At Rest with our Hubble view

[brucep]

With respect, brucep, when did Farsight say that? All I have read him say is that "the seconds are not the same", implying the 'c' invariance is a function of the differing timerate states in differing frame states. So, my naive reading of his comments so far tells me he does not argue about 'invariant c', but argues for the varying time (second) used to arrive at that agreed 'invariant c' between the differing frame states? He has just said as much in his reply to Tach, hasn't he?

What I surmise is based on the intellectually dishonest comments Farsight has made about what Einstein intended. He reaches bullshit conclusions because he doesn't understand the physics and he has no intention of making the intellectually honest attempt to learn.

He said this in a recent comment to przyk.

Originally Posted by Farsight
"This isn't relevant because in SR we use a constant speed of light. Einstein said repeatedly that this postulate had to be abandoned for GR". SR is part of the General Theory of Relativity. Most the local physics is done using the mathematics of SR. The metric which defines the spacetime tangent to the Riemannian manifold is the metric of SR. Based on Farsights comments he thinks the metric we evaluate remote measurements with is the same metric we evaluate local measurements with. I wrote it like this to show he doesn't have a clue about the real science. This is a very simple derivation for the local radial coordinate speed of light.

Starting with the polar form of the metric.

dTau^2 = dt^2 -dr^2 -r^2dphi^2

Setting r^2dphi^2 at 0 and setting dTau at 0 for light.

0 = dt^2 - dr^2 - 0

dr/dt = 1

 

[Undefined]

What I surmise is based on the intellectually dishonest comments Farsight has made about what Einstein intended. He reaches bullshit conclusions because he doesn't understand the physics and he has no intention of making the intellectually honest attempt to learn.

He said this in a recent comment to przyk.

Originally Posted by Farsight
"This isn't relevant because in SR we use a constant speed of light. Einstein said repeatedly that this postulate had to be abandoned for GR". SR is part of the General Theory of Relativity. Most the local physics is done using the mathematics of SR. The metric which defines the spacetime tangent to the Riemannian manifold is the metric of SR. Based on Farsights comments he thinks the metric we evaluate remote measurements with is the same metric we evaluate local measurements with. I wrote it like this to show he doesn't have a clue about the real science. This is a very simple derivation for the local radial coordinate speed of light.

Starting with the polar form of the metric.

dTau^2 = dt^2 -dr^2 -r^2dphi^2

Setting r^2dphi^2 at 0 and setting dTau at 0 for light.

0 = dt^2 - dr^2 - 0

dr/dt = 1

Thanks for your polite response to mine, brucep; I just caught it as I was leaving from editing typos in my equally brief/rushed posts to przyk above. Still little time today, so I am in a rush still, so briefly, two naive questions.....

Doesn't the actual "absolute number" value of 't' in the denominator 'dt' (used to calculate 'invariant c') differ in different frames, as we empirically observe with clocks at differing altitudes in the gravity well? If so, which frame's 't' is being used in your generalized derivation above?

And what exactly does "...spacetime tangent to the Riemannian manifold is the metric of SR..." mean in the real empirical experimental construct of 'GR space regions' where the 'time' in space'time' differences between altitudes in a GR gravity well as observed empirically physical effect even before any abstract 'spacetime' analytical construct came along?


Really, I must rush...back tomorrow. Thanks again brucep.

 

[brucep]

Thanks for your polite response to mine, brucep; I just caught it as I was leaving from editing typos in my equally brief/rushed posts to przyk above. Still little time today, so I am in a rush still, so briefly, two naive questions.....

Doesn't the actual "absolute number" value of 't' in the denominator 'dt' (used to calculate 'invariant c') differ in different frames, as we empirically observe with clocks at differing altitudes in the gravity well? If so, which frame's 't' is being used in your generalized derivation above?

And what exactly does "...spacetime tangent to the Riemannian manifold is the metric of SR..." mean in the real empirical experimental construct of 'GR space regions' where the 'time' in space'time' differences between altitudes in a GR gravity well as observed empirically physical effect even before any abstract 'spacetime' analytical construct came along?


Really, I must rush...back tomorrow. Thanks again brucep.

No. It's very specific what it means. It's physics. I did it in geometric units where c=1. It means the clock measuring the tick rate is local to the measurement. For instance if we measured the speed of light in a local Laboratory frame at CERN the clock and meter stick we use in the experiment is in the Local Lab frame at CERN. For the remote coordinate measurements I'll use the HST for example. For remote measurements made with the HST the tick rate is recorded on a clock at the HST. The following may help. The curvature component of the metric is 2M/r.

The remote coordinate speed of light.

dr/dt=1-2M/r

r=2M at the event horizon. Substitute 2M for r and the remote coordinate speed of light is 0. Now do it for select r=nM making sure you do it for a very large r=nM. The tangent space tells us the manifold can be approximated as flat over a segment of an objects natural path over the manifold [gravitational field]. That tangent space is where the local physics is conducted. As long as the experimental results are not effected by gravity. That tangent segment in our solar system is about an AU. Near the black hole it's much smaller. If you do what I suggested you'll find out that the difference between the local physics and remote physics is exceedingly small in the weak field. For the strong field around the black hole it can be extreme such as the remote prediction that the speed of light is 0 at the event horizon while the local speed of light is c. The only requirement for invariance is the local measurement. Another way to think about this is the local measurement for spacetime curvature is very small. So small that we can approximate a flat spacetime where it disappears. The measurement/reckoning of the remote coordinate speed of light includes the spacetime curvature over the entire path. Both the local and remote measurements are equally valid. The local DIRECT measurements are frame invariant. The REMOTE measurements are frame dependent. I'm pretty sure Farsight has this all jumbled up because he doesn't have the tools or will to learn this science. We just have to put up with his bullshit nonsense. Or hit the bricks like Markus decided to do.

 

[Cheezle]

Here is a good video with the title Hyperbolic Geometry is Projective Relativistic Geometry (full lecture).
The first couple minutes contain the important ideas.
[video=youtube;8qEGrD0Ciqo]http://www.youtube.com/watch?v=8qEGrD0Ciqo[/video]

 

[Farsight]

OK, I tried it. Oops, it seems that if expansion was the decompression of space, you would have some 'splanin' to do.

I'd hoped I'd given enough explanation for that, in that the stress-energy-momentum tensor includes shear stress, which indicates that space has an "elastic" nature, and the pressure terms indicate that it's something like a squeezed-down stress ball in your fist. When you open your fist, the stress-ball expands.

Why is it just decompressing in the deep space between galaxies?

Because where the galaxies are, it's gravitationally bound. Think of this as a stitched region of the stress ball that can't expand.

How did it get compressed.

I just don't know how are why the early universe had the qualities it had.

How can anything come from nothing.

I don't know how it can.

If you want to be associated with the mainstream you have to be able to answer some difficult questions, or acknowledge that the answers require some as yet unknowns, and require some new discoveries.

I acknowledge that we can't answer some of the questions.

Like I said to Brucep, I am looking, asking questions of the mainstream advocates, finding where they have no answers, and hypothesizing about ideas I find interesting in regard to 'splanin' things. Just a harmless hobbiest with questions you can't answer and answers that I find are internally consistent in my so called model, and not inconsistent with observational evidence and data.

Good on you. IMHO not enough people think for themselves.

 

[Farsight]

Well, if that formula does not look anything like a hyperbola to you, then I guess we are done here. No point beating a dead horse.

Nice talking to you Cheezle.

 

[Farsight]

While that is sadly true, like you say, that makes you an alternative kind of guy; you've been "outed" in the "cosmological preferences" community sense. And at the same time, it gives some unintended support to those of us who never claimed to be mainstreamers, and have therefore outed ourselves as non-mainstreamers for reasons including the incompatibility between GR and QM. How can both be right if one falsifies the other?

I think of myself as a leading-edge kind of a guy. Science advances when somebody demonstrates that "the mainstream" is wrong. And I think there is a way to reconcile GR and QM.

This sounds like a stretch, but a practical one, given that there is almost no distinction between the premise in my so called model that there is no empty space and all space is filled with energy density, and your view that space is energy. That is not grounds for you to object to my distinction that if you remove everything from space you are left with empty space, IMHO. It is close to just semantics.

It isn't. Remember my jelly analogy. When you add energy you're adding jelly. And jelly is space.

 

[Farsight]

And yet it was never abandoned.

It was abandoned in the sixties. See wiki: "Kip Thorne identifies the "golden age of general relativity" as the period roughly from 1960 to 1975 during which the study of general relativity,[18] which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics. During this period, many of the concepts and terms which continue to inspire the imagination of gravitation researchers (and members of the general public) were introduced...". You've seen the Einstein quotes and the Baez article.

In SR the speed of light is invariant in inertial reference frames, but the coordinate speed of light can vary -- even wildly -- in non-inertial coordinate systems. Simple examples of this are the coordinate speed of light in accelerating and rotating reference frames.

In SR we are dealing with light moving through space and observers moving through space. Their motion affects their observations, not reality. For example the distance between you and a star does not literally contract when you turn on your booster. We do not see space shrinking around you as you accelerate.

The invariance of c postulate holds in GR in exactly the same sense and with the same limitations and caveats as it does in SR. Nothing has changed between SR and GR as far as the speed of light is concerned. The only thing that has changed is that SR assumes the existence of globally inertial reference frames (i.e. flat spacetime) while GR relaxes this requirement (i.e. allows curved spacetime).

I beg to differ przyk. A reference frame is an abstract thing. It isn't something that actually exists.

In fact, take that GIF you keep posting, which depicts a vaying coordinate speed of light between two light clocks at different altitudes near the Earth's surface. How do you think that's actually derived?

By observing two identical NIST optical clocks. One is 30cm below the other, and goes slower than the other. You know the same applies to other clocks (apart from the grandfather clock). And you're familiar with the use of the gedanken parallel-mirror light clock in special relativity. You also know that the distance between the lower pair of mirrors has not increased.

Most of the variation depicted simply comes from working out how the coordinate speed of light varies in an accelerating reference frame according to SR, and then applying the equivalence principle. The situation would not look that way for a free-fall observer for instance, and it could even be inverted for an observer accelerating downward.

See Undefined's comments. All observers will agree that the lower clock runs slower. The variation doesn't come from any calculation using reference frames, it's empirical. And the equivalence principle only applies to an infinitesimal region. As I said, see the Synge and Ray quotes in Pete Brown's essay.

This is where you run into a problem if you try to treat the coordinate speed of light as a physical quantity and try to relate it to some idea of spatial inhomogeneity: the coordinate speed of light can vary or not vary depending on trifles like how you define coordinates or whether you're accelerating or not.

Coordinates are defined, not real. You cannot look up to the sky and see a reference frame like some kind of grid studded with coordinates. But you can look at those two clocks and see that one's going slower than the other. Again the issue revolves around empirical evidence v abstraction.

Suppose you're in a rocket in nearly empty space far away from any gravitating mass, such that the gravitational field is negligible. You do some experiments with light pulses and light clocks and find that the speed of light is invariant, just as SR says it should be. You then turn the rocket engine on and start accelerating. You repeat all your experiments and find that now, the coordinate speed of light is no longer constant, again just like SR says it should be. You furthermore find that the path light takes can bend, as depicted here for instance.

No problem. I understand SR, and I understand that my observations are affected by my motion or change in motion.

How do you explain that? Did all the space around you suddenly become inhomogeneous just because you started accelerating? Can the same region of space be homogeneous for one observer and inhomogeneous for another?

No, and no. The space I'm in didn't change a jot just because I started moving faster and faster through it. And another observer watching me will assure me that my light beam didn't bend at all. It's different for gravity. All the observers agree that the lower clock runs slower. All the observers will agree that light bends towards the star. All the observers will agree that a brick falls down. Not up.

 

[Farsight]

The REMOTE coordinate speed of light is frame dependent and can vary. The LOCAL coordinate speed of light is an invariant.

Only when "local" refers to an infinitesimal region. If "local" applied to the room you're in, those two NIST optical clocks would run at the same rate, and a brick wouldn't fall down.

 

[Cheezle]

Nice talking to you Cheezle.

I guess I am going to have to beat this dead horse some more. I can't help myself. Here is your formula.

$${s^2} = {t^2} - {x^2} - {y^2} - {z^2}$$

I am doing to dimensionally flatten to 2 dimensions (x and t) for simplicity. x,y and z are just normal 3-space so it does not change the principles.

$${s^2} = {t^2} - {x^2}$$

If we solve for s (spacetime distance) we get

$$s = \sqrt {{t^2} - {x^2}} $$

Wolfram Alpha evaluates this as an infinite cone. (sound familiar? light cone?)
http://www.wolframalpha.com/input/?i=t^2=s^2+x^2 If we plot all points of equal spacetime distance we get

$$1 = \sqrt {{t^2} - {x^2}} $$ where $$s = 1$$

This evaluates to a hyperbola. http://www.wolframalpha.com/input/?i=1=(t^2-x^2)^1/2
Which means that time and 3-space distance have a spacetime relationship that is non-euclidean (hyperbolic). The pythagorean theorem has no ability to tell us about spacetime distance from time and 3-space distance.

But let's look a little more. We can also determine that

$${t^2} = {s^2} + {x^2}$$ (also an infinite cone) If we look at all points of equal time, say where

$$t = 1$$ we get $$1 = \sqrt {{s^2} + {x^2}} $$

which evaluates to a circle. http://www.wolframalpha.com/input/?i=1=(s^2+x^2)^1/2+ Which means that 3-space distance and spacetime distance have a pythagorean or euclidean relationship. We can use it to calculate the time from the relation between 3-space distance and spacetime distance.

And finally,

$${x^2} = {t^2} - {s^2}$$

which also evaluates to an infinite cone. http://www.wolframalpha.com/input/?i=t^2=s^2+x^2 If we look at all points with equal 3-space distance (say x=1) we see that

$$1 = \sqrt {{t^2} - {s^2}} $$

which is also a hyperbola. http://www.wolframalpha.com/input/?i=1+=+(t^2-s^2)^1/2 For all equal 3-space distance points (as in a sphere) we see that the time and spacetime distance have a hyperbolic relationship and the pythagorean theorem will not aid us in calculating 3-space distance from time and 3-space distance.

The difference between a circle and a hyperbola is just a change of sign. So you see Farsight, the fact that you did not know about the hyperbolic nature of spacetime is a reflection of how deeply you have considered all of this. Which is not very deep.

 

[Motor Daddy]

IFor all equal 3-space distance points (as in a sphere) we see that the time and spacetime distance have a hyperbolic relationship and the pythagorean theorem will not aid us in calculating 3-space distance from time and 3-space distance.

Your wolframalpha says my v=(ct-l)/t has a geometric figure of a hyperbola. Are you saying that the one dimensional v=(ct-l)/t is somehow incorrect? Do you know how I created the 2 dimensional equation? I used Pythagorean Theorem. Maybe you need to look a little closer at this so you can see how Pythagorean Theorem relates to one dimension distance along the x axis, when regarding the y and z axis. Let's not forget, space (volume) is 3 dimensional distance (x,y,z)!

 

[rr6]

Brucep Appears To Be On The Mark here( imho )

Originally Posted by Farsight
"This isn't relevant because in SR we use a constant speed of light. Einstein said repeatedly that this postulate had to be abandoned for GR".

That is how I remmeber reading it the first time around also.

I also like very much Bruceps approach as follows even tho I cannot follow/grasp the formula meanings in whole and not much in parts. Intuititvely I just feel he has good grasp of the subject.

That is how I feel when I have read some of Markus' stuff in another thread. r6

SR is part of the General Theory of Relativity. Most the local physics is done using the mathematics of SR. The metric which defines the spacetime tangent to the Riemannian manifold is the metric of SR. Based on Farsights comments he thinks the metric we evaluate remote measurements with is the same metric we evaluate local measurements with. I wrote it like this to show he doesn't have a clue about the real science. This is a very simple derivation for the local radial coordinate speed of light.

Starting with the polar form of the metric.

dTau^2 = dt^2 -dr^2 -r^2dphi^2

Setting r^2dphi^2 at 0 and setting dTau at 0 for light.

0 = dt^2 - dr^2 - 0

dr/dt = 1

 

[rr6]

More On the Mark Brucep Stuff

I'm sorry I have nothing to add too or advance, only intuition says that when something intuitivle feels right, it is worth acknowledging. Wish I had the mathematics to follow specifics. Not understanding the mathematics or a lot of the mainstream physics, I have to rely on my intuitive feelings from what I have read as reference to the bits and pieces of math and physics that so many of cosmos lovers have piece-mealed together along the years of study and exploration.

Thx to brucep for the physics parts that just seem on the mark to me. If only we had some who can bring the math and concepts into more simple format for us less educated--- in the math and physics --to really appreciated and validate or not with some confidence.

r6

The REMOTE coordinate speed of light is frame dependent and can vary. The LOCAL coordinate speed of light is an invariant. Farsight probably thinks there's only the coordinate speed of light. That frame doesn't exist.

dr/dt = 1 Local coordinate speed of light. Invariant.

dr/dt = 1-2M/r The remote coordinate speed of light. Frame dependent.

We use local coordinate speed for light because there is no local proper frame for light. Not understanding the difference from where these measurement are made are the main reason why so much Farsight type nonsense is proliferated in these public forums. IE: not understanding the difference between frame invariant and frame dependent. Completely confused by reference frames. It's comical, but very annoying, when Farsight says Einstein had to abandon the notion that c is invariant so GR could evaluate natural phenomena from remote coordinates. It just screams of ignorance.

No. It's very specific what it means. It's physics. I did it in geometric units where c=1. It means the clock measuring the tick rate is local to the measurement. For instance if we measured the speed of light in a local Laboratory frame at CERN the clock and meter stick we use in the experiment is in the Local Lab frame at CERN. For the remote coordinate measurements I'll use the HST for example. For remote measurements made with the HST the tick rate is recorded on a clock at the HST. The following may help. The curvature component of the metric is 2M/r.

The remote coordinate speed of light.

dr/dt=1-2M/r

r=2M at the event horizon. Substitute 2M for r and the remote coordinate speed of light is 0. Now do it for select r=nM making sure you do it for a very large r=nM. The tangent space tells us the manifold can be approximated as flat over a segment of an objects natural path over the manifold [gravitational field]. That tangent space is where the local physics is conducted. As long as the experimental results are not effected by gravity. That tangent segment in our solar system is about an AU. Near the black hole it's much smaller.

If you do what I suggested you'll find out that the difference between the local physics and remote physics is exceedingly small in the weak field. For the strong field around the black hole it can be extreme such as the remote prediction that the speed of light is 0 at the event horizon while the local speed of light is c. The only requirement for invariance is the local measurement. Another way to think about this is the local measurement for spacetime curvature is very small. So small that we can approximate a flat spacetime where it disappears. The measurement/reckoning of the remote coordinate speed of light includes the spacetime curvature over the entire path. Both the local and remote measurements are equally valid. The local DIRECT measurements are frame invariant. The REMOTE measurements are frame dependent. I'm pretty sure Farsight has this all jumbled up because he doesn't have the tools or will to learn this science. We just have to put up with his bullshit nonsense. Or hit the bricks like Markus decided to do.

 

[PhysBang]

I'd hoped I'd given enough explanation for that, in that the stress-energy-momentum tensor includes shear stress, which indicates that space has an "elastic" nature, and the pressure terms indicate that it's something like a squeezed-down stress ball in your fist. When you open your fist, the stress-ball expands.

To prove your point, you just have to show us the equations. Show us how the actual stress-energy in an actual tensor describing it leads to expansion. Einstein did it many times.

 

[Cheezle]

Your wolframalpha says my v=(ct-l)/t has a geometric figure of a hyperbola. Are you saying that the one dimensional v=(ct-l)/t is somehow incorrect? Do you know how I created the 2 dimensional equation? I used Pythagorean Theorem. Maybe you need to look a little closer at this so you can see how Pythagorean Theorem relates to one dimension distance along the x axis, when regarding the y and z axis. Let's not forget, space (volume) is 3 dimensional distance (x,y,z)!

Uh oh, do you hear that sound? Oh no, it's a fast approaching Motor Boat with Motor Daddy water skiing behind it. He has a wild look in his eye and is swinging a torque wrench menacingly in my direction. I say we all get the heck out of here before the inevitable happens.

 

[Anew]

I think viewing is often flawed a flaw when a purport of response of 'survivalism when a viewer 'grasps at natural free motion. i.e one can encourage a plant to grow at artistic differential status i.e bonsai or expectation. Does cosmic space really need human ?direction. (I have not been a NASA emplyoyee) I do like to think that earths twin like 'rainbows come in twin exists (perhaps we are still too socially primitive to have gander to earth's elemental pal) There had been a book written years ago about how people can talk to plants, and !Yes Dr. Dolittle represented in a film feature presentation.

I hope this reply wasn't too irreletave of the idea of the conduction of the hubble vehicles activity. Perhaps someone else has fact knowledge on whether or not the hubble creates discord or it travels in objectivity 'unanimously -here unanimously used in form of not animately

 

[Aqueous Id]

Uh oh, do you hear that sound? Oh no, it's a fast approaching Motor Boat with Motor Daddy water skiing behind it. He has a wild look in his eye and is swinging a torque wrench menacingly in my direction. I say we all get the heck out of here before the inevitable happens.

Thanks for the head's-up, Cheez, I'm reaching for the high-water waders. Oh yeah, better grab that hard hat, too. I wouldn't want to have to explain the Pythagorean Theorem as it relates to Lorentz, at least not to a person who takes a Torque-o-centric view of Ultimate reality,

 

[Beer w/Straw]

MD called my posts "drivel" before.

:bawl:

 

[Motor Daddy]

Uh oh, do you hear that sound? Oh no, it's a fast approaching Motor Boat with Motor Daddy water skiing behind it. He has a wild look in his eye and is swinging a torque wrench menacingly in my direction. I say we all get the heck out of here before the inevitable happens.

I know how to properly use a torque wrench, and I'm a pretty-good slalom water skier too! I'm also an excellent snow skier. Black runs! Made it to the top ten in USAREUR!

You obviously don't know who you're messing with!

 

[przyk]

It was abandoned in the sixties. See wiki: "Kip Thorne identifies the "golden age of general relativity" as the period roughly from 1960 to 1975 during which the study of general relativity,[18] which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics. During this period, many of the concepts and terms which continue to inspire the imagination of gravitation researchers (and members of the general public) were introduced...". You've seen the Einstein quotes and the Baez article.

What does the quote you pulled from Wikipedia have to do with the coordinate speed of light? How do your Einstein quotes or the Baez article address the fact that the coordinate speed of light is just as variable in SR as it is in GR, and for the same reasons?

In SR we are dealing with light moving through space and observers moving through space. Their motion affects their observations, not reality. For example the distance between you and a star does not literally contract when you turn on your booster. We do not see space shrinking around you as you accelerate.

The distance between me and the star would shrink very literally according to any standard definition of distance you would care to use. I don't know what it is supposed to mean for "space" to contract.

I beg to differ przyk. A reference frame is an abstract thing. It isn't something that actually exists.

"Exist" as in "can be constructed/defined". In SR (flat spacetime) it is always possible to map the whole of spacetime with a globally inertial reference frame. In GR, it is not possible to map the whole of spacetime with a globally inertial reference frame if the Riemann curvature tensor is nonzero. This is essentially the only "postulate" of SR that is abandoned by GR.

By observing two identical NIST optical clocks. One is 30cm below the other, and goes slower than the other. You know the same applies to other clocks (apart from the grandfather clock). And you're familiar with the use of the gedanken parallel-mirror light clock in special relativity. You also know that the distance between the lower pair of mirrors has not increased.

This is flat out wrong. Gravitational time dilation was derived by Einstein on purely theoretical grounds as early as 1907. You yourself have frequently cited a 1911 paper in which Einstein gives the coordinate speed of light formula as $$c' \,\approx\, c(1 \,+\, \Phi/c'^{2})$$. This was long before the first experimental confirmation of gravitational time dilation. Again: do you know how these were derived?

All observers will agree that the lower clock runs slower.

This is also wrong. A free-fall observer won't necessarily agree for instance.

And the equivalence principle only applies to an infinitesimal region.

It also holds, to a good approximation, over larger distances where the spacetime curvature is small. Like near the Earth's surface, for instance.

But you can look at those two clocks and see that one's going slower than the other. Again the issue revolves around empirical evidence v abstraction.

Speaking of empirical evidence, can you cite an experiment where two clocks at different altitudes were compared by a free-falling observer?

It's different for gravity.

Since when?