Heidi Hoopes — Gizmag

It may be a little late for April Fool’s, but some skepticism is nonetheless warranted when reading that researchers have shown nanoparticles to disobey a fundamental law of physics which dictates the flow of entropy and heat in, it was believed, any situation. Specifically, researchers from three universities theoretically proposed then demonstrated that a nanoparticle in a state of thermal non-equilibrium does not always behave as larger particles might under the same conditions, with implications for various fields of research.

The second law of thermodynamics is the one that makes perpetual motion machines impossible. It states that the entropy – the measure for the disorder of a system – of any isolated system cannot decrease spontaneously, with the system evolving towards the state of maximum entropy (favoring disorder). The team has shown that a nanoparticle trapped with laser light temporarily violates this law. This seeming violation of universal law is transient, something that the researchers first derived as a mathematical model of fluctuations expected at the nanoscale.

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Figure 25.5 of “Gravitation” – the famous bible of general relativity written in 1973 by Misner, Thorne and Wheeler – shows on page 667 two curves as a function of time, both describing an astronaut in-falling from a stationary outer point onto a black hole. The two time curves at first coincide horizontally on the left. Then the upper one decays essentially exponentially reaching the horizontal x-axis of the horizon only asymptotically after infinite time. The lower curve, after initially coinciding, deviates downwards gently to after picking up speed (in a curve like the frontal part of a shoe’s profile) reach the horizon after 15 days already.

The lower curve is the proper time experienced by an astronaut falling onto a solar-mass black hole – the time it takes on the wristwatch to reach the horizon in free fall from a fixed outer position. The upper curve shows how this same in-falling process looks to an outside observer: infinitely elongated.

I am drawing your attention to this Figure in a famous book co-authored by my late friend John Wheeler because this figure – I claim – illustrates an error made by the whole physics community over many decades – notwithstanding the fact that the Figure is flawless.

The error consists in the reader’s believing that the short in-falling time experienced by the astronaut – lower curve – was “more real” because the maximally slowed-down appearance of the same process watched from the outside – upper curve – was caused by the growing and eventually infinite redshift that applies. This is the common belief in gravitation physics up to this day. Nevertheless this is a misunderstanding. How can I be sure?

My trick to convince you that the upper curve is the more real one lies in assuming that an ideal “trampoline” had been placed on the horizon – so that the motion of the in-falling astronaut is exactly time-inverted such that she is sent back up again without loss of kinetic energy. This ideal device can be assumed to be present without one’s making a formal mistake. The astronaut then automatically returns after another 15 days of her proper time. The pertinent curve – second shoe – is a mirror image of the first, touching it with its own tip at the level of the horizon to go up symmetrically to the right in order to hit the original height after 30 days of total travelling time of the astronaut. Such a second “dashed shoe” can be entered legally into the figure of Misner, Thorne and Wheeler.

Now the clinching question: Where, after these 30 days of travel experienced by the astronaut, lies the reappearance point of the astronaut on the time axis of the stationary outer observer (assuming he still occupies the same position as taken when the astronaut was released into free fall)?

My claim: The return occurs, not at 30 days of outer time as the newly added dashed curve suggests, but rather at “twice infinity” in outer time. The second dashed line – the one valid from the outside – is a mirror image of the full infinitely long upper curve added on to it on the right at t = infinity. This finishes the example.

If you are a high-school student: would you, please, ask your teacher about her or his opinion? I predict you will be told the following: The events on the wristwatch of the astronaut are only “optically elongated” such that what takes place in a short time for the astronaut looks vastly – eventually infinitely – stretched-out on the time scale of the outside world. But nonetheless “this does not add up to ‘twice infinity’ since no textbook says so and the question is too simple and important to have been overlooked over almost a century.” So the optical stretching must somehow be made up for again when the astronaut is racing back overtaking her own formerly sent-out light signals.

Can you make up your mind yourself?: Will the astronaut find a double infinity of outer time to have passed when she re-arrives (as I say), or can she hug the crew she left 30 days before? Bets are invited.

Acknowledgment

I thank my students for their skepticism which opened-up my eyes to the general interest of the question.