# Are Radio Sources and Gamma Ray Bursts Luminal Booms?

This article was published in the International Journal of Modern Physics D (IJMP–D) in 2007. It soon became the Top Accessed Article of the journal by Jan 2008.

Although it might seem like a hard core physics article, it is in fact an application of the philosophical insight permeating this blog and my book.

This blog version contains the abstract, introduction and conclusions. The full version of the article is available as a PDF file.

Journal Reference: IJMP-D Vol. 16, No. 6 (2007) pp. 983–1000.

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Abstract

The softening of the GRB afterglow bears remarkable similarities to the frequency evolution in a sonic boom. At the front end of the sonic boom cone, the frequency is infinite, much like a Gamma Ray Burst (GRB). Inside the cone, the frequency rapidly decreases to infrasonic ranges and the sound source appears at two places at the same time, mimicking the double-lobed radio sources. Although a “luminal” boom violates the Lorentz invariance and is therefore forbidden, it is tempting to work out the details and compare them with existing data. This temptation is further enhanced by the observed superluminality in the celestial objects associated with radio sources and some GRBs. In this article, we calculate the temporal and spatial variation of observed frequencies from a hypothetical luminal boom and show remarkable similarity between our calculations and current observations.

#### Introduction

A sonic boom is created when an object emitting sound passes through the medium faster than the speed of sound in that medium. As the object traverses the medium, the sound it emits creates a conical wavefront, as shown in Figure 1. The sound frequency at this wavefront is infinite because of the Doppler shift. The frequency behind the conical wavefront drops dramatically and soon reaches the infrasonic range. This frequency evolution is remarkably similar to afterglow evolution of a gamma ray burst (GRB).

Gamma Ray Bursts are very brief, but intense flashes of $\gamma$ rays in the sky, lasting from a few milliseconds to several minutes, and are currently believed to emanate from cataclysmic stellar collapses. The short flashes (the prompt emissions) are followed by an afterglow of progressively softer energies. Thus, the initial $\gamma$ rays are promptly replaced by X-rays, light and even radio frequency waves. This softening of the spectrum has been known for quite some time, and was first described using a hypernova (fireball) model. In this model, a relativistically expanding fireball produces the $\gamma$ emission, and the spectrum softens as the fireball cools down. The model calculates the energy released in the $\gamma$ region as $10^ {53}$$10^ {54}$ ergs in a few seconds. This energy output is similar to about 1000 times the total energy released by the sun over its entire lifetime.

More recently, an inverse decay of the peak energy with varying time constant has been used to empirically fit the observed time evolution of the peak energy using a collapsar model. According to this model, GRBs are produced when the energy of highly relativistic flows in stellar collapses are dissipated, with the resulting radiation jets angled properly with respect to our line of sight. The collapsar model estimates a lower energy output because the energy release is not isotropic, but concentrated along the jets. However, the rate of the collapsar events has to be corrected for the fraction of the solid angle within which the radiation jets can appear as GRBs. GRBs are observed roughly at the rate of once a day. Thus, the expected rate of the cataclysmic events powering the GRBs is of the order of $10^4$$10^6$ per day. Because of this inverse relationship between the rate and the estimated energy output, the total energy released per observed GRB remains the same.

If we think of a GRB as an effect similar to the sonic boom in supersonic motion, the assumed cataclysmic energy requirement becomes superfluous. Another feature of our perception of supersonic object is that we hear the sound source at two different location as the same time, as illustrated in Figure 2. This curious effect takes place because the sound waves emitted at two different points in the trajectory of the supersonic object reach the observer at the same instant in time. The end result of this effect is the perception of a symmetrically receding pair of sound sources, which, in the luminal world, is a good description of symmetric radio sources (Double Radio source Associated with Galactic Nucleus or DRAGN).

Radio Sources are typically symmetric and seem associated with galactic cores, currently considered manifestations of space-time singularities or neutron stars. Different classes of such objects associated with Active Galactic Nuclei (AGN) were found in the last fifty years. Figure 3 shows the radio galaxy Cygnus A, an example of such a radio source and one of the brightest radio objects. Many of its features are common to most extragalactic radio sources: the symmetric double lobes, an indication of a core, an appearance of jets feeding the lobes and the hotspots. Some researchers have reported more detailed kinematical features, such as the proper motion of the hotspots in the lobes.

Symmetric radio sources (galactic or extragalactic) and GRBs may appear to be completely distinct phenomena. However, their cores show a similar time evolution in the peak energy, but with vastly different time constants. The spectra of GRBs rapidly evolve from $\gamma$ region to an optical or even RF afterglow, similar to the spectral evolution of the hotspots of a radio source as they move from the core to the lobes. Other similarities have begun to attract attention in the recent years.

This article explores the similarities between a hypothetical “luminal” boom and these two astrophysical phenomena, although such a luminal boom is forbidden by the Lorentz invariance. Treating GRB as a manifestation of a hypothetical luminal boom results in a model that unifies these two phenomena and makes detailed predictions of their kinematics.

#### Conclusions

In this article, we looked at the spatio-temporal evolution of a supersonic object (both in its position and the sound frequency we hear). We showed that it closely resembles GRBs and DRAGNs if we were to extend the calculations to light, although a luminal boom would necessitate superluminal motion and is therefore forbidden.

This difficulty notwithstanding, we presented a unified model for Gamma Ray Bursts and jet like radio sources based on bulk superluminal motion. We showed that a single superluminal object flying across our field of vision would appear to us as the symmetric separation of two objects from a fixed core. Using this fact as the model for symmetric jets and GRBs, we explained their kinematic features quantitatively. In particular, we showed that the angle of separation of the hotspots was parabolic in time, and the redshifts of the two hotspots were almost identical to each other. Even the fact that the spectra of the hotspots are in the radio frequency region is explained by assuming hyperluminal motion and the consequent redshift of the black body radiation of a typical star. The time evolution of the black body radiation of a superluminal object is completely consistent with the softening of the spectra observed in GRBs and radio sources. In addition, our model explains why there is significant blue shift at the core regions of radio sources, why radio sources seem to be associated with optical galaxies and why GRBs appear at random points with no advance indication of their impending appearance.

Although it does not address the energetics issues (the origin of superluminality), our model presents an intriguing option based on how we would perceive hypothetical superluminal motion. We presented a set of predictions and compared them to existing data from DRAGNs and GRBs. The features such as the blueness of the core, symmetry of the lobes, the transient $\gamma$ and X-Ray bursts, the measured evolution of the spectra along the jet all find natural and simple explanations in this model as perceptual effects. Encouraged by this initial success, we may accept our model based on luminal boom as a working model for these astrophysical phenomena.

It has to be emphasized that perceptual effects can masquerade as apparent violations of traditional physics. An example of such an effect is the apparent superluminal motion, which was explained and anticipated within the context of the special theory of relativity even before it was actually observed. Although the observation of superluminal motion was the starting point behind the work presented in this article, it is by no means an indication of the validity of our model. The similarity between a sonic boom and a hypothetical luminal boom in spatio-temporal and spectral evolution is presented here as a curious, albeit probably unsound, foundation for our model.

One can, however, argue that the special theory of relativity (SR) does not deal with superluminality and, therefore, superluminal motion and luminal booms are not inconsistent with SR. As evidenced by the opening statements of Einstein’s original paper, the primary motivation for SR is a covariant formulation of Maxwell’s equations, which requires a coordinate transformation derived based partly on light travel time (LTT) effects, and partly on the assumption that light travels at the same speed with respect to all inertial frames. Despite this dependence on LTT, the LTT effects are currently assumed to apply on a space-time that obeys SR. SR is a redefinition of space and time (or, more generally, reality) in order to accommodate its two basic postulates. It may be that there is a deeper structure to space-time, of which SR is only our perception, filtered through the LTT effects. By treating them as an optical illusion to be applied on a space-time that obeys SR, we may be double counting them. We may avoid the double counting by disentangling the covariance of Maxwell’s equations from the coordinate transformations part of SR. Treating the LTT effects separately (without attributing their consequences to the basic nature of space and time), we can accommodate superluminality and obtain elegant explanations of the astrophysical phenomena described in this article. Our unified explanation for GRBs and symmetric radio sources, therefore, has implications as far reaching as our basic understanding of the nature of space and time.

Photo by NASA Goddard Photo and Video

# The Big Bang Theory

I am a physicist, but I don’t quite understand the Big Bang theory. Let me tell you why.

The Big Bang theory says that the whole universe started from asingularity” — a single point. The first question then is, a single point where? It is not a single pointin spacebecause the whole space was a single point. The Discovery channel would put it fancifully thatthe whole universe could fit in the palm of your hand,” which of course it could not. Your palm would also be a little palm inside the little universe in that single point.

The second question is, if the whole universe was inside one point, what about all the points around it? Physicists would advise you not to ask such stupid questions. Don’t feel bad, they have asked me to shut up as well. Some of them may kindly explain that the other points may be parallel universes. Others may say that there are nootherpoints. They may point out (as Steven Weinberg does in The Dreams of a Final Theory) that there is nothing more to the north of the North Pole. I consider this analogy more of a semantic argument than a scientific one, but let’s buy this argument for now.

The next hurdle is that the singularity is in space-timenot merely in space. So before the Big Bang, there was no time. Sorry, there was nobefore!” This is a concept that my five year old son has problems with. Again, the Big Bang cosmologist will point out that things do not necessarily have to continue backwardsyou may think that whatever temperature something is at, you can always make it a little colder. But you cannot make it colder than absolute zero. True, true; but is temperature the same as time? Temperature is a measure of hotness, which is an aggregate of molecular speeds. And speed is distance traveled in unit time. Time again. Hmmm….

I am sure it is my lack of imagination or incompleteness of training that is preventing me from understanding and accepting this Big Bang concept. But even after buying the space-time singularity concept, other difficulties persist.

Firstly, if the whole universe is at one point at one time, one would naively expect it to make a super-massive black hole from which not even light can escape. Clearly then, the whole universe couldn’t have banged out of that point. But I’m sure there is a perfectly logical explanation why it can, just that I don’t know it yet. May be some of my readers will point it out to me?

Second, what’s with dark matter and dark energy? The Big Bang cosmology has to stretch itself a bit with the notion of dark energy to account for the large scale dynamics of the observed universe. Our universe is expanding (or so it appears) at an accelerating rate, which can only be accounted for by assuming that there is an invisible energy pushing the galaxies apart. Within the galaxies themselves, stars are moving around as though there is more mass than we can see. This is the so called dark matter. Although “darksignifies invisible, to me, it sounds as though we are in the dark about what these beasts are!

The third trouble I have is the fact that the Big Bang cosmology violates special relativity (SR). This little concern of mine has been answered in many different ways:

• One answer is that general relativitytrumps” SRif there are conflicting predictions or directives from these two theories, I was advised to always trust GR.
• Besides, SR applies only to local motion, like spaceships whizzing past each other. Non-local events do not have to obey SR. This makes me wonder how events know whether they are local or not. Well, that was bit tongue in cheek. I can kind of buy this argument (based on curvature of space-time perhaps becoming significant at large distances), although the non-scientific nature of local-ness makes me uneasy. (During the inflationary phase in the Big Bang theory, were things local or non-local?)
• Third answer: In the case of the Big Bang, the space itself is expanding, hence no violation of SR. SR applies to motion through space. (Wonder if I could’ve used that line when I got pulled over on I-81. “Officer, I wasn’t speeding. Just that the space in between was expanding a little too fast!”)

Speaking of space expanding, it is supposed to be expanding only in between galaxies, not within them, apparently. I’m sure there is a perfectly logical explanation why, probably related to the proximity of masses or whatnot, but I’m not well-versed enough to understand it. In physics, disagreement and skepticism are always due to ignorance. But it is true that I have no idea what they mean when they say the space itself is expanding. If I stood in a region where the space was expanding, would I become bigger and would galaxies look smaller to me?

Note that it is necessary for space to expand only between galaxies. If it expanded everywhere, from subatomic to galactic scales, it would look as though nothing changed. Hardly satisfying because the distant galaxies do look as though they are flying off at great speeds.

I guess the real question is, what exactly is the difference between space expanding between two galaxies and the two galaxies merely moving away from each other?

One concept that I find bizarre is that singularity doesn’t necessarily mean single point in space. It was pointed out to me that the Big Bang could have been a spread out affairthinking otherwise was merely my misconception, because I got confused by the similarity between the wordssingularityand single.

People present the Big Bang theory in physics pretty much like Evolution in biology, implying the same level of infallibility. But I feel that it is disingenuous to do that. To me, it looks as though the theory is so full of patchwork, such a mathematical collage to cook up something that is consistent with GR that it is hard to imagine that it corresponds to anything real (ignoring, for the moment, my favorite questionwhat is real?) But popular writers have embraced it. For instance, Ray Kurzweil and Richard Dawkins put it as a matter of fact in their books, lending it a credence that it perhaps doesn’t merit.

# Universe – Size and Age

I posted this question that was bothering me when I read that they found a galaxy at about 13 billion light years away. My understanding of that statement is: At distance of 13 billion light years, there was a galaxy 13 billion years ago, so that we can see the light from it now. Wouldn’t that mean that the universe is at least 26 billion years old? It must have taken the galaxy about 13 billion years to reach where it appears to be, and the light from it must take another 13 billion years to reach us.

In answering my question, Martin and Swansont (who I assume are academic phycisists) point out my misconceptions and essentially ask me to learn more. All shall be answered when I’m assimilated, it would appear! 🙂

This debate is published as a prelude to my post on the Big Bang theory, coming up in a day or two.

 Mowgli 03-26-2007 10:14 PM

UniverseSize and Age
I was reading a post in http://www.space.com/ stating that they found a galaxy at about 13 billion light years away. I am trying to figure out what that statement means. To me, it means that 13 billion years ago, this galaxy was where we see it now. Isn’t that what 13b LY away means? If so, wouldn’t that mean that the universe has to be at least 26 billion years old? I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…) I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?
 swansont 03-27-2007 09:10 AM

Quote:
 Originally Posted by Mowgli (Post 329204) I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…)

Ignoring all the rest, how would this mean the universe is 26 billion years old?

Quote:
 Originally Posted by Mowgli (Post 329204) I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?

The speed of light is an inherent part of atomic structure, in the fine structure constant (alpha). If c was changing, then the patterns of atomic spectra would have to change. There hasn’t been any confirmed data that shows that alpha has changed (there has been the occasional paper claiming it, but you need someone to repeat the measurements), and the rest is all consistent with no change.

 Martin 03-27-2007 11:25 AM

To confirm or reinforce what swansont said, there are speculation and some fringe or nonstandard cosmologies that involve c changing over time (or alpha changing over time), but the changing constants thing just gets more and more ruled out.I’ve been watching for over 5 years and the more people look and study evidence the LESS likely it seems that there is any change. They rule it out more and more accurately with their data.So it is probably best to ignore thevarying speed of lightcosmologies until one is thoroughly familiar with standard mainstream cosmology.You have misconceptions Mowgli

• General Relativity (the 1915 theory) trumps Special Rel (1905)
• They don’t actually contradict if you understand them correctly, because SR has only a very limited local applicability, like to the spaceship passing by:-)
• Wherever GR and SR SEEM to contradict, believe GR. It is the more comprehensive theory.
• GR does not have a speed limit on the rate that very great distances can increase. the only speed limit is on LOCAL stuff (you can’t catch up with and pass a photon)
• So we can and DO observe stuff that is receding from us faster than c. (It’s far away, SR does not apply.)
• This was explained in a Sci Am article I think last year
• Google the author’s name Charles Lineweaver and Tamara Davis.
• We know about plenty of stuff that is presently more than 14 billion LY away.
• You need to learn some cosmology so you wont be confused by these things.
• Also asingularitydoes not mean a single point. that is a popular mistake because the words SOUND the same.
• A singularity can occur over an entire region, even an infinite region.

Also thebig bangmodel doesn’t look like an explosion of matter whizzing away from some point. It shouldn’t be imagined like that. The best article explaining common mistakes people have is this Lineweaver and Davis thing in Sci Am. I think it was Jan or Feb 2005 but I could be a year off. Google it. Get it from your local library or find it online. Best advice I can give.

 Mowgli 03-28-2007 01:30 AM

To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I’m sure I must be wrong.To Martin: You are right, I need to learn quite a bit more about cosmology. But a couple of things you mentioned surprise mehow do we observe stuff that is receding from as FTL? I mean, wouldn’t the relativistic Doppler shift formula give imaginary 1+z? And the stuff beyond 14 b LY awayare theyoutside” the universe?I will certainly look up and read the authors you mentioned. Thanks.
 swansont 03-28-2007 03:13 AM

Quote:
 Originally Posted by Mowgli (Post 329393) To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I’m sure I must be wrong.

That would depend on how you do your calibration. Looking only at a Doppler shift and ignoring all the other factors, if you know that speed correlates with distance, you get a certain redshift and you would probably calibrate that to mean 13b LY if that was the actual distance. That light would be 13b years old.

But as Martin has pointed out, space is expanding; the cosmological redshift is different from the Doppler shift. Because the intervening space has expanded, AFAIK the light that gets to us from a galaxy 13b LY away is not as old, because it was closer when the light was emitted. I would think that all of this is taken into account in the measurements, so that when a distance is given to the galaxy, it’s the actual distance.

 Martin 03-28-2007 08:54 AM

Quote:
 Originally Posted by Mowgli (Post 329393) I will certainly look up and read the authors you mentioned.

This post has 5 or 6 links to that Sci Am article by Lineweaver and Davis

http://scienceforums.net/forum/showt…965#post142965