Relativity, speed of light and stuff

[JesseM]

again, Occam's razor. sure, somehow the aether which really exists is smart enough to move around the Sun along with the Earth because it knows that Michaelson and Morley are set out to measure our speed through it. the aether sticks to the planet's surface no matter what time of day or what season of the year. so that's why the experiment had a null result.

Since when were we discussing the aether? Of course I don't believe in such a thing. I was discussing granpa's thought-experiment where length contraction and time dilation depend on the speed of sound, and I understood the point of this thought-experiment to be a pedagogical point about why in the real universe the speed of light is "special" in the way the speed of sound is not (essentially because the laws of physics are Lorentz-symmetric and the Lorentz transformation has c as its speed constant...if the laws of physics were symmetric under a transform that had the speed of sound as its speed constant, then the speed of sound would be 'special' in the same way the speed of light is in our universe, but they don't so it isn't).

sure, you can say that it's because of the length contraction and time dilation that we measure c to be invariant, but you offer no mechanism for why such length contraction and time dilation would happen in the first place.

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are, not "why" they are.

 

[granpa]

I think you missed the point, I was speaking in the context of your own thought-experiment where, if mach 1 is represented by the symbol s, then moving clocks slow down by a factor of $$\sqrt{1 - v^2/s^2}$$ and moving rulers shrink by the same factor. This would apply to things like the distance between air molecules in the direction of motion too, I'm assuming that all the laws of physics are invariant under the equivalent of a Lorentz Transformation with c replaced by s. In this case it would certainly be true that sound waves on the two ships would stay in line with one another as they moved.

ok. I guess you are right but what on Earth is your point? why would you want to move the air with the planes? its completely unnecessary. it adds nothing and distracts from the point I was making.

 

[granpa]

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are not "why" they are.

excellent point.

 

[JesseM]

ok. I guess you are right but what on Earth is your point? why would you want to move the air with the planes? its completely unnecessary. it adds nothing and distracts from the point I was making.

What was the point you were making? As I said to rbj, I interpreted your point like this:

I understood the point of this thought-experiment to be a pedagogical point about why in the real universe the speed of light is "special" in the way the speed of sound is not (essentially because the laws of physics are Lorentz-symmetric and the Lorentz Transformation has c as its speed constant...if the laws of physics were symmetric under a transform that had the speed of sound as its speed constant, then the speed of sound would be 'special' in the same way the speed of light is in our universe, but they don't so it isn't).

So, showing that the speed of sound would remain constant in a universe with such a symmetry even if the medium it was traveling in moved at different speeds is quite relevant to this point, which is that it is symmetries in the laws of physics that determine what speed is special (and if these symmetries have picked out a particular speed as special then other issues, like whether or not some wave moving at that speed has a medium or not, become irrelevant, since the speed will be invariant regardless).

 

[granpa]

So, showing that the speed of sound would remain constant in a universe with such a symmetry even if the medium it was traveling in moved at different speeds is quite relevant to this point

NO. the point isn't that the speed of sound would be constant when the medium was moving. the point is that the speed of sound would be constant even when the observer was moving. why would the aether move?

 

[rbj]

I'd say Occam's razor only applies to empirically different theories, not to different sets of logically equivalent axioms to be used in some formal proof.

i'd say that Occam's razor applies to "explanation of any phenomenon [and prefers those that] make as few assumptions as possible, eliminating those [assumptions] that make no difference in the observable predictions of the explanatory hypothesis or theory."

you have one explanation that the laws of physics are identical for any inertial observer, independent of how these observers are passing through the vacuum (or that the concept of a moving vacuum, a moving nothing is meaningless). from that single postulate, many relativistic consequences can be predicted to be observed.

or you can set up a world of make-believe where time dilation and length contraction occur to fast moving objects for no apparent reason. it's just magic. and then a consequence of that time dilation and length contraction (which is inexplicable) is that the speed of the electromagnetic interaction (as well as gravity and nuclear interactions) are measured to be constant. Occam's razor perfectly applies to these two explanations.

 

[rbj]

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are, not "why" they are.

excellent point.

to each his own, i guess.

i think the goal of physics is to discover what the fundamental causes and interactions are. that means discovering why some (less fundamental) phenomena occur as a consequence of more fundamental phenomena. John Baez wrote this in Wikipedia regarding fundamental physical constants:

The list of fundamental physical constants increases when experiments measure new relationships between physical phenomena. The list decreases when physical theory advances and shows how some previously fundamental constant can be computed in terms of others.

i don't think that I'm extrapolating too far to say that physical theory advances when it shows how some previously fundamental phenomenon can be derived or predicted in terms of other fundamental phenomena, thereby removing the first phenomenon from the list of fundamental interactions. that's what holy grails (GUTs) are supposed to be about.

the invariancy of the laws of physics (for inertial observers) is the fundamental principle, resulting in the constancy of c, and time dilation and length contraction are consequences of that. these are not fundamentally equivalent.

 

[atyy]

but silly and complicated explanations of observed phenomena are deprecated in favor of concise explanations. sure, you can say that it's because of the length contraction and time dilation that we measure c to be invariant, but you offer no mechanism for why such length contraction and time dilation would happen in the first place.

How about thinking about it this way:

1) We get Maxwell's equations from experiments done with currents, magnets, metal plates, metal wires, iron filings etc.

2) Maxwell's equations describe how the electromagnetic field changes when you move charges, magnets etc. These changes in the electromagnetic field provide a mechanism for length contraction, which can actually break things:

http://en.wikipedia.org/wiki/Bell's_spaceship_paradox

A good and entertaining reference is John Bell's "Speakable and Unspeakable in Quantum Mechanics".

 

[Al68]

No theory of physics offers a "mechanism" to explain why the fundamental laws of physics take the form they do. The goal of physics is just to discover what the fundamental equations are, not "why" they are.

I hate to disagree, but science is (from American Heritage Dictionary) the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. I would say that length contraction and time dilation are "phenomena".

Of course the last part of that definition is not emphasized the way it used to be in science.

Al

 

[atyy]

BTW, the whole discussion about the speed of sound being the ultimately limit, and sound still having a medium. Wouldn't that seriously change our formulation of the laws of physics? Under the present formulation of special relativity, anything traveling with constant speed in any special relativistic inertial reference frame must have zero rest mass. So if experiments suggested that the thing with constant speed in any reference frame had mass, we might have to rethink how mass-energy transforms in a frame change. Or would we have to ditch the Principle of Special Relativity?

Actually, is this discussion equivalent to: What would the consequences be for our formulation of the laws of physics if the photon were measured to have mass?

I guess the photon would be demoted to a neutrino, and the Principle of Special Relativity would remain intact?

 

[granpa]

I think you mean 'anything moving at the speed of light must have zero rest mass'. is that right?

bear in mind that space itself expanded much faster than light shortly after the big bang.

 

[JesseM]

i think the goal of physics is to discover what the fundamental causes and interactions are. that means discovering why some (less fundamental) phenomena occur as a consequence of more fundamental phenomena.

Well, I agree in general, but you weren't talking about deriving some higher-level laws from more fundamental laws, instead you were just talking about different sets of logically equivalent sets of axioms for deriving precisely the same general laws of SR.

the invariancy of the laws of physics (for inertial observers) is the fundamental principle, resulting in the constancy of c, and time dilation and length contraction are consequences of that. these are not fundamentally equivalent.

But you were talking about different sets of axioms which could be used to derive Lorentz-symmetry, which presumably is what you mean by "the invariancy of the laws of physics (for inertial observers)". But a key point here is that this description is overly vague, since without some additional assumptions it could also describe Galilei symmetry in Newtonian physics. To derive Lorentz-symmetry, you can start from the axiom that all fundamental laws of physics are the same in every inertial frame, plus the axiom that the speed of light is the same in every inertial frame; or you can start from the axiom that all the fundamental laws of physics are the same in every inertial frame, plus the axiom that in each frame rulers moving at v are measured to shrink by $$\sqrt{1 - v^2/c^2}$$ and that in each frame clocks moving at v are measured to have the time between ticks lengthened by $$1 / \sqrt{1 - v^2/c^2}$$. These two possible sets of axioms are completely equivalent in terms of their physical implications.

 

[atyy]

I think you mean 'anything moving at the speed of light must have zero rest mass'. is that right?

bear in mind that space itself expanded much faster than light shortly after the big bang.

No, I meant what I wrote. I don't think the Principle of Special Relativity and the Lorentz transformations would work with 2 invariant speeds. At least one of them must give. I'm only thinking within SR, no GR, inflation etc.

 

[JesseM]

I hate to disagree, but science is (from American Heritage Dictionary) the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. I would say that length contraction and time dilation are "phenomena".

Of course the last part of that definition is not emphasized the way it used to be in science.

Al

I don't think it's a good idea to approach questions in philosophy of science by appealing to dictionary definitions. The definition is good enough to cover most situations in science, where you're explaining some high-level laws governing a system by appealing to more fundamental laws which govern the basic parts of that system (reductionism); but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?

Here is Feynman writing about this topic in The Character of Physical Law, using gravitation as an example:

On the other hand, take Newton's law for gravitation, which has the aspects I discussed last time. I gave you the equation:

F=Gmm'/r^2

just to impress you with the speed with which mathematical symbols can convey information. I said that the force was proportional to the product of the masses of two objects, and inversely as the square of the distance between them, and also that bodies react to forces by changing their speeds, or changing their motions, in the direction of the force by amounts proportional to the force and inversely proportional to their masses. Those are words all right, and I did not necessarily have to write the equation. Nevertheless it is kind of mathematical, and we wonder how this can be a fundamental law. What does the planet do? Does it look at the sun, see how far away it is, and decide to calculate on its internal adding machine the inverse of the square of the distance, which tells it how much to move? This is certainly no explanation of the machinery of gravitation! You might want to look further, and various people have tried to look further. Newton was originally asked about his theory--'But it doesn't mean anything--it doesn't tell us anything'. He said, 'It tells you how it moves. That should be enough. I have told you how it moves, not why.' But people are often unsatisfied without a mechanism, and I would like to describe one theory which has been invented, among others, of the type you migh want. This theory suggests that this effect is the result of large numbers of actions, which would explain why it is mathematical.

Suppose that in the world everywhere there are a lot of particles, flying through us at very high speed. They come equally in all directions--just shooting by--and once in a while they hit us in a bombardment. We, and the sun, are practically transparent for them, practically but not completely, and some of them hit. ... If the sun were not there, particles would be bombarding the Earth from all sides, giving little impuleses by the rattle, bang, bang of the few that hit. This will not shake the Earth in any particular direction, because there are as many coming from one side as from the other, from top as from bottom. However, when the sun is there the particles which are coming from that direction are partially absorbed by the sun, because some of them hit the sun and do not go through. Therefore the number coming from the sun's direction towards the Earth is less than the number coming from the other sides, because they meet an obstacle, the sun. It is easy to see that the farther the sun is away, of all the possible directions in which particles can come, a smaller proportion of the particles are being taken out. The sun will appear smaller--in fact inversely as the square of the distance. Therefore there will be an impulse on the Earth towards the sun that varies inversely as the square of the distance. And this will be the result of a large number of very simple operations, just hits, one after the other, from all directions. Therefore the strangeness of the mathematical relation will be very much reduced, because the fundamental operation is much simpler than calculating the inverse of the square of the distance. This design, with the particles bouncing, does the calculation.

The only trouble with this scheme is that it does not work, for other reasons. Every theory that you make up has to be analysed against all possible consequences, to see if it predicts anything else. And this does predict something else. If the Earth is moving, more particles will hit it from in front than from behind. (If you are running in the rain, more rain hits you in the front of the face than in the back of the head, because you are running into the rain.) So, if the Earth is moving it is running into the particles coming towards it and away from the ones that are chasing it from behind. So more particles will hit it from the front than from the back, and there will be a force opposing any motion. This force would slow the Earth up in its orbit, and it certainly would not have lasted the three of four billion years (at least) that it has been going around the sun. So that is the end of that theory. 'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravity today, other than the mathematical form.

If this were the only law of this character it would be interesting and rather annoying. But what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics.

...[A] question is whether, when trying to guess new laws, we should use seat-of-the-pants feelings and philosophical principles--'I don't like the minimum principle', or 'I do like the minimum principle', 'I don't like action at a distance', or 'I do like action at a distance'. To what extent do models help? It is interesting that very often models do help, and most physics teachers try to teach how to use models and to get a good physical feel for how things are going to work out. But it always turns out that the greatest discoveries abstract away from the model and the model never does any good. Maxwell's discovery of electrodynamics was made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. But this speculation is of the same nature as those other people make--'I like it', 'I don't like it',--and it is not good to be too prejudiced about these things.

 

[Fredrik]

I hate to disagree, but science is (from American Heritage Dictionary) the observation, identification, description, experimental investigation, and theoretical explanation of phenomena. I would say that length contraction and time dilation are "phenomena".

I agree with both of you, even though you say you disagree with him. I agree with you because if we can't say e.g. that GR explains Newton's law of gravity, then we might as well remove the word "explain" from the English language since there are no better explanations than that. However, I also agree with Jesse, because he just said that science doesn't explain the fundamental laws. Newton's law of gravity isn't fundamental in GR, but Einstein's equation is. So what he said is consistent with my view, which is that GR explains Newton's law of gravity but not Einstein's equation, just like Newton's theory of gravity explains the elliptical orbits and falling apples but not the inverse square law.

Edit: Lol, you guys wrote a whole bunch of posts while I wrote this.

 

[JesseM]

BTW, the whole discussion about the speed of sound being the ultimately limit, and sound still having a medium. Wouldn't that seriously change our formulation of the laws of physics?

Wouldn't what change our formulation, exactly? The thought-experiment as I understood it was if the laws of physics transformed according to an altered transformation where the speed of light c was replaced by the speed of sound s, but sound waves were still understood as waves in a physical medium made of discrete particles. Of course this would mean very different laws of physics from the real universe, that's why it's a thought experiment! I suppose in order for waves in the air to move at the speed of sound, the molecules of air would individually have to move this fast (or they'd have to be the equivalent of tachyons, moving even faster than sound), so they'd have to have zero rest mass (or imaginary rest mass as with tachyons).

Under the present formulation of special relativity, anything traveling with constant speed in any special relativistic inertial reference frame must have zero rest mass. So if experiments suggested that the thing with constant speed in any reference frame had mass, we might have to rethink how mass-energy transforms in a frame change. Or would we have to ditch the Principle of Special Relativity?

I've forgotten precisely what additional assumptions beyond Lorentz-invariance are used to derive the relation E^2 = m^2*c^4 + p^2*c^2 (which naturally implies that if a particle is moving at the speed of light, the only way it can avoid having infinite energy is if it has 0 rest mass m, since $$p = mv/\sqrt{1 - v^2/c^2}$$ which will approach infinity in the limit as v approaches c unless m is zero). I think you might need to assume conservation of energy and momentum to derive it but I'm not sure. Whatever additional assumptions you need are pretty basic, I think.

 

[granpa]

No, I meant what I wrote. I don't think the Principle of Special Relativity and the Lorentz transformations would work with 2 invariant speeds. At least one of them must give. I'm only thinking within SR, no GR, inflation etc.

my bad. you meant 'anything moving at that speed which is constant for all observers'.

still not sure what you mean about photon mass. are you talking about air molecules that would have to move at least as fast as the sound wave. I'm not sure that holds for a solid medium though (waves can move pretty fast through a spring). but even if it did it is a fact that space itself seems to be able to move faster than light.

 

[rbj]

But you were talking about different sets of axioms which could be used to derive Lorentz-symmetry, which presumably is what you mean by "the invariancy of the laws of physics (for inertial observers)". But a key point here is that this description is overly vague, since without some additional assumptions it could also describe Galilei symmetry in Newtonian physics. To derive Lorentz-symmetry, you can start from the axiom that all fundamental laws of physics are the same in every inertial frame, plus the axiom that the speed of light is the same in every inertial frame;...

i've been in this argument before. in some other thread, i was saying (and i still maintain) that the 2^nd postulate of SR is unnecessary or superfluous when you have the first. the second postulate (the constancy of c) is a consequence of the first (that the laws of physics remain invariant for every inertial frame of reference). by "laws of physics", i mean not only the functional form of the laws, but also that the parameters (like c, G, $\hbar$, and $\epsilon_0$) in those laws remain invariant. two different sets of Maxwell's equations, identical in every respect except for the permittivity parameter, are not identical laws of physics. "identical", in the strong sense of the word, means not only qualitatively the same, but also quantitatively the same.

the "plus" is semantically not necessary.

time dilation and length contraction are a consequence of the fact that every inertial observer observe identical laws of nature in observed phenomena which means they observe identical speeds of propagation of the E&M interaction as well as all other "instantaneous" interactions (gravitation and nuclear).

 

[Fredrik]

i've been in this argument before. in some other thread, i was saying (and i still maintain) that the 2^nd postulate of SR is unnecessary or superfluous when you have the first. the second postulate (the constancy of c) is a consequence of the first (that the laws of physics remain invariant for every inertial frame of reference).

I don't think that's exactly right. You can't derive the second from the first. What I've been saying in other threads (and still maintain) is that Einstein's "postulates" are ill-defined because they use the term "inertial frame" without a definition, and that any definition of "inertial frame" that's appropriate for SR must include both of Einstein's "postulates" in some form.

Einstein's "postulates" shouldn't be treated as axioms. They are just a list of properties that he wanted the theory he was trying to find to have.

 

[atyy]

still not sure what you mean about photon mass.

I've forgotten precisely what additional assumptions beyond Lorentz-invariance are used to derive the relation E^2 = m^2*c^4 + p^2*c^2 (which naturally implies that if a particle is moving at the speed of light, the only way it can avoid having infinite energy is if it has 0 rest mass m

Hi granpa, JesseM's quote is what I'm talking about. I believe if you have the Principle of Relativity (existence of a class of reference frames moving with constant velocity relative to each other in which the laws of physics all look the same), and you also have an velocity v_i that is invariant in all the frames, from those 2 assumptions you can derive the Lorentz transformations, with v_i replacing the usual speed of light c. With some additional assumptions, which JesseM and I have both forgotten, we can derive E=mv_i², where m is the relativistic mass. From which we see that a thing moving at the v_i must be massless. So if sound were to be a thing that traveled at v_i, and it also had mass, then presumably at least one of the assumptions in getting to E=mv_i² must be wrong.

Edit:

it seem that there is no consensus among today scientist that there is no "something" like ether as opposite to vacuum...

I'm having second thoughts that a massive medium for the thing that travels at the invariant velocity causes difficulties. I'm not really sure, so I'm just going to state a bunch of stuff and let someone correct it. The dispersion relation for a phonon is like a photon. So maybe even though phonons are made from a medium, they can be considered massless. And maybe photons, by analogy to phonons, can be considered to be made from a medium. I wonder if ricmat is thinking about a model like this: http://arxiv.org/abs/cond-mat/0210040

 

[atyy]

two different sets of Maxwell's equations, identical in every respect except for the permittivity parameter, are not identical laws of physics. "identical", in the strong sense of the word, means not only qualitatively the same, but also quantitatively the same.

the "plus" is semantically not necessary.

I agree, but I think you are counting Maxwell's equations as a zeroth postulate, whereas JesseM doesn't have this zeroth postulate and puts the constancy of the speed of light as a second postulate. So the number of postulates is still the same, ie.

Maxwell's equations + Principle of Relativity = Principle of Relativity + constancy of speed of light

 

[Dale]

NO. the point isn't that the speed of sound would be constant when the medium was moving. the point is that the speed of sound would be constant even when the observer was moving.

"Six of one, half-dozen of the other"

 

[granpa]

So if sound were to be a thing that traveled at v_i, and it also had mass, then presumably at least one of the assumptions in getting to E=mv_i² must be wrong.

it isn't clear to me that the particles in a solid which is transmitting a sound would necessarily be moving at the speed of sound. one can increase the speed of sound simply by increasing the stiffness of the material and decrease the motion of the particles by simply decreasing the amplitude of the sound. or at least, I guess you can. I'm not an expert on sound. or anything else for that matter.

 

[Al68]

I don't think it's a good idea to approach questions in philosophy of science by appealing to dictionary definitions. The definition is good enough to cover most situations in science, where you're explaining some high-level laws governing a system by appealing to more fundamental laws which govern the basic parts of that system (reductionism); but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?

Here is Feynman writing about this topic in The Character of Physical Law, using gravitation as an example:

Well, if we did have a good "theoretical explanation", it would belong in a physics textbook, not a literature textbook. So I would consider it physics. The fact that we don't have such a theory doesn't mean that such a theory is not within the scope of physics.

Al

 

[JesseM]

Well, if we did have a good "theoretical explanation", it would belong in a physics textbook, not a literature textbook. So I would consider it physics. The fact that we don't have such a theory doesn't mean that such a theory is not within the scope of physics.

I repeat my question: but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws? I can't imagine what a theoretical explanation of fundamental laws would even look like (aside from boiling them down to some minimal set of axioms), so it's not clear what you're imagining here, but it sounds like you're talking about something totally unprecedented in the history of science.

 

[atyy]

it isn't clear to me that the particles in a solid which is transmitting a sound would necessarily be moving at the speed of sound. one can increase the speed of sound simply by increasing the stiffness of the material and decrease the motion of the particles by simply decreasing the amplitude of the sound. or at least, I guess you can. I'm not an expert on sound. or anything else for that matter.

Yes, hence the second thoughts in my above post. So I guess the question can be split in 2:
1) What transformations are consistent with 2 invariant speeds (speed of light and something else). I suppose this us related to doubly special relativity.
2) Can light (and gravity) be usefully modeled as a medium? For light, it appears the answer is yes. For gravity, the answer is unknown, but there are several intriguing leads (http://arxiv.org/abs/0712.0427)

 

[granpa]

2 invariant speeds?

it gets confusing since we are talking about sound but what we are really talking about is light. I never meant to say anything implying 2 invariant speeds.

 

[atyy]

Well, if we did have a good "theoretical explanation", it would belong in a physics textbook, not a literature textbook. So I would consider it physics. The fact that we don't have such a theory doesn't mean that such a theory is not within the scope of physics.

Al

I repeat my question: but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws? I can't imagine what a theoretical explanation of fundamental laws would even look like (aside from boiling them down to some minimal set of axioms), so it's not clear what you're imagining here, but it sounds like you're talking about something totally unprecedented in the history of science.

There's an interesting discussion by Wen in his Quantum Field Theory book (OUP 2004, p 12):
Chinese philosophers theorized that the division could be continued indefinitely, and hence that there were no elementary particles. Greek philosophers assumed that the division could not be continued indefinitely ... Those ultimate particles were called "atomos".

He quotes the Dao De Jing (p11): The Dao that can be stated cannot be eternal Dao. The Name that can be named cannot be eternal Name. The Nameless is the origin of the universe. The Named is the mother of all matter.

Which he mischievously translates as (footnote, p11): The physical theory that can be formulated cannot be the final ultimate theory. The classification that can be implemented cannot classify everything. The unformulable ultimate theory does exist and governs the creation of the universe. The formulated theories describe the matter we see everyday.

Preface (pviii): we still know so little about the richness of nature. However, instead of being disappointed, I hope the readers are excited by our incomplete understanding. ... The human imagination is also boundless. ... I wonder which will come out as a 'winner', the richness of nature or the boundlessness of the human imagination.

 

[atyy]

2 invariant speeds?

it gets confusing since we are talking about sound but what we are really talking about is light. I never meant to say anything implying 2 invariant speeds.

Ah, I see, the discussion was just on the second point then. Another interesting quote from Wen's QFT book, this particular one is quite uncontroversial, but he has nice imagery:
Our vacuum is more like an ocean which is not empty. Light and fermions are collective excitations that correspond to certain patterns of 'water' motion.

 

[Fredrik]

I repeat my question: but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws? I can't imagine what a theoretical explanation of fundamental laws would even look like (aside from boiling them down to some minimal set of axioms), so it's not clear what you're imagining here, but it sounds like you're talking about something totally unprecedented in the history of science.

I don't know what his answer is, but my answer would be that a deeper, more fundamental theory, can be considered a theoretical explanation of the fundamental laws in your theory. For example, general relativity is a theoretical explanation of Newton's law of gravity (the inverse square law). Newton's theory of gravity can't explain the inverse square law because it's a fundamental law of the theory, but GR can explain it because it's just one of many results that can be derived from the fundamental laws of that theory.

 

[JesseM]

I don't know what his answer is, but my answer would be that a deeper, more fundamental theory, can be considered a theoretical explanation of the fundamental laws in your theory. For example, general relativity is a theoretical explanation of Newton's law of gravity (the inverse square law). Newton's theory of gravity can't explain the inverse square law because it's a fundamental law of the theory, but GR can explain it because it's just one of many results that can be derived from the fundamental laws of that theory.

My question was, 'but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?' If a given theory turns out to be an approximation of some more fundamental theory, like Newtonian gravity is understood as an approximation of GR, that shows that the first theory (Newtonian gravity) wasn't really one of the "most fundamental laws". Of course I'm assuming here that there are some final, most fundamental laws out there waiting to be discovered; as atyy brought up, it's conceivable that it's just wheels within wheels forever, that every particle is really a composite entity made up of even smaller particles, etc.

 

[MeJennifer]

INewton's theory of gravity can't explain the inverse square law because it's a fundamental law of the theory, but GR can explain it because it's just one of many results that can be derived from the fundamental laws of that theory.

I think you are mistaken. In fact if you look how Einstein derived GR you will see he simply included the Newtonian limit as a given. Technically GR is simply Newtonian gravity plus relativistic effects. GR does not explain anything, it is simply a more accurate theory.

If you think I am mistaken, please demonstrate how it explains the inverse square law. Or an even simpler question: How does GR get to the Newtonian limit.

 

[rbj]

I think you are mistaken. In fact if you look how Einstein derived GR you will see he simply included the Newtonian limit as a given. Technically GR is simply Newtonian gravity plus relativistic effects. GR does not explain anything, it is simply a more accurate theory.

If you think I am mistaken, please demonstrate how it explains the inverse square law. Or an even simpler question: How does GR get to the Newtonian limit.

does John Baez do that here?

or maybe Sean Carroll does that http://preposterousuniverse.com/grnotes/grtinypdf.pdf ?

i think they can derive the inverse-square relationship (or maybe it's a 1/r relationship for potential energy) for the flat space-time limit. the constant of proportionality in the Einstein equation ($8 \pi G$) does come about to be compatible with Newtonian gravitation.

i can't actually do the math myself (i am ashamed to confess i never figured out tensors), but it appears that this is what they do.

 

[yuiop]

I tend to agree with Jennifer here. I can not see how a physicist isolated in a small spacestation that had never experienced gravity or even heard of it, would conclude from a knowledge of Special Relativity alone, that two particles would have to move towards each other, let alone that they accelerate towards each other with an acceleration inversely proportional to the distance separating them.

As far as I can tell General Relativity started with a knowledge that we experience "Newtonian gravity" and extrapolated or reverse engineered that knowledge to more extreme conditions than we normally experience. It is hardly surprising that Newtonian gravity is recovered from GR in the weak field limit because GR started with that assumption. lease do not get me wrong here. I am not saying there is anything wrong with GR, I am just saying that it does not fundementally explain or predict gravity and just provides a pretty good mathematical description of what we observe.

Put it another way. In multiverse theories where there are any number of possible universes each with their own laws of nature, would a universe that obeys the laws of Special Relativity have to have an inverse square law of gravity in the weak field limit or come to that, any gravity at all?

 

[JesseM]

I tend to agree with Jennifer here. I can not see how a physicist isolated in a small spacestation that had never experienced gravity or even heard of it, would conclude from a knowledge of Special Relativity alone, that two particles would have to move towards each other, let alone that they accelerate towards each other with an acceleration inversely proportional to the distance separating them.

When did Fredrik say anything like that? He didn't say you could discover the inverse-square law from pure thought, he just said that if you already know the equations of GR you can get the inverse-square law as a derived consequence. Of course you could say the same thing about the equations of Newtonian gravity in some sense, so I'm not sure this is a totally clear distinction, but at least in Newtonian gravity it's obvious from the fundamental equations whereas in GR it's not.

As far as I can tell General Relativity started with a knowledge that we experience "Newtonian gravity" and extrapolated or reverse engineered that knowledge to more extreme conditions than we normally experience.

I don't know whether or not that's true of Einstein's original derivation as a historical matter, but it is at least true that GR can be derived from assumptions that have nothing to do with Newtonian gravity--on this page Steve Carlip writes:

If you want to derive the Einstein field equations from scratch, you can do so without making very many assumptions. You must assume that

1. the geometry of spacetime is dynamical;
2. there are no extra fixed, nondynamical "background structures" that influence the geometry;
3. special relativity becomes a good approximation when gravitational fields are weak;
4. the field equations can be derived from a Lagrangian, or an action principle; and
5. the field equations involve no more than second derivatives; that is, they determine "accelerations" rather than requiring accelerations as initial data.

These assumptions lead almost uniquely to a set of field equations with two undetermined constants. One of these is Newton's constant, which determines the strength of the gravitatonal interaction. The other is the cosmological constant, Lambda.

I think it is also true that you can come up with theories that are identical to Newtonian gravity in every respect except for the fact that the strength of the force is inversely proportional to some other real power like r^2.05, whereas in GR you don't have this sort of wiggle room, trying to make it no longer obey an inverse-square law would give a very different theory (presumably it would require violating one of Carlip's basic assumptions above).