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Hello, I am attending the Cosmological themed Spring Meeting in Cardiff and would like to ask a question about a possible cosmological paradigm based on my experience of numerical modelling. Rather embarassingly I have very little maths to explain the idea but have composed a “creation myth” to try and explain it (see the attached file).
Regards
Ken WhightHi David, I wouldn’t call my proposal a Theory as I have no mathematics to directly support it. I was just trying to find a way to understand how QM and GR could be made to fit together given that the current fashion of assuming GR must be quantised seems to be stalling or at least leading to some pretty wild cosmologies e.g. Multiverse. Perhaps the reverse option should be considered i.e. QM arises from our limited view of a wider more classical universe.
I attach a paper in which a physical problem (semiconductor device simulation) was numerically solved in the type of “space” I am imagining, though the cylindrical topology may not be required (ignore the wayward points in figure 4 and beyond, a faulty mobility model implementation was to blame). Currents are flowing at all points in the space and I would guess in this particular case that convergence to a solution of given accuracy would have been fairly chaotic throughout the space (I never looked at the convergence behaviour). If this was going to be a suitable paradigm to model our universe then the physics would need to be such that the convergence was more structured, like a crystal seeding and growing from a melt.
Sorry that’s all I have but I think there are avenues to explore to explain observations like entanglement, dark energy and dark matter as I set out in my previous attachment so the proposal should be falsifiable.
Regards
KenHI Ken
Do you have a version with references? As it’s a bit difficult to track your notes without any citations and/or sources?
Regards
AdamHi Adam, I thought I had attached a reference to my last post but it seems to have failed as it’s 4.7MB. I’ve attaced zipped version that comes in at just under the limit.
Regards
Kenp.s. the Tessa paper and an second paper applying the large signal solution methos to electronic circuits is available on the legacy page of my website http://www.thewhightstuff.co.uk.
Hi Ken, in your paper you propose that ” converged to sufficient accurace” equates to the uncertainty principle. However, this is well known not to be the case. The uncertainty in quantum mechanics is not reducible to some classical analogue.
Indeed classical mechanics is based on the simplest probability theory where the sum of the probabilities add to one while while QED is based on the next more complex one where the sum of squares of the probability amplitudes add to one.
String theorists claim they have achieved the unification you seek Unfortunately, it requires 10 dimensions. Signs of these extra dimensions are being looked for in LHC data. See this https://cerncourier.com/a/the-lhcs-extra-dimension/ for example. Time will tell.
Regards Andrew
An equivalent way of saying this, though it needs considerably deeper understanding of QM, is that the uncertainty principle follows inexorably from the properties of the Fourier Transform.
The linkage is that a quantum state is fundamentally a function of complex numbers, whereas in classical mechanics everything is purely real.
Some of you may know why that the question of the existence of uncertainty principle relating energy to time, and why it has the same value as position-momentuum relation is very far from obvious, largely because time is not a quantum operator. A fascinating journey down a rabbit hole finally gives a good answer to that question, but the reasoning is very far from obvious.
Thanks for all the comments. I am aware (but don’t fully understand) that experiments to test Bell’s in-equalities prove that there is no hidden variable classical interpretation of QM but I was hoping that by “widening the stage” some of the existing certainties might be circumvented.
Classical mechanics is deterministic and the whole of history is pre-determined so that our existence is like being in a completed movie and there is no reason that we should be conscious of any particular time.
Quantum Mechanics is probabalistic and history is built by random interaction outcomes as time flows and that history, once written, is fixed.
In the world view I am suggesting our past is still evolving to the tick of the external “computer clock” and our future is also developing to this clock with everything driven ultimately by “boundary conditions”. Our conscious existance is driven through a spacelike 4D world (there may well be more dimensions to account for all the “forces”) and what we call history exists only in our memories.
Hi Ken,
So the difficulties between the quantum world and general relativity are actually more profound that just the uncertainty principle and the whole problem hinges on finding the much sort quantum theory of gravity. Let me explain…
First up, quantum mechanics. QM as governed by the Schrodinger equation is non-relativistic. We can see that because in this equation we differentiate twice with respect to position, but just once with respect to time, In relativity space and time are treated equally and that clearly isn’t the case with Schrodinger’s equation. Now the relativistic version of QM is quantum field theory. This is quite a change of quantum mechanics- in QFT underlying fields are fundamental objects not particles- and when these fields are stimulated under certain conditions, they give rise to particles- in much the same way as striking the chord A minor on a piano keyboard generate the musical sound of A minor.
Now QFT when applied to condensed matter physics is very accurate- there are problematic infinities in the equations (in order words, instead of a finite numerical value you get an infinity) but these can be renormalized away quite safely with predictions that agree very accurately with results from condensed matter physics experiments. The Fourier transform is a key part of this as it describes how the field works in terms of annihilation and creation operators. Excite the field with the creation operator and you get particles from the field, you can de-excite it until you reach the ground state (also known as the vacuum state). Since the particle is written in terms of annihilation and creation operators the particle is uniquely defined. The theory is also relativistic and can be applied to Maxwell’s equations to give a relativistic version of electromagnetism. So far so good- now to General Relativity.
General Relativity (GR) is a classical field theory and are governed by the Einstein Field Equations. On the left hand side we have quantities like the Reimann tensor which describe the curvature of spacetime, and on the right hand side we have the energy-stress tensor- this represents the matter and energy. In other words then, if we have something heavy like a star or a black hole, its matter-energy is represented by the stress tensor, and this tells spacetime how to distort and curve. Solutions to Einstein’s equations are metric tensors- these tell us (with the aid of a line element) how to measure distances in points between spacetime. The flat spacetime of special relativity is one example, the Schwarzschild spacetime is another. There are also cosmological solutions like the Robertson Walker spacetime and de Sitter spacetime solutions. These are all vacuum solutions though, and this means that outside the event horizons, the stress tensor is zero. Also the stress tensor doesn’t care what the matter and energy is made of, and has no quantum description.
So, this brings us to Hawking radiation. Clearly, all objects in the Universe have to obey all the laws of physics, not just some of them. in particular, they all have to obey the second law of thermodynamics: entropy increases in a closed system. If an object has entropy then it has heat and is coming into thermal equilibrium with its surroundings. As it turns out, black holes have a measure of entropy- this is their event horizons. As a result, black holes must have a temperature and this was what Hawking discovered. How does this help? Well thermodynamics are statistical physical processes which are governed by quantum phenomena- so in the vicinity of the event horizon, QFT and GR have to agree and work together.
The first attempts to do this properly is to put QFT into GR. This is done by replacing the stress tensor with something called the expectation value of the stress tensor- now it is composed of quantum fields rather than a generic ‘lump of matter’. This is where the problems really come in. Firstly, the vacuum (or ground state). The crux of this is the Fourier transform as I mentioned earlier. If you put the Schwarzschild back hole into QFT instead of flat spacetime, you find that there is more than one vacuum state! So the annihilation operator which de-excites you field before the star collapses to become a black hole, might no longer do so after the black holes has formed. As a result the notion of a particle is now deeply ambiguous. Worse still, the infinities!!! In flat spacetime we can renormalize them away, but energy contributes to the stress tensor- it is a potential source of gravity in general relativity and so we can’t just renormalize it! There is a process for doing so in one dimension but there is no general procedure for doing it 4 dimensions, and the processes in 4 dimension involve a mathematical technique called ‘point splitting’ which may or may not be Lorentz invariant!
So where does this leave us? Stuck, frankly! There are two approaches: string theory which has taken up a lot of money and time but delivered very little. We thought a few vacuum states was bad enough but in string theory there are something like 10^235 vacuum states and it is not clear which (if indeed any) are physically meaningful. The other approach is loop quantum gravity- here the idea is that spacetime is made up of tiny course grains down at the Planck level- however great problems remain here, for example it is not possible to recover ordinary flat space results in a low energy limit as one would expect.
The real paradigm shift will be the solution to the problems I have outlined here, they are conceptual and not just computational, and they require a deep understanding of the mathematical and physical tools we use in physics. I suspect at some point, someone will come up with a new understanding of space, time matter and energy- as far removed from general relativity as Newtonian mechanics is from special relativity. There are also many dep problems with quantum mechanics which have yet to be resolved and these do carry over to QFT. To sum up- the physics we have is very successful- it allows to build semi conductor devices and sat navs but there still remain many deep problems to solve.
Cheers,
-PaulPaul: a very nice summary!
There are other approaches to QGD. the Wikipedia article on quantum gravity lists a couple of dozen or so.
Stephen Wolfram and I have long thought that the universe may be a cellular automaton with as-yet unknown rules. A recent development by Wolfram posits that the fundamental quantities in the cellular automaton may not be occupancy (as in the classic Game of Life) but graphs. The rules convert a parent graph into another for its child. https://www.wolframphysics.org/technical-introduction/ contains a simple but lengthy exposition of his ideas. https://www.wolframphysics.org/ itself gives links to a wide variety of related topics.
There are indeed other approaches but these are the two main attempts so far, and the history of their developments allows a fairly simple introduction to the area without too much technical detail. In any case, many of them are similar in approach albeit with different wave equations (Dirac, Yang-Mills+gravity, DeWitt-Wheeler) and don’t as yet add much to the general picture I was describing for Ken.
Yes, I am familiar with Wolfram’s idea- I have to say I am not convinced at the moment. I have no issues with spacetime geometry being an emergent phenomenon, nor indeed time being an emergent phenomenon (which I’m sure it is and I wouldn’t be surprised if it has more than one dimension), but as yet I haven’t seen anything which really deals with the problems discussed here or other problems like the violation of unitarity.
cheers,
-PaulPaul:
I was pretty sure you would would be well acquainted with the field. My post was addressed primarily to those who are not (yet) so well informed. That’s why I took care to include easily accessible links to alternative theories.
For my part, Wolfram may well be on to something useful but he is a very long way from a theory of everything and I suspect that he agrees with me. My suspicion is that a paradigm shift will be needed for a successful merger between quantum fields and GR as a set of functions over a 1+3 dimensional continuum. The shift is likely to be as profound and disruptive as that which separates Newtonian/Galilean mechanics and quantum field theory as descriptions of the motions of particles.
FWIW, Stephen and I have known each other since 1982 and still keep in touch occasionally.
Good to have the two Paul’s potted descriptions of facets of cosmology. Makes for a nice read on a Saturday evening!
Richard
I agree with you Richard, thank you Paul and Paul for your replies, I just have to try and fully understand them now!
I had an enjoyable career working for Philips Research from 1973 to 2008, mainly in silicon device physics (to 1993) during the time when computing power was rapidly expanding. However, I have always had an interest in the more exotic fields of Cosmology and Quantum/Particle Physics and over the years have tried to
improve my knowledge in these areas. So now that I have completed my stellar spectroscopy project (BAA Forum topic “Spectral Line Modelling – please would somebody review the work) I think my winter project will be to try once again to improve my cosmological knowledge.In the past I have tried to work my way through quite a few books on GR (getting a little further each time) more recently I have worked through the “Theoretical Minimum” books by Lenoard Susskind and got to chapter 10 (before running out of steam!) of “Quantum Field Theory for the gifted amateur” by Tom Lancaster & Stephen j. Blundell, I have also bought “Covariant Physics” by Moataz H. Emam. It’s difficult working alone so would anybody like to join me in studying these books? Are there better books?
One last comment on this topic and I appologise if it sounds a bit mystical, but I don’t think we will get a “theory of everything” until we can fit “free will” or at least the illusion of free will into the picture something that I thought might be possible with my suggestion of a variable Planck “Constant”.
In my view, by far the best book on GR is known as MTW amongst those who study the subject. For everyone else it is “Gravitation” by Misner, Thorne and Wheeler. A web search on “MTW Gravitation” will turn up plenty of useful links.
It is now 50 years old so misses recent developments such as gravitational wave astronomy (though it does cover gravitational waves themselves), chunks of modern observational cosmology, more treatment of alternative theories to GR than would be taught these days, and so on. However, for a thorough grounding in GR it still can’t be beaten in my opinion.
Beware, though, that this is not a book for the faint-hearted dilettante. It’s roughly 1300 pages long, can do double-duty as a door stop, and assumes a background knowledge appropriate to a physics graduate. (That said, I don’t have a physics degree but Oxford chemistry appears to have been sufficiently rigorous.) Some sections are clearly marked as being at a significantly higher level of difficulty; all of these can be skipped without missing anything important for those who want a more gentle introduction.
Ken: sounds like you have the physics background to cope with this work. I’m pretty sure that you have a better grasp of classical electrodynamics than I, for example, based on what you write above.
A few minutes ago I learned of the death of Jim Hartle.
Hartle’s book on GR, Gravity: an Introduction to Einstein’s General Relativity, also has an extensive fan club. I happen to prefer MTW but please take a look at Hartle to see if it is more to your taste.
Hi Ken,
I think an deep understanding of the mathematics involved is essential- there are some popular books which give overviews of GR and particle physics but without understanding topics like differential geometry, exterior calculus, group theory and Lagrangian dynamics it’s almost impossible to accurately convey the subjects properly. It’s rather like learning a foreign language by repeating constructed sentences but not knowing the meaning of the words.
I’ve been teaching our General Relativity course at Leicester University which our 4th year MPhys students can opt to take and I would recommend:
-‘Introducing Einstein’s Relativity’ by Ray D’Inverno
-‘A short course in general relativity’ by Foster and Nightingale.Not convinced about a variable Planck’s constant for a variety of theoretical and experimental reasons at the moment.
Cheers,
-PaulPaul: Almost entirely agree. Where we may differ is in the level of understanding required. One needs to know what those words mean but one does not need to be able to conduct original research in those fields. What is required lies somewhere in between. In my opinion, anyway.
That’s a major reason why I recommend MTW. It not only defines those words, it gives a relatively gentle introduction to what they mean and how to use the concepts in practice. Though, to be fair, Lagrangian dynamics is (IIRC) treated in the advanced track and can be skipped on initial study. An STEM undergraduate level of group theory is undoubtedly very useful but may not be strictly necessary. Again, IMO.
It is not unusual for pedagogues to disagree on details. What is unusual is for them to agree on all the details.
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