appropriate for backwards-time solar system. $\endgroup$ – a4android Jun 2 '17 at 4:27
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Above answers provide scientific explanation to why it's not possible. Regular sc-fi explanations would also yield the same answer but for a different reason.

In that solar system the colonization took place already. In that solar system YOU are the BttF Butch, you are the Connor (from Terminator 2&3), you are Sarah Connor (from Terminator). Depending on your chosen time travel rules. Those people travel back in time while you are going forward.

So for example, you can't colonize the system now because of the antimatter. But in 500 years they figured out how to overcome this and send a ship. And that ship is the one that started the world you've seen 500 years earlier.

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    $\begingroup$ Huh? Is that an answer? $\endgroup$ – JDługosz Jun 1 '17 at 8:03
  • $\begingroup$ @JDługosz You have to use your Captain Marvel decoder ring to unearth all the pop culture references to let the sunshine in. $\endgroup$ – a4android Jun 2 '17 at 4:08

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