Quantum physics in three sentences?

[batmanmg]

Ok, not all of quantum physics. Mainly just the Double Slit Experiment or Wavefunctions in general.

You only have 3 sentences to teach either one (or both) to an idiot (not me) and they can't be run on sentences either.

This also has to be a math free explanation.

It's not so much a challenge of simplifying the ideas to their most succinct states as it is choosing what is important to know and what you don't really need to know.

Kindof like the desert island deal. If you could only take three facts about quantum physics with you, what would they be?

 

[tom.stoer]

Let's try something more general:

In quantum mechanics a 'realistic' description using entities (like particle trajectories with well-defined position and momentum) known from our everyday's experience is no longer applicable and becomes wrong. Instead one has to refer to an abstract mathematical formalism from which the classical world does 'emerge' in some situations, but which shows genuine (and weird) quantum behavior in other situations (double slit, entangled particles a la EPR / Bell). A typical example for the genuine quantum behavior of 'quantum objects' (which are neither particle nor wave) is the double slit experiment where the abstract formalism tells us that one single, indivisible entity like an electron sniffs out all possible classical trajectories simultaneously, i.e. 'walks through both slits' simultaneously, interferes with itself and shows partially destructive interference.

 

[Demystifier]

Ok, not all of quantum physics. Mainly just the Double Slit Experiment or Wavefunctions in general.

You only have 3 sentences to teach either one (or both) to an idiot (not me) and they can't be run on sentences either.

1. Wave function is a complex function of the space position x and time t.
2. A linear combination of physical wave functions is a physical wave function itself.
3. The squared absolute value of the wave function is the probability density for a particle to be found at the position x at time t.

 

[dextercioby]

A small ammendment to point 2. <Within a coherent subspace of the physical Hilbert space, a linear combination of physical wave functions is a physical wave function itself>.

 

[Ken G]

The quantum mechanics of wave functions and the double-slit experiment involves the union of that which we used to think were as different as night and day: the discrete and the continuous-- particle and wave. The union is accomplished by the quantization, in bundles of the Planck constant, of a dynamical quantity known as action. This quantization allows us to associate with any particle momentum a wavelength, which is a property of waves, and with any wave period a quantum of energy, which is a property of particles. These associations allow us to treat what we used to think of as disjoint wave and particle properties as two aspects of the same animal, like the trunk and the tail of a single elephant-- they allow us to recognize, rather belatedly, why particles and waves were always the same thing in different clothes.

 

[cbetanco]

1. The state of any physical system is represented by a vector in an infinite dimensional complex space, with each component representing a particular state the system can be in.

2. The state vector of any physical system evolves according to Shrödinger's equation.

3. A measurement on a physical quantity (energy, momentum, position, spin, etc.), represented by Hermitian operators, yields one of its eigenvalues, with the probability of that value being given by the square of the projection of the state vector on the given eigenvector.

(sorry, a math free explanation is not possible)

 

[Demystifier]

A small ammendment to point 2. <Within a coherent subspace of the physical Hilbert space, a linear combination of physical wave functions is a physical wave function itself>.

What is a coherent subspace?

 

[dextercioby]

The Hilbert space of states, assumed infinite dimensional and separable, is generally decomposed into a direct othrogonal sum of closed subspaces, each corresponding to discrete spectral values of the operators describing the so-called <superselection rules>. For example charge in case of a Dirac equation/field. The linear superposition between an eigenfunction with positive charge (positron) and negative charge (electron) makes no sense physically, so that a quantum state with electrons and positrons is not described by a linear combination, but by a tensor product.

An eigenspace of an operator providing a superselection rule which corresponds to an eigenvalue of that operator is called a coherent subspace. It is a separable Hilbert space in its rights, if endowed with the scalar product inherited from the full space. Linear combinations of vectors only within the same (sub)space make sense (example above), not between vectors from different subspaces, corresponding to different eigenvalues.

This is off the top of my head. As far as I remember, I think the introductory chapter from Streater & Wightman has a story on this. Also Galindo & Pascual's text on QM, or Fonda & Ghirardi's text on symmetries of quantum systems.

Needless to say, in case superselections rules are missing, the whole Hilbert space is a coherent subspace (quanta of the KG field, or spinless Galilean particle).

 

[Demystifier]

Thanks dextercioby. I have an offtopic comment, but I will open a new thread on it.

 

[DevilsAvocado]

Caveat: QM works mathematically, everybody agrees on that. However, when you start to talk and describe what 'happens', you always run into the 'dilemma' of interpretations, and my guess is that some will have scathing comments on my 'talk' below ;). Nevertheless, as of today no interpretation is proven better than any other...


Quantum Mechanics for Dummies

• Quantum mechanics describes the very small microscopic world, where things behave differently from what we are used to in the macroscopic world of 'classical' objects.
  
  
• One famous example is the Double-slit experiment, which demonstrates that matter and energy can display characteristics of both waves and particles.
  
  
• Waves in quantum mechanics are fundamental and described mathematically by the wavefunction and the Schrödinger equation, which results in some uncertainty when calculating the exact outcome for one single particle, the outcome is therefore probabilistic in its nature.

 

[jewbinson]

I would say that DevilsAvocado is the best 3 sentences so far (I will not attempt writing 3 sentences because I cannot top it). The others are good though.

If I could add one thing it would be that quantum mechanics approximates very well to classical mechanics when considering large systems, e.g. QM agrees with Newton's Laws and GR when you apply QM on a macroscopic and large scale.

I would also like to say that it is just a theory and is not necessarily the "truth"... maybe we will find a better theory in the future which is more generalized than QM. But it is the best theory we have as of now...

 

[skippy1729]

1. Quantum Mechanics is an attempt to predict the outcomes of experiments on systems so small that our intuitive notions of particle, wave, position, momentum and even space and time might not be applicable.

2. Several different properties of a quantum system may be measured but it is never possible to simultaneously measure all of them.

3. Depending on the preparation of the quantum system some of its properties may be predicted with certainty but, in general, the predictions of the outcomes of measurements are probabilistic but have tremendous experimental confirmation.

Not perfect but it is non-mathematical.

 

[DevilsAvocado]

I would say that DevilsAvocado is the best 3 sentences so far

 

[mysearch]

Ok, not all of quantum physics. Mainly just the Double Slit Experiment or Wavefunctions in general. You only have 3 sentences to teach either one (or both) to an idiot (not me) and they can't be run on sentences either.

By way of ‘gentle’ debate, rather than argument, just over a generation ago, Feynman suggested that nobody understood QM and now we appear to aspire to explain some of its central concepts to ‘an idiot’ in just 3 sound-bites. Clearly, there is hope for me yet, although Heisenberg had a go at summarising the double slit experiment and the wave function collapse in just 1 sentence:

“The path of a particle comes into existence only when we observe it."​

I also like the summary in post #10, but possibly the is in the detail, if not in the avocado, as per bullet 3:

Waves in quantum mechanics are fundamental and described mathematically by the wavefunction and the Schrödinger equation.

People might also like to review the following thread ‘https://www.physicsforums.com/showthread.php?t=541962"’, which wasn’t restricted to 3 sentences, as a yardstick as to whether any consensus was reached on its definition, let alone its interpretation. For example, do quantum waves have any physical existence?

 

[dextercioby]

According to the standard formalism of QM, there's no more distinction between particles and waves, as these 2 concepts, as I said before, actually pertain to classical physics, namely the mechanics of point particles and waves (including electromagnetism). So <quantum waves> as a concept does not exist.
The fundamental concepts of QM are: (quantum) system, states and observables of a system and virtual statistical ensembles. The rest is essentially mathematics.

 

[DevilsAvocado]

... Clearly, there is hope for me yet, although Heisenberg had a go at summarising the double slit experiment and the wave function collapse in just 1 sentence:

“The path of a particle comes into existence only when we observe it."​

Cool, I love "one-liners", less is more. In 1935 Erwin Schrödinger published http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1737068" defining the term "entanglement":

"I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."​

I also like the summary in post #10, but possibly the is in the detail, if not in the avocado

 

[DevilsAvocado]

According to the standard formalism of QM, there's no more distinction between particles and waves, as these 2 concepts, as I said before, actually pertain to classical physics, namely the mechanics of point particles and waves (including electromagnetism). So <quantum waves> as a concept does not exist.

Agreed, but if you’re going to tell 'an idiot' that the "QM world" does not exist, I suspect this 'idiot' would 'object' in some way:

– Okay... I dunno... but... why should I spend my time on something that doesn’t exist...? ​

The fundamental concepts of QM are: (quantum) system, states and observables of a system and virtual statistical ensembles. The rest is essentially mathematics.

This is of course more 'contemporary' and closer to the 'truth' than post #10. I don’t know how to get around this 'problem of language'... I get a slight feeling that the 'contemporary abstraction' of QM is so abstract, that when 'an idiot' tries to make a figurative picture in his head... he’s immediate lost.

This is from "Quantum Mechanics - A Modern Development", by Leslie E. Ballentine:

Postulate 1a. To each dynamical variable there is a Hermitian operator whose eigenvalues are the possible values of the dynamical variable.

Postulate 2a. To each state there corresponds a unique state operator, which must be Hermitian, nonnegative, and of unit trace.​

I have an idea what Ballentine is talking about, but do I get a deeper conceptual understanding from this? Well, unless I read the book, and understand the math, I’m afraid the answer is No...

I’m not trying to raise an 'argument' here, I’m just curious. What’s your answer, if 'an idiot' asks:

– Okay, "virtual statistical ensembles" sounds cool, but in case I’m not an idiot, we have single electrons in this Double-slit experiment, and afaict, we could have eons between each, so where’s your "ensemble" then??

http://www.youtube.com/watch?v=FCoiyhC30bc&hd=1
https://www.youtube.com/watch?v=FCoiyhC30bc​

 

[Cthugha]

– Okay, "virtual statistical ensembles" sounds cool, but in case I’m not an idiot, we have single electrons in this Double-slit experiment, and afaict, we could have eons between each, so where’s your "ensemble" then??

I somewhat do not get your point. If you perform such a double slit experiment it does not matter whether you perform one measurement with 12876 (non-interacting) electrons or 12876 measurements with one electron. Both experiments are basically giving the same ensemble.


For my take at the question of the begin of this topic, let me cite Neil David Mermin:
"My complete answer to the late 19th century question "what is electrodynamics trying to tell us?" would simply be this: Fields in empty space have physical reality; the medium that supports them does not.
Having thus removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics: Correlations have physical reality; that which they correlate, does not."

 

[Ken G]

I like Mermin's quote, but to correct it a little, all we can really say is that we do not yet have any reason to attribute reality to either the medium of the electromagnetic fields, or what is being correlated in quantum mechanics. That is not quite the same as being to assert that either are unreal, these are only 100 year-old theories! So what we are noticing is, physics is a process of assigning reality as needed, and in the mean time, we must adopt a stance of complete agnosticism-- or repeat the errors of our predecessors. Thus I view the various interpretations that attempt to assign reality to what is being correlated as "peeks" into a potential next theory, rather than as being able to say anything about reality currently. Mermin seems to adopt the ensemble interpretation, which is like saying "thou shalt adopt no interpretation until its time." That's a fine approach, but many physicists like to attempt a "sneak peek" all the same.

 

[Ken G]

– Okay, "virtual statistical ensembles" sounds cool, but in case I’m not an idiot, we have single electrons in this Double-slit experiment, and afaict, we could have eons between each, so where’s your "ensemble" then??
​

Yes, this is asking "what can we really know about a single particle". If the answer given by the ensemble interpretation is "nothing", this is formally correct, but seems a bit unsatisfying. Physics has never really been about knowing things, there was always some small chance that the whole experiment could blow up in our face. We are seeking effective knowledge in physics, not absolute knowledge. We are perfectly happy with idealizations, we call that "knowledge" in physics all the time! This causes considerable consternation to mathematicians, who seem to have a much more exacting definition of what it means to "know."

 

[San K]

Ok, not all of quantum physics. Mainly just the Double Slit Experiment or Wavefunctions in general.

You only have 3 sentences to teach either one (or both) to an idiot (not me) and they can't be run on sentences either.

This also has to be a math free explanation.

It's not so much a challenge of simplifying the ideas to their most succinct states as it is choosing what is important to know and what you don't really need to know.

Kindof like the desert island deal. If you could only take three facts about quantum physics with you, what would they be?

- relationships transcend time and space...;)
- just because something is small (photon) does not mean it cannot teach us big things about life/reality/universe
- don't ever assume you know it all

 

[mysearch]

Without wishing to divert the thread from the OP too much, I was hoping that somebody might be able to help me better understand a fundamental issue that confuses me about quantum mechanics (QM). In many ways, the following comment seems to summarise the accepted position of QM:

According to the standard formalism of QM, there's no more distinction between particles and waves, as these 2 concepts, as I said before, actually pertain to classical physics, namely the mechanics of point particles and waves (including electromagnetism). So <quantum waves> as a concept does not exist. The fundamental concepts of QM are: (quantum) system, states and observables of a system and virtual statistical ensembles. The rest is essentially mathematics.

The position of Einstein and Bohr can be used to characterise 2 different ‘philosophical’ stances regarding QM. Bohr’s position is said to be represented by the Copenhagen Interpretation and would appear to broadly align to the comment above. As such, the role/ability of science to describe the universe in terms of an objective reality appears to be in doubt or, at least, beyond the remit of QM. While accepting the role of mathematical models is a critical ‘tool’ of modern science, one of my questions is:

Does theoretical physics deny the existence of a physical objective reality?

I am quite new to QM and have only reviewed the key developments in QM up to the 1930’s. As far as I can see Compton affirm Einstein’s idea about light photons having a particle-like nature, which deBroglie then extended to electrons having a wave-like nature, such that the whole wave-particle duality debate re-emerged. Later, Schrodinger developed a wave solution, which although still rooted in classical wave mechanics appears to have a number of key changes. First, the switch to the complex [Euler) form allowed him to create a solution that used the 1st differential with respect to time, while also replacing the concept of amplitude with the symbol [Psi]. In this 1st differential form, he was then able to directly substitute the dispersive relationship between [k] and [w] and replace these terms with equivalent energy and momentum expressions rooted in deBroglie hypothesis. Based on classical wave mechanics, the square of the amplitude would correspond to energy, but Max Born later interpreted this concept as a probability density of finding a particle in a certain location in space. Paul Dirac then completes the mathematical transformation of the original wave equation by correlating it to relativistic energy, but in the process has to introduce 4x4 matrices, which also appear to require complex numbers in order to represent quantum spin.

So does this mathematical transformation in itself exclude the possibility of objective reality or does it simply remain agnostic on the issue?

Returning to a specific point raised in the comment above, which I am not arguing against, simply trying to better understand:

So <quantum waves> as a concept does not exist.

If the quantum wave has no objective existence, then I don’t understand why quantum wave mechanics produces valid results. It would seem that at some level it is able predict the outcome of a physical process involving energy and momentum, which semantically we refer to as particles, even though it appears we cannot define their ‘substance’ other than in terms of a wave, which QM appears to state has no objective existence. Would really appreciate any deeper insights from knowledgeable members or pointers to other references rather than 1-line sound-bites. Thanks

 

[Ken G]

Does theoretical physics deny the existence of a physical objective reality?

My opinion here, and I believe this is something Bohr would have agreed with, is that physics is moot on the issue of existence of objective reality, but it has encountered some fundamental difficulties in accessing the concept. The concept of objective reality pre-existed anything we would recognize as modern physics, so we should probably say that physics was invented to answer questions about the objective reality concept. And in true Douglas Adams-esque fashion, we have now discovered that perhaps we never really understood the question we were asking physics to answer. Now that quantum mechanics has given its answer, we are faced with the challenge of figuring out what the question was supposed to be. That is essentially the role of interpretations of quantum mechanics, but they have succeeded too well-- they produce multiple versions of the question that quantum mechanics answers!

In this 1st differential form, he was then able to directly substitute the dispersive relationship between [k] and [w] and replace these terms with equivalent energy and momentum expressions rooted in deBroglie hypothesis.

Here are two other ramifications of the first-order form to consider: it means we only need the initial wave amplitude, not also its time derivative, to predict the evolution, but this comes at the cost of requiring amplitudes to be complex. So the wave function contains all the information needed, we don't need to augment it with information about how it is changing, but even real-valued wave functions evolve into complex-valued ones. Note this is really a huge shift-- one of the main philosophical stances of classical physics is that when you don't do anything to a system, it keeps doing what it was doing before. But in quantum mechanics, systems can change in fundamental ways even when you leave them alone. The second price we pay for this feature is indeterminacy-- the system must acquire some concept of indeterminacy (with respect to some observable) to undergo a fundamental change (in that observable) without something being done to the system.

So does this mathematical transformation in itself exclude the possibility of objective reality or does it simply remain agnostic on the issue?

I would say neither-- it doesn't exclude what it cannot access, but it is not completely agnostic either-- it says, in effect, "I am not programmed to respond in that area", and since physics was invented as our program for generating such a response, it exposes some fundamental problems with the question we thought we were answering in the first place. The concept of objective reality has been seen to be a very useful notion that encounters fundamental limits that we may never be able to get around. That doesn't mean it doesn't exist, but it does mean that it might as well not exist, for all we get to know about it. But perhaps we simply need to adjust our expectations, to change the questions we are trying to answer, and we will be able to see this as a feature of physics, rather than a bug.

If the quantum wave has no objective existence, then I don’t understand why quantum wave mechanics produces valid results. It would seem that at some level it is able predict the outcome of a physical process involving energy and momentum, which semantically we refer to as particles, even though it appears we cannot define their ‘substance’ other than in terms of a wave, which QM appears to state has no objective existence.

I think you have reversed the logic that should apply to the issue of existence of objective reality. You seem to suggest that physics can only work to the degree that the concept of objective reality can give it meaning, but I would say that the concept of objective reality can only work to the degree that physics can give it meaning. All that has happened is we have discovered what seems to be a fundamental limit in the latter.

 

[mysearch]

Ken, many thanks for some very interesting and useful insights. Again, my comments are primarily to help me better understand current thinking.

My opinion here, and I believe this is something Bohr would have agreed with, is that physics is moot on the issue of existence of objective reality, but it has encountered some fundamental difficulties in accessing the concept. The concept of objective reality pre-existed anything we would recognize as modern physics, so we should probably say that physics was invented to answer questions about the objective reality concept. And in true Douglas Adams-esque fashion, we have now discovered that perhaps we never really understood the question we were asking physics to answer. Now that quantum mechanics has given its answer, we are faced with the challenge of figuring out what the question was supposed to be. That is essentially the role of interpretations of quantum mechanics, but they have succeeded too well-- they produce multiple versions of the question that quantum mechanics answers!

I agree that the idea of objective reality is a very basic assumption, which quantum mechanics makes us question in more detail. Clearly, all human perception is subjective and limited by our physiology, but we are now talking about a far more fundamental concept, i.e. does objective reality cease to have any meaning at the quantum level. If quantum mechanics can only describe the evolution of a system from A to B in terms of a mathematical model, then I guess the question appears to be whether we accept it at face value or continue to question why it works?

Here are two other ramifications of the first-order form to consider: it means we only need the initial wave amplitude, not also its time derivative, to predict the evolution, but this comes at the cost of requiring amplitudes to be complex. So the wave function contains all the information needed, we don't need to augment it with information about how it is changing, but even real-valued wave functions evolve into complex-valued ones. Note this is really a huge shift-- one of the main philosophical stances of classical physics is that when you don't do anything to a system, it keeps doing what it was doing before. But in quantum mechanics, systems can change in fundamental ways even when you leave them alone. The second price we pay for this feature is indeterminacy-- the system must acquire some concept of indeterminacy (with respect to some observable) to undergo a fundamental change (in that observable) without something being done to the system.

Fair point, although it seemed to me that the issue of matter wave dispersion within the quantum model leads to the more far reaching implications. When considering a ‘particle’ in isolation, e.g. a free electron, quantum wave mechanics seems to suggest that its associated quantum wave amplitude, i.e. its probability density, will quickly disperse over an expanding region of space and hence the subsequent need for some sort of wave function collapse. As far as I can see this concept is based on the idea that the wave packet is a superposition of quantum waves propagating with different velocities. Does quantum mechanics, as a mathematic model, provide any rationalisation of these waves or is it simply happy to accept the answers provided?

I would say neither-- it doesn't exclude what it cannot access, but it is not completely agnostic either-- it says, in effect, "I am not programmed to respond in that area", and since physics was invented as our program for generating such a response, it exposes some fundamental problems with the question we thought we were answering in the first place. The concept of objective reality has been seen to be a very useful notion that encounters fundamental limits that we may never be able to get around. That doesn't mean it doesn't exist, but it does mean that it might as well not exist, for all we get to know about it. But perhaps we simply need to adjust our expectations, to change the questions we are trying to answer, and we will be able to see this as a feature of physics, rather than a bug.

While we might possibly spiral into an argument concerning the validity of any conclusion based on the verification of its premise; as a gross simplification, quantum mechanics appears to be a valid premise in that it can verify that a system starts at A and ends at B, but seems ambiguous about the process between A and B. While this has practical benefits, it not clear to me that physicists should be content to accept this situation, even though they may or may not (?) have any better ideas at this time. However, this may just be a personal bias!

I think you have reversed the logic that should apply to the issue of existence of objective reality. You seem to suggest that physics can only work to the degree that the concept of objective reality can give it meaning, but I would say that the concept of objective reality can only work to the degree that physics can give it meaning. All that has happened is we have discovered what seems to be a fundamental limit in the latter.

I agree, this does seem to be a cause of much debate. However, if an objective reality does exist, then it exists independently of any description of physics. Likewise, whether our physics has reach a fundamental limit might also be debated. Again, appreciate the helping hand.

 

[DevilsAvocado]

I somewhat do not get your point. If you perform such a double slit experiment it does not matter whether you perform one measurement with 12876 (non-interacting) electrons or 12876 measurements with one electron. Both experiments are basically giving the same ensemble.

Exactly, that’s my point, though I suspect that an "Ensemble Interpretation'ist" would argue around this...

 

[DevilsAvocado]

I like Mermin's quote, but to correct it a little, all we can really say is that we do not yet have any reason to attribute reality to either the medium of the electromagnetic fields, or what is being correlated in quantum mechanics. That is not quite the same as being to assert that either are unreal, these are only 100 year-old theories! So what we are noticing is, physics is a process of assigning reality as needed, and in the mean time, we must adopt a stance of complete agnosticism-- or repeat the errors of our predecessors. Thus I view the various interpretations that attempt to assign reality to what is being correlated as "peeks" into a potential next theory, rather than as being able to say anything about reality currently. Mermin seems to adopt the ensemble interpretation, which is like saying "thou shalt adopt no interpretation until its time." That's a fine approach, but many physicists like to attempt a "sneak peek" all the same.

Thanks Ken G, that’s a beautiful comment.

 

[DevilsAvocado]

Yes, this is asking "what can we really know about a single particle". If the answer given by the ensemble interpretation is "nothing", this is formally correct, but seems a bit unsatisfying.

Well, I would go one step further and say; it doesn’t work...

This causes considerable consternation to mathematicians, who seem to have a much more exacting definition of what it means to "know."

You’re right, however, I would find it 'disturbing' if empirical data is 'marginalized' due to 'interpretational issues'... this can never be right...

 

[DevilsAvocado]

Does theoretical physics deny the existence of a physical objective reality?

Einstein and Bohr had a 20 year long 'epistemological' debate on the EPR paradox, but they never knew that the whole thing could be settled by an experiment.

One thing is clear (by 99%), that EPR-Bell experiments shows that we have to give up a Local Reality, i.e. the world can be non-local & real, or local & non-real, or non-local & non-real, but we don’t know which at this stage.

Most understand what non-local means, but it’s harder to comprehend non-real... What 'is' that?

According to a PhD in this forum we could use http://plato.stanford.edu/entries/physics-holism/" , in 'exchange' for non-real, but I would not dare to go into that...

Nevertheless, I think I can assure you that "the world" at the fundamental level, is not what we think it is, when using 'common sense'... empirical data show something very different.

So does this mathematical transformation in itself exclude the possibility of objective reality or does it simply remain agnostic on the issue?

In one way I think you could say that’s correct (depending on the final 'verdict'). Bell's inequality is stating that:

No physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics.​

 

[Fredrik]

I’m not trying to raise an 'argument' here, I’m just curious. What’s your answer, if 'an idiot' asks:

– Okay, "virtual statistical ensembles" sounds cool, but in case I’m not an idiot, we have single electrons in this Double-slit experiment, and afaict, we could have eons between each, so where’s your "ensemble" then??
​

The ensemble consists of the particles on which the measurements are performed (one measurement per particle) when you run the same experiment many times.​

 

[Fredrik]

Does theoretical physics deny the existence of a physical objective reality?

I don't think this is something that physics can do, under any circumstances. If the results of measurements aren't viewed as objective truths, then how can we test the accuracy of any theory's predictions? If we don't test the accuracy of the predictions, then we're not doing physics.

The closest thing to a denial of reality you can legitimately do is to deny that quantum theories describe what's actually happening to physical systems at all times. The fact that quantum theories make excellent predictions is undeniable. Some people like to take this as a definition of what statements like "the theory describes reality" or "the theory is telling us what's actually happening" mean. If we define the terms that way, then we certainly can't deny that QM describes reality. But we can leave the term "describes" undefined, and argue that our intuitive understanding of what the term means is good enough. Then we can deny that QM is telling us what's actually happening on a microscopic level.

However, this isn't physics either. We have clearly moved into the realm of philosophy. This little piece of philosophy is telling us something about what physics is telling us, and what physics isn't telling us. There is nothing in physics or philosophy that forces us to believe that one of the "things" that an accurate theory describes is reality.

 

[DevilsAvocado]

The ensemble consists of the particles on which the measurements are performed (one measurement per particle) when you run the same experiment many times.

Okay, thanks Fredrik. As I understand the Ensemble interpretation, it applies to an ensemble of similarly prepared systems or particles, right? And EI states that the wave function does not apply to an individual system or a single particle, right?

I stick out my nose (ready to get flattened), and make this completely wild guess: If you had the possibility to run 12876 separate measurements, in different galaxies, with 12876 different electrons, and then gather the result; you would get exactly the same result as Dr. Tonomura in the video.

Correct?

And if so, where is the "ensemble" in this case?

 

[DevilsAvocado]

I don't think this is something that physics can do, under any circumstances. If the results of measurements aren't viewed as objective truths, then how can we test the accuracy of any theory's predictions? If we don't test the accuracy of the predictions, then we're not doing physics.

This is damned good!

I have never looked at this way! To me, this must be a "self-consistent-logical-proof" that it must be locality that has to go!


... must talk to Mr. PhD ...

 

[Fredrik]

As I understand the Ensemble interpretation, it applies to an ensemble of similarly prepared systems or particles, right?

I prefer to say "identically prepared" or "equivalently prepared" because I like to talk about the mathematical idealizations, but in reality the preparations are of course never identical or completely equivalent, so if you prefer to say "similarly prepared" (as Ballentine does), that's fine too.

And EI states that the wave function does not apply to an individual system or a single particle, right?

I'm not sure the meaning of "applies to" is entirely unambiguous. I would say that the wavefunction isn't a representation of all the properties of a single particle. Instead I would say that it's a representation of an equivalence class of systems on which we can perform measurements, or a representation of an equivalence class of preparation procedures to be applied to a given particle species.

I stick out my nose (ready to get flattened), and make this completely wild guess: If you had the possibility to run 12876 separate measurements, in different galaxies, with 12876 different electrons, and then gather the result; you would get exactly the same result as Dr. Tonomura in the video.

Correct?

That's what the theory says.

And if so, where is the "ensemble" in this case?

You could say that it's spread out over at least 12876 galaxies, but I think it makes more sense to just think of it as the hypothetical ensemble that exists if the experiment is performed over and over. I don't see a reason to require that the ensemble actually exists.

 

[Ken G]

You’re right, however, I would find it 'disturbing' if empirical data is 'marginalized' due to 'interpretational issues'... this can never be right...

I think that depends on whether one is fundamentally an "empiricist" or a "rationalist." The empiricist allows empirical data to define the reality, a rationalist defines reality based on what we think reality is, and merely uses empirical data to check the consistency of the thought. The empiricist objects that thoughts are something different from what is real, but the rationalist counters that you have to think about data too, so at some level you have no choice but to associate thought with reality. So the debate has raged for eons.

 

[Maui]

One thing is clear (by 99%), that EPR-Bell experiments shows that we have to give up a Local Reality, i.e. the world can be non-local & real, or local & non-real, or non-local & non-real, but we don’t know which at this stage.

There is also the possibility that the world might be both local & realistic, but we may need to drop the assumption that the human brain and reasoning fits the universe at large like a glove.

 

[skippy1729]

R. Clifton, J. Bub and H. Halvorson did, in fact, reduce (finite dimensional) quantum mechanics into three statements:

1. No superluminal transfer of information.

2. No cloning. (actually they use no broadcasting of mixed systems)

3. No unconditionally secure bit commitment.

Infinite dimensional representations (if they really exist) can be approximated by large finite dimensional systems. The equivalence is proved in the domain of physical systems which can be represented by C* algebras (which includes, among other things, classical mechanics).

Although simple statements, I don't see them giving much immediate clarity to things like the two-slit experiment. Although the statements are non-mathematical, the proof of the theorem is not.

reference: Foundations of Physics 33, 1561-1591 (2003)
http://arxiv.org/abs/quant-ph/0211089

 

[mysearch]

The closest thing to a denial of reality you can legitimately do is to deny that quantum theories describe what's actually happening to physical systems at all times. The fact that quantum theories make excellent predictions is undeniable. Some people like to take this as a definition of what statements like "the theory describes reality" or "the theory is telling us what's actually happening" mean. If we define the terms that way, then we certainly can't deny that QM describes reality. But we can leave the term "describes" undefined, and argue that our intuitive understanding of what the term means is good enough. Then we can deny that QM is telling us what's actually happening on a microscopic level.

Thanks for a very logical and constructive argument, which appears to be based on a 'premise' leading to a 'conclusion'. As such, it would seem to encapsulate a number of possible variants, e.g.
1) QM is incomplete/wrong, therefore cannot fully ‘describe’ any objective reality?
2) QM is complete/right, therefore it must ‘describe’ some sort of quantum reality?
3) QM is verifiable, but the scope of its ‘description’ maybe limited to a subjective reality?
4) etc.

So the debate has raged for eons.

As it would appear that the debate is still far from any obvious conclusion, I would like to return to one aspect related to the science, and not the philosophy, of QM that was originally raised in post #15 and still puzzles me at a very basic level:

According to the standard formalism of QM, there's no more distinction between particles and waves, as these 2 concepts, as I said before, actually pertain to classical physics, namely the mechanics of point particles and waves (including electromagnetism). So <quantum waves> as a concept does not exist. The fundamental concepts of QM are: (quantum) system, states and observables of a system and virtual statistical ensembles. The rest is essentially mathematics.[/

If I have understood this comment, it would appear to suggest that classical concepts of particles and waves, including EM waves, do not align to the QM description at the quantum level of existence, i.e. they cease to be meaningful? However, if I take the inference that quantum waves are essentially a mathematical construct, I am left wondering as to what, if anything, is left on which any form of physical quantum reality could be built, i.e. what transports energy and momentum from A to B?

 

[DevilsAvocado]

Looks like Stephen Hawking could help us to sort out what constitutes a scientific theory:

Stephen Hawking – A Brief History of Time

A theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.
...
Any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.

P.S. Fredrik & Ken G, will respond ASAP.

 

[Fredrik]

Looks like Stephen Hawking could help us to sort out what constitutes a scientific theory:



P.S. Fredrik & Ken G, will respond ASAP.

I suppose I should say something, since that's a question that I've spent a lot of time thinking about. The term "theory" means a lot of different things to different people, for example:

1. Something that's believed to be true.
2. An explanation of a fact.
3. An approximate description of (some aspect of) our universe.
4. An exact description of a fictional universe that resembles our own.
5. An assignment of a unique probability to each member of some set of verifiable statements.

These "definitions" are all useful in some context. #1 is how the word is used by non-scientists. Since that's almost everyone, I'm not going to say that what they're doing is wrong. They're just wrong to think that the word means the same thing to a scientist. To someone who likes to talk about the theory of evolution, #2 is probably the most appropriate one. #3 or #4 is more appropriate for classical mechanics, but classical theories can also be considered theories of type #5 (with all the probabilities associated with pure states equal to either 0 or 1).

For quantum mechanics, I think only #5 is good enough. It's just not clear that what QM describes even resembles our universe. (I think QM can be said to describe several different things, including a much larger system such that a universe is just an "aspect" of some of its properties, and a single universe in which some of the usual laws of logic don't apply. It probably also describes lots of things I haven't even thought of yet).

Hawking's definition of "theory" is certainly good enough for a book like that.

 

[DevilsAvocado]

I suppose I should say something ...

Very interesting Fredrik, my "time machine" is running backwards today = I will answer later...

However, theory of evolution and #2 reminds me of this nice quote:

Evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away when scientists debate rival theories to explain them. Einstein's theory of gravitation replaced Newton's, but apples did not suspend themselves in mid-air, pending the outcome. And humans evolved from ape-like ancestors whether they did so by Darwin's proposed mechanism or by some other yet to be discovered.

— http://en.wikipedia.org/wiki/Stephen_Jay_Gould" ​

 

[jewbinson]

Doing maths, I find it strange that people mix up the words "theorem" and "theory". But I can understand it.

In maths, there is a clear and "obvious" distinction between a (rigorous) proof/theorem, and a theory (something which is a hypothesis but has not yet been proved).

In physics, everything is in "theories" not "theorem" because sometimes a "better theory" will come along, e.g. GR and QM are more accurate theories than Classical Mechanics. I think this transition from a "worse" theory to a "better" theory is always occurring in physics (throughout history). I guess you could argue that what a "better theory" is is subjective, but I am avoiding these philosophical thoughts and trying to present an intuitive view point. There are - and never will be - a theorem in physics unless a greater being (God) gives us a supernatural ability such that we can understand the universe in a way that we cannot even imagine now. Bu until then, we will always have theories (and good prediction), not fact.

In maths, once a theory is proved, it becomes a theorem and it stays a theorem forever.

 

[DevilsAvocado]

In maths, once a theory is proved, it becomes a theorem and it stays a theorem forever.

Well, you should call Gödel and tell him what you’ve found!

This sentence is false.

 

[Ken G]

There are - and never will be - a theorem in physics unless a greater being (God) gives us a supernatural ability such that we can understand the universe in a way that we cannot even imagine now.

Or another way to say something similar is that physics only has theorems when it becomes mathematics. There is usually a step like that in any physical theory-- the theory sets up a mathematical structure, enters that structure, and proves theorems in that structure (what Fredrik means by an exact description of a fictitious universe that resembles ours-- the fictitious universe is not another real universe that is close to ours, it is a mathematical universe, a different type of entity altogether unless you are a complete rationalist). Sometimes the "proofs" used within mathematical physics have a weaker degree of rigor than pure math is accustomed to, but there are usually mathematical physicists who are willing to work on shoring up the rigor in the background, while physicists closer to the "front lines" of experimental research are not as concerned about that-- they just want a prediction they can test, regardless of whether or not it stems from a rigorous mathematical structure.

The reason that the need for rigor is much less clear in physics is that physics is only tested empirically, and empirical facts are not "pure" facts, they have "error bars" and generally require some degree of interpretation. So there is never an experimental "proof", there is only experimental evidence of the usefulness of a theory. But rationalists tend to believe that the universe "really is" some type of mathematical structure within which the things of interest to physicists "really are" true, and can be proven true within that structure. There's actually very little evidence, from the history of physics, that this is anything but a kind of pipe dream, but what is eminently clear is that treating the universe as if it were a mathematical structure, Fredrik's "fictional universe", has reaped huge rewards. Why that holds is certainly the deepest mystery of physics, and the task of understanding why it is true is probably outside the purvey of physics itself. The real question for us is, in the context of framing quantum mechanics' relationship with objective reality: how literally shall we take that all-important "as if"?

In other words, we discover that before we can begin to answer whether or not quantum mechanics is consistent with a concept of objective reality, we must do a lot more work around what we think we mean by "objective reality" in the first place. Since physics was essentially invented as our means of saying things about objective reality, this task requires that we decide what we think physics is supposed to be doing. Interestingly, after centuries of doing physics quite effectively, we now discover (what has probably always been true) that even physicists themselves do not really agree on what they think physics is supposed to be doing. Thankfully, they can do it, all the same!

 

[Fredrik]

Doing maths, I find it strange that people mix up the words "theorem" and "theory". But I can understand it.

In maths, there is a clear and "obvious" distinction between a (rigorous) proof/theorem, and a theory (something which is a hypothesis but has not yet been proved).

In physics, everything is in "theories" not "theorem" because sometimes a "better theory" will come along, e.g. GR and QM are more accurate theories than Classical Mechanics. I think this transition from a "worse" theory to a "better" theory is always occurring in physics (throughout history). I guess you could argue that what a "better theory" is is subjective, but I am avoiding these philosophical thoughts and trying to present an intuitive view point. There are - and never will be - a theorem in physics unless a greater being (God) gives us a supernatural ability such that we can understand the universe in a way that we cannot even imagine now. Bu until then, we will always have theories (and good prediction), not fact.

In maths, once a theory is proved, it becomes a theorem and it stays a theorem forever.

I don't think I've seen anyone confuse the words "theory" and "theorem", except maybe as a typo. I don't think anyone in mathematics uses the term "theory" to refer to a statement that hasn't been proved yet. It usually refers to a collection of theorems and definitions. For example, "group theory" is the part of mathematics that deals with groups.

I'm not sure what you mean by the last statement. If you're thinking of theorems as objectively true statements, I would disagree, because they are only guaranteed to be true in the formal system defined by a set of axioms, for example the axioms of ZFC set theory and an associated proof theory.

 

[jewbinson]

I don't know much about Godel's Incompleteness Theorems in depth, but I thought all they say is that for any system of facts, there are some statements that cannot be determined to be true or false. I don't see how this means that some theorems cannot be proved.

Ken G - I kind of agree with some of what you're saying, apart from there being an objective reality... but anyway, I don't want to get into a lengthy discussion on the philosophy of reality...

Fredrik - sometimes mathematicians use the word "theory" for unproven theorem - it is not that uncommon. But yes, "group theory" is more common. Anyway, the meaning is context dependent and it is usually obvious what is meant, so it doesn't really matter...

When I say a theorem is true I mean precisely that it is true in the formal system defined by a set of axioms. Whether or not it is objectively true is again philosophy...

 

[Ken G]

The connection with Godel is that the meaning of "true" and the meaning of "provable" can never be the same thing in mathematics. Thus the words cannot be used interchangeably, which was the fervent hope of pre-Godel mathematicians. Our first problem is we cannot know the truth of the axioms, but even if we assume the axioms are true, perhaps in some definitive way (and therefore we must also assume they are consistent), Godel says there must be something that is true but unprovable by those axioms. Or, if we require that the meaning of "true" be "provable from the axioms", perhaps on the rationalistic grounds that within some axiomatic system, "true" can have no other meaning, then Godel says the axioms must be inconsistent. In other words, any attempt within some given axiomatic system to require that "true" be the exact same thing as "provable from the axioms" must fail (for interestingly rich axiomatic systems).

Thus, if we connect "knowing" with "proving", we find that the mathematician has an imperfect relationship between what can be known and what can be true. This problem is of course much worse for the physicist, who cannot really be said to "know" anything at all, but this doesn't stop physicists from adopting a kind of effective meaning of the term "know", often connected with "what can be seen to play out in a reproducible and objective way." It is in quantum mechanics where the physicist confronts most inescapably the question, is the set of everything that we can know to be true defined by the set of everything that actually is true (which is what we'd like to believe), or is the set of everything that is true simply defined by the set of what we can know to be true? We must choose, it simply isn't coherent to adopt the stance that there are true things we cannot know to be true, because in physics, there is no proving-- so that which can be known is all we have to even talk about the meaning of the word "true." No other definition of the word means anything in physics.

 

[PatrickPowers]

It so happens that I have read Godel's original proof. I would recommend that anyone with an interest do that: it is easier to read than any of the "explanations" that I have come across. But if you want another explanation, here it is.

In those days Hilbert thought that it was possible to have a few axioms and derive all of mathematics from that. It was quite a reasonable idea. There are logical systems that can be built up this way. Kurt Godel proved that when the system became complex enough that there were sentences that could not be proved this way. Later it was found that the requirements are: infinite sets, second-order logic (you have to be able to make statements about properties of every element of an infinite set), and being able to have exponents be variables, as in y = 2^x. If you had that then you could make circular statements that can't be traced down to the fundamental axioms. Nobody wanted to give up any of the three requirements, so mathematics went on its way happily unselfproved, just as it had always done.

So how does this apply to physics. In physics there is no requirement that anything be traceable down to a few axioms. The test is experiment. If it works within its domain of definition is all that is asked. In actual practice physicists try to follow the axiomatic model in order to keep excess complexity at bay. There ARE theorems in physics, but those are of the type "Joe's theory is equivalent to Alice's theory." That can be a theorem because it does not assume that either theory is correct.

Note that Godel's result could be avoided by simply giving up on infinite sets. Humans are finite so we can never observe an infinity. So all you would have to do would be to specify smallest and largest quantities and a finest resolution and you would have a system that was immune to Godel's attack. But no one is concerned enough about Godel to do this. There are better things to do.

As to whether there is an objective reality, I'm puzzled by that debate. The way I see it, if there were no objective reality then instead we would have a kind of chaos with no patterns at all, so there could be no mathematics that describes reality. We have such mathematics, therefore by my definition there is an objective reality. Humans may find it peculiar, hard to understand, or even illogical, but such opinions are beside the point.

 

[nazarbaz]

Doing maths, I find it strange that people mix up the words "theorem" and "theory". But I can understand it.

In maths, there is a clear and "obvious" distinction between a (rigorous) proof/theorem, and a theory (something which is a hypothesis but has not yet been proved).

In physics, everything is in "theories" not "theorem" because sometimes a "better theory" will come along, e.g. GR and QM are more accurate theories than Classical Mechanics. I think this transition from a "worse" theory to a "better" theory is always occurring in physics (throughout history). I guess you could argue that what a "better theory" is is subjective, but I am avoiding these philosophical thoughts and trying to present an intuitive view point. There are - and never will be - a theorem in physics unless a greater being (God) gives us a supernatural ability such that we can understand the universe in a way that we cannot even imagine now. Bu until then, we will always have theories (and good prediction), not fact.

In maths, once a theory is proved, it becomes a theorem and it stays a theorem forever.

If you want a god to teach you... Become one... That's the crux of the "anti-humanist" tradition from Nietzsche to Foucault...

 

[Len M]

As to whether there is an objective reality, I'm puzzled by that debate. The way I see it, if there were no objective reality then instead we would have a kind of chaos with no patterns at all, so there could be no mathematics that describes reality. We have such mathematics, therefore by my definition there is an objective reality. Humans may find it peculiar, hard to understand, or even illogical, but such opinions are beside the point.

I’m afraid that I am puzzled by you puzzlement. Objective reality refers to a reality that is independent of the mind. Intuitively we think of objects and facts associated with those objects as having a degree of (or complete) similarity to what we observe, directly or indirectly.

But that intuition stems from the only thing we have – our minds. How can we possibly formulate any kind of procedure in which to step outside of our minds in order to look at what exists outside of that mind?

So any attempt to be definitive about what objective reality actually refers to entails entering the world of philosophical thought, which by definition is endlessly debatable.

From my philosophical perspective, it seems perfectly reasonable to consider objective reality to be part and parcel of our minds – the stone observed by us in terms of space and time is a construct of our minds that is “our” reality. Not that it is an illusion; it’s just what “is”. What lay “underneath” that construct is quite properly the domain of mind independent reality – and that is a reality that is beyond the scientific method – it is an area where objectivity breaks down because we cannot access this reality independently of our minds.

To invoke only scientific or mathematical reasoning in order to remove the uncertainty of mind independent reality with no reference to it being primarily a philosophical question I think is wrong. For me, philosophically, mind independent reality could be a “something” with no patterns as we would think of them, and not even existing in space or time (notions that I think of as being constructs of our minds). Emerging (not in any familiar sense of the word “emerging” of course) from that could be our reality, and within that reality mathematics can describe the consistent physical patterns that we also observe. That process I think of as invoking the scientific method – it is a method that is used extremely effectively to describe “our” reality and it is objective because of intersubjective agreement that exists between all of us. But note that word “intersubjective” - our reality, as a whole, is entirely subjective, we cannot step outside of ourselves, so what we do instead is accept (without realising it) the subjective nature of our reality, but within that subjective reality we look for consistent patterns that we all perceive to be the same. But no where in that procedure is there any definitive means that enables us to step outside of that whole procedure (i.e. our minds) in order to examine if the mathematics (or observation) does describe mind independent reality. Thus whatever our position on the question of what objective reality ultimately refers to, it is a philosophical position, and can only ever be that way. There is room for debate ranging from strong realism to strong idealism - you can be anywhere on this sliding scale, but the whole scale is essentially a philosophical platform, not a scientific or mathematical one.

So I don’t think you should be puzzled by the debate over what objective reality refers to, I can’t think how it could be otherwise.

 

[jewbinson]

Fine, let's do some philosophy. Last week I held the view that all you can know is "your mind"/"your subjectiveness".

At the moment I am uncertain about subjectivity being the only reality.

There are arguments for it, but they all seem to contain some sort of "actual accepting" of an objective reality, even if the person making the argument claims they do not. It doesn't really make sense to say "I think therefore I am" without making reference to something other than yourself. If all you are is truly your subjective mind - the "ego", and/or the "intellect" - which, by the way, I think is the same thing as the ego (most philosophers do not - but I do not understand this), then what are you subjective relative to? How did you come to the conclusion that all you are is your mind's subjectivity? Somewhere along the way you must have experienced some sort of objectivism so that your "subjectiveness" has any meaning.