Displaced_0,
Rather than quibble let's cut to the chase and ask a working physicist. This is a response to a 2003 email that I sent to Dr. RObert Brown, Duke University Physics Department:
"
> Well, I'm not really an expert in differential geometry or general
> relativity, although I'm pretty competent in E&M and special
> relativity, including the "grown up" forms (group theory and arbitrary
> boosts and rotations via generators, not just kiddie-physics Lorentz
> transformations).
>
> However, I'd listen to Kaku, if nobody else, reason being some of
> "Titor"'s time-travel "facts" sound suspiciously like they came
> straight from Kaku's "Hyperspace", right down to the "who couldn't
> love strings" discussion. What, Kaku's book is STILL popular reading
> in 2036? I thoroughly enjoyed it myself, but don't see it surviving
> until then any more than anybody goes around reading "1-2-3 Infinity"
> any more.
>
> In my previous replies, I really haven't gotten started on Titor's
> physics -- or his engineering, which is even more egregious. Just
> this one last time, I will waste a few hours on this by pointing out
> only a few of the problems. Most serious physicists would probably
> not bother to waste the time -- you are just lucky I'm not a serious
> physicist;-)
>
> For example, he asserts that his black holes are "the size of an
> electron" in several places.
>
> Say what?
>
> An electron is an elementary particle. Elementary particles in
> physics have no structure -- they are not composite particle bound
> together with some additional force and hence possessed of a spectral
> structure. Contrast the electron with the atom (made up of nucleus and
> electrons; we ARE part of the structure inherent to this system
.
> With the nucleus (neutrons and protons, glued with nuclear force,
> plenty of shell structure
. With the proton and the neutron
> (elementary quarks glued with gluons, and yes, there is structure in
> the form of an SU(3) particle zoo). In all these cases the particles
> have a "size" consisting of the physical extent of the composite
> particle wavefunction.
>
> An electron or quark is NOT made up (so far as we can tell) of smaller
> particles glued together. As far as we can tell, with very high
> energy collisions, they have no physical extent and are >>truly
> pointlike entities<<. In fact, we EXPECT elementary particles to be
> pointlike entities, as if they are not pointlike (and if they are
> charged) we have to figure out what ADDITIONAL force binds all the
> charge together -- the particle suddenly has a rather large energy
> associated with its binding.
>
> So why say his BH's are the "size of an electron" when there ain't any
> such thing? Why not say they are "1.7 fermi in diameter" or "the size
> of a proton" (same order of magnitude, and this is a number that
> actually exists at least to some approximation). Or just give us the
> mass -- 10^12 kg, for example. Perhaps because there are some
> PROBLEMS with that mass, hmmm.
>
> There is actually a lot of interesting physics associated with the
> notion of e.g. electron size. Without boring you with details, there
> are lovely papers by Dirac, McManus and others concerning radiation
> reaction, preacceleration, electron size/shape in the classical
> regime. However, the most amusing result of all of this in the current
> context is that there IS one (classical) sense in which an electron
> can be assigned a "size" (and another in a quantum sense, but that is
> clearly not what he means here as the BH would be much too large to be
> believable, not that this one IS believable).
>
> If one assumes that the electron is a ball of uniform charge, and that
> the self-energy of all of this charge (bound together with some
> mythical charge-glue for which there isn't a shred of evidence to the
> best of my
> knowledge) is equal to the mass energy, then one gets (ignoring scalar
> factors of order unity and using "latex" to do ascii algebra, hopefully
> fairly clearly):
>
> \frac{ k e^2} {a} = m_e c^2
>
> which can be solved for a, the classical electron radius:
>
> a = \frac{k e^2}{m_e c^2} \approx 3 fm
>
> which is not at all coincidentally the same order as the size of the
> proton or the nucleus of your choice, which DOES confine a net charge
> of order e with a stronger attractive force but (consequently) has a
> much larger mass. The Schwarzchild radius for the electron mass is
> determined from a very similar computation (again neglecting scalar
> factors order unity)
>
> \frac{ G m_e^2} {r_s} = m_e c^2
>
> or
>
> r_s = \frac{G m_e^2}{m_e c^2} = \frac{G m_e}{c^2}
>
> which is number so tiny as to be meaningless (order 10^-57 meters,
> smaller than the Planck length and hence it IS meaningless).
>
> An amusing computation: Suppose r_s = 1 fm (somewhat smaller than "an
> electron"). Then m_BH = r_s*c^2/G, right? Plug 'n' chug. On my
> calculator, 10^-15 * 9x10^16/6.67x10^-11 \approx 10^12 kg. Let's see,
> that would be, um, a billion metric tons, the mass of a cube of water
> 1000 meters to the side (as 1000^3 = 10^9 and water conveniently
> masses a metric ton, 10^3 kg per cubic meter. How come nobody in your
> group actually did these simple computations?
>
> His suitcase contains TWO of these? He carried this suitcase on a 67
> Chevy? Man, they must put a hell of a suspension in those babies...
>
> Maybe he meant some other "radius of the electron". Alas that I don't
> know of any, as the electron doesn't have a radius in the first place
> and even the classical radius above is thus a fairly meaningless
> artifact. Still, let's suppose that he (a lay person and
> self-confessed physics idiot) was "confused" and that he meant that
> the BH's in question were around 10^-24 meters in radius, which is what
> I get for BH's that mass >>1<< metric ton. We'll use this number
> below just for the hell of it, since I vaguely recall hemming and
> hawing by him on the list that suggested that this is the order of
> magnitude of the size of his BH's. Ha.
>
> Next, Titor claims to shoot electrons into his BH to keep up its mass
> and do all sorts of other things. Oh my sweet Jesus.
>
> If you "shoot electrons into a BH", this has the unfortunate side
> effect of making the ball more and more negatively charged. This has
> all sorts of interesting (classical) consequences:
>
> a) It becomes harder to shoot each additional charge in. It is
> easy to think "Oh my, it is a black hole and hence gravity MUST be the
> strongest force present", but this is not only not the case it isn't
> even CLOSE. Compare ke^2 \approx 10^-28 to GM_b m_e \approx 10^-29
> and one sees that within a factor order ten they are the SAME, with
> electrostatic repulsion likely somewhat higher, and this is assuming,
> BTW, that the BH mass is 10^12 kg and not 1000 kg.
>
> b) Wait! Doesn't that mean that if I shoot one electron in
> (charging the black hole to -e) that the SECOND electron I shoot into
> a BH of mass around 10^12 kg is precisely unbound at the black hole
> radius? So that the black hole may be black for a lot of things, but
> not electrons? It does. For a black hole to remain bound, the NET
> FORCE on its components has to create accelerations of order c^2/r_s.
> Two electrons inside radius a have a repulsive energy (NOT attractive)
> on the same order as the gravitational binding energy of the entire
> black hole of the same radius to the same electron. Shooting the
> second electron into the black hole has a significant chance of
> knocking the first electron OUT of the black hole (as it becomes
> unbound) and REDUCING its mass. Or worse.
>
> c) Wait again, don't we have to think about quantum mechanics
> somewhere in here? We do indeed. Even in quantum mechanics the
> "classical electron radius" is an important number. It is the
> separation point where two electrons possess enough energy to think
> seriously about engaging in pair production (scattering
> electron-positron pairs out of the vaccuum), as they have enough
> energy to do so, if they have some mass around to use to conserve this
> and that in the process.
>
> In fact, another way of viewing the process classically described in
> b) is that the second electron gets close to the charged black hole,
> creates a virtual electron-positron pair while scattering off of it,
> the positron falls in (attracted by that negative charge AND gravity)
> where it annihilates an electron in the BH. The two electrons -- the
> one you shot in and the leftover from pair production -- scatter to
> infinity and "escape". The black hole itself has more internal
> kinetic energy (is "hotter"), is less massive, and less stable.
>
> IIRC the c) process roughly describes one of Hawking's instabilities,
> except that he envisions it occurring continuously near the event
> horizon of small black holes. Any charge imbalance or field imbalance
> in the electromagnetic force would be nearly instantly neutralized out
> of the vaccuum at the expense of the BH mass, and even when neutral
> vaccuum polarization makes decay a steady process. Titor shrugged off
> Hawking, which he could likely get away with since Hawking is likely
> too smart to waste his time on this sort of nonsense. If only I were
> as smart myself...
>
> One could go on and on, so I will. We argue above that a BH this size
> cannot stably be charged (or be stabilized by shooting charged
> particles into it). Can it have a magnetic moment? Not without a
> charge and a spin and it cannot have a charge (although I'm almost
> surprised that Titor didn't assert that his BH contained magnetic
> monopoles, given all his other tall tales
. Without a charge or
> magnetic moment, how do we hold on to it? How do we ENGINEER
> confinement, even in 2036? See below.
>
quote:
--------------------------------------------------------------------------------
> > (Darby's Question): Is there any chance that you can identify the attached jpg? It was
> > posted by Titor as a cutaway schematic of his gadget. It appears to
> > me to be a vacuum tube based piece of 1960's technology. It was
> > suggested to me that it's a pre-internet Arpanet server - but I
> > haven't a clue. I sent a copy to UC Santa Barbara to see if they
> > can ID it. So far, no luck.
--------------------------------------------------------------------------------
>
> Naw, I have no idea what it is -- maybe a klystron unit of some sort
> for a radar at a guess -- but who cares? This schematic is ridiculous
> as a BH confinement/manipulation mechanism. Let's start by addressing
> the question of how we hold onto a black hole that we cannot stick a
> significant charge or magnetic moment on. Or even one where we can.
>
> We don't. Not ONLY do we have to create the damn thing, we have to
> keep it from falling into Earth's welcoming gravitational well.
> Clearly, if it masses 10^12 kg, we don't. Period. Ever. I don't
> care if you are an advanced society that has been around evolving
> brain for a million years LONGER than humans -- if you start playing
> with billion-metric-ton black holes near the surface of your planet
> you are only here for a visit. This is E.E. "Doc" Smith level (e.g.
> crap) science fiction.
>
> Now, if they mass LESS than a metric ton, I don't know why one would
> bother making them at all, and as noted above this is sort of the
> number I recall from some fraction of the online discussion, so let's
> pretend that the BH's are 10^3 kg each and that Titor knows just about
> as much about the radius of the electron as the history major he
> claims to be might know.
>
> We now have TWO of these pups, each weighing a metric ton, inside of
> the little chassis below (the size of an oversized suitcase, again
> from list discussion, at any rate small enough to fit into a pickup
> truck)?
>
> Hmmm. A suitcase that weighs half as much as my Ford Excursion.
> Hmmm, my Excursion supports its not inconsiderable weight on big,
> heavy, steel girders. Even my wimpy Ford Contour (which weighs just
> about as much as this suitcase and its two black holes) uses quite a
> bit of steel in its construction, and one would really hate to run
> over a toe with its far more lightly loaded steel belted radial tires.
>
> We thus have TWO very serious engineering problems that immediately
> come to mind. Well, actually more than two, more like thirty or forty
> or fifty. However, one is keeping the black hole containers from
> ripping through the bottom of the suitcase itself. Think of the BH
> containers as being leedle support posts, cross sectional area of a
> few centimeters squared each, HOLDING UP A FORD CONTOUR. Hmmm, think
> we need a little more than four little reinforced corners on the box
> that look sort of like thingies you'd find on the corners of
> loudspeakers or a suitcase or something else with cardboard sides.
> And wait, where are the four inch I-beams in the flooring? Where are
> the grappling eyes on the side (or are humans supposed to lift this
> thing in and out by HAND?). And this thing was riding in the back of
> a small pickup truck? Hmmm, not so sure that a SMALL pickup truck
> could support my Contour as well and not blow out its tires and wreck
> its suspension, especially a pickup truck that was 70 years old and
> hard to get parts for.
>
> Then there is the even more interesting question: Fine, perhaps they
> have new materials. Maybe the case has synthetic diamond struts in
> the bottom, laced into a steel cementation so that one cm of thickness
> is enough to support a metric ton without any sort of localized
> bracing or structural forms, spread out over may 100 cm^2.
>
> EVEN SO, INSIDE of those little BH container are the BH's themselves.
> They have to be held, far from any contact with matter, by means of
> raw E&M forces (unless we're going to suggest new physics, and new
> physics here would be indefensible I assure you).
>
> The mere thought of this has me ROTFL. Seriously. I >>teach<<
> graduate E&M, and I assure you that the problem of magnetic
> confinement of thermonuclear plasmas is child's play compared to the
> problem of confining an object 10^-25 meters across with a metric ton
> of mass against the Earth's gravitational field, the presumed motion
> of the long-suffering Chevy pickup truck (gawd, accelerations in
> arbitrary
> directions!) and so forth. You see, all the fields involved have to
> satisfy the laplace equation, and this means that it is almost
> impossible to create an even weakly attractive region capable of
> suspending wimpy things like atoms that is STABLE in both a vertical
> direction and its transverse plane. Try suspending the equivalent of a
> small car not on the head of a pin, not on an atom, not on a classical
> ELECTRON, but on an area that aspires to be a mathematical point. Ho,
> excuse me, I have to wipe my eyes again. Really, a delicious picture.
> I'd sooner believe in the time travel part.
>
> And wait, where the HELL is the hardware for accomplishing this
> fu**in' miracle? Oh, yeah, those leedle balls. Hey mon, we don't
> need no stinkin' massive magnetic coils, no gigavolt capacitors, no
> bus bars the thickness of your wrist. No mon, we got room temperature
> superconductors, we got new magnetic materials mon, we got monopoles.
> We can stabilize the BH, mon, and move it around and make it bounce in
> waves. Hawking? Who is this Hawking mon? Sure, it stable against
> pair-production-mediated decay. So what if its Schwarzchild radius is
> WAY WAY smaller than the radius where vaccuum polarization electron
> pair production begins to be significant and there is enough energy in
> the gravity well to knock particles out of the vaccuum. It just
> doesn't happen.
>
> But by damn, we still got old-fashioned BNC-style wiring connectors
> mon, labelled 11. We still got klystrons and big, heavy power
> switches. And we don't need no stinkin' radiation protection mon --
> the fact that we have to shoot about eleventy-zillion electrons at
> very high energy in an intense electron beam to get ONE ELECTRON to
> impact on a highly repulsive sphere with a radius of ~10^-24 meters
> (without creating a shower of secondary particles that cause the BH to
> DECAY) means nothing, mon. We definitely don't need no bending
> magnets, no quadrupolar lenses, no accelerator. Hell mon, we can put
> a gigavolt accelerator inside of a coffee pot now mon -- it's 2036 and
> we're very tribal now -- and run it with an ordinary eco-approved
> household battery! Although we don't have to, the suitcase comes with
> its own fusion generatory mon...it could run a small city if only we
> could plug it in.
>
> Seriously, I could go on and on and on. I haven't even gotten to the
> raw thermodynamics of it all. That suitcase would require a small
> lake to cool in operation, for example. And then the culture capable
> of these miracles of technology that indicate total mastery of
> materials science, quantum mechanics, gravity, superconductors, a
> society that has in its possession a star drive (for the goddamn thing
> would clearly work as such as easily as a "time machine" -- arbitrary
> translation in four space is arbitrary translation in four space and
> they have to play all sorts of games to NOT go off into space FTL)
> then is sending somebody back to our time to get an IBM 5100, a piece
> of **** computer that is an embarrassment to IBM to this day, because
> it is somehow capable of some translation chore that appears to be
> beyond them and is related to the Unix non-problem of a 4 byte
> unsigned int counter for its current time?
>
> This is so clearly a joke that I still cannot believe anybody at all
> fell for it. It's not even a good joke (believe me, I programmed
> briefly on the 5100 and I know
.
>
> What, did all the programmers in the world suffer brain damage in the
> war? Physics got really popular and they could no longer get anybody
> to learn to program? Computers do all the programming now and
> programming in C or perl is a lost art? Computers have come to life
> and are on strike for better working conditions so they are reduced to
> finding and bringing "back" an IBM 5100 (out of ALL THE COMPUTERS THAT
> WERE EVER
> BUILT) in preference to just bringing back a goddamn programming
> reference for the language(s) they need to translate and building a
> translator with e.g. perl on a 2036 teraflop PDA?
>
> Let me be very, very clear on this. I know that there is a tendency
> to want to suspend disbelief on things like this. Heck, it is a nifty
> story, kind of science fiction thing, Orson Welles War of the Worlds
> internet style. It's "fun" to pretend to believe and kick this sort
> of thing around, but:
>
> WHO COULD POSSIBLY TAKE THIS SERIOUSLY?
>
> Screw the physics -- although I personally am by no means convinced
> that physics even >>permits<< the kind of singularity free time travel
> they (for this was surely a consortium of jokers) propose. The
> ENGINEERING is ludicrous. The COMPUTATION is ludicrous (where are the
> goddam computers in the suitcase? Where is the programming and
> control interface? Are we supposed to believe that this box has one
> knob and a switch as a control interface? Where are all the wires?).
> And as I explained in a reply to somebody else, the entire multiverse
> story totally ignores the problems of chaos, conservation laws,
> thermodynamic balance and oh, so much more -- the mere EXISTENCE of a
> multiverse has consequences in terms of detailed balance and entropy
> flow in the universe we occupy, and time travel creates a HUGE phase
> space for global entropy to increase in. You'd never get home again,
> not without a theory that permitted you to very precisely steer. You'd
> never get close. Period.
>
> I personally have never liked time travel stories (although I've read
> plenty of them) because they are so difficult to disentangle on the
> basis of chaos alone (as explored in at least one memorable story,
> where a single butterfly was killed in a visit to the Jurassic or the
> like, and upon return the entire Universe was totally different -- as
> it would be if a single ATOM were displaced a single ATOMIC RADIUS,
> let alone a butterfly). I do somewhat enjoy multiverse stories, and
> have even written (but not yet published) one.
>
> In my opinion, this isn't even a good multiverse story. Somebody is
> going to come forth one day and publish a whole book on how they made
> fun of the entire Internet with a bad story, a sad reflection on the
> gullability of our culture.
>
> And before you ask, yes, y'all can feel free to republish any or all
> of my replies on your lists, as long as you don't ask me to join them
> and keep my time-wasting interface to a minimum of a couple or three
> people. The sooner this matter is really put to rest, the sooner we
> can all return to leading useful and productive lives DOING SOMETHING
> ELSE
>
> Pardon me while I blow my nose and dry my eyes. There. I feel much
> better now.
>
> Now let's leave it alone, shall we?
>
> rgb
>
> --
> Robert G. Brown > >Duke University Dept. of Physics>"
