Time Dilation & big bang Question

[hellfire]

hellfire - Well spotted! You are correct for a decelerating universe , however Davis and Linewaver were also considering accelerating universes as is thought to be observed from the distant type Ia S/N data. In such a universe the reverse is true and it is in those universes that objects can be observed today as they were in the distant past, when their velocities were sub-luminal, which are receeding from us today at super-luminal velocities.

Again I think you are not correct Garth. To make any assertions about the recession velocitiy you shall consider the Hubble law (v = H d), where the Hubble parameter (H) is used and NOT the first time derivative of the scale factor (a -- whose second time derivative determines whether the expansion accelerates or deccelerates). Thus, the time evolution of H is relevant for the discussion and not the time evolution of a or a-dot.

In every universe with Omega Matter different from zero, the Hubble parameter decreases. Note that in an universe filled only with a cosmological constant (no mater nor radiation), the Hubble parameter would be constant (de-Sitter exponential expansion) as you can verify taking a look to any reference about inflation. Equivalently you may notice that an accelerated exponential expansion has a constant H (integrating H = Const.). Our universe contains 0.73 of cosmological constant and 0.23 of matter, which leads the Hubble parameter to decrease with time (its expansion does also accelerate, but not exponentially).

So, again, although this objetcs were closer to us (d smaller), the Hubble parameter was much greater (H greater). This leads to a greater value of the product v = H d.

I refer you again to the calculator mentioned above. It is not my calculator, although I did also implement one and I have verified the results of this one. The formulas used are in line with the Lineweaver paper. Also the results of this one agree with Ned Wrights one. You can insert a value z for any cosmological model and you will get the result for for the Hubble parameter now and in past (emission epoch), as well as the velocity now and in past.

Regards.

 

[Garth]

Hellfire - I am not in dispute with the substance what you are saying, but the appropriateness of the convention of definition of the meaning given to distance and time, basically do we define them as then or now?

 

[Chronos]

Chronos: Are you asking whether objects that we cannot see, appear to be getting younger? The question contradicts itself.

Good point. If we cannot see it now, I presume we cannot predict anything it does in the future. The question does contradict itself, as you observed. That was my point.

 

[Garth]

The important point is to remember that these objects are not moving at all, that is in the sense that we are not considering their peculiar motions (pardon the phrase!), but rather we are considering the effect of the curvature on space-time on the cosmological scale. We observe Hubble red-shift and the Friedmann equations and the Robinson-Walker metric encourage us to interpret such red-shift as recession. As Fred Hoyle showed the metric can be conformally transformed with the result that the observations can be interpreted differently.

As we cannot in general parallel transport a vector across the cosmos how do we define length and time? How do we define velocity? We have an option of which convention to choose. If that option leads us to evaluate the velocity of an observable object as super-luminal then I find that that is not necessarily an appropriate choice.

I prefer to define velocity of observed red-shift using the SR relationship in which v tends to c as z tends to infinity.

Two signals emitted in the order 1,2 from the objects, calculated by the convention described by Davis and Linewaver to be super-luminal, are received in that same order 1,2. Temporal sequence has not been reversed and therefore I prefer to think of them as sub-luminal, which indeed they are when measured by another convention.

Perhaps the confusion caused by such issues that arise in both a decelerating and accelerating universe is an argument that the universe is a "Freely Coasting" one that expands strictly linearly? [Search on this Forum for the discussions about such a model]

 

[Andrew Mason]

1. Almost any photon observed from a distant object will be red-shifted. Such red shift occurs when the object that emitted it receding from us (ones that are approaching us are blue shifted, but these are much less common in an expanding universe). Such shift was noted originally almost 100 years ago by Hubble and others and was instrumental to our understanding that we live in an expanding universe.

2. Virtually any star or galaxy consists mostly of hydrogen and helium, and exhibits a known spectrum. The amount of red shift of the observed spectrum of a distant object can then be compared to the "standard" spectrum of similar elements at rest with respect to us. The difference is explained by General Relativity as representing velocity differential.

3. Interestingly, there is actually no theoretical upper limit to the amount of this differential. In fact, many objects have been spotted that are receding from us at more than twice the speed of light. This provides experimental confirmation of theory. It also means that the classical notion of a universe expanding at a maximum of c in one direction and c in another direction are wrong.

4. Thus your premise is wrong: we can and do observe light from objects that are receding from us at speeds far in excess of c. Such light has been moving towards us for over 13 billion years. The objects that emitted them are now about 46 billion LY away.

5. The full description of all of this is beyond the scope of a post. I might recommend this paper by Lineweaver and Davis, which pretty well explains everything:

http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179.pdf

This is not the correct explanation for red shift. Red shift is a doppler effect. The source moving away from the observer results in a lowering of the frequency much the same as the ambulance going past results in the siren changing to a lower frequency. There can also be a gravitational redshift from massive objects but this is not behind the redshift/velocity relationship that fits the Hubble constant.

There is no object that is observed to be receding from us at faster than the speed of light. I defy you to provide any evidence or authority for that statement.

Andrew Mason

 

[Garth]

There is no object that is observed to be receding from us at faster than the speed of light. I defy you to provide any evidence or authority for that statement.
Andrew Mason

Actually Andrew, as has been said in the thread above, it depends on how you measure distance and time at cosmological distances, given that you define your units according to laboratory standards today but are seeing the object as it was 'billions' of years ago.

The standard convention does allow the velocity to become super-luminal, either because an originally sub-luminal object becomes super-luminal in an accelerating universe, or because the light from a super-luminal object 'catches us up' as we 'slow down' in a decelerating/contracting universe.

However temporal order is not reversed by these cosmological 'super-luminal' velocities, two signals emitted in the order 1,2 are received 1,2. Therefore we may think this convention inappropriate and choose not to accept it, but rather define their velocity as the rate of increase of the time of flight of their observed photons, measured in the cosmic co-moving frame of reference. In this case their red-shift tends to infinity as their velocity tends to c, and super-luminally receeding objects can not be observed.
It is this convention that I choose - Garth.

 

[Andrew Mason]

However temporal order is not reversed by these cosmological 'super-luminal' velocities, two signals emitted in the order 1,2 are received 1,2. Therefore we may think this convention inappropriate and choose not to accept it, but rather define their velocity as the rate of increase of the time of flight of their observed photons, measured in the cosmic co-moving frame of reference. In this case their red-shift tends to infinity as their velocity tends to c, and super-luminally receeding objects can not be observed.
It is this convention that I choose - Garth.

So you appear to be saying that the observable universe cannot exceed the speed of light but the non-observable universe can. What meaning does the non-observable universe have? Are we not getting away from physics and delving into matters of belief and speculation?

Andrew Mason

 

[Mike2]

The standard convention does allow the velocity to become super-luminal, either because an originally sub-luminal object becomes super-luminal in an accelerating universe, or because the light from a super-luminal object 'catches us up' as we 'slow down' in a decelerating/contracting universe.

Just a minute! So you are saying that portions of the universe are becoming unobservable? That some galaxies are traveling faster than the speed of light? Well then, doesn't that make them completely irrelevant to our portion of the universe. In other words, we would no longer feel their gravity, etc. What are the cosmological consequences if every portion of the universe loses contact with ever more distant portions of the universe? Wouldn't that be the same are removing mass/energy from the universe as a whole? Wouldn't that be the same a losing information down a black hole?

 

[Garth]

So you appear to be saying that the observable universe cannot exceed the speed of light but the non-observable universe can. What meaning does the non-observable universe have? Are we not getting away from physics and delving into matters of belief and speculation?

Andrew Mason

Well after taking everything that has been said on this thread about how to actually measure the velocity of a distant object, in all conventions in most models, there are parts of this universe that we cannot see. One of them is a point diametrically opposite us in our orbit around the Sun. Because we cannot see that position it does not mean that nothing is there. We assume the space in that vicinity is just as it is elsewhere and there might well be an asteroid, for example, in what is known as our L3 point.
This is also true for cosmology. The Copernician Principle is that there is "nothing special about our position in the universe", it becomes incorporated into modern cosmology as the Cosmological Principle, which is "on a cosmological scale, at any particular cosmological time, the universe is the same and looks the same from all positions within it.", "The universe is spatially homogeneous and isotropic." Given that our vision is limited by the particle horizon, beyond which are objects that we cannot see now, and the event hirizon, beyond which are objects that we will never be able to see, then by extension it is assumed that the universe beyond these horizons does exist. Yes - if you like by faith in the cosmological principle. But of course we could be wrong and perhaps beyond our horizons, "here be dragons".
Garth

 

[Garth]

Just a minute! So you are saying that portions of the universe are becoming unobservable? That some galaxies are traveling faster than the speed of light? Well then, doesn't that make them completely irrelevant to our portion of the universe. In other words, we would no longer feel their gravity, etc. What are the cosmological consequences if every portion of the universe loses contact with ever more distant portions of the universe? Wouldn't that be the same are removing mass/energy from the universe as a whole? Wouldn't that be the same a losing information down a black hole?

Well Mike, in addition to my reply to Andrew, your question about a black hole is very relevant to help us think about the extra point you mention. 'If all other 'galaxies' lose contact with us would we no longer feel their gravity.'

In the black hole scenario we do lose contact with an object that disappears through the event horizon; however the gravitational field produced by that mass has not been lost, neither has its angular momentum. There was a "black holes have no hair" hypothesis which said that those two aspects were the only things to survive after an object falls into a black hole, but Stephen Hawking seems to have changed his mind and information also is not lost. I cannot pretend that I understand what he is talking about though!

In the same way objects beyond our particle and event horizons (see my previous post) still influence us gravitationally through the cosmological curvature of space-time.
Garth

 

[Andrew Mason]

Well after taking everything that has been said on this thread about how to actually measure the velocity of a distant object, in all conventions in most models, there are parts of this universe that we cannot see. One of them is a point diametrically opposite us in our orbit around the Sun. Because we cannot see that position it does not mean that nothing is there.

That is not what I meant about a non-observable part of the universe. Information from that part of the universe is capable of reaching us so it is observable.

You are talking about a part of the universe from which information can never reach us. As such, it is incapable of being detected. It is not possible to gather evidence of its existence or non-existence. Hence, it is beyond science. You are talking about faith and beliefs, not science so arguing about its existence or non-existence seems like a waste of time.

Andrew Mason

 

[Garth]

Andrew - we have faith in the laws of nature, that they apply on the Andromeda galaxy as well as in our laboratory - there are good grounds for such faith in the laws of science and certainly cosmology would not be possible without it. It may be the case that the universe is infinite, or certainly larger than our particle or event horizons. We can reasonably assume that the universe does not end just at the limit of our horizons and therefore believe it extends beyond. But we can never prove it.
Garth

 

[Andrew Mason]

Andrew - we have faith in the laws of nature, that they apply on the Andromeda galaxy as well as in our laboratory - there are good grounds for such faith in the laws of science and certainly cosmology would not be possible without it. It may be the case that the universe is infinite, or certainly larger than our particle or event horizons. We can reasonably assume that the universe does not end just at the limit of our horizons and therefore believe it extends beyond. But we can never prove it.
Garth

I couldn't disagree more. We don't have "faith" in the laws of nature. We have evidence of them. We deduce the laws of nature from our observations. This has led to the development of models or theories. As soon as we observe something that conflicts with the model, we change the model. So our "faith" in the laws of nature is always subject to new evidence. We believe the laws are correct throughout the universe because we have evidence that they are (eg. spectroscopy, gravitational effects).

Andrew Mason

 

[Garth]

We may be using the word 'faith' in different ways.
I am using it as a general term that we all experience everyday - you climb on an aeroplane and put faith in the machine and the ability of the pilot - and a whole lot else besides. You cannot prove all these things; you have to go by trust. In the same way we only observe the photons that arrive from the depths of space and interpret our observations by applying the laws of science that we have discovered here on Earth, the laws may be different elsewhere and we cannot prove that they are not. We might be living in the "Matrix". But in order to say anything about the universe we have a reasonable faith that the laws do hold in the rest of the universe. Such reason is based on the similarity of the pattern of spectral lines for example - it is a reasonable faith that I am talking about. Astronomy and cosmology work on the principle that we discover things 'out there' by applying laws that we have discovered 'down here', that is what astrophysics is, the physics (discovered down here) of the stars (out there).

Such a faith in the existence of such laws in the first place is necessary for science to flourish. Accordingly, if we see that galaxies and quasars exist right up to the limits of our horizons it is reasonable to believe that they do so beyond.

 

[Andrew Mason]

We may be using the word 'faith' in different ways.
I am using it as a general term that we all experience everyday - you climb on an aeroplane and put faith in the machine and the ability of the pilot - and a whole lot else besides. You cannot prove all these things; you have to go by trust.

We are. I would say that is not an act of faith. We have evidence that it is safe to fly. We know there is a risk. We accept the risk and hope for the best.

In the same way we only observe the photons that arrive from the depths of space and interpret our observations by applying the laws of science that we have discovered here on Earth, the laws may be different elsewhere and we cannot prove that they are not.

I would not say that it is faith. We have a model or theory that says that the laws of physics are the same. We do not really assume it. We infer it from what we observe. We also have no evidence that the laws are different elsewhere. But it is not absolutely certain. IF we were to find evidence that they were different, we would change our theory.

Such a faith in the existence of such laws in the first place is necessary for science to flourish. Accordingly, if we see that galaxies and quasars exist right up to the limits of our horizons it is reasonable to believe that they do so beyond.

And I would not call that faith. It is reasonable inference based on available information. It is not necessary to accept hypothetical postulates in order for science to flourish. On the contrary, it is necessary to question all assumptions and entertain any possibility that is not inconsistent with the known facts.

Andrew Mason

 

[Garth]

Andrew - then we agree to disagree - in my understanding and experience to have reasonable faith ("confidence in" - OED) and to question are not incompatible, indeed I would say they are the opposite sides of the same coin in my book.

I would even go as far as to say the opposite of reasonable faith is not doubt - it is certainty.

The crucial aspect here though, in our use of terminology, is whether we are prepared to conceive of a universe beyond our horizons; as you say, "We have a model or theory that says that the laws of physics are the same." I am prepared to extend that to apply beyond our horizons, but with the caveat that we cannot be sure, just that we "entertain any possibility that is not inconsistent with the known facts.".
- Garth

 

[Neo]

We are. I would say that is not an act of faith. We have evidence that it is safe to fly. We know there is a risk. We accept the risk and hope for the best.



I would not say that it is faith. We have a model or theory that says that the laws of physics are the same. We do not really assume it. We infer it from what we observe. We also have no evidence that the laws are different elsewhere. But it is not absolutely certain. IF we were to find evidence that they were different, we would change our theory.




And I would not call that faith. It is reasonable inference based on available information. It is not necessary to accept hypothetical postulates in order for science to flourish. On the contrary, it is necessary to question all assumptions and entertain any possibility that is not inconsistent with the known facts.

Andrew Mason

I, of course, agree with Andrew. The entire situation is isomorphic to dialogue with Christian zealots claiming the theory of evolution is just another cockamamie theory that scientists have put their stock in in the same way that Christians place their faith in god. The term "theory" seems to have been hybridized by popular misconception to have the same or similar meaning to hypothesis.

Nonetheless, it's a trivial issue that we should avoid bickering over in a physics forum. Andrew, do you believe there was time dilation in the young universe due to rapid spatial expansion? Or would you imagine that time would expand with space since they're intricately connected through the continuum? Originally my conjecture was that the expansion of space would dilate time but now I'm more inclined to believe that spatial expansion caused time to expand as well.

An idea I had was that the rapid expansion of space could cause the formation of dark matter and the curvature of space would explain its clumping. This doesn't seem to hold true based on what I've recently read since apparently space can expand faster than light in vacuo without exhibiting the properties a particle would if so accelerated.

And if it is true that some implications of relativity cannot be applied to space itself as a vector, then is it possible for time to have "expanded" during the explosive growth of space in the early universe? What would this mean, exactly?

 

[Andrew Mason]

Andrew, do you believe there was time dilation in the young universe due to rapid spatial expansion? Or would you imagine that time would expand with space since they're intricately connected through the continuum? Originally my conjecture was that the expansion of space would dilate time but now I'm more inclined to believe that spatial expansion caused time to expand as well.

I can't answer your question. I don't understand time, space or mass quite well enough to make my comments worth much. I majored in math and physics as an undergraduate - and I ended up in law, so go figure.

FWIW, we have to keep in mind that in the absence of matter, space and time have no meaning. For space and time to exist, there must be a frame of reference (by which space and time are measured). Mass creates a frame of reference and without mass, there can be no frame of reference. So concepts of space and time have meaning only in relation to mass. Point one.

Energy is defined in terms of mass. Energy has meaning only in relation to mass. You cannot have a universe that is all energy and no mass. Such a universe would have no dimensions (spatial or temporal) and no meaning. Point two.

Space time and energy have meaning only if there is more than one point of matter. If there was just one point of reference, we could not measure distance. There would be no motion from one point to another. Since time is the measure of change, there would be no time. Point three.

So, the key to understanding what was happening to space and time during the big bang is to understand what was happening to matter.

If the conditions at the time of the big bang were such that matter formed spontaneously - as a sort of chain reaction in a process by which the creation of matter fed the creation of more matter - then space and time would naturally follow, in effect being created as a necessary byproduct of the creation of mass.

An idea I had was that the rapid expansion of space could cause the formation of dark matter and the curvature of space would explain its clumping. This doesn't seem to hold true based on what I've recently read since apparently space can expand faster than light in vacuo without exhibiting the properties a particle would if so accelerated.

I think of dark matter as something that defines a frame of reference but which cannot interact physically with matter or energy as we know it. Its existence would suggest that it did not result from our big bang. The big bang seems to have created matter and energy that interact with each other and obey the same laws of physics. We may be able to detect dark matter only by its gravitational effect (the way it affects space and time).

And if it is true that some implications of relativity cannot be applied to space itself as a vector, then is it possible for time to have "expanded" during the explosive growth of space in the early universe? What would this mean, exactly?

I have no idea. I am struggling with the concept of how the observable universe could be wider in light years than double its age in years (e.g 13.7 billion years old and >27.4 billion light years across. I don't get it. And I guess that's why I make my living in law.

Andrew Mason

 

[Garth]

Andrew - although meaning of language is important I am glad we are talking physics and not semantics!
You have made a number of statements as matter of fact that not all would agree with.

FWIW, we have to keep in mind that in the absence of matter, space and time have no meaning. For space and time to exist, there must be a frame of reference (by which space and time are measured). Mass creates a frame of reference and without mass, there can be no frame of reference. So concepts of space and time have meaning only in relation to mass. Point one.

Einstein's field equations have solutions when the universe is empty p=rho=o, the Milne universe [R(t) = t].

Energy is defined in terms of mass. Energy has meaning only in relation to mass. You cannot have a universe that is all energy and no mass. Such a universe would have no dimensions (spatial or temporal) and no meaning. Point two.

Einstein's field equations have solutions when the universe is full of radiation p=1/3 rho c^2, it was the radiation universe [R(t) = t^(1/2)]. Matter (as we know it) would not have existed in the first stages of the Big Bang.

Space time and energy have meaning only if there is more than one point of matter. If there was just one point of reference, we could not measure distance. There would be no motion from one point to another. Since time is the measure of change, there would be no time. Point three.

You are right to point out that in order to measure these concepts now we need matter and laboratory standard units of mass, length and time in order to compare cosmological data with, cosmology is normally happy to project these laboratory standards back into the first microsecond of the BB.

So, the key to understanding what was happening to space and time during the big bang is to understand what was happening to matter.

In this first 10^(-43) sec. until 10^(-34) sec., when Inflation is said to have set in, no particles would have existed – it was too ‘hot’, however the standard model confidently believes it understands what was happening to space and time during this epoch [R = t^(1/2)].

If the conditions at the time of the big bang were such that matter formed spontaneously - as a sort of chain reaction in a process by which the creation of matter fed the creation of more matter - then space and time would naturally follow, in effect being created as a necessary byproduct of the creation of mass.

A question, "How is matter created if not out of energy?"

I think of dark matter as something that defines a frame of reference but which cannot interact physically with matter or energy as we know it. Its existence would suggest that it did not result from our big bang. The big bang seems to have created matter and energy that interact with each other and obey the same laws of physics. We may be able to detect dark matter only by its gravitational effect (the way it affects space and time).

About Dark Matter your guess is as good as anybody else's!

I am struggling with the concept of how the observable universe could be wider in light years than double its age in years (e.g 13.7 billion years old and >27.4 billion light years across.

Einstein's equations give rise to the possibility of a flat or hyperbolic space-time, in which the universe is infinite, although we would not be able to see beyond our horizons. Do you not consider such a universe is possible? I fully understand your original post (although our dialogue led to that semantic discussion) that as we would never be able to see such regions beyond our event horizon we could only conceive of their existence by 'belief' and not observation.
Garth

 

[Andrew Mason]

Einstein's field equations have solutions when the universe is empty p=rho=o, the Milne universe [R(t) = t].

So do Newton's laws of motion. What meaning would they have?

Einstein's field equations have solutions when the universe is full of radiation p=1/3 rho c^2, it was the radiation universe [R(t) = t^(1/2)]. Matter (as we know it) would not have existed in the first stages of the Big Bang.

For the universe to begin, a frame of reference had to come into existence. A universe full of radiation but no matter would contain no frame of reference by which time or space can be measured or have meaning. As soon as you define a frame of reference, it is implicit that matter, in some form, exists.

A question, "How is matter created if not out of energy?"

I don't know. Why is there matter and energy at all? Why is there not simply emptiness? If I knew the answer to that question, I would not be practising law.
All I would say is that if there was simply emptiness, there would be no frame of reference by which to measure anything. You could say that the universe was empty or infinite. Neither would have any meaning.

Einstein's equations give rise to the possibility of a flat or hyperbolic space-time, in which the universe is infinite, although we would not be able to see beyond our horizons. Do you not consider such a universe is possible?

I see nothing that makes it impossible. My approach would be: what meaning would it have?

Andrew Mason

 

[Garth]

I, of course, agree with Andrew. The entire situation is isomorphic to dialogue with Christian zealots claiming the theory of evolution is just another cockamamie theory that scientists have put their stock in in the same way that Christians place their faith in god. The term "theory" seems to have been hybridized by popular misconception to have the same or similar meaning to hypothesis.

I am at a loss as to where this comes from.
I have used the word "faith" to mean "confidence in" (OED) as in, "I have faith/confidence in Andrew as a lawyer to get me acquitted of this false charge."

I take as understood that the word ‘faith’ is opposed to “have proof”, thus although Andrew says, “We have evidence that it is safe to fly. We know there is a risk. We accept the risk and hope for the best.” The very fact that he has to hope for the best means he does not have proof that it is safe to fly, the evidence is not ‘beyond reasonable doubt’. Therefore we have to have faith in, or put our confidence/trust in, in the pilot’s ability etc.

It is an important point, because when we are dealing with the depths of the universe we do not have ‘proof beyond reasonable doubt’. Indeed doubt is very much the issue for the sake of good scientific practice, we question and test against the observable evidence – the data - our assumptions.

May the unwillingness to use the word ‘faith’ be a desire for a certainty that the evidence will not bear?

Thus to go back to our original point I have confidence in, or faith, that the universe extends beyond our event and particle horizons, and applying the Copernican Principle, that, at a similar epoch in cosmic history, it looks pretty much the same as it does around here.

- Garth

 

[Andrew Mason]

It is an important point, because when we are dealing with the depths of the universe we do not have ‘proof beyond reasonable doubt’. Indeed doubt is very much the issue for the sake of good scientific practice, we question and test against the observable evidence – the data - our assumptions.

May the unwillingness to use the word ‘faith’ be a desire for a certainty that the evidence will not bear?

I think the distinction is between faith and 'rational inference' not between faith and 'certainty'. I can draw a rational conclusion from evidence but I need not be certain. A belief based on conjecture or speculation is 'faith', not rational inference.

Thus to go back to our original point I have confidence in, or faith, that the universe extends beyond our event and particle horizons, and applying the Copernican Principle, that, at a similar epoch in cosmic history, it looks pretty much the same as it does around here.

I would interpret "beyond our event and particle horizons" to mean "beyond its ability to affect anything that we can observe or detect". If some part of the universe or another universe has affected or could affect our part of the universe in some way, then it would not be "beyond our event and particle horizons".

Some things are unknowable. Whether a part of the universe exists that is truly "beyond our particle or event horizons" is, by definintion, unknowable. Belief in its existence is, therefore, a matter of faith. It is not a matter for science.

Andrew Mason

 

[Neo]

For the universe to begin, a frame of reference had to come into existence. A universe full of radiation but no matter would contain no frame of reference by which time or space can be measured or have meaning. As soon as you define a frame of reference, it is implicit that matter, in some form, exists.

Not necessarily true. The frame of reference could be a form of electromagnetic radiation. For instance, a photon. If you define matter as having mass, you could define a photon as a frame of reference without implicating the existence of matter.

Certainly, for the universe to begin, dimensions had to come into existence. Most importantly, time. But it is entirely possible that a universe full of cosmic background radiation would contain frames of reference for the measurement of dimensions.

 

[Andrew Mason]

Not necessarily true. The frame of reference could be a form of electromagnetic radiation. For instance, a photon. If you define matter as having mass, you could define a photon as a frame of reference without implicating the existence of matter.

I am having trouble conceiving of a photon's frame of reference. The only way I can give any meaning to a frame of reference for a photon is by referring to a point in space/time. But a photon is always moving at the speed of light relative to such a point in space/time.

Certainly, for the universe to begin, dimensions had to come into existence. Most importantly, time. But it is entirely possible that a universe full of cosmic background radiation would contain frames of reference for the measurement of dimensions.

This statement has no meaning, to me, since radiation is always moving at the speed of light with respect to all frames of reference. How do you define the frame of reference?

Andrew Mason

 

[Garth]

I think the distinction is between faith and 'rational inference' not between faith and 'certainty'. I can draw a rational conclusion from evidence but I need not be certain. A belief based on conjecture or speculation is 'faith', not rational inference.

Andrew are you not restricting the use of the word 'faith', possibly because of its religious overtones?

The word has a quite common non-religious meaning as defined in the dictionary ["confidence" - (quite apart from its other meaning 'loyalty' as in "faithful friend")] as used in the sentence, "I have faith in your ability as a lawyer to get me acquitted of this charge." I do not have the proof that you will do so, but based on your record and ability etc, and probably a bit of wishful thinking on my part, I am willing to trust my future into your charge.

And yes cosmology does also have a measure of conjecture and speculation and not a little wishful thinking as well - as in the thread on multiverses.

Newtons laws would not have any meaning in the empty or radiation filled universe but Einstein's equations do, the presence, or absence, of energy affects the curvature of space-time. The interesting prediction of GR is that an empty universe would still have geometry and a non-trivial geometry at that. It would be hyperbolic and a set of infinitesimal test particles would be able to detect that curvature. Though in itself that is just a 'gedanken' thought experiment, nevertheless the presence of that solution as an asymptotic limit is significant to a physical universe with matter in it. Just as flat space-time is significant to the Schwarzschild solution of the gravitational field around a spherical and static mass as the r goes to infinity asymptotic limit.

The galaxies beyond our event horizon still influence the overall gravitational field and hence geometry of our universe just as the mass inside the event horizon of a black hole affects the gravitational field outside it.
Garth

 

[Garth]

Not necessarily true. The frame of reference could be a form of electromagnetic radiation. For instance, a photon. If you define matter as having mass, you could define a photon as a frame of reference without implicating the existence of matter.

Certainly, for the universe to begin, dimensions had to come into existence. Most importantly, time. But it is entirely possible that a universe full of cosmic background radiation would contain frames of reference for the measurement of dimensions.

You cannot anchor a frame of reference (FoR) to electromagnetic radiation as the speed of light is invariant in all inertial frames, however you can define a FoR to the electromagnetic bath of the CMB, it is that one in which the CMB is globally isotropic. But which came first? The energy of the CMB and an 'absolute' FoR or the FoR in which the CMB is isotropic, anchored onto whatever matter was in the universe?

 

[Neo]

You cannot anchor a frame of reference (FoR) to electromagnetic radiation as the speed of light is invariant in all inertial frames, however you can define a FoR to the electromagnetic bath of the CMB, it is that one in which the CMB is globally isotropic. But which came first? The energy of the CMB and an 'absolute' FoR or the FoR in which the CMB is isotropic, anchored onto whatever matter was in the universe?

Not only is a photon a frame of reference but it's also inertial as dv/dt=0. The only thing it's not a good frame of reference for is time.

An interesting idea. Because the derivative of the velocity of time (Vt) over time (t) is nonzero, an inertial reference frame is not possible.

dVt/dt<0 for a photon in vacuo

The velocity of time itself slows down (dilates) and therefore the "acceleration of time" is non-zero (non-inertial).

Can time be thought of as a vector since it's reversible quantum mechanically? It would give more meaning to phrases like "thermodynamic arrow."

 

[Andrew Mason]

Not only is a photon a frame of reference but it's also inertial as dv/dt=0. The only thing it's not a good frame of reference for is time.

I agree that, insofar as 'acceleration' has any meaning to a photon, it doesn't have any (its speed is constant, so dv=0). But that doesn't produce a frame of reference. A photon will always be moving (at speed c) relative to any frame of reference. 19th century physicists conjured up the aether in order to give light a frame of reference. Unless you want to go back there, and I don't, matter is needed in order to give a photon a frame of reference.

An interesting idea. Because the derivative of the velocity of time (Vt) over time (t) is nonzero, an inertial reference frame is not possible.

dVt/dt<0 for a photon in vacuo

What is the velocity of time?

The velocity of time itself slows down (dilates) and therefore the "acceleration of time" is non-zero (non-inertial).

Can time be thought of as a vector since it's reversible quantum mechanically? It would give more meaning to phrases like "thermodynamic arrow."

Perhaps you could explain a little more clearly. I am missing a few of your concepts.

Andrew Mason

 

[Chronos]

Objection. Assumes facts not in evidence. A photon is not a valid reference frame.

 

[Garth]

Objection. Assumes facts not in evidence. A photon is not a valid reference frame.

I agree in general, because of the invariance of the speed of light; however a frame of reference can be defined by the electromagnetic CMB, it is that in which the CMB is globally isotropic. The nett velocity of our Galaxy with respect to the microwave background is 603 km/sec in the direction
R.A. 10.4 hr,
dec. -18 deg
(Nature 270 pg 9. 3 Nov 77).
Very interestingly - or completely irrelevantly - the Gravity Probe B satellite seems to have a tiny anomalous acceleration in the oppoiste direction to this point in the sky - almost as if it is being 'left behind' in some sense. See
http://einstein.stanford.edu/highlights/hlindexmain.html and click on highlight for 20 Aug 04, I quote from that highlight:
"About ten days ago, we began to notice that while in primary drag-free mode, the ATC was requiring more helium propellant than planned to counter an unexpected force along the spacecraft ’s roll axis—that is, in the direction of the guide star."
The guide star IM Pegasi is within 7 deg of the antipodean position to the direction of the galaxy's motion relative to the CMB bath of radiation.
Of course this is most probably caused by just a dodgy thruster or two, but it is much more interesting to think of it as an anisotropy of inertia wrt the Centre of Mass/Momentum of the entire universe!
Garth

 

[Neo]

I agree that, insofar as 'acceleration' has any meaning to a photon, it doesn't have any (its speed is constant, so dv=0). But that doesn't produce a frame of reference. A photon will always be moving (at speed c) relative to any frame of reference.

Acceleration has meaning to all particles and photons exhibit particulate behavior. I know it "doesn't produce a frame of reference;" the invariance of velocity causes photons to exhibit inertia. The interesting aspect is the reasoning that invalidates vacuum light as an inertial reference frame.

We're dealing with the invariance of luminal velocity in vacuo relative to any inertial reference frame. Now imagine a photon in the outer universe that is on a space-time manifold, which is itself expanding faster than c based on the Hubble law. The only reference frame that it is not moving at velocity c relative to is time!

The expansion of the universe over time causes the photon to move faster than c relative to time. Isn't that elegant? Can time be conceived of as a bi-directional vector quantity on the Planck microscale? Can it be conceived of as an inertial reference frame since it cannot *universally* dilate or contract? Can an observer on an inertial reference frame observe light traveling faster than c?

What happens, theoretically, if light is propagating at c in the distant universe, where space itself is traveling faster than c?

 

[Neo]

An idea of mine is that there are such things as waves of time that travel faster than luminal velocity in vacuo in the same way that it is possible for space itself to travel faster than c without invalidating relativity.

 

[Andrew Mason]

Acceleration has meaning to all particles and photons exhibit particulate behavior. I know it "doesn't produce a frame of reference;" the invariance of velocity causes photons to exhibit inertia. The interesting aspect is the reasoning that invalidates vacuum light as an inertial reference frame.

This is the first time I have ever heard of the invariance of the speed of light being called 'inertia'.

We're dealing with the invariance of luminal velocity in vacuo relative to any inertial reference frame. Now imagine a photon in the outer universe that is on a space-time manifold, which is itself expanding faster than c based on the Hubble law.

How, exactly, does the Hubble law show this? Such a phenomenon would be inconsistent with the principle of relativity.

The only reference frame that it is not moving at velocity c relative to is time!

I am not quite sure how "time" becomes a frame of reference;

The expansion of the universe over time causes the photon to move faster than c relative to time. Isn't that elegant? Can time be conceived of as a bi-directional vector quantity on the Planck microscale? Can it be conceived of as an inertial reference frame since it cannot *universally* dilate or contract? Can an observer on an inertial reference frame observe light traveling faster than c?

Not if the principle of relativity is correct. I would need evidence to show that the principle of relativity is not correct in our universe.

What happens, theoretically, if light is propagating at c in the distant universe, where space itself is traveling faster than c?

That was kind of my point: space, in the absence of matter, doesn't have a reference frame. If the principle of relativity is correct, the situation you pose cannot arise. It is not just that it cannot physically arise. It is really that our concepts of space and time are inextricably tied to the properties of matter and energy.

The question whether light can be traveling faster than c is a little like asking, "what if a second became shorter". 1. If a second became shorter and we could observe it, we wouldn't call it a second. 2. If the second became shorter because all activity in the universe sped up at exactly the same rate so that what we measured as a second became shorter, we would measure it as a second and we would have no way of knowing that the second had become shorter. Either way, a second cannot, by definition, become shorter than one second.

Andrew Mason

 

[Garth]

That was kind of my point: space, in the absence of matter, doesn't have a reference frame. If the principle of relativity is correct, the situation you pose cannot arise. It is not just that it cannot physically arise. It is really that our concepts of space and time are inextricably tied to the properties of matter and energy.

The Friedmann universe does attribute such a reference frame to space-time whether it is empty or not; it is that co-moving with the observer extended out to the far reaches of space and time.

Weyl’s hypothesis was that a true infinitesimal geometry could only restrict the space-time manifold, M, to a class of conformally equivalent Lorentz metrics and not just to a unique metric as in GR. These metrics are related through a conformal transformation.

This means there is a latitude in the definition of units of measurement M, L & T in our observation and interpretation of distant objects. However, the standard GR view is that it is possible to extend the space-time continuum, with a coordinate and unit system based on us, the observer, out to such regions and hence talk about "empty space" expanding, possibly super-luminally, with observed objects such as quasars out there being carried along with it.

As has been the subject of earlier posts in this thread the question is whether it is appropriate to speak of objects that you can see receeding faster than the speed of light when their observed temporal order has not been reversed. Would it not make more sense to re-define the units of time and distance to keep such objects sub-luminal?.

 

[Andrew Mason]

The Friedmann universe does attribute such a reference frame to space-time whether it is empty or not; it is that co-moving with the observer extended out to the far reaches of space and time.

When you create the concept of an 'observer' relative to whom light travels at speed c, you necessarily create the concept of 'mass'. By definition, then, such a universe is not empty. In the absence of mass, you simply cannot have a point in space-time relative to which light travels at speed c. To maintain that you can requires reinventing the concept of aether.

This means there is a latitude in the definition of units of measurement M, L & T in our observation and interpretation of distant objects. However, the standard GR view is that it is possible to extend the space-time continuum, with a coordinate and unit system based on us, the observer, out to such regions and hence talk about "empty space" expanding, possibly super-luminally, with observed objects such as quasars out there being carried along with it.

I don't think it is correct to say that the standard view of General Relativity is that it is possible for empty space to expand at a speed greater than c or that it would be possible for objects to be carried with it. It certainly was not Einstein's view.

As has been the subject of earlier posts in this thread the question is whether it is appropriate to speak of objects that you can see receeding faster than the speed of light when their observed temporal order has not been reversed. Would it not make more sense to re-define the units of time and distance to keep such objects sub-luminal?.

The point of relativity is that you cannot have objects with mass traveling at a speed greater than c. It is not simply that such objects would require an infinite amount of energy. It is not a matter of redefining time and distance to keeps such objects sub-luminal. In the frame of reference of such objects, light originating in them will move away from them at speed c. This is the fundamental principle of relativity. Therefore such will always appear to be moving at a speed less than c.

Or you could look at it this way: it is impossible for something from which information originates to be moving at a speed greater than c because in order to provide us with information about its existence, we would be receiving information in the form of some kind of radiation moving away from the object and traveling to us. In order for that to occur, the radiation would have to travel faster than c. This is a violation of the principle of relativity.

Andrew Mason