rjbeery

OK then, whatever description, mechanism, semantic juggling or interpretation that allows us to consider spacetime to be curved will also allow us to consider spacetime to have a particular refractive index. Call it an illusion; call it geometry; call it "purely about what we measure." Please see my comment above, I don't believe further discussion on this is constructive. Thanks Strange.

That's a strange comment, only because vacuum space does have permeability. What, exactly, is curving when we say that spacetime curves? You can't say it is "simply a volume" and then begin assigning attributes to it. To both of you, I would say that the issue has been resolved to my satisfaction. The function of refractive index as it relates to frequency varies by medium, and sometimes quite wildly. We can postulate that this function is independent of frequency for free space. Period. There is nothing preventing this, and the Einstein Lens already gives us evidence that it is true. I see no value in continuing this line of discussion. If c weren't moving more slowly for B from A's perspective, how does A explain B's light clock ticking half as fast? That involves photons which are not changing depth in the gravity well at all. To be honest, MigL, I'm here looking for objections to the analogy in the OP. If your objection is that c is literally a global constant (and not a local one) then I'm comfortable with handling that objection and don't see much value in trying to "convert" you. If it "arises from the metric" for specified circumstances then why can't we calculate a global time dilation field for that same solution and given conditions?

Free space has permittivity, permeability and energy. It's definitely an "environment", so whether we call it a medium or not is semantics. I think we can all agree that free space does not disperse or reflect light, and there is nothing restricting us from proclaiming that this is simply a property of free space. If a person wants to demand that all media must disperse light, I think that would require some theoretical support.

MigL, please consider what I'm writing before dismissing it, because this isn't a simultaneity problem. If A emits 10 signal pulses and then turns off his watch...how many signal pulses will B detect, ever? This has nothing to do with simultaneity whatsoever.

I think you're objecting to the tennis ball analogy because you're thinking that the photon analysis suffers a problem here while the wave does not, and that isn't true either. Like you said: The signal pulses that A emits and the signal pulses that B detects must be equal in number. If A emits 10 signal pulses and then turns off his watch, B must detect 10 signal pulses. Your analysis would require B to detect 20 signal pulses (at 1/2 wavelength) in order for c to remain globally constant. There is no need to go in to other scenarios because this is an insurmountable problem...unless we declare that c varies remotely. It's an extremely common misconception that Relativity claims c is constant, but it obviously is not. C is constant locally...but that's it. This should be obvious because c is a velocity vector (it has a direction) and no one denies that the path of light can be bent.

This graph is the refractive index for water. The function of refraction index is not as simply dependent on wavelength as you are suggesting. The shape of the curve depends on the medium material, among other things. I hadn't considered dispersion before this conversation, and I appreciate your input, but I've already said that the function of refractive index by wavelength through spacetime could simply be a constant (i.e. not dependent on wavelength at all). The Einstein Lens could be proof of this. If you aren't satisfied with this response that's OK, but I'm not sure any further commentary on this topic is constructive. This can't be true. Instead of peaks and troughs, imagine tennis balls. Observer A hits a ball down towards B every second, and numbers them. If observer B is receiving these tennis balls at a higher frequency than 1 per second (from A's perspective) then he would be receiving tennis balls not even served yet. We rectify this by allowing A to claim that the frequency is the same but the wavelength (i.e. distance between tennis balls) is shorter for B -- and it would literally look like that to A because hitting tennis balls into a field of dilated time is like hitting them into a puddle of syrup. The frequency remains constant, but the wavelength shortens. (Wavelength) * (frequency) = (c) locally, and (wavelength at B from A's perspective) * (frequency at B from A's perspective) = (c at B from A's perspective) which means that light is moving more slowly at B from A's perspective. I did my best to explain my perspective on cavity interactions. If you think we still harbor a difference of opinion then I would agree that further discussion isn't going to be meaningful. Thanks though, Joigus. With these objections, it makes me question the function of gamma and GR time dilation in general. Is it only useful relative to two points in spacetime? Is time dilation represented in the field equations? Can we derive even derive a complete, universally valid time dilation field in GR?

Mordred, you are giving the same objection in another form, which I have already addressed. Dispersion is not tied to refractive index, but is specific to the medium itself. Some media have wide dispersion, others have very little. The fact that gravity affects all frequencies equally, and the fact that an Einstein Lens does as well, implies that spacetime does not produce dispersion effects at all if we are modeling it as a refractive medium through which light is traveling. I've repeated it a few times now -- this idea leads to a logical contradiction. A literal contradiction. Watch A is high in the sky, while watch B is low in a gravity well. Observer A, holding watch A, claims that watch B is ticking once for every two ticks of his local watch. Observer B, holding watch B, agrees with him (2 ticks up there = 1 tick down here). The watches are large -- 1 light-nanosecond wide, which is about a foot, I believe. Two ticks on A means that the photon has traveled across the watch 4 times (= 4 feet), whereas watch B's photon has only traveled 2 feet because the "cavity interaction" has, we are supposing, delayed its transmission by a full nanosecond. Now we get silly and make interstellar photon clocks, 100 light-years wide, but put them in the same arrangement. Observer A and B both agree that for every two ticks on clock A, we have only one tick on clock B. They also continue to agree that for every two ticks on watch A, we have one tick on watch B. However, now the "cavity interaction" for the interstellar clocks must delay the photon emissions in clock B by 100 years. That's the contradiction. The photons in the clocks and watches "have no clue" how wide the watch or clock is that they are in, and neither do the absorbing/emitting atoms that make up the machinery. We simply cannot attribute gravitational time dilation to cavity interaction or radiation pressure.

I think what you're questioning here is whether or not redshift would occur using a graded refractive index in the same way that it occurs in a gravitational field. Indices of refraction keep the frequency of light constant, but vary the wavelength. It should be obvious that media with a lower refraction index would exhibit a longer wavelength. Scattering is definitely something to think about, but it occurs when there's an abrupt change in media with an associated change in refractive index. We're considering a smooth, continuous gradation so I'm not sure how optics would normally handle that. Also, the Einstein Lens apparently doesn't differentiate by wavelength so perhaps spacetime neither disperses nor scatters as a "medium". I do appreciate the input, so thank-you.

Wait, what? I thought it was obvious why the analysis was an approximation but I'll be explicit -- I modeled a photon moving in an octogon. We have no idea what the photon's actual path in in this theoretical EM mass particle, but we can bet it isn't an octogon. I also approximated various things, such as the mass of the Earth, and the value of G. Frankly, you seem curiously dismissive, which is perfectly fine but please don't ask for things insincerely. With respect, Mordred, I think you're applying your real-world experiences too heavily to this model. I don't know "how" spacetime could have a refractive index any more than I know "how" spacetime could curve due to an energy-momentum tensor. To the extent that GR works because the math works, and to the extent that this analogy works, asking "how" is another chapter.

Dispersion and scattering effects are not solely a function of the refractive index, right? The material matters. Dispersive effects can range wildly in a variety of materials. If the spacetime "material" had dispersive qualities, such that refraction depended on wavelength, then I believe gravitational mass would not equal inertial mass in all gravity fields. To me, this necessitates that the spacetime "material" displays zero dispersion, and I'd actually use the fact that the Einstein Ring distortions do not depend on wavelength as a supporting argument to the idea.

I don't doubt your credentials (and at some point I would love to ask you some questions on black holes!) but I'm having a problem understanding your objection to the refractive index. Do you have an objection to GR time dilation? Assuming not, generating a refractive index field via mapping from the GR time dilation field is trivial.

This strikes me as an aesthetic objection, and you're entitled to that, but I think you'd agree that the mathematics of GR is pretty complex, difficult, and restrictive. If we produced a new way to attack problems it could be valuable.

OK, then we can assign the refractive index to the global set of fields. Remember, we are calling this an analogy, but how does it change things if we declare that the varying index belongs to spacetime as opposed to the field(s) in spacetime? The math would be the same because the math (of time dilation) is ultimately determined by GR.

Understood, but "something" curves in GR. The "medium" of spacetime does not behave like a physical aether but that doesn't prevent whatever spacetime is from having the equivalent of a refractive index. To claim otherwise is literally to deny that GR contains time dilation at all.

Depends on the definition of medium, I suppose. If light travels through it, then it's a medium, is it not? But you didn't ask any questions about the image, at all. And most people wouldn't consider 96% "wildly inaccurate". There are no fudge factors in this spreadsheet to get that result -- I described what I was going to analyze, and then I did so. Does it contain errors? Perhaps, and you're welcome to study it and give feedback. But I find it unfair to list what I haven't provided, and then, after I provide it, claim ignorance as to its significance while making no effort to understand it. https://docs.google.com/spreadsheets/d/1S3htgtleWvubFKUSFw2I9qKjjIBo4tallq9NP6-XEeQ/ If I did this right, you can view and copy the spreadsheet above, after which you're free to adjust it all you want.

I'm not trying to invalidate GR in any way. I'm thinking that modeling GR in this way might give us new ways to analyze it. The .87 arcseconds is what you would get using the equivalence principle alone; it's also the Newtonian deflection prediction; it's also Einstein's original prediction in 1911. He later doubled that estimate to 1.75 arcseconds, but that is only for light, not mass. There are many ways to explain why light would deflect twice as much as mass, and I gave a plausible, physical reason. I posted how an EM mass particle ("made of light") would behave in graded refractive field, and got a 96% agreement on the apparent local acceleration. That was the spreadsheet calculations above. I've never considered this, thank-you. The connection between wavelength and mass is based on the Compton wavelength for this electron. You can read about it here: http://home.claranet.nl/users/benschop/homepg2/electron.pdf My immediate response would be that the medium of "spacetime" has no dispersion. Another possibility is that massive EM particles are made of the same frequency of light with varying numbers of photons in various topologies. The concept of EM mass is relatively new and I don't believe has gone beyond a modeling of the electron.

This is addressed in the fact that the wavelength of the photon in the EM mass is what determines the mass of the particle. I'm not sure what more you're asking for. If light moving in a circuit accelerates in the direction of higher refraction in a graded refractive index, and if GR time dilation is a graded refractive index, and if massive particles are nothing but photons moving in "circuits", then we have completed the analogy. I even postulated the difference between Newtonian gravitational effects (with small relative velocities) and Relativistic gravitational effects, which are twice as much, due to a greater percentage of a massive particle's photon path being perpendicular to the gravitational source.

No, submissions aren't published but the essay is literally what I posted in the OP.

Couldn't we start with a mapping of gamma relative to some arbitrary observer (i.e. infinitely distant and inertial)? I wrote this paper as a Gravity Research Foundation essay which was limited to 1500 words. The references mentioned are highly relevant. For recent work you can Google "F=ma optics". Here's an example: https://aapt.scitation.org/doi/10.1119/1.14861 Before finding work that had already been done on this subject, I had numerically calculated light bending around the sun if we treat its gravity field as a graded refractive index. This was not easy using a spreadsheet because of precision limitations, but it produced the Newtonian prediction of .87 arcseconds. I also tried to visualize how a photon moving in a circuit could "gravitate" toward a higher refractive index. You can see below that I treat the circuit as an octogon whose face is parallel to the "gravity gradient", and that we get a prediction which is in 96% agreement. Note that when an entry shows "0.000" below it isn't actually zero - that's just a function of formatting of extremely small numbers. To be honest, this work is old and it would take me a bit to remember what I was doing here, but I've seen enough to continue working under the assumption that the analogy holds. What I would really like is an analytic solution but that math is incredibly hard (for me). I've talked Physics and Math professors at UNL, and I've even met with two graduate math tutors, but no one is sure of the best way to tackle it. Studiot mentioned that Eddington did a derivation of sorts in another publication, and I'm going to look at that.

I have personally never heard of gravitational time dilation being explained via "width contraction" to maintain the global invariance of c, but I guess that would work. Varying absorption/emission times does not work. As an aside, I saw an interesting video about radiometers which claimed that the rotation comes from the edge of the fans. The face color of the fans does not matter, which makes sense if you think about it -- the energy hitting each side of the fan is the same, and the energy being emitted from the black side is the same as the energy being reflected from the white side.

Clock A and clock B are in relative motion. A claims that B is clocking slowly, while B claims that A is clocking slowly. Observer C might claim that A or B are clocking more slowly, depending on his frame. All results are relative here. Now, clock A is beneath clock B in a gravity well. A claims that B is clocking quickly, while B claims that A is clocking slowly. Observer C agrees with A and B that A is clocking more slowly than B, regardless of his frame of reference. The time dilation differential between A and B here is absolute. I'm talking about the specific A-to-B comparison at their established locations. I don't want this discussion to take semantic detours so I'll gladly use something other than "absolute", but it must be a synonym for "absolute" because "relative" does not apply. That literally leads to a logical contradiction, which I mentioned earlier. The so-called 'radiation pressure' would have to vary by the distance the photon traveled in order for the illusion to be maintained. The re-emission time would have to be delayed by a fraction-of-a-second up to many years, depending on the future path of the emitted photon. A remote variance of c does not suffer that problem. I understand this but...I'm not sure this is a scalar field theory, is it? Just as light isn't refracted within a homogeneous medium, gravitational attraction would not manifest for masses in a homogeneous time dilation field. It's the gradient (i.e. the derivative) that determines the gravitational attraction, and a single point doesn't hold enough information. I appreciate that the math is terribly complex, but that doesn't make it immutable. Does a unique solution to the Einstein field equations produce a unique time-dilation "field" (in 4 dimensions)? Anyway, I'm stuck using the tools in my toolbox, and I'm currently I'm looking at how time dilation might affect Mercury's precession.

The actual timing mechanism (photon vs spring vs something else) of a clock doesn't matter. If it did we would violate the equivalence principle. Regardless, a photon-clock is a real thing: https://www.caltech.edu/about/news/caltech-scientists-create-tiny-photon-clock-1029 The talk about absorption and re-emission doesn't and can't have any bearing on the rate of the clock ticking for a simple, logical reason that I mentioned earlier.

They have noticed. I think the analogy goes back into the 18th century. The only thing I've done is suggest that it isn't an analogy at all, but two ways of looking at the same thing. I find it odd that you agree that this would be a simplification of GR but also that, if true, you say "it is only because you have based it on GR..." If it reproduces the predictions of GR faithfully, is it redundant and trivial, or does it have value in your eyes? Thanks for the recommendation Joigus. Is this your source for claiming that gravitational time dilation can be attributed to longer absorption and re-emission times? Because I've never heard of that and I'd be interested in a proof because I don't think it's tenable.

Why do you say it doesn't produce the same results? Also, if it was shown to do so, would your reaction be dismissive? Because I'm fine discussing the details but not if you're not sincerely interested.

The "F=ma optics" analogy. The analogy claiming that mass in gravitation behaves like light in a graded time dilation field. Once the analogy is ordained "complete" I don't see the value in solving it for various special cases. I agree that "it works" but I completely disagree that it's irrelevant. It's a matter of personal preference, and how much of a philosopher-at-heart a person is, I suppose. I cannot stand the Copenhagen Interpretation, for example. It's offensive to me, and it baffles me that some folks are at peace with it. If a causal mechanism for gravity is uninteresting or redundant to you, that's OK. I suspect others might find it interesting.