- #1

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Our galaxy, for example, cannot be accelerating away from a supernova in one direction as well as another in the opposite direction.

Thanks.

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- Thread starter exmarine
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- #1

- 238

- 6

Our galaxy, for example, cannot be accelerating away from a supernova in one direction as well as another in the opposite direction.

Thanks.

- #2

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This conclusion is wrong. It is perfectly possible.Our galaxy, for example, cannot be accelerating away from a supernova in one direction as well as another in the opposite direction.

Consider ants moving on an elastic band that stretches such that at time ##t## it has total length ##a(t)##. The ants may describe their positions in terms of their fractional position on the band, e.g., an ant at the mid point would say it is at ##x = 0.5##. The actual distance between two ants at ##x_1## and ##x_2##, respectively, is then ##a(t) |x_1 - x_2|##. Given that the ants remain at fixed ##x_i##, their relative separation speed is ##a'(t)|x_1 - x_2|## (which is the ant-universe equivalent of Hubble's law) and the acceleration of their relative separation is ##a''(t)|x_1 - x_2|##. Note that this is positive if ##a''(t) > 0## regardless of whether ##x_1 < x_2## or ##x_2 < x_1##.

- #3

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Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

- #4

martinbn

Science Advisor

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Why not! Say the middle one is standing still, and the other two are accelerating away from it, one to the left, one to the right.

Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

- #5

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In Newtonian physics, the two end ants would have to accelerate away from the middle ant. In General Realtivity, all three ants can all be "at rest" (relative to the cosmological frame, the Cosmological Microwave Background frame), but due to the acceleration expansion of the universe, all three ants can and do accelerate away from each other.

Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

The "baloon" analogy is often used to illustrate how this is possible - it's only an analogy, but it may be helpful. See for instance http://www.astro.ucla.edu/~wright/balloon0.html or try google.

- #6

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You are entirely missing the point. The ants are not themselves accelerating relative to the elastic band. It is the growth of the elastic band that is accelerating and therefore the growth speed of the distance between the ants is increasing.

Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

- #7

A.T.

Science Advisor

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"Accelerate" in the context of space inflation means that the distances are increasing at an increasing rate. That is perfectly possible for 3 ants on a rubber band.Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

- #8

- 238

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Oh I see what you are saying. The a(t) is the scale factor in the Friedman metric? Got it. Thanks very much.This conclusion is wrong. It is perfectly possible.

Consider ants moving on an elastic band that stretches such that at time ##t## it has total length ##a(t)##. The ants may describe their positions in terms of their fractional position on the band, e.g., an ant at the mid point would say it is at ##x = 0.5##. The actual distance between two ants at ##x_1## and ##x_2##, respectively, is then ##a(t) |x_1 - x_2|##. Given that the ants remain at fixed ##x_i##, their relative separation speed is ##a'(t)|x_1 - x_2|## (which is the ant-universe equivalent of Hubble's law) and the acceleration of their relative separation is ##a''(t)|x_1 - x_2|##. Note that this is positive if ##a''(t) > 0## regardless of whether ##x_1 < x_2## or ##x_2 < x_1##.

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