an autodidact meets a dilettante…

‘Rise above yourself and grasp the world’ Archimedes – attribution

Posts Tagged ‘quantum mechanics

reading matters 10

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New Scientist 3244 August 24 2019

Canto: Being dilettantes and autodidacts, we engage endlessly in educational reading, bootless or otherwise, so I thought we might take the effort to talk/write about, and expand on, what we’re learning from the texts we’ve perused, rather than providing ‘content hints’ as before.

Jacinta: Well of course science mags cover a wide range of topics at very various depths, so we’re going to limit ourselves to the ‘cover story’, if there is one. 

Canto: So today’s topic comes from a New Scientist that’s been hanging around for a while, from a year ago, but since quantum theory is more or less eternally incomprehensible, that shouldn’t matter too much. 

Jacinta: Yes I’ve heard of Lee Smolin, and in fact we can listen to many of his online interviews and lectures via youtube, and he’s described as a ‘realist’ in the field, which doesn’t mean much to me at present, but neither of us know much about quantum mechanics, in spite of having read numerous articles on the topic. 

Canto: You probably have to ‘do the math’, as the Yanks weirdly say.  

Jacinta: Well we won’t be doing much of that. The cover story is titled ‘Beyond weird’, and Smolin’s idea is that we need to move beyond quantum weirdness to something more coherent and unifying. He describes current quantum mechanical theory as comprised of two different laws:

The first… describes quantum objects as wave-like entities embodied in a mathematical construction known as a wave function. These objects evolve smoothly in time, exploring alternative realities in ‘superpositions’ in which they aren’t restricted to being in any one place at any one time. That, to any intuitive understanding of how the world works, is distinctly odd. The second law applies only under special circumstances called measurements, in which a quantum object interacts with a much larger, macroscopic system – you or me observing it, for example. This law says that a single measurement outcome manifests itself. The alternative realities that the wave function says existed up to that point suddenly dissolve.

Canto: So both of these laws – and of course I’m in no position to doubt or to verify their mathematical exactitude or explanatory power – make little sense from a ‘common-sense’ or ‘realist’ perspective, in which objects must always be objects and waves waves, and, if objects, they must be in a particular place at a particular time, regardless of anything observed. So it seems perfectly cromulent to me that Einstein and no doubt many others found something incomplete about quantum theory, in spite, again, of its apparently vast explanatory power. Like it was an intellectual placeholder for something more real or coherent.

Jacinta: Well Smolin seems to be one of those dissatisfied physicists, – he mentions de Broglie and Schrödinger as others – pointing out that the two laws are in apparent contradiction, with the second law unable to be derived from the first. The theory also ‘seems to’ violate the principle of locality, in which forces are dependent on distance. Quantum entanglement does away with that principle. So Smolin sees a way out by trying to incorporate gravity into the quantum world, or at least trying to connect the general theory of relativity and quantum theory into a seamless whole, as their current incompatibility constitutes a major problem. General relativity presents ‘a smooth, malleable space-time’, while quantum theory suggests ‘discrete chunks, or quanta, of space or space-time’.  String theory and loop quantum gravity are some of the attempts to bridge this divide, but these are currently untestable theories. Also, apparently general relativity is compatible with our perception of the flow of time, whereas quantum theory is more problematic, an issue which, I think, Gerard ‘t Hooft attempts to address in his essay ‘Time, the Arrow of Time, and Quantum Mechanics‘ . 

Canto: Yes, he feels that time, with its arrow pointing eternally forward, with no need for or possibility of reversibility, must be an essential element of a grand physical theory.

Jacinta: Maybe. He’s saying I think, that any explanation of our world, any theory, is arrow-of-time dependent, as it necessarily involves preceding causes and antecedent consequences. But let’s just stick to Smolin’s article. He argues that both relativity and quantum theory have issues with the conceptualisation of time. And there are problems, such as dark matter and dark energy, which don’t easily fit within the standard model. So he feels we need to go back to first principles, ‘in terms of events and the relationships between them’. So, according to these principles, space is an emergent property of a network of causal relationships through time.

Canto: Well to keep more strictly to Smolin’s description, he has five hypotheses. One – the history of the universe consists of events and relations between them. Two – that time, as a process of present causes and future consequences, is fundamental. Three – that time is irreversible, cause can’t go backwards and ‘happened’ events can’t unhappen. Four – that space emerges from this cause-consequence chain. Five – that energy and momentum are fundamental, and conserved in causal processes. 

Jacinta: Good, and this is an ‘energetic causal set model’ of the universe, as he and others describe it, to which he’s added a sixth hypothesis, derived from ‘t Hooft, which says that ‘when two-dimensional surfaces are defined in the emerging geometry of space-time, their area gives the maximum rate by which information can flow through them’.

Canto: Now that sounds horribly mathematical. I do note that area = space and rate = time, and so this hypothesis somehow marries space-time with information flow?

Jacinta: Yes, it’s all threatening to move beyond our brains’ event horizon here. Smolin says that ‘in this picture’, and I’m not sure if he’s talking about the ‘picture’ derived from the sixth hypothesis or by all six taken together, but ‘in this picture, every event is distinguishable by the information available to it about its causal past’. This he calls the event’s sky, because the sky, or what we see (speaking about horizons) at any one instant, is what he calls ‘a view of its own causal past’. This has to do with the speed of light – we can’t see what we can’t see. And this sixth hypothesis, combined with the first law of thermodynamics, can apparently be used to derive the equations of general relativity, bringing gravity into the picture. 

Canto: I don’t get the laws of thermodynamics.

Jacinta: The first law is about energy used in a closed-system process, which can be transformed in that process but is always conserved. Anyway, we’ll try to quit before we get in too much deeper. We know that there’s a ‘measurement problem’, a problem of causality in quantum mechanics, in which it is said that a measurement, or observation, ‘collapses the wave function’ to define a particle’s specific place at a specific time. This is counter-intuitive, to put it mildly, and highly unsatisfactory to many physicists, because it seems to make a mockery of how we understand causality. It seems to be a long-standing impasse to the unification of the two major theories. So we’ve only described a fraction of what Smolin has to say here, and there’s also the problem of entanglement. In ‘classical physics’ proximity matters in a way that it doesn’t in quantum theory. Smolin describes, or mentions, a lot of work being done on ‘ensembles’ in an attempt to solve this measurement problem.

Canto: I think one of the issues that the ‘realists’ are concerned with, but perhaps deliberately not mentioned in Smolin’s piece, is the many worlds hypothesis, or the multiverse, embraced for example by Max Tegmark in Our mathematical universe. Neil Turok is another skeptic of this apparent solution to the causality impasse. 

Jacinta: Yes, I don’t think Smolin is an embracer of the multiverse, tantalising though it is in a sci-fi sort of way. Of course we don’t have the mathematical wherewithal to give an informed view one way or another, or to know whether mathematical wherewithal is what’s really needed. I’ve heard it said – possibly by Tegmark – that a multiverse fits so neatly with the mathematical equations that we need to accept it against our intuitions, which have been wrong in so much else. I don’t know… we’ll just have to watch with interest this intellectual battleground, and see if anything decisive crops up in what remains of our lifetimes.

Canto: Singular or plural…

Other references

https://www.frontiersin.org/articles/10.3389/fphy.2018.00081/full

The universe within, by Neil Turok, 2012

Our mathematical universe, by Max Tegmark 

https://en.wikipedia.org/wiki/First_law_of_thermodynamics

 

Written by stewart henderson

September 12, 2020 at 1:08 pm

reading matters 2

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The beginning of infinity by David Deutsch (quantum physicist and philosopher, as nerdy as he looks)

Content hints

  • science as explanations with most reach, conjecture as origin of knowledge, fallibilism, the solubility of problems, the open-endedness of explanation, inspiration is human but perspiration can be automated, all explanations give birth to new problems, emergent phenomena provide clues about other emergent phenomena, the jump to universality as systems converge and cross-fertilise, AI and the essential problem of creativity, don’t be afraid of infinity and the unlimited growth of knowledge, optimism is the needful option, better Athens than Sparta any day, there is a multiverse, the Copenhagen interpretation and positivism as bad philosophy, political institutions need to create new options, maybe beauty really is objective, static societies use anti-rational memes (e.g gods) while dynamic societies develop richer, critically valuable ones, creativity has enabled us to transcend biological evolution and to attain new estates of knowledge, Jacob Bronowski The Ascent of Man and Karl Popper as inspirations, the beginning….

Written by stewart henderson

June 18, 2020 at 11:46 pm