[Colin2B]

When you open a new thread, you are instructed to ask a question in the title. Maybe the instructions should be extended to make an exception for this section of the forum.
Policing sounds a bit aggressive. Moving them into new threads and leaving links behind would be kinder, but you (and other referees) would then have to coin new titles. Maybe you could use PMs to encourage offenders to do that on their own.

Can't remember where 'it is written' but the question rule is relaxed for new theories and chat etc. It's only enforced in the 3 main sections.
On policing. If it is clear what the purpose of the thread is and stated up front I would expect people to respect that. Although we do our best to be sympathetic in moderating, the moderators are unpaid volunteers and we all have day jobs or projects so we have limited time to manage people who decide to be awkward - and there are quite a few of those.
Have a think how best to set it up - if at all - and we'll do what we can to help it run.
Timey will need to write all this up in a concise form anyway if she's going to publish.

PS Don't see why Bell's is a problem for distance, great teaching aid on accelerated frames. Probably a side issue at this stage anyway, get the system analysis done 1st, detail later.

[timey (OP)]

PE is a classical concept. It doesn't make sense for objects travelling at or near light speed or for objects that have no mass.

If we look at potential energy as a time accelerant for mass, and kinetic energy as a time decelerant for mass, then mass held at rest with respect to the g-field of M will have more potential energy, where pe=mgh, and pe/m = time accelerant, which under that remit will render the time accelerant as equal for all values of m and non-existent for 0 mass phenomenon such as light, and the g-field itself.

Converting pe into ke will decrease the time accelerant as in free fall.  Changing a position at rest with respect to the g-field, to a lower potential at rest with respect to the g-field will not increase ke, but it will decrease the pe and therefore the value of the time accelerant will decrease.

Add pe to a body in the form of an accelerant (fuel) to be converted into pe that is converted into acceleration, where acceleration converts pe into ke resulting in less time accelerant and time slows down for moving body.

An observer perceives lower frequencies (i.e. red shift) when peering down a gravity well. You can interpret that as observer time speeding up due to its own mass rather than local time slowing down due to the remote object's proximity to the gravitating mass,

..."you can interpret that as observer time speeding up due to its own mass"...

I'm suggesting that the observer in this scenarios time would be speeding up not as a product of its own mass, but as a product of its proximity to M.  Get another value M and m in same proximity, i.e: at same m at same h from a different value M, will have a differing rate of time.  It is M that denotes how much potential energy m will experience at h from M, and pe=mgh, where pe/m then renders the time accelerant as being equal at that h from M for all value of m.

An observer perceives lower frequencies (i.e. red shift) when peering down a gravity well.

Yes and an observer will perceive higher frequencies (i.e. blue shift) when peering up a gravity well.
But light is a differing observation for 2 reasons. Firstly one can only see the light when it arrives at one's observation point, so one is only viewing what the light looks like at their gravity potential.
And secondly that an observer peering down a gravity well, his clock's frequency (and the frequency of all the atoms that make up his body and that of his craft) is increased at that h from M compared to how it would be at a lower gravity potential.  Whereas lights frequency is reduced at that h from M compared to what it was in the lower gravity potential.
Therefore my model states that the light being of 0 m doesn't have any pe to increase its frequency at h from M, and is only subject to the 3rd time dilation, this 3rd time dilation being otherwise and more commonly known as the accelerative and declarative force of gravity in the g-field of M that all m and light must move through when experiencing changing positions in the g-field with respect to M.

[alancalverd]

Except that time dilation applies in the absence of m.

[timey (OP)]

And how would you know that without measuring it?

And how would you measure it without involving mass?

[alancalverd]

Use a photon.

The interesting point is that we know F = GMm/r² and F = ma if m<<M, but we don't know why m_grav = m_inert

[timey (OP)]

But the photon can only be observed at one's location in the gravity potential.
And the photon emitter in the gravity potential is a mass.

Back to my Google investigations for full translation of some of those maths terms...and some thinking.

[timey (OP)]

mgrav=minert is part of the equivalence principle.

It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body.

...and if you consider the possibility that the acceleration is caused by a 3rd time dilation factor in the g-field itself, then acceleration is independent of the nature of the accelerated body - but will be dependent upon the g-field value in relation to the nature of M.

[Mike Gale]

mgrav=minert is not only part the equivalence principle, it is the equivalence principle in its entirety. In Einstein's own words, "observers falling freely in a gravitational field do not feel their own weight." The only caveats are that they do feel tidal forces and it's not clear if the principle holds when escape velocity approaches light speed.

[timey (OP)]

Yes - the equivalence principle, or concepts close to it, also imply that the caesium atom will be of the same frequency in each and every reference frame, and states the speed of light as constant.
The tidal forces being gravitational direction, are, in my model, associated with the magnetic moment/s of an atom, and accelerated in that direction by the 3rd time dilation, otherwise known as the acceleration of gravity.
If it is a time dilation related acceleration this would afford a weightless feeling, and all value of mass would accelerate at same rate.

*

Going back to the Einstein equation and the fact that without adding the mathematical expression of the constant, Einstein's equation describes a universe that is expanding...
Logically speaking, as I mentioned before, this would require that the equation without the expression of the constant has a factor that describes an expansion.
Why does this equation describe expansion?
What is the expanding factor within those mathematics?
For instance, is it distance?

*

In answer to edit:  Speed of light held relative to what rate of time?

[alancalverd]

Yes - the equivalence principle, or concepts close to it, also imply that the caesium atom will be of the same frequency in each and every reference frame, and states the speed of light as constant.

So that's all right, then. And the constancy of c can be demonstrated with a variant of the Michelson Morley experiment without invoking any time measurement. 

[timey (OP)]

Unless the Michealson Morley experiment's inline arm does not shrink for the reason that the speed of light cannot exceed the local rate of time...

[timey (OP)]

In which case, as an inverse effect, the LIGO tubes do not shrink either for the reason that the local rate of time has been affected for the duration of the gravity wave.

[Mike Gale]

I'm not entirely clear how one gets an expanding universe from the SC metric. The only formal derivation I know of is the Friedmann (FD) metric, which is something entirely different: ds² = a(t)²ds₃² - c²dt²
The quantity ds₃ comprises the spatial displacements and a(t) is an arbitrary function of time. You can use GR principles to compute a(t) for any given spatial topology (i.e. flat space, expanding space or contracting space.) The result is then parameterized to align with Hubble's data and, without a cosmological constant, expanding space is presumably the best fit. (I've never seen that calculation, but it has presumably convinced many experts.)
This calculation is entirely contrived because, unlike the SC metric, which is anchored on a gravitating mass, the FD metric is anchored on the observer. SC curvature has a physical explanation, which is the energy of the gravitating mass. FD curvature is empirical. It doesn't depend on the mass of the observer, only Hubble's data. We just give it a name - the Big Bang - and presume that it applies for all points in space.
It seems to me that a more reasonable approach would be to use the SC metric to predict how the universe looks when viewed from inside a gravity well. If you adopt the variable light speed interpretation, the speed of light (and everything else) increases towards infinity as you peer deeper and deeper into space. In this view, the expansion that we perceive from our vantage point here on Earth is primarily due to our proximity to our galactic core. An observer in intergalactic space would perceive flat space.
The reason I bring this up is that timey is trying to reconcile Hubble's data with the SC solution and that's essentially what Friedmann was trying to do.

[timey (OP)]

Ok - it just came back to me why I though Euler's method in relation to Katherine Johnson was relevant to your thread.
You are using GR time dilation to hold your coordinate speed of light relative to.  But when adding in SR spatial dilation, this fudges up your position within those GR coordinates, **unless you state your coordinate times as occurring at these variable spatial dimensions, i.e. that the GR time shifts occur not at every h from M, but occur as per extended radius held relative to variable distance**(I'll come back to this thought later)
If you go back and add more GR coordinates to the spatial dilation, then, by using the variable speeds of light within that spatial dilation to calculate, this then again affects the SR spatial dilation and you have to re-assess your coordinates...again, and so on.
Right?
It would seem to me that you can hold the speed of light relative to the rate of time at a coordinate, or you can use SR to dilate spatial dimensions, but you cannot use SR to dilate space 'and' hold the speed of light relative to coordinate time because you get a catch 22 going on. 

However, in calculating the above, you are already using a calculation that is describing the acceleration of gravity at each coordinate with an inclusion of a rendition of GM/r^2 operating within the maths.
My model has attributed the nature of this acceleration to a physical cause.  This being that a 3rd time dilation is inherent to the g-field where seconds are getting shorter and shorter nearer M, and getting longer and longer out in space.
Current maths are already calculating this phenomenon as being gravitational acceleration.

So moving on - anything with mass will be affected by gravity potential, where pe=mgh.  Where we can say that pe/m=time dilation equal for all value of m at h from M.
(It is appreciated that there may be a squaring that needs to occur in that equation, I am just illustrating that having arrived at a pe value using the mass value, that by dividing that pe value by the mass value we have an equal distribution of pe for all mass values that will result in an equal time dilation for all mass values at h from M)

Now that we have disassociated GR time dilation from the concept of time running faster for open space and the g-field itself, and attributed this phenomenon as being inherent to m in relation to M only, we can go back to looking at the acceleration of gravity and the attributed 3rd time dilation that gives physical cause for acceleration.
We know that this 3rd time dilation does not directly affect the rate of time for m,**although the acceleration that it causes does**(I'll come back to this thought later), but we can see that m is accelerated in the g-field with respect to M.

Now back to my earlier thought:

**unless you state your coordinate times as occurring at these variable spatial dimensions, i.e. that the GR time shifts occur not at every h from M, but occur as per extended radius held relative to variable distance**

Which will also give rise to problems but serves as a platform for me to say this:

If one considers that the 3rd time dilation, otherwise known as the acceleration of gravity is causing a temporal dilation...
When one holds the speed of light relative to GR time dilation, the GR coordinates will not be affected by the temporal dilation of the 3rd time dilation and the catch 22 is negated.
But... one won't need to add SR spatial dilation to describe curvature, it's already described.

But applying the principle of SR time and spatial dilation to this new picture as a phenomenon experienced by the traveller, rather than as a phenomenon observed by an observer, gets very interesting indeed!
Where I now come back to the thought:

The 3rd time dilation does not affect the the rate of time for m,**although the acceleration that it causes does**

SR (in your rendition), would be holding it's measurements relative to the coordinate speed of light.
So as the coordinate speed of light increases at h from M via being held relative to a GR time dilated shorter second, the 'constant' speed a traveler is travelling at becomes a lesser percentage of that coordinate speed of light, and the time dilation and resulting 'appearance' of spatial dilation that the traveler himself observes will trend to being shorter seconds and shorter distance.
**You may find that there isn't enough head room within a distance travelled for a traveler to experience the distance he is travelling to be lesser, or for the seconds on his clock to become shorter, unless his speed is being constantly decelerated that is...**(I'll come back to this thought)

If you add a decelerating phenomenon to the travellers speed, i.e: outbound into the decelerating force of gravity (3rd time dilation), the speed becomes a lesser percentage of the rising coordinate speed of light, resulting in the traveler experiencing faster seconds, resulting in a perceived shorter distance.
When adding an acceleration to the travellers speed on the inbound into the accelerating force of gravity (3rd time dilation), the speed traveled becomes a greater percentage of the coordinate speed of light.  The traveller will perceive a lengthening of his seconds and will perceive distance travelled as being longer.
(There is an argument here that SR time dilation effects cancel out GR time dilation effects)

So, not withstanding the matter of travelling at **constant** speed at an accelerated or decelerated coordinate, whereby it would be possible to equate the factor of a form of additional energy to action conversion that might serve to balance any anomaly in the books, I don't see any reason why an expanding universe cannot be calculated as such, using the 3rd time dilation as an accelerative/decelerative force, and also as a temporally derived curvature of distance in space...
No reason, apart from the fact that lights frequency decreases and the wavelength gets longer at distance from M, which we have put down to the light being stretched by the velocity that light sources are receding away from us, so that's ok then...

But this does nothing to explain why the expansion was caused in the first place, nor the energy required to propel this expansion.

So - to calculate my contracting model, one simply holds the speed of light relative to the 3rd time dilation instead of GR time dilation, while holding SR measurement relative to the speed of light held relative to this 3rd time dilation.
Now the travellers 'constant' speed on the outbound is an escalating percentage of the coordinate speed of light, his personal time becomes increasingly dilated with longer seconds, and he experiences a distance travelled as being longer as a result.  (A result he could just as easily attribute to GR time dilation btw)
If adding a decelerating phenomenon to the travellers speed, i.e. the decerative force of gravity (3rd time dilation), the speed becomes a lesser percentage of the speed of light of that coordinate... And if the value of the speed remains a constant percentage of the coordinate speed of light, the traveler will experience his SR effects as constant.
When adding an acceleration to the travellers speed on the inbound into an acceleration of gravity (third time dilation), the speed travelled becomes a lesser percentage of the speed of light of that coordinate...  If the value of the speed remains a constant percentage of the coordinate speed of light, the traveller will experience his SR effects as constant.
(I'm not sure if this balance can be achieved via holding the coordinate speed of light relative to GR time dilation, but perhaps it can)

I think my model works better...
By separating GR time dilation for mass from the concept of time running faster in space, we have shown that light which has no mass will not have any potential energy and will not be subject to GR time dilation.
Unlike mass, light's frequency is known to reduce in the weaker g-field, and the longer length in wavelength can be thought to be 3rd time dilation related, which re-interprets Hubble's law as being a temporally deduced red shift distance correlation rather than Hubble's velocity related interpretation.

Now we have established possible cause, we could look to a contracting universe and my model's alternative rendition of Big Bang theory...

[Colin2B]

I'm not entirely clear how one gets an expanding universe from the SC metric. The only formal derivation I know of is the Friedmann (FD) metric, which is something entirely different: ds² = a(t)²ds₃² - c²dt²

You are aware ratio observed density to critical density inversely proportional to Hubble parameter squared. You can link Hubble to cosmological via one of the Friedman Eqs using that equation. A while since I went through this so would need to work through again, but you should be able to get there.
Pity Pete won't join in, he's the expert, worked with Alan Guth and still has access for checking ideas.

[Mike Gale]

THE Alan Guth? Isn't he famously brilliant? I imagine he would be loathe to drudge through this discussion thread because we are still waxing philosophical about timey's theory. We have yet to establish the (mathematical) recipe for her 3rd dilation for example. The relativistic correction to the SC metric thread might be more up his alley: https://www.thenakedscientists.com/forum/index.php?topic=69764.0.

The density ratio you (Colin2B) speak of goes into the specification of the spatial topology in the Friedmann analysis. It's one of the parameters you fiddle around with to get the FD metric to match Hubble's data.

I encourage timey to study the FD solution though. I think his observer-centric metric might be the same as her free space dilation. (https://en.wikipedia.org/wiki/Friedmann_equations)

[timey (OP)]

When you say a recipe for the 3rd time dilation what do you mean?

Is it not enough to describe that this time dilation is the cause of gravitational acceleration.  That a body travelling at constant speed in a vacuum can be accelerated towards an M by seconds becoming progressively shorter closer to M, to the accelerative value of GM/r^2(if that is the equation that describes acceleration?)...?

I'll look at the link..

[timey (OP)]

No, those maths are too complex for me, and it sounds like a calculation of an expanding universe. So no, there may be similarities from a mathematical perspective if one were to try and calculate a contracting model, but Freidman is not calculating a contracting model, nor is he stating the accelerative force of gravity as being time dilation related, far as I can see.

[timey (OP)]

Sorry, but it took me over 3 hours to write post 293, gutted really...

[timey (OP)]

Anyway - perhaps someone can help me...
If we were to say that the value of GR time dilation, associated with M Earth, caused an acceleration to an object travelling at a constant speed, i.e. being accelerated by shorter seconds, negating any gravitational attraction or other phenomenon completely, what value of an acceleration would GR time dilation cause in metres per second squared?