Time Dilation & big bang Question

[Garth]

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

 

[Andrew Mason]

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

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

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



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 criticize it too! (And like you I find it inappropriate to define a measurement of recession that results in v exceeding c before z has become infinite)

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

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

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

Einstein and Friedmann would have disagreed with you.

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

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

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

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

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

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

- Garth

 

[Andrew Mason]

Einstein and Friedmann would have disagreed with you.

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

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

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

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

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

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

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

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

Andrew Mason

 

[Garth]

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

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

 

[Andrew Mason]

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

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

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

Andrew Mason

 

[Garth]

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

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

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

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

- Garth

 

[Andrew Mason]

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

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

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

Andrew Mason

 

[Garth]

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

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

There is no empirical evidence to support it, yet.

Hubble Red shift is normally thought to do the trick.

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

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

 

[Andrew Mason]

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

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

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

Andrew Mason

 

[Garth]

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

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

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

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

 

[Andrew Mason]

Hubble Red shift is normally thought to do the trick.

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

Andrew Mason

 

[Garth]

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

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

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

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

 

[Neo]

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

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

Relativity is not violated by space traveling faster than c.

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

 

[Andrew Mason]

Relativity is not violated by space traveling faster than c.

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

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

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

Andrew Mason

 

[Chronos]

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

 

[juju]

Hi,

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

juju

 

[Andrew Mason]

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

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

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

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

$$\therefore t_{cmb} = 559 t_0$$

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

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

Andrew Mason

 

[Garth]

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

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

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

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

Garth

 

[Wave's_Hand_Particle]

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

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

Andrew Mason

This may be resolved in the near future.

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

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

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

 

[Andrew Mason]

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

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

Andrew Mason

 

[Garth]

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

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

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

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

Garth