Every electron around every atom in the universe must be shifted as I heat the diamond up to make sure that none of them end up in the same energy level. When I heat this diamond up all the electrons across the universe instantly but imperceptibly change their energy levels.
You kind of expect the “rock stars” of physics to not spout crap like this, so it’s disappointing when they do. But this isn’t a case of him mis-speaking: he doubles down on this notion in a WSJ article.
I recently gave a lecture, screened on the BBC, about quantum theory, in which I pointed out that “everything is connected to everything else”. This is literally true if quantum theory as currently understood is not augmented by new physics. This means that the subatomic constituents of your body are constantly shifting, albeit absolutely imperceptibly, in response to events happening an arbitrarily large distance away; for the sake of argument, let’s say on the other side of the Universe.
This statement received some criticism in scientific circles. Not because it’s wrong, because it isn’t; without this behavior, we wouldn’t be able to explain the bonds that hold molecules together. The problem is that it sounds like woo woo, and quantum theory attracts woo-woo merde-merchants like the pronouncements of New Age mystics attract flies – metaphorically speaking.
Well, no. The issue isn’t the Pauli Exlusion Principle itself — that’s sound science. It’s what he’s done with it. The first, obvious problem is that relativity tells us that the communication can’t be instantaneous. The second is that the Pauli Exclusion Principle doesn’t work this way. It applies to a single system in which you have all these identical electrons, and they can’t be in the same exact state. This is because of their QM behavior if you were to exchange them — something has to be different about the two electrons. In a crystal, the energies are slightly different as a result, and you get a band of energies. But this does not extend beyond the system, be it crystal or even individual atoms — the electrons belong to different systems, which are not co-located. Exchanging electrons meaning exchanging systems as well. That’s what’s different.
Here’s a simple argument why this can’t be true: we can tell time with atomic clocks. A Cs atomic clock, for example, has electrons in one of two possible ground states, separated by an energy which corresponds to a frequency of 9 192 631 770 Hz. If the energy levels are different, as Brian contends, because of all the other electrons in other Cs atoms in the universe, we wouldn’t have this sharp energy difference and shouldn’t be able to get the part-in-10^15 kinds of accuracy (and even better levels of precision) from atomic clocks. That we can do this is a pretty strong indication that he’s wrong.
Maybe QM is so misunderstood because some prominent physicists are pitching it as mysticism instead of science. Coincidentally, I just got an offer for a copy of his new book to review. I wonder if I should accept.
Added: I should be clear that I’m good with pretty much everything else mentioned in the article. It’s the mysticism-connectedness angle, and the physics explanation, that is bogus, I don’t expect that from Brian Cox.
Added 2/25: Making my case in a little more detail
Isn’t he saying that we can model the universe as a single box with lots of electrons in it? If so, can’t we extend the notion of Pauli exclusion to that level? Now, I would say that no two electrons can be in the same state, though there can be degenerate states. He’s saying that if you make a change to one part in the box, all the energy levels move and so everything adjusts. As for the accuracy you’re mentioning, my guess is that the effect would be several dozen decimal places beyond what you’ve noted for Cs.
I guess I’m not sure, I’m just thinking about this still as I type.
=Andy
Nice post, as usual. I agree with your general take on what Brian Cox said, but I’d finesse the objection a little bit more.
QM says more about electron wavefunctions than just the Pauli Exclusion Principle: it says that the collective wavefunction of all the electrons in the universe is antisymmetric with respect to particle exchange. In this sense, all electrons in the universe really are linked together in some sort of mystical new-age “everything is connected to everything else” voodoo.
But — and this is a crucial caveat — the antisymmetrization is only of physical consequence when there’s some nonzero overlap of the spatial part of the electron wavefunctions. So it’s wrong to say — as Cox does — that anything is “shifting…in response to events happening an arbitrarily large distance away”.
Well put. I just saw this clip the other day and it was an eyebrow-raiser, to say the least. I thought I’d mull over the broader implications a bit before writing my own post on the subject, but you’ve addressed it well.
A more technical way to put it, if I were to try, is that the Pauli principle applies to the *entire* quantum state of the wavefunction, not just the energy, as Cox seems to imply. This is why we can, to first approximation, have two electrons in the same energy level in an atom: they can have different “up/down” spin states. Since the position of the particle is part of the wavefunction as well, electrons whose spatial wavefunctions are widely separated are also different.
I think the mere existence of quite narrow spectral lines (by which we identify star types and rotten apples, among others) is sufficient proof QM should not be interpreted as BC suggested.
Well… anyway, we should stop stating opinions, we should go for the proof. Let’s put all the atoms in the Universe in one big equation, calculate the solutions, add a perturbation, see what it results 😀
The point I would make is that it’s all very well treating the universe as one big system, but it’s only relevant if it’s in its ground state (in which case shifting one electron out of its energy level will alow others to move into it).
He may be talking about the “electron” as the the universal electron field, which he may be inclined to do as he’s happy to talk about an electron being “in two places at once”.
Right – no two electrons can be in the same quantum state, but quantum state ≠ energy state
Oh dear. Andy is correct, by the way. Have a look at how we teach bonding in our undergraduate course at Manchester.
http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double Well.html
“Since the position of the particle is part of the wavefunction as well, electrons whose spatial wavefunctions are widely separated are also different.” What on earth does this mean? What does a wave packet look like for a particle of definite momentum? Come on, this is first year undergraduate stuff.
For a fuller explanation have a look at my book The Quantum Universe. When you’ve understood that, if there is still an issue, I (and my colleagues) would be fascinated to hear it.
I’m glad that you, Tom, don’t need to know about the fundamentals of quantum theory in order to maintain atomic clocks, otherwise we’d have problems with our global timekeeping!
But Prof Cox, I’m not sure what the relevance of that webpage is to what you were talking about – ie that exciting one electron changes the energies of every other electron in the universe. For a start, both electrons in that example are in their lowest energy state.
This post is a little embarrassing, specially the part where you cite your experience with atomic clocks to as evidence to the contrary of Prof. Cox’s position. Surely, you must have noticed that the ‘systems’ bit can be extended to the universe and that your very precise atomic clocks will still not be able to note the difference if there were any?
“What on earth does this mean? What does a wave packet look like for a particle of definite momentum? Come on, this is first year undergraduate stuff.”
Wait, so you’re arguing from the basis of extreme wavefunctions of *definite* momentum? One of the things I learned in first year undergraduate is that those basis states are nice for simple models, but *not* how the real world works.
You know, if you want to be taken seriously on these matters, you might try actually arguing your point instead of making snarky condescending comments at folks trying clarify things.
Yeesh.
For what it’s worth, I think Brian is mostly right. Consider covalent bonding as an example. The combined energy levels of two spatially separate atoms, with an electron each, are slightly different than twice the energy levels of an atom with one electron. So it’s correct to say everything is connected in this way. If there has been any mistake here, it is the confusing statement that the equivalence principle says that electrons in separate atoms must be in different energy states. The truth is more complicated. And, of course, one cannot instantaneously affect distant atoms by jiggling electrons locally, or Einstein would be really pissed.
I’ve read all these comments and don’t know what to think.
Men of Science, start your proof engines. Fight!
Seriously, how does it work?
I think you owe it to him to read his book as he has clearly thrown down the gauntlet to you, and see if it cuts the mustard for you. I look forward to your review.
“What does a wave packet look like for a particle of definite momentum? Come on, this is first year undergraduate stuff.”
I’m glad this is first year undergraduate stuff, this way I at least can attempt to follow it 🙂 So here’s me trying to understand this a little better:
A particle with definite momentum, from what I understand, has a degenerate “wave packet” spread out over the entire space (because you’re taking the Fourier transform of the Dirac delta, right?).
I can’t see how it applies to the discussion. As far as I can see, the electrons in the diamond don’t have wavefunctions even remotely like that: they’re confined to a small space. So why doesn’t the original argument apply: the position is part of the wavefunction; the positions don’t overlap; therefore the wavefunctions are different even if the energy levels are the same; therefore the Pauli exclusion principle doesn’t exclude anything.
!
Here’s another counterpoint: if heating up a diamond affects all other electrons, then what we consider to be Fermionic atoms are no longer identical, since they will have electrons in different energy states. They are distinguishable. So individual atoms should not obey Fermi statistics.
But they do. Two half-integral spin atoms obey Fermi statistics, because they are identical. Their electrons are in the same energy states.
Forget the electrons, is anyone else wondering where Brian gets those excellent sweaters?
Trying to a apply current quantum theory on the scale of the universe simply reveals a lack of appreciation for the limits of currently available theory. The best available theory is based on a marriage between quantum mechanics and special relativity — quantum field theories (QFT). There remain issues with respect to the mathematical consistency of QFT, but neglecting those issues the fact remains that they are at best consistent only with special relativity.
Special relativity is a localization of the general theory, and it is general relativity that is the current best theory of spacetime on anything approaching the scale of the universe. We have no current useable quantum theory that is consistent with general relativity and thus one cannot meaningfully apply local quantum theory at the scale of the universe. Arguments that ignore this problem are simply not logically valid.
Short version: swansont is right and the rock star put his foot in his mouth and is having difficulty extracting it.
DrRocket,
This is of course correct – one can introduce new physics, which is why in the article I wrote for the WSJ it says “This is literally true if quantum theory as currently understood is not augmented by new physics.” Another example, less wide-ranging, would be some kind of decoherence at large distances. The statements I made do apply to QFT, as currently formulated (see below).
Swansont: you imply (as does DrRocket) that non-locality in QM is not consistent with relativity – it is. This is standard EPR stuff and no information can be transmitted, although of course wavefunctions change “instantaneously”. I also said this in the article.
Secondly – it is absolutely true that the energy levels in all the Caesium atoms in the clock are spilt – in the absence of new physics, countless times. By the way, this is how we understand bands in semiconductors, so it’s not at all controversial.
Thirdly, all atoms do exhibit this splitting of energy levels – did you read my link to a covalent bond lecture we give? Do you object to any of it? If so, why? You can’t have read it because you just repeated the error in a comment post.
Have a read of our book – as I mentioned, I would be interested to know if there are errors, but it’s been out a long time in the UK and no colleague of ours (myself and Prof. Forshaw) has brought our attention to any issues. I look forward to your review.
Massaro – apologies for the undergraduate comment. As shown in the notes I posted, it is not correct to think of separate electron wavefunctions confined to single atoms, no matter (subject to the caveat about new physics) how widely separated they are. The logic in the example does not make reference to a decoherence distance scale, and there is nothing in standard QM that would give you one.
Here is another way to think of it. In our book, we start from the path integral – we show how the wavefunction emerges from this formalism. One has to consider all paths, over all of space and time – so it’s even worse than just thinking abut non-locality in space. In non-relativistic QM, the classical action is used in the exponent and the theory is manifestly non-local. Feynman’s first calculation using path integrals, by the way, was to derive the Scrodinger equation, using the classical action in the exponent, following an earlier little-known paper by Dirac. In relativistic QM, the action is more complicated, and is ‘weighted’ (loose language) outside the light cone, but there is still a non-zero contribution from outside the light cone, which contributes to the amplitude.
And finally, the sensitive Dr. SkySkull ! What do you mean by “not how the real world works?”. The point is that the position space wavefunction does not have a preferred place in the theory. Remember that the wave function is just a collection of complex numbers given a particular choice of basis. A momentum eigenstate is no less ‘real’ than a position eigenstate, or an energy eigenstate, etc. etc. But in position space, typically the array of complex numbers representing an energy eigenstate (or momentum eigenstate) is rather large – infinite, in fact, for the momentum eigenstate of a free particle. I suppose you can argue that there is no such thing as a free particle, because there are other articles in the universe, but I would argue that on the scale of a particle, this is semantics – plane waves are most definitely part of the formalism. If you don’t like that, you have to do some pretty extreme surgery to the theory.
I enjoyed the lecture myself, but was left a little bewildered at what Prof. Cox exactly meant by his statement about his statement on everything being connected. My attention was drawn to the wave-function of the universe, which is rather outside of what one would call established physics. Anyway…
In my very limited experience of public engagement trying to say something non-trivial, in a way that people understand and not be misleading is near impossible. One has to be careful and you cannot expect to get it 100% correct 100% of the time. With that in mind I would not give Prof. Cox too much of a hard time.
I always envy the astronomers who have nice pictures!
As an aside in Manchester while I was a PhD student I attended a few of the particle theory seminars and Prof. Cox was present. I never said hello, don’t know why I am not usually shy!
Brian: after studying the “Double Well” text in more detail, I think I mostly understand it. Thank you for sharing it.
@Brian Cox: The EPR correlations are indeed non-local but they refer, for example, to a pair of photons that were created in the single state then shot off in opposite directions. It’s clear that there’s a correlation there. Of course the nature of this EPR correlation is such that it can’t be used to transmit information. However in the present discussion we’re talking about a correlation, not just of a spin direction which could give either up or down when you measure it, but in energy levels – energies can be measured, and if my excitation of an electron in London can cause an instantaneous change in an electron energy in the Klingon system, wouldn’t that mean that information can be transmitted instantaneously in principle?
Or are you invoking the energy/time uncertainty to protect you – i.e “yes the remote electron energy shifts instantaneously but the delta couldn’t be measured until the new state had hung around for a time long enough for the energy uncertainty to drop to an appropriate value” ?
Brian,
I did read the link, but the thing about science, as you already know, is that you can make all the models you want, but nature is the final arbiter. If see this band structure in individual atoms, I’d love to read the paper that discusses the discovery of it. There also the issue I raised about individual atoms following Fermi-Dirac statistics. Nature thinks they are identical, any models to the contrary notwithstanding.
Garrett,
I’m sure there is some fascinating physics to be investigated in the realm of when bonds form and the transition from individual atoms to molecules and the implications on the Pauli Exclusion Principle, but experiments confirm that distinct atoms behave as identical particles.
twistor59. The long range correlations between EPR photons are a consequence of the non-local nature of the theory – not the other way round. And no, information can’t be transmitted using the long-range correlations – this statement is not specific to EPR photons. In field theory, this is a difficult thing to prove, but as far as I know (and I am certainly not an expert in this aspect), without having to invoke the cluster decomposition principle as an axiom, one can show that QFT is causal. Have a look at Weinberg’s discussion in the Quantum Theory of Fields, chapter 4. However, this does not imply that there are no long-range correlations – just that long range correlations cannot be used to transmit information. This has nothing to do with the energy-time uncertainty principle. Remember that the uncertainty principle (and the exclusion principle) can be derived from the path integral approach. They are not axioms, and in fact they can be viewed (at least I view them) as a manifestation of the non-local nature of the sum over histories formalism. Indeed, we show this in our book.
Perhaps another way to think about this is to note that there is only one electron wave function in the Universe – it is a multi-particle wave function, and it is antisymmetric under the exchange of any pair of electrons because electrons are indistinguishable, spin half particles (the antisymmetry comes from the spin half, of course. In our book, we show that, quite generally, there are only two possibilities for indistinguishable particles, and nature takes advantage of both). Therefore, whatever you do to an electron must have consequences for the wave function as a whole, and this is the spirit of my statements in the lecture and the WSJ article. I believe this is the standard interpretation of quantum field theory. As I mentioned, proving that this still leads to a causal theory is difficult, but as far as I am aware it can be done absolutely rigorously without additional assumptions. I’m not entirely certain that Weinberg manages this in his book. I need to read it again!
swansont – I’ll give you an experimental example of the shifting nature of the energy levels in an atom due to field theoretic effects – the Lamb shift.
@Brian Re “In field theory, this is a difficult thing to prove, but as far as I know (and I am certainly not an expert in this aspect), without having to invoke the cluster decomposition principle as an axiom, one can show that QFT is causal” yes, I *think* that you don’t need cluster decomposition as an axiom, I think it automatically follows from the microcausality assumption (commutativity of Heisenberg operators for spacelike separations), but my Weinberg is at home so will have to wait till tonight !
I’m still a bit worried about long range correlations between energy measurements in the very-remote-double-well scenario. You said (presumably you were referring to these energy correlations) “However, this does not imply that there are no long-range correlations – just that long range correlations cannot be used to transmit information”. That is the bit I’m struggling with at the moment. Let’s see if I can phrase my confusion better:
I have this very widely separated double well with a fermion in each well in the system ground state which is antisymmetrized and has two incredibly close energy levels (ignore spin to keep the discussion simple).
I now tickle my local fermion up to the first excited level.
What is the state of the system just after tickling time? Is it still antisymmetric ? As far as I know, it is, but if that’s the case then if I make an energy measurement in my remote well, then isn’t there now a teensy weensy probability that I get a different value to the one I got when both fermions were in the ground state, namely I *just* might get an excited value ? So there’s a teensy weensy probability of sending some information FTL.
I think I need to go and think about this a bit more…..!
I would agree with Brian, except I don’t see the wave function in quantum mechanics as a 3 dimensional object, but as a 4 dimensional object (at least as used in current QFT, I will leave out string theory notions at this moment). Certainly if one is only able to observe the wave function in 3 dimensions it is possible it appears dynamic.
In any case, what is changing in the field is the probabilities associated with observing a particle in a possible state, the particles themselves are not being affected in anyway, only the possible outcomes of a particular observation of the particles.
Let me interject with what I believe is one source of confusion. I think many different issues are being conflated here, but as I see it the source of the claim that “everything is connected” is that energy eigenstates of two spatially separated, but nonetheless interacting systems, are entangled states. Whether you view entangled states as non-local is a matter of taste, but this is not a useful discussion to get into. That claim is true, but I think too much is made out of it.
The point is that energy eigenstates, pedagogy in UG physics courses notwithstanding, don’t have a privileged status in the theory. So for example, if you start with such a stationary state and “wiggle” one subsystem, the full system does not have to instantaneously adjust itself so that it stays in a definite energy state. The story is more complicated, and certainly is causal: if an electron 5 lightyears away wiggles, all the electrons in my body will certainly adjust, but not until at least 5 years from now. This is not much different from what happens in classical physics, where we interact in small ways with faraway objects (nor should it be different, physics is classical on those scales).
Another source of confusion is between Bose/Fermi statistics and entanglement. The wavefunction of identical particles is not a product state, even when they are not entangled. The symmetrization or antisymmetrization of the wavefunction is aimed to avoid attaching specific labels to particles which are indistinguishable, but is not by itself a source of entanglement or correlations. But again, it is true that energy eigenstates of separated particles are generally entangled.
To Moshe- I don’t follow, I’m afraid. You say the state of identical particles is not a product state, and also not entangled. Isn’t the definition of entanglement literally ‘not a product (or separable) state’?
As to the central issue, I think the clearest way to think about this is to consider the Hamiltonian of the universe. In simpler systems, whether have be single or multiple particles, we can identify symmetries in the Hamiltonian that lead to degenerate energy states- spin symmetry, or rotational invariance, etc etc. As far as I’m aware, there’s no reason to expect that the Hamiltonian of the Universe as a whole to have any sort of symmetry whatsoever, and thus it should be completely nondegenerate. Pauli exclusion leads to a huge antisymmetric state made up of every combination of each electron in each energy state, and the eigenenergies of this state do change when you do pretty much anything. So as far as I can tell, Prof. Cox is entirely correct.
Whether the state is a product state or not is description dependent, not a physical statement, If you insist on writing many-particle state for identical particles in terms of labelled one particle states, then you have to symmetrize or anti-symmetrize with respect to the choice of label. This does not introduce entanglement or correlations into the state: the results of measurements are still statistically uncorrelated, the entanglement entropy is zero, and any other physical or mathematical measure of entanglement is identical to what it is for a product state of non-identical particles. The only difference is that instead of saying: I have electron number 1 here, and electron number 2 there, you say that you have one electron here, and one electron there, without attaching labels to them. The state of those unlabelled electrons can be correlated or uncorrelated.
On the other hand, in the usual formalism of QFT, you create your Hilbert space by acting with the same creation operators on the vacuum any number of times. Bose of Fermi statistics is then automatically implemented since those creation operators are already un-labelled. But, whether a state is entangled or not cannot depend on the description, and it does not if you characterize your statement sufficiently precisely.
I wanted to provide one of my favorite sections in Veltman’s Diagrammatica. Under Chapter 3 “Interacting Fields”, Section 3.2 “Hilbert Space”:
“This needs very careful consideration. A vector in Hilbert space represents a physical state. What is a physical state? A physical state is simply a possible physical situation, with particles moving here and there, with collisions, with dogs chasing cats, with people living and dying, with all kinds of things happening. Often people make the mistake of identifying a physical state with the situation at a given moment, one picute from a movie, but that is not what we call a physical state.
The situation at some moment may be seen as a boundary condition: if one knows the whole situation at some moment, and one knows the laws in nature, then in principle we can deduce the rest.
Thus a physical state may be CHARACTERIZED by the situation at a definite moment, but the state itself refers to the WHOLE WORLD INCLUDING PROGRESS IN TIME. Conveniently, expecially for scattering processes one may use the time points /- inf.”
Under Section 3.3 “Magnitude of Hilbert Space”
“It follows for the above that we can have as many states in Hilbert space as possible situations at t = -inf. We now ASSUME the following asymptotic condition: if particles are sufficiently far apart in space they do not interact and behave as free particles. If we go sufficiently far back in time particles will be separated. Therefore we may assume that the possible situations at t= -inf are precisely the situations of non-interacting particles. Thus the Hilbert space of interacting systems is by this assumption equally large as the Hilbert space of free particles.
Clearly we still have to modify this if we want to consider stable bound states. No matter how far back we go in time, the electron and proton in a hydrogen atom do not separate. To describe such situations properly we must enlarge Hilbert space and allow states containing hydrogen atoms. Of course, such atoms again can just be considered as a new kind of particle, and the Hilbert space becomes then effectively the free Hilbert space of three (in this case) particles (electrons, protons and hydrogen atoms). ”
I really like this notion, because in my mind it conjures up the thought that any notion of observation/wavefunction collapse/decoherence is merely creating a boundary condition, the physical state is still a much larger space. Or progress to the next “situation” can then be modeled by taking our current “situation” as some number of non-interacting particles at -infinity which evolve to some set of “situations” at infinity which has some probability distribution associated with it.
/-inf should be /-inf
Nice straw man Brian. I made no statement whatever that non-locality is inconsistent with quantum theory. I am quite familiar with EPR experiments and said absolutely nothing that is contrary to the results of those experiments.
What I said is that you are applying a theory WAY outside of its domain of validity and reaching unfounded conclusions. That statement is absolutely correct.
Ok the “plus” is getting eaten somewhere. plus/minus inf
DrRocket – I do not agree with you. What is the domain of applicability of quantum field theory as currently formulated, in your opinion?
@Moshe thanks, I for one was certainly confusing the antisymmetrization/entanglement issue.
Getting back to the “perturb one of the wells” scenario, does this correspond to your understanding of how it would work:
Start with both fermions in the ground state. This is an energy eigenstate of the system with both ground state levels (very closely spaced) occupied. I can write it as 1/sqrt2(|E1>|E2>-|E2>|E1>) where |E1> and |E2> are the two very-close-in-energy single particle ground states. In the position representation I could represent it by some function Psi(x1,x2) which is antisymmetric under interchange of the first and second labels.
If I now perturb one of the fermions into the next higher level, this level will not correspond to an energy eigenstate of the double well system, all the fermion can “know” about at that time is the potential in its immediate locality. So just after the perturbation the system will NOT be in the state 1/sqrt2(|E1a>|E2>-|E2>|E1a>), where E1a is the next highest energy eigenvalue for the double well. The system state, not being in an eigenstate, will evolve in time.
Measurements made (just after the perturbation) on the remote fermion will continue to yield the value E2 until a time of the order of x/c where x is the spatial separation.
I think part of the problem is that I’ve never seen a relativistic treatment of the double well to get a feeling for the state evolution in the relativistic case. Does anyone know a reference for such a thing ?
I also find the way Brian uses Pauli exclusion principle objectionable.
Yes, the Pauli exclusion principle says that two electrons cannot be in the same quantum state, but position is part of the quantum state.
BEC is a good example, the atoms are all in the same ground quantum state so their electrons despite being fermions each have to be in the same corresponding quantum state with the sole exception being their position, Pauli exclusion principle doesn’t prevent this because they are spatially separated.
The way I understand it the Pauli exclusion principle only states that two fermions cannot have the exact same wavefunction.
Moshe- thanks for the clarification. It appears to me that the situation is this: the symmetrization/antisymmetrization requirement can act as an entangling operation (in some circumstances, at least), but until there is a way to individually address the particles (ie, until they become distinguishable again) they are not actually entangled.
Brian Cox: Re: domain of definition of quantum field theories
Again you engage in sophomoric debating tactics rather than an attempt to discuss real physics. Let’s discuss the question a bit more reasonably as no one has ever precisely defined the domain of validity for any theory. At best there qualitative assessments — e.g. Newtonian mechanics is applicable at low speeds and moderate gravitational fields. The situation with quantum field theories is even less clear as we do not yet even have theories that are rigorously defined and consistent in the mathematical sense.
I recognize that you do not agree with me. That was clear from your rather video, which started this entire discussion. No one who makes such outlandish statements could possibly agree with me.
As you should know, quantum field theories have been shown to have extreme accuracy for some purposes and in some situations, while being not at all useful in other situations. For instance, QED is quite accurate in its prediction of the anomalous magnetic moment of the electron, which I am sure even you would classify as a local effect. But when one attempts to use that theory to estimate the cosmological constant, a global phenonema, the estimate is in error by something like 120 orders of magnitude and some people consider a factor of 10^120 a significant error.
Now, quantum field theories were formulated precisely because of a need to include effects of special relativity. Special relativity is the localization of general relativity. So, one can see that the domain of validity of a quantum field theory, that domain in which it might be a reasonable approximation to the behavior of nature, can only be a subset of the domain of validity of special relativity itself. That domain is quite clearly substantially less than the entire universe, and your statement is therefore clearly outside of it.
This is getting silly. I think I am done.
I’ll be preparing a full explanation of this for publication somewhere, and will post a link here when it’s up. Thanks for the interesting debate – it’s raised additional points that require clarification, and I’ll deal with them all.
The explanation is essentially that in my book, The Quantum Universe, chapter 8, which you could read if so motivated!
Best
Brian
Brian Cox – you made a mistake. Just admit it. Don’t muddy the waters.
http://motls.blogspot.com/
Brian did really well and needs encouragement, not critisicm i feel.
After studying Science with the O.U. for 6 years (studying BSc,final year), The way Brian Cox was teaching was the first time someone has gotten close to explaining the forces of interactions smaller than electron/proton/neutron interactions (I think he was great).
Brian,
The Lamb shift is internal to an atom, so I don’t see how this matters. If you are correct, atoms of the same isotope are not identical because the electrons are in different states. So how can you form a Fermi
gascondensate? Nature thinks the atoms are identical.Brian, I think you should apologize for hurting DrRocket’s feelings. He’s oh so sensitive.
Talking of the Pauli exclusion principle, Pauli was also famous for using the expression that something was “not even wrong” which I think applies perfect to Brian Cox’s statement “imperceptibly change”. I could say when I cough all the atoms in the Universe imperceptibly change!
I often just lurk on blogs like this one, but today I feel like writing my two cents.
I see two issues with Cox’s video. One, which is being discussed extensively, is as to its scientific validity. Another, is to whether it fulfills the goal of popularizing science in a positive way.
As to the validity of his claims, it is indeed true in a trivial way. If QM is correct, and if his model is accurate, then it is true that if he shakes the crystal all electrons in the universe will adjust to it. But there is nothing novel to it. Newton’s theory of gravitation could make exactly the same claim: if Newton flicked a booger in one direction and not another, all planets in the solar system would readjust to it (instantaneously, by the way). As for the claim, it was indeed correct at the time of Newton, and nobody would dispute it then (with the risk of getting some nasty letters from Newton himself). The question is of relevancy for the effect. Show me some paper published in a decent peer-reviewed physics journal (I would even accept Physical Review Letters 🙂 ) that takes into account the effects of an Andorian shaking a dilithium crystal on the electron energy distribution of a metal on Earth, and I will quietly back from my claim. 😉
As to the goals of popularizing science in a positive way, I am on the camp that thinks it does not. I’ll explain. You do not have to make claims such as Cox’s to get people interested in science. We have many different and wonderful things that we can talk about, and which are mesmerizing to almost anybody, including scientists working on them. So, what are their effects on those not already interested in science? I am afraid that the effect is to make science even more mystifying, but, worse, to make some believe that science somehow resonate with their beliefs about how souls are interconnected or what not, or other New Age stuff, or, heck, crystals! Now I understand why my neighbor’s crystal helps with my chakra, I guess. Any claims that mystify science may do science a disservice. I believe that Cox’s claims are seem by many as almost mystical, but I may be wrong.
Anyway, enough talk (writing) from both sides of my mouth. Now, back to work.
The Jab: I think the main gripe with Cox’s statement is that the effect is instantaneous for all the electrons in the Universe which may be true in your Newtonian example but of course isn’t in general relativity or quantum field theory which enforces that no communication can be made faster than the speed of light.
“If you are correct, atoms of the same isotope are not identical because the electrons are in different states. So how can you form a Fermi gas condensate? Nature thinks the atoms are identical.”
-Swansont
As do Fermi-Dirac statistics as mentioned before! So does every computational package that constructs a multi-particle state from atomic basis states!
I don’t see what the issue is here. Surely Prof. Cox is talking about exchange correlation. Sure, the exchange integrals that quantify this correlation would be negligible (which is why we don’t have to include Saturn in quantum chemistry calculations), but the concept itself is interesting enough to discuss. Or am I missing something?
is this recent story of relevance? Seems to be…
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
Hi Morbert,
your missing the fact that too many people have a stick up their arse when it comes to attempts at science popularisation
(and yes, you are entirely correct)
Here’s a fact for you: Brian Cox believes that the phases of the Moon are caused by the shadow of the Earth falling on the surface of the Moon. This was broadcast on BBC Radio Wales on 19th January 2012. I have the recording if anyone wants it, and I have been trying to ‘undo’ this damage in conversation with people for weeks since. For me, any suggestion of scientific credibility he held prior to this collapsed in on itself instantly.
My comment is a little late because I have just today finished Chapter 8 of Prof Cox’s book. I definitely suggest you read it for clarification of his argument as he suggested. I can’t claim to be any kind of an expert in this field but I can follow a sound and logical argument, and that’s just what the book delivers.
Jon, just looked at chapter 8 and that argument at Amazonl.com. I am very glad that I did waste my money on that book.
The argumenet is indeed something that can be followed and sounds very good at first blush. Unfortunately, like many arguments in popularizations, it is a pile of crap.
All curent physical theories, and likely all future theories, have limitations. Quantum mechanics has zero basis for application across macroscopic distances except in special circumstances such as those in crystals, let alone distances at the scale of the entire universe.
Unfortunately the simple fact is that to read real physics you must read a real physics book and listen to real physicists. Swansont is a real physicist, doing real applications of physics, not someone whose reputation is based on popularizations.
Jon,
This is, perhaps, the “beautiful hypothesis slain by an ugly fact” (though the level of beauty is debatable). The result of the argument is that individual atoms (or any composite Fermions) are not identical, and so they would not obey that Pauli Exclusion Principle. But they do. At least one of the components of his argument must be false.
DrRocket, it is well understood that quantum mechanical effects are usually negligible across macroscopic distances, but they don’t disappear. They just become imperceptible.
Swansot: Hmmm, from my understanding of his chapter is he is saying that distant atoms are the same system, and so changing the electronic structure of one atom changes the structure of the entire system, albeit by an imperceptible amount, and not by any ftl communication.
@DrRocket
That’s plain nonsense. Zeilinger’s group have demonstrated quantum entanglement across the Canary Islands. What you mean is that we can’t detect any quantum correlations once the system is not isolated from interactions, but that hardly means that nature suddenly gives up with wavefunction malarky once she has to handle say a hundred particle correlations, does it?
@swansont
The only identical things in nature are the fundamental particles, leptons, quarks, and a few bosons.
Two atoms are identical in the same way two spoons are identical, they look the same and behave the same for all practical (measurable) purposes, but they are not identical like fundamental particles are identical
JG
Two atoms are identical as defined by the Pauli Exclusion Principle, which is the basis of this whole disagreement. Cox says that protons and neutrons are identical, too, yet they are not fundamental particles. You can’t pick and choose when it applies.
Well, protons are mostly a complex cloud of virtual gluons, so I doubt any two protons in the universe are exactly identical, but they’re perhaps more identical than two atoms which are more identical than two spoons … but they’re not IDENTICAL, not like two gluons are identical.
I think everyone would agree that Cox’s jiggling is not there for all practical purposes, I mean we’re talking about shifts of probability in the many googleplexth decimal place. It’s irrelevant to science in the same way the poincare recurrence theorem is irrelevant to statistical mechanics (maybe even much less relevant)
But THEORETICALLY the wavefunctions of every particle in the universe overlap.
Now it may be that the current formulation of QM will be corrected and such miniscule overlaps can be formally ignored out for other reasons, maybe QM has non-linear corrections for example.
But I doubt it.
er, I meant googolplexth
Dear all,
An update on this debate. Myself, Jeff Forshaw and Sean Carroll have been working away to see if we can get this physics clear and agreed. We’ve made some progress, but we’ve not fully converged yet. What we do all agree on is that virtually everything in Tom’s post is incorrect. In the interest of clarity, let me sort these points out.
Point (1) There is no problem with causality for entangled states, as I think many people have pointed out, even though there can be instantaneous, non-local changes. No information is transmitted instantaneously – standard EPR. Let’s leave aside for the moment whether the non-local energy eigenstates of a multi-well system can be treated like that – this is something we want to cover when we write up our ongoing debate. Myself and Jeff believe they can, but we have yet to prove this to Sean’s satisfaction – we may therefore be wrong.
Point (2) “The Pauli Exclusion Principle applies only to a single system”. Wrong. It applies to multi-well systems, and this is the way we understand bonding and the band structure in semiconductors, for example.
Point (3) The energy levels in all the Cs atoms in your atomic clock are most definitely split. Jon Butterworth dealt with this nicely on his blog
http://www.guardian.co.uk/science/life-and-physics/2012/feb/28/1
Point (4) Referring to your comments, Tom, on various web sites, you keep saying that this splitting of the energy levels within atoms would result in them not obeying Fermi-Dirac statistics because they would no longer be identical particles. This is wrong. For a composite system, it is the number of fermions within the system that determines what statistics the composite system obeys. Odd number – Fermi Dirac, Even number – Bose Einstein. See for example Helium 3 and Helium 4. Nothing at all to do with what energy levels the constituents are in – are you claiming that all Helium 3 nuclei are identical in terms of the distribution of the particles that make up their nuclei? As another related example, a proton is a tremendously complex thing, and each one has a different gluon distribution, as JG points out in the comments above, not to mention quark anti-quark pairs … look at a pdf, and you’ll see a strange quark contribution which is non-zero at low-x. But because it has three valence quarks, and always contains an odd number of fermions, it behaves as a fermion. Hence nuclear physics.
But here is the point I want to make. Everybody goofs, as Sean said in his initial tweet when this debate arose. I goof – as Stevie C points out in the comments here, I apparently said in a radio interview that the phases of the Moon are caused by the Earth’s shadow, which is clearly bollocks! Unless I was talking about a lunar eclipse, I can’t understand what I must have been thinking. Probably the end of a long day. Sean goofs – his original blog post isn’t correct about the reason for electrons being localized around atoms – it is nothing to do with electron-electron interactions. This we’ve been able to agree upon. Tom goofs (see above). But do Tom’s goofs mean that he’s full of **it? Of course not. Tom is one of the rare professional scientists who cares about communicating science to a wide audience. This is a very difficult thing to do, and eventually, everyone will goof. Science is hard.
If you didn’t see Sir Paul Nurse’s excellent Dimbleby Lecture on BBC1 on Tuesday evening, have a look for it on line. Paul, who is a Nobel Laureate and President of the Royal Society, was making the argument for a more scientific society at every level: from increased funding to evidence-based policy making in government. He outlined several basic rules of scientific discourse, and proposed that they should be adopted in politics, religion, and indeed universally. Amongst them was that debates must be conducted with humility, civility and respect. Someone will be wrong, of course, because nature is nature, irrespective of our point of view. BUT this is where science has something to teach the rest of society. We must be vocal in our disagreements and tenacious in our pursuit of good science. But, as an example to the terrible rabble that populates many internet forums, we should remain true to the axioms so eloquently outlines by Sir Paul.
In the interests of the advancement of scientific principles, therefore, I will restrain myself from saying anything disparaging about Lubos Motl.
Hmmm, I would hope that an experimental physicist would place a little more emphasis on what could either in principle or in practice ever be measured.
The difference between physics and pure mathematical or metaphysical speculation is precisely in this point. Asking yourself whether the ‘connections’ have measurable consequences is a great way of clarifying whether they represent any physical reality.
I seem to remember Einstein was good at asking this sort of question…
Stringph – forgot to link to this paper, which might answer that – the Feynman Propagator is non-zero outside the forward light cone, and this may have measurable effects
http://arxiv.org/pdf/0707.0475.pdf
Brian
1. I’m not sure where entanglement came into the picture; I don’t recall anyone making the case that these particles were entangled.
2. I said single system, not single-well system. I fact, I pointed out that the example of a crystal counting as a system in this post as being subject to the Pauli Exclusion Principle.
3. Jon made his case, but the proof of the pudding is in the eating. Why don’t we see a Pauli-induced band-structure widening of the transition? Even seems to Jon admit that the energy changes in the multi-well model are not due to the Pauli Exclusion Principle.
4. F-D statistics apply because the particles are identical. Your claim in the video is that the PEP forces the electrons into different energy states, making them non-identical, but simultaneously you seem to be claiming that each atom is still identical. If you can distinguish between the atoms, you should be able to fit more than one of them into an energy state (ignoring spin for convenience, as everyone seems to have done). But we don’t see this. We see them acting as identical particles.
Either an energy shift distinguishes the particles or it doesn’t. From my perspective it seems that you are claiming both are simultaneously true.
If I have a potential well, the PEP would allow me to drop two non-identical Fermions into it and have them be at the same energy level. This is what I meant by “not following F-D statistics”.
@Brian: I’m also of the opinion that two identical fermions in the double well system we’re discussing are *not* entangled (unless you introduce some deliberate mechanism to introduce entanglement). One of Moshe’s posts above convinced me this was the case. To be doubly sure, I raised a question on the physics stackexchange:
http://physics.stackexchange.com/questions/21677/energy-measurements-in-a-two-fermion-double-well-system
(no answers yet though !). Just to be clear, I’m talking about the model where we have a couple of fermions in the system, and any other properties which would allow them to be distinguished, such as spin, are indentical for the pair.
The argument is: after the measurement, the system would still be in the antisymmetrized energy eigenstate, so I could make no deduction about what the remote guy would measure if he were to do an energy measurement. The thing I was a bit uncertain about was: could a *local* energy measurement actually yield an energy eigenvalue of the *global* double well system ? If it doesn’t, then after the measurement, the system wouldn’t be in an eigenstate of the double well, and I could then make a deduction about what Mr Remote might measure.
Isn’t part of the problem that Quantum theory and Relativity just *aren’t* consistent with each other.
Nor is Quantum theory mathematically consistent.
(The one-particle Schroedinger equation can’t be turned into a relativistic quantum wave equation.)
To get around this problem, QFT uses re-normalisation techniques; particles” are treated as the quanta of a classical field.
Wave propagation is calculated using Feynman’s weighted integral over all possible paths.
This works for Maxwell’s electromagnetic field.
But at very high energies and small scales, QT says that virtual particles and anti-particles are created.
i.e. temporary violations of conservation of energy, so one particle can become a pair of heavier particles
This isn’t predicted by Relativity, furthermore, according to Einstein, “Action at a distance” isn’t possible.
Whereas, according to QT, it is.
The fact that Ernst Mach was Pauli’s godfather could be a clue to his way of thinking (think of his explanation of Newton’s bucket)
As could Pauli’s contribution to Carl Jung’s “Synchronicity”.
QT says that Instantaneous change to a non-local state, containing points A & B, does happen *if* they’re both part of one quantum system.
But recording such an event is observer-dependent, requiring:-
(a) Measurement of the state change, which introduces the uncertainty principle.
(b) Sending a light signal at a finite speed.
(c) The event and the observer are within the same light cone.
Which means that a “no-signalling” theorem applies
( arguments from controversial new papers aside)
Twistor59 I believe the entanglement in question is present across all indistinguishable particles. It is a weak entanglement, but still an entanglement.
@Morbert Could you explain a bit more what you mean by “entanglement across indistinguishable particles”. I can see how entanglement works in the EPR context, but I get confused when trying to apply it here.
If we take entanglement entropy as a measure of entanglement, defined as follows: the system with Hilbert space H is partitioned into 2 subsystems so H=HA X HB (X is supposed to be tensor product). The general full system state is |Psi>=sumover_j (c_j|Psi_j>_A X |Psi_j>_B) where |Psi_j>_A are a bunch of orthonormal states for HA, |Psi_j>_B are a bunch of orthonormal states for HB and c_j are constants. The entanglement entropy is then S_A = -sumover_j |c_j|^2log|c_j|^2. Applying this to the classic EPR spin 0 particle decaying into two spin 1/2 products, HA is the left hand decay product and HB the right hand one. The system state is (1/sqrt(2))(|up>_A|down>_B-|down>_A|up>_B) so the entanglement entropy is clearly positive.
If I want to compute the entanglement entropy for the double well system with two fermions though, I first need to decide how to factorize the full double well Hilbert space into the two components such that H=HA X HB where HA relates somehow to the observer at the left hand well, and HB to the other one. Having done that, I could compute the entanglement entropy for any system state and then I’d be happy about saying if it was entangled or not. I’m not sure how to factorize the double well Hilbert space in this way though.
The system requires entangled pure states to be described. The general form of the state is
|Psi> = sumover_i,j c_i,j |psi_i>_A X |psi_j>_B
Consider out two-quantum-well system, with the two wells arbitrarily far apart. The first two one-electron energy states are |psi_1> and |psi_2>. The ground state of our system will be (ignoring normalization)
|psi_1>_A |psi_2>_B – |psi_1>_B |psi_2>_A
as you can see, this is not a separable pure state. This inseparability is imposed by indistinguishability.
Hi Morbert,
I think what you’re saying is: Let’s say the double well system is symmetric about the origin, with subsystem A being that half of the system lying to the left of the origin and subsystem B to the right. Then, in order to talk about entanglement between states, we would need the full Hilbert space H of double well states to be decomposable as a tensor product of subsystem A states and subsystem B states, which is what I think you were stating in your first equation
|Psi> = sumover_i,j c_i,j |psi_i>_A X |psi_j>_B (where X = tensor)
What I can’t see, at the moment however, is how to construct those states |psi_i>_A, |psi_i>_B and hence decompose H in this way. If we want to use entanglement entropy as the measure, then this tensor product decomposition is central to the argument (see http://arxiv.org/abs/0708.2978 ).
Incidentally, do you think it would be a good idea to continue this discussion on physicsforums.com ? They have LaTeX support and it may facilitate things a bit ?
Sure. My username is Morberticus. Feel free to PM me, or to start a thread somewhere. We can discuss the maths in the forum.
This paper discusses the weak entanglement I was talking about.
http://arxiv.org/abs/quant-ph/0508078
Thanks for the ref – I’ll have a read of that and if still unclear, I’ll PM you (user “sheaf”, though I hardly ever post there).
Well, after reading several papers on entanglement in systems with identical particles, I’m none the wiser about how to apply it here. I summarize a few things I’ve read here http://physicsforums.com/showpost.php?p=3803621&postcount=108
Hey there Stevie C–might you have a recording of this? If so, please email to me @ gbfmgbfm@live.com. Thanks!
“Stevie C on February 27th, 2012
Here’s a fact for you: Brian Cox believes that the phases of the Moon are caused by the shadow of the Earth falling on the surface of the Moon. This was broadcast on BBC Radio Wales on 19th January 2012. I have the recording if anyone wants it, and I have been trying to ‘undo’ this damage in conversation with people for weeks since. For me, any suggestion of scientific credibility he held prior to this collapsed in on itself instantly.”
There’s also this: “Trailer for a radio programme on BBC Radio Wales this morning. It’s a phone-in item for programme guest Prof. Brian Cox. Little kid (sounded 5 or 6 years old) asks: Why is the moon sometime round and sometimes looks like a banana. Prof Cox: “That’s the shadow of the earth.”
-http://www.thestudentroom.co.uk/showthread.php?t=1907163
Any recordings of the trailer?
One more teensy bit of information on this issue is the following statement from Peres’ book (http://www.amazon.com/Quantum-Theory-Concepts-Fundamental-Theories/dp/0792336321) in his discussion of the cluster decomposition principle
<>
He’s using the “traditional” definition of entangled here – not one of the fancier ones I mentioned in the physicsforums link above.
Sorry, the quote didn’t get posted in that last link and I can’t edit it. It was:
An immediate consequence of Eqs. (5.37) and (5.38) is that two particles of the same type are always entangled, even if they were prepared independently, far away from each other, in different laboratories. We must now convince ourselves that this entanglement is not a matter of concern: No quantum prediction, referring to an atom located in our laboratory, is affected by the mere presence of similar atoms in remote parts of the universe.
The title of this post is, sadly, more true than ever. Perhaps the asterisks should be replaced with the appropriate letters.
Everything Brian Cox said in the above video was wrong. Instead of saying “Yes, I was wrong. I was trying to explain something to a bunch of celebrities and screwed up. Here’s what I should have said…”, he has engaged in obfuscation, changed the subject, thrown out irrelevant citations and made a host of wholly misleading remarks.
He is now being aided in this shameful exercise by other pop physicists who seem eager to help him save face. It is amusing how they stick together.
For everyone else reading this post and the comments there is only one question:
Haven’t you learned from this that it is pointless to engage those who refuse to argue and reason in good faith?
Yes–I have noted how Sean Carroll seems to be trying to save face for Brian Cox, when what Brian Cox stated is 100% WRONG!!!!
RAF–what other pop-scientists are trying to protect him, save face for him?
🙂
Come on Brian. Just admit it. You made a boo boo. Now you are trying to retrofit and obfuscate. My opinion of you is sliding down the drain.
“Prof Brian Cox is a physicist who was the main presenter of the one-hour-long 2011 BBC special, “Guide to the Moon”, among many other programs. You may expect him to know something about the Moon; you may also be wrong. ”
-motls.blogspot.com/2012/03/brian-cox-and-lunar-phases.html
Great Books – While I wouldn’t call Jonathan Buterworth a pop physicist, he does blog for the Guardian and has two posts helping Cox save face
http://www.guardian.co.uk/science/life-and-physics/2012/feb/28/1
http://www.guardian.co.uk/science/life-and-physics/2012/mar/07/1
The latter has a video from the Sixty Symbols group at Nottingham which is cringeworthy.
I’ve seen several others but I did not save the links, sorry. They were rather like the latter day Michio Kaku claptrap (he was once a physicist!).
If I find them again, or any others, I’ll put them up here.
RAF III your comments aren’t really saying anything. Why is he full of sh**t? Defenses I have heard have been perfectly reasonable.
would be better for you if you spend more time in understanding physics better and less in discrediting well established science with your non-sense crap to form some self-identity!
@sujeet,
In what way is an effect that is too small to measure and thus confirm experimentally “well-established”?
Morbert –
For his defense to reasonable it would first have to be intelligible – it is not.
Yes, I only described his actions and did not address them in detail. My remarks were intended for those who know physics. It is pointless for them to engage the likes of Cox.
For reasons of my own, it amuses me greatly to recommend the following posts of Lubos Motl, which should be read in the order given:
http://motls.blogspot.com/2012/02/brian-cox-misunderstands-locality-pauli.html
http://motls.blogspot.com/2012/03/brian-cox-and-lunar-phases.html
http://motls.blogspot.com/2012/03/energy-measurements-in-two-fermion.html
http://motls.blogspot.co.uk/2012/03/most-of-research-of-nonlocality-is.html
There you will find you will find clear, direct, and to the point explanations of the actual physics behind this dispute as well as the proper technical meanings of the everyday terms being used by Cox to mislead wider audiences.
To master the photon is to master our universe. Scientists will one day unlock the encrypted force within. The particle with no mass holds the key to the particle with all mass. The human race will be blessed with an applied technology of unparalleled usefulness.
Shhh Neo… they’re already in early stages of Bessel/tractor beams. They’ll reveal the final key soon enough. 8 to 1, 1 to 8 – please keep the Oracle’s word behind the gate.
He is not speaking at a symposium or scientific meeting.
He is over simplifying and being generalist and he is not being entirely accurate but then again he is not submitting anything here for peer review. High school science teachers do worse every day. But then teachers do qualify statements of inaccuracy with the limits of the curriculum. Perhaps Prof. Cox should acknowledge the level and audience he is trying to educate/engage.
phylo,
It would be one thing if he had subsequently clarified his remarks that way, but Prof. Cox did not.
This may seem a moot point but aren’t we confusing ‘energy level’ and ‘quantum state’?
Every electron around every atom in the universe must be shifted as I heat the diamond up to make sure that none of them end up in the same energy level. When I heat this diamond up all the electrons across the universe instantly but imperceptibly change their energy levels.
Prof. Cox was demonstrating the shift in electrons in relation to the consequence of interaction with the diamond.
Every electron in the universe would shift imperceptibly, not to ensure something did/didn’t happen but they would shift regardless.
Now if he had a bucket of diamonds and shakes it around vigorously it would shift at a subatomic level this debate to make it even more tedious.
You don’t argue when he states the universe being 13.7 bn years old or the sun being almost a third of that… regardless of the aging methuselah…. But God forbid he should talk about electrons shifting so they obey the law that no two exist in the same ‘quantum state’ or energy level. How will I sleep!
Prof. Cox, along with others, has given me a keen interest in physics, quantum mechanics and the similarities/differences between atoms in us and the atoms in space. He doesn’t condescend but presents what he belives and what Feynman describes ‘a guess, the consequence of the guess/experiment nature=result’ proves.