Null Physics anyone?

[ben m]

Although these microwaves are initially colinear with their source photons (in order to conserve energy and momentum) they are quickly (by astronomical standards, at least) scattered by the next link in what is referred to in Our Undiscovered Universe as the cosmic fusion cycle.

The strange thing is that, in Witt's actual book excerpt (ch. 15) he explicitly says that light decays in a way that loses energy---that's how he wants to avoid Olbers' Paradox. Does this make sense? Is a lucid explanation forthcoming? Do pigs fly?

 

[zosima]

The strange thing is that, in Witt's actual book excerpt (ch. 15) he explicitly says that light decays in a way that loses energy---that's how he wants to avoid Olbers' Paradox. Does this make sense? Is a lucid explanation forthcoming? Do pigs fly?

Ya, seriously, and somehow stars recycle the energy lost via decay....its gibberish.
If he had half a tick of integrity he would post his book online. He obviously has the resources and then he could really get his idea out to many more people. He claims the money from the book sales go to spread null physics but the only expense for null physics is the expense of publishing his book. Its not like he's funding null physics experiments or anything. Anyway its not like online publication would eat into his sales of paperweights, err...books, the people who would read online are probably the people who would be disinclined to buy the book, especially since it is recommended by no one who is qualified to recommend it.

 

[zosima]

Witt's white papers.

I thought people might be interested that Witt has published a couple of white papers:
http://www.nullphysics.com/menu_whitepapers.cfm?menustate=whitepapers&pgtitle=White Papers

In the second of the two he tries to explain his tired light theory. Apparently there is an invisible gravity field that exactly imitates expansion. I think insofar as it is a piece of duct tape slapped on to his theory it seems to explain, at least at a glance, why things at greater distance might appear to be moving with respect to us, but not be....It was nice to be weird, 'cause I was curious how he was gonna talk himself out of his hole, but...

Just off the top of my head I can think of a couple things it doesn't explain. The lack of observable gravitational field for one. It doesn't explain CMB temperature or anisotropy. It doesn't explain the apparent acceleration of more distant objects. It doesn't explain the coincident age of the CMB and the oldest stars.

It's not the worst woo I've seen, he certainly tries hard, but ultimately, it doesn't work. I hope everyone has as much fun with it as I did.

 

[Hermine]

Zosima, for the white papers, thank you.

BTW feel free to NOT read my stuff if that is your wish.

Blobru asks what is the CMB “scattering mechanism”?

Some information on primal – from “Prisoners of Pain” p10

“Primal pain is felt when the system experiences some kind of trauma. Primal pain is an overload – more information than the system can integrate. It is not simply a psychological reaction but literally a transmission of energy.”

P13 “If a Pain in early childhood is felt in its full intensity when it happens, it will not become an unconscious force, and there will be no neurosis. But when there is too much pain, the child is rendered mercilessly unconscious. The mercy has a price. Pain is repressed, but it remains within the child’s system precisely because it was too great to be experienced, resolved, and understood. The Pain now takes on a life of its own, out of awareness, exerting a continuous force. While it remains unfelt it takes an endless toll. While repression saves, it also begins to destroy.”

P17 “ When we block Pain, we do not block its effects. We block only the conscious experience of it. The effects of blocked pain are expressed in the form of energy. By analogy, each trauma is very much like the “big bang” origin of the universe in which the energy from the original explosion still reverberates through the cosmos. The energy of the original traumas – and they are electrical storms – also permanently reverberate through the human biologic system.

Energy is an electrochemical force which can be measured. It is not mystical, not an élan, or an id. It derives from specific events which have had an explosive effect on the organism. An explosive effect which, now contained, continues to emanate from specific stored early experiences. The reverberating energy will be found decades later in musculature as well as in the brain. Both show increased electrical activity.”

Key words: energy from early experiences is stored, continues to emanate and reverberates through the whole system.

CMB is the imprint

Blobru writes: “Could it erase the photon decay…… So should we still observe unscattered microwaves pointing back to the red-shift source (assuming a microwave frequency is dependant on how “decayed” the emitting photon is, shouldn’t redshift objects still have a sort of microwave signature: the farther away the source, the more red-shift, the more photon decay, the larger the microwavelength…)?”

Redshift, cosmological constant, CMB, black matter…….are all connected, no?

This from “Astronomy – Collector’s edition” (Jan 16 2007)

Dark Energy

“ One of the strongest arguments in favour of string theory’s landscape relates to the energy of empty space – the vacuum energy or “dark energy”. The standard explanation for this energy is that it maintains a single, unwavering value throughout space – thus becoming what Einstein called the cosmological constant.

The problem is that physicists don’t know how to calculate the cosmological constant from first principles, the hallmark of a robust theory…….

The answer may come from combining the string-theory landscape, which shows how the cosmological constant can vary, with the “anthropic principle”. The latter suggests the cosmological constant may be variable like the weather – something that changes from place to place in the universe, rather than a true constant of nature.

If a broad range of values for the constant is possible, it’s not surprising we live in a universe with a small cosmological constant, one where stars and planets can exist. In the same way, it’s not surprising we live on Earth, rather than on Venus or Pluto, where we’d either roast or freeze.”

Terence Witt – Paper 2

Lumetic Decay – Intergalactic Redshift is caused by the Universal Gravitational Field

“This effectively eliminates the matter, neutrinos and radiation in intergalactic space, leaving only space and a weak universal gravitational field as possible redshift agent.

A transformative photon experience must be facilitated by an external agent and the only weak mechanism able to act over billions of light years of neutral space is gravity.”

My point: A WEAK gravitational field is responsible for creating WEAK tired light. Why WEAK, if not from some kind of trauma, like the Big Bang? What happens in places where there is less trauma, where there’s balance between WEAK and STRONG? (see PT and see mag. Article)

Remember, we are of the universe, the universe is of us. What we observe in us we must observe out there.

Paper 1 – Einstein’s Non-Physical Geometry.

Terence Witt writes: “ The General Theory does not contain a single questionable or unreasonable assertion, and it results in a spectacularly accurate portrayal of gravitational interaction. But it also fails to show us the source of the fields it describes. It can never access this information because it is isolated from deep reality by its own postulate. Gravitational phenomenon are an indirect consequence of the underlying physical geometry, they do not define this geometry.”

In my plan ( P6 which obviously has been removed) I wrote: All visible matter first of all is made up of electrons, protons, neutrons etc along with their positive and negative charges (there is a neatly balanced package of these) which combined with weak and strong forces, gives you gravity.

 

[zosima]

@Hermine
I said this after your first post. This stuff needs to go in another thread. If you want to talk about this, start a new thread that explains your theory. Otherwise I'm not going to read what you say, I'm just going to mock you. If you post it in another thread, then I'll read what you have to say. I'm not going to promise I won't mock you then either, but at least I won't apply contempt prior to investigation.
So, please, stop spamming out this thread and make a new thread.

 

[Hermine]

Hi Zosima, I appreciate the honesty and acknowledge your point of view, but I also have mine.

About starting a new thread, I’m not interested but more to the point I wouldn’t have a clue what to do with one. As for my theory, I don’t really want to talk about it or necessarily have anyone else talk about it, I’m only interested in presenting and comparing what I’m reading on here (which is very important to me) with what I’ve come up with (in fact it’s more for my own benefit than anyone else’s).

I’m not equipped to carry out a debate in the way you people have been doing, I don’t have the expertise, I only “see” into these things from a primal perspective.

Having said that, I feel there’s plenty in my post that is relevant to the topic, leaving aside my theory and the primal bits. For eg I asked “Redshift, cosmological constant, CMB, black matter…. are all connected, no?”

Then there’s my quote from the magazine on the cosmological constant, I’d be interested in hearing views on that one. I believe it’s relevant to the discussion in more ways than one, for eg it also links back to Blobru’s query about scattered, unscattered microwaves pointing back to the red-shift source etc.

So there you are, I’m not begging to stay on here btw, that’s just how it is, your point of view as opposed to mine.

 

[zosima]

Hi Zosima, I appreciate the honesty and acknowledge your point of view, but I also have mine.

About starting a new thread, I’m not interested but more to the point I wouldn’t have a clue what to do with one. As for my theory, I don’t really want to talk about it or necessarily have anyone else talk about it, I’m only interested in presenting and comparing what I’m reading on here (which is very important to me) with what I’ve come up with (in fact it’s more for my own benefit than anyone else’s).

I’m not equipped to carry out a debate in the way you people have been doing, I don’t have the expertise, I only “see” into these things from a primal perspective.

Having said that, I feel there’s plenty in my post that is relevant to the topic, leaving aside my theory and the primal bits. For eg I asked “Redshift, cosmological constant, CMB, black matter…. are all connected, no?”

Then there’s my quote from the magazine on the cosmological constant, I’d be interested in hearing views on that one. I believe it’s relevant to the discussion in more ways than one, for eg it also links back to Blobru’s query about scattered, unscattered microwaves pointing back to the red-shift source etc.

So there you are, I’m not begging to stay on here btw, that’s just how it is, your point of view as opposed to mine.

Well I see this primal stuff as complete woo. I honestly don't see how its related to anything.

As to your questions on physics, I don't think they have anything to do with this thread's topic. If you don't want to talk about your theory and you want to ask questions about physics, then post those in a new thread. Although I'd recommend just looking this stuff up online and perhaps even learning some basic physics that doesn't involve primal theory and isn't from Terrence Witt or new scientist.

I don't mean to rude, but if you don't even understand the simple stuff in physics then you won't grasp the more complex issues that you're asking about. Plus its really the least you can do to demonstrate that you have an honest and genuine interest in understanding these topics.

 

[Hermine]

Zosima, thanks once again for your honesty and I guess that's the end of that!

 

[thubbathubba]

I've done it!

After years of lonely research, solitary contemplation, inumerable false-starts, dead-ends, and blind-alleys, I have finally reduced the origin of our universe into one single, simple, comprehensive theory. My theory is unassailable in its logic, irreducible in its expression; it is perfect.

Here it is: "Nothing Cannot Exist."

OK. It just came to me in the shower about twenty minutes ago. I may need some help with the math.

 

[phlogiston]

So, What is the mystery?

Like many I was drawn to this excellent forum out of curiosity provoked by the null physics ads that are apparently in every even vaguely science-oriented publication. Curiosity led to google and google led straight to JREF. Thanks Terry Witt.

However, it is not the questions of physics, pro or con, that interest me. I am not qualified to evaluate them. Since the standard model seems to satisfy a lot of smart people, and since its application has led to most of what we enjoy, and most of what we dread as well in the modern world, it's good enough for me.

I was drawn to Terry's claim that "Null Physics tells us why the universe exists, how the universe exists, and why it is the way it is. The mystery of our existence has beaten scientists and philosophers for so long that they are utterly convinced that reality's underpinnings are beyond human comprehension." It's the 'why' part that gets me.

I'm always interested in such speculations, but not used to paying for them. Usually they come unbidden and for free; sometimes you'd even pay not to get them. I plowed through all these posts (thanks, guys - educational and entertaining) in hopes of finding someone who actually had read the book and would tell me why, according to Mr. Witt, the universe exists. What is his null metaphysics?

Is there anyone out there who has actually read the book, even through gritted teeth, and can tell me that. I'd like to know, but I'm unlikely to buy the book until it shows up on a table at Goodwill.

 

[joe90]

The de Sitter spacetime - towards our universe is apparently approaching asymptotically - can be cast in terms of a static metric. See for example the arxiv paper 0704.3265.
Hence, at least asymptotically, the notion of expanding spacetime is, by itself, empty of physical content, being a coordinate-dependent description (i.e. peculiar to the Robertson-Walker system) and fungible via a coordinate transformation with a static universe.

In the latter, cosmological redshift is explained as due to work done by light as it propagates in a static isotropic potential that is the same for all co-moving - 'fundamental' - observers. One is free to call this effect 'tired light' if one wishes. No new physics is implied here.

I do not know the extent to which this overlaps with Terry Witt's own view of cosmology. But it should serve as a reminder that due to the general coordinate invariance of GR many alternative but equally viable (albeit coordinate-dependent) 'explanations' for the same observed phenomenon are possible, each being 'internally consistent', i.e., within its own particular coordinate system.

 

[sol invictus]

In the latter, cosmological redshift is explained as due to work done by light as it propagates in a static isotropic potential that is the same for all co-moving - 'fundamental' - observers. One is free to call this effect 'tired light' if one wishes. No new physics is implied here.

It's not at all like tired light. Photons moving away from the origin of the coordinates you are talking about blueshift - they gain energy, because they are moving down the slope of the potential. In tired light theories all photons lose energy over time; here instead nothing is time dependent, and the gain or loss of energy is only a function of the direction of motion.

As for your larger point, de Sitter space is maximally symmetric, which means you can choose many different sets of coordinates equally naturally - static, expanding, even contracting. But the universe we live in is not like that, and will only approximate it at very late times when the density of matter and stars has gone to zero. In our universe now there is a preferred coordinate system defined by the matter, and that coordinate system is expanding.

 

[joe90]

It's not at all like tired light. Photons moving away from the origin of the coordinates you are talking about blueshift - they gain energy, because they are moving down the slope of the potential.

Not if you choose the sign of the potential incorrectly. In de Sitter spacetime written in static coordinates (i.e. with a static metric) obviously you must choose the sign of the potential (actually, the coefficient of the r^2 term in g_{tt} and g_{rr}) to match observation. In doing so, the photons red-shift as they propagate. Look at it this way: There can be no observable consequences of a coordinate change, hence the static reformulation is mandated to give the same predictions.

As for your larger point, de Sitter space is maximally symmetric, which means you can choose many different sets of coordinates equally naturally - static, expanding, even contracting.

Coordinate freedom in GR has nothing to do with a particular spacetime such as de Sitter. One has the freedom to choose alternative coordinates regardless of whether or not the spacetime is maximally symmetric.

But the universe we live in is not like that, and will only approximate it at very late times when the density of matter and stars has gone to zero.

It is true that the de Sitter is a perfect match only when the vacuum term completely dominates the Friedmann equation (compared to matter and radiation). However, considered from the point of view of Robertson Walker coordinates, the universe is observed to be expanding exponentially to a fair degree of accuracy (q_0 ~ -1), so we are already in the vacuum dominated phase of the expansion. And this is exactly the characteristic of the Sitter spacetime which therefore permits characterization in terms of a static metric.

I do not want to make a dispute over how close is close (to the asymptotic behavior). The point is that to some degree - depending on your definition of closeness - the universe can be characterized as both expanding exponentially (in traditional Robertson-Walker coordinates) AND (simultaneously) static (in static de Sitter coordinates).

And I wanted to make the more general point: 'cosmological expansion' is not always a physical statement, since it is coordinate dependent.

In our universe now there is a preferred coordinate system defined by the matter, and that coordinate system is expanding.

The distribution of matter and the presence of the cosmic microwave background establishes a 'preferred coordinate system' in the sense of special relativity only. It does not establish a preferred coordinate system from the perspective of GR. There remain an infinite number of equally viable coordinate systems in GR available to describe observational cosmology, regardless of the presence of matter and CMB, and regardless of whether or not the universe is in a de Sitter phase.

 

[sol invictus]

Not if you choose the sign of the potential incorrectly.

What?

In de Sitter spacetime written in static coordinates (i.e. with a static metric) obviously you must choose the sign of the potential (actually, the coefficient of the r^2 term in g_{tt} and g_{rr}) to match observation.

That coefficient is the Hubble constant squared. If you choose it to be positive, you are in de Sitter. If you choose it to be negative, you are in anti de Sitter. In neither case does light behave as you claim.

In doing so, the photons red-shift as they propagate.

No, that's false, as I just explained. Do you want me to prove it?

Look at it this way: There can be no observable consequences of a coordinate change, hence the static reformulation is mandated to give the same predictions.

Sure - but the predictions are not what you seem to think they are.

Coordinate freedom in GR has nothing to do with a particular spacetime such as de Sitter. One has the freedom to choose alternative coordinates regardless of whether or not the spacetime is maximally symmetric.

Obviously, yes. That doesn't conflict with what I said. Try reading it again.

And I wanted to make the more general point: 'cosmological expansion' is not always a physical statement, since it is coordinate dependent.

That's true, but it's not at all like tired light.

The distribution of matter and the presence of the cosmic microwave background establishes a 'preferred coordinate system' in the sense of special relativity only. It does not establish a preferred coordinate system from the perspective of GR. There remain an infinite number of equally viable coordinate systems in GR available to describe observational cosmology, regardless of the presence of matter and CMB, and regardless of whether or not the universe is in a de Sitter phase.

You're wrong. While it's true that one can choose whatever bone-headed coordinates one insists on, in an FRW cosmology (with the exception of exact de Sitter, anti de Sitter, and Minkowski) there is a preferred choice defined by the symmetries of the spacetime. There is only one choice of time slicing which coincides with those symmetries, and it is not static (again, except in certain trivial cases).

 

[joe90]

That coefficient is the Hubble constant squared. If you choose it to be positive, you are in de Sitter. If you choose it to be negative, you are in anti de Sitter.

Correct.

In neither case does light behave as you claim.

You seem to accept that observational physics as described by GR is coordinate independent. But you do not seem to accept the immediate consequence that a change of coordinates from RW k = 0 with a(t) = exp(Ht) to static de Sitter cannot possibly change whether or not we see light as reddened from distant sources. The static de Sitter explanation for red-shift is not the same as the RW-based explanation, yet the prediction is mandated to be the same.

Let me give you another example that might be clearer. If you are familiar with the traditional RW metric, then you will know that all k = [-1,0,1] can be written in conformally flat (conformal to Minkowski) form. arxiv.org/abs/0704.2788. Because Maxwell's equations are unchanged in conformally flat spacetime, no one usually would bother trying to solve the equations in RW coordinates. They would first transform to conformal coordinates, solve Maxwell there, and transform back if required. In the k=0 case this just means redefining the RW time dt = a(\eta)d_\eta. Now, in the conformal coordinates, precisely because Maxwell is unchanged from its Minkoski form, EM radiation is not red-shifted at all; it is completely unaffected by the curvature of spacetime! Note this is true for all RW cosmologies for arbitrary sign of curvature and scale factor variation.

But it follows form coordinate invariance that there must be a satisfactory explanation for cosmological red-shift in conformal coordinates. The conformal explanation for cosmological red-shift is that matter is blue-shifted (Compton wavelengths are shrinking) whilst radiation remains unchanged by the expansion. (You can show this by writing eg Dirac equation in conformal spacetime.) Distant starlight propagates from H-atoms emitting Lyman-alpha, the energy of which lines are proportional to the electron mass. On arriving at Earth sometime later, the matter has changed so that electrons are more massive. Correspondingly, local H-atoms have higher energy Lyman-alpha transitions compared to those that sourced the radiation from distant stars. Hence that radiation looks redder than the same Lyman alpha produced locally.

Hopefully you can now see that red-shifting of starlight in transit as for example described by MTW in Gravitation is only one out of any number of possible explanations.

No, that's false, as I just explained. Do you want me to prove it?

Yes! Write down the homogeneous Maxwell's equations in de Sitter spacetime and try solving for the vector potential.

But don't bother - you'd be wasting your time! Solve the equations in Minkowski spacetime (eg plane waves) and then, using conformal invariance, transform the result to static de Sitter.

Don't need to do that either! Just introduce the metric into the Minkowski result. Each Fourier component in a plane-wave expansion in Minkowski and therefore conformal spacetimes will no longer be a single Fourier mode. The exponent is
i*k*r -> i*g(r)_{ab}*k^{a}*r^{b}
where g(r) is the static de Sitter metric.

Hence waves get red-shifted as they propagate in the static de Sitter space!

Obviously, yes. That doesn't conflict with what I said. Try reading it again.

It's still wrong the second time I read it!

That's true, but it's not at all like tired light.

Depends on your definition of tired light.

You're wrong. While it's true that one can choose whatever bone-headed coordinates one insists on, in an FRW cosmology (with the exception of exact de Sitter, anti de Sitter, and Minkowski) there is a preferred choice defined by the symmetries of the spacetime.

I generally do not write to boards such as this because it often ends up with people calling each other names, with more interest in being right than in exploring the physics.
Either be civil or else I will not reply to you further.

Don't confuse 'preferred' on the basis of mathematical expediency with 'preferred' on the basis of establishing a reference frame. CMB does the latter. The Cosmological Principle invites the former, but not the latter. There is no physical content in choosing different systems in the former case. In the latter case there is a physical reason restricting the choice of equivalent frames of reference. I wrote the original post to point out the distinction between the physical content of cosmological red-shift and its representation in terms of coordinates. The two are often confused.

Even within general RW spacetime many systems are in use - it depends to some degree on the application which is the more expedient. Traditional, harmonic, isotropic, and conformal coordinate are the systems that spring to mind. None of these does any violence to the inherent symmetry of the spacetime. Indeed, one might argue that the less-used isotropic form is more faithful in that regard.

 

[sol invictus]

I can't respond in full now. Let me just say two things:

A) I apologize if I insulted you by referring to your choice of coordinates as "boneheaded". No offense was intended.

B) What you are saying is not correct. Light does NOT redshift in de Sutter any more often than it blue shifts. The simplest way I can think of to show that to you is to point out that the expanding flat FRW coords, in which a(t) is a growing exponential, are no better than the contracting flat FRW coords, where a(t) is a decreasing exponential. But in those contracting coords, the same incorrect logic you are employing would indicate that all light blueshifts.

Perhaps an even simpler way to say it is just that since there is a time translation invariance (which follows from the existence of a static coord system) there cannot be a preferred direction of time, or any preference for red over blueshifts.

If that doesnt convince you, I will provide more detail when I can.

 

[kevin mcd]

ok so i saw the two page ad in popular science, and as someone who has always liked to learn about "modern" physics, i decided to do some research on this guy, and it led me here. from what ive read, his stuff sounds pretty much made up (esp the proton + electron = neutron part. im in high school physics, and i am pretty sure i have never even heard my teachers make a joke about that--- although i think the onion did something along those lines). so in anyones honest opinion, whether they have read it or not, should i go out and spend 60 bucks, or are there other more respectable relativity/quantum books (besides a brief history) i should get?

 

[Third Eye Open]

ok so i saw the two page ad in popular science, and as someone who has always liked to learn about "modern" physics, i decided to do some research on this guy, and it led me here. from what ive read, his stuff sounds pretty much made up (esp the proton + electron = neutron part. im in high school physics, and i am pretty sure i have never even heard my teachers make a joke about that--- although i think the onion did something along those lines). so in anyones honest opinion, whether they have read it or not, should i go out and spend 60 bucks, or are there other more respectable relativity/quantum books (besides a brief history) i should get?

Check out this thread, there are some good recommendations there http://www.internationalskeptics.com/forums/showthread.php?t=84904

 

[joe90]

@sol invictus:

What you are saying is not correct. Light does NOT redshift in de Sutter any more often than it blue shifts. The simplest way I can think of to show that to you is to point out that the expanding flat FRW coords, in which a(t) is a growing exponential, are no better than the contracting flat FRW coords, where a(t) is a decreasing exponential. But in those contracting coords, the same incorrect logic you are employing would indicate that all light blueshifts.

We need to be clear about the distinction between a spacetime and a coordinate
system. A spacetime admits any number of coordinate systems. Two different spacetimes are distinguished over some domain by the fact of not being coverable by the
same coordiante system.

Schwarzschild is a spacetime.

'Conformal' can refer either to a class of spacetimes coverable by a (set of) coordinate systems, or to the coordinate systems themselves.

De Sitter is a spacetime.

De Sitter can be written in conformal form, and therefore belongs to the class of conformal spacetimes, even if it is not written in conformal form (but in static or Rw form say).

The point of my original post is that in general one cannot say whether or not light red-shifts, blue-shifts or does neither without stating a coordinate system (not a spacetime), which statement thereof is not physics. More specifically, there is no physical meaning to the statement that light red-shifts in de Sitter spacetime, since red-shift depends on the coordinate system, which is not specified just by naming the spacetime.

Expressed in conformal coordinates plane waves do not change their wavelength or frequency in any of the RW spacetimes, including de Sitter spacetime.

In de Sitter spacetime expressed in RW coordinates (to use a shorthand) light red-shifts as it propagates due to the expansion of space due to the scale factor a(t) in the metric.

In de Sitter spacetime expressed in static de Sitter coordinates light red-shifts as it propagates due to a distant-dependent radial term in the metric.

Perhaps an even simpler way to say it is just that since there is a time translation invariance (which follows from the existence of a static coord system) there cannot be a preferred direction of time, or any preference for red over blueshifts.

The effect of the static de Sitter metric on erstwhile Minkowski spacetime plane waves (if you will) is not due to the present of an expanding scale factor, for of course there is none here. But this is not the only means by which a red-shift can occur. In this case the red-shift (or blue shift in anti-de Sitter) arises because the metric has a spatial part - which, BTW, is not space-translation-invariant.

It is enough to know that the phase factor changes as

i*k*r -> i*g(r)_{ab}*k^{a}*r^{b}

We can write this as

i*k*r -> i*k'(r)_{a}*r^{a}

where now we have a pseudo-Minkowski 4-vector (with metric g = diag(1,-1,-1,-1)) k'(r):

k'(r)_{a} = g(r)_{ab}*k^{b}

that is a function of distance. That is, frequencies and wavelengths are continuously changing as the wave propagates.

(Actually, there is a metric-induced change in the potential amplitude also, but this is hardly likely to undo the red-shift induced in the phase factor.)

 

[Wangler]

@sol invictus:

We need to be clear about the distinction between a spacetime and a coordinate
system. A spacetime admits any number of coordinate systems. Two different spacetimes are distinguished over some domain by the fact of not being coverable by the
same coordiante system.

Schwarzschild is a spacetime.

'Conformal' can refer either to a class of spacetimes coverable by a (set of) coordinate systems, or to the coordinate systems themselves.

De Sitter is a spacetime.

De Sitter can be written in conformal form, and therefore belongs to the class of conformal spacetimes, even if it is not written in conformal form (but in static or Rw form say).

The point of my original post is that in general one cannot say whether or not light red-shifts, blue-shifts or does neither without stating a coordinate system (not a spacetime), which statement thereof is not physics. More specifically, there is no physical meaning to the statement that light red-shifts in de Sitter spacetime, since red-shift depends on the coordinate system, which is not specified just by naming the spacetime.

Expressed in conformal coordinates plane waves do not change their wavelength or frequency in any of the RW spacetimes, including de Sitter spacetime.

In de Sitter spacetime expressed in RW coordinates (to use a shorthand) light red-shifts as it propagates due to the expansion of space due to the scale factor a(t) in the metric.

In de Sitter spacetime expressed in static de Sitter coordinates light red-shifts as it propagates due to a distant-dependent radial term in the metric.


The effect of the static de Sitter metric on erstwhile Minkowski spacetime plane waves (if you will) is not due to the present of an expanding scale factor, for of course there is none here. But this is not the only means by which a red-shift can occur. In this case the red-shift (or blue shift in anti-de Sitter) arises because the metric has a spatial part - which, BTW, is not space-translation-invariant.

It is enough to know that the phase factor changes as

i*k*r -> i*g(r)_{ab}*k^{a}*r^{b}

We can write this as

i*k*r -> i*k'(r)_{a}*r^{a}

where now we have a pseudo-Minkowski 4-vector (with metric g = diag(1,-1,-1,-1)) k'(r):

k'(r)_{a} = g(r)_{ab}*k^{b}

that is a function of distance. That is, frequencies and wavelengths are continuously changing as the wave propagates.

(Actually, there is a metric-induced change in the potential amplitude also, but this is hardly likely to undo the red-shift induced in the phase factor.)

Woohoo!

Some new action on this thread!

joe, welcome to jref. you can post latex on jref, if you would like. Just use 'latex' and '/latex' in brackets around your entries, thusly:

[latex] k'(r)_{a} = g(r)_{ab}*k^{b} [/latex]