Its taken as granted that physical law does not vary in space and time; everywhere and at everytime it is the same.

When was this properly suggested? My first inclination would be Newtons physical presupositions on time and space; I don't recall seeing such an observation being made in say Aristotles Physics.

But is there some reason why we can take this to be the case? Kant for example gave an a priori rationale for Newtons third law - the law of action and reaction.

Can something similar be suggested for the homogeneity of space and time?


A possible suggestion is that if physical law varied here from there; then one could according to Aristotles principle of sufficient reason concievably ask for the reason for this variation, this difference; and this reason once posited then dissolves this difference; and so on ad infinitum gives physical law homogenous in space; and similarly for time.

I'm not aware of such an argument being made; but I'm not particularly well versed in the literature on the metaphysics of space and time; has such an argument along these lines been posited, or denied?

  • The answers are good, so I'm putting this in a comment: it is reasonable for one to be interested in laws which are true "everywhere." The fact that the ones known as "physical laws" happened to appear true everywhere may be seen as just happenstance. – Cort Ammon Aug 15 '15 at 3:18

It was Galileo who first seriously suggested we remove the distinction created by Aristotle between two realms with distinctly different physics.

In "... The Two Chief World Systems ...", he introduces the notion of the inertial frame of reference, as experienced on a boat, as the normal compromise between the stationary and the moving, and suggests reasoning about the heavens as large moving objects more like boats, and less in an idealized a priori way.

Newton had already a century or so of other thinkers inspired by Galileo before he proposed a single unifying law in a mathematical form that would explain both equally well. This included Kepler, who solved the primary problem Galileo's astronomy introduced -- that circular orbits do not capture most of the subtleties of planetary motion, but elliptical ones do.

Newton has to have been moved by the quadratic nature of Kepler's astronomical geometry, and Galileo's knowledge that gravity on earth was quadratic. (The rule is captured in the book in terms of Fibonacci numbers, but that breaks down straight into squares.) So our tendency to think this was just single act of genius and not an integration of scientific details, is kind of overstated. In fact, if Hooke is not lying, both of them computed the same position of a comet based on Kepler, by fitting it to a conic section, before Newton's work was published.

In the text, Galileo does not seem to employ the principle of sufficient reason per se, but he relies strongly on the idea that needless variation, especially when it must be extreme, is an indication of a poor argument. For instance, if the stars move on the spheres, some spheres spin at different rates than others to achieve the apparently consistent motion of the skies on Earth, the farthest spheres must turn quite quickly, whereas if the Earth spins, then stars at all different distances from us just move at some fairly consistent speed.

(He also continually points out that Aristotle himself would not put up with the level of authority assigned by everyone to Aristotle himself. So he may have wanted to avoid dependency on other a priori notions in Aristotle on the modern side of his argument.)

Whitehead in "Science and the Modern World" seems to think that from Thales on, almost everyone presumed that physical laws were uniform throughout the universe. He thinks that this notion of trustworthy uniformity is somewhat characteristic of the West, reflected in Greek drama and Roman Law, and is a sort of shared para-religious impulse behind the nature of our science.

That makes Plato's and Aristotle's notion of two separate realms kind of an aberration, that was eventually ironed out.

  • Aristotle mentions the positions held by many other philosophers, occasionally held by name; generally when I mention Aristotle as an authority its really as an umbrella term for the discussions of physical phenomena in antiquity; what you say by Whitehead is interesting - and is what I'm aiming to try and uncover with this question. – Mozibur Ullah Aug 15 '15 at 15:15
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    Whitehead also thinks that this faith flows from faith in a past time when things were stable, peaceful, and egalitarian. He mentions the period after the Fall of Rome, when we installed a false 'memory' of the Pax Romana. But early on, referenced in the Bible in Daniel, and in Plato, and played out in the rituals of Saturnalia, and even the myth of Cincinnatus we 'remembered' a 'Golden Age' when everyone was a prosperous independent farmer and no one needed rulers. So we have often wished a 'return' to stability and independence with a dash of uniformity in a way others may not have. – user9166 Aug 16 '15 at 18:39

It was Aristotle who first made the qualitative difference between the physics of the sublunary region and the outer region of the aether. The sublunary region was the domain of the four elements, each having its canonical position. While the aether region hosts the stars and the planets with their circular movements.

But Newton discovered that the same natural law of gravitation explains the free fall on earth and the movement of the planets. The same natural laws hold true in both Aristotelian regions. That was a breakthrough on the way to unify natural laws on a cosmic scale.

Concerning time dependence: Some decades ago a serious discussion was initiated by Pascual Jordan, whether the gravitation constant changes on a cosmic time scale. But the general heuristics today is to formulate natural laws which do not contain time in an explicit way.

Nevertheless, the time-independent value of the fundamental constants raises the question why they have their distinguished value. In the context of multiversum speculations also universa with a different value of these constants are taken into consideration.


First you say that it is taken for granted that the physical laws do not vary in space and time. I think you first need to separate these two from each other. Many prominent scientists have said that although they agree with the statement that the physical laws are the same throughout space, there is no evidence that they remain the same throughout time. In fact, some have said that they would be surprised if they did remain the same.

Second you need to go pre-Aristotle for the universality of physical laws. The homogeneity of the physical laws has a long history. In his book Time Reborn: From the Crisis in Physics to the Future of the Universe, the author, Lee Smolin, states (Chapter 8: The Cosmological Fallacy):

...the pre-Socratic philosopher Anaximander (610-546 BC). As described in a recent book by Carlo Rovelli, Anaximander was the first to seek the causes of natural phenomena in nature itself rather than in the capricious will of the gods...The entire universe, as they understood it, was organized by the presence of a special direction--down, the direction in which things fall...If everything not fixed to the sky falls down, why doesn't the earth itself fall?...the earth must have something under it, holding it up...a turtle...Anaximander realized that a conceptual revolution was needed to make a successful theory of the universe that avoided the reductio ad absurdum of an infinite tower of turtles. He proposed an idea obvious to us but shocking in its time--that "down" is not a universal direction but simply the direction towards the Earth...Anaximander's revolution was arguably greater than Copernicus's, because his redefinition of "down" rendered moot the need to explain what held the Earth up.

The philosophers who sought to understand what holds the Earth up were making a simple mistake--taking a law that holds locally and applying it to the whole universe...but the same mistake underlies much of the confusion of current cosmological speculation. And yet nothing seems more natural, for if a law is universal, why shouldn't it apply to the universe? It remains a great temptation to take a law or principle we can successfully apply to all the world's subsystems and apply it to the universe as a whole. To do so is to commit a fallacy I will call the cosmological fallacy.

The universe is an entity different in kind form any of its parts. Nor is it simply the sum of its parts. In physics, all properties of objects in the universe are understood in terms of relationships or interactions with other objects. But the universe is the sum of all those relations and, as such, cannot have properties defined by relations to another, similar entity.

Thus the Earth is, in Anaximander's universe, the one thing that doesn't fall, because it is the thing that objects fall to. Similarly, our universe is the one thing that cannot be caused by or explained by something external to it, because it is the sum of all causes.

...If the analogy of the present period to the ancient Greek science is apt, there will be paradoxes and unanswerable questions that follow from the act of extending small-scale laws to the universe as a whole. There are both. We, in our time, are led by our faith in the Newtonian paradigm to two simple questions that no theory based on that paradigm will ever be able to answer:

Why these laws?...

...Why these particular conditions?...

The Newtonian paradigm cannot even begin to answer these two enormous questions, because the laws and initial conditions are inputs to it. If physics ultimately is formulated within the Newtonian paradigm, these questions will remain mysteries forever.

...To apply a law of nature without approximation we must apply it to the whole universe. But there is only one universe--and one case does not yield sufficient evidence to justify the claim that a particular law of nature applies. This might be called the cosmological dilemma.

The cosmological dilemma need not prevent us from applying laws of nature--like general relativity, or Newton's laws of motion--to subsystems of the universe. They work in virtually all cases, and this is why we call them laws. But each such application is an approximation based on the fiction of treating a subsystem of the universe as it it were all there is.

The author then goes on to posit that the reality of time can make for a true cosmological theory. Very interesting book.

  • I realise that Smolin holds that physical law varying with time might be one key direction to look for new theories - there are theories in which c the speed of light varies with time giving an alternative solution to some of the problems solved by inflation; suppose such a theory is successful and is applied by many people in many different directions; one can still ask the question afterwards: why this variation? – Mozibur Ullah Aug 15 '15 at 15:05
  • Its taking this question to ad infinitum shows that possibly physical law at bottom must be a kind of constant in time and space; still I realise this is all very speculative. Great to see Anaximander quoted. – Mozibur Ullah Aug 15 '15 at 15:09
  • interestingly Rovelli wrote a serious paper exploring Aristotelian physics. – Mozibur Ullah Aug 16 '15 at 13:01
  • If the laws of physics vary over time, then their dynamics certainly can be described or explained by "deeper" level laws of physics, that don't vary over time (unless you believe in such transfinite induction). Thus, the varying over time laws of physics are not the "true" laws (if one can say). – sure Aug 22 '15 at 9:16

This is a manifestation of the Copernican principle: our place in the universe is not special, by extension no place is special, as some would if the laws of nature varied. It applies to fundamental laws only, and is a methodological principle, a "regulative idea" in Kant's terms, or what Poincare called a "convention" maintained "come what may", if a law is discovered to vary we revise it, and no longer call the original one fundamental.

So the principle does not apply to any law individually, all of them are subject to empirical revision. The Hubble constant was fundamental when it was thought that the universe is expanding at a constant rate, now that we know it is accelerating dark energy was introduced and the rate varies in time and possibly in space, if the distribution of dark matter is uneven. Euclidean geometry was universal in Newton's absolute space, now we hold that it is not around massive stars where space gets bent, and have far more nuanced laws of general relativity. This is how it works: if a fundamental law is discovered to vary a varying parameter is introduced (dark energy distribution, spacetime metric), and the abstracted template becomes a new universal law.

It is not hard to give a Kantian argument for homogeneity as a condition of the possibility of a unified knowledge of nature, but one should not overestimate the absoluteness of such principles as Kant did. While they may be a priori relative to empirical laws, they too are ultimately empirical and revisable under the weight of evidence accumulated over long time. Friedman worked out a theory of such evolving relativized a priori in Dynamics of Reason based on the ideas of Marburg neo-Kantians, logical positivists Reichenbach and Carnap, and Kuhn.

A game changing what may come after all. The Pythagorean principle of uniform circular motions was maintained come what may for two thousand years, even by Copernicus, until it wasn't by Kepler. Poincare thought that Euclidean geometry would stay in place come what may just a few years before general relativity. A generalization of the Copernican principle which maintained that not only no place but also no time is special (it was used to argue for steady state models of the universe expansion until 1960s) has already been rejected by the Big Bang cosmology. Today the "drift of the fundamental constants" in time is viewed as an empirical issue. If in a distant future we encounter multiple parts of the universe where the laws work differently from ours and each other the Copernican principle will be rejected as well.

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