The Infinite Beam Problem

I shine a laser beam up in my house. It hits the ceiling and the light is scattered, absorbed for later gentle scattering, and reflected back to my eyes. The existence of the beam is validated and the loss of the energy from the laser is equated with the energy perceived by my eyes and otherwise in the room and universe.

I shine a laser beam up in a cathedral. The beam travels further with the same result. I go outside and shine the beam up at the moon. The beam hits the surface of the moon and the same effects occur.

I shine a laser up into deep space. The beam might hit a star or dust cloud or planet, but what if the beam misses those things and keeps travelling to the end of the universe? In that case the beam would never hit anything, and so reflect nothing. The beam would not be detected by the universe, the existence of the beam would not be validated except by the loss of energy from the laser, which could only equate to a permanent net energy loss from the universe.

This must happen with the light from stars all of the time. What is wrong here?

If we were that tip of the beam, flying away with instant time and insight, what would we feel like, moving for infinite time? Could we exist as this temporally and spatially infinite object?

Let us explore some solutions.

1. The beam continues to travel for a long time, waiting until an inevitable day when it impacts something and validates the existence of the beam, settling the energy imbalance debt. The downside with this hypothesis is that a beam shining out at the edge of the universe is unlikely to ever impact anything.

2. The beam bends back towards the universe and then collides with an object. This would equate to a closed universe. This would be a neat solution to the problem. Does this match the current universe? Is there any observational evidence of our universe to support this?

3. A 'quantum' option. The beam continues for infinity but does not exist. The firing of the beam can be validated by the loss of energy in the laser emitter but this is balanced by an energy gain in all of the universe on average, a radiating but non-localised field which contains the energy. This spreads in all directions equally.

If the beam hits a distant object, like my ceiling, the field will instantly vanish, coalesced into the beam alone. How would this coalescence occur at longer ranges, because it seems that the information about the beam hitting the ceiling is instantly transmitted from the ceiling to all points of the field, ordering the field to collapse and jump to the ceiling.

If the beam continues forever into distant space, this field must itself impact into objects and at some point return its energy because if not, it would be the same as not existing, so the field itself must be able to liberate energy too.

4. Perhaps our concept of a laser of a perfectly straight beam is flawed. Over a short distance this is true, but as ranges grow, the scattering effect of a laser grows, until, at the scales of an infinite universe it behaves more like a point light, shining in all directions rather than a straight beam, so perhaps our problem does not exist. This does not solve the problem however, for like the light of a distant star, at least some component of the beam could still head out towards the endless boundary of the universe, and be lost.

5. Even when flying away, the beam constitutes part of the universe and so is not lost, even if it remains forever undetectable. Its energy remains in the universe, but it can never interact with anything and so is useless. The information about it is permanently lost. In this case, the net energy in the universe would remain equal but the net information would decrease over time.

This rate of this loss could be calculated, as the light shone from the outer edge of a rim of stars at the boundaries of the universe would be lost, and the energy shone into the universe would not, although, like playing Snooker on a boundless table, all of the information would be lost at some point.

This would seem to be a logical validation of the concept of entropy, but it also has problems. If the information about the existence of something is permanently lost, is this not the same as its energy being permanently lost, because it is the same as the thing itself being permanently lost?

Perhaps so, and perhaps then the net energy in the universe must decrease too. Net existence must decrease over time. We are all born and we all die. It seems reasonable that this applies to the universe itself, however much we might hope for something infinite or immortal.

Mark Sheeky, 29 August 2018