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They'd have to spend a good deal of that trip accelerating and decelerating. During the deceleration phase, giant engines are probably pointed at Earth, and those will throw off heat or mass or both. We should have a few months lead time.
That assumes they are using our current technology for space travel.
We can't just imagine some additional physics into being. Newton's laws and relativity were conceived as explanations for observed phenomena. We have no observed phenomena that allow us to create, for example, reactionless engines, or allow us to violate thermodynamics.
So my assumption is that our understanding of physics is relatively complete, and there are no hitherto unknown forces to exploit for travel purposes. Thus any interstellar approach must adhere to these basic principles.
Newton's laws have withstood every attempt to be worked around. Relativity didn't throw Newton's laws out -- it just special cases them (Newton's laws are a subset of relativistic laws where speeds are low).
Basic principles:
(1) Thermodynamics: Engines require energy to produce inertia/momentum changes, and using that energy produces heat. (2) Newton: To change your velocity, you need to apply a force, and that requires something to push against. (3) Mechanics: To slow down requires time, even at the highest levels of deceleration (and faster deceleration makes the first two more visible).
There are potentially some stealth approaches: (1) Using a heat pump to create a cold shield on the front facing side, and radiating your heat behind it. (Circumvented if we have any sort of probes behind it looking back towards us.) (2) Using directed energy (photons or similar) as your reaction mass and pointing it at an off-axis angle (at a loss of efficiency, and circumvented by detecting secondary illumination or by probes that are in line with that light). (3) But these still require stopping time. And the total energy to stop is literally astronomical.
Perspective. To decelerate a single kg that is approaching earth at .99c, the amount energy needed is approximately equal to converting 6x that amount of mass to pure energy. Basically to decelerate 1kg, you'd need to bring 3kg of matter and 3kg of antimatter and have them perfectly annihilate in such a way that 100% of that energy were put into deceleration. This is roughly equal to 6x the size of the Tsar Bomba explosion (largest nuke ever detonated). If you have a spaceship of any realistic size approaching earth at .99c, it's putting out a shittonne (technical term) of energy to stop.
Seriously, any alien looking to destroy us wouldn't bother with slowing them down. They'd just ram those 1kg objects directly into earth at .99c and obliviate us without ever being detected.
I share your pessimism but 95% of the mass of the universe is still unaccounted for. GR and QM aren't compatible. So there is still some wiggle room for the unknown.
Hossenfelder is a particulary pragmatic physicist and even she sees gaps that could make it possible.
https://youtu.be/9-jIplX6Wjw?si=jQ5l2IsZM0l0Kk1z
Every time Webb takes a picture it contraddicts everything we now, so i kind of disagree
What with the 99%?