Do you Weigh More in Denver or New York? (Feb, 1932)
A quirky article that tries to explain gravity and relativity.
Do you Weigh More in Denver or New York?
by JAY EARLE MILLER
Maybe you think you weigh the same in Denver as you do in New York, but that’s because you don’t know your Einstein or your relativity. You really weigh more in New York, Why? Read this article and find outâ€”we defy you to begin Mr. Miller’s story and lay it down without finishing it.
A FEW weeks ago a British Air Force cup racing plane, piloted by Lieut. G. H. Stainforth, took off from the waters of the Solent, that protected arm of the sea lying inside the Isle of Wight, and flashed eastward over a measured course at more than 415 miles an hourâ€”just under 7 miles a minute.
The trim little racer weighed something more than two tons just before the start. Roaring down the eastward course all out, she weighed something less than that. Coming back, westbound, she weighed a bit more than before she took off.
Want to Reduce? Go to Denver
Stainforth, on the ground, tipped the scales around 145 pounds. Eastbound he didn’t weigh so much; westbound, like his ship, he weighed more.
Does that sound complicated? Then listen to this:
A pound of butter, measured out in Denver, weighs more than a pound when delivered in New York, and you weigh more in New York than you will in Denver. You weigh more on the ground than you do up in an airplane, you weigh more in an airplane flying west than in one flying east, and you weigh more in the daytime, on the ground or in the air, than you do at night with the moon overhead.
All of which goes to prove that many of the accepted facts of life aren’t facts at all, but only relatively true. Besides weight, time, space, speed, motion and matter all have definitions which are based on our own limited experience, or lack of experience, in one small and quite insignificant portion of the universe.
No Weight on a Rocket Ship
We say that a year on Jupiter, the most distant of the planets until Pluto was discovered last year, is twelve years long, and that a year on Mercury, the planet nearest the sun, is only three months longâ€”and we are wrong both times. A year is a year no matter where it is, for a year is the time it takes a planet to make one trip around its orbit. If we want to be correct we must say that Jupiter’s year is twelve times as long as ours, and Mercury’s only one-fourth as long as an earth year.
But getting back to weight, the world is getting inter-planetary conscious, with experimenters in this country, France and Germany trying to build space flying rockets. Suppose you were to make a trip to the moon, or Mars or Venus in a rocket ship. What would you weigh en route?
If your rocket ship got up a speed of seven miles a secondâ€”which is just about 60 times as fast as Lieut. Stainforth flew his Schneider Cup racerâ€”you would not, at that point weigh anything. In other words, your weight isn’t a property of your bodyâ€” has nothing in particular, in fact, to do with youâ€”but is merely the attraction which the earth’s force of gravity has for your mass. So, at a speed of seven miles a second, which is sufficient to overcome gravity, that attraction would cease, and so would your weight.
No Up or Down in a Rocket Ship
If your rocket attained that speed and broke free from the earth it would not need any more speed, or any more fuel, to keep on flying, any more than the moon, or planets or stars or meteors need fuel to keep on flying. Only, if your rocket didn’t have fuel to keep on increasing its speed you would be one space sick passenger, for, when your weight ceased to be, all the balances of your inwards also would cease, and the sensation would be like that of a rapidly falling elevator, multiplied indefinitely.
That’s one trouble about space flying. Theoretically it is fairly easy to overcome gravity and go shooting out into space, but to be comfortable, and, perhaps, to live through the experience, you would have to go on and on, constantly accelerating, at least for one-half your journey. Past that point you could start your forward rockets going to decelerate, which would merely feel like acceleration in the reverse direction.
Problems of Space Flying
At the moment of the change you would fly up to the ceiling, which then would become the floor, but otherwise you would experience no bad effects. Scientists have calculated that a successful passenger carrying rocket ship should accelerate constantly at the rate of 22 miles per hour per second through the first half of the journey, and decelerate at the same speed through the latter half.
In other words, if your speed at any given second was at the rate of 7,000 miles an hour, it should be at the rate of 7,022 miles per hour during the next second, 7,044 miles per hour the next, and so on. That 22 miles per hour per second acceleration corresponds to the acceleration of falling bodies near the earth, in other words it is the gravitational pull to which we are accustomed.
The probable destination of your rocket would be the moon, or Mars or Venusâ€” the moon because it is closest, the planets because there is a possibility you might be able to climb out and move around on them in an atmosphere containing enough oxygen to sustain life and under a temperature somewhere within the reasonable limits of what you could stand.
You couldn’t get out on the moon except in an airtight suit provided with oxygen flasks, but that need be no burden, for your weight, again relatively speaking, would only be about one-sixth what it was on earth. Eighteen-foot steps or forty-foot jumps would come easy there.
Fire a Gunâ€”Hit Yourself in the Back!
And if you could reconstruct one of the German long range guns you could have a peck of fun on the moon. Instead of a seventy-five mile range it would shoot 2250 miles, according to calculations of Dr. F. E. Wright, of the Carnegie Institute, and with only four more degrees of elevation you could shoot a shell entirely around the moon and, if your aim was good, hit yourself in the back!
Even a 75 millimeter field gun would have, instead of a 5 to 8-mile range, one of 230 to 280 miles! Dr. Wright suggests that, if the craters on the moon are really of volcanic origin, their clear cut lines are due not only to the lack of air and water to provide erosion, as on earth, but to the fact that the extruded matter, weighing but one-sixth what it would on earth, was shot so far that none fell back into the hole.
Weight Varies With Motion
It is a long jump from a definition of time or weight to Einstein’s theory of relativity, yet an understanding of how the accepted facts of life can be changed with time and place paves the way for an understanding
of just what he is aiming at. In fact, with seven-mile-a-minute airplanes already a fact, and rocket ships in the offing, relativity, in some of its simpler manifestations, is beginning to play a practical part in our lives.
Consider the old catch problem of whether a train eastbound from Chicago to New York weighs the same, or more or less than the same identical train westbound from New York to Chicago. The answer is less.
If you want to know why consider some simple manifestations of centrifugal force. When vou whirl a bucket of water over your head the contents are not spilled. When a fly wheel bursts the pieces go flying off into space with terrific velocity. If they could maintain their initial speed they would never fall to earth. That’s what a rocket ship will have to do to break away from gravity.
Here’s the Reason For It All
Now, the earth is turning on its axis in space at, roughly, 1,000 miles per hour at the equator, or about 800 miles per hour in the latitude of Chicago and New York. The train standing still in the Chicago station is moving through space at that speed. When it starts eastward at 00 miles an hour its speed in space is 60 plus 800, or 860 miles per hour. If it kept on going faster and faster until eventually it flew off into space it would weigh nothing at the moment of departure. But it would not lose its weight all in that one instant. It would be losing it gradually and steadily from the moment it began to move.
The same train westbound would be traveling in space at 800 miles less 60 miles, or only 740 miles. Obviously it must weigh more than the eastbound train, when the space-speed difference between the two is 120 miles an hour.
Another old catch question is which rail of a north-south railroad wears out the first. The answer is the west one, because it carries more than its share of the load. If you stand sideways in a moving street car you put weight on your foot nearest the rear when the car is moving forward, and shift weight suddenly when it slows down to stop. In the same way the world under the north-south railway is turning toward the east on its axis, and therefore more weight is thrown on the rear, or west rail.
Clock Fast as Light Could Not Tell Time
Time seems a hard and fast thing, but is one of the most relative things we have, for it is based on the accident of our earth’s distance from the sun, its speed of rotation on its axis, and its period around its orbit. All three of those factors probably are changing, slowly, it is true, but nevertheless the length of the day and of the year, which is the basis of what we call time, is gradually changing.
One interpretation of a mathematical formula is that time varies with speed. Carried to its logical conclusion that means, for example, that a perfectly accurate clock, if moving through space with the speed of light, would show no time elapsed. The argument by which science arrives at that conclusion seems, to the lay mind, quite fantastic, but some of its logical conclusions are not so hard to fit into other facts we accept without difficulty.
Live Longer by Moving West
Take the age of a man born in San Francisco who moves to New York and eventually dies there. If he dies at 11 a. m. in New York it is only 8 a. m. in San Francisco, and obviously he is three hours younger than his apparent age, in New York.
Or consider the traveler who circumnavigates the globe traveling westward. In mid-Pacific he loses a day, so that year, if it is a normal year of 365 days, he has lived but 364 days. Or if he went in the opposite direction he gained a day. The loss seems apparent, even if not real. And if a traveler during his life-time could make 365 trips around the world he apparently would have gained or lost a year, depending on the direction in which he traveled.
Time Varies With Speed
You don’t have to go around the world to experience the unreality of time. Take a trip across a time zone in your auto. Westbound you crowd 25 hours into one 24-hour day, or eastbound you come out an hour short. You can live your life faster or slower, at will..
Andâ€”get thisâ€”while that seems easy, as you move along the path toward Einstein’s relativity, things become more complex, for, says he, time moves faster in a parked automobile than in one in motion, for time varies with speed. The best way to get by that one is to admit we have no conception of what time is and cannot describe it. The trouble, of course, is that our definitions of time, space, matter and motion all apply to observations on our own planet and make no provisions for the rest of the universe. And, finally, they all may be the same thing, just a different manifestation of electrical energy, or something akin to it. Matter is nothing but a force, and the others may be the same.
The connection between time and speed is easy to illustrate in another way. An aviator attempting to fly around the world, at the equator, in one day would have to travel 1,000 miles an hour. A man a little more than seven miles from either pole could walk around the world in 24 hours by traveling at a speed of one mile an hour. But suppose the aviator spends his day in camp instead of flying and the polar traveler rests in his snow hut. The aviator has been traveling through space at 1,000 miles an hour while sitting still and the polar explorer has been moving a mile an hour while resting.
One thing few people have clearly understood about Einstein’s theory is that the word “relativity” describes not the new theory but the fact that the old laws of physics were not universally true; that they were true only in the limited sphere of our own inaccurate observations on this earth, in other words only relatively true.
Einstein’s latest effort is to create a system of fifth dimensional mathematics to reconcile the facts of gravitation and magnetism, both things of which we know nothing beyond some of their effects.
The great German mathematician once used as an illustration the story of a man suspended in outer space in a perfectly dark cage. He would weigh nothing, and could move freely in any direction. Then suppose a cable were attached to the top of the cage, and used to draw it swiftly in the direction of a line from the bottom to the top of the cageâ€”you can’t say upward because there could be no upward out in space.
The man in the cage would not know what was happening, but would suddenly acquire weight, and discover he was being drawn against the bottom of the cage. From the outside the observer could see that the bottom was being drawn toward the man and not the man toward the bottom, as he would believe. And the greatest scientist, equipped with all available apparatus, could never determine, if he was in the cage, which of the two things was actually happening.
And that, concluded Einstein, may be what gravitation is, just a new form of motion which we have not discovered.
As for Einstein’s theories about the curvature of space, or its warping in the presence of concentrated matter, consider this statement by Eddington:
“A globe of water of five hundred and seventy million kilometers radius would have extraordinary properties … It would have no center, and no boundaries . . . Nothing could enter or leave the mass, because there is no boundary to enter or leave by . . . There could not be any other world anywhere else, because there isn’t any ‘anywhere else’.”
Under the influence of so much gravitational mass assembled in one place, time and space both should be warped. So don’t be surprised to discover you only weigh 160 pounds, in a relative way, at sea level, in the daytime, and while standing still!