As I mentioned here https://news.ycombinator.com/item?id=24837545 a few days ago in an earlier post on the same topic, I raised the matter of how this finding gels with other related physics. There, I asked physics experts to explain the issues to this dummy but so far none have been prepared to take the bait.
If, for instance, particles can exceed c0 (the speed of light in a vacuum) during tunnelling then how does this fit with the fact that vacuum permittivity and vacuum permeability 'also sets' the speed of c through the relationship:
c = 1/(μ0 ε0)^0.5
This means that either a particle has to completely 'vanish' from the physical world during tunnelling or that μ and ε don't apply during this time, or that they change value. It seems to me the ramifications of this are very significant.
The corollary of this is that if the wave function collapses outside spacetime then it's meaningless to discuss the particle's speed. That said, some months ago I read a report that some group actually measured (or estimated) the time of an election's quantum jump from one shell to another. If this is actually measurable time then it seems that the wave function is not outside or independent of spacetime (perhaps at these super-fast speeds/super-short times we're seeing the granularity of matter and or the intersection of the quantum and relativistic worlds). That would be fun wouldn't it.
That's a super rough outline of my point (it's too involved here to go into other possibilities that arise from QED etc., and I don't claim sufficient fluency to put them cogently). There's a bit more in that earlier post (but sorry I didn't explain what I was driving at very well).
This means that either a particle has to completely 'vanish' from the physical world during tunnelling or that μ and ε don't apply during this time, or that they change value.
The standard quantum mechanical interpretation is that the particle does not have a single position during tunneling. Instead, its position is a distribution best thought of as a wave, or as a function of an underlying wave. You can interpret this as "many worlds" or you can interpret it as "measurement matters", you get the same results either way. The speed of the particle is also not a single value, but rather a different function of the same underlying wave.
Right, it was the fact that we can now seemingly measure the time it takes for such events to occur that caused me to take note.
The fact that the electron has been observed in two places at once as it makes a smooth transition from one state to the other is big news I reckon. Note, I've posted two links about this above (re the pdf, at this point I've only had time to read the abstract).
"Tunneling" refers to the process by which a particle may pass through a classically-forbidden potential barrier. It is like bowling, and finding your ball in the next lane over. You didn't throw it hard enough to hop the lane barriers, but there it is.
> particles can exceed c0 (the speed of light in a vacuum) during tunnelling
No particle's speed is measured here, so it cannot exceed c.
What does "during tunneling" mean? Tunneling means measuring its position here, and then over there. You can't do that simultaneously with measuring its speed in between, because of the uncertainty principle.
The wavefunction can be thought of as a probability distribution. That can be updated instantly, even if it becomes very bimodal, because it's just a change in knowledge.
As I mentioned elsewhere, some months ago there was report that the time that an electron takes to jump from one shell to another was measured for the first time. If true, then it seems to me this changes things. When I was leaning physics I was told that this was either infinitely fast or indeterminate (in keeping with QM).
By this account, same would go for tunnelling I'd reckon (that's just my extrapolation from that report).
We'll just have to wait and see whether it's fact or not.
I am not really answering your question, but there is one piece of your argument/setup that should probably be expressed more clearly (maybe I am just misunderstanding it). The constants μ0 ε0 are not the fundamental constants setting the speed of light, rather they are historically the parameters we used at first when writing down the laws. It might be more reliable to think of c as being the fundamental constant, and μ0 ε0 as being the parameters dependent on c and our rather arbitrary choice of engineering measurement units (μ0 ε0 are necessary because of the arbitrary choice of what an Ampere/Coulomb/Volt/etc mean).
[First, to avoid confusion, I first mentioned this matter in my post to HN's story of several days earlier: https://news.ycombinator.com/item?id=24837545, unfortunately this story here is a duplicate, thus we've split posts.]
"The constants μ0 ε0 are not the fundamental constants setting the speed of light, rather they are historically the parameters we used at first when writing down the laws."
Well, it seems to me that depends on how one views the matter. It's not my idea, but μ0 are ε0 are actually defined as fundamental constants, so how do we bring this together? Clearly, some deep, still-far-from-understood, aspect of nature precisely relates these seemingly immutable constants to one another. Richard Feynman—and others (who likely go back as far as Sommerfeld's time)—seem to prefer the description when the equation is headed with the fine structure constant alpha α, (aka Sommerfeld's constant), presumably because α is a dimensionless constant:
α = e^2/(4πεħ0c), but also as c = 1/(μ0 ε0)^0.5. Now, if I've not screwed it up, that becomes:
α = (μ0/4π) ((e^2 c)/ħ)
Thus, now we've also tied in μ0, so we see they're all inextricably linked together with alpha being the kingpin (my words). Linking all these constants including c to α then allows all and sundry to wax lyrically over alpha's 'mystical' value, that of course being ≈1/137. Quoting from here: http://www.feynman.com/science/the-mysterious-137/
"If you have ever read Cargo Cult Science by Richard Feynman, you know that he believed that there were still many things that experts, or in this case, physicists, did not know. One of these ‘unknowns’ that he pointed out often to all of his colleagues was the mysterious number 137."
So how do we progress from here? If we don't understand what underpins the reason for the mysterious value of α then how can we say that c is intrinsically more important than the other constants herein? Clearly, the equation says c isn't intrinsically more significant than say Planck's constant, h or the electric charge, e. Thus, it seems to me that if we essentially stick to Maxwellian/Classical Electromagnetism as our reference then we cannot rank any one constant including c above any of the others, except to say their relationships are best summed up by using α as the reference, it being a dimensionless ratio/scalar.
To me, that explanation still seems to be unsatisfactory, so where to next? Moving along, I'll make a few observations that involve some related matters in the hope it will put things into perspective. It's probably best that I approach them more from an observational or philosophical standpoint, this way it's easier for me to discuss them without having to resort to a mathematical explanation, which, here, clearly would be impractical—moreover (and likely more importantly) I won't need to overtax my limited knowledge of physics in the process. ;-)
The first issue is that we know light travels in a vacuum at velocity c, but how and why does that occur, and what's the description of the underlying process? Leaving QED explanations aside for the moment, let's go back to the old now-discounted luminiferous aether theory which says that for light waves to travel then they must do so within some form of medium. Back when I was first leaning about this stuff, the luminiferous aether was considered a joke and we were told that it didn't exist, nevertheless that notion has never really ever gone away (but rather the understanding thereof has metamorphosed across many very different interpretations over the last 120 or so years). For instance, somewhat later, Lorentz came up with is his own Lorentz aether theory, still later others followed suit from the likes of de Broglie, Dirac to Einstein and others, all of which who had different views about the matter. Our present-day incarnation of the 'aether' now comes from quantum field theory; very loosely, it states that a vacuum is a condition wherein a quantum vacuum (minimum energy) state exists and that this manifests as a sea of foaming 'virtual' particle pairs that continually appear and then just as easily disappear out of existence.
What's relevant in this context is that we can now imply that light does travel in an aether and that its 'dynamics', its velocity etc., are determined by the values of the fundamental constants ε0 and μ0 which, ipso facto are also fundamental properties of that aether! Some even go on to suggest that an electromagnetic wave travelling though this 'vacuum' aether should also exhibit a minimum quantum noise (generated by its interaction with aether's virtual particles). We could imply that these virtual particles set the minimum 'granularity' of the quantum vacuum. Well, anyway, that's the basics of descriptive version (of course it's gets considerably more complicated when we go on to consider the full implications of QED and other matters that I mention below.
[My personal view is that often textbooks do not pay sufficient attention to the importance of the fundamental constants vacuum permittivity, ε0, and vacuum permeability, μ0, and how they relate to the speed of light through the relationship c = 1/(μ0 ε0)^0.5. Moreover, the emphasis placed on various aspects and understandings of this relationship often differs substantially between physics and electrical engineering texts.]
Moreover, the above explanation of a vacuum is not the only instance in electrodynamics wherein Classical Electromagnetic theory breaks down and fails to describe the phenomenon adequately; others involve potentials and static electric and magnetic fields, the theoretical underpinnings of which are difficult and tricky matters to understand. Simply, how do we explain why one's fridge magnets stay put—or slightly more precisely—what exactly is going on within these static electric and magnetic fields—that allows them to remain static (fields) but that they're also able to radiate their 'influence' away from the source at the speed of light and in accordance with the inverse square law? (Superficially, it looks as if we've perpetual motion, as it seems we've 'surplus' energy that we can't account for, but no such luck, that's not what happens.)
Perhaps if we look at the following simple but excellent example then we'll gain a better understanding. That is to compare your fridge magnet with say that of a normal wax candle. Your magnet conveniently remains static in one place and it does so indefinitely. Effectively, it's in stasis and 'stuck' to your fridge until you apply external force to move it—and it continues in this state without ever running out of energy (as with a battery going flat). At the same time, as mentioned, any unconstrained 'field' 'radiates' away from the magnet at the speed of light. Whereas for the candle to radiate electromagnetic energy in the form of heat and light, it actively has to consume energy contained within the wax. As both of these examples are electromagnetic phenomena, then what's the explanation for the difference?
If we want a reasonable description of why the magnet doesn't run out of energy (one which is consistent and in harmony with other physical laws) then, to say the least, the explanation gets very tricky. And for that we need to enter the depths of QED to find an explanation, and it comes by way of a complex mathematical explanation that involves potentials and virtual photons, etc.: it shows that whilst the field remains static, only the influence of the 'field' 'radiates' out from the magnet at the speed of light (note I've used 'field' in inverted commas for this reason).
If that explanation still doesn’t make much sense then it's because it doesn’t! The trouble is that to understand physics at this level we cannot use our usual real-world/pictorial analogies as they break down and no longer make any sense. Thus, for a full and proper explanation, we have to rest content with the mathematical description, and often that's either very difficult to understand and interpret or it's impossible to do so. Moreover, it gets worse as one gets deeper into the mire, eventually we need to consider QED and its relationship to both QCD and the Standard Model, etc.
(It's somewhere about here along this road that my understanding gets sketchy, and its mathematics gets so intense that my brain goes into meltdown—note, this it's not my day job)!
Next comes quantum gravity etc., and already we know the propeller-heads have been struggling with that for years and are still doing so. Just on that point it's worth trying to work through raattgift's two post below (near the end). They're quite remarkable in that they're both succinct and very broad in coverage and also for the fact that he discusses just about every aspect of theoretical physics that's in anyway related to these matters.
The second issue I've already mentioned elsewhere in another post, which is that if the experimental evidence is eventually verified that an electron can actually be seen to exist in two states whilst it simultaneously moves from one state to another in a smooth and deliberate manner and that it does so over a finite (measurable) time, then this seems to imply that quantum states such as an electron's transitions between orbitals, and when in quantum tunnelling, etc. may actually occur within spacetime itself (it's just that the process is incredibly fast). It may also follow that these particles may mot be fully isolated and confined during quantum transitions. In other words, if true, then it's possible that couplings may exist between spacetime and the quantum state, and that they too actually may be measurable.
Right, that sounds quite outrageous, as it would put an altogether different view and complexion about the way we explain light travelling within and though dielectrics, as well as why dielectric constants are the way they are, it may also provide us with more nuanced explanations of tunnelling, the Casimir effect, solid state physics and condensed matter physics, etc.
Now we'll all just have to wait and see what happens next.
You are raising a couple of great questions! There are a handful of extra (disjoint) pieces of information that I think are important to this conversation. You might be aware of some of them, but I will enumerate them just in case.
The "speed of light" c is much more fundamental than simply the speed of EM waves in vacuum. While humanity first learnt of this constant in classical EM, in modern physics its roots are much deeper. Here are a few equivalent "definitions" of c that do not involve EM:
- c is the speed at which massless particles travel in any reference frame (from special relativity)
- c is the maximal speed at which information can propagate (vaguer, but present in relativity, quantum, and QFT)
- if a given force fields (for whatever force) has the form ~charge/distance^2, then the carriers of that force field will propagate at the speed c (both EM and gravity)
As you can see, c is much more important than mere EM. Thus, it is important to start with c, not with μ0 and ε0, because c appears in parts of physics that do not know of μ0 and ε0 (e.g. theory of gravity).
But let us get back to μ0 and ε0. I will focus on ε0 first. This constant lets us relate an amount of charge to the force that charge will create. Historically, we have ended up with measurement style in which we measure force in Newtons and charge in Coulombs. But this is just an engineering prescription. In that particular prescription we need ε0 to have units and a specific clumsy value, because of the historical clumsy choice of Newtons and Coulombs.
You can see how Coulomb is indeed arbitrarily defined here https://en.wikipedia.org/wiki/Coulomb If instead we had defined a charge unit (or a current unit) from first principles, we would not have needed this extra ε0 to fix our silly choice of units. An example of a first-principles less-arbitrary choice of unit of charge is the Franklin https://en.wikipedia.org/wiki/Statcoulomb
Thus both ε0 and μ0 are present just because at some point in history we decided to use Coulombs to measure charge, etc. Similar to how Na, Avogadro's number, is just an arbitrary fixed number of atoms, that we use so that our textbooks do not have to say "use 10^20 atoms of this compound". Na is not a fundamental constant either.
Lastly, while we can dispense of ε0 and μ0 simply by picking a better system of units for our measuring devices, we can not do that for c and α. As already mentioned, "c" is the speed at which information propagates (which is important for fundamental notions like locality and causality), while α is related to the ratio between fundamental forces.
By the way, in cgs units α does not contain μ0.
In conclusion: at the end you have two reasons to say that c and α are more fundamental than ε0 and μ0:
- you can not remove c and α from your equations simply by changing the units of measurement (well, you can set c=1, but this is another can of worms unrelated to this discussion)
- c appears in fields unrelated to EM, while ε0 and μ0 are only in EM
First, I agree with your comments and I'll get to them shortly, but I'd like to begin by mentioning how these posts came about, as it has a bearing on what many of us say in response to HN stories, this includes myself. I'll start by saying many of the comments here are excellent in that they're considered and thought provoking (HN attracts a high quality crowd). Nevertheless, from my experience, ad hoc or impromptu internet discussions about QM are often perilous affairs for those of us who dare to respond. Almost nothing equals QM's ability to draw a crowd to comment when some controversial finding is made that may have the potential to alter QM theory. Unfortunately, sometimes confusion arises from the fact that many of us come to the subject from different directions and with different levels of skill. Comments here are no exception.
This HN thread, the second of two about the same story, began from a popular press report pitched to a broad cross-section of readers who are assumed to have some scientific knowledge, that is they're already familiar with the basic concepts of the subject. The same would also be assumed for HN readers. Few of them will be true experts in said matter but some will be and that will significantly influence the posts. My initial comment to the first story was a quick throwaway-like response pitched at the level of the article (or that's what I'd initially intended anyway). In hindsight, I should have expressed it more carefully as there's always someone who'll pick up a loose comment. That isn't a criticism as one want's comment and feedback but the discussion is tighter if we express ourselves more precisely. The trouble is I'm not particularly good at doing that.
The other problem is that when one has readers who have wide-ranging skills where do you draw the line in assumed knowledge? There's little point defining everything that's involved before discussing the issue or the majority of readers won't bother to continue. I'm not much good at judging that either. Probably the best thing to do is not to bother and just pitch one's comments at the level one's most comfortable at doing, as raattgift has done with his comments. That way, readers will find comments pitched to their own level. As I see it, this is a particular problem when discussing QM. Let's face it, for many of us this topic is difficult even at mid-level let alone the extremes, unfortunately it's easy for QM topics to slide into the extreme category seeming without effort.
For instance, in the post to which you replied I found it difficult to explain in simple terms the nature of the static magnetic field for two reasons. The first is that the underlying physics is very difficult to comprehend in day-to-day terms and is best explained by mathematics which itself is complex; and second, that whilst I do have some understanding of the physics, I don't understand the principles to the extent that I should. Whilst there are those who've a much more in-depth understanding of this physics than do, I'd also hazard to suggest that no one fully understands this physics well (this further complexes the problem of trying to provide understandable analogies). I've no time here to give you my reasons but I'd be happy to do so in another post if anyone wants me to.
Now to your points:
The "speed of light" c is much more fundamental than simply the speed of EM waves in vacuum. While humanity first learnt of this constant in classical EM, in modern physics its roots are much deeper.
I totally agree. I made those longwinded points above for the very reason that it's hard to discuss QM at one level without sliding into a deeper meaning. By referring to the relationship between c, μ0 and ε0 alone without mentioning relativity specifically meant that I was effectively still using the classical electrodynamics approach. Here's the confusion: I quoted those equations specifically as they're widely used nowadays and they normally would not be contentious; moreover, they're even a notch up on the classical Maxwell/Heaviside mathematical statement of electrodynamics given that they're quantum mechanical expressions in that α and h are involved.
Essentially, I've stated the quantum view but not the relativistic quantum one. Unfortunately, this sort of misstatement reigns supreme everywhere. Nevertheless, it's understandable and it's hard to avoid as the next level up in 'precision' has to involve relativity and this then complicates matters considerably as the equations and mathematics get considerably more complex (so does the understanding thereof).
You can see what I mean in my post to the new HN story I've linked to above. In his video, Derek Muller makes the point that we cannot know the 'true' speed of light due to the 'clock' problem. That's to say that if we measure the speed of light in a vacuum, then owing to the fact that we need two directions to do so, c could actually be 299,792,458 m/s in one direction and instantaneous in the other and we would not know the fact. He points to the fact that Einstein set the premise upon which he based relativity only by convention (Einstein Synchronisation Convention), which is that c is the same in both [all] directions. He then points to the equation in Einstein's paper that sets that convention 2AB/(t'A- tA) = c where A and B are the paths.
My point is twofold, the first is that the way we define things in physics often leads to a problem and this extends to their mathematical descriptions, and the second is that the complexity of those definitions sets our level of understanding of them. At a superficial level, we have one understanding; at a more complex level, we have a deeper and more nuanced understanding. That is stating the obvious but to keep things simple it is not often stated in the textbooks. In mechanics, we don't often start out by saying 'learn F=ma' and yet in the same sentence also say 'it'd be better if you learned it from a Lagrangian perspective' but then add 'that as this is just another interpretation of Newtonian approximation, then you'd really be better off learning relativity'. Right, it just doesn't work that way for good reason but by not doing so can lead to later confusion. I reckon it's especially a problem with QM and relativity (I cite my own case in that I should have been taught Lagrangian mechanics much earlier than I was).
Muller's raising the issue of Einstein Synchronisation Convention with respect to c points again to the matter that I initially raised, which is that c, μ0 and ε0 are somehow interlocked irrespective of the importance of c (and I'm not down-rating c by saying that). Similarly, that is if the equation c = 1/(μ0 ε0)^0.5, which is a quantum relationship, is to hold true then either the Einstein Synchronisation Convention was hardly worth the effort of stating it in the first instance, as QM would be wrong, or that QM is wrong and there's something fundamentally wrong with our interpretation of μ0 ε0. QED! (Yeah, I know, QM came later so he had to state it, but you get my point.)
The fact that Muller does not mention that if c were instantaneous in one direction then the values of μ0 and ε0 in that direction would also have to be different to our understood values, is I reckon a failing. If true then it would make a complete monkey out of our understanding of QM. If direction asymmetry of this sort were actually a fact in vacuum space then our whole understanding of the quantum vacuum, zero point energy, etc. would be total nonsense.
Again, this illustrates the complexity of the matter and the dangers of oversimplifying things. Here, it seems apt to quote Einstein on the matter: "Everything must be made as simple as possible. But not simpler."
I also need to discuss your other points including gravity, etc. and especially the cgs/MKS matter so I'll post that separately as soon as I get a chance. (I'm afraid of again exceeding HN's maximum allowable post space as I did with the earlier post (I had to shorten it to fit and some of my meaning was lost in the process).)
That was interesting (the mechanical simulation reminded me of the one done some years ago to demonstrate the Bohm/de Broglie Pilot Wave* interpretation of QM)
Anyway, now I'd suggest you have a look at the link I've posted above about the transition of the electron from one shell to another.
> [Bohm/de Broglie Pilot Wave interpretation of QM] is interesting despite being debunked by Bell's, etc
No, the pilot wave interpretation is not debunked by Bell’s theorem. That is a persistent misrepresentation of Bell’s theorem. In Bell’s own words:
“My own first paper on this subject ... starts with a summary of the EPR argument from locality to deterministic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables.”
Ha, perhaps I should not have used the word 'debunked'. Let me briefly explain. Long before Yves Couder did those experiments about a decade ago, I was intrigued with why the Bohr/Copenhagen model became the main QM orthodoxy and why the 'shut up-and-calculate' attitude became so entrenched. (One of my other subjects was phil., so I was never fobbed off by being told to just 'shut up-and-calculate'). It seems to me the main reason for why this view prevailed and still does is that it works so successfully well in its practical applcation.
Einstein, Podolsky and Rosen were right not to be satisfied with the then mainstream view of QM and question its underlying mechanics—even if they were wrong (science doesn't advance if theories/ideas aren't questioned). Same goes for de Broglie when he initially proposed the pilot wave theory at Solvay '27 (although it seems to me that he caved in a bit too quickly under pressure from Pauli). When I was doing physics, de Broglie–Bohm, not seeming to have any practical application, hardly entered the picture.
It was only later I discovered David Bohm's pilot wave work in more detail when I was learning about the Aharonov–Bohm effect (which itself is an intriguing matter). Not only did I find de Broglie–Bohm fascinating but by accident I also learned about Bohmian trajectories which may possibly explain some effects I'd seen years earlier with electrons being focused and scattered in a vacuum (that's still unresolved). Of all QM theories, de Broglie–Bohm is the one I found the most interesting and provocative, and it would be a neat solution if the multitude of seeming objections to it were resolved (that said, I'd bet they'll all be resolved well before, say, many-worlds will).
The reason why I used the word 'debunked' is that some while after Yves Couder's work came out a flock of papers started appearing (perhaps in response to his work) that claimed the death knell for de Broglie–Bohm; Bell, if I recall, was often cited as the principal reason. As I'm not in QM research, (my work's more in its application), I'm not up to date on its latest developments but from various science news reports I've glimpsed recently, it seems to be resurfacing again (obviously you're much more au fait about this than me).
BTW, David Bohm seems to have been a most fascinating character, from what I've read of him, he's the sort of guy I've have liked to have met (reckon I could have talked with him for hours).
I share many of your views, and so I think you will enjoy Jean Bricmont’s “Making Sense of Quantum Mechanics”. The book clarifies there is no reason to doubt the pilot wave interpretation, or Bohmian mechanics.
For a more popular account that delves into the personalities of the physicists involved, I also recommend Adam Becker’s “What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics”.
Well, thank you for that info, I'll definitely check both books out. Incidentally, I've nothing against popular accounts so long as they're not trivial or trite, I look forward to reading Becker. Moreover, I've often found that well written popular accounts not only tackle the subject matter from a different perspective to textbooks but also they can provide useful information that's not commonly available elsewhere. On several occasions I've had eureka moments reading such books long after I'd finished with the textbooks. Here, Roger Penrose's The Emperor's New Mind comes to mind.
Also, I've ever so briefly checked the web link, I see there's hours of material there.
Agreed, I mentioned the mass aspect in my earlier post a few days ago but I got a bit sidetracked by alpha and other stuff and didn't explain what I meant very well.
As I see it, the crucial aspect is whether or not the claim that the wavefunction collapses in a finite measurable time can be verified.
If it can be measured then it seems to me that we then have to concern ourseles with all that other stuff, the electric constant, alpha and so on.
Only if the particle has energy. This leaves the door open for information without energy. Quantum physics generally adds energy to measure.
Though information should have energy, I can't say information must be either mass or light. So maybe there is a second relativistic effect for massless, lightless particles.
Good question, see if you can figure it out from the Landauer Principle links I've posted above (QM overload fatigue has set in from too many unresolved questions for one day, I'll worry about later).
I must admit it makes sense, but ages ago when I first came across the notion that say a kilo of matter had a definite limit on the amount of information it can contain is a bit overwelming, especially so when one realises how huge that number is. That reminds me of a Feynman quote about there being 'pleanty of room at the bottom'.
So it seems if it would be possible to have/process information without energy those limits would be infinite. At least my layman reasoning leads me to believe this.
"<...>a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately 1075 mathematical computations per second.<...>"
Yeah, right, it's a number so large on a human scale that it's essentially incomprehensible. However, if you think about it for a moment you can begin to imagine the enormity of the complexity. Leaving aside how you'd calculate said figure or dream about how it could ever be implemented, just try to consider the humongous amount of information that's contained in just one gain of sand.
One must account for the amount of information contained within the configuration or quantum state of the trillions upon trillions of atoms and molecules along with all their constituent particles, electrons, protons, quarks—all of which contain information that's arisen from the quantum states of the various binding forces—the state of electromagnetic, strong and weak forces.
Then there's information generated by the couplings and various physical characteristics of all the crystal lattices including all geometric information contained in each crystal's facets to be considered, not to mention various charges/interconnecting effects involved with crystal binding such as van der Waals forces and other quantum effects/fluctuations. Then we've also to consider all information generated from the sand grain's thermodynamic state (and that alone would be enormous).
And that's not all, even information from phonon movement (noise) generated from within each crystal as well all noise coupled from external sources must be included. Vibrational/phonon energy, which in the real world is lossy, generates information from its dissipated thermal energy (even information is generated from the physical state/properties of matter that actually cause those losses).
Thus, the total amount of information in just one grain of sand alone is simply mind-boggling.
Now extrapolate all that to all those other grains of sand until we get to earth-size. And now also take into account the fact that when all those many grains are closely packed together, they generate even more information by virtue of their couplings (van der Waals forces now act between individual grains of sand, and so on and so on).
'Mind-boggling' doesn't come even close to describing the informational complexity!
Huh? Their rest mass is 0, but, they have energy, E = h * frequency iirc, so, shouldn't they therefore have a relativistic mass? (if one is going to use the concept relativistic mass at all that is)
It doesn't work for photons, if you want to calculate the momentum (mass) of photons it will be planck's constant / λc.
Going going by the standard relativistic mass calculation of SR alone m = γm0, γ = 1/[square root of (1 − v2/c2)], you get a division by zero which is well a no no, but this is where as you approach the speed of light your mass becomes infinite comes from.
Right. So, if one wants to talk about the "relativistic mass" of a photon, the result is (Energy of the photon)/(c^2) = h/(λc) = h*(frequency)/(c^2) , which is what was implied by what I was originally saying, and which is not 0 .
So, the relativistic mass of a photon (if one wants to use the concept of "the relativistic mass of a photon" at all, which one might quite reasonably not want to, and which yes, does depend on the frame of reference) is not 0, in any frame of reference.
Again that's not relativistic mass, relativistic mass in special relativity is dependant on the velocity, the momentum of a photon is not dependant on the velocity of the photon in vacuum or in any medium. A photon of a given wavelength (energy) has the same momentum regardless of medium it's traveling in, it's also not affected by the center of momentum as in there is never a frame of reference where the rest mass of a photon is equal to its relativistic mass for a given observer.
In general you shouldn't consider relativistic mass to be a "thing" for either massless massive particles, special relativity is useful, but it doesn't attempt to describe the universe as we know it.
As for GR well it's more complicated, GR doesn't give you the ability to calculate the invariant mass of a given system, that's arguably one of its weakest points or at least it's weirder points it's also where people try to poke holes in the theory looking for violations of the equivalence principle.
Is the relativistic mass required to be dependent on the velocity or on the reference frame ? For most massive particles, depending on the one should be equivalent to being dependent on the other, right? Seeing as for massless particles , the velocity is always c and therefore "dependent on the velocity" doesn't really make sense, why isn't "dependent on the reference frame" the appropriate extension of the concept?
The [the quantity I described] definitely depends on the reference frame for which the photon is being described, because the photon's frequency and wavelength depend on ones reference frame.
I don't know why you brought up the photon traveling through different mediums. I've been assuming it was traveling through a vacuum. Bringing in a medium seems like it would just complicate things. Maybe you thought I was thinking of it moving in a medium so that it was sorta moving at less than c, so that there could maybe be reference frame for which it is at rest? This is not what I was thinking of. I mean to address only the case of a photon in a vacuum.
And yes, of course there would be no reference frame in which the photon's [the quantity I'm describing] becomes equal to its rest mass, which is 0. That is implied by what I've said, namely, that the [the quantity I'm describing] is never 0, but changes with the reference frame. There are reference frames in which [the quantity I'm describing] is arbitrarily close to 0, but none in which it is 0.
The footnotes at the bottom of the wikipedia article on "Photon" do describe photons as having non-zero relativistic mass, though also notes that some prefer not to use the concept of relativistic mass.
In any case, at the very least, if one is to speak of the relativistic mass of a photon, it is not 0. If anything it is either "nonsense quantity" or [the quantity I have been describing] . Not 0.
The wikipedia entry is a bit of a hit and miss, but in general "relativistic mass" isn't a concept that is used, in fact many SR courses don't skip it per-say but don't call it that way.
The point is if you apply any of the relativistic momentum formulas to photon you will not get a sensible result, basically you'll either get 0 or 0 over 0, same goes for other mass related things in special relativity such as center of momentum and center of mass also break down.
The "mass" of a photon doesn't come out of special relativity, and trying to calculate it using SR will not work, photons have linear momentum this comes out of Planck's law and the photoelectric effect.
If, for instance, particles can exceed c0 (the speed of light in a vacuum) during tunnelling then how does this fit with the fact that vacuum permittivity and vacuum permeability 'also sets' the speed of c through the relationship:
c = 1/(μ0 ε0)^0.5
This means that either a particle has to completely 'vanish' from the physical world during tunnelling or that μ and ε don't apply during this time, or that they change value. It seems to me the ramifications of this are very significant.
The corollary of this is that if the wave function collapses outside spacetime then it's meaningless to discuss the particle's speed. That said, some months ago I read a report that some group actually measured (or estimated) the time of an election's quantum jump from one shell to another. If this is actually measurable time then it seems that the wave function is not outside or independent of spacetime (perhaps at these super-fast speeds/super-short times we're seeing the granularity of matter and or the intersection of the quantum and relativistic worlds). That would be fun wouldn't it.
That's a super rough outline of my point (it's too involved here to go into other possibilities that arise from QED etc., and I don't claim sufficient fluency to put them cogently). There's a bit more in that earlier post (but sorry I didn't explain what I was driving at very well).