# Einstein-Rosen bridge

The paper in question is Ref. 1. This is a traversable Einstein-Rosen bridge. However, this paper calculates that an in-falling observer will cross the throat of the wormhole in finite proper time but infinite frame time. Now, I am a bit concerned with the infinite frame time part. Does that mean that people who cross the wormhole in a ship will do so without aging much but on earth centuries would have passed? Can anyone explain what it physically means for infinite frame time?

Reference:

1. E. Guendelman, E. Nissimov, S. Pacheva and M. Stoilov, "Einstein-Rosen "Bridge" Revisited and Lightlike Thin-Shell Wormholes", Bulg. J. Phys. 44 (2017) 85-98, arXiv:1611.04336.
• It means exactly that, the "throat" of wormhole is an event horizon just like the event horizon of a Schwarzschild black hole. Sep 7, 2020 at 6:30

So this actually happens with any black hole. In fact, it happens with any accelerating observer. In special relativity, before you get to general relativity and the equivalence principle, you have the first-order Lorentz boost formula. This says that when you travel with uniform acceleration $$\alpha$$, clocks ahead of you by a coordinate $$x$$ will tick faster, or behind you tick slower, by a factor $$1 + \alpha x/c^2.$$ One prediction of this formula is a sort of “wall of death” behind you at coordinate $$x=-c^2/\alpha$$ where clocks appear to stop ticking. So everything that passes you seems to tick slower and slower as it falls upon this plane.

What has actually happened is somewhat more pedestrian: the relativistic rocket starting from rest at the origin appears to an inertial observer to move like $$x(t) = \frac{c^2}\alpha \left(\sqrt{1+\left(\frac{\alpha t}c\right)^2} - 1\right),$$ which is a hyperbola limiting to the asymptote $$x= ct-c^2/\alpha.$$ The inertial observer sees all of the clocks keep ticking, but their light can no longer reach the rocket once they pass behind the rocket a certain distance, because light rays are parallel to this asymptote.

So very often, when there are accelerations involved, special relativity predicts this phenomenon called an event horizon. Things pass through the event horizon in a finite amount of their time, and then no more information comes back from them. But in terms of your time, watching them fall into the event horizon, it appears to take them forever to traverse the horizon, and their clocks appear to slow down correspondingly.

General relativity says that the natural thing to do in space-time is to freefall. Everything else is an acceleration. Standing on a planet's surface for example is an acceleration away from the planet’s center, because you are not freefalling through the surface. Therefore, you will see a wall of death beneath you (well, you would, but there is a floor in the way) and you will see clocks above you tick faster than they should.

Side note: I like it when theories are so well confirmed that they actually become engineering details; relativity's “nothing goes faster than the speed of light” is a required engineering detail for any synchrotron for example, they just would not work if dumping more and more energy into a particle did not lead to it going closer and closer to the speed of light, so that a fixed ring size works. This prediction of general relativity was actually a required engineering detail for the satellites in the GPS cluster that helps you navigate your car. It turns out that all that they do is broadcast the current time to the world, you locate yourself based on the discrepancies in the times reported between the different satellites. A GPS system that didn't account for this would have your location on a map drift by something like 10 km every day.

Anyway, the claim is that this Einstein-Rosen bridge also has an event horizon, you passed through it and what is a finite time for you, but your light stops streaming back to a distant observer, and they see you appear to slow down as you slowly take forever to squish onto its surface.

• I understand all of that. But does frame time mean the time passing on earth or time passing for a distant observer ? Sep 7, 2020 at 18:41