One day clockwork that was put into place by the ancient builders of Zerogland clicked into place. Suddenly there was a rather obvious up and down! Everyone and everything that wasn’t tied down found itself on the ‘bottom surface’ officially called ‘Side A’ of Zerogland. Many died. Poodles were crushed. The insides of all but the buildings on Side A were heavily damaged or in a complete pile on Side A. What could have happened?
The emperor got all the remaining smart people together and even some leaders from the church as a special task force to study ‘The Event’. The talk was very busy with plenty of hand waving and some swearing, mostly from the religious group. After several hours of wrangling the Emperor asked for a report. The group had divided into three distinct factions. Two of the factions were created by a split in the physics group and a third group formed by the church. The first to report were the physics/accelerator group…
“Emperor. Dr. Zell here. We have made some careful calculations and even some preliminary experiments (one of the members had dropped his donut and another timed it’s being hit by Side A). We have determined that somehow our calm and beautiful box is now accelerating through space at approximately 9.8 m/s/s. Watch and I can prove it. He then raised a donut to head height and released it. Now understand in the millennia preceding ‘the event’ a ‘dropped’ donut did not fall. The word fall in fact is not in the Zeroglandian dictionary. Since their whole world was floating in space there was no where to fall to! All eyes watched as he released the donut. You see? The physicist exclaimed. Do you see how Side A moved headwards (there’s no word for up yet but clearly the floor must have accelerated in a direction from their feet to their heads.) and struck the donut? The strange feeling we are all now experiencing on the bottoms of our feet and, for those sitting, on your bottoms, is Side A constantly pushing against us. This guarantees that we too are being pushed through space at 9.8 m/s/s. Should anything become dislodged from Zerogland then it is temporarily no longer being accelerated since there is nothing pushing it. For that time Zerogland makes up ground on the dislodged object just as it did with the donut. I shall call this temporary apparent motion of the donut (actually the motion of Side A) hovering.
Puzzled looks all around followed by murmuring of agreement and arguing in equal measure. A raised hand,
“Professor, if what you say is true then watch this”. Dr. Emory quickly jumps up and just as quickly back down. “When I jump off the floor why don’t I just keep going like I used to before the event and travel to the opposite side of our cube”?
Zell is quick though. “Good question but remember while you are doing exactly what you used to do, that is spring off of Side A and thus give yourself a constant speed toward the opposite side the whole time you are doing that now Side A keeps accelerating. When you are as far from Side A as you are going to get is where it has matched your speed. Now it begins to exceed your speed ever more until it catches you and you are once again on Side A”.
And, I have more! We can also prove it dynamically. We are all well familiar with Cooper’s second law that states that a body’s acceleration is equal to the ratio of the net force to the inertial mass, right”? Nods of agreement. “Here I have a well calibrated force meter and a standard 1 kilobran mass. Watch. I’ll attach the 1 kilobran mass to the force meter and we record a force of 9.8 Coopers. 9.8 Coopers divided by 1 kilobran is exactly 9.8 m/s/s. There you have it. Excellent agreement with our kinematic measurements.
“Can anyone think of an experiment to disprove what I am suggesting”? Silence filled the room. After a bit Professor Crittendon stood up. “I represent the grabitational group. Hear me out”.
“As it turns out some of our graduate students have been pouring over some ancient texts housed in the initial layers of the library. Through a grant they have formed a collaboration with the ancient language and Archeology department. While their research is not ready for publication they have some initial results that may be very enlightening given our current predicament”.
“There is strong evidence to suggest that Zerogland was put into motion from a planet thousands and thousands of years ago. A planet is a huge solid sphere typically thousands of miles in diameter. Way back then people lived on the surface of such huge spheres”. Outrage filled the room. Shouting, “How the hell are you supposed to stay on the surface of the sphere”?
“Good question. What we are beginning to understand is that a rock of this size has what seems to be called grabity. This force is a mutual attraction that exists between all materiel objects. We have never noticed it here in Zerogland because it takes planet sized objects to form a measurable force. There is a plausible story line that has us being launched into space, perhaps to save some of humanity from a coming cataclysm back on our home planet, and now after these many generations we have arrived at some new planet that our predecessors had found for us. Gentleman (rarely a woman physicist even in Zerogland!) I contend that we have LANDED!* The reason Dr. Zell’s donut struck side A was due to grabity. We are sitting still on a planet whose grabity just so happens to pull things at 9.8 m/s/s! I suggest we cut a big hole in an adjacent side and have a look around.
“Are you nuts”? Shouts an outraged professor, “What if you’re wrong? You’ll have us all sucked out into empty space? We need an experiment that will allow us to determine if we are accelerating through empty space at 9.8 m/s/s or sitting on a planet whose gravity is 9.8 m/s/s.
Much brain storming and arguing happened then. The church group was asleep. Then, “I HAVE IT”!
A young undergraduate stands up. How about we release a massive ball and a not so massive ball. If they strike (or are stuck by) Side A together wouldn’t that suggest that it is the accelerator group that is correct since the masses are not moving at all really just waiting for Side A to hit them?
Professor Crittendon jumps in. “That’s not good enough. As you know with your experiments in the lab, a body with twice as much inertia as another will take twice the force to give it the same acceleration. What if grabity is exactly twice as big on bodies with twice the inertia? Then they will have the same acceleration and strike Side A together. The experiment will look the same in either situation.
“Dr. Crittendon, that’s pretty bleeding convenient don’t you think”, suggested Dr. Franz? “First you suggest a force we’ve never heard of and now you suggest that it depends on the inertia of the interacting bodies just so. Sounds a little too perfect to me”.
“Ah HA”! From the back of the room. Dr. McNeil had woken up. “I have it! To circumvent Dr. Crittendon’s argument we need to observe the motion of a massless object. Something with no inertia would not be affected by the grabity force. If we see a massless object approach Side A can we not then conclude beyond a shadow of a doubt that we are accelerating and not sitting on a new plantain”?
“That’s planet”. Dr. Crittendon corrects. “Sorry, Planet”.
Agreement all around. The experimentalists (who had been really having at the donuts) were given the task of sending a light beam across the breadth of Zerogland. Light was well know to be a source of energy but that it did not carry mass. One pass across the cube would take 25,000m/3x108 m/s or 8.33 x 10-5 s If the beam was originally 1 meter off of Side A and if Side A is accelerating at 9.8 m/s/s then when the light reaches the opposite wall, Side A would have caught up by 3.4 x 10-8 m. This is a distance that the experimentalists can easily measure. The laser and measuring equipment were put into place and the experiment was about to begin when a grad student who had previously been quiet piped up.
“Hold on a minute. How do you intend to make sure you are aiming the laser directly across the cube? You certainly can’t use the laser! If you make it hit a point one meter above the wall on the opposite side to start with you are begging the question. That won’t prove anything”.
Dr. McNeil has the answer. “Wait, what if we DO arrange it that way. If the whole cube is accelerating and we hit the one meter mark on the opposite wall it must mean that we aimed the laser up a little to shoot what to us would look like a parabola of light. In that case the height of the beam in the middle of the cube would be slightly greater than a meter! General agreement all around.
The experiment was done and repeated again and again. Variations were tried using different walls. In all cases the beam was slightly higher in the middle than it was at either end. The physicists concluded that their cube was indeed accelerating and they would re-build their world accordingly and scrap any plans to drill holes in their walls. The government canceled the grant for further research into the ancient scrolls. And so it goes inside Zerogland.
Explorers on the planet Lathos come upon a strange sighting. Obviously not natural occurring. Clearly manufactured. A huge shiny cube several miles in each dimension. Observations show the rocket engines and landing pods on the lower surface. Clearly this huge artifact has landed here from somewhere else. How strange. Plans are made to perhaps cut into the cube to learn more about it.
* Landing….. Lets say you turn on the engines to produce 1g of acceleration pointing away from the planet. You do this when local gravity is way less than 1g. Could you time it such that two things coincide: 1. Your speed reaches zero 2. Your are on the surface. Usually to land you create a force greater than gravity to slow you down. But at 1g way out there where gravity is 0.01 g you will begin to slow down. Just have to get to zero speed at the same moment you touch the surface and then shut down the engines. People inside would feel 1 g the whole time. What some fun? Given an initial speed toward earth find at what position you should turn on your engines so as to satisfy the conditions above, namely, a = 9.8m/s/s, final velocity = 0 at 1 earth radius.
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Now then. What didn’t the Zeroglandians know? Well, they didn’t have Dr. Einstein on board. Einstein would have stood the above arguments on end. He would have claimed that BECAUSE there is no experiment to separate uniform acceleration with a uniform gravitational field that light WOULD bend in a gravitational field. This of course led to the famous Eddington experiment to measure the deflection of starlight passing very near our sun.
This is Einstein’s
brilliance: BECAUSE, light would appear to bend in an accelerating box it would HAVE to bend in a gravitational field as was verified by the famous Eddington experiment. The details are in the math but his brilliance is that simple.
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