The crux of space-time is that it is one thing to have abstract concepts of absolute space & time,and it is other thing to describe the actual motion of an object in terms of measured changes of position during measured intervals of time.

Perhaps Newton understood this very well; in the Principia, he remarks

But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them... And so, instead of absolute places and motions, we use relative ones.

Now, what did Newton mean by this statement? What space cannot be seen? What is sensible measure? Please help me in understanding the bold phrases.


closed as off-topic by bobie, ACuriousMind, Rob Jeffries, Kyle Kanos, Danu Jan 3 '15 at 15:10

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In the beginning of the Principia, Newton is making a philosophical argument in favor of the existence of absolute space (and time). He is trying to make the case for their existence in the abstract, but he is also an empirical scientist and so is concerned with how we can actually analyze such abstract ideas.

Backing up a bit, the ontological status of absolute space was a major point of contention between Newton and Leibniz.1 The latter held the position that all that really existed in the universe were objects and distances between them. Assigning Cartesian coordinates to all objects such that the Euclidean distances between coordinates matched the associated distances between objects (this would be an embedding in modern mathematical parlance) was a convenience, but it didn't require believing that that Cartesian grid existed in some fundamental way.

Newton disagrees, and in fact the underpinnings of all his mechanics are formulated keeping in mind the notion of absolute space being something real, something more than a mathematical convenience to get the right answer. Consider Newton's preceding paragraph:

As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be moveable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions.

In my own words, I would summarize this argument as follows:

  1. Objects can be spatially ordered; there is a spatial structure to reality. Even Leibniz would probably agree with this.
  2. In order for (1) to hold, objects must have a place in space. One cannot get spatial structure without something like space existing (Leibniz would probably disagree). That is, we conclude space exists.
  3. A place in space (as the location of an object) is naturally located in a place in space (an immutable part of space). Moreover these two notions of place are one in the same. Therefore we conclude space is absolute; there is a fundamental notion of "at rest."

So now Newton feels he has justified his absolute space with abstract reasoning, but he realizes there is an empirically-minded dissenting argument to be made:

  • How can we measure absolute space? If it cannot be measured even in principle, are we so certain it must exist?

Your quote is the beginning of Newton's counterargument to the empirical objection:

But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them.

He proceeds to detail how we can do all empirical science with just relative space, defined relative to some agreed-upon object. That is, we use only the relative distances between objects -- the two ingredients that Leibniz insists are all we have or need -- and we proceed know everything about the system. Newton is assuring the reader that our inability to build a device that returns absolute spatial coordinates is not a hindrance to doing science, even to doing science in his "absolute space really exists" framework. He even admits that

it may be that there is no body really at rest.

1I'll refer to the anti-Newtonian view as though it were entirely Leibniz, since he was Newton's contemporary. In reality, Newton seldom deigned to directly address Leibniz. He actively tried to frame his arguments as overturning the ideas of Descartes. (Cynically, this was the easy thing to do, since Descartes was long dead by then. Less cynically, Newton probably felt his ideas held too much sway, given how flawed they were in certain areas, such as holding circular motion to be as good as linear motion in the law of inertia.) In any event, the Cartesian/Leibnizian philosophy was eventually picked up by Mach, who in turn was the inspiration for Einstein (whose relativity may not be quite so anti-Newtonian in philosophy as he held, ironically enough).

  • $\begingroup$ Nice answer, but from my reading you should replace "Leibniz" with "Descartes". Newton apparently viewed Descartes as his one and only true intellectual rival, and that much of that scholium was a veiled attack on Descartes, not Leibniz. $\endgroup$ – David Hammen Jan 3 '15 at 12:39
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    $\begingroup$ " Newton seldom deigned to directly address Leibniz" , sure, he shrewdly, as usual, did it by proxy, but you are right, his oppositor was Leibniz, who had already buried Descartes' obsolete and untenable ideas. The question, anyway, can be answered in a very simple way. $\endgroup$ – bobie Jan 3 '15 at 13:28
  • $\begingroup$ At the end of the Principia Newton seems to prove that mechanics is relative, after all. He got the correct answer, even though he didn't like it. $\endgroup$ – CuriousOne Jan 3 '15 at 15:19

And so,instead of absolute places and motions,we use relative ones.

I think what Newton meant that he and his co-centuriers couldn't measure distance, time, velocity using some kind of absolute units. Only thing they had relative units.

But now, we can measure time and distance.

Second is the duration of $9192631770$ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the $\ce{Cs}-133$ atom.

And meter is $1/299792458$ of $1$ light second.