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 in Rottweil on January 12, 2016

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

It is maximally simple and yet maximally absurd in its consequences. Such a coincidence is unprecedented. This lad was a gift to the planet.

Just embark on an Apollo-like rocketship in your mind. 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 if you brought along your pocket laser-pointer and a pocket frequency counter. Thirdly, you may bring along a smoke-filled glass tube through which to send a laser pulse while the tube lies on the floor or is glued to the ceiling, so as to take snapshots of an internally advancing light pulse 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 tube) you can also use inside a huge church tower on earth, with predictably the same measurement results. The experiment is so simple that “mere thinking” suffices to make valid predictions. This is what Einstein did in 1907 with all the mentioned equipment not being available as of yet.

The least surprising prediction 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 had already predicted gravitational light bending a century before in 1804.

The most famous surprise found 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 – despite the maintained distance. For during the time the light is ascending with its limited universal velocity c, the tip did continue 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. Nonetheless Einstein’s “gravitational redshift” is confirmed everyday by the GPS in our cars. The satellites overhead make for the ceiling of a rather high church tower indeed (their fast motion does not abolish the effect).

Pointing the laser downwards from the tip will show the opposite effect – an increase in the count rate compared to what holds true above when measuring downstairs.

What else can we do with this mental or real toy? The second big implication seen by Einstein applies when the tube with the smoke in it is lying on the bottom while watched from the tip. Einstein predicted correctly that the light speed inside will look reduced from above: A second absurd prediction made out of the blue by sheer thinking. And when you look from the bottom up to the ceiling, the transversal speed of light will look increased there (a fact that remained unmentioned).

The correctly predicted observable change in c caused Einstein to fall silent on gravitation for almost 4 years. For the theory of special relativity with its by definition globally constant c had produced an implication that amounts to a contradiction-in-terms. This illogical state of affairs is still the accepted teaching of to date. I hope you did enjoy the ride. But: is there not something missing here?

When staring a bit longer into the Einstein-Apollo-rocket, we may suddenly realize that the light ray, while visibly “creeping” across the floor (or else visibly “zipping” across the ceiling), is not moving horizontally as this was assumed so far. The tilt – an upwards tilt in either case – is owed 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 in the meantime (or else has come somewhat closer to the bottom from above, respectively). Hence the no longer horizontal light ray has re-gained in either case the universal speed c – as originally presupposed.

At this point, an encouragement from the part of the reader or listener is vital because the relative upwards slant seen is not part of the narrative since 1907. Can Einstein have possibly overlooked this detail?

The Virtual-Reality-like thoughts described – which hopefully will soon be part of a computer game – were so taxing for Einstein that they “singed” his brain as he once confessed. He feared to go crazy and looked for 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 come out eventually: the Einstein field equation. Does that equation contain the “relative upwards slant” proportional to vertical distance that we just spotted jointly? The answer is in the negative.

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 establishment has gone astray for so long?

“Thinking helps” according to Hewlett-Packard. The new “relative upwards slant” of light rays hugging the horizontal floor inside the Einstein rocketship, valid relative to above (or below), repairs the so far accepted violation of c as a global constant of nature in the vacuum. A well-known result from special relativity – that the speed of light inside a transversally receding light tube appears reduced (or increased if approaching) was overlooked. So everything is fine again: c remains a globally (and not just locally) valid constant of nature in a return to the pre-1911 Einstein.

Why be hesitant? The reader will be appalled to realize that the retrieved global c entails that the cosmos cannot expand any more since distant points can no longer recede from each other at more than c as everyone believes does occur. By denying the Big Bang you will make yourself a laughingstock among your peers when you tell them that you approve of the above “mental analog computer” of the Einstein-Apollo rocketship. So you will have to decide whether rather to trust your own firm judgment or let yourself be bullied into behaving like a dogmatist. In science and elsewhere, dogmas have a knack for being deadly. Therefore: Is the above conclusion (“relative upwards slant”) correct or is it not?

I for one am sure 99 percent of the time that it is correct. One reason to remain skeptical is the fact that it is such an immense fun to be more right than 3 ½ generations of specialists from the year 1911 on. This feeling, if legitimate, is accompanied by an immense gratitude to this young amateur scientist of 1907 who took on the whole establishment with the verve of a total outsider. I need not tell you that at present, the scientific community is gladly betting the planet on the above story being false. But this is another tale. Thank you for having lent me your ear, my young colleagues, gentlegirls and gentlemen.

Paper dedicated to the late Wolfgang Rindler (who liked it as he wrote me).

07.10.2019