Ok, I have an argument for how light must exceed C from a time dilated frame.
And the time dilation in this is all general relativity, and the way time slows in a gravity field, and that this also applies to G-force (inertia) due to the equivalence between acceleration and gravity.
But first a few dry runs…
First let us make a light speed measuring device with 2 light sensors (A and B) that are 1 meter apart (or whatever distance is required by the state of technology to measure light speed accurately, 20km or 20,000km would also be acceptable), but we will have 2 high resolution clocks, the signals from light sensor A goes to both clocks, as do the signals from light sensor B.
The 2 clocks if they are both working correctly will measure the same period of time between a photon hitting sensor A, and then sensor B.
Note: If you want you may skip ahead now to the lines of hyphens that reads “The Actual Experiment” and read from there, but if you have any objections it might be best to read the rest of the dry run section below:
BUT we are going to suppose that one of the clocks is faulty so that it measures less time between these 2 events.
If we did not know of this fault, we would have the curious answer that the speed of the same photon travelling between the same 2 sensors moved at C according to one clock and exceeded C according to the other clock.
But this is in no way interesting you say, the clock is just wrong, and of course you are right, the clock is simply wrong.
Next we replace the faulty clock with one that has been fully checked out to be good, and we repeat the experiment, but we place this second clock (only) in a time dilation field somehow (artificial or highly localized gravity field, or centrifugal force, or magic).
This time we should get the same result, the time dilated clock has not measured as much time pass between the signals, it tells us that light is exceeding C between the sensors, the same light moving between the same sensors that communicated the same signals to the other clock that said the speed of light IS C.
But this time the clock is not incorrect in the time it keeps, but it is experiencing time (due to GR time dilation, or magic) to be slower than the space between the sensors.
This would be similar to falling into a black hole and seeing a distant bright pulse of light illuminate dust particles, from your time dilated perspective that is faster than the light should be moving, but not in any way interesting, because of the time rate difference between you and the light.
Ok, so far I still have not said anything even vaguely interesting, sorry about that.
The Actual Experiment:
We will now look closer at those 2 light sensors, they are shaped like CD’s (have a hole in the center for mounting) and are transparent for light to pass through, so making sure the holes are aligned at the same distance as before, we rotate them in the same fashion as 2 CD’s would if you stacked 2 CD drives on top of each other and then separated them to the 1 meter (or 1km if you rather) distance, keeping the axis of rotation of both sensors aligned.
If we let them rotate fast enough that time slows for these sensors due to GR’s time dilation from acceleration, enough to be measurable. And we have one of the clocks rotating with the sensors, and one of the clocks not on the rotating frame.
Now we have the sensors detect the passage of the same photon, no not the same photon as in the previous experiments, we will splash out on a new one! (sorry couldn’t resist)
The signal is split as before with the signal from sensor A being both communicated (possibly by a commutator, or perhaps it is fibre optic) from the rotating rig to the non rotating clock, and to the clock experiencing time dilation as the sensors are.
Sensor B is connected in the same manner to the 2 clocks.
So what should we have as the result?
The light hits sensor A, the time dilation slightly slows rate at which the signal moves to the clocks, one half of the signal gets sent to the normal time clock, and the other half gets communicated to the time dilated clock, it will take the signal slightly longer to get to the time dilated clock since the signal is slowed the whole way. But this does not matter as it slows down the signal from sensor B to the time dilated clock just as much.
So while the time dilated clock will obviously measure less time between the 2 sensors being tripped, the delay in propitiation will not interfere with the separation between the 2 signals, just add an equal delay (assuming equal length paths to the clock) to the reception of each signal.
Ok, so we can agree (I assume) that the rotating clock has measured less time passing between sensor A and B being tripped than the non time dilated clock will have measured.
This means that either the time dilated clock measured light to be at C, and the non time dilated clock measured light to travel less than the speed of light, slower than it can justify.
-Provided of course we are doing this in a vacuum and expected C in the first place.
Or because the space between the 2 sensors isn’t rotating with he sensors, and neither is the photon source, we may assume that the results for the non time affected clock will match the obvious results of the earlier thought experiments.
Additionally if the rotating sensors make such a big difference to the measured rate, then we could have a non rotating pair of sensors (A2 and B2) almost touching the rotating sensors like this: A|A2------------------------------------B|B2
If the rotating sensors really change the measured speed of light for the non time dilated clock, then we would expect to find that sensors B and B2 trigger at notably different times, not as you expect which would be indistinguishable from simultaneous unless you have really mastered measuring vanishingly small periods of time.
Yes, they would essentially have to be measuring different photons not to see both trigger at the same time.
So it seems certain that it is the time dilated clock that sees the light as moving faster than the speed of light.
But it gets worse, if we for a moment pretend it is linear motion not rotation, then if you were moving with the sensor, or not would change your view on the path light takes.
If you move with the sensor, because you are moving at right angles to the path of the light your velocity bends the path of the light so that instead of going straight between the sensors, from your perspective the light is on an angle and hence has further to move to traverse between sensors A & B.
Back to the rotating frame, the light would seem to be spiralling from your rotating perspective making for a longer path, and since a lot of rotation consists on instantaneously linear motion this longer path view is perfectly valid.
If it weren’t valid then motion wouldn’t be relative, if motion is relative angles must change.
So you view the path the light takes as longer, and you are measuring less delay (due to your slowed experience of time) between sensor A and b being triggered!
You are now seriously measuring light be be moving a lot faster than the speed of light, it is completing a longer course in a shorter time!
That would actually still be true even if you believe that sensor B and B2 do not trigger almost simultaneously (detect the same photon in essentially the same position at 2 very different times).
Actually the rear sensor B2 would in that case detect the photon long (comparative speaking) before B does!
Because remember the light has a longer path.
So now you would need the light to slow down in it’s journey between the 2 sensors from the non-rotating frames point of view even more if you want it not to exceeds the speed of light in the rotating frames point of view.
It must slow down so that it makes up for both he time dilation and longer path that from the lab frame isn’t the loner path.
This means that sensor B2 has to trip even more before sensor B. Despite sensor B being slightly closer.
So did I just discover time travelling light?
Make light that exceeds C (at least according to one perfectly valid POV)?
Discover that motion isn’t relative?
Discover that GR acceleration time dilation isn’t logically consistent with the speed of light always being C?
Break Special Relativity with General Relativity?
Discover that a photon may be detectable in one state of motion in a certain at a certain location, but be not detectable in that same moment in that same location with a different state of motion (not just motion actually, but acceleration).
Also while I selected this form of the thought experiment since it is maybe easier to grasp the anomaly, rotation is not required firstly vibration could produce the same anomaly if violent enough to create strong G forces, and this would give the light a zigzag path relative to the sensor POV.
Additionally it could also be performed in a linear manner across a quickly accelerating train with sensors put on opposite windows, the G-forces would create time dilation, the motion would give the light shot directly across the tracks (from the ground) a slant (actually a bend! like light being bent by gravity) from the trains accelerating perspective.
One clock on the train, one on the track under the train with signals from the window relayed by brush contacts, or fibre optics.
Yes SR would also expect that further time dilation be heaped on the rotating frame (or train frame) since it has instantaneous linear motion relative to the lab frame, making matters worse still! (and producing various other paradoxes)
A few words to reduce useless replies which help no one:
If you reply, especially with any objections or questions, please ensure you read the entire message.
I want replies, but a lot of bother can be avoided by not selectively reading things.
And this is a thought experiment that is perfectly plausible to at least work out what Relativity should expect to happen. I tried to cover all possible conclusions, but if you think I missed a set of conclusions that have this make sense, do not object, correct!
Instead please tell me (for all parts of the experiment) what should occur and why that result doesn’t break various parts of Relativity.
Additionally please avoid making any objections that cover only the rotating example, or only the train example, an objection should probably cover all 3 examples to be valid, or if not, then different objections should be presented for each of the 3 forms of this experiment.
Finally, it is not wrong to disprove a theory even if you don’t have an alternative, if a theory is wrong then it needs to be acknowledged that it is broken, and like anything broken it either needs some very real repair (alterations) or it needs to be thrown out and a replacement looked for (or a replacement looked for so you can throw it out for good).
Furthermore there is a perfectly fine alternative that as far as I am aware fits all the evidence for Relativity even better than Relativity does and is easy to understand, logically consistent and has no paradoxes and is falsifiable. But let’s stick to one thing at a time.
Oh, and I am aware that light speed the a constant is an Axiom of Relativity and not explained, but if it is a provably impossible one, then the whole theory must be thrown or altered out if it’s axiom is obviously false, at least if you think science should be connected to reality or truth at least vaguely.