Is probability a fundamental aspect of quantum mechanics?

[juzzy]

I watched this video http://www.youtube.com/watch?v=aJ0FVez0FSc&list=UU_fHG6JygMd7oIvQ5S_cSIg&index=7&feature=plcp and the guy says that we don't know wether probability is a fundamental description of the particle or wether it is because of our lack of knowledge of the underlying system (ie as in measuring temperature).

Would it be correct to say that we don't know? Doesn't the delayed choice quantum eraser prove that at it's most fundamental, nature is probabilistic.

 

[Maui]

I watched this video http://www.youtube.com/watch?v=aJ0FVez0FSc&list=UU_fHG6JygMd7oIvQ5S_cSIg&index=7&feature=plcp and the guy says that we don't know wether probability is a fundamental description of the particle or wether it is because of our lack of knowledge of the underlying system (ie as in measuring temperature).

Would it be correct to say that we don't know? Doesn't the delayed choice quantum eraser prove that at it's most fundamental, nature is probabilistic.

Well, that would be interpretation dependent, but with propability being a fundamental part of quantum reality, you get a visual picture of how a 'particle' moves(i.e. through successive measurements). Extrapolate that to bigger systems - atoms and molecules and you'd get a picture how atoms and molecules move. I have no idea how a wavefunction moves in the BI(the implied ftl signaling makes it even more awkward). I guess the whole plethora of interpretations are there because some people need a crutch for the ERH(external reality hypothesis), hence they'd want to convince you of there being hidden variables at play, hidden realities, other worlds and other tricks. There has been a rather long debate between Einstein and Bohr about the probability in qm and it's generally accepted that Einstein lost the debate(certain tests of realism have since confirmed the notion as well, the uncertainty principle upholds the notion too). Those who like to stay out of metaphysics will likely claim that only results of measurements are meaningful and leave the deeper issues to philosophers.

 

[Mark M]

Different interpretations can vary on the issue of determinism. For example, Many-Worlds and de Broglie-Bohm are deterministic. However, the textbook interpretation of quantum mechanics, the Copenhagen Interpretation, holds that the results of a quantum event are fundamentally probabilistic.

 

[juzzy]

Thanks for the replies so far,
Maui, I'm not sure it's wise to leave the deeper issues to philosophers lol. I'm just wondering you see, if the actual 3 dimensional structure of an atom (carbon for instance) is described by a probability function, and cannot be described at all classically, isn't this evidence strong enough to prove that probability is fundamental. If you add to that the result you see in the double slit experiment, and in particular the delayed choice version of the experiment, then I don't really see how that isn't conclusive proof. In other words how would you build a deterministic picture from the results of that experiment, because even the many-worlds interpretation isn't deterministic in my opinion, it just says that all 'probabilities' exist in some way or another? Or am I misinterperating the theory?

 

[Maui]

Thanks for the replies so far,
Maui, I'm not sure it's wise to leave the deeper issues to philosophers lol. I'm just wondering you see, if the actual 3 dimensional structure of an atom (carbon for instance) is described by a probability function, and cannot be described at all classically, isn't this evidence strong enough to prove that probability is fundamental.

It is sort of classically described, as a collection of measurements done with electron tunneling microscope(the 3D 'images' you've seen of atoms). Otherwise, the wavefunction of an atom is a probability function(confirmed by the experiments with buckyball molecules).

If you add to that the result you see in the double slit experiment, and in particular the delayed choice version of the experiment, then I don't really see how that isn't conclusive proof. In other words how would you build a deterministic picture from the results of that experiment, because even the many-worlds interpretation isn't deterministic in my opinion, it just says that all 'probabilities' exist in some way or another? Or am I misinterperating the theory?

With a healthy dose of imagination and assumptions(even unwarranted), you could picture anything. That's why the operational interpretation is a minimalist one - that which is measured/observed is meaningful for the theory, not the underlying mechanics which does not behave classically. Quantum theory doesn't have problems, people do. As i said it gets philosphical when you ask who has false beliefs about the world?

 

[juzzy]

It is sort of classically described, as a collection of measurements done with electron tunneling microscope(the 3D 'images' you've seen of atoms). Otherwise, the wavefunction of an atom is a probability function(confirmed by the experiments with buckyball molecules).

I didn't mean images of atoms as such. I mean the mathematical description of the atom in QM, which leads to a probability distribution for the electron(s) and hence describes it's geometry intuitively as a 3d object, which is in accordance with observation of the 3d structure of molecules etc. However, in the classical description the atom would just collapse in on itself.

I'm not sure this has anything to do with philosophy really, it just seems obvious from these kind of results in QM, that probability is the most fundamental thing because only after the observation is made can we say anything deterministic about the result. The initial result of the measurement is random as far as I can tell

It's just that the guy in the video said we don't know, but I wonder how many physicists would agree that we don't know or would most say we do?

 

[Maui]

I didn't mean images of atoms as such. I mean the mathematical description of the atom in QM, which leads to a probability distribution for the electron(s) and hence describes it's geometry intuitively as a 3d object, which is in accordance with observation of the 3d structure of molecules etc. However, in the classical description the atom would just collapse in on itself.

As i said earlier, the mathematical description for the electron(s) around the nucleus is a probability wave(this is the standard interpretation, there are others though).

I'm not sure this has anything to do with philosophy really, it just seems obvious from these kind of results in QM, that probability is the most fundamental thing because only after the observation is made can we say anything deterministic about the result.

I agree with that, but the best thing one can learn here(beside the facts) is getting to know where physics ends and philosophy begins. Your topic covers both physics and philosophy - there are more ways than one of dealing with the quantum weirdness.

The initial result of the measurement is random as far as I can tell

It's just that the guy in the video said we don't know, but I wonder how many physicists would agree that we don't know or would most say we do?

I'd say that most accept that nature is fundamentally indeterministic at the quantum level, but a minority would disagree.

 

[StevieTNZ]

Bohm Mechanics has the particle go through one slit (pre-determined), yet an interference pattern emerges if we do the double-slit experiment. This is because of the guiding wave of the particle - that goes through both slits.

 

[the_pulp]

I'd say that most accept that nature is fundamentally indeterministic at the quantum level, but a minority would disagree

Im part of that minority. I think, similar but not equal to Ballentine, that an experiment tipically can be modeled by correlating:

1) an instrument state which has an eingenvector related to the indicator state (lets say "ind") and an eingenvector related to the state of the millons and millons of macroscopically uncontrolled particles that conform the instrument (lets say "m")
2) a system state (lets say "r")

and letting time goes by (that is to say, applying the evolution operator to the correlated state). Mathematically:

U(r\otimesind\otimesm)

If r is an experiment eigenvector then the final state eigenvector should be ind(r) (the value of the indicator related to the system state "r"):

U(r\otimesind\otimesm)=U(r\otimesind(r)\otimesm')

m' is another state of the uncontrolled variables that they can take due to the interaction with the system.

If r is not an eigenstate, then the experiment makes the system go to an experiment eigenstate ("r(i)"):

U(r\otimesind\otimesm)=U(r(i)\otimesind(r(i))\otimesm'')

With probability calculated from the Born Rule.

However, the evolution, as it is implicit in the last equation, is purely deterministic. The probability arrives due to the macroscopic ignorance of the "m" state. And, due to some theorems (see saunders "Derivation of the Born Rule From Operational Assumptions"), the only possible way that this probability can depend on only the initial state "r" (otherwise the experiment would not be considered an experiment but merely an interaction whose result depends on some controlled parameters) is that it is calculated with the Born Rule.

So, to me, the probabilities are something apparent to us, humans, who are not able to know every component of the instrument, but in reality evolution is deterministic (as Schrodinger equation or every equation that describes the evolution of a system).

Im not a profesional so I could be totally wrong!

 

[bhobba]

Well really we don't know because it is not known, nor in principle can it be, what future research will discover.

What we do know is, as far as we can tell today, that at the most fundamental level nature obeys the superposition principle. Now there seems to be only two possibilities - such states are deterministic or we can only predict probabilities. The first is actually contained in the second - but the probabilities are 0 or 1. Now there is a very important theorem that is not as well known as it should be - that the only way to define probabilities if the superposition principle holds (ie the states are a vector space) is the standard way it is done in QM - it is called Gleasons Theorem. Not only that but assuming only 0 or 1 can be assigned to such a space leads to a contradiction ie nature at it fundamental level is probabilistic. Its really unavoidable if the superposition principle holds. There are a number of outs such as introducing assumptions of contextuality but really to me they all seem a bit contrived.

Why the principle of superposition? Check out:
http://www.colorado.edu/philosophy/vstenger/Nothing/SuperPos.htm

Thanks
Bill

 

[Jano L.]

Maui, I'm not sure it's wise to leave the deeper issues to philosophers lol. I'm just wondering you see, if the actual 3 dimensional structure of an atom (carbon for instance) is described by a probability function, and cannot be described at all classically, isn't this evidence strong enough to prove that probability is fundamental. If you add to that the result you see in the double slit experiment, and in particular the delayed choice version of the experiment, then I don't really see how that isn't conclusive proof. In other words how would you build a deterministic picture from the results of that experiment, because even the many-worlds interpretation isn't deterministic in my opinion, it just says that all 'probabilities' exist in some way or another? Or am I misinterperating the theory?

Juzzy, here is what I think:

Physics is essentially part of philosophy, so one important work of the physicist _is_ to think about deep issues and explanation of the things. If he denies this, than he is giving up the possibilities.

and cannot be described at all classically...

It is difficult to prove that classical theory cannot handle this or that. Classical theory is not some rigid structure that can be disproved by disproving one or two old ideas. Flogiston, ether were dismissed, molecules were accepted, and the classical theory get to a better shape. It is possible the same will happen in future. It may require further revisions and improvements, but these will not bring down all classical physics.

isn't this evidence strong enough to prove that probability is fundamental?

Some concept can be fundamental within a theory (like probability in quantum theory), but the physical theory itself cannot possibly be fundamental as a The Correct Theory of Nature. There never was such a thing in science and the physicists themselves prefer to have more humble goals.

Niel Bohr put it himself perfectly:

'There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.'

— Niels Bohr
http://todayinsci.com/B/Bohr_Niels/BohrNiels-Quotations.htm

Furthermore, there are scientists who argue that probability is more a matter of logic than that of physical laws. In their view, the probability is just a subjective measure and is not fundamental even on the level of physical theory. They have very convincing arguments - see, for example,

E. T. Jaynes, G. Larry Bretthorst, Probability theory - the logic of science 2003.

 

[juzzy]

Thanks for all the replies so far, I've read them with interest. I will take it that the guy in the video therefore made a legitimate statement. And also I should say I hope I didn't offend any philosophers in my earlier post, my comments were in jest I assure you.

Ok then, I still have to disagree with any deterministic picture. In a simple zach-mender interferometer, the particle would be detected at both detectors with a probability of 1/2 if the particle was behaving deterministically. The fact we only see a build up at one detector can only be if the particle went both ways and interfered with itself, which seems deterministic in the sense that you know it will always go both ways, but actually follows probalistic laws. By that I mean it has an equal chance of going both ways and so does , as opposed to going one way or the other.

Yes I guess I am slipping into philosophy it's almost impossible to avoid with this subject

 

[lugita15]

What we do know is, as far as we can tell today, that at the most fundamental level nature obeys the superposition principle. Now there seems to be only two possibilities - such states are deterministic or we can only predict probabilities. The first is actually contained in the second - but the probabilities are 0 or 1. Now there is a very important theorem that is not as well known as it should be - that the only way to define probabilities if the superposition principle holds (ie the states are a vector space) is the standard way it is done in QM - it is called Gleasons Theorem. Not only that but assuming only 0 or 1 can be assigned to such a space leads to a contradiction ie nature at it fundamental level is probabilistic. Its really unavoidable if the superposition principle holds. There are a number of outs such as introducing assumptions of contextuality but really to me they all seem a bit contrived.

Why the principle of superposition? Check out:
http://www.colorado.edu/philosophy/vstenger/Nothing/SuperPos.htm

How does Bohmian mechanics get around what you're saying?

 

[krd]

Niel Bohr put it himself perfectly:

'There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.'

— Niels Bohr

Well maybe that's a cop out. Probability does not actually explain anything.

Also Bohr's statement leaves the possibility open for mathematical fictions - where the maths agrees with results, but theory is either wrong or absent. His idea may be based on flawed idea that all the world can be accurately expressed through maths - which is true, but at the same time flawed. You can describe a mountain in terms of polygons - but you're still just left with a bunch of polygons.

He could be dead right. But when you ditch the real world for abstract models, you run the risk of missing something.

He could be dead wrong. What appears random, could be deterministic - just the mechanism is well hidden. The actual mechanisms could be a lot stranger than current ideas.

It could be a bit like listening to a radio of station. If you didn't know how they playlist the music, you might assume the music just plays at random - you might be able to calculate the probabilities of certain songs being played. But your assumption of randomness would be wrong.

There is no DJ. There is only an abstract quantum physical description of a DJ.

 

[bhobba]

How does Bohmian mechanics get around what you're saying?

Bohmian Mechanics is explicitly contextual - ie it attacks the assumption of non-contextuality which is the hidden assumption in Gleasons theorem ie the probability associated with a projection operator does not depend on the other elements of a resolution of the identity it is part of.

You will find discussions on this issue scatterd about the place eg:
http://physics.stackexchange.com/qu...-to-obtain-born-rule-in-many-worlds-interpret
'I note that Gleason's theorem has played a small role in the reception accorded to a completely different interpretation, Bohmian mechanics. Gleason's theorem was at one time taken as a proof of the impossibility of hidden variables, but John Bell pointed out that it's only inconsistent with noncontextual hidden-variable theories, in which all observables simultaneously have sharp values. Bohmian mechanics is a contextual theory in which position has a preferred status, and in which other observables take on their measured values because of the measurement interaction. This runs against the belief in ontological equality of all observables; but perhaps reflecting on the status of Gleason's theorem within the Bohmian ontology will tell us something about its meaning for the real world.'

It is an out but like I said strikes me as rather contrived and against symmetry/invariance which lies at the heart of much of physics.

Thanks
Bill

 

[lugita15]

It is an out but like I said strikes me as rather contrived and against symmetry/invariance which lies at the heart of much of physics.

But is there not some basis in ascribing a reality to position that other observables do not have, since presumably it is the only directly observable quantity in nature? Isn't everything else indirectly observed via an appropriate pointer basis?

 

[bhobba]

But is there not some basis in ascribing a reality to position that other observables do not have, since presumably it is the only directly observable quantity in nature? Isn't everything else indirectly observed via an appropriate pointer basis?

Why do you think it is the only directly observable quantity (it isn't - energy is for example is directly observable - but curios why you think so)?

And even if true - so? That does not change the fact that Bohmian Mechanics is rather contrived - you have this pilot wave you can not in principle observe all for the express purpose of having nature behave how you would like it to behave. It reminds me of the aether of LET - yea its a valid theory but you have to ask - why bother? Of course the answer is philosophical - I however prefer the simpler answer of no pilot wave and no aether - but everyone is different - to each his/her own.

Thanks
Bill

 

[lugita15]

Why do you think it is the only directly observable quantity (it isn't - energy is for example is directly observable - but curios why you think so)?

How is energy or any other quantity directly observable except through the use of position? In order to measure anything don't we need a detector of some kind, and isn't reading (say) the position of an indicator or dial the only way to get information from a detector? How do acquire any information about the world at all except from position?

That does not change the fact that Bohmian Mechanics is rather contrived - you have this pilot wave you can not in principle observe all for the express purpose of having nature behave how you would like it to behave.

Actually, I think the pilot wave is just the imaginary part of the wave function, so that's not the contrived part. Rather, I think the unobservable thing that is just postulated for philosophical reasons is the hidden variable, namely the position of each particle.

It reminds me of the aether of LET - yea its a valid theory but you have to ask - why bother? Of course the answer is philosophical - I however prefer the simpler answer of no pilot wave and no aether - but everyone is different - to each his/her own.

I think there's another connection between Bohmian mechanics and aether: I vaguely recall someone saying that the nonlocality somehow leads to there being a preferred frame, so that Bohmians are effectively believers in the Lorentz aether theory without the physical aether.

 

[bhobba]

How is energy or any other quantity directly observable except through the use of position? In order to measure anything don't we need a detector of some kind, and isn't reading (say) the position of an indicator or dial the only way to get information from a detector? How do acquire any information about the world at all except from position?
Actually, I think the pilot wave is just the imaginary part of the wave function, so that's not the contrived part. Rather, I think the unobservable thing that is just postulated for philosophical reasons is the hidden variable, namely the position of each particle.
I think there's another connection between Bohmian mechanics and aether: I vaguely recall someone saying that the nonlocality somehow leads to there being a preferred frame, so that Bohmians are effectively believers in the Lorentz aether theory without the physical aether.

Energy changes in an atom are measurable for example by a spectrograph and can be displayed in a digital readout or recorded into computer memory to avoid any connection to position such as some kind of pointer.

The pilot wave is entirely contrived so as to guide the particle - can't quite recall exactly if and/or how it relates to the imaginary part of the wavefuntion - you can check that out for yourself. It however has a real existence in that theory but is not directly measurable:
http://en.wikipedia.org/wiki/Pilot_wave
'According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities. (Unlike standard quantum mechanics, where particles and waves are considered to be the same entities, connected by wave-particle duality). The pilot wave guides the motion of the point particles as described by the guidance equation. Ordinary quantum mechanics and pilot wave theory are based on the same partial differential equation. The main difference is that in ordinary quantum mechanics, the Schrödinger-equation is connected to reality by the Born postulate, which states that the probability density of the particle's position is given by. Pilot wave theory considers the guidance equation to be the fundamental law, and sees the Born rule as a derived concept.'

I am no expert in Bohmian Mechanics so I will/can not really comment any more than what I said above. If you want to discuss it I suggest a separate thread where experts in it can comment. And yes it is related to the existence of an aether.

Thanks
Bill

 

[krd]

'According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities. (Unlike standard quantum mechanics, where particles and waves are considered to be the same entities, connected by wave-particle duality).

The pilot wave guides the motion of the point particles as described by the guidance equation.

Does it explain the double slits experiment done with a single electron? In that experiment the electron passes through both slits. If it's a point, it should only go through one slit. If you're doing the Young slits with a flood of photons, then the pilot wave idea might look okay.

I've heard one description of this - that the point goes through one slit, but then travels back and goes through the other slit - then it covers every possible path, and then collapses. To be honest that sounds stupid. It's like there's a particle fairy being helpful and convenient.

 

[mfb]

Does it explain the double slits experiment done with a single electron? In that experiment the electron passes through both slits. If it's a point, it should only go through one slit. If you're doing the Young slits with a flood of photons, then the pilot wave idea might look okay.

With the de-Brogle-Bohm interpretation, the electron passes through one slit only, while the pilot wave passes through both and guides the particle to some position on the screen (with the usual interference pattern as limit for many particles).

While this interpretation needs some specific frame to perform calculations, the resulting physics is the same in all frames afterwards.

 

[Ken G]

It reminds me of the aether of LET - yea its a valid theory but you have to ask - why bother? Of course the answer is philosophical - I however prefer the simpler answer of no pilot wave and no aether - but everyone is different - to each his/her own.

I agree with you that interpretations are fundamentally personal and subjective, and anyone that can get the answer right is not making any kind of mistake even if they use an approach that we might view as unsavory in some way. But I think in the case of interpretations of quantum mechanics, there is more going on than just a search for personal cognitive resonance. Underneath it is all is very much the question of what is physics trying to be. This question has been resolved age by age throughout history, and is constantly changing, and ultimately is controlled by whatever works, more so than whatever we would like to work. But until we know whatever will work in the case of the next theory after quantum mechanics, we can still recognize that the different interpretations are asking us to think differently about what physics is.

I feel the issue comes down to what I see are three separate possibilities here, aligned with the three main ways to think about what physics is: rationalist, empiricist, or realist.

The rationalist approach says that physics is a search for the laws that the universe actually follows, and tends to frame the universe as a mathematical structure (we often hear words to the effect that "God is a mathematician" in this school of thought). But this is more than just a philosophical framework from which to regard physics, it makes genuine claims about what the process of doing physics should be trying to do (to wit, it should be searching for "the laws", or "the theory of everything".) I believe that approach not only colors what we think physics is, it actually changes what we think physics is. The many-worlds approach to quantum mechanics is often aligned with this style of thinking.

The empiricist approach says that physics is a set of observations that we are trying to understand, but the physics is the behavior, not the postulates we invent to approximate, idealize, and understand the behavior. Bohr was the consummate example of this approach, as he said "there is no quantum world" (anti-realist) and "physics is what we can say about nature" (with emphasis on "we", it is anti-rationalist). Again this is more than just a philosophical bent, it changes how we teach and perform physics, it changes what physics is trying to be.

The realist approach says that physics is trying to use a marriage of mathematical and empirical techniques to determine what reality is "really like". It says there is a reality out there, and physics is trying to find out what it is, more or less at face value. Einstein was a realist, indeed he was so radical of a realist that he didn't even like the realist approaches of de Broglie and Bohm because they embraced some unreal elements (the pilot wave) as the price of admittance to the sphere of being able to talk about the "real" positions and trajectories of particles. Einstein's approach has largely earned him disfavor, as he was considered to have lost the Einstein/Bohr debates, and his EPR paradox is no longer viewed as a paradox. But de Broglie's realism has generally been viewed as fully consistent with quantum mechanics, as you say. My point is that if we adopt the deBroglie-Bohm approach, we are not just choosing a philosophical favorite, we are again taking a stand on what we think physics should actually be.

So I agree with you that we don't at present know what physics should actually be, and the interpretations of QM all work, so we are at the moment left with a purely subjective and personal choice about how we like to frame it. I'm just saying that underneath that choice, there is a real struggle happening, like water piling up behind a dam and we don't yet know which path that water will take when it reaches its breaking point (which here will be some new observation that is not described by quantum mechanics). But what we should expect is that ultimately this issue will be far from moot-- it will determine the future direction of what physics becomes, be it a primarily rationalist, empiricist, or realist endeavor. I think it's exciting that we can't foresee which path future physics will take, but I think the "all three, you choose" approach cannot last forever!

 

[krd]

With the de-Brogle-Bohm interpretation, the electron passes through one slit only, while the pilot wave passes through both and guides the particle to some position on the screen (with the usual interference pattern as limit for many particles).

While this interpretation needs some specific frame to perform calculations, the resulting physics is the same in all frames afterwards.

In a way, or in a few ways, it sounds like a terrible idea. Not that I have a better idea - I'm only tinkering with quantum physics as a hobby - and it will take a few years for me to get up on the maths.

I don't have an interpretation to proffer - but I think the actual explanation could be uglier and neater at the same time. It could be really weird - it could be the waves are an emergent property of classical space time - just we can't see what's doing it. Not that it would make them absolutely deterministic. A resolution of spooky action at a distance may be, there is no distance.

It's a real headache - strictly speaking, the wave never becomes a particle. The detectors only detect the occurrence of another kind of wave.

 

[krd]

So I agree with you that we don't at present know what physics should actually be, and the interpretations of QM all work, so we are at the moment left with a purely subjective and personal choice about how we like to frame it.!

In parts of the ancient world, the theory that a giant scarab beetle, made the sun rise and set, "worked".

There's a danger in theory becoming religious dogma - maths is just maths, anyone who puts it on a pedestal is up to something religious.

 

[Ken G]

There's a danger in theory becoming religious dogma - maths is just maths, anyone who puts it on a pedestal is up to something religious.

And yet maths should be on some kind of pedastol in physics, that much is clear-- the issue is how high? I don't object to putting it on a pedastol, the problem is putting it in a monolithic tower! In short, the problem is in expecting it to be the truth, an error that every generation seems to make over and over without ever learning the lesson until the next revolution in thought comes along.

 

[bhobba]

There's a danger in theory becoming religious dogma - maths is just maths, anyone who puts it on a pedestal is up to something religious.

Sorry to burst your bubble but maths is more than maths - it is the language of physics and so should be on a pedestal. Why that is is a very very deep mystery - but nonetheless true.

Whenever I see remarks like that I get the sneaky suspicion the person writing it doesn't quite understand modern physical theories. For example Noethers Theorem is just maths but it has shocking physical implications ie statements like energy conservation are nothing more than tautological statements about a systems symmetry (in the case of energy time symmetry) - without the math it would have remained hidden. Indeed at it's deepest level physics to a large extent is about symmetry - this is a profound truth about nature - but it took math to reveal it.

Thanks
Bill

 

[bhobba]

And yet maths should be on some kind of pedastol in physics, that much is clear-- the issue is how high? I don't object to putting it on a pedastol, the problem is putting it in a monolithic tower! In short, the problem is in expecting it to be the truth, an error that every generation seems to make over and over without ever learning the lesson until the next revolution in thought comes along.

True - no very true. Math is the language of physics and of course because of that should be on a pedestal - however it is not physics. It helps reveal profound truths like the importance of symmetry but the truths thus revealed is physics - not math.

Thanks
Bill

 

[krd]

And yet maths should be on some kind of pedastol in physics, that much is clear-- the issue is how high? I don't object to putting it on a pedastol, the problem is putting it in a monolithic tower! In short, the problem is in expecting it to be the truth, an error that every generation seems to make over and over without ever learning the lesson until the next revolution in thought comes along.

I've been racking my brain trying to remember precisely where the idea originated - I think from some of the Greek mathematicians. An idea that everything in reality can be represented through mathematics. Which is true - but what is very important not to forget, is that mathematical representations are just representations. They are not to be confused with the underlying reality itself.

"The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell."

-- Saint Augustine


I'm not saying the mathematicians are in league with the devil. It's just they may get carried away with themselves.

 

[krd]

Sorry to burst your bubble but maths is more than maths - it is the language of physics and so should be on a pedestal. Why that is is a very very deep mystery - but nonetheless true.

Maths is not a deep mystery. It's a system of representation.

It's hard to shake the idea, that there is something magical in it. Isaac Newton spent most of his time investigating magic, and trying to turn base metals into gold, than he did on the work he's remembered for. John Dee, the English mathematician is worth looking into too.

The peculiar mystical ideas in regard to maths, have a history. And it's the same with astronomy. In that in the past astrologers and astronomers were one and the same thing.

The marvel in a mobile phone working, is that it works, not the maths that describes its working.

 

[Hurkyl]

The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.

e.g. orthodox quantum mechanics would use a wave-function to describe a particle.

But for some strange reason, someone who insists that the state space has properties "position" and "momentum" would call himself a realist, despite those ideas appearing nowhere in the scientific description of "what is".

 

[lugita15]

The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.

e.g. orthodox quantum mechanics would use a wave-function to describe a particle.

But for some strange reason, someone who insists that the state space has properties "position" and "momentum" would call himself a realist, despite those ideas appearing nowhere in the scientific description of "what is".

To me the use of the word realism is perfectly consistent. It is the belief that the observable properties of the particle are real.

 

[Ken G]

Maths is not a deep mystery. It's a system of representation.

The issue was insightfully explored by Wigner: http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

 

[Ken G]

But for some strange reason, someone who insists that the state space has properties "position" and "momentum" would call himself a realist, despite those ideas appearing nowhere in the scientific description of "what is".

To me the use of the word realism is perfectly consistent. It is the belief that the observable properties of the particle are real.

I think this debate raises a very important weakness in the concept of "realism": what is it anyway? If we take the approach that realism means the things we observe are real, it's not clear we are making any kind of claim other than we observe consistencies. We can all agree that when we observe something, we are really observing it, but most people want "realism" to mean more than that-- they want it to mean the existence of something independent of our observing it. But the language quickly becomes incoherent when we start trying to talk about things that are independent of our observations, given that our observations are all we have to build our language.

Yet, we can easily see the need for some kind of realism if we consider this example: my daughter asks me if unicorns are real, I tell her that her love for unicorns is real but unicorns themselves are not. So what is the difference? She observes her love for unicorns, and she observes drawings of unicorns, but she does not observe real unicorns. So we need a word like "real" to navigate those distinctions. But when we talk about our theoretical constructs, does the word still apply?

Personally, I view realism as an element of a physical theory as an essentially empty concept-- if the language is used carefully, there is no need for any concept like realism in physical theories. Indeed, I would argue that realism is what leads every generation to make the same mistake, of thinking that their own world view is "what is actually happening", whereas everyone before them was laboring under some misconception or other! But when we see the historically obvious point that science is always provisional on what we know and what tools we have, then we see realism in science for what it is: a crutch that came become, if not used carefully, a lie.

 

[Ken G]

The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.

I completely agree. Indeed, this is by beef with the PBR theorem-- the authors claim you need to be some kind of radical anti-realist if you are not willing to accept the concept that "properties" are real and therefore must be what actually determines behavior (which sounds to me closer to hidden variables, just as you say, because even if we are able to observe the properties, it is still "hidden" how these are supposed to determine the behavior).

To me, a property is more like the opposite of what is real-- a property is how we think about something, how we make sense of it, how we organize our perceptions around it. It's not even a pure perception, and even if it was, it still has us embedded deeply in it. Yet to be a "realist", we need to ignore our role in the concept of properties, and pretend, quite completely independent from any evidence, that we have nothing to do with properties. And that makes us a realist!?? Instead, I would offer a more sensible definition of realism as simply the imagining of a gap between, on one hand, our perceptions and logic and abilities, and on the other hand, what is "out there" independent from us. The act of recognizing how wide that gap is is exactly what I would call realism, and yet that is exactly what other people call anti-realism!

 

[bohm2]

An idea that everything in reality can be represented through mathematics. Which is true - but what is very important not to forget, is that mathematical representations are just representations. They are not to be confused with the underlying reality itself.

This makes sense to me. An arguably anologous mistake (in my opinion) is made in the cognitive sciences as Searle points out:

The same mistake is repeated by computational accounts of consciousness. Just as behavior by itself is not sufficient for consciousness, so computational models of consciousness are not sufficient by themselves for consciousness. The computational model of consciousness stands to consciousness in the same way the computational model of anything stands to the domain being modeled. Nobody supposes that the computational model of rainstorms in London will leave us all wet. But they make the mistake of supposing that the computational model of consciousness is somehow conscious. It is the same mistake in both cases.

http://users.ecs.soton.ac.uk/harnad/Papers/Py104/searle.prob.html

Unfortunately, unlike some mental stuff where we have intrinsic "access" to it (so that we can see that mathematics is not enough), the same cannot be said with respect to stuff described by physics. Some argue that the underlying "reality" will forever remain from our grasp, so that:

the propositions of physics are equations, equations that contain numbers, terms that refer without describing, many other mathematical symbols, and nothing else; and that these equations, being what they are, can only tell us about the abstract or mathematically characterizable structure of matter or the physical world without telling us anything else about the nature of the thing that exemplifies the structure. Even in the case of spacetime, as opposed to matter or force—to the doubtful extent that these three things can be separated—it’s unclear whether we have any knowledge of its intrinsic nature beyond its abstract or mathematically representable structure.

http://mitpress.mit.edu/books/chapters/0262513102pref2.pdf

Maybe that's why many physicists believe that physics has to 'free itself' from ‘intuitive pictures’ and give up the hope of ‘visualizing the world'? Steven Weinberg traces the realistic significance of physics to its mathematical formulations:

we have all been making abstract mathematical models of the universe to which at least the physicists give a higher degree of reality than they accord the ordinary world of sensations' ( e.g. so-called 'Galilean Style').

 

[Hurkyl]

To me the use of the word realism is perfectly consistent. It is the belief that the observable properties of the particle are real.

It's inconsistent, because that's not in orthodox QM's description of "what is". Momentum is not an observable property of a particle. The closest you can get is the facts

• For most states, one 'can' perform a "momentum measuring experiment" and get a number
• Most states yield a probability distribution over the outcomes of such an experiment
• That probability distribution describes the distribution of results of repeated identical tests

But the idea that a particle has a particular numeric value for momentum? It simply isn't present in the scientific theory, and so the belief that it does is not realism. Instead, you are asserting a hidden variable theory, and presumably applying realism to the hidden variable theory instead of to orthodox QM.

 

[yoda jedi]

I've been racking my brain trying to remember precisely where the idea originated - I think from some of the Greek mathematicians.
An idea that everything in reality can be represented through mathematics. Which is true - but what is very important not to forget, is that mathematical representations are just representations. They are not to be confused with the underlying reality itself.

"The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell."

-- Saint Augustine

i agree.

“Naturally one cannot do justice to [the argument] by means of a wave function. Thus I incline to the opinion that the wave function does not (completely) describe what is real, but only a to us empirically accessible maximal knowledge regarding that which really exists [...] This is what I mean when I advance the view that quantum mechanics gives an incomplete description of the real state of affairs.”
Einstein.

 

[lugita15]

It's inconsistent, because that's not in orthodox QM's description of "what is". Momentum is not an observable property of a particle. The closest you can get is the facts

• For most states, one 'can' perform a "momentum measuring experiment" and get a number
• Most states yield a probability distribution over the outcomes of such an experiment
• That probability distribution describes the distribution of results of repeated identical tests

But the idea that a particle has a particular numeric value for momentum? It simply isn't present in the scientific theory, and so the belief that it does is not realism. Instead, you are asserting a hidden variable theory, and presumably applying realism to the hidden variable theory instead of to orthodox QM.

No, this discussion is getting a bit too philosophical, but you don't say that you are a realist with respect to a particular theory. Realism is the belief that the measurable outcomes of an experiment correspond to real properties of the object being measured, i.e. properties that the object possesses even when unmeasured (although the act of measurement can change the properties of the object, so realism is compatible with contextuality). So we can judge what theories are in agreement or disagreement with this philosophical stance. I think it's pretty clear that quantum mechanics disagrees with it, whereas classical mechanics and hidden variable theories agree with it.

 

[bhobba]

Maths is not a deep mystery.

Math is not a mystery - its why its so effective is describing nature at its deepest level - that is the mystery - a very very deep one:
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Thanks
Bill

 

[bhobba]

The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.

To me its biggest problem is like a lot of words used in a philosophical context even what it means is subject to an intense philosophical dialectic. When I hear stuff like its just math it can't be reality I really have to bite my tongue and not say - oh really - mind telling us what reality is.

I actually hold the view, similar to guys like Roger Penrose, that the math is the reality.

Thanks
Bill

 

[bhobba]

Maybe that's why many physicists believe that physics has to 'free itself' from ‘intuitive pictures’ and give up the hope of ‘visualizing the world'?

I think that physicists in general don't really give such things much thought. What they have found is that when theories are subject to deeper and deeper mathematical investigation, deep insights turn up such as what Noethers Theroem revealed. They simply accept it as fact.

Wienberg has indeed written some interesting stuff about it - especially regarding what philosophers of science such as Kuhn say:
http://www.cs.utexas.edu/~vl/notes/weinberg.html

'Why does anyone bother? If one scientific theory is only better than another in its ability to solve the problems that happen to be on our minds today, then why not save ourselves a lot of trouble by putting these problems out of our minds? We don't study elementary particles because they are intrinsically interesting, like people. They are not--if you have seen one electron, you've seen them all. What drives us onward in the work of science is precisely the sense that there are truths out there to be discovered, truths that once discovered will form a permanent part of human knowledge.'

And mathematics has shown itself to be the tool in helping to reveal those truths.

Thanks
Bill

 

[yoda jedi]

No, this discussion is getting a bit too philosophical, but you don't say that you are a realist with respect to a particular theory. Realism is the belief that the measurable outcomes of an experiment correspond to real properties of the object being measured, i.e. properties that the object possesses even when unmeasured (although the act of measurement can change the properties of the object, so realism is compatible with contextuality). So we can judge what theories are in agreement or disagreement with this philosophical stance. I think it's pretty clear that quantum mechanics disagrees with it, whereas classical mechanics and hidden variable theories agree with it.

being a realist goes beyond properties,
properties (attributes,qualities,characteristics,features) are predicate of things, objects.
objects exist not because qualities it has, their atributes are secondary.
in any case quantum mechanics have to agree too with the existence of objects because without objects there are no properties. .

 

[bhobba]

being a realist goes beyond properties, properties (attributes, qualities, characteristics, features) are predicate of things, objects.objects exist not because qualities it has, their atributes are secondary. in any case quantum mechanics have to agree too with the existence of objects because without objects there are no properties.

I think what is what is 'real', what being a realist precisely entails, etc, is subject to so much philosophical debate you can't really make such statements as some kind of generally accepted truth - the most you can do is say its what you hold to. Personally I believe the mathematics is the reality meaning it tells us all we can really know. Most physicists I think would hold to that - but many, including me, and guys like Roger Penrose, go further, and believe in a Platonic type realm that is the reality and what we perceive is simply a projection of it.

Thanks
Bill

 

[yoda jedi]

"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality"

 

[bhobba]

"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality"

Yea a theory in mathematical language is just a theory - mathematics is basically logic - so?

Or do you think Einstein meant something different?

Thanks
Bill

 

[Jano L.]

Bhobbha,

wow, are you saying the only thing that is real in the world is mathematics? Are you a mathematician, or a physicist?

There never was a perfect mathematical understanding of any part of the nature. There are things that are not described mathematically at all. What about music, war, love? These are very real things. But there is no mathematical definition of them. Mathematics just describes some things, in an imperfect way, always open to improvement.

 

[bhobba]

wow, are you saying the only thing that is real in the world is mathematics? Are you a mathematician, or a physicist?

There never was a perfect mathematical understanding of any part of the nature. There are things that are not described mathematically at all. What about music, war, love? These are very real things. But there is no mathematical definition of them. Mathematics just describes some things, in an imperfect way, always open to improvement.

I would classify myself as a mathematical physicist.

I am not saying the only thing in the world is mathematics, what I am saying is the laws that govern fundamental physics is derived from a Platonic realm with an independent existence.

This is not the place to really discuss it - but much has been written about such a view:
http://www.scienceandreligiontoday.com/2010/04/01/is-mathematics-invented-or-discovered/

Nor do I concur with Roger Penrose on his view of QM and AI - but I do believe, along with him, that mathematics has an independent Platonic existence and it may be 'the mathematical reality of the Platonic world gives reality to these worlds (the physical)'.

Thanks
Bill

 

[mathal]

I'm old enough to remember home film cameras that shot 8 frames a second. The 'action' was smooth enough that you didn't 'really' notice the jumps between frames unless you watched the film frame by frame. When we 'percieve' 'reality' by any means available now there are still going to be jumps betweeen frames of reality. QM and the math therin just describes the fact that there are jumps between frames without specifically itemizing what is going on (if anything) between frames. IMO.
mathal

 

[Ken G]

Of course anyone can have a personal view about what is the reason that mathematics works in physics, what is probably more relevant is how that view causes us to frame the endeavor of physics itself. The rationalist view (that bhobba chooses to align with) is that physics should be the search for the actual laws that really govern nature. The criticism I would level at that way of framing physics is that it leads us to fall into the same fallacy, over and over throughout history, that the laws we currently espouse are in some sense correct, or when that becomes clearly not true, that they contain some kernel of the actual truth of the actual laws that govern reality. But what's missing in that position is any evidence that nature is "governed" by laws at all, when all that science has ever been able to show, or ever needed to be able to show, is that we gain some mastery over nature by imagining that it is governed by these laws. Invariably, we discover the "laws" we thought nature was "governed" by are not actually laws at all, more like useful idealizations in various limits.

So I would argue that physics is never served by framing it as a search for laws that nature actually obeys, it is served by treating it like it is: an effort for us to understand whatever it is that nature is actually doing. Why would we ever need to say physics is something other than what it quite demonstrably is, and always has been, simply because we have a hard time believing it should work?

 

[bhobba]

Yea - Ken - all true. But like the interpretations of QM each view sucks in their own way - even mine - actually especially mine.

I certainly classify myself as rationalist but there is no doubt my Platonic views are out there being only held by a small minority of physicists or mathematicians - but that minority is far from zero - very far from it. And I also get the sneaky suspicion a lot more hold to it but won't admit it - its this weird feeling you get when looking at the math of the fundamental laws

Thanks
Bill