substitutematerials

If this is the case, then my second conjecture must also be true- that local regions have also subdivided. I am standing where some past event occurred, prior to this region becoming gravitationally bound, and another distant observer may be occupying space with the same shared lineage. I can't see how you can have one statement and not the other. Do you guys understand what I am hung up on here?

I get this. But then I would then be inclined to say, "the big bang happened in every direction." Not "everywhere." I am not occupying space formerly occupied by the big bang. That spatial coordinate would be some horizon beyond the observable horizon.

Yes that is the equation I was referring to, and I was using a generator. I will try to handcraft them in the future. Also is there a preview button I'm missing? Well I think that answers my question, thanks a lot Mordred. The answer is then no-- present regions of space do not share a lineage, I.e. 2 regions cannot be said to have emerged from one. Back to the original statement then-- wouldn't it be wrong to say "the Big Bang happened everywhere?

HI Mordred Thanks, this is great information. I am familiar with a similar equation to calculate lookback time (it won't let me post the equation, says the latex image is too large), which I learned as the Hogg Equation. It makes sense to me from this expression that the universe would go through the eras you mention, simply because the density of each term has a different exponent. I'll definitely check out these links. In my original question, I was trying to get at this question: Is it correct to think of one finite region of space becoming many? Take one cubic meter of expanding space. Does it become many cubic meters of adjacent space in its expansion? Is there any meaning to the shared lineage of these newly-minted meters? Could multiple future observers in the new larger volume somehow detect that they are occupying what was once the same space?

Thanks MigL, I see that a star would be above the density necessary to reverse expansion. Revise my question then-- to a region in space where a lone proton and electron once combined, in a region below the critical density. Could the idea apply to this situation, that one region of space has become many? Could people in a much larger present region of space now say, "I am standing where that particular proton and electron once combined?" Also to pick bones, isn't it true that expansion throughout history has been primarily inertial? So we don't need to refer to the force behind expansion, because the universe has mostly coasted to its present size. Dark energy is a force that drives expansion, but it has only become significant in the latter half of history, right?

All observable space emerged from the same hot dense point, and the universe has no center or preferred direction. You can't point in a direction and say, "the universe began over there." It began on the tip of a flea's nose in France, and in a far corner of Andromeda. We can all say "I am standing right where the universe began 13.7 billion years ago." If we agree on that, my question is: Why can't we apply this logic to events that weren't global in extent like the big bang, but only occurred in a isolated region of space. Let's imagine that a star formed in the early universe, when the scale factor was 1/100 of present. Could we then say that somewhere out there, a region of space exists with a radius 100 times larger than the ancient star's radius, where that star had once formed. People in this region could say, "I am standing where that ancient star formed."

I think you are right, clocks ticking at a slower rate necessitate a change in length to preserve c. This is the case in the transformation from expanding coordinates to time-dilated coordinates for cosmological expansion, correct? So if we add length to the fiberoptic cable, or more bounces in the beam path at LIGO, a clock acceleration would cause us to observe the light traveling just slightly further or less than the actual rest length that we added. Totally nonsensical?

I don't think the hypothetical effect necessitates a change in c. In fact the constancy of c is necessary for the doppler measurements in the Pioneers' telemetry. In the clock acceleration interpretation, the spacecraft are not actually slowing down, the deceleration is then an artifact of the clock error. I think you could use refractive index to add light delay in an experiment, as long as you can precisely account for it. The only criteria is a delay between the 2 clock signals or laser wavelengths; the vacuum is not inherently necessary I don't think.

Wow this is great Swanson, thanks. I had to do some reading on lasers. If the effect manifested as a discrepancy in length as I was thinking, it looks like it would be hard to set up an experiment without LIGO level precision. However if Strange is right: then maybe a several km fiber delay inserted into one side of an interferometer would work, because we could observe the interference pattern change over time. If we use 10 km of fiber, and the 50% delay due to the index of the glass you mentioned, this calculation (possibly butchered) suggests that a 500nm laser will go a half-wave out of phase in 4.3 million seconds, or ~50 days. Would this be immeasurable due to frequency instability of the laser? It seems to me that general relativistic dilation could be ignored because the single laser source is necessarily at a single gravitational potential. But if it does phase in and out, how the laser "know" where it should be in that process? What if you interrupt and restart the beam? I'm not positive that this is a logically consistent idea.

I have wondered if such an equivalence could be made. I know that time dilation is factored into type 1A supernova analysis at high redshifts, for instance. Also, it perks my interest that the Hubble parameter, 71 km/s/mpc, is more properly written as 2.27E-18 sec^-1, since there are units of distance in the numerator and denominator. This number is quite close to what the Pioneers displayed if you interpret the anomaly as a clock acceleration, 2.9E-18 sec^-1. Just sayin... Pulling back from grandiose speculation, I still wonder if an experiment on Earth could be conducted, under the assumption that light travel delay puts us in contact with past clocks. Koti suggested LIGO, which seems to me to have some promise, although not as it is configured to detect gravitational waves. Here's my attempt at the numbers: The 4 km beam path is traversed 280 times by the lasers, giving a complete travel distance of 1120 km, and thus a .0037 second light delay. If the entire Pioneer Anomaly (2.9E-18) was attributed to a clock acceleration, we can check to see if LIGO is sensitive enough to see it. If we encoded a synchronized clock signal onto the 2 lasers, and one of them bypassed the long beam path, while the other one traversed it, the one that made the long journey should be behind a greater amount than could be attributed strictly to it's light delay. The actual time lost would be 1/2at^2 assuming a constant clock acceleration, so 1.985E-23 seconds. This is well below the 10^-18 accuracy of the best clocks I could find reference to, so it doesn't seem like it would work. You'd need to increase the travel time to an entire second to get to a 1:1 signal to noise ratio, or 75,000 bounces down the beam path. I have no idea if this is possible. Alternately I wonder if you would even need a clock signal. If there is an equivalence of redshift/clock acceleration such as Strange mentioned, the wavelength of the laser light would have to change with the clock change, right? So you could use the interferometer setup already there. I can't quite grasp how to estimate this degree of accuracy, but if it's just c(delta(t)), then it would be 5.95E-15 meters for the regular beam path, or the same order of magnitude as the width of a proton. Popular accounts of LIGO indicate that it can detect changes of 1/10,000th the width of a proton. Which is bonkers, by the way. But so if this is right, a change of clock time would manifest as a change in interference between the 2 beams, one on a short path, one on a long. It does seem a bit far fetched to me to imagine that this effect would not have been observed by now, in one way or another. What do you think?

Don't we inherently have contact with past reference frames just through the delay of light travel time? I see the moon as it was a second ago, the sun as it was 8 minutes age, Andromeda as it was 2 million years ago, 3C 273 as it was 2 billion years ago, etc. So if time ran at a different rate 2 billion years ago, and I could observe a clock hanging out at 3C 273, it would either gain or lose seconds relative to my clock. Yes?

Ha thanks, I like the term "archaeological" time rate. Like you say, there is nothing in the Pioneers' telemetry that isn't accounted for at this point, since they seem to have sealed the deal on the uneven thermal emisisons. Just the same, can you imagine an experiment designed to look for such an effect? The most obvious thing I can think of would be duplicate the situation of the Pioneers: Send out 2 more ballistic probes, spin-stabilized so that they are not firing thrusters, and track the doppler shift of the returned clock signal, accounting for all known forces. Special care could be taken to make sure thermal radiation from the probes is uniform in all directions. This, however, is not a cheap or speedy experiment. Could there be anyway to run a comparable test on Earth? Somehow delay a clock signal, maybe by bouncing light in an optical cavity, long enough to demonstrate such a clock drift? Figuring out that experimental design is also way over my pay grade.

I think that's the crux of the question, how do you establish an alternate reference frame. Is it possible to compare a clock rate now, to a clock rate in the past? I believe that in the Pioneer analysis, the clock signal is sent from Earth to the probe, where it was phase-locked and then sent back to Earth, so the discrepancy would be a result of the light travel time there and back, comparing the rate of the same clock from 2 different times.

In the principle study of the Pioneer Anomaly, John Anderson and Slava Turyshev suggest a speculative explanation for the apparent deceleration of the spacecraft, as an acceleration of the clock rate used for telemetry back on earth. To be clear, this explanation has been discounted, although it was explored further in this paper. The Pioneer Anomaly is generally considered solved, being due to asymmetric thermal radiation from the probes. My question is, if such a universal change in clock time did exist, i.e. that every subsequent second ticked by faster or slower than the one before it, how could we detect it? Can anyone imagine an Earth-based experiment? As I understand it, the effect that Anderson was proposing would be universal, effecting all clocks equally. Such an effect would be independent of special or general relativistic time dilations, occurring without any specific circumstances of motion or gravitation (although these effects would need to be subtracted from any experiment).The magnitude of the effect if it were to explain the Pioneer Anomaly, 2.9E-18 sec^-1, would exceed the uncertainty of an ordinary cesium atomic clock in a week. I'm not sure if it should be related to an observer's proper time, or cosmic time, or what coordinate system. I'm not asking if this effect is real, I'm asking if we could make a practical experiment to detect something like it, or if it could even be logically possible for such an effect to exist.