Gravity 2: The Road to General Relativity

by Shane L. Larson

Science is, to some extent, a skill set that can be learned. Like playing piano or solving Rubik’s cubes or cooking Belgian cuisine. Using scientific thinking and applying it to the world is in large part a matter of practice and relentless dedication to getting better. But like all artforms, there is a small element of je ne sais quoi to it as well — a hidden reservoir of intuition and stupendous insight that is unleashed only sometimes.

einsteinAppleApple once had an ad campaign built around the mantra, “Think Different” (grammarians, hold your tongues, and your “ly”s and follow the mantra!). There were images of famous thinkers through the ages who approached the world differently than the rest of us. One of those was Albert Einstein.

Among a community of bright and creative people, it gives me pause to consider those people that we all think of as being remarkable. Albert Einstein is arguably the most famous scientist in history of the world, commanding the respect not just of the general populous, who have grown up immersed in his legend, but also the respect of the scientific community. Why is that? My colleague Rai Weiss, now an emeritus professor at MIT, recently noted that it wasn’t just that Einstein was smart, it was that he exhibited tremendous intuition. His great ability was to look at the same world the rest of us look at every day, and think different.

When Einstein began his quest to refine our understanding of gravity, he knew he was going to have to “think different” — this was, after all, what had led to special relativity in the first place! One of the earliest musings on the road to general relativity was a simple question: how do you know if gravity is pulling on you?

Everything I need to start developing some new ideas about gravity!

Everything I need to start developing some new ideas about gravity!

It’s a seemingly simple question, but it led to an interesting thought experiment. Imagine you and I are each in a small, windowless room with nothing but an apple and our smartphones (so we can text each other the results of the experiment I am about to describe).

Each of us drops our apple, and we see that it accelerates downward — it falls!  The apple starts from rest (at our hands) and speeds up as it falls toward the floor of our small room.  We excitedly text the result to each other and tweet pictures of apples on floors. Should we conclude from these experiments that we are both conducting experiments under the influence of a gravitational field?

[Top] You and I conduct identical experiments (dropping apples) in enclosed spaces and get identical results. [BOTTOM] The reality of what is outside our little rooms may be completely different! A falling apple is equally well explained by the gravity of a planet, or by an accelerating rocket!

[Top] You and I conduct identical experiments (dropping apples) in enclosed spaces and get identical results. [BOTTOM] The reality of what is outside our little rooms may be completely different! A falling apple is equally well explained by the gravity of a planet, or by an accelerating rocket!

Einstein realized the answer to that question should be “No!” There are multiple ways to explain what we saw.  One way is to assume our little rooms are sitting on the surface of planet Earth, where the planet’s gravity pulled the apple down. But another, equally valid way to explain this experiment is to assume the little rooms are really the space capsules of rocket ships, accelerating through empty space (the apple is pressed down to the floor — “falls” — the same way you are pressed back in your seat when a jetliner takes off).  What Einstein realized is that there is no way, based on our experimental results, to tell the difference between these two cases. As far as experiment is concerned, there is no fundamental difference — that is to say, no observational difference — between them. Einstein knew that the laws of physics had to capture this somehow.

[TOP] You and I both find ourselves weightless, floating without feeling forces acting on us. [BOTTOM] The reality external to our rooms could be that we are floating in space, or that we are in a freely falling elevator plummeting to our doom.

[TOP] You and I both find ourselves weightless, floating without feeling forces acting on us. [BOTTOM] The reality external to our rooms could be that we are floating in space, or that we are in a freely falling elevator plummeting to our doom.

What if we consider a slightly different case? Imagine you and I both suddenly found ourselves and our apples drifting weightlessly in the middle of our small rooms. We excitedly text each other that we finally made it to space and tweet messages that we are officially astronauts. Should we conclude that we are both deep in interplanetary space, far from the gravitational influence of a planet? Once again, Einstein realized the answer to that question should be “No!” There is no way to know if we are drifting inside a space capsule in deep space, or if we are merely inhabiting an elevator whose cable has snapped and we are plummeting downward toward our doom!

tweetEquivalence_smallIt is this freefall experiment that really illustrates how we have to learn to “think different” when expanding our understanding of Nature. In Newtonian gravity, we always look at problems with an exterior, omniscient eye toward the problem. A Newtonian approach to the free fall problem says “Of course you are falling under the influence of gravity! I can see the Earth pulling you down from the top of the skyscraper toward your doom at the bottom of the elevator shaft!” But Einstein asked a different question: What does the person in the elevator know? What experiments can they do to detect they are in a gravitational field? The answer is “none.”  There is no observational difference between these two situations, and the laws of physics should capture that.

The critical point here is that if you are in free fall, you feel no force! Einstein’s great insight was that the central difficulty with gravitational theory up to that point was that it was anchored in thinking about forces. This thought experiment convinced him that the right thing to think about was not force, but the motion of things.

This thought experiment came to Einstein in 1907 on a languid afternoon in the Bern patent office. Later in his life, Einstein would recall that moment and this idea with great fondness, referring to it as the happiest thought of his life.  This experiment is known as the “universality of free fall,” which physicists like to give the moniker “the Equivalence Principle.”

This is how I often imagine Einstein’s life during the years he worked in the Bern patent office! [From "The Far Side" by Gary Larson]

This is how I often imagine Einstein’s life during the years he worked in the Bern patent office! [From “The Far Side” by Gary Larson]

I have a very strong memory of my father first telling me about the universality of free-fall in about fifth or sixth grade. When you’re not used to it, the notion that falling in an elevator is the same as floating in outer space engenders a spontaneous and vehement response: “That can’t be true!” We had many long debates about this (it was following hot on the heels of my meltdown over the existence of negative numbers — maybe my dad was trying to forestall another meltdown…), and I don’t think it ever quite sank in. I, of course, feigned understanding and dutifully repeated the tale of the falling elevator to my classmates, reveling in their confusion and indignant denial of the logic of it.  I was a tween — what did you expect?

The "Leaning Tower of Niles," a half-scale replica of the tower in PIsa. Located in Niles, IL (a suburb of Chicago).

The “Leaning Tower of Niles,” a half-scale replica of the tower in PIsa. Located in Niles, IL (a suburb of Chicago).

But now, many years later and with a LOT of physics under my belt, I know that that the outcome of these thought experiments derive from a very old result that we are all familiar with — that all objects fall identically, irrespective of their mass. Galileo taught that, at least in folklore, by dropping various masses off of the Leaning Tower of Pisa. The obvious question to ask is “how is Galileo’s experiment connected to Einstein’s thought experiments?”

For the moment, imagine the various parts of your body as having different masses.  Your head masses about 5 kg (a little bit more than the 8 pounds you learned from watching Jerry Maguire), where as a good pair of running shoes may mass about 1.5 kg.  If you are standing happily in the elevator when the cable snaps, the traditional explanation is that everything begins to fall.

If objects of different mass fell at different rates, then your head would be pulled down faster than your shoes — you would feel a force between your head and your shoes. That force could be used to deduce the existence of a pulling force.  But Galileo taught us that is not the way gravity works — your head and your shoes will get pulled down at strictly the same rate in a uniform gravitational field. Every little piece of you, from your head to your toes, your kneecaps to your freckles, falls at the same rate — there are no different forces between the different parts of your body and so you feel (you observe) yourself to be weightless. This is sometimes called the Galilean Principle of Equivalence, or the Weak Equivalence Principle.

Okay — so what? Apples and freefall, elevators and rockets. What does any of this have to do with developing a deeper understanding of gravity?

What this thought experiment reveals, what the Equivalence Principle tells us, is that thinking about forces is not the best way to think about the world because we can’t always be sure of what is going on! Instead, we should think about what we can observe — how particles move — and ways to describe that. That simple intuitive leap would, in the end, change the face of gravity. Particles move through space and time, which had brilliantly been unified by Einstein’s teacher and colleague, Hermann Minkowski, into a single unified medium called “spacetime.”

What is spacetime? It is the fabric of the Cosmos —  it can be stretched and deformed. The fundamental idea of general relativity is that gravity can be described not by a force, but by the curvature of spacetime, the medium on which particles move.  That will be the subject of our next little chat.

—————————————

This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru

38 responses to “Gravity 2: The Road to General Relativity

  1. In one of G B Shaw’s books, he explained relativity somewhat along the following lines: a minute spent with one’s would-be mother-in-law sounds like an hour; an hour spent with one’s girl friend feels like a minute!

  2. hiroji kurihara

    Composition of the vector : Free fall

    Vector of gravity and inertial force is possible to compose. It seems to show that the two are inviolable and non-interference each other (it will be the same on two gravity). It will be the same also on vector of gravity and inertial force that act at an optional point of an elevator cabin in free fall.

    Sorry, I cannot receive E-mail. I do not have PC.

    http://www.geocities.co.jp/Technopolis/2561/eng.html

  3. hiroji kurihara

    Equivalence Principle

    Let’s start from accelerated motion. Many substances (solids, fluids, etc) are moving in various accelerated motion. According to this motion, inertial force occurs. Imagine water of a current. Involvement between inertial force and gravity will be on resultant force only.《P.S.》Acceleration is not relative and inertial force is not fictitious. The two are corresponding qualitatively and quantitatively.

    Sorry, I cannot receive E-mail. I do not have PC.

    http://www.geocities.co.jp/Technopolis/2561/eng.html

  4. Hiroji Kurihara

    Gravitational acceleration
    Who started to say gravitational acceleration ? Is it a technical team really ? It seems to be an adjective.

    Is there a difference between an acceleration caused by an ordinal force ? If there is not a difference, a thing called gravitational acceleration will not exist.p

  5. Hiroji Kurihara

    Turn your eyes to accelerated motion and inertial force. It does not matter what gravity is.

  6. Hiroji kurihara

    About MM experiment

    In a moving passenger car, MM experiment is being done. On the ground, an observer stands. To this observer, are constancy of light speed and Lorentz contraction compatible ? And also, are constancy of light speed and time dilation compatible ?

  7. Free fall

    Every inertial force is measurable. Every gravitational force is measurable also. Principally. In an elevator in free fall, there is no exception.

  8. Are the two indistinguishable? The vector of the two are opposite.

  9. Falling of non free

    Imagine an elevator cabins are falling in various density of air. Hydrodynamics tell motions of these elevator cabins. Equivalence principle is invalid.

  10. Free fall
    There are inumerable vectors of inertial force and gravity everywhere. On an elevator cabin, why they are making a big fuss ?

  11. Inertial force

    On a slope (no friction), a body is sliding down. Action is gravity mg. Then, how about the reaction ? It is resolved to two vectors. Inertial force is not fictitious.

  12. Equivalence principle is nonsense (I say again)

    An elevator in free fall is explained fully by Newton. No different explanation is possible. And it is the same even if limited to the infinite small area.

  13. Inertial force is not fictitious

    On a plane, there are two bodies. One is at a standstill, the other is accelerating. Acceleration (a) and inertial force (ma) both are not fictitious.

    There are two disks. One is not rotating, the other is rotating. Acceleration and inertial force both are not fictitious.

  14. Space is rest frame

    Into space, let us draw plural vectors of acceleration a. Space will be rest frame absolute.

  15. Equivalence principle (I say again)

    Vector of inertial force is shown as an arrow. Vector of gravity cannot be shown as an arrow generally. The two are different as facts of physics.

  16. About inertial force (I say again)

    On a plane, there are two passenger cars. One is accelerating and the other is at a standstill. Difference of the motion of the two is not relative but absolute.

    On a plane, a passenger car is accelerating. On the floor (no friction), a body is put. This body is not accelerated (to everyone). From physics of 20th century, nonsenses overflow.

  17. Sagnac effect

    Sagnac effect will be explicable by Ritz’s emission theory. There is a light path of equilateral triangle (formed by a light source and two mirrors). Three apices is three emission points and can be regarded as three different inertial frames (inertial frame at the moment of emission).

  18. Accelerated motion of a light source

    Light emitted from an accelerated source will follow instantaneous speed of the source. In short, light is will scceed motion vector of instantaneous speed of the source.The emissionm theory imply the above.

    I say again, the emission theory will be valid for a few seconds only after the emissinohn. After this, light follows aether.

  19. There is a web site as follows. “Orders of magnitude (acceleration) – Wikipedia”. GRT will be nonsense.

  20. Perihelion shift of Mercury

    Mercury revolving is divided in two (semisphere A facing the sun and the other B). Inertial force is A<B and gravity is A>B. It must be the most natural explanation of perihelion shift of Mercury. Because the value of perigee movement of the moon is remarkable (around 8.85 years). On the other hand, value of asteroids will not be found. Common explanation is not acceptable.

  21. Perihelion shift of Mercury

    Perihelion shift moves forward constantly. It cannot be explained by gravity of other planets.

    On asteroids, no perihelion shift will be observed. Some size is needed.

    Cause of perigee movement of the moon is written to be the sun. Not consistent. Because it will be the same phenomenon to perihelion shift of planets.

  22. Perihelion shift of Mercury

    The value of perihelion shift of planets is constant. It will not be three body ploblem or many body problem. And it will be the same to binary star.

  23. Equivalence principle (I say again)

    An elevator cabin is accelerating horizontally (no friction : at 2g). At every mass point (at every infinite small area), acceleration is 2g.

  24. Perihelion shift of Mercury

    “It can be safely said that gravity of other planets has no effect on the perihelion shift of Mercury”. It’s in a website.

    Imagine that with long radius of orbit of Mercury, the space of the solar system is divided into left and right. The probability that other planets exist on the two is equal. There will be no shift of perihelion in one direction at constant speed (common view is wrong).

    But main cause of perihelion shift of Jupiter and Saturn will be mutual effect of gravity. Each perihelion is shifted every moment.

  25. Perihelion shift of Mercury

    There is a model of Mercury. A long lod penetrates a true sphere and at the both ends of the lod, weights are set. This model is rotating horizontally and is moving on the orbit of Mercury (two planes fall on). Main forces acting on the weights are gravity of the sun and inertial force (centrifugal force). And each force acting on the outside weight and inside weight is different.

    Inertial force pulls the orbit to the outside. But actual orbit of Mercury is pulled to the inside. Gravity of the sun acting on the two weights is inversely proportional to the square of the distance (not come out even. not plus minus zero). In Mercury, the action of gravity will be superior.

  26. Perihelion shift of Mercury

    A model of Mercury is shown previously. Now, there are plural models. Length of lord and mass of weight each is different. These are revoleved around separately on the real orbit of Mercury. Maybe, all will be explained by Newton’s theory (including 575 arcsec).

  27. Absolute rest frame (Aether)

    What distinguishes acceleration from non-acceleration ? Only inertial force can. And it is based on aether. Yes, aether exists. Evidently, aberration shows it.

  28. Perihelion shift of Mercury

    The perihelion shift of the earth is 11.45 arcsec / year. Main cause will be its size (size of sphere). It is the same to Mercury. In addition, the earth has a moon as a satellite that Mercury does not have. The inertial force of the moon and gravity of the sun acting on the moon are also considerable. And like Mercury, effect of other planets must be slight and unstable.

  29. Perihelion shift of Mercury

    Value 5.75 arcsec/year seems to be an observed value. In a website, contribution of other planets to this value is shown. These are added simply !! And value 5.75 arcsec (and contributions) seems to be constant every year !! Unthinkable !!

    I say again, other planets will not be main cause of this value 5.75 arcsec.

  30. Perihelion shift of Mercury

    Mercury has an own size as a sphere. Therefore, the sun’s gravity will have a different effect on Mercury than it does on the center of gravity. Strength of gravity is inversely proportional to the square of the distance. Actual orbit will be different from that the center of gravity must follow. On Mercury, it will be the main cause of the perihelion shift.

  31. Perihelion shift of Mercury

    Let’s reconsider the main cause of perihelion shift again. On Mercury or Venus, main cause will be the size of sphere. On Earth or Mars, effect of satellite is added. On asteroids each, effects of size is negligible. On Jupiter or Saturn each, the powerful and unstable effect of the other will act. On Uranus or Neptune each, slight and unstable effect of the other all planets will act. Anyway, common view on Mercury is wrong.

  32. Perihelion shift of Mercury

    This is the top of tall tower. Two rods of equal mass and different length are arranged vertically (heigtht of center of gravity is the same). Now, two rods start to fall at the same time. The fall of center of gravity will not be the same. Because the strength of gravity is inversely proportional to the square of the distance. This will be the main cause for perihelion shift of Mercury.

  33. Perihelion shift of Mercury

    In an binary system (formed by main star and companion star), periapis is shifted also. Motion of companion star (apsidal shift) will be depending considerably on its size. Common view (says main cause is pertubation of other planets) will be invalid.

    Main cause of perihelion shift of Mercury is said to be gravity of the other planets. But position of other planets move (also position of perihelion of Mercury moves). If so, values 5.75 secarc/year is unthinkable. Main cause lwill be in Mercury itself. And also it will be the same on values of perihelion shift of the other planets.

  34. Perihelion shift of Mercury

    Suppose that Mercury revolving is devided in two (hemisphere facing the sun A and the other B). Main forces acting on the two are gravity of the sun and inertial force (centrifugal force). Inertial force is A<B and gravity of the sun is A>B.

    Yes, each force acting on the outside and inside is different. Inertial force pulls the orbit to the outside. But actual orbit of Mercury is pulled to the inside. Gravity of the sun acting on the two is inversely proportional to the square of the distance (not come out even. not plus minus zero). In Mercury, the action of gravity will be superior.

  35. Perihelion shift of Mercury

    In Mercury, the non-uniformity of the Sun’s gravity (in the size of Mercury) will be the main cause of perihelion shift. Even in artificial satellites, the effects of non-uniformity of the Earth’s gravity (the position of the center of mass and the center of gravity are different) are also mentioned.

  36. Perihelion shift of Mercury (an essay)

    A celestial body called Vulcan is revolving on orbit of Mercury. It has the same mass and revolution cycle as Mercury. And diameter is twohold (the both stars are uniform in density). Since the sun’s gravitational field is non-uniform, the sun’s gravity acting on both stars will be slightly larger in Vulcan and smaller in Mercury. The value of perihelion shift also likely will be similar. In short, the size of the celestial body (close to the gravitational source like Mercury) will be the main reason for the perihelion shift.

    Imagine a cone with evenly spaced concentric circles on its surface. The non-uniformity of gravity will be exponential non-uniformity.

  37. Propagation of gravity

    The propagation of gravity will be done in an instant. For this, here are two reasons. One reason is that two-body problem, many-body problem are true for celestial bodies. The other reason is that the whole solar system is in an uniform linear motion and planets are in elliptical revolution on their revolution planes.

  38. Inertial force, centrifugal force, centripetal force (an essay)

    Between accelerated motion and non-accelerated motion (uniform linear motion), there is an immovable distinction. And accelerated motion is always accompanied by an inertial force (corresponding to the vector of motion). These are based on the existence of absolute rest frame.

    A motion of a disk rotating is an acceleration motion. And the disk is accompanied by an inertial force called centrifugal force. It is said that centrifugal force depends on the situation of observer. But the physical phenomenon (centrifugal force) cannot be influenced by observers. Centrifugal force will show the same value to everyone.

    The wiki defines centripetal force as “the force that moves an object in a curved motion”. But is that the correct definition? Is mere external force centripetal force also? Isn’t tension, tensile stress, gravity, etc. all the same? Is there any commonalities (grouped together)?

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