How to straighten Spacetime

The introduction of an increment of time into the structure of space has caused space to be described as “curved”. This temporal measure is given a spatial form equal to the time it takes for light to travel between two points in space-time. The line element including this measure of time is written as…

ds² = c²dt² - dx² - dy² - dz².

The argument goes that the reason space looks so Euclidean or flat is because the effect of the c^2dt^2 term is so small.

One way to straighten out the curvature of spacetime is to eliminate the spatial measure of time (c²dt² ) from the description of space. However to do so would appear to do away with General Relativity and since the correlation to observation is so well established, such talk sounds like nonsense.

However it is possible to propose a structure to spacetime that still includes the temporal relationship imposed by relativity but also preserve the Euclidian structure of space, and keep the locally observed relationships of General Relativity.

Imagine a matrix like configuration of points in spacetime, like the location of atoms in a salt crystal.

All points keep their relative positional value in terms of the spatial distance and the temporal distance between all the points in this metric of spacetime. This is a flat or Euclidian Space. Now lets curve it yet keep it Euclidian.

If we take this matrix of points and uniformly expand them, it will take a certain amount of time to cause this expansion. This passage of time is uniquely different from the time interval between points in it’s geometric interpretation.

Since this is a proportional expansion, all the relative measures between the points have preserved their Euclidian relationships.

But what about the relative time interval between the two points? (Remember, this is the incremental term that curves space). In order to keep the relative measures of the intervals of time between the two points the same, it must take light the same measured interval of time to pass between the two points. Also, all other possible local measures of this interval of time must correspondingly show the same relative passage of time. Such an expansion preserves the locally observed “flat” structure of space. The increment of time between points becomes trivial since it directly corresponds to the distance measure and is thus not an additional component.

This perseverance of all local measure of time sounds impossible; it is not. It is possible to derive a theoretical model that predicts that the interval of time associated with a photon traveling between two points will decrease in direct proportion to all physical measures of time, be it orbiting periods, rotational rates, mechanical clocks, vibrating crystals, or oscillating atoms.

Such a theoretical metric is locally Euclidian, everything is orthogonal and “relative” time does not distort space locally.

However, from a historical perspective, space is changing over time, causing a curvature to space. This curvature could be plotted over the passage of time describing a relationship of how space expands over time. In order to do this, some “absolute” reference frame or “eye of God perspective”, exempt from the expansion is required to be established in order to describe how this expansion of space, and the resulting curvature results. Were it not for the fact that it takes time for a photon or object to pass though space, there would be no indication of the curvature of space.

Two dimensions of time are being established. The relative time interval between points, (which is also a local measure of time) and an Absolute or historical measure of time used to describe the rate of expansion between points.

General Relativity confuses the two dimensions of time and inserts the curvature due to expansion as apart of the metric between the points in spacetime. General Relativity still works locally because the “present” relative measure of an interval of time is nearly identical to the “present absolute measure” and all formulations using general relativity incorporate a time interval consistent with the time interval over which spacetime expands. As a photon, (or mass) travels from point to point there is an effective curvature that would be observed since the metric of space has expanded. Over the course of cosmological scales, the geometric relationship between the two dimensions of time become important. Any prediction of the effect of gravity on a cosmological scale of observation will prove to be inaccurate, hence the problem with the rates of rotation of stars in spiral galaxies, which has resulted in the invention of “dark matter”.

Since space is expanding, it becomes curved based upon historical measures. The effect of gravity varies according to cosmological measures of time. Spacetime is locally flat or Euclidian.

John Kulick AKA snowflake.

What's your prediction?

Hi A Thousand Pardons

You asked “What’s your prediction?”

The prediction is that the effect of gravity is a temporally dependent measure.

There are two ways to explain how the stars in the perimeter of spiral galaxies are retained. One is to assume that the effect of gravity is constant, resulting in the assumption of some kind of unobserved, undetected mass that “holds” these stars in place. The other is to assume that the effect of gravity can be modified. Since my model requires the effect of gravity to be dependant on temporal or historical measures, the latter choice falls out of the proposed model.

John

I don't want to speak for A Thousand Pardons, but I'd be wanting something a little more specific. For example, here's the rotation curve for a reasonably typical spiral galaxy, NGC 2403. Here's some more detailed information about it, including links for detailed data, and it should be easy enough to track down any further information you might want. Now, how does your model fit the observed rotation curve?

I still don't understand your two different "dimensions" of time. I think you are misusing the term dimension. What you have in mind are two scales, two different ways of measuring the same thing.

Here's a question for you: what is the "relative" time interval between today (2005 June 8 ) and the explosion of the supernova of 1054 (1054 July 4)? What is the "absolute" or "historical" time interval between those two dates? Are they different? If so, by how much and why? Are they the same because the interval is not large enough to discriminate between the two? I can understand that. In that case, what about the relative and historical intervals between today and the creation of the Solar System? Same thing, are they different? If so, by how much and why?

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Hi Grey and A thousand Pardons

You asked for something more specific regarding the application to the dark matter assumed in galaxies to keep galactic structure.

I will try to answer this question but it will be a rather crude answer with a lot of loose ends. Not much different from the technique using the assumptions of dark matter, but it will help briefly explain how the model works.

(One comment, this is a bit of a digression from the primary focus of the original posting, which was a geometric method of preserving the Euclidian nature of space locally yet which still allows the relationship of time to curve space based upon historical measures).

One way to show how the effect of gravity varies across a galaxy is to apply the same technique that dark matter modelers use to predict the pattern of dark matter distribution necessary to preserve celestial stability. It is not a very satisfying technique since it is not produced from theoretical considerations, but such an approach does characterize the necessary predictions the theory should conform to. Instead of stating that so much dark energy is there, one simply states that the effect of gravity is increased by the appropriate amount.

Since the proposed model asserts that the effect of gravity is a function of absolute or historical time, in order to vary the effect of gravity across a galaxy, the historical location of stars within a galaxy becomes important. Since these are now historical separations, the curved aspects of spacetime associated with general relativity are appropriate to use but with a different geometric interpretation. Instead of visualizing gravity wells one visualizes time wells. The cores of galaxies are the “wells” or depressions in the plane of time and are “younger” than the outer parts of a galaxy. (Young stars are observed in the perimeter of a galaxy because it takes so long for the gas clouds to coalesce where the effect of gravity is not as intense. Also since the cores of galaxies are located where matter first enters the universe in this model (multiple “singularities” as opposed to one, (actually the core is were inrushing strands of a rapidly rotating of matter enter our universe)) the cores also contain some of the oldest matter in the universe. I said that there would be a lot of loose ends.)

Anyway, the gravitational relationship of stars in the perimeter to the stars in the core becomes greater that that locally assumed because of the increased effect of gravity based upon their historical locations in which the gravitational relationships are established. It takes a bit of “fitting” of the relationships to preserve the relationships, the “well of time” has to be shaped to yield the increased gravitational relationships necessary to preserve necessary gravitational effect.

This fitting is not that artificial since certain boundary constraints exist in the model. Presently there should be a universal decelerative effect on the stars in the perimeter of galaxies of the order of c x Ho. (Masreliez in his modeling of a scalar expansion predicts precisely this http://www.estfound.org/galaxy.htm , where as I have this term reduced by the square root of two, This is also near the value M. Milgrom arrives at in his Modified Newtonian Model http://en.wikipedia.org/wiki/Modifie...onian_dynamics ). (Note Masreliez work is based upon relative measures. While the forms the equations look different, once my absolute measures are translated to relative measures, the forms of the equations become similar.).

John

Hi Celestial Mechanic

My definition of dimension..

Dimensions describe change.
(I know that this is too simple, but bear with me, simple is better).

If some physical property can be described as changing, then that change is described by a dimensional measure. How many times I smile in a day can be correlated to a “smile dimension”. The universe is composed of many dimensions.

Physics is more restrictive in the application of dimension. Dimensions should be unique or I prefer “fundamental”. This simply means, as you know, that a dimensional measure or description is not the result of a simple scalar product of an existing dimension. (My smile dimension could be correlated to a more fundamental “happiness dimension” ).


What is physics?
Physics is the mathematical description of nature.

What tools does a physicist have to describe nature?

Rulers and Clocks.

(A mass is so big, accelerates so fast, an electric charge is so “strong” and accelerates so fast in an electric field, etc. etc. Everything is defined by rulers and clocks.)

Relativity defines time as the time interval between points. All applications of special and general relativity are all described by the interval of time between points.

Is this enough to describe reality?

No.

Every point has a unique location in history relative to the beginning of time.

It may be argued that this historical measure of time is just a scalar multiple of relative time. Such a belief would be wrong.

Where you are now is a unique moment of time. Nowhere in all the applications of relativity is their any dependence on when the measures are made. (Except somewhere in the bogus inflation theory) Relativity ignores a fundament physical measure of reality.


You also asked for examples of absolute and relative measures of time.

If we look objects in the past, this is a measure of absolute time. An object observed 1 billion light years away is observed 1 billion absolute years in the past.

How ever in the billion years that it has taken light to reach us, more than one billion years of relative time has passed. Relative time and Absolute time are hyperbolically related. This means that in absolute measures the universe is finitely aged but based upon our relative measures of time, the universe is nearly infinitely aged. A uniformly expanding universe has characteristics of the Big Bang model and a Steady State model.

Sample problem

An object is observed 4 billion light years away. What is that objects Absolute location in time? How much relative time has passed while the light has traveled the 4 billion years? Assume the Universe is 8 billion years old.

The objects absolute location in time is 4 billion years from the beginning of time, using “today’s” measure of time to establish a universal correlation.

In the past, all clocks and physical measure ran faster. The relationship is hyperbolic. When the universe was ½ its present age, clocks ran twice as fast. (The geometrical proof of this will be posted soon). The cumulative time is the sum or integral of the relative measure of time. The formula for that is

te = To(ln(To/T1) Equation 12

te = 8 (ln 8/4) = 5.54 billion years. In the time it took for light to travel 4 billion light years, 5.5 billion “experiential” years have elapsed.

Thank you for your questions. I will post the geometric explanation for the assertions soon.

John AKA snowflake

You are confusing elements of General and Special relativity. The metric you've given above is for flat space in the context of Special relativity. See Minkowski Metric. It has nothing to do with curved space, but rather lays the groundwork for the fact that the spatial and temporal distances between events will depend on the relative motion of the observer, but the space-time interval will be the same for all observers.

Curved space is introduced in General Relativity and the metric can be much more complicated with 16 elements that vary in space and time in correspondence with the distribution of mass and energy.

Hi CharlesEGrant

Thank you for the clarification. But my argument does not change. The distance between two points (ds^2) in Flat Minkowski space includes time like measures (c^2dt^2) . Perhaps stating that space is curved is inconsistent with the standard description in which such a Minkowskian space is “Flat” but the addition of a time element into the distance between points wrecks havoc with a much simpler spatial application of Euclidean geometry.

What I am trying to do is end up with a Minkowskian – Friedman type cosmology but the physical explanation for the time element is not due to the time interval between points, but it is historically introduced due to expansion. Mathematically the relationships will be the same, however the underlying physical geometry is different.

Again thank you for the clarification.

John

Using terms that have long standing and precise technical defintions in idiosyncratic ways makes communication difficult. In physics saying a space is curved means it has non-zero Gaussian Curvature which implies that the fifth postulate of Euclid does not hold. It doesn't mean complex vs simple.

So having agreed that curved space is not actually the point here, would it be more accurate to re-title this thread "How to simplify space-time"? The problem with simplifying away the Minkowski metric is that it comes straight out of special relativity, and special relativity has far more experimental evidence backing it then any cosmological model you care to name. So you've got quite a row to hoe: you either have to provide evidence that special relativity is incorrect, or you have to find an alternative theory that reproduces the success of special relativity and extends them.

But surely that is a relative measure too, 1 billion years in our current time-frame relative to our current now?

Also isn't the travelling light subject to the same time-dilation that you describe for "experiential" time?

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Hi CharlesEGrant

Again, I thank you for your clarification of the terms.

You stated, “you either have to provide evidence that special relativity is incorrect, or you have to find an alternative theory that reproduces the success of special relativity and extends them.”

What is missing from Special Relativity is an “absolute” reference frame, or what I often call “the Eye of God “ perspective.

All our measures or reality are relative measures, so the rules of physics must be consistent with relative rulers, and relative clocks, which is what Special Relativity does superbly. I have no intention of getting rid of the relationships of Special Relativity and General Relativity, they are simple incomplete and the geometric explanation is not quite correct. Everything is not relative. The cosmic background radiation has a bipolar red/blue shift. We are moving relative to something. But isn’t this in conflict with the analysis of the Michelson-Morley Experiment? Wasn’t the fact that there was no interference change associated with relative velocity the justification for Special Relativity in the first place?

The difference between the red/blue shift to the cosmic background radiation and the MM experiment is that the MM experiment has the testing apparatus moving with the Earth, which opens a whole can of worms in terms of the assumptions used for the consistency of the length of the apparatus.

There is a small group of dedicated dissidents that are trying to get the proper physical explanation for the relationships of special relativity but most physicists in the mainstream just assume that they are trying to negate the physical effects or the mathematical formulas, which is not the case. They are trying to give a better physical explanation.

Snowflake

Hi Paul Mitchell

Thank you for looking over the comparison of the rates of relative and absolute measures of time.

You stated the following

"But surely that is a relative measure too, 1 billion years in our current time-frame relative to our current now?

Also isn't the travelling light subject to the same time-dilation that you describe for "experiential" time?"

Lets pretend that all our clocks and all our physical processes are all slowing down at the same rate. How could we describe such a slowing? All our local measures of time are in step with each other.

To do this we would need some kind of “absolute” or unchanging clock. Thus we would now have two measures of time. A local or relative measure and an absolute measure.

This raises another issue, How could we compare the two measures of time?

To do this requires setting some kind of common point of comparison. The simplest is to use “now” to establish a standard. The relative measure of a “second” that is established at this moment in history can be used as means or method of comparing relative measures of time at other locations in absolute or historical time.

Now more specifically, you make a good point about the object 1 billion light years away. That distance measure describes the absolute measure of time in the past, as it was 1 billion years ago. That is not how much time as passed. If you believe in the expanding universe, then the following analogy may help. If an object is observed to be 1 billion light years away, is it that far away now?

Snowflake

The Theory of Relativity does not assert that everything is relative. In fact, as has been jokingly remarked by several authors, it could be equally well called the Theory of Invariants. While the intervals of space and time that we used to think were absolute are relative to the reference frame from which they are measured, the space-time interval defined by the Minkowski metric is the same the same for all intertial frames. That is, dt^2 and dx^2+dy^2+dz^2 will have different values in different reference frames, but the combination c^2dt^2 - dx^2 - dy^2 -dz^2 will have the same value in all reference frames.

There is no conflict between the result of MM and the doppler shift of the CBMR. The difference between the two is that the MM experiment assumed that the speed of light would depend on the state of motion of the observer through the luminiferous ether. You aren't claiming that the speed of light varies with motion in respect to the CBMR are you? You are perfectly free to choose a reference frame stationary with respect to the CBMR, just as you are free to choose a reference frame staionary with respect to the earth (approximating the earth as an intertial frame for the moment). The laws of physics will be the same in both frames.

Hi CharlesEGrant

The rules of relativity allow any reference frame to describe the same physics, ie they are invariant. But this “invariance” idea is a concept that is carried too far, typically is used to show that there is no “absolute” reference frame.

However, absolute reference frames are indicated in nature. I would not call the cosmic microwave background an arbitrary reference frame (or what Mach or others call the reference frame of the background of stars).

Similarly consider a variation of the twin “paradox” , but this time all we see are two space ships passing by each other. It is only by the passage of time that it is revealed that one of the twins in one of the ships is aging slower than the other. But from what reference frame are we determining who ages faster? Lurking in the background of relativity is the idea of an ‘absolute’ or “preferred” reference frame.

John

Do you think the laws of physics differ between a frame stationary with respect to the earth and a frame stationary with respect to the CMBR? If not, what makes the CMBR a prefered frame?

That's nothing but failing to understand relativity. The twin that ages faster is the one that moves more slowly... but which one moves more slowly depends on the observer. There's no lurking absolute frame in this notion, and there's no basis at all for singling out either twin as the one "really" aging faster.

Cheers -- Sylas