Einstein told us that the speed of light must always, not only appear, but BE the same in every frame of reference no matter how fast we are moving towards or away from it. So even if you are moving at half the speed of light towards a light beam, the entire universe must conspire to either "speed up" or slow down your "time" to account for this difference.
If that makes sense to you, you are no longer sane. You cannot create scenarios of two mutually exclusive events at the same time and call that reality. This is fundamental to reason.
To show this contradiction, consider you are running away from a light beam and towards another at the same time. You move at half the speed of light. Of course in real life you will encounter the light you are moving towards first, but in Einstein's universe both beams MUST (in your world) hit you at the same time. However, in Einstein's universe, someone else will see them hit you at different times because they also MUST see light travel at a certain speed. This is just plain fucking stupid.
At best you can have an illusory effect, but to confuse that with a real difference in simultaneity is to truly give up on reason itself.
Einstein quote is just a description of how speed of observation distort objective reality for moving observer due to finite speed of observation (speed of light in this case). Nothing more, nothing less.
If you will observe same "two simultaneous events" using sound waves instead of electromagnetic waves, you will get exactly same math, but with speed of sound instead of speed of light. If you will use post pigeons to observe events, then you will get fucking speed of fucking pigeons in math instead of speed of light.
Dumb kike just silently omit the simple fact that he "look", i.e. use that slow EM waves of visible range to make his observations. And that explains everything, if you take speed of observation (speed of light or speed of sound) into account.
That's it.
And this absolutely does not mean that events could not be simultaneous. Problem of syncronisation of two distant clocks solved long ago, and solution is routinely used today in NTP protocol invalidating Einstein nonsense billions of times per day on planet Earth and even around. Just fucking take into account speed of information exchnage, and that's all. You will get two syncronized clocks at a distance without any problem and events happened at same time on both clock will always be simultaneous, regardless of what some observer see.
But to Einstein and his supporters they are stating it as a real effect vs. an apparent effect. What you're describing is an apparent effect based on our observations needing to wait for light to travel to our eyes. If Einstein wanted to express this idea he could have done so explicitly (and should have if that is his intention). So if this is an omission it is intentional.
But specifically on this idea, I'm still not sure I follow it. I can think of a simple example of a training moving near the speed of light and we are observing it from rest. A light beam is sent from the back of the train to the front HOWEVER the train is filled with air and not a vacuum. Thus the light beam will be pushed forward via the General Sagnac effect.
As an observer the limitation of the speed of light reaching me (in order to observe the event) should only produce a delay in the first data point reaching my eye, as the beam first leaves the source. However anything after that should still convey to me the correct information about velocity, provided we limit the window we record data to when the train is about to pass us until it has just passed us. The small displacement of distance should not be sufficient to delay the light by any significant degree...
Think about a straight line coming in perpendicularly to the observer vs a line 1 degree off from that for the second measurement. The distance light travels to us in the second measurement is only L/cos(1 degree), which is a 0.02 percent change in distance traveled to reach us compared to the initial L of the first measurement. Thus no issue observing this increased speed of light in the train for that effect.
Just never forget that everything you see, you see with a delay proportional to the distance from you to the object you observe. If oblect you observe moves with speed close to the speed of light, light from different parts of object (head and tail of your train, f.e.) need additional time to reach your eyes.
Meanwhile, there is funny thought experiment that always make relativists hang indefinitely.
They often talk about time dilation effect. However, you could make a clock using speed of light as a source of time intervals. Pulse a LED into a sensor through mirror at a distance (or fiber) and use delay as a clock sync. Use delayed pulse from sensor to pulse LED again. You will get a simple clock base frequency generator. Since there is constant speed of light dogma in relativity, then this clock just can't have any dilation effect, regardless of any relative movements and inertial frames. :) Whoever observe this clock, he will have to see exactly same tick-tock in all cases. :) Even more - all such clocks in a universe will be syncronized by definition. And gravity also could not dilate that clock - speed of light is always the same, and clock using speed of light as a frequency source just can't run faster or slower. :) It's their own dogma. :)