# Dark energy lorentz invaraince

Dark energy (or the cosmological constant) is stated as Lorentz Invariant, form websites like: http://cerncourier.com/cws/article/cern/28917

In newtonian mechanics, this is correct. But time dilation in relativity seems to make the cosmological constant higher the faster you move.

Here is the experiment: Throw two rocks at almost the speed of light at a very slight inward angle (almost parallel), starting them a meter apart. Have 5 meter sticks placed very far apart to measure the rock's separation.

If the angle is chosen carefully, the rocks will never touch. In this case, the 5 measurements could look something like: 1m, 0.5, 1, 2 4.

In the center of mass of the rocks frame, the meter sticks are still a meter long (they are moving perpendicular to the motion so don't Lorenz contract), and the measurements are the same.

The key is that the rocks are moving at an ultra-relativistic speed. No matter how much more kinetic energy energy you pump into them, they will take (almost) the same path as light would and still be 4 meters apart at the 5'th stick. However, giving them twice the energy will cut in half how much time they experience before they reach the 5'th stick (because of time dilation). Thus, the rocks see dark energy stop and reverse their motion in an arbitrarily short time!

• What is the paradox? The energy density and pressure (really tension) of the dark energy is the same in every frame, which is all that the statement about Lorentz invariance means. It certainly doesn't imply that any old dynamical scenario should look the same in every frame. One of the rocks sees the other rock moving towards it at different velocities, hence the turnaround time (if such exists) has every right to be different in each case. – Michael Brown Sep 24 '13 at 6:58
• By the way, photons in place of rocks always meet unless they were emitted beyond each other's horizon (in which case the thought experiment is pointless since they never "see" each other doing something wierd). So what actually happens as you increase the speed of the rocks is that eventually they no longer turn around and fly apart: rather they collide. The critical speed for the change in behaviour depends on the initial separation and the Hubble constant. – Michael Brown Sep 24 '13 at 7:04