N. David Mermin

Here is a puzzle quantum computers won't solve:

1. We have a randomized ASCII extended string X1 transforming the plaintext.

2. We have a randomized ASCII extended string X2 creating the key characters.

X1 & X2 = n (0 to 255)

X1 (n 0 - 255) + X2 (n 0 - 255) = X3 | Mod256

That is all we need to understand when using modular arithmetic. For example let the character E on our first string X1 be at position 228 and the first character K on our second string X2 which holds the value of 075.

228 + 075 = 303 | Mod256

256 -

47 =

In the extended ASCII table 47 represents '/ ' and that is the only information an attacker would gain intercepting a cipher. Every new plaintext character is encrypted in a new unique permutation, changing the statistical properties this character holds.

Now let's look at Shannon's entropy H ( ) which has become H (M |C) = H (M).

H (M) = - ∑ (P (M) log (P (M)

H (K) = - ∑ (P (K) log (P (K)

RMLM ≤ RKLK



I must send this to Mermin.… (plus d'informations)

Newbie: “I know very little about this subject, and understand even less, but what follows are my confused ramblings about travelling faster than the speed of light ( C ). Much appreciated if someone could put me straight on any/all the bits I've got wrong :)

If, when travelling faster through space, time slows down for the traveller, does not this mean that we, and everything else in the universe, are actually always moving at the speed of light if we add up all the speeds we are travelling in all the 4 dimensions?

1 - A proton travels through the 3 dimensions of space at C but doesn't move through the dimension of time at all.

1C + 0C = 1C

2 - If I travel at half of C then time moves at half speed for me.

1/2C + 1/2C = 1C

3 - So, I presume, if we don't move physically then we travel through time at the SOL . (My lazy normal state).

0C + 1C = 1C

SO

either nothing can possibly go faster than light because there is no other speed anything can ever move at

OR

to travel through space at more than C you would have to move backwards through time.

The existence of other dimensions might change this, but only if they were big enough for us to fit in them - ie those hypothesized Superstring dimensions are all so small that I can't see how we can possibly be moving in them so we have no speeds to add on to get greater than C.”



Me: “Yes, you're mostly right actually. I'm surprised and quite impressed that you came to that realization on your own quite frankly. You can interpret relativistic dynamics as meaning you always travel at speed c through spacetime. The faster that you move in space, the slower you must then move in time. This is manifest when you talk about four-positions and four-velocities: the four-velocity of object along its own world line is c. But you don't add them like that. You take the squares and add them, just as you would resolving vectors components along orthogonal directions. (That is, you use the Pythagoras' law). So 1: is (1c)^2 + (0c)^2 = (1c)^2 and likewise for 3, but for case 2 you have: (c/sqrt(2))^2 + (c/sqrt(2))^2 = (1c)^2. So for the second case the speed of motion through space and through time is c over sq root 2 and not c over 2.

I'd be careful with how you state your conclusions, though. Moving backwards in time is exactly the manifestation, in this picture, of the breaking of causality caused by objects that travel faster than light. But, none of this proves that that's not possible, we just don't think it is so.”

Newbie: “Thank you for your kind words, corrections, and explanations (even if "just as you would resolving vectors components along orthogonal directions" makes me go "whaaaaat?").

So, when calculating what happens to time if you are travelling faster than light, you need to find the square root of a negative number? And there is no such thing. I would have thought that makes it impossible.

I've also wondered if (if everything is always moving at C in spacetime) it wouldn't make just as much sense to say nothing ever actually moves, it just seems like it does. That's the point where I put on my knotted hankie and grunt ‘My brain hurts’.”

Me: “Crazy as it sounds, it is possible to take the square roots of negative numbers! We define the imaginary number i= sqrt(-1). So, for example, if x=sqrt(-2), then x=+/-sqrt2*i. In general, a complex number will take the form of z=x +iy, where x is the real component, situated along the real number line, and iy is the imaginary part, situated along the imaginary number line, which sits at right angles to the real one.”

Me: “Additionally, let me clarify something first: actually, you don't add the squares you need to subtract them, so don't go quoting the numbers I gave you because they're not right; I just wanted to give you the idea that you take squares and don't just add things up. But actually it's a little more complicated even than that because the squares are in Minkowski space, so you need to subtract components. That probably doesn't make sense to you (hence why I left it easier before), but looking back at it I wanted to clarify that what I wrote before is only a simple picture and not properly correct.

Resolving components of vectors is easier than it sounds and looks; maybe this helps.

So, when calculating what happens to time if you are travelling faster than light, you need to find the square root of a negative number? And there is no such thing. I would have thought that makes it impossible.

The equations you see above (and elsewhere) are derived from a situation where it is implied you can't move faster than light. It's an implicit assumption you make in the construction of the equations. They break down (i.e. give answers that don't make sense, like roots of negative numbers) because they were never constructed in order to work in those situations in the first place. Hence they themselves don't prove that faster than light travel is not possible because you already made that assumption when you constructed them. It's a circular argument. If I derive equations assuming x=0, I can't then claim that the equations tell me that x must be 0, because I myself put that into them in the first place! Thus, if you could travel faster than light, you would need a whole new theory of mechanics and you can't just read it off the current equations.

I've also wondered if (if everything is always moving at C in spacetime) it wouldn't make just as much sense to say nothing ever actually moves, it just seems like it does.

Which "move" do you mean? Do you mean movement in spacetime, or movement in space alone (what we normally call "move"). We all move at the same speed in spacetime, we have no choice about that, but we can move at whatever speed we like in space (as long as it's less than c). That freedom to move in space alone is real -- we really have that choice, and different objects can choose to move differently, so, no, movement isn't an illusion: different objects do move in space differently even though their complete motion in spacetime is still always the same as everything else's.… (plus d'informations)

Why Quark Rhymes with Pork: And other Scientific Diversions. N. David Mermin. 400 pp. Cambridge U.P., New York. 2016 Price $29.99 (hardcover) ISBN 978-1-107-02430-4. (John G. Cramer, Reviewer), published in the American Journal of Physics

The centerpiece of this book is the collected Reference Frame columns written by Cornell University theoretical physicist N. David Mermin and published in Physics Today from 1988 to 2009. Many of these columns bear titles that begin as "What's Wrong With ...", providing a hint of the critical and somewhat iconoclastic eye with which Mermin regards the physics community, its activities, and its peculiarities. In addition to the columns, the book contains unpublished excerpts from lectures and reminiscences about Mermin's interactions with colleagues. I would have to say that despite Mermin's remarkable wit and style, in overall impact the book is for the practicing physicists rather than the non-specialist reader interested in science. As examples, it contains criticism of the attempts of sociologists to apply cultural anthropology arguments to physics, an extended discussion of the systematic misspelling of the word lagrangian in the physics literature, satirical accounts of the activities of one Professor Mozart, who suffers at the hands of NSF proposal reviewers and has other Mermin-like adventures, and it also contains meandering inquiries probing the foundations of quantum mechanics. While the physicist readers may find these discussions interesting, the non-physicist interested in physics is likely to find them peculiar and parochial. Further, I confidently predict that Chapters 23 and 28-33, a sizable part of the book, will be unintelligible to the non-physicist (and to many physicists as well).

Mermin's book takes its title from his December-1993 column discussing the pronunciation of the word quark. In the afterword of that chapter, Mermin mentions that Victor Weisskopf told him the column was silly. I would have to agree, since in the multiple pages of discussion about the word quark and its pronunciation, Mermin fails to mention how Murray Gell-Mann came up with the term in the first place. It is well known that the inspiration came when Gell-Mann found the word quark in James Joyce's Finnegans Wake:

Three quarks for Muster Mark!
Sure he has not got much of a bark
And sure any he has it's all beside the mark.

From Joyce's alliteration it is abundantly clear to me (and should be even to Mermin) that quark must rhyme with bark and mark. Certainly in two decades of attending physics meetings in
which the quark-gluon plasma was the focus of discussion, I never heard even one physicist pronounce quark to rhyme with pork. On the other hand, as the writer of a regular column mainly about physics, I understand how hard it is to come up with something clever to say in print every month or so, and I suspect that Mermin was scraping the bottom of the barrel here. That, however, does not explain the use of this peculiar piece as the title for his book.

On the other hand, there are many things to be learned from a careful reading of Mermin's essays. In my recent book I used "Shut up and Calculate!" as the message implicit in the Copenhagen interpretation, but I had not realized that that Mermin was its originator. Mermin explains the famous Schor algorithm for factoring large numbers into primes using a quantum computer as based on the facility with which a quantum computer can produce and recognize patterns in modular arithmetic. He clarifies the Greenberger–Horne–Zeilinger scheme for demonstrating nonlocal correlations in systems of three entangled photons, showing that it leads to a more unambiguous demonstration of quantum nonlocality than do EPR two-photon correlations. Mermin's description of his stress-filled attendance as a guest at the Nobel Prize Award Ceremonies in Stockholm is enlightening and entertaining. Unfortunately, that account gratuitously appears twice in the book, suggesting that his editor should have intervened. I should add that the book contains an excellent joke about the difference between theoretical physicists and mathematical physicists, which I have unapologetically lifted and used in the science fiction novel that I am presently writing.

My main complaint about Mermin's book is the mantle he assumes as a Bayesian Pied Piper, leading the naive and unsuspecting children of Quantum Town down the rodent hole of Bayesian quantum mechanics, which Mermin and others call QBism (for quantum Bayesianism). It is bad enough that the Copenhagen knowledge interpretation requires us to believe that the solution of a simple 2nd order differential equation relating mass, energy, and momentum somehow miraculously becomes an encoded description of knowledge in the mind of a hypothetical observer measuring the system. Now Mermin wants to double down on this dubious assertion by splitting up that general Copenhagen observer and his knowledge into specific individual observers, each with his or her own expectations and predictions to which Bayesian probability and statistics must be applied. This QBism goes on for several chapters of the book. Its main virtue is that it is quite unconvincing as a way of understanding what is going on in quantum systems.

The real strength of Mermin's book lies in his descriptions of his interactions with several major figures in condensed-matter physics: Daniel Fischer, Walter Kohn, Ken Wilson, and Sir Rudolph Peierls. These chapters are gems, and they are well worth the price of the book for their clear and insightful descriptions of truly excellent physicists at work.

In conclusion, I think this is a somewhat flawed book that nevertheless should be of interest to practicing physicists and to those interested in the tribal customs of the physics community. The curious non-physicist would certainly find parts of the book interesting, provided he or she was willing to "surf over" the opaque technical parts and the wrongheaded quantum mechanics.

John G. Cramer is Professor Emeritus - Physics at the University of Washington, Seattle. For five decades he has taught physics and done experimental and theoretical research in nuclear and ultra-relativistic heavy ion physics. He is the originator of the transactional interpretation of quantum mechanics, the subject of his new book The Quantum Handshake - Entanglement, Nonlocality, and Transactions, Springer (2016). He has also written two hard-SF novels, Twistor and Einstein's Bridge, and his bi-monthly science column is published in Analog Science Fiction/Fact Magazine.… (plus d'informations)