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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

Nikos M.
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    I would like to refer you to The Character of Physical Law by Richard Feynman. http://en.wikipedia.org/wiki/The_Character_of_Physical_Law . There he raises the questions that you pose, (and succeeds in answering, in mu opinion) and some relevant ones which stem from those as well. – Boluc Papuccuoglu Jul 07 '14 at 19:28
  • @BolucPapuccuoglu, yes Feynman has made several remarks about areas of science with a cutting edge clarity, i have already read the passage (as well as several of Feynman's lectures and his biography). i would like this question to investigate this topic a little more (or a little differently if you like) – Nikos M. Jul 07 '14 at 22:44
  • @BolucPapuccuoglu, of course if you want to post this as an answer (maybe adding your own elaboration as well), you are certainly welcome to so so – Nikos M. Jul 07 '14 at 22:46
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    The things that aren't so broadly applicable don't get called physical principles. – user2357112 Jul 08 '14 at 01:58
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    It seems to work fine so far – PlasmaHH Jul 08 '14 at 10:30
  • Why should the same principle be aplicable to such different systems (different in the sense stated above)? I don't this systems are different with respect to e.g. Newton laws. This laws deals with forces acting on mass. The mass is same, as the forces are. – jnovacho Jul 08 '14 at 12:50

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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.".

ACuriousMind
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  • i am not disapointed, you actually gave an answer, in the sense that this is a datum (if i may use this term), although i think the part on induction is a bit irrelevant, one can still believe in universal induction even with a custom principle per case – Nikos M. Jul 07 '14 at 17:28
  • @Nikos M.: Correct, you can believe in induction then, but then it would be pretty meaningless, wouldn't it? If the set of events any custom principle can be generalized to consists of exactly one element, then induction is a trivial step. It adds nothing (which would make it vacuously true, so you would actually be right by believing in it). – ACuriousMind Jul 07 '14 at 17:33
  • yes correct, even thougb the same arguments can be made that one cannot test all cases, so it can be a belief (even meaningless). i was hoping for an answer that tried to derive this from some other principle, but the answer you gave is a valid one, will wait a bit longer – Nikos M. Jul 07 '14 at 17:35
  • I think your last paragraph is stating Godel's Incompleteness Theorem. Reading about that may provide more interesting information about this. – Wutaz Jul 07 '14 at 18:05
  • @Wutaz: I don't think so. I am simply stating that there must be axioms, which are only by definition (motivated by experience), not by deduction true. Gödel's Theorem states that every axiomatic system is either inconsistent or has statements which are true within it (i.e. they are implied in the sense of logic by the axioms), but which are not provable (i.e. I can state the statement in the language of the axioms, and I can test it for every case, but I cannot show that it is true). It is an interesting area of mathematics, but it doesn't say anything like what I said. – ACuriousMind Jul 07 '14 at 18:12
  • 'at some point or another, the question "Why?" becomes so meaningless that the only possible answer is "Because."'. That is saying that some part of the system can't be proven from within the system. Did you not notice that I referred to your last paragraph at the exclusion of the others? – Wutaz Jul 07 '14 at 18:18
  • @Wutaz: I noticed that, but with "Why?" becoming meaningless I mean that it essentially asks "Why are the axioms true?". And for any axiomatic system, the answer is: "Because." The Gödel sentence, which is the unprovable statement, is essentially impossible to sensibly construct (yet Gödel did it), it is very vaguely of the form "Statement Nr. 123 is unprovable" when it itself has been given the number 123. It seems very unlikely to me that we should ever encounter an actual Gödel sentence in the course of our thinking about the world (I could be wrong, of course). – ACuriousMind Jul 07 '14 at 18:27
  • @ACuriousMind Say you construct a machine which depends on a specific frequency of a pendulum and transport it on the Moon. It would work differently there. Say you would construct your machine at the position of the Earth after the Sun went supernova, it would again not work the same. Say it didn't have this pendulum dependence, then it would work differently in the middle of a volcano etc etc. In this sense, you assume physical laws singling out equivalent situations of the machine beforehand and thus find the empirical confirmation automatically. – Void Jul 07 '14 at 18:56
  • @Void: You have to take the talk of "they work the same" with a grain of salt. The "the same" is meant in the same sense in which "time translation invariance" is meant in physics - of course things won't behave the same in a billion years from now in this exact spot, but, extropolating from all that we now, they will happen by the same laws. Your point that the physical laws single out, in a sense, the situations they apply to is quite valid though. If one uses induction, one must specify onto which larger set one induces. We naturally choose the set on which induction will be valid ;) – ACuriousMind Jul 07 '14 at 20:45
  • @ACuriousMind: The point is - we dissociate the observed facts into elements which are universal and those which are particular. Universal are usually called laws and are agreed upon until in need of revision. We find violations of induction and resolve by postulating new laws and identifying the particularity of our last situation. Stating that "universal laws apply" is tautological after we have successfully organized observed reality into particular configurations and laws. "Empirical confirmation" of the scientific method is in the fact that we are successful in such an organization. – Void Jul 07 '14 at 21:29
  • @ACuriousMind I.e. the particular configuration would be "the machine isn't in lava" but the law would be "the machine works when not in lava". – Void Jul 07 '14 at 21:32
  • @Void: I could quibble with your lava example, but in general I think you are right (and I am not certain if you think we disagree). We indeed commit ourselves to a tautology of some kind since we say "We apply the laws to the cases where they apply". The marvel of nature is now that the cases where they apply is indeed far greater than the cases which we observe. Induction works, but it is beyond our reach to ever ask why. – ACuriousMind Jul 07 '14 at 21:36
  • Let us continue this discussion in chat. – Void Jul 07 '14 at 21:41
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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.

PhotonBoom
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  • yes i see your point, althougn i think it kind of reverses the question. you say there is no reason, and then you use an epistemic reason, that this is needed for science. i wont disagree although it reminds me of some kind of anthropic principle – Nikos M. Jul 07 '14 at 17:31
  • Well just remember that science explains what happens and not why something happens. – PhotonBoom Jul 07 '14 at 17:51
  • hmm i wont agree with that, there are various levels of why,how,what that are actually answered by science. if you imply that this why (refering to the question) is not in this set, maybe – Nikos M. Jul 07 '14 at 17:56
  • You are right that is what I was trying to say. Its the fundamental whys (like this one I believe) that have no answer (yet) – PhotonBoom Jul 07 '14 at 18:02
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    This answer is correct. We assume that the principle in question holds because this agrees with observation. Furthermore, science would be useless if we did not use it as a starting point for our theories unless there is an underlying framework for describing the dependence on position. – Frederic Brünner Jul 08 '14 at 10:47
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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.

Void
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  • i think i understand where you getting. one note: the question (and physics in general) does not imply that exactly the same "laws" hold in all time and space (if you notice i talk about equivalence classes) and this is the point that the equivalence classes are not singleton sets but actually contain more elements (in various points in space and time etc..) although not necesarily all the points of space/time and all that jazz :). on the other hand i understand you take this to be an irreducible question (related to very deep aspects of cosmology etc..), valid point – Nikos M. Jul 07 '14 at 23:00
  • among other answers (valid nevertheless from various points of view). i will select this one, which in a sense summarizes many of the other answers. (ps i also have an answer to this question, but this is about other answers not mine) – Nikos M. Jul 08 '14 at 15:21
  • Yes, it can be reformulated as equivalence. But slicing up observed evidence into uncountable sets of equivalence classes based on particulars (sources, configurations...) is not trivial and we cannot really assume we can do that beforehand. A violation of this slicing up is quantum mechanics, where some of the most brilliant minds of physics have failed to find particulars (the buzzword would be "hidden variables") describing the difference of observationally (real-physically) inequivalent situations. I.e. there seems to be a "different law" describing the result of every quantum experiment. – Void Jul 08 '14 at 18:32
  • Why I mention cosmology is because of the question of the "First Mover", should we start to refer to some classics. That is, why this configuration of particulars, why homogeneous etc. etc. And this chain never ends, just may join up some threads into a more and more entangled pattern. And then questions like why these laws spring up. This is what I mention in the last paragraph. The second thing is - we truncate situations into separate, but this is also non-trivial, every complete theory should not truncate and then you have only one complete situation - the universe. No equivalence class. – Void Jul 08 '14 at 18:41
  • i will disagree on the comment about QM though, although i understand what is meant, one can easily express the theory in a way that meets the criteria of the question (for example, stationary probabilities, averages etc..) – Nikos M. Jul 08 '14 at 19:58
  • So in a Stern-Gerlach experiment with a coherent beam of particles with spin perpendicular to that of the orientation of the magnet, we let just one particle go through (or a few, one is just to make the argumentation clear). We repeat the physically equivalent situation, we get a completely opposite result. The situations are equivalent as to physical classification but bring different observation. In this sense, physics fails to be a universal law applying in every situation but only as a constraint spread out over situations. That is, there seem to be no universal laws in the strong sense. – Void Jul 09 '14 at 08:53
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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.

Hausdorf
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  • good, i have 2 points to make, 1st (if i understand correctly), your answer takes the why = because thats how it (is observed to) be (i.e it is a datum). 2nd, conserning relativity and covariance, i would say this is a manifestation of the point in question and not necesarily the answer (or why) – Nikos M. Jul 07 '14 at 22:53
  • Yes, Nikos, you are correct. To your second point, I recognize that my answer is basically the same thing as saying "that's just how it is," but it uses a hierarchical approach rather than a purely observational one: space and time don't affect physics not just because that's what happened in literally every experiment ever, but because space and time also follow the set of rules that is physics, so it doesn't make sense that physics would change in either space or time. Not quite concrete, but I think it's higher-level than citing the evidence alone. – Hausdorf Jul 07 '14 at 23:12
  • ok, the question uses the terms "space and time", and the answer (following GR) takes these as (lets say) derived (or secondary) concepts (derived from some "fundamental laws"), thus it is kind of expected result that sth like this can hold. although i dont use the terms "space/time" in a strictly relativistic sense, yet it is a nice point and interesting – Nikos M. Jul 07 '14 at 23:17
  • I wouldn't say space or time are derived concepts. I would put them in the same class as matter (whatever you would classify matter as) - space and time have properties which make up fundamental laws (position, time, like mass), but they aren't derived from anything. – Hausdorf Jul 07 '14 at 23:36
  • ok, my fault, nevertheless there are formulations of quantum gravity which actually take this route (i.e the whole space-time, which btw i did not use in the question, is a derived or constructed concept etc..) – Nikos M. Jul 07 '14 at 23:50
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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.

Doryan Miller
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  • i like the connection with properties of space (like homogeneity and isotropy), although in a strict sense these do hold for specific systems (that have translational and/or rotational symmetry), but one may generalise a bit. i think though the question is a bit more general than the isotropy of space, one can presumably think of another principle that is not related to this (it was meant as a simple example in the question). The main point is why modulo equivalence classes of systems – Nikos M. Jul 08 '14 at 12:24
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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.

Sanat
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  • i dont think i follow your answer, can you explain it a little more, im not sure i understand (or mis-understand) – Nikos M. Jul 07 '14 at 17:39
  • "I think that may be because we are governed by a set of laws", this is a re-phrasing of the question, of course if that is what you want to give as answer, it is up to you – Nikos M. Jul 07 '14 at 17:48
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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.

sure
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  • Seems to me that pobjects and structure are unnecessary to the conclusion that the laws of physics are everywhere the same--possibly even superfluous. – Kyle Kanos Dec 16 '14 at 14:46