@freemo Because then everything is a convention, if we do it your way. Which is fine by me, all theories, in the end, *are* conventions.
Any theory and any framework is a set of choices, these are postulate. You say that calling it a "postulate" says something about the true nature of things, or reality, but it doesn't. As long as you have a consistent set of postulates that can describe measurements, you have a working model of reality. But you can also have a different set of postulates that describe the same measurements. In that sense, all postulates are conventions. I prefer to keep the word "convention" for details within a theory, not its building blocks.
@freemo Yeah I'm writing the other reply. I think we actually agree in a certain sense. You want to call it a "convention" because of your view of reality as you explained it, I want to call it a "postulate" because of the way I see theory and reality. It's a philosophy discussion at this point (this is not meant to be disparaging).
@freemo I get the point, I'm not missing it. But I am saying that it doesn't matter.
A reality that is fundamentally hidden from us is not a reality at all.
The points regarding symmetry are not moot. Our *understanding* of reality, measurements,...anything really, is impossible without these arguments.
These are issues that we settle before and regardless of experiments and measurements.
@freemo My point is not to pretend that the world is Newtonian, I simply meant our state of knowledge, our working theory was Newtonian. I was answering the question of "How do we prove relativity to be correct in the first place?" And that is by finding a contradiction between the Newtonian view and the measurements made within the Newtonian view.
@freemo Again, I am not contradicting what you said earlier (the round-trip speed of light is constant). This is not the point I’m arguing.
You mention the use of Lorentz transformation. What is Lorentz transformation, how do you get it? You either derive it from the postulates of special relativity, there’s only two of them, the second one is that the instantaneous speed of light is constant in all frames, OR you can find it from a complicated and convoluted way from Maxwell’s equations, which also yield a constant instantaneous speed of light in all directions.
The point I’m trying to make is that you talk about experiments as if they are objective and model independent. They are not.
@freemo Now let's consider the symmetry thing.
If we allow a *fundamental* theory to differentiate between directions (and in your case, it's even the same direction but with a negative sign) then we are building a very ugly *fundamental* view of the world. It's actually more than just ugly, we don't know where to go from there. In free space, we *postulate* homogeneity and isotropy and the isotropy of time as well. Because, why it be any different?
Now, this is not really about the world any more. This is about *us* understanding the world. We have to build a simple model, then complicate things by adding stuff to it. That's how we understand anything. You may say "how do you know free is space is homogeneous and isotropic? Maybe it's not. Have you measured it?" I would say that free space is homogeneous and isotropic because I said so, not because of any measurement. Measurements can then be made within this model.
If we make experiments that show that free space is not so symmetric, well then we will come up with another model of the world in which there is some other entity, more *fundamental* then space, and explain space in terms of that new entity. We will *postulate* that this entity is symmetric and that there are objects inside that entity that breaks the symmetry and produce a space that is not homogeneous and isotropic. If things are not simple, we just construct a deeper level of understanding, MAKE it simple and then explain complexity within it.
@freemo So how do we "prove" relativity is correct?
We are Newtonian people, then this guys comes along and says the speed of light is constant, so we set up an experiment to measure the speed of light (one trip, round trip, doesn't matter). We are Newtonian people, so we have absolute space and absolute time and absolutely no problem synchronizing distant clocks. And we find that the speed of light, in our Newtonian understanding of what it means to measure it, is constant. But that breaks our Newtonian understanding! We thus find a contradiction between theory and experiment even though the experiment was interpreted within the theory. What now?
The guy then comes and says: I told you so. The speed of light is constant, and here's how you should think about space and time from now on.
Someone says: but the way you set up the understanding of space and time makes it impossible for the speed of light to be *measured* to be any different!
The guys replies: Exactly my point!
@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.
Hi, I don't mean to spam you. I just found three interesting posts in a row and I was just having a similar conversation about the same themes and thought to share
Explaining that knob and its mechanism requires a theory that supersedes relativity. Testing the effect of the knob should then be done within the context of this new theory. Just like relativity itself came with its own set of rules of how to make and interpret experiments.
Empirical evidence always comes with some theoretical baggage. There’s always some model within which an experiment is defined…I think.
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?
In Einstein’s relativity, light has a constant speed because we say so. It’s a postulate. We cannot test statements withing the paradigm that is built on them.
Before we adopted relativity, we had the older notions of absolute space and time and, within that paradigm, we can make a meaningful test of the speed of light and find it to be constant.
So, your final conclusion is correct, it’s impossible to test the speed of light BECAUSE of relativity. But if you accept relativity, then you have already accepted that the speed of light is constant, and it’s not a matter of experiment.
We can, however, test consequences of relativity, like length contraction, time dilation etc.
I was literally having this conversation a couple of hours ago, almost the same time you posted this!
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