When Cap, Ant-Man and Tony returned to
New York in 2011,
why didn't J.A.R.V.I.S. detect a second Arc Reactor, or Tony's suit?
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Iron Man’s suits have developed and moved on a lot over the years and it has been 12 years since 2011 by the time of the five year gap in Avengers: Endgame as it is in 2023. It stands to reason that he’s developed his suits a lot in this time and moved on from the tech used then so J.A.R.V.I.S. might just not have the technology to detect Tony’s new suits.
On top of that J.A.R.V.I.S. is no longer in use in Avengers: Endgame having been used to create Vision in Avengers: Age of Ultron in 2015. Since then Tony has been using F.R.I.D.A.Y. which will undoubtedly have a different interface than J.A.R.V.I.S.. We even have Tony’s own words that J.A.R.V.I.S. has developed over the years to support this.
Tony Stark: Started out, JARVIS was just a natural language UI. Now he runs the Iron Legion. He runs more of the business than anyone besides Pepper.
Avengers: Age of Ultron
Lastly, it is worth noting that there is no indication that J.A.R.V.I.S. has the technology to detect the arc reactors or Tony’s suits, or at least isn’t actively monitoring for them. Tony normally interfaces with him rather than the other way around and seeing as he now uses F.R.I.D.A.Y. this is no longer the case so J.A.R.V.I.S. wouldn’t detect him logging in because he never would have done.
It’s also worth noting that Tony might have had the suit in “airplane mode” and so offline so any satellites or whatnot that Stark does run would never have picked him up anyway.
There is a detailed answer below, however generally Stark was breaking into his own home and in the same way that your home alarm doesn't go off when you enter, Stark almost certainly had a deactivation code to override his own defenses. He could simply ask F.R.I.D.A.Y. to deactivate J.A.R.V.I.S. or command it to ignore them. But see below for all the details:
A J.A.R.V.I.S. interface did not exist in the Mark LXXXV he was using in Endgame. J.A.R.V.I.S. was destroyed by Ultron in Age of Ultron, what remained of J.A.R.V.I.S. was reconfigured and became the Vision.
VISION: The Avengers cannot defeat Ultron. Not alone.
ROGERS: Why does your Vision sound like Jarvis?
STARK: We reconfigured Jarvis's matrix to create something new.
ROGERS: I think I've had my fill of new.
VISION: You think I'm a child of Ultron.
ROGERS: You're not?
VISION:I'm not Ultron. I am not Jarvis. I am... I am.
Vision died in Infinity War when Thanos removed his Infinity Stone.
Stark’s new AI computer system was called the Female Replacement Intelligent Digital Assistant Youth (F.R.I.D.A.Y.).
Since Age of Ultron she has been Stark's main computer interface, which was integrated into the MK-LXXXV suit.
J.A.R.V.I.S. needed to have some interface to control the earlier suits. It was integrated into each model. Without this interface J.A.R.V.I.S. may only have detected an incoming object if 2023 Stark was not in stealth mode. Since Tony Stark was sneaking up on himself, it would seem very unlikely that he would not know how to conceal himself from his own older systems. Even assuming he could not conceal himself from J.A.R.V.I.S. he would likely have chosen a different location to retrieve the stones, or sent a different Avenger on this mission.