November 18, 2011

essay 0159

by: Paul R. Martin

Einstein wrote that he was inspired toward some of his ideas by considering a thought experiment in which he would travel at the speed of light alongside a beam of light just to see what that would be like. In this essay, we want to go along with Einstein on that journey but this time we want to set up some experimental apparatus ahead of time so we can make some measurements. We also want to make some predictions, in the tradition of science, and see whether the measurements will bear out our predictions.

We want to ride along with Einstein because the most difficult part of this experiment is in achieving light speed and in being able to make observations as we do. Since it would be easy to dismiss our experiment as being preposterous, or even impossible, we want to take refuge behind the credibility of Einstein and claim that if Einstein could pull this trip off, we should be able to do the same, in fact, we'll even invite Albert along on our trip.

The experimental apparatus we need to set up ahead of time will not be nearly as hard to accept as the trip itself. All of the components and activities we will need have either already been done or they are believable extensions to what humans have achieved already. So let's get started.

First, we explain the plan to Albert. We will ask him to be involved in recording some data which he will observe on his trip. We explain that we will take him and a big payload of experimental apparatus with us on a fairly routine space-ship journey to beyond the limits of the solar system. We have already sent spacecraft out there, so this is not a preposterous proposal, especially for a thought experiment.

We will park a vehicle containing the receiver apparatus to catch Einstein and his light beam when he returns. From there, we will proceed in a straight line to the star Proxima Centuri.

Somewhat short of the star, outside its equivalent of the Oort cloud, in order to minimize interference, we will park the other half of our apparatus, containing Einstein's launch point. From there, we will shoot the light beam back to our receiving station, and Einstein will make his second trip following alongside a light beam at light speed, just as he did in his first experiment of this type.

So the funds are acquired, plans and arrangements have been made, and we board our spacecraft with Einstein to set up and conduct our experiment. We achieve orbit around the sun at a distance of about a light year, which puts us well beyond any significant gravitational or radiation influences from the solar system. Our orbit brings us to a position directly in line between the sun and Proxima Centauri, at which point we fire retro-rockets to bring our craft to a dead stop directly in the line between the two stars.

We are about a quarter of the way to Proxima Centauri, which is about 4.2 light years away from the Sun. We have learned that the Oort cloud equivalent of Proxima Centauri is 1.2 light years from the star, so our destination for the sending half of our apparatus is 2 light years away from our present location, which is one light-year from the Sun.

With our spacecraft in a dead stall, it begins to fall toward the Sun. That is part of the plan. The acceleration is fairly slow, especially compared with the huge one light-year distance it has to fall before it hits anything. So we simply let it fall.

The crew, however, sets to work deploying the most crucial part of our apparatus. Housed in several giant cargo vehicles we have brought with us, is a continuous roll of extremely fine magnetic tape.

Magnetic tape has been in widespread use since at least the '50s and we have had half a century of experience in refining it. What we have brought with us is simply a very believable upgrade to this technology. The substrate, rather than being mylar, is a new nanotechnological molecular structure of carbon atoms only a few atoms thick and yet extremely strong. The ferrous coating is likewise extremely thin and fine.

With this marvelous tape, it is possible to deploy a straight stretch of tape between our two experimental stations two light-years apart.

One end of our tape is securely fastened to the receiving station, which will remain parked. The bulk of the tape will be taken with us on our journey to set up the sending station. The tape will be unrolled as we go. The gentle tug of the Sun against the receiving station, and the equally gentle tug in the opposite direction provided by the acceleration of our space ship, will keep the tape taut and straight. There is no wind or gravitational fields other than those of the two stars, so our tape will stay nice and straight for the entire length. This should sound no more preposterous than the first deployment of a trans-Atlantic cable when you consider the technology available to people in those days. And, of course we have the great benefit of doing only a thought experiment, not a real one.

We say goodbye to the crew on the gradually falling receiving station as we push off and begin accelerating our spaceship toward Proxima Centauri, with all those cargo vessels in tow. We don't accelerate fast, because we need to unroll the tape reels as we go and we don't want to break the tape. Our acceleration rate will be the same as the acceleration of our fellows back on the receiving station. This makes the net force on their vehicle strike a balance and settle down to zero. They are no longer falling toward the Sun.

As we proceed, we are careful that the tape is deployed so that it stays exactly in one plane and does not get twisted. That is no problem for our excellent navigators, who have surmounted much more significant problems just to get us this far.

At some point, we cross between the influence of the Sun's gravity and that of Proxima Centauri. Here, we begin to decelerate by controlling our fall toward Proxima Centauri at just the right rate so as to keep the tension on the tape just right to keep our receiving station right where it is.

Our trip takes a long time because of our relatively slow speed. This gives us plenty of time to talk with Albert about the expectations for our experiment. When we finally launch Albert and his beam of light, it will take 2 years for him to reach the receiving station. We have gotten Albert to make some modifications to the light beam he used in his first such thought experiment. Instead of a beam of light, we have talked him into accepting just a single photon, a nice red photon which vibrates at a frequency of 400 THz. And he had no objections to our request to polarize the photon.

The isolation of a single photon is a common experimental trick so it requires no stretch of the imagination to make it part of our experiment.

The plan is to have this photon travel between our two stations in a line that is not only exactly parallel to our stretched out magnetic tape, but that line will be so close to the tape that the lines of magnetic force from the magnetic moment of the photon will intersect the oxide layer of the tape. The photon will be polarized so that its electric field will be parallel to the tape and the magnetic field will be perpendicular to the tape.

This, again, is not unreasonable when you consider the impressive improvements in tape technology that we have seen over the past half-century. Back in the day, comparisons used to be made between the "flying heights" of read/write heads over oxide coated surfaces in various magnetic storage devices, and a 747 flying so many inches above a dry lake bed. We are simply asking that our tape technology be sufficiently improved so that we can record a bit on the tape for each vibration of our red photon as Einstein watches it travel ever so close to our tape for that two-year trip.

At the end of the trip, after Einstein is safely on the receiving station, and while the rest of us are making our way back home, the crew of the receiving station will reel all that tape back in and count the bits as they do. We do some calculations to predict how many bits they should count.

The photon vibrates at 400 THz, which is 4 x 10**14 vibrations per second. The trip takes two years and there are 6.3 x 10**7 seconds during that period of time. Multiplying the two numbers we get 2.52 x 10**22 vibrations. That's a lot. We send that number back to the receiving station to let them know what to expect when they count bits, and they relay the prediction to the eager news agencies back on earth to record in anticipation of the final results when Einstein eventually returns to Earth to report on the experimental results.

As a secondary method of counting vibrations, we ask Albert if he would mind somehow counting the vibrations of his photon as he rides along with it observing it. He agrees.

At long last, our spacecraft has reached the end of the tape and we stop at our destination 1.2 light-years from Proxima Centauri. The big day of the launch has arrived and Einstein gets into whatever vehicle he used in his first thought experiment. The special photon source is aimed down that long strip of tape toward the receiving station. We say goodbye to Albert, and the button is pushed. Albert and his photon start their two-year journey back to the receiving station at the speed of light. We leave a counterweight attached to the end of the tape, set our spacecraft free of it, and head for home ourselves. We of course won't achieve anything near light speed so it takes us quite a while to get back to the station.

When we get there, the results of the experiment are still not known because they are still reeling in the tape counting bits. Einstein, of course, has already arrived at the station and reported his observations.

When we greet Einstein we are eager to hear his report. He tells us that since the photon did not need to accelerate to achieve light speed it was up to light speed immediately. And it remained at light speed for the entire trip right up to being stopped at the receiving station. Since the photon was traveling at the speed of light, the time experienced by the photon, and also by Einstein, was slowed down by relativistic effects to zero. No time elapsed for them. So the number of vibrations experienced by the photon and the number observed by Einstein was zero. Einstein said, "It was weird. The instant they pushed that start button two years ago, I found myself here at the receiving station in the same instant. There was just no time for any vibrations of that photon at all."

In the meantime, we checked in on the laboratory that was busy reeling in that tape and counting bits. They had only half of it reeled in by the time we checked in and they showed us the tally which was in the ballpark of 10**22. It would still take several years to count the rest of the tape, but it looked very much like the count would reach 2.52 x 10**22 just as we predicted.

It will take at least a year to get our report transmitted back to Earth, and longer yet to get our bodies back there, so we will have some time to ponder and come up with an explanation for the huge discrepancy between our very large measured number of vibrations and Einstein's count of zero.

Something is clearly wrong.

I am in your thought experiment, but you didn't see me because I am in another dimension. I watched your thought experiment with interest. I need to make an analogy to explain what I perceived.

You 3 dimensional creatures can understand the thought experiment of 2-D Worm Guy. He lives in a groove in an LP record, and in his entire life time he can only go forward and backward in about 4 or 5 measures of the first song on the LP. He knows that if he had over 100 lifetimes he could experience the grooves of the last song, but it is only a dream. Every measurement Worm Guy makes tells him that the universe is straight. Stylus Guy is able to skip from one groove to another, and defy all laws of physics that Worm Guy could ever determine in his universe.

I watched in amusement while you reeled out your magnetic tape being careful not to let it twist. If Worm Guy strung out a long tape, all measurements that he could make would indicate that it was in a straight line also.

When you were reeling out the tape, from my perspective, the tape was following a twisty path in space, but in your little 3-D world you thought it was a straight line. To me, your magnetic tape looked like the ribbon coming off a spinning reel, but think of it as thin toilet paper instead of a ribbon, and then instead of being all strung out in a spiral, slide it back on the spool and think of the space that your magnetic tape is in is looking like a roll of toilet paper to my perspective. Its like Worm Guy thinking his groove universe is straight, but you, in your extra dimension can see that Worm Guys space is really twisted.

Of course since it is a thought experiment we want to think of the grooves in the LP record that Worm Guy is living on really contain no thickness, so Stylus Guy can jump from one groove to any other in zero time. By the same token, now reduce the thickness of the toilet paper to zero. Guess what? There are about 2.52 x 10**22 wraps of that toilet paper, and Einstein and Photon Man just stepped through all the layers of toilet paper in zero time, marking the magnetic tape at every revolution of the toilet paper space as they passed through each layer.

Am I going nuts? It makes sense to me.