I'm not convinced people perceive intervals consciously. Certainly space-time intervals are embedded in today's physics. My curved-space radial-time model preserves and illuminates such intervals with Euclidean interval-time coordinates. This model simply rearranges the space-like interval formula to get rid of the nagging minus sign. Otherwise space, time and interval are well preserved with no distortion and no added dimensions (e.g. hyperspace) to add complexity.Jorrie wrote:The spacetime interval seemingly does not exist in the Rovelli model, where it is just our perception to assist us in calculations.

Clever but even more complex in that unidirectional time is not explicit in the model. We don’t experience 2-way hyperspace in any testable way that I'm aware of.Jorrie wrote:So things like the hyper-radius and Hubble radius can go both ways and are not entropy related.

Faradave wrote:Remember it's the unidirectionality of time in a curved-space, radial-time model which enforces a natural speed limit c (a ratio of space to time) which is finite, universal, constant, isotropic, and invariant.

Nonsense! Other models postulate limit c. My model uniquely explains it (simply & geometrically). Huge, advantage! Other models don’t show how light can get to the future (of the cosmos) and yet not age. My tangent interval path does. Your welcome.Jorrie wrote:This is not unique to your model. All space-propertime representations sport that.

"Why is the speed of light the same in all reference frames? I don’t know the answer to that question, and I don’t even know how to approach it. … The constancy [invariance] of the speed of light is unexplained." - Styer p.21

If that's the world you want to live in, fine. Not only does it "complicate calculations horribly" but one has to labor to create a model where light has a different speed on the return trip. What are we to do with one-way relations like c = λf? I prefer the simplest model possible, which is what Phyxed endeavors to offer.Jorrie wrote:the one-way speed of light is a chosen convention for convenience, not an absolute one. It is only the two-way average of the speed of light that is absolute.

If you stop neglecting the invariant zero-interval path of light, there are physically no two ways about it. There is no path either way (direction yes, path length no). Embrace null vectors.

What it means is given by the half life of a radioactive sample of particles (or even a single muon). Drop the sample straight into a black hole. As it approaches the event horizon the half life increases without bound. Its aging (or “clock”) has slowed while the cosmos keeps getting older (bigger). This would be true for thermal clocks as well. The sample approaches absolute zero toward the event horizon, where even quarks in the nuclei must slow down.Jorrie wrote:there is no reason to think that early particles aged slower than late particles, whatever that may mean.

When the mass-energy of the cosmos was much higher (as uniformly as you like and similar to a quark star if not a black hole) the clocks of those particles were running slower than the clock of the cosmos (its unidirectional radius). That gives you a physical readout as a function (i.e. scale factor) of the radius.

Jorrie wrote:No, gravity does not slow clocks down, it is gravitational potential differences that do, in the sense that a clock situated in lower gravitational potential region records less time than an identical clock sitting in a higher potential region.

"…in every gravitational field, a clock will go…according to the position…" Einstein p.81

I'm suggesting the size (age) of the cosmos ignores this. The future (of the cosmos) is invariant. Aging (of cosmic contents) is relative.

All light is received from the past, no matter who or where the observer is.Jorrie wrote:Yes, we observe everything that has happened in the distant past as redshifted, but another hypothetical observer on a very distant galaxy observes us as redshifted to the same degree

The observer down there sees the cosmos expanding much faster, he might even call it "rapid inflation".Jorrie wrote:In the case of a black hole, things lower down its well looks redshifted to us, but we look blue-shifted to an observer around there.

This compares clocks in the cosmos to each other rather than to the size of the cosmos at large (i.e. the cosmic clock).Jorrie wrote:due to the Milky way, Sun and Earth's gravity wells, everything at early times was in a lesser gravitational well than what we are today.