Time Dilation & big bang Question

[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

 

[Garth]

Andrew - Violation? the Principle of Special Relativity but not General; actually I agree with you but you will find from the earlier posts on this thread that many(the GR community) do not!
- Garth

 

[Andrew Mason]

Andrew - Violation? the Principle of Special Relativity but not General; actually I agree with you but you will find from the earlier posts on this thread that many(the GR community) do not!
- Garth

I don't pretend to understand General Relativity in any great depth. But I think I understand the principle of equivalence and the concept that gravity/acceleration affects the structure of space-time as observed in the frame of reference of the accelerating mass or the gravitational field. I don't really see how the existence of matter traveling at a speed in excess of c is consistent with General Relativity. Perhaps you could enlighten me.

[Note: about acceleration and gravity: A body experiencing a constant acceleration will experience a continuous increase in speed, at a constant rate intially. As its speed approaches the speed of light, its (relativistic) mass will increase rapidly. But it will not approach infinity because as the mass increases, its acceleration will decrease proportionately so that its rate of change of relativistic mass will approach 0:
<br /> \lim_{t\rightarrow\infty} \frac{dm}{dt} = 0 \implies \lim_{t\rightarrow\infty} m \ne \infty<br />



That mass limit can be worked out. The object will ultimately be observed as a much more massive object moving at constant speed. So, as I see it, the kinematics under general relativity approaches that of special relativity at speeds approaching c.

I think this is must correct but I am just working from first principles. If it isn’t, I am misunderstanding something, which is certainly possible.]

 

[Garth]

Andrew - the answer lies in earlier posts in this thread, if you can sort them out!
Firstly, the SR continuum of space-time is extended, potentially to infinity.

Secondly, "the presence of mass tells space-time how to curve and curved space-time tells mass how to move" according to Einstein's field equation.

Thirdly, by assuming homogeneity and isotropy, the Copernican Principle applied to the whole universe, that field equation can be solved for the whole universe. This allows three possibilities: the universe is spatially spherical and finite, that it is hyperbolic and infinite, or that it is mid way between the two and flat and infinite. Whether it is finite or infinite depends on whether the average density (which controls the cosmological curvature) is more than, or less than, the critical density. The actual density hovers so near this value that for seventy years it has been too close to call.

Fourthly, the universe is either expanding or contracting - we observe Hubble red shift so that is interpreted as expansion.

Fifthly, it is space-time itself that is expanding, the galaxies are simply being carried along with it, this is fundamentally different to the SR case of objects moving within space-time. Ideal galaxies are at rest embedded in an expanding space-time. As the velocity of recession is proportional to distance, at a certain distance that velocity reaches, and beyond exceeds, light speed c.

Sixthly, and this has been the subject of much of this thread, according to the standard convention of measuring cosmological distance and time it is possible to observe objects whose velocity you calculate to be greater than c. In an decelerating universe the light from a super-luminal object can eventually catch up with us as our space-time has slowed down and as we are embedded in it we 'slow down too', in an accelerating universe the light from a sub-luminal object can eventually reach us by which time the space-time of that object has accelerated beyond c. As temporal order has not been reversed I prefer to define time and distance so that as such an object's cosmological red-shift approaches infinity its velocity approaches c.
- Garth

 

[Andrew Mason]

Fourthly, the universe is either expanding or contracting - we observe Hubble red shift so that is interpreted as expansion.

Hubble's Law, which says that the speed of a distant object is proportional to its distance from us, is exactly what one would expect if all the objects in the universe had a common origin.

Fifthly, it is space-time itself that is expanding, the galaxies are simply being carried along with it, this is fundamentally different to the SR case of objects moving within space-time. Ideal galaxies are at rest embedded in an expanding space-time.

This is by no means established by evidence. The concept is inconsistent with the principles of Relativity. Are you not reinventing the concept of aether?

As the velocity of recession is proportional to distance, at a certain distance that velocity reaches, and beyond exceeds, light speed c.

That does not follow at all. Hubble's Law, like Newton's Laws, is derived from observations of objects moving at non-relativistic speeds. You cannot keep a simple linear relation and extrapolate to infinity.
If all matter and energy arose from the Big Bang, the fastest objects define the outer edge of the universe. There is no reason to think that Hubble's Law extends beyond that.

Sixthly, and this has been the subject of much of this thread, according to the standard convention of measuring cosmological distance and time it is possible to observe objects whose velocity you calculate to be greater than c.

This is not possible without abandoning the principle of relativity. How does the light ever reach us? The red shift of an object traveling at the speed of light would reduce the energy to 0 (infinite wavelength).

In an decelerating universe the light from a super-luminal object can eventually catch up with us as our space-time has slowed down and as we are embedded in it we 'slow down too',

How does such light ever leave the super-luminal object? How does it avoid redshift to 0?

In an accelerating universe the light from a sub-luminal object can eventually reach us by which time the space-time of that object has accelerated beyond c. As temporal order has not been reversed I prefer to define time and distance so that as such an object's cosmological red-shift approaches infinity its velocity approaches c.

So how do we know that it has accelerated beyond c? You seem to be ignoring relativity in all this.
BTW I assume that you mean that the wavelength of light from the receding body would approach infinity. The redshift cannot exceed the frequency of the light.

Andrew Mason

 

[Garth]

Andrew - I have just given a 'bog standard' account of the answer to your question according to the normal understanding of GR. If you look elsewhere in these forums you will find I do not necessarily accept that theory and I am prepared to criticize it too! (And like you I find it inappropriate to define a measurement of recession that results in v exceeding c before z has become infinite)

Hubble's Law, which says that the speed of a distant object is proportional to its distance from us, is exactly what one would expect if all the objects in the universe had a common origin.

Precisely Milne's point in his exposition of Kinematic Relativity
[Milne, E.A.: 1935, Relativity, Gravitation and World Structure, Clarendon Press, Oxford.
Milne, E.A.: 1948, Kinematic Relativity – A sequal to Relativity, Gravitation and World Structure, Clarendon Press, Oxford.]

This is by no means established by evidence. The concept is inconsistent with the principles of Relativity. Are you not reinventing the concept of aether?

Einstein and Friedmann would have disagreed with you.

That does not follow at all. Hubble's Law, like Newton's Laws, is derived from observations of objects moving at non-relativistic speeds. You cannot keep a simple linear relation and extrapolate to infinity.
If all matter and energy arose from the Big Bang, the fastest objects define the outer edge of the universe. There is no reason to think that Hubble's Law extends beyond that.

i. Hubble's Law is not linear, except as z goes to zero. Whether the linear, low velocity, form should be replaced by a SR form or a GR form, in which latitude exists in the definitions of time and distance, is the subject of many of the posts on this thread.
ii. Your second statement would be true of matter expanding into a SR space-time (as in Milne above) but normally it is understood that it is the (possibly infinite & homogeneous)) space-time that is expanding, in which case recession velocities do exceed light speed - our particle horizon.

This is not possible without abandoning the principle of relativity. How does the light ever reach us? The red shift of an object traveling at the speed of light would reduce the energy to 0 (infinite wavelength).

How does such light ever leave the super-luminal object? How does it avoid redshift to 0?

So how do we know that it has accelerated beyond c? You seem to be ignoring relativity in all this.
BTW I assume that you mean that the wavelength of light from the receding body would approach infinity. The redshift cannot exceed the frequency of the light.

I agree that this would be a sensible way to define cosmological velocities, on the other hand others do not. However for a standard view see the links provided earlier by Dr.Chinese
http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179.pdf
&
http://bat.phys.unsw.edu.au/~charley/papers/0310808.pdf

- Garth

 

[Andrew Mason]

Einstein and Friedmann would have disagreed with you.

I guess I don't understand what is meant by expanding space time. If it means that, by our measurements, all objects in the universe are getting farther apart as a function of time, that's fine. But I don't think you need a special concept for that. If it means that objects, are embedded in some notional frame of reference which can move more rapidly than c with respect to some other frame of reference, it seems to me that it violates relativity.

If expansion of space-time is simply an explanation for the appearance that the universe is larger than it could be if it originated at a single point in space-time and expanded at sub-c speed, then I would first question whether the appearance is really correct.

i. Hubble's Law is not linear, except as z goes to zero. Whether the linear, low velocity, form should be replaced by a SR form or a GR form, in which latitude exists in the definitions of time and distance, is the subject of many of the posts on this thread.

What is your authority for the statement that Hubble's law is not linear?
v_{exp} = H_0 d seems pretty linear to me.

ii. Your second statement would be true of matter expanding into a SR space-time (as in Milne above) but normally it is understood that it is the (possibly infinite & homogeneous)) space-time that is expanding, in which case recession velocities do exceed light speed - our particle horizon.

I view the particle horizon as the longest distance that anything (including light) could have traveled to us since the big bang. How does a particle horizon imply expansion at velocities greater than c? Any measurement of the particle horizon requires an accurate age of the universe. Until that can be determined accurately, it is a very imprecise distance.

I agree that this would be a sensible way to define cosmological velocities, on the other hand others do not. However for a standard view see the links provided earlier by Dr.Chinese
http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179.pdf
&
http://bat.phys.unsw.edu.au/~charley/papers/0310808.pdf

It is one thing to create a consistent theory. It is quite another to show that it is a correct explanation for the world we observe. Cosmology should be based on physics, not the other way around, it seems to me.

Andrew Mason

 

[Garth]

I guess I don't understand what is meant by expanding space time. If it means that, by our measurements, all objects in the universe are getting farther apart as a function of time, that's fine. But I don't think you need a special concept for that. If it means that objects, are embedded in some notional frame of reference which can move more rapidly than c with respect to some other frame of reference, it seems to me that it violates relativity.

As I said before it violates special relativity, which does not apply to gravitational fields where the space-time suffers curvature. If you are not happy with the idea of curvature, think of it as a conceptual method that obtains the correct answers for planetary orbits, light deflection by the Sun etc. This is the "instrumentalist" approach. If you are an "idealist" then you would consider that space-time is actually curved in some higher dimension.
Cosmology is applying the physics of the local fields i.e. in the solar system to the universe as a whole. The further away you get the more tentative become your conclusions, however not everybody knows that!
Garth

 

[Andrew Mason]

As I said before it violates special relativity, which does not apply to gravitational fields where the space-time suffers curvature. If you are not happy with the idea of curvature, think of it as a conceptual method that obtains the correct answers for planetary orbits, light deflection by the Sun etc. This is the "instrumentalist" approach. If you are an "idealist" then you would consider that space-time is actually curved in some higher dimension.
Cosmology is applying the physics of the local fields i.e. in the solar system to the universe as a whole. The further away you get the more tentative become your conclusions, however not everybody knows that!
Garth

I don't think it is correct to say that something can violate special relativity. It is correct to say that SR applies to inertial frames of reference and does not deal with the effects of gravity or acceleration. If I understand it correctly (which is by no means a given) GR says that gravity can bend light but does not say that gravity will slow it down. If the gravity is strong enough, time will slow down but the observer in the gravitational field will always measure the speed of light to be c. If I am not correct on this, please explain with a reference to some authority.

I am not unhappy with the idea of curvature of space-time as a conceptual model to describe what it is that gravity does. Not at all. I would go further and say that mass creates space-time. Without matter, there would be no meaning to distance or time because there would be nothing to which a frame of reference could be attached.

Andrew Mason

 

[Garth]

Andrew - the curvature of space-time applies to time as well as to space. This has the effect of introducing an extra time dilation over that caused by relative velocity as in SR. I am not saying SR is violated, it is just not adequate, or appropriate, to deal with gravitation/acceleration.

As I have said before when dealing with cosmological expansion the understanding of GR is that just as it is the 'empty space-time' that is 'curved' in the vicinity of the Sun that gives the Earth its elliptical orbit in space, a 'straight' geodesic in space-time, so also it is 'empty space-time' that is expanding and carrying everything with it in the cosmological solution.

SR deals with velocities within space-time, GR deals with the dynamics of space-time itself, geometrodynamics, and predicts accelerations and therefore velocities between otherwise mutually stationary objects that are caused by its curvature. The first chapter of Misner Thorne and Wheeler's 'Gravitation' explains the concept beautifully.

In the cosmological solution such velocities caused by the expansion of space-time, not those within space-time, can exceed light speed.

- Garth

 

[Andrew Mason]

In the cosmological solution such velocities caused by the expansion of space-time, not those within space-time, can exceed light speed.

And I don't disagree with anything you have said except the last sentence (above). It appears to me that the expansion of space-time is a mathematical construct introduced to explain certain features of the current universe that GR mathematical solutions do not explain. There is no empirical evidence to support it, yet. While it may solve these problems mathematically, the theory appears to offer no physical explanation for space-time expansion.

I am not so concerned with the possibility of space-time expansion in the very early stages of the universe (ie. the first few pico seconds of its existence). My concern is with the concept of expanding space-time in the current universe.

Andrew Mason

 

[Garth]

It appears to me that the expansion of space-time is a mathematical construct introduced to explain certain features of the current universe that GR mathematical solutions do not explain.

The expansion of space-time is a mathematical construct that is the (cosmological) solution of the GR field equation.

There is no empirical evidence to support it, yet.

Hubble Red shift is normally thought to do the trick.

My concern is with the concept of expanding space-time in the current universe.

Actually Andrew it is also my concern. The answers I have been giving you are the standard answers from GR, you might care to look at some of the other posts I have made and my particular approach to gravitational theory/cosmology called Self Creation Cosmology (SCC).
https://www.physicsforums.com/showthread.php?t=32713&page=1
https://www.physicsforums.com/showthread.php?t=41370
https://www.physicsforums.com/showthread.php?t=42286 for a start!
- Garth

 

[Andrew Mason]

SR deals with velocities within space-time, GR deals with the dynamics of space-time itself, geometrodynamics, and predicts accelerations and therefore velocities between otherwise mutually stationary objects that are caused by its curvature.

I am not sure what you mean by "otherwise mutually stationary objects". I don't know how you can have mutually stationary objects (ie. objects separated by a distance and having no relative motion) being accelerated due to each other's gravity. If the intial relative velocities are insufficient for the objects to separate indefinitely, they will either enter into orbital motion or their paths in space-time will intersect.

I also think we have to be careful in drawing fundamental distinctions between SR and GR (I am not saying you are doing that, but you may be). They are mutually consistent theories. For example, GR says that a point object that experiences acceleration due to gravity is unable to determine from local observations, that it is accelerating. It appears to itself to be an interial observer. Consequently, light will move away from such object at the speed of light. I don't see GR as leading to any result that is inconsistent with SR.

Andrew Mason

 

[Garth]

I am not sure what you mean by "otherwise mutually stationary objects".

Co-moving; a conceptual leap is required by the Friedmann cosmological solution to the GR field equation in which a fundamental separation is made between the peculiar motion of a particle within space-time and the dynamics of space-time itself. In practice it is difficult to separate the two except by reference to the isotropic CMB frame of reference.

I don't see GR as leading to any result that is inconsistent with SR.

Not in local laboratory physics in an Lorentz inertial (freely falling) frame. But in a larger laboratory tidal effects can be measured - the sign of curvature and a non-trivial Riemann tensor - and on a larger scale objects and photons can be seen "freely falling" on all kinds of orbits in a way that cannot quite be explained by a Newtonian gravitational force.
SR is consistent with observation within the scope for which it was constructed in which case GR reduces to it.
- Garth

 

[Andrew Mason]

Hubble Red shift is normally thought to do the trick.

Doppler effect seems to by the simplest and most obvious explanation for the Hubble redshift. I don't quite see how the redshift could be explained by the stretching of space-time; stretching of space, perhaps, but not time because the speed of light is not changed. just wavelength.

Andrew Mason

 

[Garth]

. I don't quite see how the redshift could be explained by the stretching of space-time;

Solve the Robertson-Walker metric for a null-geodesic.

stretching of space, perhaps, but not time because the speed of light is not changed. just wavelength.

That is correct; in the Robertson-Walker metric space-time does "stretch" in the space-like direction.
Garth

 

[Neo]

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.

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.
Andrew Mason

Relativity is not violated by space traveling faster than c.

My conjecture is that time splits the universe into three-dimensional progressions by a type of "instataneous" wave action. It would be similar to the propagation of g waves except that rather than having greater g wave propagation from strongly curved regions of space, there would be less "temporal wave" propagation, accounting for the time dilation in areas of high space curvature. Abstractly speaking, it's as if the entire temporal dimension is the pulsation of the vector components of space rotating around their own axes.

 

[Andrew Mason]

Relativity is not violated by space traveling faster than c.

I don't understand the concept of space traveling at any speed, let alone faster than c. Space cannot provide a frame of reference that has any meaning, as far as I can see. So space traveling would seem to have no meaning if matter is not carried with it. And if matter is carried with it. the speed of the matter cannot exceed c - not if the principle of relativity is correct.

My conjecture is that time splits the universe into three-dimensional progressions by a type of "instataneous" wave action. It would be similar to the propagation of g waves except that rather than having greater g wave propagation from strongly curved regions of space, there would be less "temporal wave" propagation, accounting for the time dilation in areas of high space curvature. Abstractly speaking, it's as if the entire temporal dimension is the pulsation of the vector components of space rotating around their own axes.

Nice conjecture. I am not sure I understand it. Well, actually I am quite sure I don't. Unfortunately physics is based on evidence, not conjecture.

Andrew Mason

 

[Chronos]

I didn't quite follow that either, Andrew. I would put it this way. In the very early universe all entities possible for us to observe were within our light cone [causally connected]. Once that connection is made it is unbreakable, no matter how fast the subsequent expansion took place [including superluminal expansion]. The light cone was merely stretched causing the severe redshifts in distant [ancient] objects we currently observe. They are also time-dialated in our reference frame, which is why they appear to have barely aged since their light first reached us in the early universe.

 

[juju]

Hi,

The stetching of space produces an expansion of the interval between bodies embedded in that space. However, the relative motion between the bodies (limited to c) produces a length contraction of that interval , which would limit the apparent expansion rate to C.

juju

 

[Andrew Mason]

The light cone was merely stretched causing the severe redshifts in distant [ancient] objects we currently observe. They are also time-dialated in our reference frame, which is why they appear to have barely aged since their light first reached us in the early universe.

The redshifts can be explained with relativity without the need to conjure up stretching of light cones. Why do you have to stretch space-time?

The time dilation is easy to calculate. The redshift of the cosmic microwave backgound is about 1100 which indicates that the outer parts of the universe are moving at about .9999984 c relative to us. The time dilation is just:

t_{cmb} = t_0 / \sqrt {1 - v^2/c^2}

\therefore t_{cmb} = 559 t_0

If t_0 = 13.7 \times 10^9 years, then
t_{cmb} = 24.5 \times 10^6 years.

So the region at the edge of the universe appears to have aged less than 25 million years while we have aged 13.7 billion years.

Andrew Mason

 

[Garth]

The redshifts can be explained with relativity without the need to conjure up stretching of light cones. Why do you have to stretch space-time?

The redshifts can be explained with relativity without the need to conjure up stretching of light cones. Why do you have to stretch space-time?

I presume by “relativity” you mean SR; the reason we talk about the ‘stretching’ of space-time is because that is the prediction of GR in the Robertson-Walker metric. Of course you could do away with GR and use a SR modified perhaps with a Newtonian scalar to explain gravitational forces, however such attempts are internally inconsistent (MTW pg181-6). The fact that GR ‘works’ accurately as a theory in solar system experiments gives us confidence to apply it cosmologically where it predicts cosmological red shift as a result of a space-like “stretching” of space-time or cosmic expansion.

If you look at some of my other posts you will realize that I am a maverick and personally think GR falls short in some areas of cosmology, as it requires inflation, exotic dark matter and dark energy to explain cosmological observations - none of which has yet been discovered or verified in laboratory physics even after about thirty years of intensive research, but the ‘stretching’ of space-time is not one of them.

Garth

 

[Wave's_Hand_Particle]

And I don't disagree with anything you have said except the last sentence (above). It appears to me that the expansion of space-time is a mathematical construct introduced to explain certain features of the current universe that GR mathematical solutions do not explain. There is no empirical evidence to support it, yet. While it may solve these problems mathematically, the theory appears to offer no physical explanation for space-time expansion.

I am not so concerned with the possibility of space-time expansion in the very early stages of the universe (ie. the first few pico seconds of its existence). My concern is with the concept of expanding space-time in the current universe.

Andrew Mason

This may be resolved in the near future.

T. Padmanabhan is about to make some interesting alternate suggestions with respect to these very issue's.

I believe it has to do with TWO paramiters of Constant Expansion, ie Space Expands separate from Space-Time?

I have seen a little on the ideas that all Spacetimes with matter(Galaxies) are thought to be in Contraction, and all of intervening Space external to Spacetimes, is what we actually see as Universe Expansion, but this is quite speculative.

 

[Andrew Mason]

I presume by “relativity” you mean SR; the reason we talk about the ‘stretching’ of space-time is because that is the prediction of GR in the Robertson-Walker metric. Of course you could do away with GR and use a SR modified perhaps with a Newtonian scalar to explain gravitational forces, however such attempts are internally inconsistent (MTW pg181-6). The fact that GR ‘works’ accurately as a theory in solar system experiments gives us confidence to apply it cosmologically where it predicts cosmological red shift as a result of a space-like “stretching” of space-time or cosmic expansion.

Actually I meant both SR and GR. I understand the concept of stretching of space-time due to gravity. That is a corollary to the principle of equivalence. But it is a local phenomenon. What I have problems with is the inflationary stretching of space-time for the entire universe. This is not needed to explain doppler and gravitational redshift.

Andrew Mason

 

[Garth]

Actually I meant both SR and GR. I understand the concept of stretching of space-time due to gravity. That is a corollary to the principle of equivalence. But it is a local phenomenon. What I have problems with is the inflationary stretching of space-time for the entire universe. This is not needed to explain doppler and gravitational redshift.
Andrew Mason

If GR works within the solar system, predicting the precession of Mercury's orbit etc. and is then applied, via the cosmological principle, to the universe as a whole, it predicts the space-like expansion of space-time which would lead to Hubble red shift, primordial nuclearsynthesis and the CMB, all of which have been observed.

Hence the expansion of the space-time of the universe is taken as verified scientific fact.

The going does then get tougher with unverified Inflation, and undiscovered Dark Matter and Dark Energy - but that is another story discussed in these forums elsewhere!

Garth