# Thread: The speed of light exceeded many times

1. ## The speed of light exceeded many times

During the inflationary period of the BB.

While it neatly explains the smoothness, horizon and flatness problems, it means the expansion briefly occured at many, many times the speed of light.

Has there ever been any explanation how this could at all be possible, or are we just accepting it as a given?

2. Actually, you don't need inflation to have expansion faster than the speed of light. According to the Hubble Law and the Cosmological Principle, all you have to do is go far enough from Earth and you should find expansion that is faster than light, although you won't have any way of actually observing it in action. What I must clarify is that when I refer to "expansion", I mean the rate of increase of the distance to various things. It is not always the case that we equate the rate of change of distance with "speed" however. It is more standard to think of speed as the motion relative to observers who move with some local coordinate system, and in cosmology, the most useful local coordinate system is called the "comoving frame", i.e.., the reference frame that follows the prevailing average movement of the nearby matter. Thus we have a situation where the "speed" of objects, measured locally in that frame, will never exceed c, but the rate of change of the global distance from us to those objects can exceed c. The explanation normally given to help picture this is that "space itself is expanding", a picture which applies for comoving coordinates and is also what is happening in inflation. The point is, actual speed measurements are local, and those are the things that cannot exceed c. Conceptualizing distant motions can give you arbitrary answers, depending on how you are doing the conceptualizing (which in turn relates to how you are defining distance).

3. I don't think it's accepted as given. It's one of those somewhat open questions right now. There are many models of early expansion, and even a few proposals that don't require FTL expansion. The latest WMAP results seem to bear out the FTL inflation idea, but it's a very complicated issue, and I don't pretend to understand much of it (except that it is complicated!).

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Originally Posted by gzhpcu
During the inflationary period of the BB.

While it neatly explains the smoothness, horizon and flatness problems, it means the expansion briefly occured at many, many times the speed of light.

Has there ever been any explanation how this could at all be possible, or are we just accepting it as a given?
gzhpcu, in GR, the limitation for speed of light is local, and only applies for objects moving within space. There is no corresponding limit for space itself. There are several different inflationary models, and as snarkophilus points out, current observations support a FTL inflation model.

5. I am a bit puzzled: in the classical BB theory, based on GR, as I understand it, the galaxies are moving away from each other because the space between them is expanding (the old inflating ballon example). (I was not aware that the expansion speed could exceed c.... thanks...)

So, concievably, there could be cosmological objects where the space between them and our galaxy is expanding at a rate greater than c, that we will never be able to detect (as long as the rate of expansion never slows down below c).

In some of the M-theory, D-brane based cosmologies, our universe is a colossal D-brane. Close by is another D-brane and in cycles of some n trillion years the two D-branes collide, separate, come together again, collide, etc. ad infinitum. With each collision there is a BB which populates the D-Brane with energy/matter. This model does not need the inflationary stage, since the BB does not start as a singularity but rather simultaneously over a large area (eliminating all the problems in the classical BB theory solved by inflation)
So it seems to me, that this model says that space (the D-brane) was pre-existing, and is therefore not expanding.
This is the ekyroptic model of the universe. More here: http://wwwphy.princeton.edu/~steinh/npr/

6. Originally Posted by gzhpcu
So, concievably, there could be cosmological objects where the space between them and our galaxy is expanding at a rate greater than c, that we will never be able to detect (as long as the rate of expansion never slows down below c).
Right, if you certify that you mean we'll never in the future detect what they are doing now. We can actually see what they were doing in the past, even though they may be going faster than c now, that's what happens in the accelerated expansion model that is currently favored.

Originally Posted by gzhpcu
So it seems to me, that this model says that space (the D-brane) was pre-existing, and is therefore not expanding.
Whether or not the space pre-existed (a difficult proposition to evaluate in any kind of measurable way) has nothing to do with whether or not it is expanding (which is a useful characterization of well-established observations). Indeed, even inflation and expansion are very different concepts, and the elimination of the inflation hypothesis eliminates neither the Big Bang model nor the expansion description of said model.

7. Originally Posted by Ken G

Whether or not the space pre-existed (a difficult proposition to evaluate in any kind of measurable way) has nothing to do with whether or not it is expanding (which is a useful characterization of well-established observations). Indeed, even inflation and expansion are very different concepts, and the elimination of the inflation hypothesis eliminates neither the Big Bang model nor the expansion description of said model.
Yes, except that the BB model needs expansion of space, since it postulates it began with a singularity and nothing existed prior to T=0, whereas the D-Brane model does not need expansion, because the D-Brane and hence space pre-existed the BB, which does not arise from a singularity in this case.

8. The Big Bang model doesn't "need" the expansion of space, the model admits that interpretation. The model merely quantifies the history of the distances between galaxies, characterized in the form of a global "scale parameter". The model also relies on the equations of general relativity, which answers how distances evolve given what the current conditions are. None of that requires an expansion of space, but it is a very useful picture. It is also not necessary for the Big Bang to "begin" with a singularity. The theory essentially starts with today and works backward in time, you can stop the calculation at any point but if you keep extrapolating backward you do come to a singulariy. To be truly useful you must at least go back beyond the nucelosynthesis epoch of a few minutes after the singularity, but the singularity itself plays no essetial role in the model. Finally, the D-brane model absolutely does require expansion, in the sense of increasing distances, redshifts, etc. This is an observed fact. There is actually extremely little difference between the Big Bang and the D-brane model, which is why current observations cannot distinguish them.

9. Originally Posted by gzhpcu
So it seems to me, that this model says that space (the D-brane) was pre-existing, and is therefore not expanding.
This is the ekyroptic model of the universe. More here: http://wwwphy.princeton.edu/~steinh/npr/
No, they're still saying the universe is expanding.

Originally Posted by Paul J. Steinhardt
Does the new theory contradict the Big Bang model?

Here we must be careful. There are some skeptics who have written "the Big Bang never happened", by which they mean that the universe is not exapnding today and it never has been. They say this despite overwhelming evidence in favor of expansion and cooling today and for the last 15 billion years. Our model does nothing to contradict this story. That is, the universe has been expanding for the past 15 billion years.

What our model does is amend the earliest moments of the story. Instead of beginning with nearly infinite temperature and density, the universe began in a very different state - cold and nearly vacuous. The hot expanding universe we know came as a result of collision that brought the universe up to a large but finite temperature and density. The rest of the story is as the Big Bang model would have it, but the beginning is different.
They aren't saying that space is not expanding, they're just changing some of the initial circumstances. And it looks like even the proponents think it would be premature to abandon the inflationary model and adopt this one, at least until they and others have had more time to look at the idea.

Originally Posted by Paul J. Steinhardt
Cautionary note:

As a final remark, we feel that it is important to realize that inflationary theory is based on quantum field theory, a well-established theoretical framework, and the model has been carefully studied and vetted for twenty years. Our proposal is based on unproven ideas in string theory and is brand new. While we appreciate the enthusiasm and interest with which the paper has been received, we would suggest some patience before promulgating these ideas in order to leave time for us to produce some follow-up papers that introduce additional elements and to allow fellow theorists time for criticism and sober judgment.
Last edited by Grey; 2006-May-27 at 02:21 PM.

10. Originally Posted by Ken G
The Big Bang model doesn't "need" the expansion of space, the model admits that interpretation. The model merely quantifies the history of the distances between galaxies, characterized in the form of a global "scale parameter". The model also relies on the equations of general relativity, which answers how distances evolve given what the current conditions are. None of that requires an expansion of space, but it is a very useful picture. It is also not necessary for the Big Bang to "begin" with a singularity. The theory essentially starts with today and works backward in time, you can stop the calculation at any point but if you keep extrapolating backward you do come to a singulariy. To be truly useful you must at least go back beyond the nucelosynthesis epoch of a few minutes after the singularity, but the singularity itself plays no essetial role in the model. Finally, the D-brane model absolutely does require expansion, in the sense of increasing distances, redshifts, etc. This is an observed fact. There is actually extremely little difference between the Big Bang and the D-brane model, which is why current observations cannot distinguish them.
Sure expansion is needed, but whether it is expansion in space or space expanding are two different things. Don't see why the D-Brane model needs space expanding...

11. Let me ask you this: does the D-brane model refute general relativity? Of course not, thus it has the same global universal dynamics as the Big Bang, starting from a slightly modified initial condition. As I said before, neither model needs to make that distinction, but the space-expanding view is a highly useful picture for both models. It comes from nothing beyond the application of general relativity in the interpretation of current observations.

12. The D-Brane model, as well as M-theory, are both still in their infancy. M-theory does not refute GR, but it predicts the graviton. If gravity is merely the curvature of spacetime formed by the presence of matter then what is a graviton? If the graviton is a quantum particle depicting gravity as a force, where does warped space come in?

13. You may rest assured that theories of gravity may evolve with time, but you may also be confident that the basic prescription of general relativity, perhaps with some modification by cosmological-constant-esque terms, will always be very useful on cosmological scales. Look at how much the theory of gravity has evolved since Newton, yet Newton still works fine in 99% of the applications. The overarching point is, the idea that "space was created" in the Big Bang is not a fundamental aspect of that theory, it is dependent on a particular interpretation (i.e., "way to imagine", or if you prefer, "coordinatization") of general relativity. So often I see people mistaking scientific models for unique descriptions of reality that I have tried my best to point out this fallacy. It's a little like mistaking the analogy for the thing you are actually trying to understand. The point is, pure physics is a minimal set of rules for how to do observations and how to make predictions that apply to those observations. But we add a lot to that to try to "picture" what we are doing, both because it gives us a warm fuzzy feeling, and because it helps us actually carry out the necessary calculations. Language gets involved, and pretty soon people are writing paragraphs to explain a couple mathematical statements to make them "understandable". That's fine, it's great in fact, but it's not physics, it's, dare I repeat the word, pedagogy (there's your \$1 Jeff).

14. Originally Posted by Ken G
You may rest assured that theories of gravity may evolve with time, but you may also be confident that the basic prescription of general relativity, perhaps with some modification by cosmological-constant-esque terms, will always be very useful on cosmological scales. Look at how much the theory of gravity has evolved since Newton, yet Newton still works fine in 99% of the applications. The overarching point is, the idea that "space was created" in the Big Bang is not a fundamental aspect of that theory, it is dependent on a particular interpretation (i.e., "way to imagine", or if you prefer, "coordinatization") of general relativity. So often I see people mistaking scientific models for unique descriptions of reality that I have tried my best to point out this fallacy. It's a little like mistaking the analogy for the thing you are actually trying to understand. The point is, pure physics is a minimal set of rules for how to do observations and how to make predictions that apply to those observations. But we add a lot to that to try to "picture" what we are doing, both because it gives us a warm fuzzy feeling, and because it helps us actually carry out the necessary calculations. Language gets involved, and pretty soon people are writing paragraphs to explain a couple mathematical statements to make them "understandable". That's fine, it's great in fact, but it's not physics, it's, dare I repeat the word, pedagogy (there's your \$1 Jeff).
Well, that is a statement I agree with! That is why I say that 0 dimensional points do not correspond to reality in respect to fundamental particles.

15. I think the problem is, how do you even define the phrase "correspond to reality"? I think it has to mean "is a useful way to picture reality", that's the closest we ever get.

16. Originally Posted by Ken G
I think the problem is, how do you even define the phrase "correspond to reality"? I think it has to mean "is a useful way to picture reality", that's the closest we ever get.
Could you define what you mean by the phrase "a useful way to picture reality"?

17. To me, all of science is predicated on utility. We do it because it works, in short. It is impossible to say if a particular theory "is" the way reality works, so we content ourselves to say that acting as though the theory was reality has benefit. The benefit can be in the form of useful technology, or being able to communicate meaningfully about the phenomena around us, or simply being able to predict the outcome of various situations at a level of precision that contents us. The "best" theory for the job generally depends on both the parameters of the situation, and the desired level of precision. Reality just is.

18. Well, this is also what I have been saying, that science explains how things work, but not what they are. That is why I have been harping against the 0 dimensional points in QM. Good to explain how things work (except for extreme conditions but not to be taken literally)

But nevertheless, it is interesting to speculate what it could really be. This could be the "correspond to reality" speculation...

19. Originally Posted by gzhpcu
Well, this is also what I have been saying, that science explains how things work, but not what they are. That is why I have been harping against the 0 dimensional points in QM. Good to explain how things work (except for extreme conditions but not to be taken literally)
And I have always agreed with that, my point was that is always true in science, there's nothing special about 0 dimensions as opposed to 3. They are all conceptualizations that have value in various situations. Reality is oblivious to these conceptualizations in all cases, yet they have value.

20. I'd forgotten to respond to this earlier. I hope you'll forgive me for replying to a message that's a couple weeks old.

Originally Posted by gzhpcu
Well, this is also what I have been saying, that science explains how things work, but not what they are. That is why I have been harping against the 0 dimensional points in QM. Good to explain how things work (except for extreme conditions but not to be taken literally)

But nevertheless, it is interesting to speculate what it could really be. This could be the "correspond to reality" speculation...
I differ with Ken G in my opinion about this. That is, I think that a picture that predicts with phenomenal accuracy how something behaves is like to correspond in some meaningful way with what it "really is". For example, I'd say that the nuclear model of an atom with its electrons in various energy levels describes the behavior of an atom so well that we can be confident that atoms "really are" objects that are composed of protons, neutrons, and electrons, arranged in a specific manner. Of course that leaves the question open as to what those particles "really are", but it would seem strange to me to suggest that we don't really have any idea what an atom is because all we really know is how an atom behaves, and it's just a mathematical model (that happens to match all the observations that we make).

In fact, I think the line between these two (what things are and how they behvae) is much blurrier than you're suggesting, gzhpcu. Even if we decide to talk about macroscopic objects, I don't think you can tell me what anything is in a way that I can't immediately change into a description of how it behaves. For example, you might tell me an apple is a solid red object with a certain shape, taste, and so forth. But the fact that it's red is just a result of how it behaves when it interacts with light of various frequencies. The fact that it tastes like an apple is just a matter of how the chemicals in the apple affect the chemicals that make up your taste buds. Its solidity comes from how atoms behave as they interact with each other electromagnetically, and so forth. All these traits that we associate with "apple-ness" are statements of how an apple interacts with other things in the universe. If I were to find something which interacts with everything exactly the way an apple behaves, I would say that it really is an apple.

21. But how about gravity? Newton's model, which was sufficient for 200 years, is radically different from Einstein's model. One posits a force, the other a geometric distortion of space, and then we have the graviton...

22. Reason
changed my mind

23. Originally Posted by Grey
That is, I think that a picture that predicts with phenomenal accuracy how something behaves is like to correspond in some meaningful way with what it "really is".
I don't disagree that there is a meaningful correspondence, I'm saying that the meaning comes from us. When we form concepts about reality we tend to think we are understanding it for what it reallyl is, but in fact our concepts never leave the inside of our heads. That this approach works at all is amazing, and must say something about how intelligence develops so as to be useful and effective. But it still seems quite unlikely that our concept of reality is really all that close, even in terms of concepts like particles and energy levels, etc. I wonder if alien intelligences couldn't be just as successful at describing reality using physical notions that would seem quite, well, alien to us. But of course the basic skeleton of the mathematics must be the same, as the predictions must come out the same. The words used, however, might be untranslatable.

Originally Posted by Grey
In fact, I think the line between these two (what things are and how they behvae) is much blurrier than you're suggesting, gzhpcu.
Indeed, I would say there is no line at all, in terms of our ability to penetrate the truth. The meaningful line is that between what "is", and what we "think" about what is. An example is numbers. Clearly numbers play a huge role in physics, but it is not obvious to me that "nature" has any use at all for numbers. Wait, you ask, if nature didn't have a concept of a number, then how does it "calculate" where things go? But nature cannot calculate where things go, the computing power would be astronomical-- all those little particles that we conceive of must just go where they are supposed to go, automatically, with no need for any numbers. Reality just is, we project the numbers onto it in our effort to understand it. So why is the concept of numbers so useful? I have no idea, it's quite a deep mystery how our minds are able to interpret our reality. And why does our greatest accuracy often come in applications that are the most removed from our experience, and from anything that could remotely be considered a survival advantage? That's a real poser!

24. And I am not excluding correspondence. I am just saying the priority is to figure out how things work, not what they really are. IMHO, mathematical models are idealizations and approximations anyway.

25. Originally Posted by gzhpcu
But how about gravity? Newton's model, which was sufficient for 200 years, is radically different from Einstein's model. One posits a force, the other a geometric distortion of space, and then we have the graviton...
I'm not saying that we always have to be right. It's presumably the case that only one of these could be the "correct" picture of gravity, and maybe none of them is right. I often wonder if quantum mechanics and general relativity will only really be unified when someone can find a way that curved spacetime and an exchange of gravitons are really just different ways of looking at the same thing. I have no idea how to do that, of course.

Originally Posted by gzhpcu
And I am not excluding correspondence. I am just saying the priority is to figure out how things work, not what they really are.
What I'm suggesting is that what things are and how they work are the same thing. An apple is something that behaves like an apple.

Originally Posted by gzhpcu
IMHO, mathematical models are idealizations and approximations anyway.
All models are, whether mathematical or not. But I don't think that means that we should assume that nothing in a model is actually anything like the real thing.

26. Originally Posted by Grey
I'm not saying that we always have to be right. It's presumably the case that only one of these could be the "correct" picture of gravity, and maybe none of them is right. I often wonder if quantum mechanics and general relativity will only really be unified when someone can find a way that curved spacetime and an exchange of gravitons are really just different ways of looking at the same thing. I have no idea how to do that, of course.
Warped space - particle duality? Warped space when you don't measure, a particle when observed?

Originally Posted by Grey
What I'm suggesting is that what things are and how they work are the same thing. An apple is something that behaves like an apple.
That is something I have a hard time accepting. For example, we can say that elementary particles appear very small and can be modeled, for all practical purposes, as 0 dimensional points (my apologies for harping on this...), but if they actually are 0 dimensional points, I find very hard to accept (and just the fact that we are looking at strings or branes is evidence for this)...

Originally Posted by Grey
All models are, whether mathematical or not. But I don't think that means that we should assume that nothing in a model is actually anything like the real thing.
I would not assume that either, just that it is not the prime motivation for defining the model...

27. Originally Posted by Ken G
That this approach works at all is amazing, and must say something about how intelligence develops so as to be useful and effective. But it still seems quite unlikely that our concept of reality is really all that close, even in terms of concepts like particles and energy levels, etc.
Actually, I disagree. I think the reason that this approach works is exactly because our concepts correspond to elements of reality. I think that modeling an atom as being composed of a nucleus of protons and neutrons with bound electrons nearby works well because an atom is so composed.

Originally Posted by Ken G
I wonder if alien intelligences couldn't be just as successful at describing reality using physical notions that would seem quite, well, alien to us. But of course the basic skeleton of the mathematics must be the same, as the predictions must come out the same. The words used, however, might be untranslatable.
I'm fairly convinced that this would not be possible. That is, I think any alien's description of matter would end up having terms that are equivalent to what we call atoms, electrons, nuclei, and so forth. Even for concepts that seem fairly abstract, like energy and momentum, I'd be willing to bet that there would be equivalent terms used by alien physicists. Sadly, we don't have any aliens around to ask about this, so I don't think we'll ever be able to settle such a bet.

Originally Posted by Ken G
I have no idea, it's quite a deep mystery how our minds are able to interpret our reality. And why does our greatest accuracy often come in applications that are the most removed from our experience, and from anything that could remotely be considered a survival advantage? That's a real poser!
I'd agree that it's pretty impressive that minds that evolved to handle hunting and gathering seem to also be adept and pondering the mysteries of the universe. But maybe I find it less amazing that the transition worked so well, because I think that the best way to adapt well to the external universe is to be able to internally model it. The better the correspondence between your internal model and what's really out there, the more likely you'll be able to deal with it well.

28. Originally Posted by Grey
I think that modeling an atom as being composed of a nucleus of protons and neutrons with bound electrons nearby works well because an atom is so composed.
This is a proposition that can only be falsified (by inventing an equivalent formulation without those concepts, quite a challenge), but never proven. And there's the rub-- in science, you only get to know something works until something else works better, you never get to know you "got it right". When does an extremely useful idea become the truth? Within the context of science, there is an imperfect mechanism for that transition, but outside science, in any absolute sense, that transition simply never occurs. Philosophers have tried for a long time, with very little success, in my view. Instead, we just compromise what we mean by "truth" to accomodate our limited intelligence.
Originally Posted by Grey
Yes, that is a shame. Especially if they were very different from us, perhaps lighter than air floaters, or dolphins or something (with opposable thumbs, of course.)
Originally Posted by Grey
The better the correspondence between your internal model and what's really out there, the more likely you'll be able to deal with it well.
But that doesn't explain why the models that work the best are the most divorced from anything we had to actually deal with while we were developing our intelligence.

29. For some time, I was arguing against taking "0 dimensional" points literally, saying "how can a fundamental particle have zero volume". Am beginning to suspect, that I am really making some wrong assumptions. There is no such thing as a universal model of reality.

In our every day world, the see-touch world, we have our model of reality, i.e., size, volume, cause and effect. In the sub-atomic world, we can neither see nor touch, so that the concepts of size, volume, shape, etc. no longer apply. Our understanding of the cosmos is divided into realms of experience. In the realm of "mechanics", for example, we are dealing with a limited number of macro physical entities. Here "mass", "position" and "velocity" are observables which appear. If we are dealing with a very large number of small entities like molecules, then thermodynamics applies, and "pressure", "temperature", "entropy" are observables relevant.

In the subatomic world, "color", "loudness", "rough", "smooth", etc. do not apply. So, I guess my objection to the volume of a fundamental particle does not really exist, because it is a concept which does not apply to the realm of fundamental particles.

30. Now you are thinking like a physicist rather than a philosopher, and applying the concepts that work well in physics but make us all scratch our heads if we try to ponder them philosophically!

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Originally Posted by Grey
I often wonder if quantum mechanics and general relativity will only really be unified when someone can find a way that curved spacetime and an exchange of gravitons are really just different ways of looking at the same thing.
I've pondered if what happens is that gravitons interact with spacetime (or maybe the Higgs), causing the curvature. But then, I don't have enough of a background in QM to give anything definite. (but it is fun to think about it).

Originally Posted by Grey
I have no idea how to do that, of course.
Well, if you did, you'd get that free trip to Sweden.

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