So are you saying that when we use the Lorentz contraction to convert from one frame to another and then take into consideration the time that it takes for the light to get to us that the effect that the Lorentz transformation has vanishes and the universe once again appears Newtonian in nature?
I am of course referring here to the Galilean transformations when I say Newtonian in nature.
If this is the case, is the Lorenz transformation just there to simplify parts of the math and is ultimately not needed?
No that's not what he is saying. Galilean view and relativistic view are not equivalent; Lorentz transformation is very much a necessary component of the relativistic view.
What he was saying is that the effects of Lorentz transformation implied by the way things are PLOTTED in a spacetime graph, is not at all the same thing as what the observers actually see. We don't see the light in its travel, we only observe it when it actually "touches" us.
The spacetime diagram version of that circumstance is entirely dependent on what do you take the simultaneity of events to be in the frame you are representing. That is an open parameter, and not a measurable quantity at all.
Don't mistake any of the following as claiming that relativistic view is irrelevant. All I'm pointing out is a rather silly way that relativity is commonly viewed.
If both observers see the same thing, one on the ship and one on earth won't the observer on the ship conclude that he is traveling far faster then light?
That depends on what is meant by traveling faster than light. In the convention of relativity, no he is not said to be moving faster than C. Think about this;
The earth observer PLOTS the moving observer as time-dilated so much, that only 28 years are measured by its clocks, while 2 000 000 years are measured by the earth clocks.
I'm sure you find it easy to agree with the above since you've heard about time dilation. But now notice, the flip side of the same coin is the ship must think it made it across all that distance in just 28 years. So, how does that play out?
Well, the moving observer PLOTS the distance between Earth and Andromeda galaxy as length contracting so much that it only takes 28 years to make it across that distance, without anything moving faster than C in its frame; i.e. in the CONVENTION of special relativity, the distance traveled is taken to be less than 28 light years, because it is PLOTTED as contracted during the travel. If you shrink the distance you plot, you will be able to say the time derivative of the distance comes out as less than C.
But, at the same time, the moving observer will in fact pass all the milestones placed between Earth and Andromeda galaxy, so was he moving across 2 000 000 ly in just 28 years, or was the rest of the universe kind enough to shrink itself during the travel?
Because it is fundamentally impossible to measure one-way speed of light, we cannot say whose distance reference is correct. That is why it is self-consistent to say what relativity says. In a funny way, the very fact that we cannot possibly know what C is in any single direction, is the cornerstone upholding relativity. Compare this to the common misconception, that relativity is based on us having measured the speed of light in whichever way direction. That common view is almost entirely upside down from the knowable hard facts (Which Einstein understood perfectly well himself, mind you).
And here we get into the actual semantical stupidity of special relativity, when people take it to literally mean the same thing as ontological reality. Is it smart to think the universe shrinks itself for our convenience to make that trip? No of course not. Is it not little bit smarter to realize we are really only talking about epistemological correlation between our definition of distance, isotropic C, simultaneity, and time measurements.
None of this means newtonian view is more correct. It is far far less correct.
I have always been under the impression that the observer on earth would be able to watch the whole trip unfold over a period of around 2 000 000 years and if the ship then returned they could then watch this as well. Are you saying that this is not the case and that in fact the ship can arrive long before the observer on earth can even consider seeing him and then return to earth before a person on earth can ever see the ship returning?
No that's not what it means. If you think the above comments through you can probably figure out how it works without anything passing past C in any plot. If not, I can explain it with more detail.
This is represented by the dependence on x in the transformation on the time axis and an assumption about when to call events simultaneous in the experiment. But I am wondering, are you saying that this is also just an illusion as well, and that when the time that it takes for light to travel is considered, then any time dilation will also vanish?
No, I'm just saying that any possible setup proposing to measure the one way speed of light, must propose what is the simultaneity of events; typically it is just tacitly assumed (without the proposer even realizing he is making that assumption) to be the lab-frame reference, which is the same thing as assuming isotropic C. A very short circle of belief.
If you understand fully the mechanism with which that ship makes it over 2 000 000 ly in 28 years in its own time, you can understand how that same idea extends to infinity. The ship can keep accelerating without running into any universal speed barriers. At any point of the trip, we could start considering the inertial frame of the ship as being in rest, and repeat the same thought experiment to some place that is in 2 000 000 ly away in terms of that frame, rinse and repeat, ad infinitum.
The flip side of that fact is that the concept of a "center frame" is meaningless. That is exactly the same thing as saying you cannot establish the simultaneity of two separated events. And thats the same thing as saying you can't measure one-way speed of light. And it's the same thing as saying there's no preferred frame.
It always amazes me how many people can accept the assertion "there is no way to tell which observer is moving" together with the assertion "near the speed of light a spaceship would not be able to accelerate anymore" without getting massive cognitive dissonance.
To resolve that dissonance is to understand what relativity actually means.
But the length of the other observer is not the only factor. The rest observer will say that the moving observer is racing away from the star, meanwhile the moving observer will say that the rest observer is racing toward the star. Are you saying that this has no effect on the situation?
It does have an effect, it's called aberration of light. See my very first posts to this thread, they discuss exactly this effect.
Note that it's an effect that must be accounted for as an optical illusion, otherwise navigation is impossible. When it is accounted for, the distance measurements work exactly like the OP described. The reason I brought it up was precisely to point out how this issue must be handled to be consistent.
Note that the relativistic version of aberration is different from the newtonian version; this is in fact a result of the difference in the definitions of length/time measurement (which are the flip sides of the same coin). Relativistic version would see almost all of the light approaching from the direction of travel, which is roughly (but not entirely!) the same idea as in Newtonian view the spaceship traveling much faster than C; e.g. moving fast enough to make it across 2 000 000 ly in 28 years. In relativistic view, this is still considered less than C.
OK lets start with the Newtonian case first and suppose that the ship has a constant length. In this case the spacing between the photon detectors must be farther apart. Since the light entered the ship at two points a fixed distance apart and since the ship was moving away from the source it spent a longer amount of time in the ship and so had a longer time to spread out.
The correction in this case is simple just take into consideration the time that the light spent in the ship and add the distance traveled by the ship in this time to correct the equations so that both can come to the same distance to the star. At this point I think it is worth pointing out that if we used the reference frame of the moving observer then he would see the other ship as moving towards the star and so would conclude that the light is not going to spend as much time in his ship before hitting the photon detectors and so to make their results the same would conclude that he needs to subtract some number from the length of his ship to calculate the same distances.
Your analysis is mostly correct. The only thing is that aberration is kind of a third layer on this whole conundrum;
1. Q: What do things look like in a spacetime plot?
A: Length contracted
2. Q: What distances does a spaceship measure in its own frame via the mechanism described in the OP?
A: Exactly the same distances regardless of its speed vs the speed of the universe.
3. Q: What optical effect the so-called "aberration of light" adds to this soup
A: Exactly what relativistic aberration describes, which the ship must compensate for in its calculations, otherwise it will eventually think the universe is condensed into a point up ahead.
Now lets suppose that, as you seem to be suggesting, the Lorentz contraction is just right that the ship at rest and the moving ship measure the same distance between their photon detectors
No, that's not what I'm suggesting, and that's not how it works either. In terms of the spacetime diagram plotted by the rest observer, the length contraction of the moving ship is never of the same amount as the aberration effect. You can find rough approximated amounts of these effects from my earlier posts. These effects are not directly related.
That is, I have assumed that the rod defines a sense of simultaneity of events. I have measured the one way speed of light but only by wrongly assuming that light will only travel one way though the device for any given speed of rotation, that is if a laser is set up on the other end it will pass though just as easily in the other direction. I have defined simultaneity by the position of the wheel and assumed that this is valid.
Yeah exactly, which means the propagation speed of C has already been defined prior to measurement. All the possible measuring systems you could imagine are a function of the propagation speed of C, and the way you imagine they behave is a function of the propagation speed of C. You can't measure C without knowing how they behave, and you can't know how they behave without knowing C.
You probably realize by now that this is also just the flip side of the same old mantra; there's no way to define preferred frame, and there's no way to say who is moving and who is at rest.
How is this shown to be true? First of all, after my analysis above I can't side with anyone that says length contraction will just make things look shorter, which was my first impression, but rather it seems that the observed length of the ship will depend on what direction the ship is going, towards or away from the observer. Which is not something that I have heard before but on closer inspection of the Lorentz transformation I can't just dismiss this as just totally impossible as there is a dependence on v and x where there seems to be some effect on the actual sign used.
I will agree with you at one point though, if two observers are standing in the middle of their ships moving past each other, when they are even with each other, they will agree on the length of their ships. But after this point they will each say the other ship is shorter while, before this point they will each say the others ship is longer.
No that is wildly incorrect, you are just confusing aberration effect with length contraction; two quite different things.
Things are plotted in spacetime diagram as length contracted (shrunk) whether or not they exist in front or behind the direction of travel, because the notion of simultaneity is redefined in the transformation (think about this; to measure the length of a moving object, you must know where the front end and the back end of that object was at any given single moment. You can't know this, because you can't know the simultaneity of separated events. But also since you can't know this, you can just decide something as long as your transformation is consistent. Redefine the simultaneity, also means you redefine the length of the object! That is what length contraction is; ignorance regarding the speed of C).
Aberration effect appears to move everything forward, which is the same thing as saying that objects residing directly behind the ship, will appear to be closer when measured with the method described in the OP. You already described this mechanism yourself so I'm sure you can figure it out.