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# The Big Bang Theory – Part II

After reading a paper by Ashtekar on quantum gravity and thinking about it, I realized what my trouble with the Big Bang theory was. It is more on the fundamental assumptions than the details. I thought I would summarize my thoughts here, more for my own benefit than anybody else’s.

Classical theories (including SR and QM) treat space as continuous nothingness; hence the term space-time continuum. In this view, objects exist in continuous space and interact with each other in continuous time.

Although this notion of space time continuum is intuitively appealing, it is, at best, incomplete. Consider, for instance, a spinning body in empty space. It is expected to experience centrifugal force. Now imagine that the body is stationary and the whole space is rotating around it. Will it experience any centrifugal force?

It is hard to see why there would be any centrifugal force if space is empty nothingness.

GR introduced a paradigm shift by encoding gravity into space-time thereby making it dynamic in nature, rather than empty nothingness. Thus, mass gets enmeshed in space (and time), space becomes synonymous with the universe, and the spinning body question becomes easy to answer. Yes, it will experience centrifugal force if it is the universe that is rotating around it because it is equivalent to the body spinning. And, no, it won’t, if it is in just empty space. But “empty space” doesn’t exist. In the absence of mass, there is no space-time geometry.

So, naturally, before the Big Bang (if there was one), there couldn’t be any space, nor indeed could there be any “before.” Note, however, that the Ashtekar paper doesn’t clearly state why there had to be a big bang. The closest it gets is that the necessity of BB arises from the encoding of gravity in space-time in GR. Despite this encoding of gravity and thereby rendering space-time dynamic, GR still treats space-time as a smooth continuum — a flaw, according to Ashtekar, that QG will rectify.

Now, if we accept that the universe started out with a big bang (and from a small region), we have to account for quantum effects. Space-time has to be quantized and the only right way to do it would be through quantum gravity. Through QG, we expect to avoid the Big Bang singularity of GR, the same way QM solved the unbounded ground state energy problem in the hydrogen atom.

What I described above is what I understand to be the physical arguments behind modern cosmology. The rest is a mathematical edifice built on top of this physical (or indeed philosophical) foundation. If you have no strong views on the philosophical foundation (or if your views are consistent with it), you can accept BB with no difficulty. Unfortunately, I do have differing views.

My views revolve around the following questions.

These posts may sound like useless philosophical musings, but I do have some concrete (and in my opinion, important) results, listed below.

There is much more work to be done on this front. But for the next couple of years, with my new book contract and pressures from my quant career, I will not have enough time to study GR and cosmology with the seriousness they deserve. I hope to get back to them once the current phase of spreading myself too thin passes.

# Tsunami

The Asian Tsunami two and a half years ago unleashed tremendous amount energy on the coastal regions around the Indian ocean. What do you think would’ve have happened to this energy if there had been no water to carry it away from the earthquake? I mean, if the earthquake (of the same kind and magnitude) had taken place on land instead of the sea-bed as it did, presumably this energy would’ve been present. How would it have manifested? As a more violent earthquake? Or a longer one?

I picture the earthquake (in cross-section) as a cantilever spring being held down and then released. The spring then transfers the energy to the tsunami in the form of potential energy, as an increase in the water level. As the tsunami radiates out, it is only the potential energy that is transferred; the water doesn’t move laterally, only vertically. As it hits the coast, the potential energy is transferred into the kinetic energy of the waves hitting the coast (water moving laterally then).

Given the magnitude of the energy transferred from the epicenter, I am speculating what would’ve happened if there was no mechanism for the transfer. Any thoughts?

# 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

It turns out the article was in the March 2005 issue.

I think it’s comparatively easy to readwell written. So it should help.

# Twin Paradox – Take 2

The Twin Paradox is usually explained away by arguing that the traveling twin feels the motion because of his acceleration/deceleration, and therefore ages slower.

But what will happen if the twins both accelerate symmetrically? That is, they start from rest from one space point with synchronized clocks, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it seems that when the two clocks are together at the end of the journey, at the same point, and at rest with respect to each other, they have to agree.

Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one. In SR, every clock that is in motion with respect to an observer’s clock is supposed run slower. Or, the observer’s clock is always the fastest. So, for each twin, the other clock must be running slower. However, when they come back together at the end of the journey, they have to agree. This can happen only if each twin sees the other’s clock running faster at some point during the journey. What does SR say will happen in this imaginary journey?

(Note that the acceleration of each twin can be made constant. Have the twins cross each other at a high speed at a constant linear deceleration. They will cross again each other at the same speed after sometime. During the crossings, their clocks can be compared.)

# Superluminal Laser Dots

A discussion in the Science Forums on the appearance of a laser dot on a ceiling. It is thought that if you pointed a laser dot on a ceiling and turned the laser gun fast enough, you could create superluminal laser dots. Could you, really?