0 Members and 1 Guest are viewing this topic.

c = 1 // Mly / My H0 = 0.0000756 // Mly / My / Mly photon = { x: 0, // distance traveled in Mly wavelength: 500 // original wavelength in nm } // create targets at distance 100 Mly apart nextTarget = 0 targets = [] for (var i = 100; i <= 10000; i+=100) targets.push({x: i, start: i}) // time starts at zero t = 0 while (targets[nextTarget]) { // increment time by 1 My t++ // move the photon forward at c + H0 * D dx = c + photon.x * H0 photon.x += dx // the expansion of space stretches the wavelength wavelength = photon.wavelength * dx // calculate z using the current and original wavelength z = (wavelength - photon.wavelength) / photon.wavelength // move the targets for (target of targets) target.x += target.x * H0 // if the photon has reached a target if (targets[nextTarget].x <= photon.x) { //output the time, the distance, and the z console.log(t, targets[nextTarget].start, z) nextTarget++ } }

c = 1 // Mly / My H = 0.0000756 // My / Mly photon = { x: 0, // distance traveled in Mly frequency: 6e5 // original frequency in hz } // create targets at distance 100 Mly apart nextTarget = 0 targets = [] for (var i = 100; i <= 10000; i+=100) targets.push({x: i, start: i}) // time starts at zero t = 0 while (targets[nextTarget]) { // increment the master clock by 1 My t++ // find the time interval experienced by the photon for this distance dt = 1 - photon.x * H // move the photon forward at c for the time interval dx = c * dt photon.x += dx // calculate the photons frequency over this interval frequency = photon.frequency * dt // calculate z using the current and original frequency z = (photon.frequency - frequency) / frequency // if the photon has reached a target if (targets[nextTarget].x <= photon.x) { //output the time, the distance, and the z console.log(t, photon.x, z) nextTarget++ } }

The timestep for the program is 1 My, and the speed of light is 1 Mly/My. The value used here for H0 (variable "H0" in the code) is 74 km/s/Mpc, the often cited SH0ES team measurement. This is first converted to km/s/Mly, or 22.69 km/s/Mly. This is then converted to Mly/My/Mly so it fits with the units of time and the natural units of the speed of light used, which is 0.0000756 Mly/My/Mly.

Hubble's 'constant' is not a constant at all, but rather a value that has remained stable to within its known precision within the history of human's ability to know of it. Mly/My/Mly reduces to 1/My which is just the inverse of the age of the universe. Your relatively high choice of 74 km/s/Mpc yields an age of 13.2 BY for the universe. If constant expansion is to be correctly modeled, H0 is not a constant at all, but rather the inverse of the cosmological time, which you are incrementing with the simulation. You need to reflect this in your code.

Quote from: Halc on 26/03/2021 12:06:26Hubble's 'constant' is not a constant at all, but rather a value that has remained stable to within its known precision within the history of human's ability to know of it. Mly/My/Mly reduces to 1/My which is just the inverse of the age of the universe. Your relatively high choice of 74 km/s/Mpc yields an age of 13.2 BY for the universe. If constant expansion is to be correctly modeled, H0 is not a constant at all, but rather the inverse of the cosmological time, which you are incrementing with the simulation. You need to reflect this in your code.I think that's taken for account in the code by advancing the targets at their proper distance (target.x) rather than co-moving distance (target.start).

// increment time by 1 Myt++// move the photon forward at c + H0 * Ddx = c + photon.x * H0photon.x += dx

Sorry for slow replies, but I’ve limited time to put to this. I’m also insufficiently familiar with java to write anything in it. I’m more used to more type-strict languages like C where variables need to be declared before being used.

Moving the targets with target.x += target.x * H0 is again producing exponential movement, not linear. You’d see this if you plot target distance over time, say every billion years.

The second half of the post considers what you call linear expanding time, whatever that means since time isn’t something that expands.

What you seem to be attempting is plotting the same action using comoving coordinates, comoving distance (as opposed to proper distance). You then interpret this as light speed slowing down (decrease in comoving distance per second) when light speed is defined as proper distance per second. So if you change c over time instead of the proper size of a comoving meter over time, then all the constants (G for intance) need to be adjusted. Earth would be shrinking steadily and losing mass, violating all sorts of conservation laws.

The expansion of space needs to increase the distance between the photon and its source, as well as the source from the targets. Due to the Hubble flow, the photon appears to pick up speed away from the source. It will however be moving at c relative to any target it meets.Here are the values it produces. Does it not match expectations?

QuoteThe second half of the post considers what you call linear expanding time, whatever that means since time isn’t something that expands.True. But that is the hypothesis being proposed.

In this hypothesis there are no co-moving coordinates, because there is no expanding space or changing scale factor.

The idea isn't that light slows down, but cosmologically redshifted light experiences time differently.

Then you need to define what it means for time to expand. Time gets bigger over time? Does that sentence make any sense??

Time dilates over distance, is more like it.The idea, is that the time interval applied to the photon decreases with distance.In a non-relativistic theory, this entails the photon having a clock that begins synced with the master clock, and falls off.In a relativistic theory, it would have to mean something different.

Such as the photon veering into a time-like trajectory.

Again, photons do not have clocks. The interval between events on a light-like worldline is zero, so I don't see how that can 'fall off'. So I don't understand your redefinition of 'interval' or what you mean by photons having clocks.

That means that there can be an inertial object (one stationary in its own frame) with which light cannot keep up. Are you really suggesting that? In your picture, one event at the origin, the other outside the red curved light cone, but inside the blue one delimiting the boundary between time-like worldlines and space-like worldlines. There can always be an inertial object whose worldline connects any two events with time-like separation, and here you have a photon going to the left which is outrun by a stationary object. Sounds pretty contradictory, so maybe I'm not understanding your words immediately above.

OK, I'm referring to Minkowski spacetime, and the universe definitely isn't Minkowskian. If I fire a ballistic object to the left at a peculiar velocity of just under light speed, its peculiar velocity will drop off dramatically over the sort of time frame indicated in your chart. So it will stay within the bounds of your red curve and not outrun light. BTW, what's the green curve then?

I am by no means an expert, but I am familiar with this. Is the "formal" way to say this s^{2} = c^{2}t^{2} - x^{2}? And s=0 for a photon. The spacetime interval is invariant?

Imagine photon A from galaxy A is emitted in the direction of galaxy B which emits photon B.In general relativity, photon's A and B could follow the same null geodesic, assuming they were heading the same direction.

In this hypothesis, the path through spacetime a photon takes changes as D increases to cosmological scales. Either the photon leaves the null geodesic when it redshifts, or photon A and B are on two separate geodesics that just happen to overlap for a bit.

I'm sure to experts in relativity, neither sounds particularly appealing.

A photon from a galaxy with redshifts z=1 should experiencing time at 1/2 the rate as we do.

Moving at > 0.5c in the other direction, would, hypothetically, be able to outrun that significantlly redshifted light.

We should be able to test for this, by finding extra Doppler shifts by looking at high-z galaxies on the horizon at different times of the years

It would hypothetically be possible then, to broad cast a signal to the edge of our Hubble volume, where the redshifted signal is picked up, corrected, and retransmitted, and the signal leaving our Hubble volume. Communication between Hubble volumes.

I will end with a question, the answer of which that can bring this all together. If we could stand inside a blackhole, and observe the universe, from the black hole reference, what would we see? assume only space-time and no material or energy opacity to block the view.

So you're proposing something other than what I just said above. The photon from galaxy A has aged more and will not forever track with the new photon emitted by B. That's a pretty extraordinary claim which requires some pretty extraordinary evidence.

You claim that light ages. The falsification test seems simple enough. Fire a laser at some target somewhere, triggered by old light received from a distant object. The light continuing on to the target from the distant object should arrive later than the 'new light' from the laser pulse.

Relative to our inertial frame of reference (say the redshift as seen from Earth of a spaceship departing at high speed, a redshift of z=1 indicates a receding speed of 0.6c which results in the ship time being dilated by 20% relative to Earth frame, not 1/2 as you suggest.

Quote from: Halc on 30/03/2021 16:49:31So you're proposing [that] the photon from galaxy A has aged more and will not forever track with the new photon emitted by B. That's a pretty extraordinary claim which requires some pretty extraordinary evidence.Correct.They take the same route through space, but not through time, so it's a slightly different route through spacetime.The evidence of this claim is the redshifts themselves.

So you're proposing [that] the photon from galaxy A has aged more and will not forever track with the new photon emitted by B. That's a pretty extraordinary claim which requires some pretty extraordinary evidence.

Also consider a probe out past Jupiter that can detect supernovae. If a supernova occurs at a high enough z, this hypothesis says (I think) that the probe could send us a message about the supernova that reaches us before the supernova does.

My calculations for z=1 of cosmological redshift put the observed frequency at half the original.