Does simultaneity have any meaning?

 Someone on Quora asked me a question about simultaneity with respect to Einstein’s special theory of relativity (SR), so I referenced a 30min video of a lecture on the subject, which I’ve cited before on this blog. It not only provides a qualitative explanation or description, but also provides the calculations which demonstrate the subjectivity of simultaneity as seen by different observers.
 
Below I’ve copied exactly what I posted on Quora, including the imbedded video. I’ll truncate the question to make things simpler. The questioner (Piet Venter) asked if there is experimental evidence, which I ignored, partly because I don’t know if there is, but also because it’s mathematically well understood and it’s a logical consequence of SR. Afterwards, I’ll discuss the philosophical ramifications.
 
Does the train embankment thought experiment of Einstein really demonstrate relativity of simultaneity?
 
Actually, there’s a very good YouTube video, which explains this much better than I can. It’s a lecture on the special theory of relativity (SR) and you might find the mathematics a bit daunting, but it’s worth persevering with. He gives the perspective from both a ‘stationary’ observer and a ‘moving’ observer. Note that he also allows for space-contraction for the ‘moving’ case to arrive at the correct answer.

 
To be specific, he uses the Bob and Alice scenario with Bob in a spaceship, so Bob’s ‘stationary’ with respect to the light signals, while he’s ‘moving’ with respect to Alice. What I find interesting is that from Bob’s perspective, he sees what I call a ‘true simultaneity’ (though no one uses that term) because everything is in the same frame of reference for Bob. The lecturer explains both their perspectives qualitatively in the first 6 mins, before he gets into the calculations.
 
When he does the calculations, Bob sees no difference in the signals, while Alice does. This infers that Bob has a special status as an observer compared to Alice. This is consistent with the calculations if you watch the whole video. The other point that no one mentions, is that Alice can tell that the signal on Bob’s ship is moving with respect to her reference-frame because of the Doppler shift of the light, whereas Bob sees no Doppler shift.

 
I commit a heresy by talking about a ‘true simultaneity’, while physicists will tell you there’s no such thing. But even the lecturer in the video makes the point that, according to Bob, he sees the two events recorded by his ‘clocks’ as happening at the same time, because everything is stationary in his frame of reference. Even though his frame of reference is moving relative to others, including Alice, and also compared to anyone on Earth, presumably (since he’s in a spaceship).
 
I contend that Bob has a special status and this is reflected in the mathematics. So is this a special case or can we generalise this to other events? People will argue that a core tenet of Einstein’s relativity is that there are no observers with a ‘special status’. But actually, the core tenet, as iterated by the lecturer in the video, is that the speed of light is the same for all observers, irrespective of their frame of reference. This means that even if an observer is falling into a black hole at the speed of light, they would still see any radiation travelling at the speed of light relative to them. So relativity creates paradoxes, and I gave a plausible resolution to that particular paradox in a recent post, as did David Finkelstein in 1958. (The ‘special status’ is that Bob is in the same frame of reference, his spaceship, as the light source and the 2 resultant events.)
 
In another even more recent post, I cited Kip Thorne explaining how, when one looks at the curvature of spacetime, one gets the same results if spacetime is flat and it’s the ruler that distorts. If one goes back to the Bob and Alice thought experiment in the video, Alice sees (or measures) a distortion, in as much as the front clock in Bob’s spaceship ‘lags’ his rear clock, where for Bob they are the same. This is because, from Alice’s perspective, the light signal takes longer to reach the front because it’s travelling away from her (from Bob’s perspective, it’s stationary). On the other hand, the rear clock is travelling towards the light signal (from her perspective).
 
When I was first trying to get my head around relativity, I took an unusual and novel approach. Because we are dealing with light waves, it occurred to me that both observers would ‘see’ the same number of waves, but the waves would be longer or shorter, which also determines the time and distance that they measure, because waves have wavelength (corresponding to distance) and frequency (corresponding to time).
 
If I apply this visualisation trick to Alice’s perception, then the waves going to the front clock must get longer and the waves going to the rear must get shorter, if they are to agree with the number of waves that Bob ‘sees’, whereby from his perspective, there’s no change in wavelength or frequency. And if the number of waves correspond to a ‘ruler’, then Alice’s ruler becomes distorted while Bob’s doesn’t. So she ‘measures’ a longer distance to the front from the light source than the rear, and because it takes longer for the light to reach the front clock, then it ‘lags’ (relative to Bob’s recording) according to her observation, using her own clocks (refer video).
 
So, does this mean that there is a universal simultaneity that we can all agree on? No, it doesn’t. For a start, using the thought experiment in the video, Bob is travelling relative to a frame of reference, which is the spacetime of the Universe. In fact, if there is a gravitational gradient in his space ship then that would be enough to put his clocks out of sync, so his frame of reference is idealised.
 
But I would make the point that not all observations of simultaneity are equal. While observers in different locations in the Universe would see the same events happening in different sequences; for events having a causal relationship, then all observers would see the same sequence, irrespective of their frame of reference. Since everything that happens is causally related to past events, then everything exists in a sequence that is unchangeable. It’s just that there is no observer who can see all causal sequences – it’s impossible. This brings me back to Kant, whom I reference in my last post, that there is an epistemological gap between what we can observe and what really is. If there is a hypothetical ‘universal now’ for the entire universe, no single observer within the universe can see it. Current wisdom is that it doesn’t exist, but I contend that, if it does, we can’t know.