A good book that explains quantum physics like I'm an idiot?

[arfa brane]

M'kay, you probably have heard about the pencil-standing-on-end argument about symmetry. When the pencil is upright and balanced, the direction it will fall is unknown, but by symmetry it must be one of a possibly infinite number of directions. When it does fall the symmetry is broken.

Introduce a force to "restore" the symmetry (prosaically, lift the pencil back up onto its tip). Now you have to think about which symmetry is global, and which is local, and in respect of which fields.

Another common symmetry-breaking example is ferromagnetism. A bar of unmagnetized iron can point in any direction (let's place the bar inside an opaque sphere), but when it is magnetized the direction can be measured because of the magnetic field lines--the symmetry is broken. Spherical symmetry breaks when you identify a pair of antipodal points (because you have direction).

 

[arfa brane]

Probably has got a fair way from a good book that explains it like i'm an idiot.

I've seen the argument that the easiest approach is the computational one. It helps to understand logic gates, and why Boolean logic, by itself, is irreversible. This is intuitive if the AND and OR gates have multiple inputs and one output. In quantum logic, the important feature is that n inputs have n outputs, information cannot be lost or erased, only converted (eventually to classical measurements). Unitarity is required, hence Hermitian operators (the Pauli operators), and hence matrix exponentiation. The global phase symmetry (the electric field can have any value in spacetime equivalent to the matter wave having any phase) means there is a factor $$ e^{i\theta} $$, for some phase angle $$ \theta $$.

If you have studied physics, you might have noticed that a lot of physical processes evolve exponentially, which is to say, many physical systems can be expressed as a Taylor expansion. Say you have a tank full of water, and you open a valve at the bottom of the tank, the flow will begin strongly and taper off to a trickle--the force of the escaping water follows an exponential curve. So if you know all the physical parameters, you can write this flow as a Taylor expansion.

I've seen a claim that the universe is itself a Taylor expansion, and we don't know all the parameters in it just yet.

Anyway, the article by t'Hooft: this is in the Scientific American June 1980 ed. so it's quite old. But he discusses gauge theories for all the four forces, he goes into Yang-Mills theory, it's been one of those "I'll read that later" magazine articles, for me. So there's a public domain copy of the article here

 

[Q-reeus]

...In quantum logic, the important feature is that n inputs have n outputs, information cannot be lost or erased, only converted (eventually to classical measurements). Unitarity is required, hence Hermitian operators (the Pauli operators), and hence matrix exponentiation...

Tempted to but refrained from making in another thread, on cosmology, what should be an obvious point. Never seen it raised - apart from myself some time back elsewhere in an expert dominated forum. And no-one was game to respond. It goes like this:

Unitarity i.e. conservation of information is a holy cow principle, so sacred not even 'black holes' can defy it's universal legitimacy.
Let's briefly switch to consider standard BB cosmology. Where 'at the beginning' something either exactly or fapp close enough to a spacetime singularity corresponded to the start of, and encompassed the entirety of, our universe. Of which the present observable universe may be only an arbitrarily small part of a huge or some think an infinitely large whole. And many cosmologists allow the latter as a valid cosmological solution of lambda-CDM model FLRW metric.

If so, it automatically implies an infinite amount of total information content, given an obviously non-zero mean matter density. Well that's interesting. Either an infinite amount or just a humongously huge amount of information (if finite sized universe). Rigorously subject to Sacred Unitarity at all times. All that information content springing from a BB beginning assumed to be spatially much smaller than a Planck length in radius. But let's be generous and allow for a whole Planck length or thereabouts.

Best I know, every viable contender for a quantum gravity theory posits that the smallest sensible length possible is of order the Planck length. And what's more, at most one or a few bits of info could fit into such a 'primitive cell' region.

The not overly dull among you SFers can maybe see a potential issue here? Anyone game to offer a *rational* resolution? Notice I didn't say reconciliation. Not asking for the impossible.

 

[arfa brane]

Cosmology has to speculate about the nature of the universe prior to recombination, because the information in the CMB is the first classical 'output' of the universal algorithm. Prior to this, particle interactions were indistinguishable. Prior to particles interacting, the four fundamental forces (aka symmetries) were indistinguishable and particles were "theoretical".

 

[arfa brane]

Here is a screenshot of the first two diagrams I mentioned. This describes the global symmetry of the electron field as the interference pattern not changing (an invariant). I believe the initial term used for "gauge" was "eich invarianz". So the gauge symmetry here is expressed in the pattern on the screen (or particle counter). I assume the editors would have made sure the diagrams are 'realistic' in that the peaks on the screen are because of the coincidence of peaks in the matter wave (the diamond shapes where the "waves" interfere). I note that the phase shift is equivalent to moving the screen by half a wavelength).


Now, these two diagrams have a different pattern--peaks are interchanged with troughs--and in the left diagram, the phase shift is again equivalent to moving something half a wavelength, i.e. the lower slit.
The last diagram, if you inspect the pattern of interference (compare it with the first two above), seems to be saying that constructive interference 'shifts' to destructive interference. Read that last caption carefully, it does say there is a field perpendicular to the direction of propagation of the electron beam.

Now, in Stern-Gerlach experiments, the magnets are asymmetrical and so is the field between them, this separates a beam of unpolarised electrons into two spin-polarised beams (one up, one down). But in the above, electrons pass through a magnetic field which is linear, so they should accelerate (move in a curve), and so they should emit photons, and so . . . they should change phase. (!)

 

[Q-reeus]

Cosmology has to speculate about the nature of the universe prior to recombination, because the information in the CMB is the first classical 'output' of the universal algorithm.

Strictly true in the sense of 'directly available' optical info. But (and discounting the ludicrous oft-repeated claim of one chronic poster that "only the first 10^-43 seconds is in doubt"), we now have ample reliable physics up to the multi-TeV scale, and that in turn can be readily fitted into hot BB phase model at such energy scale.

Prior to this, particle interactions were indistinguishable.

No. At recombination time, energy scale was in the eV range and not just perfectly standard particle physics but chemistry was operative. Maybe you are confusing with the speculated end=of-inflation period.

Prior to particles interacting, the four fundamental forces (aka symmetries) were indistinguishable and particles were "theoretical".

You now make a giant leap back to well before inflationary epoch even entered! To a truly speculative arena that may or may not correspond in reality to one fused 'superforce'.
In any event all that neatly sidesteps the key issue I raised. For which there can be but two possibilities.

1: Unitarity is indeed inviolable just as e.g. Leonard Susskind assumes and crows in his triumphalist claim to have 'won the BH wars' against rival Stephen Hawking. Which in turn implies the universe could never have begun in a state anywhere remotely near as compressed as standard BB model assumes and allows.

2: Unitarity can and must have failed spectacularly during standard BB evolution at least at early times.

I had actually expected no response (consensus-mongers would always be trusted to just hide in their fox-holes). So at least an attempt was a bit of a surprise.

 

[arfa brane]

No. At recombination time, energy scale was in the eV range and not just perfectly standard particle physics but chemistry was operative. Maybe you are confusing with the speculated end=of-inflation period.

At recombination time, there was a vacuum. Prior to this there wasn't, so there was no chemistry.

You now make a giant leap back to well before inflationary epoch even entered!

Well, I haven't discussed all the epochs of the BB, just two of them. It's strongly suspected that the four forces were united at some point, and that particles didn't exist (although the laws of physics did) at that time (an extremely brief time).

What I'm saying (I think) is that it doesn't really make sense to have particles interacting in the very early universe when it had no vacuum, and no particles.

 

[Q-reeus]

At recombination time, there was a vacuum. Prior to this there wasn't, so there was no chemistry.

Err, no. Recombination is basically *defined* as the coalescence of proton-electron plasma into neutral hydrogen atoms & molecules. Before that, a rather dense and hot plasma - hardly a vacuum. Before that again, it's supposed there was a 'reheating' when an almost-perfect false vacuum (inflaton field) decayed into an elementary particle/field soup. Check terms and definitions at e.g. Wikipedia articles on cosmology/BB. But all this is secondary quibbling.

Well, I haven't discussed all the epochs of the BB, just two of them. It's strongly suspected that the four forces were united at some point, and that particles didn't exist (although the laws of physics did) at that time (an extremely brief time).

What I'm saying (I think) is that it doesn't really make sense to have particles interacting in the very early universe when it had no vacuum, and no particles.

Still evading the key issue - as per #63. You say that physics was in place even if particles weren't. Well according to the likes of gurus such as Susskind, unitarity is an absolute bedrock physical principle. Integral to the working of QM/QFT. And presumably QG. I claim to have shown, rather simply, that necessarily either it fails, or standard BB cosmology. You wish to have your cake and eat it to? Then show how.

 

[arfa brane]

Recombination is basically *defined* as the coalescence of proton-electron plasma into neutral hydrogen atoms & molecules.

Ok, atoms and molecules have electron orbitals, so there must be a vacuum for these orbitals to exist in. Prior to electron orbitals, the plasma was actually Hydrogen and Helium nuclei, with electrons neutrinos and photons. I assume we're both talking about the event roughly 380,000 years after the universe began, for which the CMB is a remnant.

You say that physics was in place even if particles weren't. Well according to the likes of gurus such as Susskind, unitarity is an absolute bedrock physical principle. Integral to the working of QM/QFT. And presumably QG. I claim to have shown, rather simply, that necessarily either it fails, or standard BB cosmology.

I don't actually understand your unitarity argument, nor that you have shown it fails. But wait

All that information content springing from a BB beginning assumed to be spatially much smaller than a Planck length in radius. But let's be generous and allow for a whole Planck length or thereabouts.

Inflation made every space in the early universe which was a Planck length radius into a space larger than a proton in ~ 10^-33 s, not just the one we're in, i.e. our Hubble volume. That's a common misconception, sorry. When cosmologists talk about the size of the early universe, they mean our observable universe.

 

[Q-reeus]

Ok, atoms and molecules have electron orbitals, so there must be a vacuum for these orbitals to exist in. Prior to electron orbitals, the plasma was actually Hydrogen and Helium nuclei, with electrons neutrinos and photons. I assume we're both talking about the event roughly 380,000 years after the universe began, for which the CMB is a remnant.

Non-sequitur stuff not worth arguing over.

I don't actually understand your unitarity argument, nor that you have shown it fails. But wait

All that information content springing from a BB beginning assumed to be spatially much smaller than a Planck length in radius. But let's be generous and allow for a whole Planck length or thereabouts.

Inflation made every space in the early universe which was a Planck length radius into a space larger than a proton in ~ 10^-33 s, not just the one we're in, i.e. our Hubble volume. That's a common misconception, sorry. When cosmologists talk about the size of the early universe, they mean our observable universe.

Err, no. They mean the entire universe (originally supposed to be in causal quasi-equilibrium) - or at least most do. According to current paradigm, once inflation kicked in, exponential expansion rate meant both huge dilution of matter-energy density and progressive exclusion of vast bulk of total content to outside our (or any other) causal patch. The latter situation reversing only after inflation ended. And, it's supposed, reversing yet again as 'dark energy' took hold.

The bottom-line issue was made clear enough, but accepting the implications is another matter entirely. People so love to feel orthodox.

 

[arfa brane]

Err, no. They mean the entire universe (originally supposed to be in causal quasi-equilibrium) - or at least most do.

Well there's the thing, the entire universe could be infinite, we don't know how big it is because we can only observe the part we're in.
Cosmology is necessarily speculative, for that reason and others.

 

[Q-reeus]

Well there's the thing, the entire universe could be infinite, we don't know how big it is because we can only observe the part we're in.
Cosmology is necessarily speculative, for that reason and others.

I made that first point back in #63 (but as an 'according to some'), and stated it implied an infinite total information content. Which logically could never fit within *any* finite volume - as a BB beginning or otherwise. The notion of a spatially infinite universe having a finite ~ 13.8by 'point singularity' beginning is imo ludicrous and an insult to reason. Current surveys show large scale spatial flatness that requires the universe to have an extent orders of magnitude larger than the visible portion, but still finite.

But it's beside the real issue, which only requires dealing with the fact that an assumed tiny volume beginning is logically at odds with Sacred Unitarity coupled to the necessarily enormous information content just in our visible patch. You just can't cram virtually unlimited info content into a Planck volume or even many orders of magnitude larger. Something has to give. As stated earlier. I happen to know from another area of my own research that unitarity can indeed fail via quite ordinary and indeed classical processes, but I don't want to go there. It need have no impact on current considerations involving just cosmological evolution.

Look, it's ok to just admit to recognizing the validity of my basic argument, and frankly acknowledge to having no resolution. Really.

 

[arfa brane]

I made that first point back in #63 (but as an 'according to some'), and stated it implied an infinite total information content. Which logically could never fit within *any* finite volume - as a BB beginning or otherwise.

But there is an obvious solution to your perceived problem: limit everything to the observable universe, and you have a finite number of particles (but a much larger number of 'unitary' interactions).

But it's beside the real issue, which only requires dealing with the fact that an assumed tiny volume beginning is logically at odds with Sacred Unitarity coupled to the necessarily enormous information content just in our visible patch. You just can't cram virtually unlimited info content into a Planck volume or even many orders of magnitude larger.

Well, the universe began with a very high temperature, not an infinite temperature. Moreover, energy is conserved, if information is also conserved, maybe there is a connection.

 

[Q-reeus]

But there is an obvious solution to your perceived problem: limit everything to the observable universe, and you have a finite number of particles (but a much larger number of 'unitary' interactions).

Do you make it a habit to offer a 'resolution' only to find that 'resolution' was in fact already made the very same post you quote?
Here's an 'equation' I've come up with: arfa brane = artful dodger. Seems to rigorously hold.

Well, the universe began with a very high temperature, not an infinite temperature.

I somewhere stated or even implied an 'infinite temperature' beginning? Based on Planck units physics, it's supposed ~ 10^32K is the upper T limit. Maybe you are somehow equating 'infinite T' with 'infinite energy density' with 'infinite information density' - or something. And in some vague way, that might resolve something. You keep requiring the reader to guess and try and make connections from unstated assumptions.

Moreover, energy is conserved, if information is also conserved, maybe there is a connection.

Well here's your chance to offer a possible resolution. By quoting a reputable source stating just that. Problem is, I will immediately confront that with two 'facts':

1: The majority opinion within GR/cosmology community is that energy is simply not conserved on a cosmological scale.
2: To repeat, the likes of highly respected Susskind and many others, claim unitarity aka conservation of information is an inviolable fundamental physical principle. Thus in conflict with 1: above - that is if based on your proposed 'resolution'.

Need I keep repeating such things, or can real progress be made - at least to converging on a recognition of an actual and imo bleeding obvious genuine issue?

 

[arfa brane]

You keep requiring the reader to guess and try and make connections from unstated assumptions.

Well, I'm still not sure what it is you're getting at.
And you seem to think I'm now trying to "solve" a cosmological problem, when all I've done really make a few comments, some of which don't seem to have impressed you so much.

Then there's the puzzling aspect: you introduced the subject (of the cosmological implications of unitarity, I suppose).

 

[Q-reeus]

Well, I'm still not sure what it is you're getting at.
And you seem to think I'm now trying to "solve" a cosmological problem, when all I've done really make a few comments, some of which don't seem to have impressed you so much.

Then there's the puzzling aspect: you introduced the subject (of the cosmological implications of unitarity, I suppose).

Consider applying for a diplomatic posting. I will offer to vouch for your skills.
Anyway, clearly no progress will be forthcoming here. Still, you and you alone actually made an effort, so that all by itself is a plus.