Viewing a Time-Dilated Space

Question

I'm fascinated by space and physics but not exactly well-versed in them, so I'll try to keep this question as simple as possible.

Imagine a person acting as an observer in a room with two large sub-rooms or "bubbles" of space that we will call Bubble A and Bubble B. Each area has a hamster wheel in it, in which a hamster is running in motion perpetually. These areas (and I guess the room itself, by necessity) exist in different time-scales.

The mechanics of this are not important for this question, as I'm mostly interested in the visuals. You can imagine it as being created by some science-fiction gizmo if you like. The main thing to remember is that each bubble is clearly defined and surrounded by a clearly defined "membrane" that is also transparent for the sake of our observer.

In Bubble A, time is moving more slowly than the room the observer is in. In Bubble B, time is moving more quickly than the room the observer is in. The amount of difference can be adjusted.

What would it look like for the observer (who is outside of both Bubbles A and B) to look into Bubble A or Bubble B? Would Bubble A look redshifted, and Bubble B blueshifted? Would the image "curve" around the bubble in some sort of lensing effect?

As Bubble A's timescale changed so that it was moving even slower than the observer's time, would it look as though the hamster wheel had come to a virtual stop altogether? Would it begin to fade away as less light "escapes" from the bubble? Let's assume that it cannot go so slow as to become effectively a black hole.

Similarly, would Bubble B look like things were moving in fast-motion, or so fast as to become imperceptibly fast? Would the hamster wheel become a blur? Would this bubble look extremely bright, approaching complete whiteness?

I'm curious how similar this is to the event horizon of a black hole. I'm assuming an observer stepping into one of the two Areas wouldn't "notice" as they instantly adjust to whatever time frame they are in. But what if they reached out their hand into Bubble A or Bubble B? For instance, if our observer-person stuck their hand into Bubble B, in which time is moving faster than that of the room they are presently in, would their hand age before their eyes? If they pulled back their hand, might they pull back only bony remains (or nothingness if enough time had passed)?

Thank you for your help!

Answer 1

Your scenario can't physically exist. You can't separate areas of space within bubbles and adjust time within them arbitrarily then compare them.

Time dilation occurs due to speed or gravitational potential.

This means you can't instantly step from one place where time is running normally to one where it is running faster. This is because you need to adjust your speed (accelerate/decelerate) to match the speed of another frame of reference OR if you're in a gravity field they change gradually so you need to move a fair distance before it changes appreciably.

Red shift occurs when you move away from a light source (or the light source is moving away from you) and blue shift occurs when you move towards a light source (or the light source is moving towards you). This is similar to the Doppler effect with sound. It's a shift in frequency due to speed of the source or of the observer. In your scenario you don't have movement of source or observer so there won't be any red/blue shift.

Edit: An observer watching a spaceship travelling at relativistic speeds will note that time has appeared to slow down on the spaceship. This effects everything equally, so that clocks run slower, electrical signals travel slower, people move slower, computers calculate slower. Because everything is slowed down at the same rate a person on the ship moving slowly won't notice they are moving slowly as they are also thinking slowly. From their perspective time is running at it's normal rate and any experiment they perform to check the flow of time will perform exactly the same as in the stationary observer's frame of reference.

The two frames of reference are equally valid and can't be distinguished between without outside information. It is only one reference frame's observation of the other that notes the time dilation.

It is also important to note that due to the speed difference in these two frames of reference you can't ever hop instantly from one to the other (e.g. in your question, place your hand in a zone where time is running faster). You would need to accelerate your hand up to relativistic speeds to experience this, at which point you have lost your hand as your body is still stationary.