I Is the Universe a 3-sphere or a 4-sphere?

[Nugatory]

Does light "climbing" "out" of a gravitational potential experience redshift?

It depends on the observer. If two observers are moving relative to one another as they pass through the point where the redshift is being measured, they will in general measure different redshifts, or even blue shifts.

The gravitational redshift you’ll read about in popular treatments can be said to be caused by light “climbing out” of a potential well, but this is a special case: limited to spacetimes in which the notion of potential is meaningful; and then comparing the redshift measured by observers at different heights in that well and using a particular definition of “at rest” relative to one another. The intuition you get from considering this special case is of very little value in understanding cosmological expansion.

 

[metastable]

I'd expect to see redshift from the pre-agreed transmission frequency if the nearby sender was moving directly away from me at the transmission time, assuming I've also detected no accelerations or fictitious forces since the transmission time.

What if I detect redshift from the pre-agreed transmission frequency and both myself and the sender have escape velocity along the same vector directly away from the center of nearby supermassive black hole, and I am "above" the sender with respect to the black hole, neither of us detect accelerations or fictitious forces, can I be certain my distance from the sender has increased since transmission time?

 

[PeterDonis]

Could such a setup lead to observations in our "universe portion" of "increasing" measured redshift over time observed in all directions statistically correlated with distance from our position & according to known laws?

No. We would not observe redshifts to be isotropic (the same in all directions, on average) in the setup you describe.

 

[PeterDonis]

What if I detect redshift from the pre-agreed transmission frequency and both myself and the sender have escape velocity along the same vector directly away from the center of nearby supermassive black hole, and I am "above" the sender with respect to the black hole, neither of us detect accelerations or fictitious forces, can I be certain my distance from the sender has increased since transmission time?

No. In fact, the way you have specified the scenario--you and the sender both have escape velocity, but you are above the sender--you can be certain of the opposite, that your distance from the sender will decrease with time, without even looking at the frequency of the signals you're receiving.

 

[metastable]

*sorry I meant "at least" escape velocity... both have at least escape velocity.

 

[metastable]

No.

Ok suppose the black hole has an event horizon radius equal to the present observable universe radius. The receiver has at least escape velocity directly away from the center of the singularity at a distance from the center of 2 event horizon radii. The sender is 1 billion light years directly “above” the receiver with respect to the singularity. Assume in the scenario “spatial expansion” = 0 and at transmission time the sender is approaching the receiver. At the same time as the pulse is received, the sender is also approaching the receiver. There are no other gravitational bodies than the singularity and the 2 craft, and neither craft detects acceleration or fictitious forces. Can the receiver detect redshift from a pre-agreed frequency?

 

[PeterDonis]

Can the receiver detect redshift from a pre-agreed frequency?

It depends on how fast the sender is approaching the receiver when the pulse is sent, as compared to the difference in height between them.

 

[metastable]

It depends on how fast the sender is approaching the receiver when the pulse is sent, as compared to the difference in height between them.

So if it’s “possible” then to detect redshift from a distant approaching object when both the observer and object have at least escape velocity from a large singularity which is outside their observable universe, and the equations describing this redshift are already known, why is “spatial expansion” via an “unknown” mechanism considered a “more likely” explanation for the observation of red shifts which vary in proportion to distance from an observer?

 

[PeterDonis]

why is “spatial expansion” via an “unknown” mechanism considered a “more likely” explanation

First, the mechanism is not unknown; it's just inertia from the Big Bang.

Second, as has already been pointed out, redshifts in your scenario would not be isotropic. But we observe them to be isotropic.

 

[Ibix]

why is “spatial expansion” via an “unknown” mechanism considered a “more likely” explanation for the observation of red shifts which vary in proportion to distance from an observer?

All versions of your scenario imply an overall "upwards" and a "downwards" direction to the observable universe, with different redshift-versus-distance profiles if you look "up" or "down". We don't see that - once you correct for our velocity compared to a comoving observer the redshift profiles are the same in all directions - isotropic, as PeterDonis says.

 

[metastable]

Second, as has already been pointed out, redshifts in your scenario would not be isotropic. But we observe them to be isotropic.

^If a formation of transmitter spaceships all at rest with respect to the receiver (also comoving, assume spatial expansion = 0) at transmission time were all traveling close enough to light speed directly away from the singularity in the scenario (each separated by either 1b or 2b ly from receiver at transmission time - some higher, some lower, some same height above singularity as receiver), I thought that most light emitted by these ships, even light emitted in a very “downward” direction from their rest frame, would actually end up traveling in a very “upward” direction with respect to the singularity, and become redshifted due to the relativistic aberration... Is this correct? I thought with increasing separation between craft, the light must climb higher out of the singularity’s gravity well in transit between craft and thus the pulses become more redshifted with increasing separation distance . In other words, with enough velocity away from the singularity can relativistic aberration redirect nearly all light emitted by the craft away from the singularity and thus produce redshift from all directions in the receiver’s relativistic rest frame with respect to the singularity?

 

[PeterDonis]

with enough velocity away from the singularity can relativistic aberration redirect nearly all light emitted by the craft away from the singularity and thus produce redshift from all directions in the receiver’s relativistic rest frame with respect to the singularity?

No.

 

[PeterDonis]

The OP question has been answered, and the current subthread is verging on personal speculation. Thread closed.