I vaguely remember years ago, in SSSF, suggesting that “laws of physics” might just be logically necessary artifacts of the attempt to construct empirically accurate models that are logically self-consistent. In other words, they’re not physically “real” constraints at work in the world, but logical constraints at work in a particular disciplined approach to describing that world, the approach of science. I seem to remember applying this thinking specifically to conservation laws, but the idea being poo-pooed by SSSF physicists.

Now I’ve discovered that a 20th century mathematician, Emmy Noether, actually devised a theorem that seems to say much the same thing, at least as described (non-mathematically) by Victor Stenger in his “God & the Multiverse”. To quote him:

>In 1915 Noether published a theorem that completely transformed our philosophical understanding of the nature of physical law. Until I learned about it, I always thought, as most scientists still do, that the laws of physics are restrictions on the behaviour of matter that are somehow built into the structure of the universe. Although she did not put it in those terms, Noether showed otherwise. Noether proved that for every continuous space-time symmetry there exists a conservation principle.

Three conservation principles form the foundational laws of physics: conservation of energy, conservation of linear momentum, and conservation of angular momentum. Noether showed that conservation of energy follows from time-translation symmetry; conservation of linear momentum follows from space-translation symmetry; and conservation of angular momentum follows from space-rotation symmetry.

What this means in practice is that when a physicist makes a model that does not depend on any particular time, that is, one designed to work whether it is today, yesterday, 13 billion years ago, or 13 billion years in the future, that model automatically contains conservation of energy. The physicist has no choice in the matter. If he tried to put violation of energy conservation into the model, it would be logically inconsistent.

If another physicist makes a model that does not depend on any particular place in space, that is, one designed to work whether it is in Oxford, Timbuktu, on Pluto, or on the recently discovered galaxy MACS0647-JD that is 13.3 billion light years away, that model automatically contains conservation of linear momentum. The physicist, once again, has no choice in the matter. If she tried to put violation of linear momentum conservation into the model, it would be logically inconsistent.

Similarly, any model that is designed to work with an arbitrary orientation of a coordinate system, to work whether “up” is defined in Iceland or Tasmania, must necessarily contain conservation of angular momentum.

Since these three principles form the basis of classical mechanics, it can be said that they are not “laws” that govern the behavior of matter. Rather, they are human artifacts that follow from symmetry principles that govern the behaviour of physicists, forced on them if they want to describe the world objectively. There is no reason to think that the laws of physics are the construction of an extraphysical lawgiver.<

…He’ll go into a deeper discussion of the philosophical implications of this notion later in the book, but I thought it was worth mentioning at this stage, for those like me who hadn’t previously heard of Emmy Noether and her theorem :)

You know, I’m almost certain that Noether’s Theorem would have been part of the physicist pooh-poohing. ;-)

How much of the symmetry is a human construct is the question…

That’s a nicely phrased explanation of the implications of Noether’s theorem, the best I’ve seen

From my work on fluid mechanics, I’ve been aware for many decades that the law of conservation of angular momentum can be derived directly from the equations of the law of conservation of momentum. Later, looking at General Relativity, the conservation of mass-energy and the law of conservation of momentum both come out of the same equation del dot T = 0, where T is the stress energy tensor. In GR, the time dimension gives conservation of energy and the three space dimensions together give conservation of momentum. Noether’s theorem gives us a deeper understanding of both relationships.

MartinB said:

How much of the symmetry is a human construct is the question…

Well, the suggestion here: “Rather, they are human artifacts that follow from symmetry principles that govern the behaviour of physicists, forced on them if they want to describe the world objectively”…is that the symmetries arise as a result of the physicists’ desire to construct models that are objective, rather than constituting the point of view of one particular observer. If such models “work”, this presumably implies there are no inexplicable fundamental laws that need to be taken into account (which may ultimately mean there are no “fundamental laws” at all, merely the logical requirements of a physics that is able to demonstrate that fact).

Indeed that can be suggested but it remains to be demonstrated… (Although maybe it can’t be.)

KJW was certainly of the opinion that indeed it was the symmetries that are most fundamental and that the actual content of physical law (whatever that means) flows from them, which is similar to that suggestion.

Bubblecar said:

I vaguely remember years ago, in SSSF, suggesting that “laws of physics” might just be logically necessary artifacts of the attempt to construct empirically accurate models that are logically self-consistent. In other words, they’re not physically “real” constraints at work in the world, but logical constraints at work in a particular disciplined approach to describing that world, the approach of science. I seem to remember applying this thinking specifically to conservation laws, but the idea being poo-pooed by SSSF physicists.

Now I’ve discovered that a 20th century mathematician, Emmy Noether, actually devised a theorem that seems to say much the same thing, at least as described (non-mathematically) by Victor Stenger in his “God & the Multiverse”. To quote him:

>In 1915 Noether published a theorem that completely transformed our philosophical understanding of the nature of physical law. Until I learned about it, I always thought, as most scientists still do, that the laws of physics are restrictions on the behaviour of matter that are somehow built into the structure of the universe. Although she did not put it in those terms, Noether showed otherwise. Noether proved that for every continuous space-time symmetry there exists a conservation principle.

Three conservation principles form the foundational laws of physics: conservation of energy, conservation of linear momentum, and conservation of angular momentum. Noether showed that conservation of energy follows from time-translation symmetry; conservation of linear momentum follows from space-translation symmetry; and conservation of angular momentum follows from space-rotation symmetry.

What this means in practice is that when a physicist makes a model that does not depend on any particular time, that is, one designed to work whether it is today, yesterday, 13 billion years ago, or 13 billion years in the future, that model automatically contains conservation of energy. The physicist has no choice in the matter. If he tried to put violation of energy conservation into the model, it would be logically inconsistent.

If another physicist makes a model that does not depend on any particular place in space, that is, one designed to work whether it is in Oxford, Timbuktu, on Pluto, or on the recently discovered galaxy MACS0647-JD that is 13.3 billion light years away, that model automatically contains conservation of linear momentum. The physicist, once again, has no choice in the matter. If she tried to put violation of linear momentum conservation into the model, it would be logically inconsistent.

Similarly, any model that is designed to work with an arbitrary orientation of a coordinate system, to work whether “up” is defined in Iceland or Tasmania, must necessarily contain conservation of angular momentum.

Since these three principles form the basis of classical mechanics, it can be said that they are not “laws” that govern the behavior of matter. Rather, they are human artifacts that follow from symmetry principles that govern the behaviour of physicists, forced on them if they want to describe the world objectively. There is no reason to think that the laws of physics are the construction of an extraphysical lawgiver.<

…He’ll go into a deeper discussion of the philosophical implications of this notion later in the book, but I thought it was worth mentioning at this stage, for those like me who hadn’t previously heard of Emmy Noether and her theorem :)

I’m a little surprised that you hadn’t previously heard of Emmy Noether and her marvellous theorem. I’ve certainly mentioned Noether’s theorem several times, both here and on the old SSSF, (and I think also on Nick’s forum), and I’ve also linked to biographical info on Emmy in various discussions on women in science and mathematics.

I’m fairly sure that Magic Chicken (and possibly Cusp) wrote about Noether’s theorem. And I’m quite certain that various other physics-inclined SSSF posters mentioned Noether’s theorem in various contexts, including Martin B, mollwollfumble, KJW, and MZL.

Note that it’s called a theorem, not a theory. That’s because it’s not “merely” a theory of science, it’s a mathematical theorem, and hence provable.

Essentially, Noether’s theorem says that in a particular class of mathematical structures that can be used to model physics (the Langrangian formulation) the symmetries that arise are mathematical equivalent to conservation laws. So (for example) saying that the equations of a closed system are invariant with respect to a displacement in time is mathematically equivalent to saying that energy is conserved in the system.

But I’m not quite sure what is meant by

Rather, they are human artifacts that follow from symmetry principles that govern the behaviour of physicists, forced on them if they want to describe the world objectively. There is no reason to think that the laws of physics are the construction of an extraphysical lawgiver.

The way I see it is that talking about physical law in terms of symmetries is just an alternate but equivalent description to talking about physical law in terms of conservation principles. So if you want one you must, by mathematical necessity, have the other. But that doesn’t prove that the conservation laws / symmetries are true. FWIW, symmetry seems more physically fundamental than conservation to me, so I prefer to think of conservation laws arising because of symmetry, even though I know they’re mathematically equivalent.

Of course, none of this explains why the observed symmetries / conservation laws are actually physically present. OTOH, I have a hard time imagining a physical universe that didn’t have at least some of the symmetries we’re familiar with. Or should I say, I have a hard time understanding what such a universe would be like and how we’d mathematically model it. :) Eg, it’s hard to see how any kind of regularity could even arise in a universe that didn’t have time symmetry / energy conservation, and it’s hard to do science when you don’t have some kind of regular pattern of phenomena to work with.

Yes I wouldn’t be surprised if Noether & her theorem have been mentioned quite a lot, but my eyes probably glazed over on account of the maths :)

>FWIW, symmetry seems more physically fundamental than conservation to me, so I prefer to think of conservation laws arising because of symmetry, even though I know they’re mathematically equivalent.

Presumably his point is that symmetry doesn’t require an underlying cosmic legislature. He’ll be discussing these things more fully later in the book (I hope. It’s not a great book – seems put together in rather a hurry, and he died before it was actually released – but it’s nonetheless an interesting brief “refresher course” on the history of cosmology leading to the current multiverse ideas).

Bubblecar said:

Yes I wouldn’t be surprised if Noether & her theorem have been mentioned quite a lot, but my eyes probably glazed over on account of the maths :)

Fair enough. However, most mentions of Noether’s theorem on our forums haven’t gone into the gory mathematical details (unless they were posts by KJW…). OTOH, many times Noether’s theorem was invoked when arguing with people who were presenting crackpot stuff that violates conservation of energy, etc, so you may have been avoiding such threads anyway.

Bubblecar said:

>FWIW, symmetry seems more physically fundamental than conservation to me, so I prefer to think of conservation laws arising because of symmetry, even though I know they’re mathematically equivalent.

Presumably his point is that symmetry doesn’t require an underlying cosmic legislature. He’ll be discussing these things more fully later in the book (I hope. It’s not a great book – seems put together in rather a hurry, and he died before it was actually released – but it’s nonetheless an interesting brief “refresher course” on the history of cosmology leading to the current multiverse ideas).

Presumably, but as I said earlier, I don’t see how that follows, even though I think of symmetry as more fundamental than conservation laws. Just saying that the universe ought to have various symmetries doesn’t explain why it, in fact, does so. But I will agree that saying a universe naturally has various mathematical / physical symmetries seems a little less contrived than saying it comes equipped with a bunch of physical laws.

PM 2Ring said:

Bubblecar said:

Yes I wouldn’t be surprised if Noether & her theorem have been mentioned quite a lot, but my eyes probably glazed over on account of the maths :)

Fair enough. However, most mentions of Noether’s theorem on our forums haven’t gone into the gory mathematical details (unless they were posts by KJW…). OTOH, many times Noether’s theorem was invoked when arguing with people who were presenting crackpot stuff that violates conservation of energy, etc, so you may have been avoiding such threads anyway.

Bubblecar said:

>FWIW, symmetry seems more physically fundamental than conservation to me, so I prefer to think of conservation laws arising because of symmetry, even though I know they’re mathematically equivalent.

Presumably his point is that symmetry doesn’t require an underlying cosmic legislature. He’ll be discussing these things more fully later in the book (I hope. It’s not a great book – seems put together in rather a hurry, and he died before it was actually released – but it’s nonetheless an interesting brief “refresher course” on the history of cosmology leading to the current multiverse ideas).

Presumably, but as I said earlier, I don’t see how that follows, even though I think of symmetry as more fundamental than conservation laws. Just saying that the universe ought to have various symmetries doesn’t explain why it, in fact, does so. But I will agree that saying a universe naturally has various mathematical / physical symmetries seems a little less contrived than saying it comes equipped with a bunch of physical laws.

If a universe came equipped with a bunch of physical laws would that give credence to it being designed by a creator

Cymek said:

If a universe came equipped with a bunch of physical laws would that give credence to it being designed by a creator

Sort of; at least, it’s a relatively common argument from those who defend some form of creationism. So non-creationists would like an explanation that has the laws naturally arising through mathematical / logical necessity rather than being the result of some cosmic legislation.

OTOH, more subtle brands of creationism say that you can never prove the existence of God through logic or empiricism, although you may find persuasive evidence. And that any so-called creator who can’t avoid leaving greasy fingerprints over his work is insufficiently omnipotent to deserve the title. :)

Of course, maybe we’re just looking at this stuff the wrong way, and we’re just imposing patterns derived from human society (laws and law-makers) onto a structure that could be described better using different terminology.

I think it is probably often possible that we are looking at things through ways that are uniquely human.

PM 2Ring said:

Cymek said:

If a universe came equipped with a bunch of physical laws would that give credence to it being designed by a creator

Sort of; at least, it’s a relatively common argument from those who defend some form of creationism. So non-creationists would like an explanation that has the laws naturally arising through mathematical / logical necessity rather than being the result of some cosmic legislation.

OTOH, more subtle brands of creationism say that you can never prove the existence of God through logic or empiricism, although you may find persuasive evidence. And that any so-called creator who can’t avoid leaving greasy fingerprints over his work is insufficiently omnipotent to deserve the title. :)

Of course, maybe we’re just looking at this stuff the wrong way, and we’re just imposing patterns derived from human society (laws and law-makers) onto a structure that could be described better using different terminology.

You could also have an almost infinite number of failed universes were some physical law is different and certain processes never arrive, from suns never igniting, to life never occuring.

Are any forumers multi lingual?

poikilotherm said:

Are any forumers multi lingual?

wrong thread…derp.

Cymek said:

If a universe came equipped with a bunch of physical laws would that give credence to it being designed by a creator

PM 2Ring said:

Sort of; at least, it’s a relatively common argument from those who defend some form of creationism. So non-creationists would like an explanation that has the laws naturally arising through mathematical / logical necessity rather than being the result of some cosmic legislation.

Cymek said:

You could also have an almost infinite number of failed universes were some physical law is different and certain processes never arrive, from suns never igniting, to life never occuring.

Indeed; I’m rather fond of that approach. If that idea appeals to you you may enjoy The Life of the Cosmos

Wikipedia said:

The Life of the Cosmos is a 1997 book by theoretical physicist Lee Smolin. In the book, Smolin details his Fecund universes [theory] which applies the principle of natural selection to the birth of universes. Smolin posits that the collapse of black holes could lead to the creation of a new universe. This daughter universe would have fundamental constants and parameters similar to that of the parent universe though with some changes, providing for both inheritance and mutations as required by natural selection. However, while there is no direct analogue to Darwinian selective pressures, it is theorised that a universe with “unsuccessful” parameters will reach heat death before being able to reproduce, meaning that certain universal parameters become more likely than others.

poikilotherm said:

Are any forumers multi lingual?

Yes. But not me. :) (I studied French in high school, but I’m certainly not fluent in it, and I have studied bits and pieces of various other languages, including Sanskrit and the constructed language Loglan ).

Although MZL tends to use English in a somewhat cryptic fashion in his posts, I think it’s fair to say that MZL is actually fluent in English, although it’s not his mother tongue.