*[This is a transcript of the video embedded below.]*

Today I will tell you how to be just as annoying as a real physicist. And the easiest way to do that is to insist correcting people when it really doesn’t matter.

**1. “The Earth Orbits Around the Sun.”**

Well, actually the Earth and the Sun orbit around a common center of mass. It’s just that the location of the center of mass is very close by the center of the sun because the sun is so much heavier than earth. To be precise, that’s not quite correct either because Earth isn’t the only planet in the solar system, so, well, it’s complicated.

**2. “The Speed of Light is constant.”**

Well, actually it’s only the speed of light in vacuum that’s constant. The speed of light is lower when the light goes through a medium, and just what the speed is depends on the type of medium. The speed of light in a medium is also no longer observer-independent – as the speed of light in vacuum is – but instead it depends on the relative velocity between the observer and the medium. The speed of light in a medium can also depend on the polarization or color of the light, the former is called birefringence and the latter dispersion.

**3. “Gravity Waves are Wiggles in Space-time”**

Well, actually gravity waves are periodic oscillations in gases and fluids for which gravity is a restoring force. Ocean waves and certain clouds are examples of gravity waves. The wiggles in space-time are called gravitational waves, not gravity waves.

**4. “The Earth is round.”**

Well, actually the earth isn’t round, it’s an oblate spheroid, which means it’s somewhat thicker at the equator than from pole to pole. That’s because it rotates and the centrifugal force is stronger for the parts that are farther away from the axis of rotation. In the course of time, this has made the equator bulge outwards. It is however a really small bulge, and to very good precision the earth is indeed round.

**5. “Quantum Mechanics is a theory for Small Things”**

Well, actually, quantum mechanics applies to everything regardless of size. It’s just that for large things the effects are usually so tiny you can’t see them.

**6. “I’ve lost weight!”**

Well, actually weight is a force that depends on the gravitational pull of the planet you are on, and it’s also a vector, meaning it has a direction. You probably meant you lost mass.

**7. “Light is both a particle and a wave.”**

Well, actually, it’s neither. Light, as everything else, is described by a wave-function in quantum mechanics. A wave-function is a mathematical object, that can both be sharply focused and look pretty much like a particle. Or it can be very smeared out, in which case it looks more like a wave. But really it’s just a quantum-thing from which you calculate probabilities of measurement outcomes. And that’s, to our best current knowledge, what light “is”.

**8. “The Sun is eight light minutes away from Earth.”**

Well, actually, this is only correct in a particular coordinate system, for example that in which Planet Earth is in rest. If you move really fast relative to Earth, and use a coordinate system in rest with that fast motion, then the distance from sun to earth will undergo Lorentz-contraction, and it will take light less time to cross the distance.

**9. “Water is blue because it mirrors the sky.”**

Well, actually, water is just blue. No, really. If you look at the frequencies of electromagnetic radiation that water absorbs, you find that in the visual part of the spectrum the absorption has a dip around blue. This means water swallows less blue light than light of other frequencies that we can see, so more blue light reaches your eye, and water looks blue.

However, as you have certainly noticed, water is mostly transparent. It generally swallows very little visible light and so, that slight taint of blue is a really tiny effect. Also, what I just told you is for chemically pure water, H two O, and that’s not the water you find in oceans, which contain various minerals and salt, not to mention dirt. So the major reason the oceans look blue, if they do look blue, is indeed that they mirror the sky.

Well, actually the gravitational pull of a black hole with mass M is exactly as large as the gravitational pull of a star with mass M. It’s just that – if you remember newton’s one over r square law – the gravitational pull depends on the distance to the object.

**10. “Black Holes have a strong gravitational pull.”**Well, actually the gravitational pull of a black hole with mass M is exactly as large as the gravitational pull of a star with mass M. It’s just that – if you remember newton’s one over r square law – the gravitational pull depends on the distance to the object.

The difference between a black hole and a star is that if you fall onto a star, you’re burned to ashes when you get too close. For a black hole you keep falling towards the center, cross the horizon, and the gravitational pull continues to increase. Theoretically, it eventually becomes infinitely large.

How many did you know? Let me know in the comments.

You can join the chat on this video tomorrow, Thursday Dec 31, at 6pm CET or noon Eastern Time here.

How many did you know? Let me know in the comments.

You can join the chat on this video tomorrow, Thursday Dec 31, at 6pm CET or noon Eastern Time here.

(4) Centrifugal force is a convenient fiction.

ReplyDeleteYeah, I constantly hear people say that. They're usually not physicists.

DeleteThe centrifugal force correcting coordinates is fictitious. The balancing force for centripetal force, outwardly directed induced centrifugal force between rotating particles is real.

DeleteIn classical mechanics the real force must hit to something material. If it hits to empty space, it's pseudo.

"Yeah, I constantly hear people say that. They're usually not physicists."

DeleteAh, now that's interesting to me. My formal education was in Physics, but I'm not any kind of physicist; I do, however, happily say that centrifugal force is a convenient fiction. Usually to people asking about it, whereupon I say that it must be a fiction, because there's nothing causing any such force (no atoms are coming close to each other, no interactions are happening that generates the force in question) and with no cause there simply can't be any forces of this nature - you simply need atoms to get near each other and do their electromagnetic magicks in order to generate any such force. These forces don't exist, they must thus be fiction, QED. I do stand by to be fully corrected.

So what do actual physicists say? I do recall that "fictitious" has a specific meaning, but in this case the simple English meaning seems pretty applicable too.

About the psychology of this issue:

DeleteI need to first point out how precisely the physical experience of gravity plays out. The sensor cells throughout our body, reporting back to the brain, report a sensation of compression. When you are standing up: the weight of your head compresses your neck, your head plus torso compresses your legs, all of your body compresses the soles of your feet. You not only feel compression, but your system is aware that your feet have to carry _all_ of you, and your neck only your head.

Anytime we feel that sensation of directional progressive compression our evolution honed brain automatically/subconsciously infers gravity.

Now you are in a car that is taking a corner agressively.

The door of the car is pushing your shoulder, causing centripetal acceleration. The reports reaching your brain convey an overall pattern of directional progressive compression, but now the direction of compression is towards the door of the car.

You cannot stop your evolution honed brain from inferring you are subject to a centrifugal force towards the door of the car.

It is sort of a convenient fiction, but still really wrong. We can say the same thing about gravitation. I feel a force pulling me down, or so I think. Yet really the force on me is due to bulk material beneath me that is preventing my free fall that "cancels out" gravity.

DeleteIf we move into space and colonize it I suspect rotating habitats will be the standard. People inside these will experience this "gravity" though from the equivalence principle we know they are experiencing the floor pushing up on them so they are on an accelerated frame. If they drop something or throw a mass, it will follow an arc similar to that of a mass thrown on Earth. Of course there will be a small Coriolis acceleration, but ignoring that. The centrifugal force is an artifact of being on an accelerated frame.

About the case of a car taking a corner agressively (hence forces will arise):

DeleteTo simplify you must think of your body as a sphere, with all force exerted upon it acting upon the center of the sphere.

The car is cornering agressively.

As the car enters the corner the door starts exerting a force upon you; centripetal force. In response to the centripetal force your inertial mass starts exerting a force in centrifugal direction upon the door.

The door wins: the centripetal force prevails. The door wins because the door is attached to the car, and the car has traction on the road. (You are sitting in the car; you have no traction.)

The concept of centrifugal force is about getting attribution right. In the cornering car: we do have that a force-in-centrifugal-direction is being exerted. It is being exerted by you: upon the door.

BTW: Will you be doing a video on the Fermi Percolation solution and why it doesn't work for you?

ReplyDeleteNo. I don't know why people find the Fermi paradox interesting. It's been talked about to death and I've nothing to add.

Delete"I don't know why people find the Fermi paradox interesting."

DeleteIt's a great hook for some excellent SF. David Brin's "Existence" was (I thought) a very witty spin on it.

Thanks, great points. Regarding 5. Quantum Mechanics is it actually agreed in the community that superposition exists without exception in macroscopic systems and wouldn't this require that the wave function doesn't collapse?

ReplyDeleteNo, it isn't agreed. I don't know why you'd think so.

DeleteBecause if you say "for large things the effects are usually so tiny you can’t see them." I thought it is agreed that superpositions which are tiny but do exist (unobservable though) without limitation. If this is agreed doesn't it imply that the wave function doesn't collapse during measurement and thus unitarity holds without limitation?

DeleteTimm, are you referring to EQM, Everettian QM? No agreement regarding the measurement problem (or, if it is a problem) in the scientific community. And probably never will be...

DeleteSabine, since this is my first post, let me thank you for your blog and videos. Also just finished your book and it has given me lots to think about (I'm from another branch of physics).

Petri

No, it isn't agreed. I don't know why you'd think so.

DeleteOne of my favorites: why does a mirror reverse left and right, but not top and bottom? Explained by ... uh, it's either Neil Diamond or Richard Feynman. https://www.reddit.com/r/science/comments/9ddqj/feynman_explains_why_a_mirror_reverses_left_and/

ReplyDeleteI never ever understood why people get confused about this in the first place. Isn't it obvious that if you look into a mirror, the mirror is in front of you?

DeleteIf you hold a book up to a mirror, and want to see what happened to the text, you have to turn the book around. Turn it around a vertical axis? text is reversed left-right. Turn it around a horizontal axis, text is flipped up-down. Never mind what a mirror actually does. What we THINK it does depends on how we turn around.

DeleteHah! Serves me right for not watching Feynman. I was so proud of myself for the "turning around" explanation, and there he is. I was going to write a short paper called "The Starfish in the Mirror" because a starfish doesn't have left and right - it has clockwise and counter-clockwise. Well, back to nonlinear PDE...

DeleteIn front of a mirror if you move your right hand further to the right the image you see in the mirror moves the same way. This is the same if you move your hand up and down or to the left etc. If a mirror inverted up and down this would not be a mirror image, but a parity inversion.

DeleteSabine wrote:

Delete"I never ever understood why people get confused about this in the first place. Isn't it obvious that if you look into a mirror, the mirror is in front of you?"

It is not obvious. The point is that up and down are regular vectors while left and right are axial-vector.

Vectors parallel to the mirror do not get flipped in the mirror, while vectors perpendicular do flip.

For axial vectors it is the opposite. parallel axial vectors flip, while perpendicular vectors don't.

Isn't it more simple to say that left/right concept is dependent on measurer but up/down isn't - or that mirror and observer have common directions up/down, not left/right?

DeleteSabine:

ReplyDelete“Light is both a particle and a wave.” … Well, actually, it’s neither. Light, as everything else, is described by a wave-function in quantum mechanics…Well, actually… :)

If a photon (light) is neither a particle nor a wave, then it cannot be described

onlyby a wave function, any more than it can be describedonlyby a particle function.A

wavefunction, as observed from a classical space perspective by using statistical sampling on large ensembles of closely similar situations, has the mathematical appearance of a spatially dissipative mathematical entity. The dissipative behavior stems from the phases of each component of its Fourier spectrum component remaining stable relative to each other for an indefinite period, specifically until the wave “collapses.”A

particlefunction, in contrast, has Fourier component phases that shift continuously to maintain a single region in classical xyz space in which they are always in synch.Particle functions are inherently non-Einstein-local since the continuous phase shifts are equivalent classically to rotating infinitely long cylinders ‘all at once’ along their entire lengths. They are also energy-limited since tighter localization requires phase synchronizing higher momentum frequencies.

(Note the deep irony there: ‘classical’ particle-like existence, which is what allows you to sit there reading this, depends entirely on just such unutterably non-local phase shifts throughout all of space. Without such shifts, you would dissipate into meaningless noise, a fate that is also very inappropriately called the “many worlds” interpretation. It is only causality, the ‘information’ created by the phase shifts, that remains adamantly speed-of-light local, not the particle function itself.)

The mystery, then, is how phase-lock (wave) or phase-shift (particle) behavior comes to dominate the Fourier spectrum of some entity in a given situation. In deep space, the wave version dominates. In condensed matter, the particle function utterly dominates up to the limit of available energy (think atoms).

We do know that when wave and particle functions exchange momentum, the particle function always wins. Momentum is a critical part of the synch process.

Observant readers will have noticed that using Fourier functions is an outrageous cheat since they are wave functions. One cannot explain away waves by first describing everything as waves!

The resolution is oddly simple: Quantum mechanics’ wave side is just as emergent as the particle side,

and just as imprecise. They are opposing partners in an intricate dance that is always finite and mass-limited. It just happens that it is a masterfully deceptive dance that allows us to extrapolate smoothness from all those rough stats we see coming out of actual experiments with large ensembles. The smooth Fourier transforms themselves are simply another aspect of that illusion.As a brilliant string theorist once said, “You don’t need calculus, you just need a few little discrete rules.” [1] With great sadness, I must add that I just found out Steven Gubser died in a climbing accident last year. He was a remarkable and admirable man, and his passing was a terrible loss, I am sure, both to those who knew him and to the entire physics community.

Finally, as Gisin hints, there is far more to resolving particle-wave duality than the naÃ¯ve solution of “going digital,” especially at some non-sensical Planck foam level. Just this week, I had to recognize that bits are no more fundamental than are waves. Instead, they are the ultimate extremum of classical physics — the implicit building blocks underlying classical space, time, causality, and even gravity.

One cannot build the quantum word from bits, ever. The quantum world instead builds them for us to enable our very existence.

[1] Steven Gubser,

Quarks, Flux Tubes and String Theory Beyond Calculus. Simons Foundation, December 9, 2015.https://www.youtube.com/watch?v=vqn2iYYGNxw&feature=youtu.be&t=1483

Actually, the idea that “Water is blue because it mirrors the sky” was promoted by no less a physicist than Lord Rayleigh himself. During a voyage from England to India, another physicist, C.V. Raman questioned this explanation. How he came up with the correct explanation is described in https://en.wikipedia.org/wiki/C._V._Raman#Blue_colour_of_the_sea

ReplyDeleteTherefore, it is okay for a physicist to think or talk like a physicist while questioning physics orthodoxy. But I can see how physicists can sound pedantic while talking to laypeople.

An astronaut moving at high speed will age more slowly than a person on earth. But from the astronaut's point of view, it's the person on earth who is moving fast and ages more slowly.

ReplyDeleteThe twins have equal and opposite displacement, velocity and acceleration(law of kinematics) ...then how could their clock times differ?

DeleteI think of wave particle duality as like an elephant. At one end you have a trunk and at the other end you have a tail, but they are both part of the same elephant.

ReplyDeleteI was going to say that sound waves come out of the trunk and particles come out of the tail, but I thought better not.

Hi Steve,

DeleteFrom an engineer's point of view, I completely agree with you. But from a scientist's point of view, it's all a nightmare because no one can tell who turns the elephant when and how, so sometimes you see the tail and sometimes the head.

Sabine always writes on such occasions that it is neither wave nor particle but a wave function. But then she runs into the "collapse of the wave function" dead end. "Collapse of the wave function" sounds scientific, but it is not. It is only another word for "divine magic trick".

But from an engineer's point of view, modern physics is a feast.

Many greetings Stefan

Stefan,

DeleteSince it's a common confusion, let me point out that in my videos, unless explicitly otherwise noted, I give people the currently most widely accepted explanation, which is not necessarily the one that I myself think is correct. It isn't hard to find out that I have written several papers explaining why wave-function collapse is nonsense.

Stefan - Sabine didn't say "it is", but "is described by".

DeleteI am quite fond of superdeterminism since it resolves wave-particle duality in a delightfully straightforward way: There are only particles.

DeleteSuperdeterminism (any determinism, after factoring in Bell results) requires that all of spacetime pre-exist as a block. Time-locked observers looking at particles from

insidethe block will only see wave packets with varying degrees of blurriness. However, an observer outside of spacetime could use tomographic methods to extract the data encoded by the entirety of a particle’s worldline and interactions. With that, she could resolve with exquisite precision its exact position at any given moment within any of its wave function, no matter how blurry.Superdeterminism necessarily encompasses de Broglie and Bohm’s pilot-wave theory. It is a superset, however, since in superdeterminism the pilot wave no longer does anything. It becomes an incomplete, correlation-deficient illusion created only by the observer’s limited time perspective.

The other waves-only extremum in particle-wave interpretation is the many-worlds interpretation or MWI.

MWI, alas, fails trivially by encoding infinite information on top of finite energy. That violates everything we observe and is why there are frequency gaps between radio-wave stations. Expanding from photon waves to matter waves does not change this point in any meaningful way. In practice, we only observe enough mass-energy to encode a single matter-wave “station” — a spectrum-hogging beast more commonly known as

the universe.Of course, one can assume a

deeperinfrastructure with limitless information resources. For unexplained reasons, the universe hides this from us in excruciatingly innovative ways. For example, renormalization attempts to “see through” such hidden information infrastructure without creating infinities. Theoretical structures that assume information storage levels beyond what local mass-energy supports are what I callinformation singularities. Attempting to encode all of Wikipedia into the letter “M” would be an example of a classical-scale information singularity.If the waves-only MWI extremum of QM interpretation results in information singularities, does the particles-only extremum also do this?

Well, sure. Those infinitely long and infinitely precise particle worldlines necessarily encode unimaginable amounts of history and thus information. Even one slice of one particle path is an issue. If a particle is infinitely small, it requires infinite digits of information to specify its xyz location. That, too, is an information singularity.

In contrast to MWI, superdeterminism has the advantage of hiding its singularities beneath quantum uncertainty. A particle accelerator can access higher levels of the information singularities, but only by

addingmore energy. The result is a delightful ambiguity: Are the observed finer details beingcreatedby adding more energy, or are they beingobservedby adding more energy? This ambiguity is an example of the Spekkens principle of kinematic/dynamic QM tradeoffs at work.However, as with MWI, all that information detail again creates a gravitational collapse risk: the vacuum density problem. In particle-only models, it is possible to balance this out using negative quantum energy levels, at least in principle (no one has done it yet).

Me?

I am okay with being stuck in the middle, inside a stretchy, mass-limited elastic bag that can reach out to but never quite reach either end. After all, there is a lovely simplicity to defining particles and waves as nothing more than two

statesof a single Fourier spectrum. It matches actual observations and avoids magical definitions of what a “point particle” might be. The smeared-out1sorbital of a hydrogen atom in this perspectiveisthe electron.Terry,

DeleteNo, superdeterminism is not a theory of particles. It can work full well with wave-functions. Please see section 4 of this paper.

Sabine, your paper is fascinating! In a quick smartphone read of section 4 (technically, I'm still technically asleep... :), I was completely surprised by your assertion that your superdeterminism

Deletemodifies(shades of MOND!) standard QM. I am now looking forward to beginning the New Year with a deep read of this and your other papers on superdeterminism. Intriguing!Hi Terry,

DeleteHappy you like it. Let me know in case you have questions. And happy new year!

Sabine,

DeleteIt's good news that a new paper on superdeterminism has been published. In fact, I've seen it on arxiv a month ago, but I was waiting for the opportunity to discuss it with you here. Now, the opportunity has arrived.

The abstract reads:

"Superdeterminism is presently the only known consistent description of nature that is local, deterministic, and can give rise to the observed correlations of quantum mechanics"

This is certainly true, but I think the way it is formulated hides the most important aspect of superdeterminism. A mainstream physicist, like Arkani-Hamed, would probably dismiss superdeterminism when reading this abstract, on the grounds that determinism was refuted by Bohr 100 years ago, or something along those lines, and why should he bother with yet another attempt to resurrect a classical view of physics?

I think your argument would be much stronger if the word "deterministic" would be replaced by "fundamental" like this:

""Superdeterminism is presently the only known consistent description of nature that is local, fundamental, and can give rise to the observed correlations of quantum mechanics"

Few physicists could honestly dismiss your article now as most of them are trying to find such a local and fundamental description of nature. The deterministic aspect is not an assumption, but a logical implication of locality + fundamentalness, as per EPR.

Hi Andrei,

DeleteThis paper hasn't been published. Indeed I didn't submit it for publication. I strongly doubt it would pass peer review, so why bother. It's really just there because I think a lot of people are interested in understanding superdeterminism but don't know where to start. So now they can use my paper as a starting point.

I appreciate your suggestion to improve my argument, but without the word "deterministic" the sentence is wrong.

Sabine,

Delete"I appreciate your suggestion to improve my argument, but without the word "deterministic" the sentence is wrong."

No, it's not wrong. Let me copy my version of the EPR argument here:

Let's take a look at EPR's reality criterion:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

Let's formulate the argument in a context of an EPR-Bohm experiment with spin 1/2 particles where the measurements are performed in such a way that a light signal cannot get from A to B:

1. It is possible to predict with certainty the spin of particle B by measuring particle A (QM prediction).

2. The measurement of particle A does not disturb particle B (locality).

3. From 1 and 2 it follows that the state of particle B after A is measured is the same as the one before A is measured (definition of the word "disturb")

4. After A is measured B is in a state of defined spin (QM prediction)

5. From 3 and 4 it follows that B was in state of defined spin all along.

6. The spin of A is always found to be opposite from the spin of B (QM prediction)

7. From 5 and 6 it follows that A was in a state of defined spin all along.

Conclusion: QM + locality implies that the the true state of A and B was a state of defined spin. The superposed, entangled state is a consequence of our lack of knowledge in regard to the true state. So, QM is either an incomplete (non-fundamental) description of a local deterministic hidden variable theory or it is non-local.

So, as proven above, local theory+fundamental theory+reproducing QM predictions gives determinism. So, it's OK to replace determinism with locality+fundamentalness in this context as they are logically equivalent.

I have minimal experience with publishing a paper but I see no reason why superdeterminism, if correctly defended with rock-solid logical arguments (as I think the one presented above is) would not be accepted.

I would present the proof that superdeterminism must be the way (the only local theory able to reproduce QM), show that all other interpretation are either non-local (Copenhagen+collapse, Bohm, GRW) or non-fundamental (instrumentalist Copenhagen, QBism). I find consistent histories interpretation very interesting as I think it's just superdeterminism in denial.

I think some boldness is required here. It's not that superdeterminism is some possible solution, it is the only local solution. This should force the Bohr-fans out of their den and start defending their untenable position.

Please let me know if you find something wrong with the above approach!

What's wrong with your argument is that you just assumed the theory is deterministic. You can't conclude from this that it's deterministic.

DeleteSabine,

DeleteNone of the premises of my argument implies determinism. As stated, 1 and 4 and 6 are implied by QM (no dederminism assumption from my part), 2 is the locality condition ( a measurement at A does not instantly disturb B) and 3 is analytic and has nothing to do with determinism either. Please explain where I am being circular!

Andrei,

DeleteBut that's exactly the point. They do not imply determinism.

Andrei: In your steps (5) and (7), you say "all along." So, "all along" since when?

DeleteThe moment A and B became entangled?

That is as far back as you can logically go; that immediately after the moment of entanglement A and B had opposite spins.

You do not offer a theory as to how the opposite spins arose, so it could plausibly be a "fundamentally" entirely random selection, and NOT deterministic at all.

Determinism would mean that prior to entanglement, sufficient information about the environment would make the spins of A and B computable with certainty.

"Deterministic" is a far more constrained claim than "Fundamental".

Sabine,

DeleteYou have accused me of presented a circular argument. This means that at least one of the premises implies determinism. Now you agree that this is not so.

I fail to see your point. Yes, none of the premises imply determinism, but the conclusion of the argument does. This is how a sound argument behaves. You get more than you put in. You put locality and the truth of QM's predictions and you get determinism in regards to the measured properties. If you measure position, it's predetermined. If you measure momentum, or spin, they are predetermined.

Dr. A.M. Castaldo,

Delete"Andrei: In your steps (5) and (7), you say "all along." So, "all along" since when?

The moment A and B became entangled?

That is as far back as you can logically go; that immediately after the moment of entanglement A and B had opposite spins."

Not only A and B had opposite spins, they had those spins that will later be revealed by measurements. Sure, it's possible that A and B had some other property (not spin itself) that, upon measurement, uniquely determined the observed spins.

So, if you measure A and get 1/2 you can be certain that A was, since its creation, in a state that determined it to produce a 1/2 result upon measurement. This is determinism. The superposition does not only imply opposite spins, but that those spins had exactly the observed values (in this case A:+1/2, B: -1/2). Once you deny that, you get non-locality.

"You do not offer a theory as to how the opposite spins arose, so it could plausibly be a "fundamentally" entirely random selection, and NOT deterministic at all."

True, this argument only covers the entangled state, once it is created, not the previous time. But now you have Bell's theorem, which says that there is no way to randomly produce pairs of opposite spins and get the correct results. So, the pairs cannot be produced at random, but they have to be correlated with the experimental environment which contains the detectors' settings. If you want to account for a Bell test in a local way you need that.

Andrei,

Delete"You have accused me of presented a circular argument. This means that at least one of the premises implies determinism. Now you agree that this is not so.No, I do not agree. You seem to not understand what I am even saying. You are claiming that a local theory which explains the observed correlations is necessarily deterministic. You present several steps that do not contain any information whatsoever about determinism. This means you have simply assumed it is deterministic without any reason as to why that should be, which is why it's circular.

The problem with your above accusation is that what you now want to claim is your "argument" is merely the steps that do not contain any statement about determinism. I am saying that these steps do not support what was your original argument, namely that the word "determinism" is superfluous. You are moving the goalposts. I have zero patience for things like this and if you continue stupid games like this the conversation stops here.

Sabine Hossenfelder1:18 AM, January 04, 2021

Delete"I have zero patience for things like this and if you continue stupid games like this the conversation stops here. "

I think the wannabe Emperor of Spacetime, Luke Barnes, is about to be told very publicly that he is wearing no clothes.

Sabine,

DeleteI am sorry for misunderstanding you. I'll try to explain my point the best as I can.

First, yes, you are right. The argument presented above does not in itself establish "full" determinism. What it establish is that any local theory that gives the right predictions must ascribe a well defined spin value prior to measurement. So, if the measurement result of A is +1/2 and of B is -1/2, we can be certain that, if the world is local, that those particles must have had those properties even before the measurement. In other words, the argument establishes that any local theory giving the right predictions must be of a hidden-variable type.

Agreed, this theory could be only partly deterministic, in that the measurement results are predetermined at the time the particles are created, but the creation itself could be a stochastic process. This valid point was raised by Dr. A.M. Castaldo as well.

At this point however, we can switch to a different result, the one established by Bell's theorem, which says that the only local, hidden-variable models able to give correct predictions must be superdeterministic.

So, my argument eliminates local theories that do not contain hidden variables, and Bell's theorem eliminate all hidden variable theories that are not superdeterministic. In the end superdeterminism is the only surviving local theory possible.

Again, please excuse me for my sloppiness!

Andrei,

DeleteOk, thanks. Bell's theorem doesn't prove that the theory must be deterministic. I don't know why you think it does. Bell's theorem shows that if you HAVE a deterministic, local, hidden variables theory that violates the inequality, then that has to violate statistical independence. It does not show that this is the only way to do it. Spontaneous collapse models are a counterexample. They're local and reproduce quantum mechanics, yet they're not deterministic, hence don't need to violate SI. For this reason, as I said above, the word "deterministic" in my sentence is necessary to make it correct.

Sabine,

DeleteI disagree that Bell’s theorem assumes determinism. It assumes locality, statistical independence and the existence of hidden variables that determine the measurement outcome. Bell’s theorem is perfectly compatible with the assumption that the hidden variables are stochastically determined at the time of emission. In the paper, "On The Einstein Podolsky Rosen Paradox", Bell writes in the conclusion:

“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote.”

So, Bell only requires that the measurement results are determined by the hidden variable, which is exactly the limited determinism that my argument establishes.

Let me explain this better using a reductio ad absurdum argument based on the Bell experiment. The test is performed in such a way to preclude a local correlation (simultaneous choice of the measurement settings, after the entangled pair was emitted).

P1: Let’s assume, for the sake of the argument, that there exists a certain phenomenon in nature which is fundamentally random. Let’s use this phenomenon to set the detector’s orientations.

P2: No signal can travel instantly from the source to detectors or between detectors (locality).

P3: After the emission of the entangled particles, they are described by some hidden variables that determine the measurement outcomes.

P4: QM's predictions are reproduced.

My previous argument, based on EPR-Bohm experiment establishes P3 from the locality assumption. And P1 + P2 establishes that the hidden variables must be independent on the measurement settings, as they are chosen by a process assumed to be fundamentally random. We know from Bell’s theorem that such a theory (local hidden variable+independence) cannot give the right predictions, so we have arrived at a contradiction with P4. So, at least on of the premises must be false. If we want locality, we cannot make P2 false. We cannot give up P3 either since it contains the only local option. So P1 must be false. There is no such thing as fundamental indeterminism. Determinism has been proven.

Sabine,

DeleteCan you give me an example of spontaneous collapse model that is local? GRW is non-local.

Andrei,

DeleteYou wrote:

"I disagree that Bell’s theorem assumes determinism. It assumes locality, statistical independence and the existence of hidden variables that determine the measurement outcome. Bell’s theorem is perfectly compatible with the assumption that the hidden variables are stochastically determined at the time of emission."I didn't say that Bell's theorem assumes determinism. What I said was:

"Bell's theorem doesn't prove that the theory must be deterministic. I don't know why you think it does. Bell's theorem shows that if you HAVE a deterministic, local, hidden variables theory that violates the inequality, then that has to violate statistical independence. It does not show that this is the only way to do it."My point is exactly that it does NOT tell you the theory has to be deterministic. In contrast to what you claimed above.

As you probably know, there's a special relativistic version of GRW. I can't say I find that convincing, but really I don't have to. You are the one who claimed that you can show determinism is a necessary requirement. I don't think it is.

Sabine,

Delete"I didn't say that Bell's theorem assumes determinism."

You said:

" Bell's theorem shows that if you HAVE a deterministic, local, hidden variables theory that violates the inequality, then that has to violate statistical independence."

The word determinism should not be there. This is the correct version:

"Bell's theorem shows that if you HAVE a local, hidden variables theory that violates the inequality, then that has to violate statistical independence."

Anyway, I have presented above the proof that Bell's theorem (not alone, but in conjunction with my previous argument based on EPR) does prove determinism.

In regards to GRW, take a look at this paper:

"Non-local common cause explanations for EPR"

European Journal for Philosophy of Science volume 4, pages181–196(2014)

arxiv: https://arxiv.org/ftp/arxiv/papers/1312/1312.2801.pdf

On page 14 we read:

"Consider, for the sake of illustration, Einstein’s thought

experiment with one particle in a box: the box is split in two halves which are sent in opposite directions, say from Brussels to New York and Tokyo. When the half-box arriving in New York is opened and found to be empty, all accounts of quantum mechanics that recognize the uniqueness of measurement outcomes agree that the particle is in the half-box in Tokyo"

"The difference between Bohmian mechanics and the GRW mass density theory thus is the following one: on the latter theory, non-local causation means that a physical entity disappears in one place and appears in another;"

This is explicit non-locality. Indeed, I make the strong claim that there is no such thing as a local, indeterministic theory that can produce a local account for EPR/Bell. Superdeterminism is the only option.

Andrei,

DeleteYou are not following. This is my last try. I was saying: IF YOU ALREADY HAVE A DETERMINISTIC THEORY, THEN.... Bell's theorem shows you so and so. Which exactly means that YOU DO NOT NEED IT TO BE DETERMINISTIC. In contrast to what YOU claimed.

I don't know what "GRW mass density theory" is supposed to be, and in any case I don't know how it matters.

"Indeed, I make the strong claim that there is no such thing as a local, indeterministic theory that can produce a local account for EPR/Bell. Superdeterminism is the only option."Well, how about this. Try to prove it, publish it, and then show us the published paper. I have tried to tell you sufficiently often now why what you say is wrong.

Sabine,

DeleteHow about showing me a single example of a local, non-deterministic theory that explains EPR? It should be easy to find. You will not find it. Collapse theories are non-local.

I understand that you've lost your patience, fine. You can revise the arguments presented here at some other time if you wish. You should be happy as they prove your superdereministic approach beyond any reasonable doubt.

Andrei, You can make any local, deterministic hidden variable theory into a non-deterministic one just by claiming that the hidden variables are fundamentally randomly distributed. Of course that's entirely pointless, but it's perfectly possible. What you say is trivially wrong.

DeleteAnd just to be concrete, you can use for this any superdeterministic model that has ever been put forward, including my own.

DeleteSabine,

Delete"You can make any local, deterministic hidden variable theory into a non-deterministic one just by claiming that the hidden variables are fundamentally randomly distributed."

A random distribution of the hidden variables does not imply indeterminism. It can simply be a property of the initial state. Non-determinism means that a certain state could evolve into at least two different states.

"And just to be concrete, you can use for this any superdeterministic model that has ever been put forward, including my own."

Well, if you do that your theory would fail to violate Bell's inequality. Remember, the point is not to produce wrong theories, but theories that give correct predictions. A local, non-deterministic theory cannot do that, it's a dead end.

A superdeterministic theory passes Bell's theorem because the hidden variables are correlated with the measurement settings. If you allow a non-deterministic process to set the detectors you have no way to enforce that correlation. Yes, you transformed a superdeterministic theory into a non-deterministic one, but you also ruined the theory as its predictions would be wrong.

Delete"A random distribution of the hidden variables does not imply indeterminism. It can simply be a property of the initial state."Of course it CAN be a property of the initial state. But it doesn't have to.

"Non-determinism means that a certain state could evolve into at least two different states."Nope, it can as well mean that there is no "certain" state.

Delete"Well, if you do that your theory would fail to violate Bell's inequality. "That's just bluntly wrong. It doesn't matter whatsoever if you have a random distribution whether you think it's fundamentally random, or random just because you do not know what it is determined by. Same thing for the outcome.

Let's consider your paper, "A Superdeterministic Toy Model", page 8:

Delete"The reason this works is that the dynamical law explicitly depends on the measurement settings at the time of measurement. This may appear as if it goes against the arrow of time, but note that one could express the measurement settings at the time of measurement by an initial state of the detector and all those system which will influence its dynamics at the time of preparation, it’s just that the relation between the two might be very difficult."

The reason the above fragment is correct is that the theory is deterministic. The state of the detector at the time of the measurement is uniquely determined by its past state. Otherwise, this whole mechanism does not work. The model becomes worthless.

Andrei,

Delete"The reason the above fragment is correct is that the theory is deterministic. The state of the detector at the time of the measurement is uniquely determined by its past state. Otherwise, this whole mechanism does not work. The model becomes worthless."What you say is wrong, once again, and this time for several reasons.

First, the quote from my paper correctly refers to the MEASUREMENT SETTINGS. You, in contrast, refer to the "state of the detector". Different thing entirely.

Second, as the sentence says very clearly you "could" express the final state by an initial state, but there is nothing in the model that *requires* you to do that, as you claim.

"First, the quote from my paper correctly refers to the MEASUREMENT SETTINGS. You, in contrast, refer to the "state of the detector". Different thing entirely."

DeleteFor a Bell test with photons, those settings are nothing else but the position of the polarizer. If that position depends on something that is not deterministic (say an electronic device of some sort) you cannot guarantee what it will be at the time of detection. And in this case the model either fails or it requires non-locality to work.

"Second, as the sentence says very clearly you "could" express the final state by an initial state, but there is nothing in the model that *requires* you to do that, as you claim."

OK, but if it is the case that the measurement settings at the time of measurement CANNOT be expressed "by an initial state of the detector and all those system which will influence its dynamics at the time of preparation", then, according to your words, "it goes against the arrow of time", isn't it?

Andrei,

Delete"For a Bell test with photons, those settings are nothing else but the position of the polarizer. If that position depends on something that is not deterministic (say an electronic device of some sort) you cannot guarantee what it will be at the time of detection. And in this case the model either fails or it requires non-locality to work."A) I didn't say the setting is non-deterministic. I said the position of the settings is not the only degree of freedom of the detector. All the other ones can do whatever you want and be non-deterministic as they please.

B) I do not need to "guarantee" anything. The model only requires the setting at the time of measurement. How that setting came about, deterministically or non-deterministically, does not matter at all for the predictions of the model.

Note again that I am decidedly NOT saying it makes sense to consider a non-deterministic time evolution for this model, but it is arguably possible, in contrast to what you claim.

"OK, but if it is the case that the measurement settings at the time of measurement CANNOT be expressed "by an initial state of the detector and all those system which will influence its dynamics at the time of preparation", then, according to your words, "it goes against the arrow of time", isn't it?"No, I don't know why you think so. Just because something is non-deterministic doesn't mean it goes against the arrow of time. Quantum mechanics itself is a good example.

Sabine,

Delete"I didn't say the setting is non-deterministic. I said the position of the settings is not the only degree of freedom of the detector. All the other ones can do whatever you want and be non-deterministic as they please."

Sure, but then, if the non-deterministic part of the model does not really matter for the experiment you still have a deterministic model. It's like saying that by changing randomly the color of a planet you have a non-deterministic model of gravity. As long as that color has no relevance on the gravitational field you still have the same theory of gravity. Same here. If the detector's paint changes its color without any influence on the setting you cannot say that your model is non-deterministic. It's just a non-deterministic decoration of an otherwise deterministic model.

" I do not need to "guarantee" anything. The model only requires the setting at the time of measurement. How that setting came about, deterministically or non-deterministically, does not matter at all for the predictions of the model."

But yow need those settings at the time of detection (td) to determine the hidden variable at the time of preparation (tp), right? The hidden variable is not time dependent if I understood correctly. My question is how would you do that in a local way? If the settings are based on a non-deterministic process taking place just before detection, how are you going to "insert" them into the hidden variable, in the past locally?

Andrei,

Delete"Sure, but then, if the non-deterministic part of the model does not really matter for the experiment you still have a deterministic model. It's like saying that by changing randomly the color of a planet you have a non-deterministic model of gravity"If you make those details non-deterministic it does not matter for the AVERAGE of the outcome. It matters for the outcome itself, which is no longer determined. Ie, both theories reproduce quantum mechanics. Which is why with current experiments you can't tell them apart, that being my point. You cannot use Bell's theorem to argue that the theory needs to be deterministic.

"But yow need those settings at the time of detection (td) to determine the hidden variable at the time of preparation (tp), right? The hidden variable is not time dependent if I understood correctly. My question is how would you do that in a local way?"Well, as you just said, the hidden variables aren't time-dependent, so I don't know what you think the problem is.

"If you make those details non-deterministic it does not matter for the AVERAGE of the outcome. It matters for the outcome itself, which is no longer determined. Ie, both theories reproduce quantum mechanics. "

DeleteThis does not work for measurements performed on the same orientation. Those need to be perfectly anticorrelated, always. If the result itself depends on some random parameter that is only present at each detector you will have failures.

"Well, as you just said, the hidden variables aren't time-dependent, so I don't know what you think the problem is."

The hidden variable exists before detection, yet the settings cannot be known before detection if they are randomly produced just before detection. Hence, the hidden variable cannot be set in the past to depend on those settings. But this is essential for the model to work.

Andrei,

Delete"This does not work for measurements performed on the same orientation. Those need to be perfectly anticorrelated, always. If the result itself depends on some random parameter that is only present at each detector you will have failures."At this point I think you are just fundamentally misunderstanding how the model works to begin with.

"The hidden variable exists before detection, yet the settings cannot be known before detection if they are randomly produced just before detection. "You generally don't know the settings before they've been set, but what you know or don't know has no bearing on whether it was determined or not. And in any case, your comment doesn't answer my question.

Sabine,

Delete"At this point I think you are just fundamentally misunderstanding how the model works to begin with."

You are probably right. Not being a physicist I have a hard time understanding this kind of abstract models. If you find some time in the future it would be great to write a blog post about your model and made it more explicit to the non-physicists. What I have in mind is a kind of "story" describing how the information flows during the experiment, how the detectors evolve, how their state at the time of detection gets "imprinted" in lambda, etc. This is useful to make the locality of the model explicit.

"You generally don't know the settings before they've been set, but what you know or don't know has no bearing on whether it was determined or not. And in any case, your comment doesn't answer my question."

My (probably wrong) understanding of the model is this. You have the hidden variable after tp, but before td. The hidden variable contains information about the detectors' settings at td. If the model is deterministic this is not a problem because the settings at td are determined by the state of the detectors in the past, before tp. But if the settings are randomly produced at td there is no way for them to be present, in any form in the past, so the hidden variable cannot include them before td.

Andrei,

DeleteI don't know what it even means for information to flow. As the title of the paper already says, this is a toy model. It doesn't tell you anything about where the hidden variables come from or what the detectors do in detail. The point I am tryin to convey is that you don't need to know this; the model will give the same average predictions regardless of those details, which means it could be either deterministic or non-deterministic.

Now, as I have said a few times, it doesn't make much sense to me to consider a replacement for quantum mechanics that is also non-deterministic, so I am certainly not advocating this. I am merely saying that just because you have a local hidden variables theory that violates SI doesn't mean it necessarily has to be deterministic.

"My (probably wrong) understanding of the model is this. You have the hidden variable after tp, but before td."The hidden variables are time-independent, so I don't know what this means.

"The hidden variable contains information about the detectors' settings at td."No, they don't. The hidden variables (all of them) are uniformly randomly distributed in the complex unit disk.

Sabine,

DeleteLet me ask you a few (probably stupid) questions about your model.

1. About the hidden variables you say:

"The reader can think of these variables as encoding the detailed degrees of freedom of the detector"

I do not understand how a complex number can encode this kind of information. At least in my understanding, those detailed degrees of freedom are the parameters required to describe all electrons and nuclei that make up the detector, right?

2. Where do these variables come from? Are they created together with the entangled pair, at the source? At the big-bang? If so, how does the source "access" the detector's degrees of freedom? I understand the model is not detailed, but it should at least make its locality manifest. If you just postulate that the information relevant at the location of the detector somehow exists at the source it appears non-local.

3. You also say:

"It’s not like the prepared state actually interacts with the detector before measurement, it just has the required information already in the dynamical law."

Again, why is this local? Do you just postulate that for some reason the future detectors' settings exist inside the source at the time of preparation?

The above questions pertain to the "information flow" I was speaking about. A local model, even if not detailed, should say how a certain information "travels" during the experiment, at or below the speed of light. In a deterministic system the problem is not so serious, because in a way, the information exists in some way or another at all times. In a non-deterministic system you need to take into account when a certain information is created and how far it can get at the speed of light.

Andrei,

Delete1) It's a toy-model. It does not say anything about where the hidden variables come from. The only thing you need to know about them, as I already said, is that they're uniformly distributed in the complex unit disk. (And they're uncorrelated.)

I merely suggest the reader thinks about them as the detector's degrees of freedom because I personally find that useful. There is nothing in that model which suggests that this is what the hidden variables actually are. It's not necessary to know this. If you don't find that useful, just ignore it.

As to your question:

"I do not understand how a complex number can encode this kind of information."I don't know what the problem is. All degrees of freedom, for all we currently know, are described by coefficients of wave-functions that are complex numbers.

2) The detector settings don't "exist inside the source". I have no idea what this even means.

Sorry, I screwed up the numbering. 1) should be 1+2) and 2) should be 3).

DeleteWell, actually...

ReplyDeleteYou reveal, not that the other is 'wrong', but that you and your interlocutor occupy different universes of discourse. In other words, the complaint is that she is not speaking Physick.

For instance, by 'weight' most civilians mean 'the number reported by the bathroom scale' -- which is, indeed, a measure of the gravitational attraction between their mass and the mass of the Earth, at some specific point in time (and modulo all other masses, the measurement errors of the instrument, and other factors down to the Hizen^H^H^HHeisenbu^H^H^HI am uncertain how to spell the fellow's name), as compared to a similar measurement taken now. And, in the event, is often not a measurement at all, merely an appreciation that he has taken in his belt a notch or two, comfortably.

By way of analogy, consider the word 'data'. Pedants [he said, thus revealing himself to be one] insist that it is plural; the singular form is 'datum'. And that is true... in Latin. English has borrowed the word, filed off the serial numbers and driven it over the state line: it has become, not just a simple plural, but also a collective noun for an unnumbered aggregate of points of observation, down to and including an aggregate of a single such point. And 'datum' is what happens when she** swipes right.

**[I apologise to the more generously gendered amongst us, for the cisgendered wordplay. Love, too, is not simply Physick-al.]

[[ See? You don't have to be a physicist to be annoying! ]]

No1. is frame dependent. In the frame of the Earth, the Earth is not moving at all.

ReplyDeleteThe Sun's motion measured by an Earth observer is well-documented.

DeleteThe Earth's motion measured by a Sun observer is unknown and untestable...conflicting with the testability clause of the SciMeth.

“The Earth Orbits Around the Sun.” and not the Sun around the Earth.

ReplyDeleteIn daily life it does not matter. But in philosophy?

I have heard the first several times from philosophers. A student in philosophy, at least in Germany, must read I. Kant’s “Kritik der reinen Vernunft”. Kant thought that we are sure that we found the truth in natural sciences in two cases: the geometry of Euclid and the physics of Newton. For Kant Newtons physics was not just a perfect description of the world. It was the truth. How is it possible for men to recognize the truth was Kant’s starting point.

I met philosophers that still have this view (most of them are believers of the Holy Trinity Kant, Hegel & Marx).

Thank you for your always so very interesting insights.

ReplyDeleteRegarding the form of the earth, see this article: https://www.newscientist.com/article/dn20335-earth-is-shaped-like-a-lumpy-potato/

I did not know H2O was actually blue.

ReplyDeleteI did not know gravity waves were not distortions of space time, I thought in fact that is how we detected them. I'm still not sure I understand the distinction.

The rest I knew.

In Oceanography a specific type of wave motion has the name 'gravity wave'. (This type of wave motion has of course nothing to do with relativistic physics.) So that is a case where two branches of physics happen to use the same name for different things.

DeleteOne attempt to distinguish would be to insist that the GR phenomenon should exclusively be referred to as 'gravitational waves', leaving the name 'gravity wave' for oceanography, but most people are using 'gravity' and 'gravitation' as interchangeable words, so that's not going to work.

A gravity wave is a fluid dynamics with gravity, usually just plain near surface constant g = 9.8m/s^2, as a force normal to the direction of the waves. Two layers of atmosphere moving past each other set up turbulent eddies this way. Then by Bernoulli principle has lower pressure in the turbulent eddies between the layers and creates stripped clouds patterns. Gravity waves in oceanography are much the same, but with different flows of water.

DeletePicky: light cannot be described by quantum "mechanics" which implies that if you treat it as a particle, that particle has nonzero mass.

ReplyDeleteIts correctly treated by a relativivtic quantum field theory. Its classical counterpart is the classical relativistic field equation called Maxwell's equation. The photon has zero rest mass.

Picky.

When one loses mass, one also loses weight since weight is dependent on mass. Both are correct in the context wherein gravity is a constant. However, I do like to ask die-hard fans of the metric system of units..."How much do you weigh?", and then they inevitably answer "XX kg". Heh.

ReplyDeleteHow to understand the mirror problem and welcome the new year.

ReplyDeleteFirst get your self some string and some duct tape and stand in front of the mirror. Duct tape some string to your right shoulder then duct tape the other end of the string to the image of the shoulder with the string attached to it. Do the likewise for the left shoulder. Tie the string around your big toe and duct tape the other end of the string to the image of your big toe in the mirror. Duct take the string to your nose and duct tape the other end to the image of your nose in the mirror.

Now if you have done a good job all the strings will be parallel illustrating why you see what you see. Then shout out happy new year at the top of your lungs. Problem solved!

Actually this is a question. About falling though the event horizon - As the force of gravity increases as you get to the event horizon time appears to slow down , to an outside observer. The passage of time stops at the event horizon.

ReplyDeleteSo why does many books on this topic talk about falling through the event horizon. Time stopped means "never" doesn't it?

Thanks - JoeB

The observer falls through the horizon in finite proper time.

DeleteTo expand a bit. The infalling observer crosses the event horizon in a finite time period. The observer from the outside witnesses clocks and time slow down, photons from the infalling observer red shift and this slows to an asymptotic crawl up to the horizon. Also there is the Lorentz contraction which makes the infalling observer paper-thin as they reach r = 2m. Also by optical effect this observer appears to spread around the horizon as well.

DeleteThe force of gravity that is real is the tidal pull on the infalling observer. Two test masses approaching a central gravity field such as a black hole will separate and along a radial direction with distance D this is the acceleration a = 2GMD/r^3. So as you fall towards a black hole your feet will accelerate away from your head. This is a gravitational form of a medieval rack. For a solar mass black hole you would not get within a few thousand times the horizon radius without being ripped apart. The massive black hole SgrA* at the Milky Way center you could cross the horizon, though you would be feeling the tidal pull. Within not too many seconds you would be then pulled apart. This is called spaghettification.

Now suppose you are suspended by a tether, and you want to approach the horizon slowly, but not cross it. Then there is a force pulling up that will increase enormously as you are lowered to the event horizon. This diverges to infinity, at least classically, as you approach the horizon. There is a quantum limit or Planck scale limit of an acceleration 10^{52}m/sec^2. That is quite huge. Of course you would not survive that, and in fact no probe of any extension in size or composite structure would. Also there is no tether with that tensile strength. Maybe though a superstring or cosmic string would work, at least in part.

all of them

ReplyDelete"It is however a really small bulge, and to very good precision the earth is indeed round." Navigation based on the assumption that the earth is a sphere will go wrong quickly and put you in the wrong spot after a relatively short distance (a few km). GPS uses the WGS-84 ellipsoid model, which describes the earth as an oblate spheroid: https://en.wikipedia.org/wiki/World_Geodetic_System

ReplyDeleteAd 5 and 6:

ReplyDeleteIn November I was attacked by Small Things. My Body Mass Index changed from 23,4 to 20,3. Now it is 21,4.

Take the vaccin, not the real stuff. Happy New Year.

Well, ACTUALLY, in your transcript you call it a "slight taint of blue", but you surely meant a "slight tint of blue".

ReplyDeleteA "taint" is indeed a trace of something, but always bad or distasteful, like an infection, or bad odor, or rot.

A "tint" just means a pale or dilute color.

Do I get a cookie?

Dr Castaldo,

DeleteYou are right of course, sorry about that.