I am inspired today, once again, by the idea of duality and its fundemental role in our physical reality, from electrical duals, to quantum duals, to the round trip of light (earlier post) and so on...
The more time goes by and the more I think of the world as an expression of Duals (the formal term) the more I realize that duality itself may be the unifying property of the universe that all things emerge from.
I cant help but think that duality is a profound insight of the universe, but I havent quite connected the dots yet... All I know is everything we talk about seems to be only valid in duals and becomes unknowable when we try to seperate those duals in some way...
I am going to call it "The Iron Curtain of Duality"... but I feel like I need to invest time thinking about this, something is there.
Maybe because the only way we (part of the universe) can understand anything is by breaking it into smaller parts and study the relations between them? It's always the relation that we call "law". And relations need at least two parts. Maybe?
@3ammo the problem with that logic is that we already can experementally prove that relativity is correct so any conventional measurement is moot going in.
Moreover the idea that speed of light is a constant is not what is the issue. The speed of light **is** a constant when measured round-trip, that is experimentally provable. What is not a postulate and the part we cant prove is that the speed of light is a constant one-way regardless of orientation. We take that to be the case in relativity as a matter of **convention** not as a postulate. The reason we do so is because even if it is not symmetric it wont change any of the results, therefore any arbitrary convention works, so we pick the easiest one.
Regardless you still cant actually measure it one way, if you do so conventionally you wont account for time dilation at all and get an incorrect answer where using the relativity approach you will get a more accurate answer but it will be interently a two-way measure.
@freemo I think I get your point about the round trip, I'm not trying to contradict that (though I think there's something to be said here).
But, as far as I understand, the speed of light (when said like this, refers to the instantaneous speed in any direction at all times) is taken to be constant as a postulate, not a convention. It's not about "measuring" it to be constant, the theoretical construction itself is built on this postulate. Relativity doesn't work only by saying "any measurement of the speed of light (which might be possible only as a round trip) will yield a constant". Relativity works by asserting the general invariance of the speed of light (all times, all directions, all position, all frames).
For example, take the derivation of the Lorentz transformation from the two *postulates* (1. principle of relativity, 2. constancy of the speed of light). Einstein's derivation depends on the constancy of c, not on round trips, not even on measurements. There are derivations of other things based on this constancy as well.
This is not a matter of convention, it is a matter of necessity. Because it is about more than just measuring things, it's about building a framework for understanding the world. Only *after* such framework has been constructed can we talk about experiments and measurements.
You use the word "prove". How can we prove that relativity is correct? Experiments and measurements are not an objective, theory-independent proofs of anything. Any experiment is interpreted within a given theory. More on this in a bit, this reply is already toot long.
@3ammo So here is why its a convention and not a postulate… simply speaking if you pick some other convention that ensures the round-trip is unchanged but it is asymmetrical, all the math we do will give the same final results. Thus its a convention because it doesnt really matter since everything is eventually a round-trip anyway, so we just pick the easiest way to get the answer.
As an example imagine a world at the most extreme asymmetry where light travels at c/2 in one direction and instantaneous in the other. If you use this convention and then apply the new form of lorentz transformations to any thought experiment that could be carried out as a literal experiment, you get the same result as you would get if c was symetrical. What happens is the error is just enough that it cancels out and produces the same results.
Consider communicating with a distant astronaut and how we perform the very simple lorentz transformation there to synchronize time. Lets assume we know the real time (I will abbreviate it RT) and lets assume there is a meassured time, ill call this MT.. here is how it works out assuming C is symetrical.
Astronaut flys 1 light hour away, experiment starts, RT 0:00
Earth sends light signal to astronaut saying “The time here is 0:00” (RT)
Astronaut receives message claiming time is 0:00, he knows he is one light hour away so he now sets his clock to 1:00 (MT), he then replies “message received, I have now set my clock to 1:00” and sends this back home.
Home base gets the message saying the astronauts MT is 1:00, knows again it is one light hour away so concludes after lorentz transformation that the MT is now 2:00. Looks up at his clock, the RT, and sees it says 2:00. Concludes the astronaut clock and home clock are set to the same time.
But now lets look at the same scenario where the speed of light is c/2 in one direction and instantanious in the other, but the scientist dont know this so use the convention that c is symmetric. Being just a convention it should all work out (if it were a postulate then it would be meaningful and thus effect results and things would break here).
Astronaut flys 1 light hour away, experiment starts RT 0:00
Earth sends light signal “The time here is 0:00” (RT)
Astronaut receives signal, assumes c is symetric, therefore performs the same lorentz transformation as before and determines that the time must be 1:00 (MT), in reality because c/2 the RT is 2:00, so the astronauts clock is technically off by an hour. Astronaut replies “I have now set my clock to 1:00”.
Home base again gets the message of the astronaut claiming the time being 1:00, home base again assumes time is symmetric so gets the same result he did in the earlier experiment assuming that the astronauts clock must be 2:00 by the time they hear the return message (which took an hour to get to them).. sure enough they look up at the wall and it matches RT of 2:00… but in reality the signal was not symmetric and the return time for the light signal was instantaneous instead. That means by the time homebase heard “my clock is set to 1:00” and they assumed it was RT 2:00 by the time they heard it this was wrong, the reply was instantaneous and in reality the astronauts clock was 1:00 by the time they got their response and their transformation was wrong, and the clock is still slow by 1 hour. However it appears to them everything is correct, the full round trip time was still c, they got all the same answers at all the same times they would have if it was symmetrical. So even though it is technically wrong, the results work just as well
In fact you can pick any arbitrary asymetrical convention you want, so long as the round-trip results in a average speed of c, and you will get the exact same results and both sides of the communication would be unable to tell any difference at all.
This is why its a convention, you can pick any asymmetry you want and none of the results will ever change, therefore a convention is picked arbitrarily to be easy. No one needs to say “this is how it is” because nothing changes whether it is that way or not
@freemo Yes. Postulates are definitions. That’s what I keep trying to say. The speed is light constant “because we say so”. I repeated that multiple times. It is a definition, we don’t use the word “convention” for this kind definition, we use “postulate”. And that has nothing to do with any assertion about reality. Reality exists, but you can only see it through the lens of some model/theory. If you want a lens that says “in reality, the speed of light is different in different directions”, you can do that, and your measurements will agree with my lens that says “the speed of light is constant in general”. Reality doesn’t care about our definitions of space, time, velocities and how we communicate times and clocks. This is us, not the world.
@3ammo alright fair, just a difference in definition then.to me the definition of a postulate tends to suggest what is.. the way you are using the term postulate sounds more like an axiom to me.