Is the Universe Expanding or Are Galaxies Moving Apart?

[Born2Perform]

I don't understand what you mean with: universe is expanding.

Is space that -as an elastic membrane- is expanding or galaxies have a proper velocity?

And however, shouldn't all become bigger during the expansion?

for example, in a sphere-universe of diameter 100 metres there is a galaxy of diameter 5 metres.
If the diameter of the universe become 10,000 meters also the diameter of the galaxy must become 500 metres; because space inside the galaxy would grow too.
If you deny this, you also must deny that space does not drag along galaxies, so they don't move.

I send back to my first question.
Thanks

 

[EL]

I don't understand what you mean with: universe is expanding.

Is space that -as an elastic membrane- is expanding or galaxies have a proper velocity?

And however, shouldn't all become bigger during the expansion?

for example, in a sphere-universe of diameter 100 metres there is a galaxy of diameter 5 metres.
If the diameter of the universe become 10,000 meters also the diameter of the galaxy must become 500 metres; because space inside the galaxy would grow too.
If you deny this, you also must deny that space does not drag along galaxies, so they don't move.

I send back to my first question.
Thanks

This has been discussed in some threads earlier, and when you dig deep into the problem it's really not that simple at all. However, I'll try to give some intuitive "first step" answers:
The expanding universe solution really only holds on large scales where the universe can be seen as homogenious and isotropic. As soon as you get down to scales small enough that you start to see "clumpsiness" in the matter distribution, the equations of General Relativity give you other spacetime solutions.
For example our solar system is well described by the Robertson-Walker metric in which space does not expand with time. The solar system itself lives in our galaxy, which must be described by some other new metric...and so on...It's first when we reach scales large enough that the universe can be well described by the FLRW-metric, which predicts the expansion of space we talk about, that we really can see the expansion.

Maybe an even more intuitive (although not as "correct") way to look at it is like this:
In a galaxy the stars are gravitationally bound to each other, and the expansion of space at those scales are not "fast enough" to overwin the gravitational attraction. Only clumps of matter that are far enough from each other will move away from each other due to the expansion.

 

[Born2Perform]

This has been discussed in some threads earlier, and when you dig deep into the problem it's really not that simple at all.

under "expansion" there are 497 results.. can you link me just the more significant thread?

 

[EL]

under "expansion" there are 497 results.. can you link me just the more significant thread?

Here's one I can find (the discussion starts some posts down):
https://www.physicsforums.com/showthread.php?t=102775

 

[MeJennifer]

I don't understand what you mean with: universe is expanding.

Cosmologists come up with the most strange conclusions, at least to me, of course for them it is perfectly "explainable".

For instance they claim that objects are apparently traveling away from us faster than the speed of light.
Then if you ask them how that is possible, they answer, well it is because space is expanding. So much for Einstein's "nothing that has mass can reach the speed of light".
Or when cosmologists speak about the age of the universe as if there suddenly is some sense of absolute space and time afteral because of the background radiation. There is supposed to be no preferred frame of reference, and there is covariance and so, but everything cosmological now seems to be measured from the new absolute space and time reference frame.
Or am I misinformed?

 

[EL]

Or am I misinformed?

Yes you are.
You are drawing false conclusions due to a lack of understanding of the differences between Special and General Relativity.
If you tell us what level you are at, maybe you could have some books recomended.

 

[MeJennifer]

So are you agreeing that objects can travel faster than light because space is expanding?
Edited:
Never mind, I will open a topic on this, seems like a question that can improve my understanding.

 

[Jenny]

I read somewhere a funny joke about the expansion of space. (it isn't lame, a clever funny joke)
If the atom, the person, the Earth and the Solar system expanded just as the rest of space expanded (ie. space between each elementary particle expanded and the space each elementary particle occupies expanded in the same ratio etc etc... how this happens I dont' know...) then the human wouldn't even be able to observe the expansion of space!
The author went so far as to joke: maybe space isn't expanding, merely matter shrinking within it =) It would produce the same observed affect (given it's ideal homogenous shrinking of gravitationally bound stuff, where all distance ratios within a system remain eternally equal. The ratio of distances between systems to distances witin the system would increase =)

 

[chronon]

There is supposed to be no preferred frame of reference, and there is covariance and so, but everything cosmological now seems to be measured from the new absolute space and time reference frame.

Cosmologists have chosen a particular coordinate system, which disagrees with the coordinate system suggested by Special relativity. This choice is often to be presented as the only one possible, but it isn't. See http://www.chronon.org/Articles/stretchyspace.html for more of my argument against this choice.

 

[MeJennifer]

The expanding universe solution really only holds on large scales where the universe can be seen as homogenious and isotropic. As soon as you get down to scales small enough that you start to see "clumpsiness" in the matter distribution, the equations of General Relativity give you other spacetime solutions.

To me it seems that scientists are simply plugging in data by measurements they make in the different regions and making it work with GR. How can we say we can derive all this from GR when we have constants, scale factors, dark matter, de Sitter spaces, energy vacuums etc?

For example our solar system is well described by the Robertson-Walker metric in which space does not expand with time. The solar system itself lives in our galaxy, which must be described by some other new metric...and so on...It's first when we reach scales large enough that the universe can be well described by the FLRW-metric, which predicts the expansion of space we talk about, that we really can see the expansion.

So you are saying it is not possible that we simply have no clue as to why the numbers at very large distance are so different, and that instead we simply plug in some new metric that makes the numbers fit?

Maybe an even more intuitive (although not as "correct") way to look at it is like this:
In a galaxy the stars are gravitationally bound to each other, and the expansion of space at those scales are not "fast enough" to overwin the gravitational attraction. Only clumps of matter that are far enough from each other will move away from each other due to the expansion.

So you are saying that gravitational attraction stops expansion?

If we take a simple example in GR of a sphere with a certain volume and mass we indeed see that the volume is reduced.
However from within the sphere no such conclusion is made, it is only outside the sphere that the reduction is visible.
Now we live in the universe, how could we possibly see a volume reduction effect on the expansion?

What about the time part of space-time?
Is only space expanding or is time expanding as well?
So did time run faster in the past?

 

[Parlyne]

To me it seems that scientists are simply plugging in data by measurements they make in the different regions and making it work with GR. How can we say we can derive all this from GR when we have constants, scale factors, dark matter, de Sitter spaces, energy vacuums etc?

The geometric model of cosmology comes from applying two observations about the universe on large scales to the field equations of general relativity. Astronomers have known for some time that the universe on large scales looks pretty much the same in every direction (it's isotropic) and in every place (it's homogenous).

It can be shown that the only geometries allowed by general relativity in the case that the sources of gravity are homogenous and isotropic have line elements that look like:

ds^2 = - dt^2 + a^2(t) \left (\frac{dr^2}{1-kr^2} + r^2 (d\theta^2 + \sin^2\theta d\phi^2) \right ),

up to a general change of coordinates. The value of k (which can only be 0, 1, or -1 to begin with) and the time dependence of a(t) are determined by the specific properties of the sources of gravity. This is where things like dark matter and dark energy become relevant. They are necessary to make a(t) and k behave as we observe them to behave.

So you are saying it is not possible that we simply have no clue as to why the numbers at very large distance are so different, and that instead we simply plug in some new metric that makes the numbers fit?So you are saying that gravitational attraction stops expansion?

If we take a simple example in GR of a sphere with a certain volume and mass we indeed see that the volume is reduced.
However from within the sphere no such conclusion is made, it is only outside the sphere that the reduction is visible.
Now we live in the universe, how could we possibly see a volume reduction effect on the expansion?

What about the time part of space-time?
Is only space expanding or is time expanding as well?
So did time run faster in the past?

As I implied above, the cosmological metric really only applies on large scales, because it is only on large scales that the universe is homogenous and isotropic. When we look as smaller scales things are pretty clumpy; so, the metric must deviate from the above in response to that .

The simple answer about small scale structures is that on such distance scales the effects of expansion are very small - much smaller than the gravitational attraction between objects composed of normal or dark matter. So, gravitationally bound systems remain unaffected by the expansion.

As for the nature of expansion itself, as you can see in the line element above, the scale factor, a(t), only plays a role in the spatial part of the geometry; so, space is expanding over time.

 

[robheus]

I read somewhere a funny joke about the expansion of space. (it isn't lame, a clever funny joke)
If the atom, the person, the Earth and the Solar system expanded just as the rest of space expanded (ie. space between each elementary particle expanded and the space each elementary particle occupies expanded in the same ratio etc etc... how this happens I dont' know...) then the human wouldn't even be able to observe the expansion of space!
The author went so far as to joke: maybe space isn't expanding, merely matter shrinking within it =) It would produce the same observed affect (given it's ideal homogenous shrinking of gravitationally bound stuff, where all distance ratios within a system remain eternally equal. The ratio of distances between systems to distances witin the system would increase =)

Yes, and that is of course true by definition, because all physical phenomena are independent of the ruler (units of measurements) you choose. If tomorrow we choose a new meter unit as 0,5 of the old meter unit, we would have to rewrite all our physics books to adjust to that, but apart from that, nothing in the universe would change. The physics laws and phenomena stay the same.
This is even true if the ruler we choose is time variant.

So physically this outlook is perfectly ok, yet it is a little unpractical to choose the distance between two far away galaxies as your unit of measurement.

 

[azzkika]

The geometric model of cosmology comes from applying two observations about the universe on large scales to the field equations of general relativity. Astronomers have known for some time that the universe on large scales looks pretty much the same in every direction (it's isotropic) and in every place (it's homogenous).

It can be shown that the only geometries allowed by general relativity in the case that the sources of gravity are homogenous and isotropic have line elements that look like:

ds^2 = - dt^2 + a^2(t) \left (\frac{dr^2}{1-kr^2} + r^2 (d\theta^2 + \sin^2\theta d\phi^2) \right ),

up to a general change of coordinates. The value of k (which can only be 0, 1, or -1 to begin with) and the time dependence of a(t) are determined by the specific properties of the sources of gravity. This is where things like dark matter and dark energy become relevant. They are necessary to make a(t) and k behave as we observe them to behave.



As I implied above, the cosmological metric really only applies on large scales, because it is only on large scales that the universe is homogenous and isotropic. When we look as smaller scales things are pretty clumpy; so, the metric must deviate from the above in response to that .

The simple answer about small scale structures is that on such distance scales the effects of expansion are very small - much smaller than the gravitational attraction between objects composed of normal or dark matter. So, gravitationally bound systems remain unaffected by the expansion.

As for the nature of expansion itself, as you can see in the line element above, the scale factor, a(t), only plays a role in the spatial part of the geometry; so, space is expanding over time.

If it expands over time, what kind of time would it be when it's expanding >c as is observed at present. and i repeat a question from another post, what causes the reduction of speed of space expansion to <c thus allowing galaxies which were once moving >c to be seen.

 

[JimJast]

What about the time part of space-time?
Is only space expanding or is time expanding as well?
So did time run faster in the past?

Actually you may say that the time run slower in the past and that's why we see the Hubble redshift. Yet the cosmologists don't consider such a possibility despite that it is the only scenario consistent with the global conservation of energy and supplies the means of calculating theoretically the Hubble constant. For some reason the cosmologists prefer expanding distances and "dark energy" to conservation of energy and theoretical predictions of parametrs of this (apparent in such a case) expansion.

 

[JimJast]

If it expands over time, what kind of time would it be when it's expanding >c as is observed at present. and i repeat a question from another post, what causes the reduction of speed of space expansion to <c thus allowing galaxies which were once moving >c to be seen.

Nothing in nature can expand faster than c since whenever some distance from us gets increasing with high speed the time at the moving end of this distance starts running slower in relation to us and the result is that it can never crosses the speed of light. It is elementary relativistic physics and our world happens to be relativistic. Physicists don't worry about >c stuff so you don't need neither. If some of your calculations (not observation since there is even no way to observe >c) give you >c result your have to check your calculations since they are obviously false.

 

[marcus]

If it expands over time, what kind of time would it be when it's expanding >c as is observed at present. and i repeat a question from another post, what causes the reduction of speed of space expansion

could you be more explicit about what you mean by "It".

the universe does not have a definite speed of expansion so I suppose you are not talking about the universe expanding >c.

but a lot of the distances beween stationary points have always been increasing at rates >c, so by "It" maybe you mean some particular distance, like, to some galaxy? A galaxy which is approximately at rest relative to CMB and the distance to it increasing >c?

the matter density causes slowing. there is a term in one of the two Friedman equations that gives the second time-derivative a''(t) of the scalefactor a(t) in terms of the matter density and also positive pressure (if there is any measurable positive pressure)

============

to <c thus allowing galaxies which were once moving >c to be seen.

we are able to see galaxies which have always been receding >c. We see them all the time. they are a large part of the galaxies available for study. You just point the telescope at them and look. How this happens is explained in the Lineweaver SciAm article whose link is in my signature. check it out. good article. they use it to teach with at Princeton. simple and lots of picture.

what you said there shows some misunderstanding because a galaxy's recession speed does not have to slow down to <c in order for it to be seen. the distance to it does not have to increase at a rate lower than <c to allow (as you say) the light to get here.

we've been over this a lot at the forum but at the moment I can't get you a link to a thread. have a look at Lineweaver, that draws pictures of how it happens and makes it clear.
================

Kikkah, check this out.
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html
put in the standard 3 parameters (.27, .73, 71) and try redshift z=2.4

You will see that any galaxy we are now looking at that has redshift of 2.4 or more has ALWAYS been receding faster than c. the distance to it has been increasing >c. Not that the thing has been moving relative CMB. I am talking about recession, not local motion.

But we still see the suckers. We see hundreds of thousands of galaxies with redshift 2.4 and up. the fact that they are receding at such a big rate doesn't prevent this.

 

[Garth]

I read somewhere a funny joke about the expansion of space. (it isn't lame, a clever funny joke)
If the atom, the person, the Earth and the Solar system expanded just as the rest of space expanded (ie. space between each elementary particle expanded and the space each elementary particle occupies expanded in the same ratio etc etc... how this happens I dont' know...) then the human wouldn't even be able to observe the expansion of space!
The author went so far as to joke: maybe space isn't expanding, merely matter shrinking within it =) It would produce the same observed affect (given it's ideal homogenous shrinking of gravitationally bound stuff, where all distance ratios within a system remain eternally equal. The ratio of distances between systems to distances witin the system would increase =)

That is not a joke, it is one way of describing a conformal gravity theory such as Fred Hoyle's mass field theory, "On the Origin of the Microwave Background", Ap.J. 196:661-670 1975 March 15, in which the masses of fundamental particles varied from event to event.

As particle masses varied so would their size with the result that our interpretation of an expanding universe with fixed rigid rulers would be reinterpreted as a static universe with shrinking rulers.

Hoyle proposed this theory to resurrect some idea of his Steady State Theory in the light of the discovery of the CMB radiation.

In this theory the mass field went negative beyond a zero mass field surface. He postulated that as photons went from a -mass field to a +mass field region they were thermalised and thus became the microwave background, which would then be simply the light from galaxies beyond that zero-mass field surface.

A similar reinterpretation of the expanding universe is also found in the Jordan Conformal frame of http://en.wikipedia.org/wiki/Self-creation_cosmology .

Garth

 

[mysearch]

Query on the timeline of similar threads
This thread appears to have been originally opened 07.11.06 and had an interesting exchange up to 07.25.06. Strangely, a ‘joke’ about the expansion of space was raised on 07.23.06 (#8), which then got a response on 07.03.08 (#12). This appears to be quite a delay between the punchline and audience laughter! Subsequently, another thread `The physical meaning of expansion in cosmology` opened on 07.24.08, which in parts seems to parallel the same issues. Was just curious!​

As somebody relatively new to the details of cosmology, I am only trying to build a framework around the standard model built on accepted physics rather any suggestion of any ‘alternative’ theory. So, as a general statement, much of modern cosmology seems to be built on the assumption of relativity, especially GR, in the form of Friedmann’s equations. Now it is said that Friedmann’s solution is derived from Einstein’s field equations, but today much of this theory is shrouded in the complexity of Riemann geometry, differential geometry, conformal geometry etc, much of which I am assuming was not available to Friedmann. It is also highlighted that the basic form of Friedmann equation can still be derived from the assumption of the conservation of energy, although aspects of GR are said to question this basic axiom of classical physics:

[1] H^2 = \frac {8}{3}\pi G \rho + \frac{2 E_T}{mr^2}

The last term may look a bit unfamiliar because it is usually substituted as

[2] - \frac {kc^2}{a^2}

Which might suggest that:

[3] k = \frac{2E_T}{mc^2}

Of course, measurements to-date suggests that [k=0], at least, in approximation. As such, equation [1] would reduce to

[4] H^2 = \frac {8}{3}\pi G \rho

Now the value of [H] appears to be based on measurements of redshift, which are then linked to assumptions about luminosity of distant objects, from which it has been concluded that H=v/d, where [v] is the recessional velocity with distance [d]. Therefore, knowing the value of (G), we can calculate the critic density \rho_c. As understood, the standard model of cosmology assumes this density contains all forms of mass-energy, e.g. matter (4%), dark matter (23%) and dark energy (73%). However, only matter and dark matter can be linked to gravitational attraction, because dark energy corresponds to a ‘force’ linked with the observed expansion of the universe. As such, it appears that we have a model that describes expansion in terms of a balance between some unverified expansion source, e.g. dark energy, and gravity. This is simply a statement of my current understanding of the basic model, which is open to correction. So my first question is:

How does gravity slow H in this model?

What I referring to is the classical concept of a centre of gravity, which a homogeneous and isotropic universe is said not to have. If so, I am finding it difficult to resolve how the net effects of a `gravitational slow down` works within this model. I accept that I am no expert of GR either, but the concept of a model of a homogeneous universe, where the matter density is analogous to ‘dust’ suggests that much of the complexity of GR theory is confined to relatively small sections of the universe, where gravitational potential is higher, e.g. galaxies.

However, in contrast to all this apparent definite talk about expansion, the thread `The physical meaning of expansion in cosmology` appears to highlight some level of both philosophical and technical doubt about the reality of any expansion. However, referencing the 1st post in the current thread, the premise seems to assume expansion of the universe and everything in it. Whereas the standard model only seems to assume a relative ‘expansion’ of the universe. As such nuclei don’t expand, atoms don’t expand, neither do solar system or entire galaxies, only the large-scale space between galaxies. If so:

Can we say there must be, at least, some relative expansion of the universe with respect to smaller objects not apparently subject to any net expansion; otherwise the standard model itself would be inconsistent?

Does this imply there is a threshold where expansion, if it exists, overcomes the internal forces that hold any given structure in place?

I recognise that some of these questions may seem naive to the experts, but if so, they will hopefully not have to resort to tensor notation and relatively obscure ideas about 4-D manifolds to outline how the basic model works, at least, in general principle. Thanks

 

[Garth]

As Parlyne has already said, the FRW equation can be derived without GR, simply from the condition of maximally symmetry space, i.e. from the Cosmological Principle of a homogeneous and isotropic universe.ds^2 = - dt^2 + a^2(t) \left (\frac{dr^2}{1-kr^2} + r^2 (d\theta^2 + \sin^2\theta d\phi^2) \right ),The condition of maximally symmetry space is then applied to the GR field equation to obtain its cosmological solution that determines a(t). The specific solution of a(t) and k depends on the content, matter (dark and otherwise), radiation and DE that you put into the field equation.

1. Gravity does not "slow H", the gravitational field of positive mass and energy within the universe decelerates its expansion, just as gravity slows a rising rocket, which may or may not escape the Earth's gravitational field depending on its initial velocity.

H is determined by a(t) and its time derivative and those are determined by the cosmological gravitational field. If the positive mass and energy content of the universe were to be increased then the value of H would increase, perhaps this is what you are thinking of...

2. There is a real increase of the distances between distant galaxies as measured by a ruler constructed of atoms, a steel rule. All measurements are relative to the standard by which they are being compared...

3. The standard model is consistent with the principles upon which it is based.

4. In the standard model cosmological expansion does not apply on 'local' structures which are gravitationally bound.
Garth

 

[mysearch]

Response to #19

Garth: Many thank for the helpful and concise summary. By way of response, I was trying to rationalise a basic model in which the FRW metric, as defined by Parlyne (#11), reduces to the form:

ds^2 = - dt^2 + a^2(t) dr^2

This form only looks at the equatorial expansion along a radial path and assumes k=0. As also pointed out by Parlyne (#11),

As for the nature of expansion itself, as you can see in the line element above, the scale factor, a(t), only plays a role in the spatial part of the geometry; so, space is expanding over time.

To which you have added the qualification:

The specific solution of a(t) and k depends on the content, matter (dark and otherwise), radiation and DE that you put into the field equation.

In other words, the expansion may have varied in time depending on the makeup of the energy density [\rho]. While I am taking a deliberately simplistic approach, as far as I can see my basic model doesn’t violate anything being implied above or current measurements. However, I am less clear about the following statement:

Gravity does not "slow H", the gravitational field of positive mass and energy within the universe decelerates its expansion, just as gravity slows a rising rocket, which may or may not escape the Earth's gravitational field depending on its initial velocity.

Again, from a basic approach, classical physics only defines 4 fundamental forces, 3 of which are effectively neutralised at the atomic level leaving only gravity to operate on the cosmic level. I would define ‘pressure’ as an aggregate ‘force’ caused by individual kinetic collisions between components within the makeup of the energy density being considered.

Now if pressure is an expansive ‘force’ what is slowing down the expansion?

I know GR prefers not to describe gravity as a force, but rather a geodesic path or a gravitational field gradient. However, I assume that these two concepts can be transposed and a 'force' can be used to described a geodesic path.

So where is this path? Is the implication that each unit volume of space has a gravitational curvature or field that slows the expansion due to dark energy pressure?

As I pointed out, I don’t understand how the concept of a net gravitational field within a homogenous universe can be considered without some form of centre of gravity. Therefore I would appreciate any further clarification of the mechanism that is used to explain the slow down of the expansion within the standard large-scale homogeneous universe model.

 

[Garth]

Garth: Many thank for the helpful and concise summary.

You are welcome

By way of response, I was trying to rationalise a basic model in which the FRW metric, as defined by Parlyne (#11), reduces to the form:

ds^2 = - dt^2 + a^2(t) dr^2

This form only looks at the equatorial expansion along a radial path and assumes k=0. As also pointed out by Parlyne (#11),

As for the nature of expansion itself, as you can see in the line element above, the scale factor, a(t), only plays a role in the spatial part of the geometry; so, space is expanding over time.

To which you have added the qualification:

The specific solution of a(t) and k depends on the content, matter (dark and otherwise), radiation and DE that you put into the field equation.

In other words, the expansion may have varied in time depending on the makeup of the energy density [\rho]. While I am taking a deliberately simplistic approach, as far as I can see my basic model doesn’t violate anything being implied above or current measurements.

In a maximally symmetric space all one can have is density and pressure, other forms of stress, angular momentum etc. are set to zero.

However, I am less clear about the following statement:

Gravity does not "slow H", the gravitational field of positive mass and energy within the universe decelerates its expansion, just as gravity slows a rising rocket, which may or may not escape the Earth's gravitational field depending on its initial velocity.

Again, from a basic approach, classical physics only defines 4 fundamental forces, 3 of which are effectively neutralised at the atomic level leaving only gravity to operate on the cosmic level. I would define ‘pressure’ as an aggregate ‘force’ caused by individual kinetic collisions between components within the makeup of the energy density being considered.

Now if pressure is an expansive ‘force’ what is slowing down the expansion?

Gravity. Counter-intuitively pressure actually decelerates the expansion! This is because adding pressure to a model adds extra energy and energy, together with mass, is a source of gravitation.

I know GR prefers not to describe gravity as a force, but rather a geodesic path or a gravitational field gradient. However, I assume that these two concepts can be transposed and a 'force' can be used to described a geodesic path.

A geodesic path is a 'straight line' across a surface. The point about GR is that it is the surface that itself is bent, just as a straight line can be drawn on a sheet of rubber and then the sheet can be deformed, the 'straight line' drawn on it is still the shortest distance along the surface of the bent sheet, it is a geodesic of the surface.

In GR it is the 4D space-time manifold that is curved by the presence of mass and energy, so freely falling objects, such as the Earth on its orbit is traveling on a 'straight line' through a space-time curved by the presence of the Sun.

The field equation of this theory predicts the orbits of planets, particularly Mercury, more accurately than any model that uses a Newtonian type force in flat space-time.

So where is this path?

Cosmologically the path is the freely falling trajectory of a member of a cloud of representative particles at rest wrt the CMB.

Is the implication that each unit volume of space has a gravitational curvature or field that slows the expansion due to dark energy pressure?

The expansion is decelerated by positive mass, energy and pressure, DE accelerates the expansion because it has a high negative pressure.

As I pointed out, I don’t understand how the concept of a net gravitational field within a homogenous universe can be considered without some form of centre of gravity. Therefore I would appreciate any further clarification of the mechanism that is used to explain the slow down of the expansion within the standard large-scale homogeneous universe model.

In the cosmological solution there is no centre of gravity because there is no centre, every point is expanding away from every other point, like dots on an expanding balloon.

I hope this helps,
Garth

 

[marcus]

... modern cosmology seems to be built on the assumption of relativity, especially GR, in the form of Friedmann’s equations. Now it is said that Friedmann’s solution is derived from Einstein’s field equations, but today much of this theory is shrouded in the complexity of Riemann geometry, differential geometry, conformal geometry etc, much of which I am assuming was not available to Friedmann...

just a footnote, Mysearch. Riemann geometry, differential geometry have their roots in an 1850 lecture by Riemann. They were available to Friedmann (circa 1923) and to the other Einstein contemporaries.

I don't mean to say that Einstein (1915) used all the differential geometry machinery that was available by 1915---a great deal of work had been done already in the period 1850-1915. But his formulation depends in an essential way on differential geometry.

Cosmology is based very broadly on General Relativity, not only through the Friedmann model. GR is how we see dark matter by gravitational lensing of the background, and how we understand black holes, quasars, pulsars, the detailed map of the CMB (which involves special GR effects like energy-boosting* not contained in the Friedmann model).

Whatever alternative derivations there may be, the young Friedmann thought what he was doing was deriving a special set of solutions to the Einstein equation--working from and within the GR context--and he introduced his results to Einstein on that basis. Tragically, the older man did not acknowledge their validity until after Friedmann's premature death around 1925.

So I would say that cosmology is built very much on the GR basis, and not only via Friedmann but far more broadly than that.

What you say you find shrouding GR (differential geometry, basically) was largely already there in 1915, not put in afterwards. It could even be that the subject has gotten easier since 1915. Some modern textbooks may use streamlined notation and make things more intuitive. I don't know because I haven't compared with antique textbooks. But that's what one would hope.

To me you seem completely able to understand this stuff and to have the motivation, so I encourage you to take it head-on.

*boosting by so-called integrated Sachs-Wolfe--one problem with the subject is the name-heavy nomenclature. the energy boosting effect is simple to understand and calling it by two names most people have never heard of DOES shroud a bit and put folks off.

 

[mysearch]

Acknowledgement to #21 & #22

Garth & Marcus:
I just wanted to acknowledge & thank you both for your responses. In particular, Garth, I really appreciated the concise breakdown of the points I raised. This now allows me to go and research those gaps in my understanding of this subject. So I will now stop pestering you with my questions and follows Marcus' advice and try to get to grips with some of the maths. Again, many thanks.

P.S. Which way is it to the maths forum

 

[marcus]

P.S. Which way is it to the maths forum

BTW I expect you've noticed, we have a S&G Relativity forum here at PF!
https://www.physicsforums.com/forumdisplay.php?f=70
It's actually in the physics section, though it could equally well be in maths.

Over the years when I've been watching, it has often collected a really helpful and knowledgeable group. Of course quality on a real-time board fluctuates depending a lot on the kind of people who come and ask questions. I haven't checked recently so I don't know what the average level, or anything, is at the moment. simply can't say.

But in any case one thing you could do, which might actually be constructive and contribute to the general tone and level of discourse over there, is to go to S&G and ask a hell of a lot of intelligent questions and ask them to explain things about General Relativity that you find are obstacles. George Jones is a name that comes to mind. He might be checking in now and then over there. And there are plenty of others who could be, I just haven't looked.

If it happens to be a slack time and no one especially helpful is around there responding at the moment, you are cordially welcome to keep trying us for explanations at cosmology. That's true in any case! BTW does anybody have any convictions about what is the best GR textbook, say for someone at Mysearch stage of inquiry? Is there an appropriate free online one? Would Sean Carroll's free online GR text be good to recommend? Are there any better ones that you can download?

 

[azzkika]

my apologies. there are too many contradictions and disagreements in physics, as in another post i read we can observe galaxies that were traveling >c because they no longer weren't traveling >c.

 

[marcus]

my apologies. there are too many contradictions and disagreements in physics, as in another post i read we can observe galaxies that were traveling >c because they no longer weren't traveling >c.

Don't get discouraged, Kicker. The vast majority of working astronomers agree on a single model (LCDM cosmology model) and a common bunch of explanations. Lineweaver is one of the leaders, so you can take his SciAm article as presenting the mainstream picture.

At PF we get a lot of unfiltered stuff---people who promote alternative non-standard concepts, or who simply don't understand what they have read and who explain things wrong. If you find that confusing, all I can suggest is learn to ignore them. There is even a way to put posters on automatic ignore. If you find someone's post repeatedly unreliable or eccentric you can always put them on ignore.

I'd suggest you read the Lineweaver SciAm article. The link is in the signature at the end of this post. It explains that the reason we can observe galaxies is NOT because they are now receding <c. Many if not most of the galaxies we are observing at this time are still receding >c. Lineweaver explains how this works, using some diagrams.

It sounds like you read a post on some other thread that contradicts this. Please give a link to the post---I'd like to check it out. I basically sympathize with your feeling that there is too much contradiction---essentially too much noise on the channel.

But hang in there. Maybe the Mentors will find a way to tone it down to more moderate levels. Or bell the cat somehow. In the meantime just think of it as exciting controversy (even if not statistically representative of present-day* real-world science.)*I guess by present-day I mean since 1998, when the LCDM model came in.

 

[JimJast]

You are drawing false conclusions due to a lack of understanding of the differences between Special and General Relativity.
If you tell us what level you are at, maybe you could have some books recomended.

I'm a doctoral student doing my phd work on Einstein's universe. Do you know any books that explain the mechanism that causes the illusion of accelerating expansion in static universe?

 

[Garth]

I'm a doctoral student doing my phd work on Einstein's universe. Do you know any books that explain the mechanism that causes the illusion of accelerating expansion in static universe?

I don't think there is one!

I think you need to clarify several points.

First are you simply researching the history of the Einstein static model a la 1920's, or are you trying to resurrect it as an alternative model in the light of, and despite, all the discoveries made since?

If it is the latter, and your questions indicate that this is the way you seem to be going, then you have many hurdles to cross before you have a viable alternative.

For a start...

As I have said elsewhere you need first a mechanism to explain Hubble red shift, i.e. the standard evidence interpreted as an expansion of the universe.

Such mechanisms might be: Tired Light or a variable mass field theory, such as that of Hoyle and Narlikar.

Next you would have to explain in the static model the relative abundance of the elements, the Cosmic Microwave Background, its Power Spectrum, and finally Cosmic Acceleration.

You will find links to references, papers and books in the links I have given you.

I wish you luck!

Garth

 

[JimJast]

First are you simply researching the history of the Einstein static model a la 1920's, or are you trying to resurrect it as an alternative model in the light of, and despite, all the discoveries made since?

It's the latter since (i) it is more fun for a physicist and (ii) it is the only possible model that is consistent with the global conservation of energy. The former, is interesting to a historian or a sociologist who would like to find out how it happened that physicists ever agreed that the energy can be created (form nothing, not even to mention the whole universe). It might be that contemporary science became more as contemporary art... (an issue for a sociologist to investigate).

If it is the latter, and your questions indicate that this is the way you seem to be going, then you have many hurdles to cross before you have a viable alternative.

I've got an alternative already (from Einstein) and I'm just checking its viability. It looks promissing though since even Ned Wright coudn't falsify the simple idea behind Einstein's universe that I presented him with (or didn't have time for something consider invalid by top guys including Einstein himself).

For a start...

As I have said elsewhere you need first a mechanism to explain Hubble red shift, i.e. the standard evidence interpreted as an expansion of the universe.

Such mechanisms might be: Tired Light or a variable mass field theory, such as that of Hoyle and Narlikar.

It turned out to be neither of those. It turned out to be the special type of time dilation produced by inability of nature to create energy from nothing, apparently overlooked by Einstein, an because of this by the matematicians who took it over from Einstein not suspecting that there may be more physics in it than Einstein already discovered. Apparently it needed a physicist to look at the problem . The Hubble redshift turned out to be a purely relativistic effect depending on the curvatue of space only, and as such completely negligible in Newtonian gravitation with its flat space. Probably that's why it was missed until now since astronmers, accustomed to Newtonian gravitation, might have very vague understanding of one of the basic roles of the curvature of space in gravitation. Some might not even believe that without the curvature of space there wouldn't be any gravitation at all since the time dilation is coupled to it (as Feynman has already noticed). Now it can be demonstrated that they can't be separted at all. We have to have as much of one as we have of another. Not to mention even the quantum nature of Einstein's gravitation. So as you can see Einstein left a lot of material to work on. And none of it is expanding (unless in imagination of some cosmologists, especially those supported by the Templeton Foundation).

Next you would have to explain in the static model the relative abundance of the elements, the Cosmic Microwave Background, its Power Spectrum, and finally Cosmic Acceleration.

Cosmic acceleration comes together with this peculiar time dilation (luckily as it is observed) so this one down, unfortunately many more to go. But I still have 3 or 4 years to do the job, until thy kick me out of the program.

You will find links to references, papers and books in the links I have given you.

I wish you luck!

Garth

Thanks for the refs. I might need all the help I can get .

 

[jonmtkisco]

Hi Jim,

Some might not even believe that without the curvature of space there wouldn't be any gravitation at all since the time dilation is coupled to it (as Feynman has already noticed). Now it can be demonstrated that they can't be separted at all. We have to have as much of one as we have of another.

I would appreciate if you could refer me to a citation where Feynman and maybe others have made this specific point. I find the subject of spatial curvature to be particularly curious.

Jon

 

[JimJast]

Hi Jim,

I would appreciate if you could refer me to a citation where Feynman and maybe others have made this specific point. I find the subject of spatial curvature to be particularly curious.

Jon

Fenman lectrures on physics, vol. 2, page 42-14: It is impossible with space and time so intimately mixed to have something happen with time that isn't in some way reflected in space.

As you may know in Newtonian gravitation the "gravitational attraction" is caused by the effect of gravitational time dilation (as discovered by Einstein). The effects of curvature of space are neglected in Newtonian gravitation, which allowed Einstein to make his general relativity theory by discovering those effects. In Landau's Theory of fields, where he describes Einstein's theory, somewhere around page 285, Landau shows that the curvature of space is necessary to keep the energy of a particle constant while changing its position during free fall. Following Landau, one finds that to keep the energy of a particle constant in free fall, the relative amount of curvature of space has to be the same as the relative amount of time dilation. Which then shows "space and time so intimately mixed" that it is impossible to have gravitation without their mutual dependence. And the "gravitational force" may be derived from differentiation of Launday's equation (which you may do as an exercize). Then one may derive the redshift in static space, as equal per unit of distance, z = 1/R_E, where R_E is Einstein's radius of his universe, which happens to be about what we observe, eg. in case of http://en.wikipedia.org/wiki/Pioneer_anomaly" about the mainstream cosmology.

 

[Garth]

As you may know in Newtonian gravitation the "gravitational attraction" is caused by the effect of gravitational time dilation.

We don't know.

In Newtonian Gravitation gravitational attraction is caused by the effect of a force - the gravitational force - that accelerates freely falling masses relative to a straight line trajectory through flat space-time.

In GR gravitational attraction is the effect of the 'straight line' geodesic paths of freely falling masses converging because of the geometry of the curvature of the space-time in which they are embedded.

It is space-time curvature that is important so it is not at all surprising that "it is impossible with space and time so intimately mixed to have something happen with time that isn't in some way reflected in space." Feymann was not the first to notice it - Einstein was - and it is part and parcel of mainstream cosmology.

Garth

 

[JimJast]

We don't know.

Now you know .

Hi Garth,

The phrase "in certain theory" might be understood as how it is according to the discoverer of the theory and how it is really. I've been talking about how it is really in Newtonian gravitation, and what Einstein discovered. How he could construct his theory of gravitation without knowing about the grevitational time dilation being the reason for the illusion of gravitational force?

In Newtonian Gravitation gravitational attraction is caused by the effect of a force - the gravitational force - that accelerates freely falling masses relative to a straight line trajectory through flat space-time.

What you write is a popular understanding of Newtonian theory not even accepted by Newton himself since he never agreed to existence of some gravitational force acting at the distance. And of course he was right and popular explanation of this apparent force is wrong. At least according to Einstein. The gravitational force is a popular "Newtonian" (quotes, since rejected by Newton himself) explanation of Newtonian math, implanted in physics by generations of physicists so stongly that even 300 years later it is believed in by most physicists who don't bohter with learning GR even approximately to know its basics. They just learn by heart that:

In GR gravitational attraction is the effect of the 'straight line' geodesic paths of freely falling masses converging because of the geometry of the curvature of the space-time in which they are embedded.

What I said above might be seen immediately after trying to calculate gravitational force using this definition. And apparently gravitational force is the simplest force in nature, know from the times when humans started dropping from trees. And yet only less then 100 years ago the nature of this force was discovered, and, even stranger, the discovery stayed unknown to most physicists who still maintain that it is a real (fundamental) force of nature different from EM (except for my friend sweetser) and not just an inetrial force due to one particle pushing the other out of its worldline, and so acting only when one particle is in contact with another (as inetrial force is supposed to do) and so unable to act at the distanace. Have you never noticed that in GR there are no gravitational forces, except inertial, like e.g. tidal, Coriolis, centrifugal etc. (yet for some reason my inertions, coriolisons, and centrifugons, are consistently removed from wikipedia when I add them as different types of gravitons)?

It is space-time curvature that is important so it is not at all surprising that "it is impossible with space and time so intimately mixed to have something happen with time that isn't in some way reflected in space." Feymann was not the first to notice it - Einstein was - and it is part and parcel of mainstream cosmology.

So why there is no definite relation between the space curvature and the time dilation, which would terminate all discussions about "flatness" of space or spacetime? Apparently only Feynman new the secret that the space is curved the same as the time is dilated.

 

[Garth]

The phrase "in certain theory" might be understood as how it is according to the discoverer of the theory and how it is really. I've been talking about how it is really in Newtonian gravitation, and what Einstein discovered.

You are confusing two paradigms.

Einstein might not be explaining how it "really is" either.

All we can say is that here we have two theories of gravitation, one uses force-at-a-distance, the other geometry of space-time. When tested it so happens that Einstein's theory fits the data better than Newton.

Whichever you use, and Newton is still the one most used when it is accurate enough in the weak field limit, you have to be consistent.

How he could construct his theory of gravitation without knowing about the grevitational time dilation being the reason for the illusion of gravitational force?

He used the Equivalence Principle.

What you write is a popular understanding of Newtonian theory not even accepted by Newton himself since he never agreed to existence of some gravitational force acting at the distance. And of course he was right and popular explanation of this apparent force is wrong.

You will have to give a reference for this extraordinary statement.

In his day Newton was criticised for being a mystic because he did advocate 'force-at-a-distance'.

"I deduced that the forces which keep the Planets in their Orbs must reciprocally as the squares of their distances from the centers around which they revolve." Newton quoted by Barrow "The World within the World" 1988 pg 68.

At least according to Einstein. The gravitational force is a popular "Newtonian" (quotes, since rejected by Newton himself) explanation of Newtonian math, implanted in physics by generations of physicists so stongly that even 300 years later it is believed in by most physicists who don't bohter with learning GR even approximately to know its basics. They just learn by heart that:

In GR gravitational attraction is the effect of the 'straight line' geodesic paths of freely falling masses converging because of the geometry of the curvature of the space-time in which they are embedded.

Those physicists who do bother to learn GR also describe it as such, or perhaps as: "Matter tells space-time how to curve, curved space-time tells matter how to move".

When they want to know exactly how space-time curvature is determined by the presence of matter then they solve the GR field equation:

G_{\mu \nu} = 8\pi GT_{\mu \nu}

. Have you never noticed that in GR there are no gravitational forces, except inertial, like e.g. tidal, Coriolis, centrifugal etc. (yet for some reason my inertions, coriolisons, and centrifugons, are consistently removed from wikipedia when I add them as different types of gravitons)?

Of course I (we) have considered it; the relationship of the concept of 'gravitons' to the concept of 'space-time curvature' lies at the heart of all attempts to produce a quantum gravity theory.

So why there is no definite relation between the space curvature and the time dilation, which would terminate all discussions about "flatness" of space or spacetime? Apparently only Feynman new the secret that the space is curved the same as the time is dilated.

What do you mean by this statement, we have already said that from the beginning Einstein and others knew that space curvature and time dilation are both part of the one united space-time curvature, are you saying here that they are equal parts? (Feymann wasn't saying that) If you are doing so then in order to make such a statement the questions that have to be answered are:
1. "How do you measure space curvature and how do you measure time dilation independently of each other to make the comparison?"
2. "What units, what dimensions, are each measured in?"
As both the spatial and temporal components are frame dependent, then
3. "What frame of reference are both components to be measured into make this comparison?"

One clue to answer these questions is to look at the Robertson parameter \gamma in the PPN formalism, which determines the amount of space curvature caused by unit mass (actually GM) and compare that component with the remainder which is by elimination due to time dilation per unit GM.

If you look at the deflection of light by a mass the deflection is given in the frame comoving with the deflecting mass by:

\theta = \frac{4MG}{R} \frac{1 + \gamma}{2}

where in GR \gamma is unity so here the component due to space curvature and time dilation are equal. Perhaps this is where you are getting your idea from...

However they are not always equal, in the precession of the perihelia the precession per revolution is given by:

\frac{6\pi GM}{L}\frac{2 - \beta + 2\gamma}{3}

Where in GR \beta = 1, so the space curvature component is here twice the time dilation component, as it is for the geodetic precession of orbiting gyroscopes being measured by the Gravity Probe B experiment.

Garth

 

[jonmtkisco]

The debate between "action at a distance" and "spacetime curvature" sounds to me like the old religious debates about how many angels can dance on the head of a pin. As long as one accepts the mathematical results of the GR equations, there appears to be no meaningful distinction between which of the two physical mechanisms is more "real." And there won't be until the underlying physical mechanism of gravity is discovered.

If gravity causes spacetime to curve, why is that "less spooky" than action at a distance (e.g., a force mediated by particles moving at the speed of light)? Curved spacetime is a damn weird concept, despite the elementary textbook explanations, which explain nothing. By what physical agent does spacetime become curved by being near a massive object? And in a physical, tangible sense, what is spacetime anyway? How do we know it goes beyond a mathematical concept and is actually physical?

If we fill an empty box with "intrinsically curved space" from within a gravitational field, and then fly the box far away from the gravitational source, will the space inside the box retain that gravitation-induced curvature? Of course not. Why can received gravitational energy be permanently "stored" by a massive particle (by means of the particle's gravitationally acquired change in momentum) but not by "spacetime", if the latter is physical?

If spacetime curvature is physically real, then it clearly is an ephemeral manifestation of instantaneous proximity and trajectory with respect to the source mass. An instantaneous change in spacetime curvature does not physically occur at a point near or far from the gravitational source any sooner than permitted by the travel speed of light. (Doesn't that suggest the need for a mediating particle or wave moving through space?) Sppacetime attributes cannot reasonably be treated as an intrinsic attributes of any physical structure or substance ("space") located within the coordinate dimensions affected by the gravitational source. Empty vacuum is not viscous or malleable, nor can it assume or retain any definite shape, nor can it move or remain stationary, in any normal meaning of those words. How can empty vacuum itself be physically substantial enough to deflect a passing photon's worldline?

One can, if one wants, treat any force or pseudo-force as a manifestation of spacetime curvature. When a constant wind blows, the "spacetime geodesic" of a flying arrow becomes curved, and the arrow's path curves off in the downwind direction. It must do so in order to conserve its energy. All moving objects follow the path of least resistance. Does this mean they are "moving in a straight line through curved space?" Does it "prove" the physical reality of spacetime curvature?

The concept of spacetime curvature seems like a "safe" place to mentally retreat to when one is confounded by the apparent mathematical complexity of gravitational action at a distance.

Jon

 

[JimJast]

You are confusing two paradigms.

Einstein might not be explaining how it "really is" either.

All we can say is that here we have two theories of gravitation, one uses force-at-a-distance, the other geometry of space-time. When tested it so happens that Einstein's theory fits the data better than Newton.

The Einsteinian predictions are exact (as far as we know of course) the Newtonian predictions are wrong (which we know for sure). It is enough to reject Newtonian theory as physics. It is just an approximate math sufficient for many engineering applications (so Newton's is not physical but phenomenological approximate desription of gravitation). We even know what is missing in Newtonian physics: the curvature of space. It is only the math describing the time dilation part of physics of gravitation. The missing part is in Landau's Theory of fields desribing Einstein's gravitation. The (apparent) gravitational force is there as -dE/dx^i, where E is rest energy of the particle mc^2\sqrt{g_{00}} where g_{00} is time-time component of spacetime metric, and dx^i is the displacement vector of the particle. So we have here the concrete rest energy of the particle and curvatures of spacetime and no forces, just enrgies and their conservation following from the fact that nature is unable to create enrgy out of nothing. If it were able, then our "gravitational force" as predicted by Einstein wouldn't be the same as Newtonian, yet it is. Which means energy conservation holds in Einstein's physics the same way as in Newtonian but it does not need a mysterious "potential energy" to be valid since it comes out of first principles through the relation between time dilation and space curvature.

In his day Newton was criticised for being a mystic because he did advocate 'force-at-a-distance'.

"I deduced that the forces which keep the Planets in their Orbs must reciprocally as the squares of their distances from the centers around which they revolve." Newton quoted by Barrow "The World within the World" 1988 pg 68.

It does not say anything about Newton believing in attraction coming through empty space from the Sun. It says only about the math of the phenomenon which according to Newton was the only legitimate conclusion that one can draw from observations without undue speculatons about the mechanism of the phenomenon.

[...] space curvature and time dilation are both part of the one united space-time curvature, are you saying here that they are equal parts? If you are doing so then in order to make such a statement the questions that have to be answered are:
1. "How do you measure space curvature and how do you measure time dilation independently of each other to make the comparison?"
2. "What units, what dimensions, are each measured in?"
As both the spatial and temporal components are frame dependent, then
3. "What frame of reference are both components to be measured into make this comparison?"

1. Use weak enough field that there are linear relations only (one does not influence the other) and measure deflection of light knowing that the Newtonian part is due to the time dilation, so the rest is due to the curvature of space (as Einstein's did with the bending of light rays in vicinity of the Sun when both part turned out to be equal).
2. The dimensionless relative changes.
3. The frame of any observer.

The debate between "action at a distance" and "spacetime curvature" sounds to me like the old religious debates about how many angels can dance on the head of a pin. As long as one accepts the mathematical results of the GR equations, there appears to be no meaningful distinction between which of the two physical mechanisms is more "real." And there won't be until the underlying physical mechanism of gravity is discovered.

But the underlying physical mechanism of gravity is discovered almost a century ago by Einstein. It is just not taught in high schools for some reason so it stays mostly unknown to anybody except doctoral students specializing in gravitation. While even most of them can't explain in simple English the reason for the illusion of gravitational force.

If gravity causes spacetime to curve, why is that "less spooky" than action at a distance (e.g., a force mediated by particles moving at the speed of light)? Curved spacetime is a damn weird concept, despite the elementary textbook explanations, which explain nothing. By what physical agent does spacetime become curved by being near a massive object? And in a physical, tangible sense, what is spacetime anyway? How do we know it goes beyond a mathematical concept and is actually physical?

The mechanism of rest energy of a particle diminishing along its displacement vector directed towards the source (of energy that for some reason bends the spacetime) is rather simple (see the top of this post). Why the energy bends the spacetime we don't know and it is not the subject of theory. It is a measurable conclusion since we can measure the amount of bending and it fits the theory through the principle of conservation of energy and the value of gravitational constant which origins we don't know yet just may try to guess. Maybe I'll do before I'm through with my phd project , then I might tell you. But there is no such potential in math of Newtonian gravitation so we may dismiss it as a candidate for delivering any understanding of the universe. We shouldn't even teach it to high school students since it only confuses them later in life, and the Einsteinian gravitation is also much simpler (the mystery of force acting through vacuum repalced by rather easy to understand inability of nature to make energy out of nothing).

If spacetime curvature is physically real, then it clearly is an ephemeral manifestation of instantaneous proximity and trajectory with respect to the source mass. An instantaneous change in spacetime curvature does not physically occur at a point near or far from the gravitational source any sooner than permitted by the travel speed of light. (Doesn't that suggest the need for a mediating particle or wave moving through space?)

Of course. And don't you know particles that carry energy from one atom to another? Just call this energy "gravitational", which it really is since numerically it is responsible for gravitational force (see top of this post) and you have the answer.

Spacetime attributes cannot reasonably be treated as an intrinsic attributes of any physical structure or substance ("space") located within the coordinate dimensions affected by the gravitational source. Empty vacuum is not viscous or malleable, nor can it assume or retain any definite shape, nor can it move or remain stationary, in any normal meaning of those words. How can empty vacuum itself be physically substantial enough to deflect a passing photon's worldline?

Of course it can't and it does not. A prticle taking a geodesic worldline is not deflected, unless some other particle pushes it away from its wordline. That's why gravitational force (the same as any other inertial force) can't be propagated through empty space and that's why the notion of "universeal gravitational attraction" is silly. Math without any physics.

One can, if one wants, treat any force or pseudo-force as a manifestation of spacetime curvature. When a constant wind blows, the "spacetime geodesic" of a flying arrow becomes curved, and the arrow's path curves off in the downwind direction. It must do so in order to conserve its energy. All moving objects follow the path of least resistance. Does this mean they are "moving in a straight line through curved space?" Does it "prove" the physical reality of spacetime curvature?

The concept of spacetime curvature seems like a "safe" place to mentally retreat to when one is confounded by the apparent mathematical complexity of gravitational action at a distance.

In addition to all of this, we (the lazy humans) try to choose a reference frame in which the calculations are the simplest (so we rather don't choose the frame of flying arrow) so we don't need to bother with everything what's there. But even if we choose the best frame we can't get rid of curvature of space which means it might be real. But we never observed action at a distance (especially instantaneous; all that looked like action at a distance turned out to be illusions) so we don't need to believe that it is real.

 

[jonmtkisco]

Hi JimJast,

The Einsteinian predictions are exact (as far as we know of course) the Newtonian predictions are wrong (which we know for sure). It is enough to reject Newtonian theory as physics. It is just an approximate math sufficient for many engineering applications (so Newton's is not physical but phenomenological approximate desription of gravitation).

I don't think you'll find anyone on this forum who claims that Newton's theory of gravity is mathematically better than or equal to Einstein's, or that it provides any useful physical description of the underlying physical mechanism of gravity. Of course it is a phenomenological approximation as you say. It just happens to be a particularly excellent approximation for a weak field. Newton was every bit as much a genius in his historical context as Einstein was in his.

But dismissing Newtonian theory answers nothing about the question whether spacetime curvature is physically "real" or just a superb mathematical tool.

1. Use weak enough field that there are linear relations only (one does not influence the other) and measure deflection of light knowing that the Newtonian part is due to the time dilation, so the rest is due to the curvature of space (as Einstein's did with the bending of light rays in vicinity of the Sun when both part turned out to be equal).

Please explain what you mean by "the Newtonian part [of light deflection] is due to time dilation." One doesn't typically see time dilation described as a Newtonian theory. Maybe it's just semantics. (I understand your point about space curvature.)

The mechanism of rest energy of a particle diminishing along its displacement vector directed towards the source (of energy that for some reason bends the spacetime) is rather simple (see the top of this post). ... It is a measurable conclusion since we can measure the amount of bending and it fits the theory through the principle of conservation of energy and the value of gravitational constant which origins we don't know yet just may try to guess.

The idea that GR allows a particle in freefall in a gravitational field to conserve its energy as it accelerates towards the gravitational source, and eliminates the Newtonian distinction between kinetic and potential energy, has always been a fundamental element of GR mathematics. I don't understand how a formulation derived from Landau is different from standard GR, or why you expect it to change our fundamental perception about gravitational action.

But even if we choose the best frame we can't get rid of curvature of space which means it might be real.

I disagree with this statement. In fact, in GR spatial curvature is ALWAYS frame dependent, and can be eliminated through a suitable change in coordinate systems. For example, an observer orbiting somewhat close to the event horizon of a black hole will measure the local space to be curved. But a plunging, freefalling observer who was initially at rest an infinite distance from the black hole and is accelerated towards the black hole by its gravity, and who falls through exactly the same local space, will measure that local space to be absolutely flat and Euclidian. This observer will continue to measure locally flat geometry even after plunging through the event horizon.

Curvature effects that are frame dependent aren't covariant, and arguably they are not universally "real" phenomena.

Jon

 

[MeJennifer]

Spatial curvature is a coordinate effect while spacetime curvature is coordinate independent.

 

[jonmtkisco]

Hi MeJennifer,

Yes I agree that spatial curvature and spacetime curvature are fundamentally different and distinct concepts. One should never treat the two as interchangeable for any purpose, or create ambiguity about which meaning is intended.

Jon

 

[JimJast]

Spatial curvature is a coordinate effect while spacetime curvature is coordinate independent.

Could you present some support for the idea that "Spatial curvature is a coordinate effect"? This is just opposite to what I'm accustomed to believe in. So if my belief is false I'd like to verify it and this way improve my understanding of Einsteinian gravitaton.

 

[JimJast]

I don't think you'll find anyone on this forum who claims that Newton's theory of gravity is mathematically better than or equal to Einstein's, or that it provides any useful physical description of the underlying physical mechanism of gravity. Of course it is a phenomenological approximation as you say. It just happens to be a particularly excellent approximation for a weak field. Newton was every bit as much a genius in his historical context as Einstein was in his.

Isn't it funny that one has to be a kind of genius to discover the inverse squares law of changing of some physical variables? What does it say about the rest of us? Aren't we, including famous philosophers, physicists and mathematicians who didn't find what Newton and Einstein found, just a bunch of idiots?

But dismissing Newtonian theory answers nothing about the question whether spacetime curvature is physically "real" or just a superb mathematical tool.

Please explain what you mean by "the Newtonian part [of light deflection] is due to time dilation." One doesn't typically see time dilation described as a Newtonian theory. Maybe it's just semantics. (I understand your point about space curvature.)

If you look a little deeper into gravitation then you see there a "tiny" effect of gravitational time dilation. Generally it is considered a "one more Einsteinian prediction that turned out to be right". It is "a tiny effect" because the Einsteinian gravitation is not taught in high schools and so physicists, if ever, learn about it only in their doctoral studies as a part of GR. This way they waste about 10 years of their best years and when they finally learn about the gravitational time dilation they think that first they have to understand tensor calculus before they can get involved in any thinking about the physics of gravitation. They are overwhelmed by the math and tend to think that the math is the key to understand Einstein (I live among them ). They are in no mood to pay much attention to physics and to particular curvatures. At least not that much as Einstein did. Since Einstein didn't have any tensor calculus yet to worry about. Just the plain physics.

So Einstein, by noticing that the Newtonian physics, if it is treated as physics and not math only, requires the gravitational time dilation, and knowing that nature must be consistent saw that this "tiny" effect is the basis of Newtonian gravitation. And it might have been causing the (apparent) gravitational force. Which in reality is an illusion caused by the time dilation. His genius was in the fact that the time dilation was not even observed then. So to postulate such an effect to explain the whole Newtonian gravitation was an act of faith in consistence of phisics that unlike the math must be consistent if it says something true about the nature. Afterwards he added the curvature of space, equal, as to its relative "strengh", to the time dilation, discovering this way all parts of gravitation (so far no other has been discovered, in nearly 100 years) justifying Einstein's leaving his theory to mathematicians to polish it after he solved his equations for the universe and discovered in the process the cosmological constant that mathematician tried to dismiss since it didn't appear "elegant" tho them. Then Einstein said "If you are out to describe the truth, leave elegance to the tailor." Now we know that Einstein's gravitation makes no sense without the gravitational constant, we don't agree yet to "Einstein's value" of it since it collides with the present model of the universe which is surely not Einstein's.

So as you may see, the Newtonian part of gravitation, is the time dilation being half of the reason for the deflection of light ray near the Sun. There is equal second part which has to be the space curvature (at least according to Einstein) and if Einstein is wrong you need to develop a new gravitational theory in which space can be flat. Then I should wait with my work until you do since my present work is based strictly on Einstein's gravitation and the curvature of space being the same as the time dilation. If it is wrong I don't need to go on and should find better use for my free time.

The idea that GR allows a particle in freefall in a gravitational field to conserve its energy as it accelerates towards the gravitational source, and eliminates the Newtonian distinction between kinetic and potential energy, has always been a fundamental element of GR mathematics. I don't understand how a formulation derived from Landau is different from standard GR, or why you expect it to change our fundamental perception about gravitational action.

Of course you are right. I learned it rading Landau, that's why I describe Landau. I could learn it from any other textbook. Why do you think that Landau is not standard GR?

In fact, in GR spatial curvature is ALWAYS frame dependent, and can be eliminated through a suitable change in coordinate systems.

You may draw a flat map (or a set of maps) of the Earth surface. Do you think it elininates the curvature of the Earth surface by "a suitable change in coordinate systems"? You wouldn't advise "flat Earth" even if to some people it is "impossible to understand" how come people in Australia don't fall off the Earth (and so they suspect the government fooling them for ideological reasons). Even worse, knowing that according to Einstein there is no "attractive gravitational force" in nature?

 

[MeJennifer]

You may draw a flat map (or a set of maps) of the Earth surface. Do you think it elininates the curvature of the Earth surface by "a suitable change in coordinate systems"? You wouldn't advise "flat Earth" even if to some people it is "impossible to understand" how come people in Australia don't fall off the Earth (and so they suspect the government fooling them for ideological reasons). Even worse, knowing that according to Einstein there is no "attractive gravitational force" in nature?

A false analogy.

Curved spacetime is intrinsically curved, independent of how it is charted but whether 3-surfaces in spacetime are curved entirely depends on how they are "sliced" from spacetime.

 

[jonmtkisco]

Aren't we, including famous philosophers, physicists and mathematicians who didn't find what Newton and Einstein found, just a bunch of idiots?

Well as they say, it's all relative, so compared to Newton and Einstein we could perhaps be considered idiots, but compared to clams we're all geniuses. Don't feel bad, no individual's intelligence comes within even an order of magnitude of the genius of perfect hindsight. In 2028 we're all going to feel really dumb about all the things we failed to comprehend in 2008 that will seem so obvious in 2028. And by 1955, Einstein in retrospect had any number of reasons to kick himself for missing many discoveries in his field made by others in the prior 40 years that were within the capabilities of his genius and subject matter expertise to discover himself.

If you look a little deeper into gravitation then you see there a "tiny" effect of gravitational time dilation.
...
So Einstein, by noticing that the Newtonian physics, if it is treated as physics and not math only, requires the gravitational time dilation, and knowing that nature must be consistent saw that this "tiny" effect is the basis of Newtonian gravitation. And it might have been causing the (apparent) gravitational force. Which in reality is an illusion caused by the time dilation.
...
So as you may see, the Newtonian part of gravitation, is the time dilation being half of the reason for the deflection of light ray near the Sun.

JimJast, after reading this I feel no closer to understanding why you say that Newtonian gravity is nothing but time dilation. I don't recall reading this anywhere else, and I assume I'm not the only one. Can you please give us a quote from a textbook or other source that describes how this conclusion is derived?

Why do you think that Landau is not standard GR?

I don't, but it was my impression that you claimed in an earlier post that mainstream cosmologists don't understand GR as you have conceptually derived it from Landau, and your PhD thesis is going to enlighten them about it. Maybe I misunderstood.

Jon

 

[yuiop]

The idea that GR allows a particle in freefall in a gravitational field to conserve its energy as it accelerates towards the gravitational source, and eliminates the Newtonian distinction between kinetic and potential energy, has always been a fundamental element of GR mathematics.

Are you suggesting that the rest mass energy of a falling particle changes as it falls so that the potential energy of the gravitational field does not have to be invoked to conserve energy?

If that is the case then I have derived this equation for Total Energy (TE) that satisfies those requirements with the assumption that the initial velocity of the particle at infinty is zero:

TE = \sqrt{m_0^2 c^4 \left( 1- \frac{2GM}{c^2R} \right) +m_o^2 v^2 c^2 }

Is that the sort of thing you had in mind?

Also note that energy is conserved without requiring potential energy of the field in the coordinate measurements of an observer that remains at infinity, but not from the point of view of local non inertial observers. For example local observers see the frequency (and therefore the energy) of a falling photon as increasing while the frequency in coordinate measurements remains constant.

 

[JimJast]

JimJast, after reading this I feel no closer to understanding why you say that Newtonian gravity is nothing but time dilation. I don't recall reading this anywhere else, and I assume I'm not the only one. Can you please give us a quote from a textbook or other source that describes how this conclusion is derived?

Jon, I found a quote for you in Wolfgang Rindler's Relativity, Special, General and Cosmological, chapter 9.4 Newtonian support for the geodisic law of motion. On p. 189 Rindler writes (as a conclusion about geodesic lines for slow motion in weak fields):

"A deformation of the time dimension therefore has a first-order effect on the length of those lines, wherease a deformation of the spatial dimensions has only a second-order effect. [...]".

And then comes the metric with Newtonian potential in time-time component and flat spatial part, as a sufficient approximtion of gravitation for velocities < 50km/s as producing error < 3x10^{-8} (as propotional to v/c squared).

 

[JimJast]

A false analogy.

Curved spacetime is intrinsically curved, independent of how it is charted but whether 3-surfaces in spacetime are curved entirely depends on how they are "sliced" from spacetime.

Of course you are right if no "suitable change in coordinate systems" is applied. Then certain ways of slicing can produce zero curvatures and others, non zero curvatures.

With a "proper scaling" of coordinates one can make any slice flat. This is done for the maps of the surface of the Earth (which are usually orthogonal to the time coordinate and so they are surely of a curved surface) so the analogy with a "suitable change in coordinate systems" is still exact.

 

[mysearch]

First, I would like to get clarification of Kev’s post #44, as I know he has spent some considerable time looking that the issue of relativity. Which observer perceives the conservation of energy, the distant observer or onboard observer?

[1] Distant Observer v_R = c\left( 1+ \frac {Rs}{r}\right)* \sqrt {\frac {Rs}{r}}

[2] Onboard Observer v_R = c\sqrt {\frac {Rs}{r}}

Now equation [1] suggests that the observed radial velocity goes to zero, while the onboard radial velocity goes to [c] at [r=Rs]. I would have thought only [2] was consistent with the conservation of energy?

#36: The Einsteinian predictions are exact (as far as we know of course) the Newtonian predictions are wrong (which we know for sure).

If possible I would like to try and get a better idea as to the scope and scale of the ‘errors’ in Newtonian predictions in comparison with GR. As an initial statement, it was my understanding that the discrepancies between Newtonian physics and Relativity only become apparent under the extremes of gravitational potential, i.e. space curvature, and/or the velocity of an observed frame approaching [c].

#43: JimJast, after reading this I feel no closer to understanding why you say that Newtonian gravity is nothing but time dilation. I don't recall reading this anywhere else, and I assume I'm not the only one.

I would also like to get a better understanding of the details of the premise on which the original statement was based. Have only just seen #46, which may address this question.

#36: So we have here the concrete rest energy of the particle and curvatures of spacetime and no forces, just energies and their conservation following from the fact that nature is unable to create energy out of nothing. If it were able, then our "gravitational force" as predicted by Einstein wouldn't be the same as Newtonian, yet it is. Which means energy conservation holds in Einstein's physics the same way as in Newtonian but it does not need a mysterious "potential energy" to be valid since it comes out of first principles through the relation between time dilation and space curvature.

Classically, while we refer to many forms of energy, they are said to all reduce to just 2 forms, kinetic and potential. If I remove `potential energy` from my vocabulary:

- How do I semantically describe the conservation of energy?

- Is the statement above implying that the conservation of kinetic energy is balanced by time dilation and space curvature?

Accepting the tenet of GR that gravitational force does not exist, but rather the path of an mass object with kinetic energy [Ek] is described by a geodesic path:

- Does this prevent an equivalent model being constructed based on the concept of force and potential energy?

- If the kinetic energy is conserved by space curvature, is there any implication that this curvature must require a source of energy and, if so, might we call it – potential energy?

Finally, I wanted to see if there was a comparative yardstick by which we could judge the scope and scale of the results provided by Newtonian & GR physics. In Newtonian physics, the total energy [Et], excluding rest energy, can be derived based on the conservation of energy:

[3] E_T = 1/2 m\left(v_r^2 + v_o^2\right) +\left (-\frac{GMm}{r} \right)

Where [vr] is the radial velocity and [vo] is the orbital velocity with the middle term corresponding to the kinetic energy, whilst the right term corresponds to the potential energy of gravitation. I believe the next equation is an equivalent form of [3] derived from the Schwarzschild metric, when divided thorugh by [d\tau], which has its roots in GR.

[4] E_T =1/2 m\left(v_r^2 + v_o^2\right) - \frac{GMm}{r} \left( 1+ \frac{v_o^2}{c^2}\right)

The similarities of [3] and [4] seem obvious, except for the term on the right, which now has an extra component that corresponds to the orbital velocity. If this equation is a valid assumption, it would suggest that the radial free-fall energy of both equations is comparable in Newtonian physics and GR, at least, to an onboard observer, as only the orbital kinetic energy changes as [vo] approaches the speed of light. As such, the discrepancy appears, in this specific example, to be associated with the orbital conservation of energy, only when [vo] approaches [c].

I would appreciate any clarification of the points raised. Thanks

 

[Garth]

There are a few ground rules to get cleared up.

First GR does NOT in general conserve energy, it conserves energy-momentum instead, which is different.

Energy is a frame dependent concept. When observers in inertial 'freely falling' frames are accelerating relative to each other, because they are at different positions in a gravitational field, then they will measure energy differently to each other, particularly the kinetic energy of other bodies. However they will all agree on the energy-momentum of a third body.

Emmy Noether showed that GR belongs to a class of theories she called "Improper Energy Theories" that do not in general conserve energy.

You can try to construct a gravitational theory that does conserve energy but that would be an alternative theory, not GR, and the challenge would be to get it to pass all the observational tests that GR has passed.

However, there are special cases in GR when energy is conserved, when there is a temporal or time-like Killing vector. One such case would be the static field of a spherical body, such as the Earth, ignoring other gravitational bodies in the universe, as observed from a frame co-moving with the Earth.

In this case for example you (on the Earth's surface with a clock and ruler) can watch an apple fall to the Earth and observe that its kinetic energy, and therefore total energy, increases as its falling velocity increases. This is so even though there are no forces operating, no work is being done, because the Earth and the apple are simply following their geodesic paths through curved space-time.

However this increase in kinetic energy is compensated by the increasing time dilation the apple experiences as it falls further into the Earth's field. The clock and the gravitational field are 'carried' by the Earth.

On the other hand we can transpose ourselves into the apple's frame of reference with clocks and rulers of measurement now being carried by the clock.

In this frame of reference the Earth is seen to fall towards the apple, and constantly increase in its velocity and kinetic energy.

Now the clock is being carried by the apple while the field is being carried by the Earth. As a consequence the time dilation operates in the opposite sense and does not compensate for the increasing kinetic energy, but the reverse.

I hope this helps.

Garth

 

[JimJast]

I would appreciate any clarification of the points raised. Thanks

I'll do it from the beginning, and only for Einstein's gravitation: Total energy of a particle is E = \frac{m}{\sqrt{1-\frac{v^2}{c^2}}}c^2\sqrt{g_{00}} (Landau's Theory of fields, p. 285). Being total this energy is necessarily conserved. You may check it by taking derivative with respect to displacement along its free fall path to see that after a few transformations it comes out as \frac{dE}{dx}=0. By putting v = 0 (no kinetic energy) you get also a force F = -\frac{dE(v=0)}{dx}=mg that used to be called "universal gravitational attraction" (not anymore though since it is plainly an inertial reaction resulting from forcing v=0). Ain't Einstein's gravitation neat?

 

[Garth]

Being total this energy is necessarily conserved.

Why is it necessarily conserved? Are you assuming a time-like Killing vector?

And yes Einstein's gravitation is 'neat' but if it wasn't it would not have worked and stood up so long under so many experimental tests.

Garth