Four Indistinguishable Phenomena?

[Ontophobe]

It seems to me, and so I'm really just checking to see if I understand it all correctly, that there are four phenomena in nature that are indistinguishable from one another: (1) crossing beyond an observer's cosmic horizon, (2) crossing the event horizon of a black hole, (3) accelerating toward and nearly reaching the speed of light, and (4) approaching and nearly reaching zero degrees Kelvin. In all four cases, an observer in an inertial frame of reference would see you redshift into invisibility ( I say "you" as if "you're" the one accelerating beyond the observer's cosmic horizon, or the black hole's event horizon, etc). I'm just starting to wrap my head around these concepts, so I'm just checking to see if I understand these four phenomena correctly by (a) venturing a hypothesis; i.e., these phenomena are as indistinguishable from one another as gravity is from acceleration, and I'm (b) testing that hypothesis; i.e., I'm asking y'all if it's true.

 

[Orodruin]

They are not indistinguishable (as in physically equivalent). Although 1-3 have certain similarities, 4 has nothing to do with the others.

 

[PeterDonis]

these phenomena are as indistinguishable from one another as gravity is from acceleration

Gravity is not indistinguishable from acceleration.

For your phenomena, none of them are indistinguishable from the others. (1), (2), and (3) do happen to have one common feature, which you describe as "redshifting into invisibility". (On a sufficiently generous interpretation of "redshifting", one could argue that (4) has that property as well; but the interpretation has to be generous.) However, having one common feature does not make them indistinguishable; that would imply that they had all possible features in common, which they don't.

 

[Orodruin]

On a sufficiently generous interpretation of "redshifting", one could argue that (4) has that property as well; but the interpretation has to be generous.

Average wavelength of a black body spectrum? That is generous ...

 

[PAllen]

The big difference is that for 1-3, small lab detects nothing unusual, while for 4, the lab scientists need very good coats.

 

[Ontophobe]

Since the "redshift" of a black body approaching absolute zero isn't caused by a Doppler effect, I see why it's a stretch to call it a "redshift."