To Frame My Frame…(Frame I : Newton) – 3. The Scholium

December 7, 2005

Among the beginning sections of Newton’s Principia is a wonderful section titled Scholium. In it, Newton with his natural grandeur wrote about absolute space and absolute time and presented an argument for absolute space and absolute time that has ever since puzzled physicists and philosophers alike.

You may be wondering why I am spending so much time on Newton when my declared intention is to talk about GR, the theory by Einstein.
That’s because I believe that the thrill of the roller coaster descent that relativity is, is lost to those who had not yet heard about(or who are not yet convinced about) the absolute space and the absolute time of Newton.

So, Here we go. The scholium starts off with the assertion that there is an absolute space and time and “true” motion is the motion with respect to this absolute space and time. This, Newton said, should be distinguished from “relative” or “apparent” motion where one body moves in relation to another. Similarly, the “true” time is just the absolute time. Whereas relative or apparent time is the time measured by a certain clock or some repeating motion like the motion of the sun, for example. This, Newton insisted, is NOT the absolute time since all days need not be equal in duration.

Indeed, Newton wrote,

I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space;…

Now, all this is O.K. But, still, the question remains- How do you detect absolute,immovable and whatever space ? Indeed what is the necessity of assuming the existence of such a thing if all we can observe is one thing moving with respect to another. If there is no way whatsoever to tell whether you are moving absolutely or not, what’s the point anyway ?

The point is,(and as far as I know, Newton was the first to realise this) that the argument given above is WRONG ! It is NOT true that absolute motions are unobservable. Some absolute motions do have observable effects. Of course, I am talking about cases where we observe a pseudo-force.For example, if you are sitting in a moving bus, and the driver applies a break, you feel a jolt. Now, if I ask why you felt a jolt, you would say – “well, I felt a jolt because the bus came to halt !”. But, notice, as far as you are concerned, you are sitting in the same seat as before. So, with respect to the bus, you are at rest. So, whether you feel a jolt or not cannot be determined by your position relative to the bus,

So, there should be something out there, relative to which if you reduce your speed, you will feel a jolt. That something, Newton triumphantly concluded, is the absolute space ! This indeed is among the most strange things in this world. Consider these facts – Number one, If you move with a constant speed along a straight line with respect to the absolute space, there is no way you can find it out. Number two, If, however you CHANGE your speed or the direction or both, it is very straightforward to tell whether that “change” is an absolute one or a relative one. It is really weird that the jolt I feel is determined by whether I am moving with respect to something out there rather than my motion with respect to the nearby bus ! But, such is the world, and physics is interesting precisely because it’s a weird weird world we live in ! But, as you might have very well guessed, physics has a lot more things to say about this mystery.

I took jolt as an example and once you get the idea, it’s not difficult to notice how nature allows you to find out your “true” motion.
The Foucault pendulum is among the interesting things you can think of in this context. In the year 1851, the French physicist
Jean Bernard Léon Foucault demonstrated the earth’s rotation with respect to the absolute space through a long and heavy pendulum that bears his name. The basic idea is that, if you allow such a pendulum to oscillate the plane of oscillation keeps on rotating, thus betraying the fact that earth is rotating with respect to the absolute space !

O.K,in one sentence Newton’s argument is this-The absolute space is such a thing that if you accelerate with respect to it, then you feel a force. And as is easily demonstrated, such a thing does exist.

This argument for existence of absolute space stood the test of many centuries. Not everyone was happy with it, but it worked. And theories of physics achieve immortality not through a scripture but through the fact they work where they are supposed to. And, Newton’s theory worked not because it was written down by Newton, but because Newton could rightly decipher the rules that nature played by. Newton was gone, days passed, days became years, years became centuries.

Until one fine day, Einstein stared at the definition Newton gave The absolute space is such a thing that if you accelerate with respect to it, then you feel a force. And muttered- well, that looks like the definition of a gravitational field …! Ahem ! The birth of general relativity !

” So the principles which are set forth in this treatise will, when taken up by thoughtful minds, lead to many another more remarkable result; and it is to be believed that it will be so on account of the nobility of the subject, which is superior to any other in nature.”
GALILEO GALILEI

(Continued here)

Bibliography

1
Thanks to Eigenspace and its editors Shanth and Akash for giving me this opportunity and thanks to all those juniors (especially Karan and Charu) who inspired this article. I truly owe my understanding in relativity(whatever little that is there) to discussions with my juniors!
2
The whole text of Newton’s scholium can be found here.

One Response to “To Frame My Frame…(Frame I : Newton) – 3. The Scholium”

  1. nayagam Says:

    Carlo Rovelli explains it better in an article titled Quantum spacetime:What do we know?

    Descartes .. gave a fully relational definition of localization (space) and motion.. According to Descartes, there is no “empty space?. There are only objects, and it makes sense to say that an object A is contiguous to an object B. The “location? of an object A is the set of the objects to which A is contiguous. “Motion? is change in location. That is, when we say that A moves we mean that A goes from the contiguity of an object B to the contiguity of an object C . A consequence of this relationalism is that there is no meaning in saying “A moves?, except if we specify with respect to which other objects (B, C,… ) it is moving. Thus, there is no “absolute? motion. This is the same definition of space, location, and motion, that we find in Aristotle.

    In the footnote, he writes

    Aristotle insists on this point, using the example of the river that moves with respect to the ground, in which there is a boat that moves with respect to the water, on which there is a man that walks with respect to the boat . . . . Aristotle’s relationalism is tempered by the fact that there is, after all, a preferred set of objects that we can use as universal reference: the Earth at the center of the universe, the celestial spheres, the fixed stars. Thus, we can say, if we desire so, that something is moving “in absolute terms?, if it moves with respect to the Earth. Of course, there are two preferred frames in ancient cosmology: the one of the Earth and the one of the fixed stars; the two rotates with respect to each other. It is interesting to notice that the thinkers of the middle ages did not miss this point, and discussed whether we
    can say that the stars rotate around the Earth, rather than being the Earth that rotates under the fixed stars. Buridan concluded that, on ground of reason, in no way one view is more defensible than the other. For Descartes, who writes, of course, after the great Copernican divide, the Earth is not anymore the center of the Universe and cannot offer a naturally preferred definition of stillness. According to malignants, Descartes, fearing the Church and scared by what happened to Galileo’s stubborn defense of the idea that “the Earth moves?, resorted to relationalism, in Le Monde, precisely to be able to hold Copernicanism without having to commit himself to the absolute motion of the Earth!

    Further

    Relationalism, namely the idea that motion can be defined only in relation to other objects, should not be confused with Galilean relativity. Galilean relativity is the statement that “rectilinear uniform motion? is a priori indistinguishable from stasis. Namely that velocity (but just velocity!), is relative to other bodies. Relationalism holds that any motion (however zigzagging) is a priori indistinguishable from stasis. The very formulation of Galilean relativity requires a nonrelational definition of motion (“rectilinear and uniform? with respect to what?).

    Newton took a fully different course. He devotes much energy to criticise Descartes’ relationalism, and to introduce a different view. According to him, space exists. It exists even if there are no bodies in it. Location of an object is the part of space that the object occupies. Motion is change of location. Thus, we can say whether an object moves or not, irrespectively from surrounding objects.Newton argues that the notion of absolute motion is necessary for constructing mechanics. His famous discussion of the experiment of the rotating bucket in the Principia is one of the arguments to prove that motion is absolute.

    This point has often raised confusion because one of the corollaries of Newtonian mechanics is that there is no detectable preferred referential frame. Therefore the notion of absolute velocity is, actually, meaningless, in Newtonian mechanics. The important point, however, is that in Newtonian mechanics velocity is relative, but any other feature of motion is not relative: it is absolute. In particular, acceleration is absolute. It is acceleration that Newton needs to construct his mechanics; it is acceleration that the bucket experiment is supposed to prove to be absolute, against Descartes. In a sense, Newton overdid a bit, introducing the notion of absolute position and velocity (perhaps even just for explanatory purposes?). Many people have later criticised Newton for his unnecessary use of absolute position. But this is irrelevant for the present discussion. The important point here is that Newtonian mechanics requires absolute acceleration, against Aristotle and against Descartes.Precisely the same does special relativistic mechanics.

    and

    Similarly, Newton introduce[s] absolute time. Newtonian space and time or, in modern terms, space-time, are like a stage over which the action of physics takes place, the various dynamical entities being the actors.

    The key feature of this stage, Newtonian spacetime, is its metrical structure. Curves have length,
    surfaces have area, regions of spacetime have volume. Spacetime points are at fixed distance the one
    from the other. Revealing, or measuring, this distance, is very simple. It is sufficient to take a rod and
    put it between two points. Any two points which are one rod apart are at the same distance. ….. If a particle deviates with respect to this straight line, it is, according to Newton, accelerating. It is not accelerating with respect to this or that dynamical
    object: it is accelerating in absolute terms.


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