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The Einstein Rocketship explained to Young and Old

Otto E. Rossler

Faculty of Science, University of Tuebingen, 72076 Tuebingen, Germany

Abstract: Popular talk given at the Nell-Breuning Highschool at Rottweil on January 12, 2016

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It is fun to picture this rocketship, the most beautiful brainchild of that young man who always called it “the happiest thought of my life.” What is it that is so “happy” about it? Can a mere thought be happy?

This one is maximally simple and yet maximally absurd in its consequences. Such a coincidence is unprecedented as a gift to the planet. May I continue?

Just embark on an Apollo-like rocketship in your mind, painted white and red on the outside. Unlike the real one it is not filled with propellant throughout: in the middle, it has a narrow passenger cabin that runs along the whole length and width of the ship. Therefore you can make simple experiments on board in case you brought along your pocket laser-pointer and a pocket frequency counter. Thirdly, you may bring along a glass tube with a regenerated laser pulse moving back and forth inside whilst the tube either lies flat on the floor or else is fastened to the ceiling, so that its counter can be read-off as a clock from above or below. The ship is assumed to be accelerating constantly in outer space while you make the measurements.

The same equipment (pointer, counter and glasses) you can also use inside a huge church tower on earth, with predictably the same measurement results. The experimental set-up is so simple that “mere thinking” suffices to make valid predictions. This is what Einstein did in 1907, with all the mentioned equipment still unavailable.

The least surprising predicted outcome is that when you hold the laser pointer horizontally at any height inside the accelerating rocketship, the horizontal light ray that comes out will be gently downward-curved inside the accelerating rocketship. This effect is very small since the rocketship is so slender. Moreover, von Soldner did already predict gravitational light bending a century ahead of Einstein in 1804.

The famous surprise prediction made by Einstein is the following: When the laser is pointing upwards from the floor and you count the pulses at the tip, the counter will show a reduced ticking rate compared to what is valid on the bottom even though the bottom does not fall back. For during the time the light is ascending with its limited universal velocity c, the tip continued picking up speed away from the emission point. Hence a Doppler effect applies like the slowed pitch of a receding ambulance.

This was Einstein’s main prediction. It appeared totally absurd at the time. Nevertheless Einstein’s “gravitational redshift” (as it is called) gets confirmed every day by the GPS in our cars. The satellites overhead do correspond to the ceiling of a rather high church tower (whilst their fast motion makes for a lesser change).

Pointing the laser downwards from the tip will make for the opposite effect – an increase in the observed ticking rate. What else can we do with our mental or real toy? The second big thing seen by Einstein -- light creeping -- applies when the tube is lying flat on the bottom whilst getting watched from the tip. Einstein predicted correctly that the light speed inside will look reduced from above: his second absurd prediction made out of the blue sky by sheer mental imagery in 1907. And when you look from the bottom up to the ceiling, the transversal speed of light observed up there will look increased (a fact that remained unmentioned).

His correctly predicted manifest change in c caused Einstein to fall silent on gravitation for almost 4 years. The obvious reason: the theory of special relativity with its by definition constant c had produced an implication (propagation of light at less than c) which amounts to a contradiction-in-terms. This illogical state of affairs does actually still represent the official teaching today. I hope you enjoyed the ride. But can the discrepancy be resolved?

When staying a bit longer with our mind inside the Einstein-Apollo rocketship, we may suddenly realize that the light ray in question, while visibly “creeping” across the horizontal floor, is not actually moving horizontally there even though the light tube is lying flat: A constant tilt applies owing to the fact that, when the propagating light ray reaches the next spot on the horizontal floor, the previous point has already fallen back a bit relative to the tip somewhat. So the locally upwards-slanted (rather than horizontal) light ray with respect to the tip has actually preserved its universal speed c – just as presupposed.

At this point, an encouragement from the part of the reader or listener is vitally needed because the relative upwards slant just seen is not part of the scientific narrative since 1907. None of the many learned texts says a word to that effect. Can Einstein and his followers possibly have overlooked this detail?

The Virtual-Reality type thoughts that we just entertained will hopefully be part of a computer game soon. They were maximally taxing to perform again and again by Einstein himself in the absence of such a thinking aid being conceivable. So the again and again repeated mental analog computer simulation would eventually “singe” his mind as he said. He feared to go crazy and had to solicit mental shelter from his longtime friend, mathematician Marcel Grossmann, in order to continue functioning. Everyone knows that the most difficult dynamical equation of history would eventually come out from their cooperation: the Einstein field equation. But does that latter equation contain the “relative upwards slant” in proportion to the vertical distance traversed that we just spotted jointly? The answer is no.

But the present playful text is supposed to be a kindergarten version of Einstein’s "equivalence principle" between gravity and ordinary acceleration, is it not? Virtually all specialists (except Wolfgang Rindler) scoff at texts without equations: Can it be that the mathematically educated scientific community has gone astray for so long by failing to go through all the necessary steps of a mental computer game?

“Thinking helps” according to Hewlett-Packard. The new “relative upwards slant” of light rays hugging the horizontal floor in the Einstein rocketship happens to repair the so far accepted violation of c. For Einstein's strongest brain child was based on the special theory of relativity with its constant c but had produced a consequence violating c: a nonsequitur. Only because a well-known result from special relativity – that the speed of light inside a transversally receding light tube appears reduced -- had gone overlooked. Now, everything is fine again: c remains a globally (and not just locally) valid constant of nature in the above accomplished return to the pre-1911 Einstein.

But why am I still hesitant? The retrieved global c entails that the cosmos cannot expand any more because sufficiently distant points can now no longer recede from each other at a superluminal speed as everyone on earth believes is the case in reality. But will your denying the Big Bang not make a laughingstock out of you among your peers when you tell them that you are approving of the above “mental analog computer” of the Einstein-Apollo rocketship? Therefore you will have to decide eventually whether or not to trust your own judgment or else let yourself be bullied into behaving like a dogmatist. In science, dogmas have a penchant for ending deadly. Therefore: Is the above-reached conclusion (“relative upwards slant downstairs”) really true or is it just  a mental mirage caused by lazily shunning the use of equations?

 I for one am sure 99 percent of the time that the mirage is none. One reason to remain skeptical though is the fact that it is such an immense fun to be "more right than almost 4 generations of specialists" from the year 1911 on. So a big element of temptation accompanies the triumphant thought. This feeling -- if legitimate -- is combined with an immense gratitude towards this young amateur scientist of 1907 who took on the whole establishment with the verve of a complete outsider. I need not tell you that at present, the scientific community is gladly betting earth on the above story for kids being false (!). So much the more do I have to thank you for your having so kindly lent me your ear or eye, my dear young colleagues, gentle-ladies and gentlemen.

Dedicated to the memory of Wolfgang Rindler.

Oct. 8, 2019

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