Register to reply 
The use of probability in QMby juzzy
Tags: probability 
Share this thread: 
#19
May2812, 03:00 AM

Sci Advisor
PF Gold
P: 2,449

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 waveparticle 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 Schrödingerequation 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 


#20
May2812, 08:52 AM

P: 131

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. 


#21
May2812, 10:49 AM

Mentor
P: 11,574

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


#22
May2812, 12:36 PM

PF Gold
P: 3,080

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 manyworlds 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" (antirealist) and "physics is what we can say about nature" (with emphasis on "we", it is antirationalist). 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 deBroglieBohm 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! 


#23
May2812, 04:44 PM

P: 131

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. 


#24
May2812, 04:53 PM

P: 131

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. 


#25
May2812, 09:48 PM

PF Gold
P: 3,080




#26
May2912, 12:47 AM

Sci Advisor
PF Gold
P: 2,449

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 


#27
May2912, 12:50 AM

Sci Advisor
PF Gold
P: 2,449

Thanks Bill 


#28
May2912, 08:44 AM

P: 131

"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. 


#29
May2912, 09:12 AM

P: 131

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. 


#30
May2912, 10:00 AM

Emeritus
Sci Advisor
PF Gold
P: 16,099

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 wavefunction 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". 


#31
May2912, 10:10 AM

P: 1,583




#32
May2912, 10:33 AM

PF Gold
P: 3,080




#33
May2912, 10:45 AM

PF Gold
P: 3,080

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. 


#34
May2912, 10:56 AM

PF Gold
P: 3,080

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 antirealism! 


#35
May2912, 11:14 AM

PF Gold
P: 674

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: 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: 


#36
May2912, 12:51 PM

Emeritus
Sci Advisor
PF Gold
P: 16,099




Register to reply 
Related Discussions  
Conditional probability  Probability of spotting a downed airplane (really basic)  Set Theory, Logic, Probability, Statistics  3  
A simple probability problem involving the law of total probability  Calculus & Beyond Homework  1  
Probability question; Conditional probability and poisson distribution  Precalculus Mathematics Homework  1  
[probability theory] simple question about conditional probability  Precalculus Mathematics Homework  1 