Time Dilation & big bang Question

[Neo]

With respect to time dilation...

During the Big Bang, when space was expanding explosively (probably at light speed?) -- what was time doing? Was time at a standstill (or very dilated) during the explosive growth of the three spatial dimensions? Or was time expanding explosively since it's in a continuum with space?

[Nenad]

With respect to time dilation...

During the Big Bang, when space was expanding explosively (probably at light speed?) --
about 3 seconds into the big bang, space expanged a lot faster than the speed of light, it had a growth spur. If you look a the age of the universe, (15 billion years), the size of it is more that 15 billion light years, making its expansion more than light speed at the beginning. And about your time question, Im not sure what you mean?

[Neo]

about 3 seconds into the big bang, space expanged a lot faster than the speed of light, it had a growth spur. If you look a the age of the universe, (15 billion years), the size of it is more that 15 billion light years, making its expansion more than light speed at the beginning. And about your time question, Im not sure what you mean?

Interesting but that is not a proof that space expanded faster than the speed of light. For instance, imagine that one part of space expanded diagnally downward toward the left and another part of space expanded diagnally upward toward the right -- both expansions at the speed of light. If you measure space from the bottom left to the top right, it is going to be more than 15 billion light years, but that is merely because space was travelling in different directions simultaneously. Right?

My question was about, what seems to me, a contradiction in the predictions of relativity theory. For instance, as a massive object expands at the speed of light, time comes to a stop. But what about the expansion of spatial dimensions? Did the expansion of the spatial dimensions during the Big Bang period slow down time or speed it up? That is, relativity implies that time slows (and eventually stops) for something that approaches the speed of light. It also teaches that space and time are in an inseparable continuum. So does time dilation not apply to the expansion of the spatial dimensions?

In other words, did time slow down during the Big Bang because space was expanding at light speed? Or does time dilation not apply to space itself?

[DrChinese]

Interesting but that is not a proof that space expanded faster than the speed of light. For instance, imagine that one part of space expanded diagnally downward toward the left and another part of space expanded diagnally upward toward the right -- both expansions at the speed of light. If you measure space from the bottom left to the top right, it is going to be more than 15 billion light years, but that is merely because space was travelling in different directions simultaneously. Right?

You are switching back to a more classical reference frame, and imagining that the diameter of a the universe is 30 billion LY. Actually, it is more like 150 billion light years in diameter for a 13.7 billion year old universe. That's a lot of expansion!

But you have a good point. Certainly there was a lot of time distortion in the early universe. As far as anyone knows, the rate of expansion of space itself is not affected by gravity. But experimental accuracy on this is poor at this time.

On the other hand, there may be interesting consequences on the development of the universe due to time dilation. DoctorDick has started a couple of threads to discuss this in Theory Development, and you might find the discussions there to be relevant.

[Neo]

You are switching back to a more classical reference frame, and imagining that the diameter of a the universe is 30 billion LY. Actually, it is more like 150 billion light years in diameter for a 13.7 billion year old universe. That's a lot of expansion!But you have a good point. Certainly there was a lot of time distortion in the early universe. As far as anyone knows, the rate of expansion of space itself is not affected by gravity. But experimental accuracy on this is poor at this time.On the other hand, there may be interesting consequences on the development of the universe due to time dilation. DoctorDick has started a couple of threads to discuss this in Theory Development, and you might find the discussions there to be relevant.

It doesn't have to be only 30 million LY based on my suggestion. I only described two dimensions with the diagnals. If you add depth to this, you might be able to account for the entire diameter. Besides, how was "150 billion years" derived?

But I think another way to account for it is because time itself was dilated by spatial expansion. That is, nothing ever moved faster than the speed of light, conforming to relativity. Instead, space expanded at the speed of light but because time itself was dilated, what seems to be 15 billion years was far longer in non-dilated time -- perhaps 150 billion years. The question arises if non-dilated time even exists if the expansion of all of space itself dilates time.

It seems to me that expansion of space is necessarily affected by the curvature of space ("gravity"). That's how the "Big Crunch" is derived.

Thanks but unfortunately I didn't find DrDick's threads remarkably insightful nor do I think he reached the same conclusions as I. They seem to be strewn with ad hominem and meaningless personality conflicts.

[DrChinese]

It doesn't have to be only 30 million LY based on my suggestion. I only described two dimensions with the diagnals. If you add depth to this, you might be able to account for the entire diameter. Besides, how was "150 billion years" derived?

But I think another way to account for it is because time itself was dilated by spatial expansion. That is, nothing ever moved faster than the speed of light, conforming to relativity. Instead, space expanded at the speed of light but because time itself was dilated, what seems to be 15 billion years was far longer in non-dilated time -- perhaps 150 billion years. The question arises if non-dilated time even exists if the expansion of all of space itself dilates time.

It seems to me that expansion of space is necessarily affected by the curvature of space ("gravity"). That's how the "Big Crunch" is derived.


For the calculation of the 150 billion LY value: Click here (http://www.space.com/scienceastronomy/mystery_monday_040524.html)

There are still multiple issues to consider here.

Much if not most of the universe is receding from us at a speed that exceeds the speed of light. A substantial portion recedes from us faster than 2c. Objects have been observed as much as 3+c and there are certainly some objects moving considerably faster apart than that. The speed of light is a limit in a local reference frame per special relativity. It is not a limit when the expansion of space-time itself is considered as a component of velocity.

But I still think the point you are making is worth discussing. It would seem logical to me that time was dilated in the very early universe and that dilation would have been a significant component for a period of time. It would need to be considered in the early evolution of space and energy, but I wonder for how long? Seconds? A million years? Or maybe seconds that dilated into a million years? I haven't seen much on that subject.

[Neo]

For the calculation of the 150 billion LY value: Click here (http://www.space.com/scienceastronomy/mystery_monday_040524.html)

There are still multiple issues to consider here.

Much if not most of the universe is receding from us at a speed that exceeds the speed of light. A substantial portion recedes from us faster than 2c. Objects have been observed as much as 3+c and there are certainly some objects moving considerably faster apart than that. The speed of light is a limit in a local reference frame per special relativity. It is not a limit when the expansion of space-time itself is considered as a component of velocity.

But I still think the point you are making is worth discussing. It would seem logical to me that time was dilated in the very early universe and that dilation would have been a significant component for a period of time. It would need to be considered in the early evolution of space and energy, but I wonder for how long? Seconds? A million years? Or maybe seconds that dilated into a million years? I haven't seen much on that subject.


Hmm...they don't demonstrate the derivation of "150 billion" though. I doubt its validity. Nonetheless, the idea of applying the Hubble law is interesting and (apparently) falsifies my idea -- that perhaps expansion of space causes time dilation. Or could it be possible that in regions where space itself is moving at greater than C there is a time loop. That is, where space is traveling greater than C, everything in that region travels backward in time?

[Neo]

Could this explain space's "infinite" nature? To clarify, if you move out enough, you'll be traveling faster than the speed of light. In these regions of space, time forms a loop upon itself. If you go to the edges of space, you will be traveling faster than the speed of light and will travel backward in time.

This would uphold the "infinite" nature of the universe. There is no limit -- it's just a time cycle.

[Neo]

Is it possible that the Heisenberg Uncertainty Principle be explained by relativity?

Electrons travel at close to the speed of light -- there must be a great degree of time dilation for electrons. Could this time dilation be one of the causes for the Uncertainty Principle?

[DrChinese]

Hmm...they don't demonstrate the derivation of "150 billion" though. I doubt its validity. Nonetheless, the idea of applying the Hubble law is interesting and (apparently) falsifies my idea -- that perhaps expansion of space causes time dilation. Or could it be possible that in regions where space itself is moving at greater than C there is a time loop. That is, where space is traveling greater than C, everything in that region travels backward in time?

The 156 billion LY diameter has some imprecision in it, no question. As we discover more and more high redshift (high z) objects it will be refined. But the basic idea is that an object traveling at N times the speed of light from us when it was emitted X billion years ago will be about (N * X) billion years away now. Plus add some for the subsequent expansion of the universe, and you get the answer. The point is there is a multiplier because as redshift (z) increases, so does N.

Dilation of time occurs even when there is no expansion of space, as has been shown in accelerators in many experiments. As far as anyone knows, there is no theoretical point at which time would move backward for anyone when objects move apart faster than c.

[Neo]

The 156 billion LY diameter has some imprecision in it, no question. As we discover more and more high redshift (high z) objects it will be refined. But the basic idea is that an object traveling at N times the speed of light from us when it was emitted X billion years ago will be about (N * X) billion years away now. Plus add some for the subsequent expansion of the universe, and you get the answer. The point is there is a multiplier because as redshift (z) increases, so does N.

Dilation of time occurs even when there is no expansion of space, as has been shown in accelerators in many experiments. As far as anyone knows, there is no theoretical point at which time would move backward for anyone when objects move apart faster than c.

I don't personally place much stock in the calculations -- they're indirect and not necessarily true, which is the point that I believe we both agree upon.

Are you implying that expansion of space at light speed cannot cause formation of matter and/or time dilation? If so, why?

In relativity, acceleration of a particle to luminal speed in vacuo as its limit causes formation of baryonic matter as a result of the energy-matter equivalence. What stops the speed of space expansion itself from causing formation of dark matter?

What if there are two subtypes of this close to light energy-to-matter conversion?

The first being what we normally expect:

1. Accelerate a mass particle to close to the speed of light and it will gain baryonic matter (due to energy-to-mass conversion).

2. Accelerate the universe to close to the speed of light and it will gain dark matter (due to the same).

Theoretical physicists don't seem to apply the implications of E=mc^2 to space itself -- why?

[mee]

For the calculation of the 150 billion LY value: Click here (http://www.space.com/scienceastronomy/mystery_monday_040524.html)

There are still multiple issues to consider here.

Much if not most of the universe is receding from us at a speed that exceeds the speed of light. A substantial portion recedes from us faster than 2c. Objects have been observed as much as 3+c and there are certainly some objects moving considerably faster apart than that. The speed of light is a limit in a local reference frame per special relativity. It is not a limit when the expansion of space-time itself is considered as a component of velocity.

But I still think the point you are making is worth discussing. It would seem logical to me that time was dilated in the very early universe and that dilation would have been a significant component for a period of time. It would need to be considered in the early evolution of space and energy, but I wonder for how long? Seconds? A million years? Or maybe seconds that dilated into a million years? I haven't seen much on that subject.


If the universe has a width it has a center? Has anyone tried to find the center?

[Mike2]

For the calculation of the 150 billion LY value: There are still multiple issues to consider here.

Much if not most of the universe is receding from us at a speed that exceeds the speed of light. A substantial portion recedes from us faster than 2c. Objects have been observed as much as 3+c and there are certainly some objects moving considerably faster apart than that. The speed of light is a limit in a local reference frame per special relativity. It is not a limit when the expansion of space-time itself is considered as a component of velocity.

But I still think the point you are making is worth discussing. It would seem logical to me that time was dilated in the very early universe and that dilation would have been a significant component for a period of time. It would need to be considered in the early evolution of space and energy, but I wonder for how long? Seconds? A million years? Or maybe seconds that dilated into a million years? I haven't seen much on that subject.
If we can never actually observe anything that is receding faster than the speed of light, then how can you say ANY portion is receding faster than c?

[DrChinese]

If we can never actually observe anything that is receding faster than the speed of light, then how can you say ANY portion is receding faster than c?

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:

Inflation and the CMB, 34 pages, PDF format (http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179.pdf)

[Neo]

Do you think it's possible for a singularity to exhibit wave-particle duality?

Is it impossible for a wave to affect the curvature of space?

[russ_watters]

Electrons travel at close to the speed of light -- there must be a great degree of time dilation for electrons. Could this time dilation be one of the causes for the Uncertainty Principle? Electrons don't travel anywhere near the speed of light except when in a particle accelerator. And when talking about the speed of electrons around an atom, the term doesn't really have any meaning.

You may have the (common) misconception that when you flip a light switch, the light turns on when the electrons that were at the switch reach the light. In fact, its just like water in a pipe - when you open a valve, the wave-front moves at the speed of sound while the water itself may move relatively slowly. Thus, if a pipe is already full, opening a valve almost immediately results in water flowing out of the pipe - a wire is already full of electrons when you flip the light switch.

[Neo]

Do you think it's possible for a singularity to exhibit wave-particle duality?

Is it impossible for a wave to affect the curvature of space?


Singularities don't exhibit wave-particle duality because they are not in motion?

Wave motion from moving massive objects causes ripples in spatial curvature...

Are gravitational waves the only type of waves that affect spatial curvature?

Can non-gravitational waves affect curvature of space, such as, perhaps temporal waves? Is it possible to conceive of time as a wave that affects the curvature of space?


It is possible for a moving massive object's wave motion to temporarily weaken/reverse the supergravity of a singularity through gravitational wave "destructive resonance?"

[Chronos]

Singularities don't exhibit wave-particle duality because they are not in motion?They are in motion.Wave motion from moving massive objects causes ripples in spatial curvature...Agreed.
Are gravitational waves the only type of waves that affect spatial curvature?Gravitational waves do not affect spatial curvature, they follow the curvature.Can non-gravitational waves affect curvature of space, such as, perhaps temporal waves? Is it possible to conceive of time as a wave that affects the curvature of space?There is no observational evidence of that.It is possible for a moving massive object's wave motion to temporarily weaken/reverse the supergravity of a singularity through gravitational wave "destructive resonance?"Not according to current theory.

[Neo]

They are in motion..

Please clarify. If singularities are in motion and wave motion from moving massive objects causes ripples in spatial curvature, then why do singularities not exhibit wave-particle duality? Or is duality unnecessary for wave motion to result from a moving dense particle?


Gravitational waves do not affect spatial curvature, they follow the curvature.

"Gravity waves are ripples in the overall geometry of space and time." http://www.physics.gmu.edu/classinfo/astr103/CourseNotes/Text/Lec06/Lec06_pt2_txt_relativityGeneral.htm

But let us for the moment say that g waves don't affect space curvature. How is it then that you propose the effect of the massive body propagates? Apparently curvature does not instantaneously change -- a wave (that we call a gravity wave) curves space differentially at light speed.

There is no observational evidence of that.
My idea is that waves can affect curvature, just in different ways than particles. It seems that the influence of particles on curvature is highly localized whereas the influence of waves is (more) universal. It is as if the particle displaces an energy field and causes these gravity waves to propagate across time-space as a result.

Waves can cause pressure. Can a singularity be thought of as pressure on space? Perhaps it is possible for certain types of waves to affect curvature.

[Jim Beam]

you must forgive me when i say that i have trouble believing that the universe is, or ever has expanded at speeds faster than that of light. it would be believable if space time itself, by that term i mean tha amount of space possible for there to be objects present expanded at speeds far greater than c. as an analogy, i will use a cup of water. water flows from the faucet at a certain maximum speed and can't flow any faster. lets assume that this speed happens to be able to accupy a space, say, a figure pulled off the top of my head, 20 mL/second. it is flowing into a container that has a capacity of 1 liter. I can stand here watching it and if my sink was big enough, and i was strong enough, i could carry a bathtub and set it down in place of the liter sized container at a speed of a few seconds. in a few seconds, the water will only have filled up less than a cL. in a few seconds, i will have added (lets say 20 gal) of possible space for the water to accupy. that speed is far greater than the spead of the "expanding" water.

bottom line is that there is much more than meets the eye when it comes to our world, and saying that certain theories/laws are the way it has t be or the way it is quite foolish

[RingoKid]

wouldn't a singularity need a medium to propagate in as a wave and if that singularity then inflated outwards to become the universe then one would have to assume the medium was infinite and the universe finite but expanding infinitely into infinity ???

With regards to the wave affect,

If spacetime is water and an object beneath the surface repersents a body that causes the water to bend around it.

Then by virtue of the object moving, it creates ripples in the surrounding water that then interact with the ripples being created by every other object in motion. These would eventually even out to be discerned as no motion in spacetime or very hard to detect given that everything in the universe is in motion in relation to everything else.

Have i mentioned waves/ripples in a spherical pond before travelling outwards at the speed of light ???

[DrChinese]

you must forgive me when i say that i have trouble believing that the universe is, or ever has expanded at speeds faster than that of light. ... bottom line is that there is much more than meets the eye when it comes to our world, and saying that certain theories/laws are the way it has t be or the way it is quite foolish

You have only to believe the persuasive evidence. Many Type 1 supernovae have been seen which are receding from us far in excess of the speed of light. Theory is being adapted to be consistent with observation.

Personally, I think it is foolish to ignore evidence you don't like. The purpose of the scientific method is to remove personal prejudice from the equation.

[Garth]

You have only to believe the persuasive evidence. Many Type 1 supernovae have been seen which are receding from us far in excess of the speed of light. Theory is being adapted to be consistent with observation.

Sorry this just isn't correct. If the Type 1 supernovae were receding from us in excess of the speed of light they would be beyond our cosmic event horizon and their light would be "more than" infinitely red shifted so we couldn't see them.

I have no doubt that there are galaxies and supernovae beyond the event horizon which cannot be seen, however their superluminal velocity does not contravene SR because it is space-time itself which is expanding in GR, the galaxies etc. are just being carried along with it.

The Type 1 supernovae referred to are probably those distant S/N that are observed to be dimmer than expected by the standard theory previous predictions. It is therefore concluded (theory dependent - ancient S/N might just be intrinsically dimmer than more recent ones) that the universe has accelerated in its expansion rather than the usually predicted deceleration.

I hope this is helpful, Garth.

[jcsd]

Sorry this just isn't correct. If the Type 1 supernovae were receding from us in excess of the speed of light they would be beyond our cosmic event horizon and their light would be "more than" infinitely red shifted so we couldn't see them.

I have no doubt that there are galaxies and supernovae beyond the event horizon which cannot be seen, however their superluminal velocity does not contravene SR because it is space-time itself which is expanding in GR, the galaxies etc. are just being carried along with it.

The Type 1 supernovae referred to are probably those distant S/N that are observed to be dimmer than expected by the standard theory previous predictions. It is therefore concluded (theory dependent - ancient S/N might just be intrinsically dimmer than more recent ones) that the universe has accelerated in its expansion rather than the usually predicted deceleration.

I hope this is helpful, Garth.

No we can see objects in the universe that have recession velocites greater than c*

* http://bat.phys.unsw.edu.au/~charley/papers/0310808.pdf

[Garth]

Now that was an interesting paper - thank you for bringing my attention to it.

However I believe confusion can still reign! We note that apart from their peculiar motion cosmological red shifts are not caused by the objects moving at all, cosmological red shift can be understood as a gravitational red shift caused by the photons being emitted deep in the universe's gravitational well, when it was smaller and more dense.

To measure velocity we have to measure distance and time. We therefore have to define both, and in an expanding universe specify whether we are talking about metric time, conformal time or some other transformation of time. Distance can be defined from time if the assumption is made that c is constant. (If we allow c to vary then other things vary with it such as the fine structure constant and we can become even more confused!)

Time can be defined so the universe isn't expanding at all, such as in Hoyle's mass-field theory and in the Jordan frame of Self Creation Cosmology.

Davis & Linewaver define the distance used to derive velocity to be the Proper distance D along a surface of constant time, dt=0, (Their paper quoted above eq 12 pg 18).

So such super-luminal objects referred to above are exceeding the velocity of light today, not when they emitted the photon that is received today.

I agree with that, under certain circumstances such velocities can exceed the speed of light.

My definition of velocity was their velocity at the time of emission, measured as the rate of change of distance along the surface of constant time then, not now.

[Mike2]

However I believe confusion can still reign! We note that apart from their peculiar motion cosmological red shifts are not caused by the objects moving at all, cosmological red shift can be understood as a gravitational red shift caused by the photons being emitted deep in the universe's gravitational well, when it was smaller and more dense.
Garth, do you feel this view has wide acceptance among cosmological scientists. I'm under the impression that they are ignoring changing gravitational effects of the universe as a whole. Thanks.

[Garth]

Mike2 - Cosmological Red shift of recession and cosmological gravitational red shift are the same thing interpreted from different perspectives. The former is as interpreted by a "3+1" observer, the latter as interpreted in "4" space-time. Remember we do not see galaxies/quasars/S/N receeding at all, we see red shift and interpret it as recession.
Garth

[Mike2]

Mike2 - Cosmological Red shift of recession and cosmological gravitational red shift are the same thing interpreted from different perspectives. The former is as interpreted by a "3+1" observer, the latter as interpreted in "4" space-time. Remember we do not see galaxies/quasars/S/N receeding at all, we see red shift and interpret it as recession.
Garth
Thank you, but my question is how prevalent is this alternative interpretation of redshift being due to universal gravity. Is this main stream, or are you only talking about your own understanding of the situation? Thanks.

[hellfire]

My definition of velocity was their velocity at the time of emission, measured as the rate of change of distance along the surface of constant time then, not now.
If I understood your definition correctly I think you are incorrect anyway. An object having a speed v = c wrt to us now, had a speed v > c wrt to us in the past. This is due to the fact that, although it was closer wrt to us, the Hubble parameter was greater (much greater) than now. Try some values of z in this calculator:

http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html

for Matter Density = 0.27, Cosmological Constant = 0.73 and Hubble parameter today = 71 and look at ?speed away from us now? and ?speed away from us then?. The calculator is based on a mumerical integration of the Friedmann equation.

[Garth]

Mike2 - It is sometimes acknowleged, and was stressed by maverics like Fred Hoyle. The mathematics is to be found in Synge - "Relativity the General Theory" 1955 and referred to by people like Dicke. Synge had an interesting twist to the interpretation. His view was that all gravitational red shifts, even between objects that are at rest wrt each other at different levels in a gravitational potential well are doppler shifts. The worldlines of such objects are just diverging in space-time due to curvature. This interpretation of Synge has been criticised in the publications although I don't have the reference now.
My view is that taking the '4' view of a block space-time there is no movement. World lines may diverge or converge because of curvature or inertial forces and one 'draws' the null-geodesics between them. Two wave fronts originating on one object's worldline cross another's worldline at a greater or lesser local time interval apart and hence the phenomena is interpreted as a red or blue shift. If there is no movement in such a view, as time is already in the diagram, then it may be misleading to call it doppler shift as Synge does, gravitational red/blue shift will do very nicely. It also confuses between gravitational or cosmological red/blue shifts and actual doppler shifts caused by real motion within space-time. So I call gravitational red shift just that and understand that cosmological red shift may be interpreted as the same phenomenum.

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.

If cosmological red shift is interpreted as cosmological recession then the crucial distance may not be that along our present space-like 'now' membrane dt=0 when observed, but along the space-like 'then' membrane when emitted. It is a matter of interpretation and definition.

Converting red shift to velocity is theory dependent, which formula do you use? The classical one, the SR one or a GR one? Davis and Linewaver are perfectly entitled to use their definition but there are others who would see things differently and who therfore may come to different conclusions to them. The confusion they refer to may be just one of convention (of definitions) rather than substance.

In my view, if cosmological red shift is to be understood as velocity rather than gravity then I prefer to understand that the red shift approaches infinity as the velocity approaches c and hence the object cannot be seen if v = c or v > c.

[DrChinese]

... 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.

If cosmological red shift is interpreted as cosmological recession then the crucial distance may not be that along our present space-like 'now' membrane dt=0 when observed, but along the space-like 'then' membrane when emitted. It is a matter of interpretation and definition.

Converting red shift to velocity is theory dependent, which formula do you use? The classical one, the SR one or a GR one? Davis and Linewaver are perfectly entitled to use their definition but there are others who would see things differently and who therfore may come to different conclusions to them. The confusion they refer to may be just one of convention (of definitions) rather than substance.


You are saying that the "extra" red shift - which places apparent recession velocity in excess of c - as being due to a change in relative gravitional wells? (Is that the red shift equivalence principle?)

I don't see that at all. It is due to the ongoing dynamics of the universe. This can been seen because their red shifts are also correlated to their distance from us in accordance with the basic Hubble relationship.

[Garth]

In an accelerating universe the cosmological velocities of mutually receding objects accelerates with the general accelerating expansion of the universe. Therefore an initially sub-luminal velocity of mutual recession can become a super-luminal one. In a decelerating universe the reverse is true.

It is to these objects that Davis and Linewaver were referring.

If the initial velocity was super-luminal in an accelerating universe the light would never catch up with you, the distance of separation would be increasing at a faster rate than light speed.
Garth

[DrChinese]

In an accelerating universe the cosmological velocities of mutually receding objects accelerates with the general accelerating expansion of the universe. Therefore an initially sub-luminal velocity of mutual recession can become a super-luminal one. In a decelerating universe the reverse is true.

It is to these objects that Davis and Linewaver were referring.

If the initial velocity was super-luminal in an accelerating universe the light would never catch up with you, the distance of separation would be increasing at a faster rate than light speed.
Garth

Yes, just wanted to be sure we were discussing the same thing. The strange thing is that means that more and more galaxies will disappear from our field of view until... our observable universe will consist of ourselves and a few local galaxies. (That prospect reminds me of a Star Trek episode in which Capt. Picard and Dr. Crusher are the only crew on the Enterprise...)

[Chronos]

The notion that light cannot reach us from an object receeding faster than c is illogical. If that were true, wouldn't such objects appear to be getting younger?

[krab]

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

[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:

Inflation and the CMB, 34 pages, PDF format (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 travelling 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 travelling 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 travelling 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 travelling 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:

\lim_{t\rightarrow\infty} \frac{dm}{dt} = 0 \implies \lim_{t\rightarrow\infty} m \ne \infty




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 criticise 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 travelled 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).
http://physicsforums.com/showthread.php?t=32713&page=1
http://physicsforums.com/showthread.php?t=41370
http://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 travelling 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 apparant 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 realise 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 seperate from Space-Time?

I have seen a little on the idea's 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