Make out the position of Andromeda

[marcus]

I also want to take a moment to thank the moderators and participants on Physics Forums for giving me so many interesting things to think about.
...

thanks to you as well, nc, for the mind-mill's grist you contribute,
you give as good as you get, by my rough reckoning

 

[Kea]

Nightcleaner,

Your thoughts are an inspiration to us all.

 

[Spin_Network]

I agree! If for no other reason is right.

I am still fumbling with the wording of that CNS prediction. As Smolin stated it in a 1995 paper, it is put in a positive way:

(remember he wants to say that we have a parameters which are as good as they can get for prolific black hole production, so any change should make black holes less prevalent if it changes things at all, so he says)

"Any small change you could make in the parameters of the standard physics and cosmology models would cause black holes to be fewer, or leave their number unchanged."

One has to be careful of the vast number of predictions about Blackhole Production factories?..Black Holes are the singularity 'end' of certain Stella Mass Production lines?..if Stars create Blackholes as an emerging singularity phenomena, then either the standard model is wrong..or god forbid, Smolin is way off target?
prolific black hole production must be ongoing..as the Universe age's and wain's out..so must the Blackholes by fact of lack of Stella Source's, fewer Blackholes will always prevail at a distant future, by fact of above..the Universe past cannot therefore have 'Less' Blackholes.

I have to point out that a number of authors have papers detailing the that the Universe could not have produced a finite number of Stars at the same instant as a finite number of Blackholes?

 

[Garth]

nightcleaner - Thank you for your comments and questions.

The 'rubber sheet model' is only an analogy.

Three points.

First, in order to be able to picture it one space dimension has been suppressed.

Secondly this rubber sheet in the language of GR is the 3D space all around us.

Thirdly, and here I refer to "This leads us into the frozen instant", which is why I said, "take a slice through space-time of simultaneous events", you are right, such a slice is a frozen instant! The extra dimension you mention in Einstein's thought is the dimension of time, that is why you have to talk in terms of a 4D space-time and not just space or time. (Notice how I also highlighted these three separate concepts in my post above.)

If you do not want to picture the analogy by ‘standing outside the model’ consider the intrinsic curvature measured by the behaviour of ‘straight’ or ‘parallel lines’ drawn in the surface. It is this curvature that the ‘bent light ray’ observation was measuring.

There is a mystery in why the presence of mass should cause space-time curvature. Density can be connected to “the moment of rotation of the curvature” through the basic Einstein field equation; in the large textbook “Gravitation” by Misner, Thorne and Wheeler this is dealt with in chapters 15 and 17, but I cannot quickly deal with it here.

Does Einstein's concept of curved space-time work? Well it has been tested again and again and so far it seems to! GPB is the latest, and most expensive, (!) in a long line of experiments. However SCC also predicts the same results in all experiments up to the present date, so GPB could still be interesting!

Finally what is GPB measuring? As with the rubber sheet analogy all I can give you is a picture, the real explanation both for the gravitational field itself and the GPB experiment is to be found in the mathematics and the concepts they encapsulate. GPB measures two precessions of a gyro-compass (actually four of them) in a circular polar orbit predicted by GR (and SCC), the gravito-magnetic, or ‘frame-dragging’ (Lense-Thirring effect) precession in an E-W direction, and the geodetic precession in a N-S direction. The gravito-magnetic precession is caused by the spinning Earth dragging the inertial compass of space-time with it. The geodetic precession can perhaps be described by the inertial-compass, the gyro’s axis, being ‘tipped over’ in a N-S direction by the slope of that curved ‘rubber sheet’.

I hope this helps.

Garth

 

[nightcleaner]

Very helpful indeed, Garth, and thank you for being patient with my ignorance. I wish I could read the mathematics but that language is not yet fluent for me. I can make out bits here and there but still need help to get the story line.

So the two dimensional sheet is an analogy, of course, or as I said, a model. What does it mean in three dimensional space? Well, first off, the idea seems to be that the gravitating object "stretches" or somehow deforms space nearby, using the inverse square rule as a guide. Space close to the object is deformed more than space farther away from the object. We may imagine then a region of "free space" in which there is no deformation, and take that undeformed region as a place to establish our meter. When we take the meter from the undeformed region and compare it to the same meter in the deformed region, there is a difference, the difference of course being a measure of the amount of deformation.

The meter near the gravitational object is compressed compared to the meter in free space. This is apparent from the convergence of the lines in the model. It is a little hard to get the visualization correct since the gravitating object in the model stretches the lines, making them longer in the radial direction, but leaves them unchanged or even shorter in other directions. This seems to me to be an artifact of the model. In the real three dimensional space, the gauge lines must be compressed in all three dimensions.

That's why it seems to me to make more sense to speak of spacetime density near gravitating objects. Space and time, I think, are compressed by the gravity field, not stretched, and the compression is very nearly uniform in every direction from any point in the affected space. In this way gravity can be seen as an expansion of spacetime units as the observor moves outward through the gravitational field, and their expansion can be seen as identical with the expansion of the universe as an entire entity. Cosmic expansion and local gravitation seem to me to be two views of the same effect.

Hi Kea, thank you darling, I am becoming quite fond of you. And Marcus, of course, don't be jealous, and welcome to Spin network.

Be well,

Richard

 

[Garth]

The rubber sheet analogy or model allows us to visualise the concept of curvature 'from the outside'. However, as you point out, space-time is all around us, we are 'inside'. That is why I carefully explained that curvature can be described 'from the inside' by the intrinsic behaviour of 'parallel lines', actually two adjacent and initially parallel geodesics, the paths of two freely falling test particles. If they converge, or diverge, or rotate around each other, then although you may be also in a freely falling laboratory, and ‘weightless’, you may conclude that there is a gravitational field, and by measuring how these test particles are behaving relative to each other you detect curvature by measuring tidal forces.

Another way of measuring curvature is to parallel transport a vector around a closed circuit until it is back where it started. If you find that it has in fact rotated with respect to its initial direction then you again conclude that there is curvature i.e. a gravitational field. This is indeed what the GPB geodetic precession measurement is doing.

I am intrigued by your suggestion that a metre would be compressed when it is brought into a gravitational field. The question is, "How do you measure the change?" - by another metre rule? In which case it too will suffer the same deformation and you will not be able to detect a change. In GR the metre rule is defined to be ‘rigid’ i.e. of unchanging length.

However in SCC the metre rule does change, albeit in the opposite way; that is it is shortened when lifted out of the gravitational field. This is because, as it is lifted, it gains gravitational potential energy and hence (according to SCC) rest mass. As the diameter of an atom is inversely proportional to its mass, other things being equal, the ruler shrinks. Clocks also speed up.

But how do you measure these changes in SCC? By comparing the size of atoms and behaviour of clocks with the wavelength and frequency of a photon. What do you then observe? Gravitational red shift! But now interpreted, not as a loss of energy by the photon, but a gain of (P.E.) rest mass by the apparatus measuring it.

Garth

 

[nightcleaner]

Hi Garth

I came by the idea that spacetime is compressed near a gravitating object by means of considering what the idea of the word "bent" is. You take two points connected by a line, impose a force causing the line to "bend," and the result is that the original, unbent line is now longer than the distance between the two points. Hence, the resulting line is bent like a bow, and the new shortest distance between the two points is like the bowstring.

But that is just another model, we are not practicing archery. The "bend" could just as easily be seen as a compression or increase in density of the line.

I think when using these models we need to be more careful of our idea of dimensionality. If we start from the definition of the point in a space without undefined qualities (Machian space I think would fit this category) then two defined points make a straight line, since a straight line can be defined in the space from the two points.

It may be useful to ask how we came by two points. We started with a single defined point, in an otherwise undefined space. It has the quality of being, which means it has something within. It contains the category of itself. This requires the definition of the opposite of within, which is the undefined space outside the defined object, in this case, a point. You see, I hope, the sense of evolutionaly steps I am trying to establish for a higher dimensional geometry.

The second point is necessarily outside the first point, so that we may have a basis for counting. It initially could be anywhere outside the first point, and so everywhere outside the first point. It is a sense of representation of two conflicting ideas. One idea is that it is outside the first point, not further defined. The other idea is that it is somehow like the first point, so that a new category can be formed containing two points in otherwise undefined "Machian" space. Since it is outside and somehow like, there must be an outside that is somehow unlike, or else like has no meaning. In this way, by a self-reflective bending, a self creation if you will, the geometry of the universe can be mentally traced from the first point.

I refer the reader interested in details of geometric evolution up through the third dimension to Euclid.

My position then is that our universe, however many dimensions you count after that, is evolved according to geometric principles. The fundamental laws of the universe are all self evolved from geometry, and in no case is there an outside finger poking new holes in reality. A hole, in this idea, is just a point. Instead, the second point and all the points thereafter are evolved from within the first point.

Every point is the same, so there is no way to distinguish between the first and second point or any point evolved thereafter. Every point evolves the same way. In this way the universe is a self creating burgeoning of form into undefined space. It is expanding from every point in every possible dimension.

What is a possible dimension? Well, from the first point came the second point, which we have as a single dimension. The point itself is zero dimension. The line is one dimension. Bend the line, and you have another dimension, which you can confirm by laying a strung bow on a table. You see that the curve is in the dimension of the table top, which is two dimensional, having length and width. This is again, just a model, but with the caveat in place, it serves to communicate the geometric idea, as long as we stick to the math and don't get distracted by the archery.

I have gone on too long, but I hope you see that the notion that the "meter" in its "metric" can be usefully thought of as smaller when near gravitating objects. And then we can carry that image to its conclusion, which is that eventually the metric approaches zero in the presence of sufficient mass, which is where spacetime collapses into singularity.

The idea of a collapsing meter makes it very hard to talk about the radius of any space containing a black hole, if indeed a black hole can be contained. Its a paradox Zeno would recognise. We can, however, measure the radius of a black hole from the outside, with the understanding that the size of the hole will then be a variable dependent on the conditions we bring into play in the attempt to make a measurement. In a sense, the size of the hole depends on where you stand when you make the measurement!

You said "However in SCC the metre rule does change, albeit in the opposite way; that is it is shortened when lifted out of the gravitational field. This is because, as it is lifted, it gains gravitational potential energy and hence (according to SCC) rest mass."

I am not clear on your idea of rest mass. Are you saying that rest mass depends on distance to local gravitational objects?

Eager to hear more.

Thanks,

nc

 

[Garth]

I am not clear on your idea of rest mass. Are you saying that rest mass depends on distance to local gravitational objects?

In SCC there are two convariant frames of measurement.

In its Einstein conformal frame the rest mass of fundamental particles is constant and the theory reduces to General Relativity.

In its Jordan conformal frame the energy of a photon remains constant when measured in a preferred inertial frame selected by Mach's Principle, the co-moving Centre of Mass/Momentum frame.
In this frame the rest mass of a particle includes gravitational potential energy, so m = m₀exp(Phi_N) where m₀ is its mass at 'infinity' and Phi_N is the dimensionless Newtonian gravitational potential
Phi_N = GM/(rc²).

Garth

 

[nightcleaner]

This is interesting to me, and I hope my conversation is not boring you. I have looked at the idea of Machian space in the bucket problem. In my mind, I have retained the idea of Machian space as beginning point from which to proceed in an evolutionary fashion in building the geometries that should lead us to an understanding of the reasons for the standard models having so many seemingly arbitrary parameters.

Well let us assume a Mach kind of space, at least in the context of events which occur near the Planck scale, or perhaps just under the Fermi scale. These events are so local that nothing much at our scale affects them appreciably anyway. If I understand correctly, you are preferring an inertial frame in which all particles of interest possesses a co-moving center of mass and differ little from each other in terms of angular momentum. In my words, they are not spinning, orbiting, or translating through at relitivistic velocities. Does this seem to match up with your understanding?

We might think of a bunch of rocks that happen to be moving together somewhere out in the distant reaches of intergalactic space perhaps, where any local field is likely to be mostly pretty flat, so that perturbations can be ignored. These rocks are not spinning like tops nor orbiting around each other nor are they rushing toward or away from each other with any great velocity. Pardon me for repeating the landscape in different words but I want to get as clear an image as possible. We might then gedank an apparatus in such a space, such as a massive and very dense torus, and consider what light does as it passes near the center of mass, which of course would be in the hole. We can aim a laser beam of light as close to or on either side of the hole as we like, and see where it comes out the other side. Is it deflected by the center of mass?

I think it certainly should be.

If we substitute a beam of relitivistic particles for the beam of laser light, we can likewise measure where they come out on the other side.

If I understand correctly, you are saying that in this gedank tank light will be deflected more than will the relitivistic particles? That makes some sense to me. The light has no momentum and so will not have any inertial reason to resist being bent. The particles, having momentum, will be bent less. The more massive the particle, the less it will bend. Is this what you are talking about? Or have I missed the point completely again?

Thanks for being here, Garth. I am enjoying this conversation, and learining about the Jordan conformal frame.

nc

 

[Garth]

I'm not sure about your gedanken set up, however, there are one or two other things I would like to comment on.

First light does have momentum, but not rest mass, because light travels very quickly the deflection is very small compared to the deflection of a solid body such as a space craft. If we are talking about gravitational deflection then rather than talking about light (paths) being bent it is better to think that it is the space-time itself, in which their null-geodesics (world-lines) as embedded, that is curved by the presence of mass and energy.

The hypothesis of SCC, (in its Jordan frame), is that, whereas light travels along these (null) geodesic paths, non-relativistic matter is perturbed from them by the scalar field force. The result being that light 'falls' more quickly (at 3/2 the acceleration) than matter. In my post #34 I explained that because the measurement of the deflection of light measures two effects, one of which in SCC increases by a factor 3/2 whereas the other decreases by 1/2, the net result is the same as in GR.

Garth