I have a paradox that I don't know the answer to. Special relativity has no preferred frame, but it seems like adding an exponential expansion to space introduces such a frame.(adsbygoogle = window.adsbygoogle || []).push({});

The Setup

Suppose we're in a universe with a much faster expansion rate, where the space between any two objects doubles every minute. Place two balls a meter apart, wait one minute, and they'll be two meters apart.

Additionally, say we have some inertial frame F and two ships. One ship is at rest with respect to F, while the other is moving at 0.99c. The ships are equipped with arms, for placing balls that then drift away due to the expansion of space.

As the moving ship crosses above the stationary ship (with respect to F), they both release a ball one meter away from their side (in a direction perpendicular to the relative velocity between them).

Before release:

During release (retract the arms), when the ships are on top of each other:Code (Text):

ship

Stationary Ship: ------◇------○ ball

arm (1m)

^ ^

Moving Ship: ^ ------◆------● ^

^ ^

0.99c 0.99c

One minute later:Code (Text):

retracting arms...

---◈--- ◉

(*ships on top of each other; length contraction not to scale at all)

Two minutes later:Code (Text):

◆ ●

... far away ...

◇ ○

-----2m-----

Etc.Code (Text):

◆ ●

... far far away ...

◇ ○

-----------4m-----------

Same Factor, Different Durations

The stationary ship can check that the ball's distance does in fact double each minute by bouncing photons off of the ball and seeing that it takes twice as long for the photons to return.

But now consider things from the perspective of the moving ship. Things are twice as far apart one minute laterin the rest frame,but in the moving frame clocks run slower by a factor of ~7. In order for things to stay consistent, it seems like the ball's distance must double every 8.4 seconds (with distance measured by bouncing photons off of the ball, and time measured by a clock on the moving ship) in order for there to be a consistent picture of spacetime. Meaning the ships will disagree about the expansion rate.

So it seems like moving increases the apparent expansion rate of space, and there should be some special frame where the expansion rate is minimal.

Question

The obvious question is: where's the stupid oversight? Probably something to do with the relativity of simultaneity like it always is...

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# Does the Hubble expansion of space have a preferred frame?

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