Why should a (physical) principle be applicable to different systems in different positions in space and time?

Question

This is a question with a philosophical, as well as physical, flavor.

Why should a physical principle (or a description of one), be applicable to different systems that can be in different positions in space and time?

In other words why should there be such (modulo) equivalence classes (with respect to a physical principle)? Why not a "custom (physical) principle per case"?

Let me give one simple example. Newton's laws are applicable to my desk, to my table, to your desk, to your table and to someone's table, say 1 year from now (or 1 year ago).

Why is this? Why should the same principle be aplicable to such different systems (different in the sense stated above)?

Anyone know how to approach such a question?

Note in order to avoid misunderstandings:

regardless of the tags of this question, this is not specifically about covariance, the tag was used, by an editor, because the original tag laws-of-physics was removed for other reasons

Answer 1

I think there are two answers to this, one emprical and one theoretical.

First, the theoretical one: What you describe is essentially induction, the belief that we can generalize from a subset of a class events/situations to the whole class of events/situations. This belief is, by necessity, unprovable, only falsifiable, since proving it would require looking at all situations that there are, which is obviously impossible. But without the belief in induction, all we do is describe what we have seen happening in the past or elsewhere. What would be the use of a theory that makes no predictions? What would be the use of formalizing only that which we have already observed? There is nothing to be gained by only describing what has happened - for science to be useful, we must believe that induction is a valid mode of argumentation, so we can build machines that work by the principles we have induced, so that we can try to bring order into the world of observations where previously was none. However, be the very same logic, we must also keep in mind that nothing except constant and diligent testing of our predictions protects us from inducing things that are simply not true.

Now, the empirical one, more specialized to your question about time translation and symmetries: Because that is the way the world works, every single time. All our first principles, all our axioms are lastly only validated by observations. And what would be a better axiom than something which is so manifestly true in the world: Machines don't care whether they are here or 100km away, they work the same. Stones fall the same way now as they did in my youth. And so on, and so forth. There are so many things that are so evidently, by our everyday experience, invariant under such transformations that it is the most natural things to take this as a starting point of our theories. In other world, we generalize the observations we have made and make them a general principle. Induction as described above.

You may be disappointed by such an approach. You may protest, "But you haven't told me why!" And that is true. Because at some point or another, the question "Why?" becomes so meaningless that the only possible answer is "Because.". What possible answer could you conceive of that you would not be tempted to ask again "Why?"? The question "Why?" turns everything into a Matroshka of reasoning, into an infinite onion of more and deeper explanations. We always seek the most beautiful set of axioms, the most comprehensive explanations, but at their very core, when you ask "Why is this true?" the only possible answer can be "Because the world works that way.".

Answer 2

There is no reason why physical laws should be absolute. But observation tells us they are. If you think about it, if the laws of the universe did change from place to place or if they were different at different times, there would be no laws, and there would be no science.

Answer 3

Let me try a more down to earth example: Let's say I formulate a law "I can kick with my leg in front of me without getting hurt." This law is indeed true in many cases, but in some cases it is not because there is a wall right in front of me and my leg kinda hurts after kicking. That is, the world is not everywhere the same.

Say I come to the same place in fifty years after the wall has been torn down and try to kick in front of me - I do not get hurt. So I can surely say that the world isn't everytime the same.

Thus, the same action at different places and different times gives different results. So what the heck are these physical laws saying that the world is the same everywhere and everytime? That's the funny thing, this is how fundamental physical laws are defined and formulated - as the stuff that applies at any time and at any place. If it does not apply the same at different points of space and time, it is not considered a physical law.

That is, we postulate that such a thing as physical laws does exist and then try to find them. We have to rid every situation of what is different and find and document repeating patterns. The difference of every point of space and time is expressed in things such as initial conditions and sources.

If for example tomorrow we found out that the "laws of gravity have changed" or apply differently for different objects, we would not throw away physics, we would say that our previous law was only effective, "local" and seek a deeper law that would describe this change of our local effective law. We could however also postulate a source which affects the phenomena we observe. A case analogous to the latter is the phenomenon of dark matter - we consider it either as an unknown source of gravitation or a consequence of a modified gravitational law.

In fact, this happens all the time throughout the history of science, but mainly through looking at different scales - we found different laws applying to the case of an atom and that of a macroscopic object. We didn't say there are just particular laws, we formulated a unified theory called quantum mechanics.

However, the most amazing thing is that every time so far, we have been able to find such a new law unifying more and more phenomena and have managed to reduce again and again the amount of types of sources and initial conditions (even though bearing more and more specific information about the situation). This is just what we find, there is hardly any explanation to it.

Nevertheless, there are some reservations towards the amazing might of the physical-laws-method. This follows from the fact that from a certain point of accuracy in the microscopic world, we have not managed to find any kind of pattern in the results. Our inability to predict this certain precision of results is reflected by the statistical nature of quantum mechanics and may as well be the final limit to the realm of physical laws.

The last remark is that we would require to somehow explain the sources and initial conditions - why in the end space and time really are different at different points. This is a conundrum mainly discussed in the science trying to encompass the whole of space and time, cosmology. And sincerely, nobody really knows if the scientific method can even in principle answer the questions of the type why the world is the way it is. Nevertheless, we presume the world will in our eyes continue to get organized into more and more wide and entangled patterns by more and more unified theories with more and more particularly arranged sources and configurations.

Answer 4

As the others have said, it's simply true because it is a fundamental axiom upon which we build the the entirety of our physical laws. You can also approach an answer from a different perspective, though: relativity.

In studying special and general relativity, one of the most important (and most difficult) concepts to grasp is that of 4-dimensional spacetime. Not only do you have to accept that space and time are inherently related; you must realize that spacetime is not some overarching, all-powerful entity - spacetime is governed by the laws of physics. In accepting this axiom, it becomes apparent that neither space nor time have the power to change physical laws or principles, rather they are slaves to physics.

Answer 5

Occam's Razor and Observation are the reasons. The properties of the physical laws that you mention are called the Homogeneity and Isometry of Space, and are the two key elements in the Cosmological Principle which merely states that space is the same everywhere, and it doesn't matter which way you go, things will always be the same. This is of course on a large scale, but Cosmologists have reasoned out how this leads to the laws of Physics being the same everywhere. But even though the only way to prove this is to actually go out an measure, why do we typically hold the notion that the laws of Physics are the same everywhere as axiomatic? Simply because it's simple! Complexity is beauty. Occam's Razor states that the hypothesis that should be chosen is the most descriptive with the least moving parts/makes the least assumptions. If we were too take the laws of Physics to be different everywhere, not only would that make gaining evidence for the theory incredibly difficult ( thus harder to (dis)prove ) it opens up even more complex formulations of Physics, which can then in turn be complicated further, especially for a hypothesis like that. It's just a lot easier and faster for us to take the simple hypothesis and gain evidence for or against it's viability.

Answer 6

This is the question of the universal laws of gravitation. I think that may be because we are governed by a set of laws. And going against the nature you cannot set predefined restrictions to the dimensions of space and time. These are in the untraceable aspects of science. Maybe someday you could get a possible mathematical custom principle applied to it.

Answer 7

This is the so called "principle of uniformity". Basically, it stipulates that the laws of physics are the same everywhere in space and time. Now, why should we believe in such principle ? I have thought a bit about that, and here is my reasoning.

Let's define two "types" (in the sense of logic) of "objects". Call pobject, any physical object you can see, touch, or interact with. The existence of pobjects is "concrete" or explicit if you wish. Call structure, the laws governing these pobjects, that is, what constrains them and specifically their change.

A table as we call it (supposely composed of what we call atoms and so on) is of pobject type. Yourself are of pobject type too. Now, the laws of physics (say, the principle of inertia or the second law $F = ma$) are of structural type : any pobjects is constrained by them and in any case we need a pobject to express them and to see something non trivial happening). Basically, a structure is what encodes the potential "change" or the dynamics in the world (the lattice of relations between pobjects), while a pobject is something that effectively changes (that is, interacts with other pobjects) and whose realized (non potential) change is constrained by this structure.

Now, call principle of structure the following : there exists an atemporal and transcending structure that constraints pobjects and their interactions in order to make the world a consistent place.

The question is, why should we believe in such principle of structure ? Because the world is a consistent place, and it appears that there are laws constraining and governing it.

Now supposing we believe in such principle, can we show that the principle of uniformity (laws of physics are the same at any places and at any times) is credible ?

Quite simply, yes. If the principle of uniformity is true, then there exists a structure that is realized in the whole universe and that constraints all pobjects inside it. In particular, if the laws of physics we found have a dynamics, then by the principle of structure, there must exists some structure governing this dynamics that can now be seen as a pboject, the primer being atemporal. Thus, unless you believe that there exists a transfinite recursion (that is, each structure we find in nature is dynamical and governed by another dynamical structure up to infinity), there must exists a rank where this hierarchy stops, and hence, principle of uniformity holds.