Quantum Tunnel Shows Particles Can Break the Speed of Light
quantamagazine.org
quantamagazine.org
The Larmor clock doesn’t measure a proper time as in spacetime distance between two events. Instead it measures the rotation of a dipole in an electromagnetic field.
The experimenters apply a combination of an electrostatic field (the barrier) and a magnetic field (the timer driving Larmor precession). In the frame of reference of the spinning particle, this is exhibited as a sum of two electrostatic fields. The barrier is a locally uniform repulsive electrostatic field, while the the timer is a radially varying axial electrostatic field. The particle is a dipole, tilted from the timer axis by the precession angle. When the particle tunnels through the barrier, it also tunnels through the timer field, without precessing over the tunneled distance just as the particle is not exhibiting repulsion from the barrier over the same distance.
This is experimentally verifiable as the amount of missed precession has a lower bound proportional to the sine of the angle between the magnetic field and the barrier.
I would be interested if the Lamor clock also shows a shift in the reflected particles. Because that would mean, also the reflected particles spend some time inside the barrier.
Of course, but it is less than one. Hence the measurement underestimates the proper time interval.
https://www.scientificamerican.com/article/quantum-tunneling...
This argument doesn't make a lot of sense to me. One particle arriving can signal information that some event has occurred at the source. Re: structure/complexity I imagine you could use different elements (and maybe spin too?) to form several bits.
Looking at the paper being discussed here - https://iopscience.iop.org/article/10.1088/1367-2630/abb515/... - the authors also don't seem to have an explanation.
One final caveat worth noting is that our results do not definitively prove that an ensemble of free particles will always be a preferable method of transmitting a signal to an ensemble of tunneled particles. It is our intention to include a discussion of this in a follow-up paper.
This is basically the scenario you're talking about, forming several bits out of different particles and using them in conjunction to send information faster than light. The researchers aren't sure why this wouldn't happen in their model.
Any form of FTL causes problems with causality - or at least with current assumptions about causality. So physicists tend to work back from that to "Therefore this is impossible."
But those assumptions may turn out to be wrong and relativity may be violated in specific quantum contexts. And then all kinds of interesting things happen.
Incidentally, this is an example of the kind of thing Hossenfelder was talking about. You could spend $20bn on a new collider, or you can spend a couple of million - at the absolute most - to check there's nothing unexpected happening here.
It's a wild bet, but given the up side it's hard to characterise it as poor value.
At worst you'll get some insight into the interface between QM and relativity, with another situation where Relativity Wins Again - but you understand why, in detail.
At best you'll get something more challenging and interesting.
Just out of interest, I use the extremely fast switching times of tunnel diodes to make quick determinations of oscilloscope rise-times. When used as a switch their rise-times are much faster than most oscilloscopes so the rise-time seen on the oscilloscope is actually that of the scope itself.
https://en.m.wikipedia.org/wiki/Floating-gate_MOSFET
Tunnel junctions are used in applications such as photovoltaics as well as high frequency circuits e.g. tunneling diodes.
Edit: Just to fix a confusion, by 'reliable' I meant, one electron sent, one received. I know one 'bit' isn't typically sent as one electron, but being reductive for comparison's sake. Obviously with enough current you can make the tunnel happen, but you'd need far more electrons and 'time' to do so.
The reason we don't often use tunneling diodes today in most devices is that they are expensive to make compared to many other modern diodes, they are still used in more unique applications including very sensitive scientific equipment and space applications.
In general there many types of semiconductors that employ a Quantum Well https://en.wikipedia.org/wiki/Quantum_well this means that these SCs do RELIABLY utilize quantum tunneling by either inducing it under very specific conditions, or averting it.
I'm really not sure what you are skeptical about, without use being able to utilize QT reliably we wouldn't be able to make modern semi-conductors they would either not work because we can't make tunneling happen when we need it too, or won't work because we randomly induce it to happen.
It doesn't mean we fully "understand" Quantum Tunneling as in understand exactly why it happens, but we know enough to predict and control it, Quantum Tunneling is to the SC industry what fire was to humanity in general for milenia. We still probably can only roughly model the physics of fire, especially since at the end it's governed by QM effects, but we don't need that in fact we don't even need to understand combustion that well to utilize it.
But if you want single electron tunneling then yes it's possible there have been papers about it for a few decades with the latest ones also including some experimental work https://arxiv.org/ftp/arxiv/papers/1204/1204.5539.pdf
Single electron transistors are also being actively worked on https://en.wikipedia.org/wiki/Single-electron_transistor
Sounds awesome. And thanks for the explanation.
If you send some some particles every time event occurs and occasionally they are received, even a single detection now gives the receiver information: that event occurred.
If the particles were sent FTL, you can now setup the standard causality paradoxes.
In this case in particular, if you receive no particles you know that the event either did not happen _or_ it did happen and you failed to detect the particle. If you do receive a particle you know that either the event happened at least once _or_ it did not happen and you have a false positive from your detector _or_ there was a particle but it was introduced by quantum noise. To make sure what actually happened you would need more signal, more particles per transmitted bit.
However, it is entirely possible that this reduction in effective bit rate will slow down actual bit rates back down to "normal" subluminal speeds.
(Where, the bit rate, bits/second, would, I think, be a measure of bandwidth. I could be wrong.)
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).
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.
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).
> 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.
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.
https://www.discovermagazine.com/the-sciences/scientists-cat...
[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.
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)
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.
However, there are systems of units in which ε0 and μ0 are simpler. The cgs system of units is a great example. Check out the values of ε0 and μ0 in that system https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%...
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 EMFirst, 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).)
Particle escapes it wave, so it no longer bounded by speed of wave in medium, when it in a tunnel.
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.
___
* Off topic, but this is interesting despite being debunked by Bell's, etc. https://m.youtube.com/watch?v=W9yWv5dqSKk
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.”
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).
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”.
Both books came to me via the reading list at https://bohmian-mechanics.net.
Also, I've ever so briefly checked the web link, I see there's hours of material there.
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.
That's a new ballgame, methinks.
That's why photons still have momentum and can exert pressure.
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.
/amateur scientist
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.
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!
Photons have inertia not mass, or relativistic mass.
The formula for relativistic mass is [invariant mass] / the square root of (1 - [speed of the observer]^2/C^2)
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.
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.
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 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.
This is a good video that might explain the concept/confusion when it comes to relativistic mass https://www.youtube.com/watch?v=LTJauaefTZM
tldr: there’s a calculation you can perform in quantum mechanics that suggests particles can tunnel through barriers faster than they could have traveled through free space at the speed of light. Scientists have now measured this more precisely, and this effect seems to hold up, but is still very small, so it’s hard to understand the ramifications of this for things like causality.
Re causality etc., as I mentioned above, if the duration of wavefunction collapse can actually be measured then this puts a whole new spin on the matter (sorry, puns aren't my forte but it seemed appropriate here). ;-)
My guess it it is a straightforward calculation, and that it is real. We'll have a hard time dealing with it existentially, but the math will be right and the physics will eventually be shown to correspond.
We'll have something where a particle can be entangled with its past/future self, the future self being affected by the past self and vice versa. And that should be okay. It'll reignite the debate of the possibility of changing the past vs the lack of free will, effect preceding cause, but in a way it will push the "shut up and calculate" forward because it's all math.
At least, that's what I somewhat hope will happen. It kind of reminds me of the relativity revolution. There was an inconsistency in E&M theory due to the constant speed of light, and we invented all kinds of ways to work around that, when it turned out that if you just assume constant speed of light then it worked out. Same thing here, we're philosophically rejecting FTL communication but perhaps the right thing is to accept it, follow the math QM gives us, and recognize that it's possible, that it's all just math, and while it's mind-bending, it's not actually all that spooky. Relativity is just the limit case of zero tunneling.
QM is tricky, as soon as you think you have it cornered with a contradiction, it slips away at the last second. My guess, we'll discover that yes it is possible in a closed system for a cat to send the signal back in time that triggers the gun that shoots its former self. But it's not possible for that contradiction to escape the system, so upon opening the box, you'll always see a live cat. Or something like that.
Light travels 182km in 0.61ms so it would be significantly slower than light.
It was even discussed on HN: https://news.ycombinator.com/item?id=23917908
Here is an article about some physicists who think weak measurements are suspect: https://physicsworld.com/a/are-weak-values-quantum-after-all...
It's only an impossibility in space-time. But the quantum world, until the wave function collapses, exists outside of space-time. Entanglement is under the same effect -- space-time simply isn't involved. It's the collapsing of the wave function that brings it into space-time. At least that's how I understood it.
Moreover, one of the most important results that confirmed entanglement is possible was the no-communication theorem, that proved that it is impossible to use entanglement to communicate faster than light. This is also suggests that wave-function collapse of an entangled system can't really be a physical phenomenon.
Can you say more about that? What are the alternatives to being a physical phenomenon?
Now the physical meaning of these 2 different rules are debated. In the standard (Copenhagen) interpretation of QM, it doesn't make sense to talk about the properties of particles until you measure them, so neither the wave function nor the Born rule can be given a physical meaning.
In the MWI interpretation, all results of the Schrodinger equation exist in different worlds, so there is no collapse, the detector just finds out "in which world you live".
In superdeterministic theories, the Schrodinger equation is just an approximation of a currently unkown fully deterministic theory of motion.
In pilot-wave theory, the Schrodinger equation describes an actual wave that particles generate themselves (the motion of the wave and the motion of the particle influence each other); entangled particles are just particles that live on the same wave. There is no collapse here, but the wave from each particle exists in the whole universe and can change non-locally.
Alternatively, I'm just not sure what you mean by saying that it ( wait, what is the "it"? "the quantum world"? But the world is the quantum world?) "exists outside of space time" .
If one said "the number 3 exists outside of spacetime", that would make sense to me, as saying that it isn't a thing with a location in spacetime, but just a thing.
But I don't think I know what you mean.
Although in general physicists believe a lot of things from spacetime for QM, like that information can't travel faster than light, it isn't actually baked into QM.
That's my understanding at least.
There are several textbooks[1] covering extensions of this approach to curved spacetimes generally, and one will encounter the https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation#... in graduate school settings. Quantum mechanics on some specific curved spacetimes are exactly Klein-Gordon solvable.
The Standard Model of Particle Physics incorporates the Poincaré Group, which is the group of Minkowski spacetime ("flat spacetime") isometries. This means that the Standard Model particles are the same independent of where and when they are in empty flat spacetime (3 spacelike and 1 timelike translation invariances), their orientation (rotational invariance about the three spacelike axes), and they transform reliably under boosts (differences in constant velocity along the spacelike axes). So the Standard Model is defined by flat spacetime: and the causal structure of flat spacetime (in which the constant c plays a key role) is very much baked in. Studying modern quantum mechanics mostly means looking at patches of effectively flat spacetime in which there are particles of the Standard Model occupying different locations in the patch, boosted relative to each other, and interacting via the other mechanisms captured in the Standard Model's formulation.
We inhabit a type of curved spacetime in which General Relativity guarantees at least an infinitesimal patch of exactly flat spacetime around every point in the universe. In regions with only gentle curvature -- like laboratories on the surface of the Earth, or in space probes in the solar system -- any curvature corrections to the assumed exactly flat spacetime of the Standard Model are tiny, because the region of effective (rather than exact) flatness is very large compared systems of particles under experimental study of their quantum behaviour. "Pretend it's flat" works exceedingly well in practice. When a researcher has to consider curvature (e.g. in relativistic massive objects like neutron stars) she or he can continue to work perturbatively against a flat-by-definition spacetime.
The problems arise in the difference between a guarantee of a microscopic region of flat spacetime and an infinitesimal region of flat spacetime: if the radius of curvature is small compared to the spatial extent of a particle, things get ugly quickly, especially as we take the wavelength of the particle smaller (which means the energy of the particle climbs, and that is the sort of energy which creates spacetime curvature, so we get a nonlinear feedback, and classical General Relativity and Quantum Field Theory in Curved Spacetime make annoyingly different and incompatible predictions about what happens as one takes the limits of high particle energy and high curvature. Fortunately this incompatibility seems likely to occur only hidden inside event horizons, so it is a problem for the theories rather than a practical problem for all of us who are not actually rapidly approaching death within a black hole -- there also may be consequences for as-yet-undiscovered ancient tiny black holes, or stellar black holes many trillions of trillions of years in our future, so again we can take our time to understand the theoretical conflict).
A bit more technically, the problem arises in perturbative approaches to QFT on curved spacetime: at low energies and low curvatures we have a fairly small number of correction terms which can be written out as a https://en.wikipedia.org/wiki/Taylor_series which we can truncate because the higher-order terms are demonstrably irrelevant. As we increase energies and curvature, irrelevant terms become marginal, then relevant; additionally, we start having to add more non-irrelevant terms. https://en.wikipedia.org/wiki/Renormalization allows us to squash some of these terms together, but eventually we get an overwhelming growth of non-ignorable corrective terms and lose the ability to make predictions using this approach.
This breakdown in perturbative renormalization ("perturbative quantum gravity" [2][3]) gives a useful qualitative definition of "strong gravity": it's where the perturbative approach breaks down. In terms of Feynman diagrams, it's where loops of gravitons enter into the picture; a bit more colloquially, it's where "gravitation's self-gravitation starts becoming non-ignorable".
Although not a dead area of research, looking for ways to make renormalization work for strong gravity is less fashionable than looking for non-perturbative quantum gravity that (a) matches perturbative quantum gravity right up to the weak-side boundary of strong gravity, including classical General Relativity in weak gravity, (b) is calculable in practice, and (c) solves other non-gravitational problems that plague high energy particle physics that are amenable to testing, since we probably can't extract observational or experimental data from regions of strong gravity.
Additionally, classical General Relativity fairly generically predicts the presence of gravitational singularities in spacetimes with significant amounts of matter[4]. Such singularities destroy the total predictability of the entire spacetime from a total sample of all the variables on an arbitrary slice across the whole space at a given time coordinate. In other words, there's an incompatibility between classical General Relativity and traditional initial values surfaces approaches to solving physics problems. This problem worsens in the presence of Quantum Fields because of Hawking Radiation: instead of a literal singularity there is instead a trapping structure that evaporates (or mostly evaporates, in "remnant" proposals) in the far future of most black hole systems. But the matter that is released in the evaporation cannot be predicted from the matter that was thrown into the black hole before evaporation, and at late times we lose the ability to account for quantum entanglements that existed when the black hole was growing. Unfortunately there are numerous black hole candidates in our universe, which we also know is filled by matter representable by quantum fields. Although this is not strictly an incompatibility of General Relativity and Quantum Field Theory, quantum physicists are very keen on preserving https://en.wikipedia.org/wiki/Unitarity_(physics) which is lost in black hole evaporation as is understood today. Preserving unitarity in the presence of strong gravity is a fourth goal of modern research into quantum gravity.
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[1] e.g. Parker & Toms, QFT in Curved Spacetime (2009), https://books.google.co.uk/books?id=5nNuGMBBTjMC&dq=L.+Parke...
[2] http://www.staff.science.uu.nl/~hooft101/lectures/erice02.pd...
[3] https://en.wikipedia.org/wiki/Canonical_quantum_gravity
[4] https://en.wikipedia.org/wiki/Raychaudhuri_equation is a good place to start
Collapsing the wave function doesn't bring a system into the domain of relativity. That happens at a fuzzy point where a system become massive enough for relativistic effects to become significant.
In thoery, we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity.
There is semiclassical gravity; which essentially says that the quantum fields described quantum mechanics occurs in the curved spacetime of relativity. This is (by design) just an approximation of the still unknown theory of quantum gravity; and we don't have good experimental evidence telling us how accurate of an approximation it is.
The only incompatibility is between quantum mechanics and general relativity - quantum mechanics can't work with the general relativityequations for a curved spacetime or for the gravitational effects of particles being in multiple places at once. These are the things that a theory of quantum gravity must solve.
(In fact, you can even do quantum mechanics in curved spacetime, as long as the spacetime has a predefined fixed curvature. But in GR, the curvature depends on how the matter and energy inhabiting the spacetime are distributed. That is what gives quantum gravity theorists trouble.)
The Standard Model of Particle Physics incorporates the Poincaré group, which is the isometry group of the flat spacetime of Special Relativity, so it has an exact concept of spacetime built right into the formulation.
Quantum mechanics and Special Relativity were unified in the 1920s by Dirac. Solutions for some curved spacetimes came not much later, and are now taught in several textbooks. The problem is that we don't have a general solution for quantum mechanics on arbitrary curved spacetimes (and some curved spacetimes are known to make quantum field theories insoluble with current methods).
I refer you to my sibling comment https://news.ycombinator.com/item?id=24877746 for more details.
> (by design) just an approximation of the still unknown theory of quantum gravity
Kind-of. It is manifestly an approximative approach because the equation includes "mean" angle-brackets around the stress-energy tensor, which, speaking roughly, indicate that the curvature is generated by the averaged value of the stress-energy generated by the quantum field(s) are used, rather than an exact value at each and every infinitesimal point in the solution. This "classicalizes" the source term of the classical curvature, erasing quantum effects.
It is not really in the strictest sense an approximation to a theory of quantum gravity, however any candidate quantum gravity theory had better explain results from semiclassical gravity that find some support in astronomical observations.
Contrasting approaches -- like canonical quantum gravity -- "quantumize" the metric, leaving the source term fully quantum mechanical and non-averaged, and results from such approaches also find some support in astronomical observations. These are arguably approximations to a full theory of quantum gravity since one can cast them as a series of terms similar to a Taylor series; the problem is that the set of such terms appears to grow without bounds as one takes energy-momentum into the "ultraviolet" regime (UV ~ extreeeeeemely high energy-momentum densities). Worse, the relative weight of the contribution of some of the far-from-leading-order terms grow stronger in the UV limit, so not only can't we just ignore them, we also can't apply perturbative renormalization. Fortunately this probably only happens inside black hole event horizons and near the big bang, one of which is probably not observable, and the other of which is at high enough individual energies that the Standard Model doesn't predict results even if their collective mutual gravitation (and the contribution of dark matter and other energy-densities) could be factored out.
> we would probably expect to see some relativistic effects in entangled systems; but predicting what those effects are requires a theory of quantum gravity
We can calculate the effects of a boost, even an ultraboost, on particles with mutually-entangled properties just fine thanks to the Poincaré invariance baked into post-Dirac relativistic quantum mechanics. If you were flying past from an entanglement experiment in deep space at ultrarelativistic speeds, one could predict your observed redshift (etc) of the entangled properties exactly with no worries. (If you were flying radially to or from an Earthbound experiment at ultrarelativistic speeds you might want to incorporate some corrections from the https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultrab... for greater accuracy. The post-Newtonian expansion leading-order corrections attributable to Earth's gravity will not be large; linearized gravity is enough. Errors from the next-to-leading-order corrections will not be measurable with current technology, and we can brute force calculate at least next-to-next-to-leading order corrections, which is good enough for accelerating down towards the surface of a neutron star, like the material that is blown onto the Hulse-Taylor binary members.
What are the minimum properties that constitute an effective "barrier" to jump?
Would a single atom serve as a barrier to jump?
Could we set up a particle accelerator that is just a circle of single atoms to jump, at faster than the speed of light?
You can word play if you chose, but it's not clever.
You can't send information faster than the speed of light.