## Can a Really, Really Fast Spacecraft Turn Into A Black Hole?

by Steve NerlichThis question was posed in an Astronomy Cast episode a while back. It offers an interesting thought experiment, although a reasonably definitive answer to the question can be arrived at.

Imagine a scenario where a spacecraft gains relativistic mass as it approaches the speed of light, while at the same time its volume is reduced via relativistic length contraction. If these changes can continue towards infinite values (which they can) – it seems you have the perfect recipe for a black hole.

Of course, the key word here is *relativistic*. Back on Earth, it can appear that a spacecraft which is approaching the speed of light, is indeed both gaining mass and shrinking in volume. Also, light from the spacecraft will become increasingly red-shifted – potentially into almost-blackness. This can be partly Doppler effect for a receding spacecraft, but is also partly a time dilation effect where the sub-atomic particles of the spacecraft seem to oscillate slower and hence emit light at lower frequencies.

So, back on Earth, ongoing measurements may indicate the spacecraft is becoming more massive, more dense and much darker as its velocity increases.

But of course, that’s just back on Earth. If we sent out two such spacecraft flying in formation – they could look across at each other and see that everything was quite normal. The captain might call a red alert when they look back towards Earth and see that it is starting to turn into a black hole – but hopefully the future captains of our starships will have enough knowledge of relativistic physics not to be too concerned.

So, one answer to the Astronomy Cast question is that yes, a very fast spacecraft can appear to be almost indistinguishable from a black hole – from a particular frame (or frames) of reference.

But it’s never *really* a black hole.

Special relativity allows you to calculate transformations from your proper mass (as well as proper length, proper volume, proper density etc) as your relative velocity changes. So, it is certainly possible to find a point of reference from which your relativistic mass (length, volume, density etc) will seem to mimic the parameters of a black hole.

But a *real* black hole is a different story. Its proper mass and other parameters are already those of a black hole – indeed you won’t be able to find a point of reference where they aren’t.

A real black hole is a real black hole – from any frame of reference.

(I must acknowledge my Dad – Professor Graham Nerlich, Emeritus Professor of Philosophy, University of Adelaide and author of The Shape of Space, for assistance in putting this together).

this question may have been answered at length.

I’ve never been able to wrap my head around the idea of string theory and someone talking about membrane theory may as well be talking to me in Chinese.

my question is this.

what does string theory say about black holes? string theory sais that there are 11 dimensions. is that correct? my understanding is that black holes only effect the 4 known dimensions of space-time. does string theory make any predictions for the effects of a black hole on the other 7 dimensions? As a thought experiment, if we could travel to another dimension could we travel to the inside of a black hole?

this is a fascinating question.. what confused me is your reference to the ‘proper rest’ frame.. my recollection of relativity was that all inertial frames, are, well equal..

I googled ‘proper rest’ and came up with this Quote:

http://www.physicsforums.com/archive/index.php/t-74178.html

“Before I write a long response, are you looking for someone to explain your misconceptions about relativity or not?

There is no such thing as a “proper rest frame” in relativity – it does not matter which reference frame one adopts as far as observations go”

So now I’m really confused.

Surely the concept of relativity is that if it looks like a duck and quacks like a duck then it ‘is’ a duck – at least in that frame of reference.. no?

utunga,

A proper rest frame is the inertial (traveling at a constant velocity) reference frame from which the object is at rest. If you’re in another reference frame, the length and mass of an object can change.

I think what that person was referring to is that there are never any real inertial frames because there is always some force acting on an object so that any reference frame where that object is at rest is accelerating and thus non-inertial. However, we sometimes assume (when they aren’t accelerating “too” much) that they are inertial so we can calculate what they are doing.

Well, seeing an ever accelerating rocket go like that would make a fun picture.

The real fun thing is that you can’t observe a contraction. Well, not as a contraction as such, as explained by theoretical physicist John Baez:

“Oddly enough, though Einstein published his famous relativity paper in 1905, and Fitzgerald proposed his contraction several years earlier, no one seems to have asked this question until the late ’50s. Then Roger Penrose and James Terrell independently discovered that the object will not appear flattened [1,2]. People sometimes say that the object appears rotated, so this effect is called the Penrose-Terrell rotation.

Calling it a rotation can be a bit confusing though. Rotating an object brings its backside into view, but it’s hard to see how a contraction could do that. Among other things, this entry will try to explain in just what sense the Penrose-Terrell effect is a “rotation”.

[…]

Now let’s consider the object: say, a galaxy. In passing from his snapshot to hers, the image of the galaxy slides up the sphere, keeping the same face to us. In this sense, it has rotated. Its apparent size will also change, but not its shape (to a first approximation).

The mathematical details are beautiful, but best left to the textbooks [3,4].”

On the issue of proper mass, the link takes you to: “The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c2, which is equal to the mass of the system as measured on a scale. If the system is one particle, the invariant mass may also be called the rest mass.”

@ dimtick:

Let’s hope some string theorist will answer your question. Meanwhile, it is my understanding that:

“what does string theory say about black holes?”

You can make it predict the same effects as the semiclassical theory, i.e. entropy goes as area et cetera.

“string theory sais [sic] that there are 11 dimensions. is that correct?”

The full blown theory, M theory, predicts that all versions of string theories are the same modulo dualisms. So the 10 dimensional string theory hides an 11th one, which is the maximal number of dimensions in super-symmetry M-theory (else you have 26, IIRC):

“The original string theories from the 1980s describe special cases of M-theory where the eleventh dimension is a very small circle or a line, and if these formulations are considered as fundamental, then string theory requires ten dimensions. But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is not described by a real number, but by a completely different type of mathematical quantity. So the notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.[4] [Wikipedia]”

“does string theory make any predictions for the effects of a black hole on the other 7 dimensions? ”

The other dimensions are usually taken to be microscopic, so not affected as such.

But there is variants where the weakness of gravity is explained as a a type of string that interacts through a 5th dimension. Still no specific change in black holes, but gravity.

“if we could travel to another dimension could we travel to the inside of a black hole?”

The remaining dimensions aren’t part of the macroscopic emergent spacetime, so no dimensional travel. But we can travel to the inside of a black hole fine all the same, into the event horizon, same as the light that can’t pass out again and so makes the black hole “black”.

@ PIKA:

And presumably general relativity tells us how to do that calculation between all frames in principle, hence its name.

The relationship between string theory and black holes is deep, and you have to wrap your mind around quantum holography. Susskind and Lindesay have written a moderately technical book on the subject

http://books.google.com/books?id=cxJCBRUNmVYC&pg=PP3&lpg=PP1#v=onepage&q=&f=false

For anyone with a reasonable background in physics should read this book. It is a book which requires some familiarity with some advanced concepts in physics at the BS level or first year graduate school. The upshot is that if you watch a string fall towards a black hole the transverse modes of the string are observed by a stationary observer to slow down. In effect very high energy or UV modes are then transformed into low energy or IR modes. Further, since the black hole will quantum mechanically decay, the string you observe interacts with the quanta tunneling out. Some of the quanta tunneling out are from the string you are observing. So in effect the occurrence of quantum states and the notion of iterated sequences of events (time ordering etc) no longer applies as known.

The quantum state of a black hole is then given according to this distant observer on a membrane just outside the event horizon. So fields in three dimensions are determined by a boundary one dimension lower. This is one reason it is called the holography principle, and this dimensional relationship between a boundary and a space is one reason our usual notion of trajectories and the ordering of events is liberalized. In supergravity theories holography is generalized into the AdS/CFT correspondence, which is a bit beyond my ability to write about in a short blog post.

The apparent black hole of some relativistic body is its time dilation and length contraction. In special relativity the length is contracted by

L’ = Lsqrt{1 – (v/c)^2).

If the length is contracted to near the string length, L_s ~ 10L_p, L_p = sqrt{G hbar/c^3} = 6e^{-33}cm the quantum modes of matter composing the body are redshifted away and the body has no signature except its mass. For a one meter object this is length contraction is

L’/L ~ 10^{-34},

and so

v/c = sqrt{1 – (L’/L)^2} ~ .99999999999999999999999999999999

or very close to the speed of light. This is a form of the holography due to Lorentz boosts.

LC

Sounds to me more like a bunch of back-slapping, convoluted, ego-stroking gobbledegook to me. When are physicists going to start talking about the physical again?

Physics has taken us further away from a classical notion of things. As we have pushed deeper into foundations the implications of things run counter to our ordinary expectations of things.

LC

There’s nothing wrong with a good thought experiment.

So basically, this means that there can be a percieved black hole, which makes sense, as you are traveling as fast or faster than the light from an object behind you. If that light never catches up to you.

Light from an object ahead of you would be very blue shifted, enough that it might even “feel” like gamma rays, which would suck. Is this accurate?

Forgot to finish a sentence:

If that light never catches up to you the object that’s emmitting the light should appear to go black. 🙂

Dark Gnat hits on an important thing here. A much closer flat space analogy to a black hole is an accelerated frame. An observer suspended by some means which provides an outwards acceleration close to the event horizon of a black hole observes physics in a way nearly identical to what an accelerated observer would see. An accelerated observer, with a very significant acceleration I might add, observes a type of event horizon behind them. This horizon splits the spacetime into a Rindler wedge which is the domain of observation accessible to this accelerated observer. So an observer accelerating in a certain direction can drop a mass and watch it move away as it approaches this event horizon — called a particle horizon. So the mass appears continually red shifted and time dilated according to this observer. If this mass is a string then its transverse modes of oscillation are observed to continually slow down. Lorentz boosts are also a bit strange, particularly when they involve incremental boosts, or local gravity changes. The mass not only appears shortened, or really rotated in a way, but it also appears to be distended. The gravitational lensing by galaxies illustrates this. The background galaxies lensed by the gravity field not only appear squashed in the radial direction, but distended or stretched in the angular direction. A picture of this http://en.wikipedia.org/wiki/File:Gravitationell-lins-4.jpg%5D gravitational lensing illustrates this point. So by extension, and the analysis is somewhat involved, a string approaching a black hole is observed to stretch out and wind around the black hole event horizon.

This results in some deep changes in our ideas about what is meant by space. Fundamentally the field configurations in spacetime are not at points, but rather in distributed configurations, such as strings. This results in a very different notion of what is meant by space and the notion of events in space. There is an analogy with some aspects of modern art. I will try to illustrate some of this here, which requires some basic mathematics, which below is fairly standard stuff in quantum holography. This is meant to try to illuminate some salient points of this without creating too much confusion. This is a subject with requires you reload the “programs” by which you think about things.

The holographic principle tells us that the high frequency components of a quantum field, or a string, become red shifted arbitrarily as these field approach the event horizon. This is related to the size of the transverse modes of a string on the stretched horizon Dx (Dx is the use of capital D to mean the Greek letter capital Delta), which is the probe size one measures a quanta of energy

E_{Dx} ~ hbar c/Dx, hbar = quantum unit of action or angular momentum.

A black hole with a mass E_{Dx}/c^2, the distances we probe will be defined by regions on the other side of the horizon with a radius 2GM = 2 E_{Dx}/c^2 — here c = 1 in natural units.. Thus the energy of a quanta has a spread with E_{Dx} ~ hbar c/R with an upper bound at E_p, or equivalently a length scale bounded below by L_p. This defines a type of spacetime uncertainty, or an underlying noncommutative structure to spacetime, for the length propagation to the screen Dy ~ cDt with

DxDy = Dx(cDt) ~ 2GM hbar /c^2 ~ 2L_p^2.

The factor of 2 is a Nyquist relationship of using a probe with a certain frequency to measure a system with another frequency. We may then also consider the result for the distance to the screen Dy = TDS/F = hbar DS/(2pi kc). Here the DS is a change in entropy, and this enters into the picture as a Bekenstein result on the Birkoff theorem recently found by Verlinde. For now I will just use the result, and if there is interest later here I can break this out. The Dy = cDt is again restored, and to make this equation invariant we replace the coordinate time with a proper time

Ds = 4GM e^{-Dt/4GM},

with the replacement Dy = cDs. The uncertainty Dx, or noncommutative uncertainty principle is an entropy determined result with

Dx = 2L_p^2/Dy ~ (L_p^2/2GM)e^{Dt/4GM} = 2pi kcL_p^2/(hbar DS),

Or that the entropy difference DS is determined by the noncommutative uncertainty

DS ~ (4pi GMkc/?)e^{-Dt/4GM}

For the black hole composed of N Planck units of mass M_p = sqrt{hbar c/G} we have

DS ~ 4pi Nke^{-Dt/4GM}.

So these results illustrate how the resolution of the size of a string near the event horizon Dx is conjugate to an entropy difference. So as the resolution observed decreases, information diffuses across the event horizon. For a zero resolution time Dt –> 0 the change in entropy is maximum. In doing this analysis on the keyboard here I have an additional 4pi here which appears to be some sort of error, but it is a minor problem.

This means that spacetime has a commutator structure that is very nonstandard. Noncommutative geometry was proposed by Alain Connes, for which he won the Field Medal in mathematics. This structure can best be heuristically visualized in the cubist art of Pablo Picasso and Diego Riviera. People 80 years ago had trouble wrapping their minds around these artistic portrayals of space and objects, and currently many people have trouble with the holographic paradigm. This may only be the beginning, for I and some other have been working to understand this black hole complementarity in a way that involves modular transformations between quantum field configurations observers outside and inside a black hole would record. This results in not just noncommutative geometry, but nonassociative structure as well. So things may be even stranger —- a reading of Louis Carroll might be in order before giving this subject serious thought, for it requires a radical change in how you think about space and events distributed in spacetime.

LC

LC

I think that the average person is still going to be somewhat confused by your method of explanation. Obviously, you are well versed in physics, but I feel at times your manner of addressing these issues narrows your audience to just those with a similar background. I see this frustration in many of those who respond to your comments. This is not in any means a personal criticism, just an idea to help others (such as myself) receive the full benefit of your insight.

Here is what I feel would help me and others:

1. Don’t use prerequisite terminology Ex. “Nyquist” “transverse modes”

2. Avoid explaining with math

3. Use visual viewpoints to explain. What does the viewer from the relativistic craft see when looking behind? In front? Are there any links to accurate renderings?

I know you may feel a full explanation requires your method of explanation but I feel simpler more straightforward lay-mans explanations would be more effective for the broader readership.

Kind Regards,

UF

Sorry if this was a bit abstract. Some questions were raised about the relationship between strings and black holes. This is an interesting area of research, for I do think that black hole physics determines the structure of elementary particles.

LC

Dark Gnat asked:

1. So basically, this means that there can be a percieved black hole, which makes sense, as you are traveling as fast or faster than the light from an object behind you. If that light never catches up to you the object that’s emmitting the light should appear to go black.

A: You can’t have a scenario where the light that used to be able to catch you, now can’t catch up with you – because that would mean you are travelling faster than light (and you can’t). It’s just that the frequency drops to red, then infra-red etc (i.e. red shifted) as outlined in the article.

2. Light from an object ahead of you would be very blue shifted, enough that it might even “feel” like gamma rays, which would suck. Is this accurate?

Light emitted ahead of you is indeed blue shifted. Gamma rays are plausible.

Right, the speed of light is a universal invariant. If you are travelling at a relativistic velocity away from a source of light those photons reach you at the speed of light, but their wavelength is stetched out or Doppler shifted.

If you head directly towards a source of light it is blue shifted. Further, if you accelerate at a constant g = 10m/sec^2 then within about a year’s time the cosmic background radiation in microwave band will appear as X-ray radiation, and eventually as gamma radiation. This radiation will then destroy your spacecraft — and you along with it.

LC

It’s understandable.

Regards,

UF