Exploring Dark Energy: Relativity and the Expansion of Space

[Sachabloke]

TL;DR Summary

Is dark energy a manifestation of relativity?

Consider a particle traveling near the speed of light towards a planet- relativity states that the space according to the particle shrinks between the particle and the planet as the particle accelerates toward the planet.
My question is - would the space behind the particle expand relative to an observer watching it accelerate away?
If this is true this would create the impression of expanding space between objects moving away from each other (dark energy).
Dark energy = solved!

 

[Ibix]

would the space behind the particle expand relative to an observer watching it accelerate away?

No. Length contraction is just a coordinate effect, and applies to all lengths parallel to the direction of motion, independent of the position of what it is you are measuring.

If this is true this would create the impression of expanding space between objects moving away from each other (dark energy).

This is not what dark energy is. Dark energy is a negative pressure term in the stress-energy tensor, not a coordinate effect.

 

[Nugatory]

relativity states that the space according to the particle shrinks between the particle and the planet as the particle accelerates toward the planet.

This is a very common misunderstanding, but that is not what Special Relativity says. One way to see this is to consider the situation from the point of view of an observer midway between the particle and the planet, so that both are approaching from opposite directions at the same speed. Clearly the the distance between the particle and the planet is getting smaller - that's what "moving towards one another" means - but there's no reason for space to be shrinking anywhere. It is also worth spending some time with the classic pole-barn paradox (google will find many good discussions) of SR to get a better feel for how length contraction does work.

In any case, the answer to your question

would the space behind the particle expand relative to an observer watching it accelerate away?

is "No."

 

[Sachabloke]

Thanks for the quick reply! To clarify- lengths parallel to the moving body would decrease (Lorentz contraction) but space would also decrease in the direction of the moving object relative to an object it is moving toward, can you confirm this?
Many thanks!

 

[Ibix]

To clarify- lengths parallel to the moving body would decrease (Lorentz contraction) but space would also decrease in the direction of the moving object relative to an object it is moving toward,

This seems to be rather confused. Length contraction means that any length you measure where the end points are moving with respect to you is shorter than when measured by someone who sees the end points at rest. This does include distances between objects, yes. But it isn't really due to "space contracting". It's more closely related to the fact that distance between two lines depends on the angle you measure at (but you have to think about time as a dimension for this to make sense).