You should work toward becoming more aware of the profound limitations of your awareness.
In other words, relative space and relative time are measurement outcomes.
No. The relativity of space and time can be observed via measurement, but that relativity is not an outcome of measurement.
According to Einstein's theories of relativity, both special and general, space and time are relative because there are infinitely many equally valid points of view (mathematically: coordinate systems, charts, atlases) that are consistent with the outcomes of measurement, and different points of view can factor spacetime into space and time in different ways. There is no one true factoring of spacetime into space and time; there are infinitely many equally valid factorings, so what counts as space and what counts as time is, within constraints that are precisely formulated by Einstein's theories, an arbitrary choice.
A popular misconception about relativity is that there is a unique point of view for each observer. That misconception derives from the fact that, in the special theory of relativity, it is generally convenient for unaccelerated observers to prefer a point of view in which they are at rest. Even in the special theory, there are infinitely many such points of view, if only because the spatial directions up, down, north, south, east, and west are arbitrary. The general theory of relativity adds even more arbitrariness to one's choice of chart (local coordinate system), partly because (in general) no one chart (coordinate system) is capable of describing all of spacetime; to describe all of spacetime, you generally need an
atlas of charts.
And Einstein provided a framework to relate those measurement outcomes for inertial observers.
For
all observers, actually.
Mike Helland refers here to inertial observers because, while
Mike Helland understands next to nothing about special relativity, he understands absolutely nothing about general relativity. That's important to note, because it is impossible to understand what is meant by expanding space in the ΛCDM model without some understanding of general relativity.
I've got a question for you.
When space expands in general relativity, is that considered a linear transformation?
Or because lines become unparallel it's non-linear?
Because going back to this laughing stock:
As
Ziggurat noted,
Mike Helland's next question was the laughing stock:
And reviewing linear algebra, I don't think the transformation suggested here is linear.
I'm not even sure if it's orthonormal.
It seeeeeeeems to me..... and my profound ignorance, if the spacetime wasn't orthonormal, and was slightly longer in the time direction, but so slight it would only be noticed after something traveled at top speed for a 100 million years, that would wrap it up pretty nicely.
But I am delusional.
That last sentence is true. The previous sentences were nonsense.
Spacetime is a pseudo-Riemannian manifold, which is a far more complicated concept than a vector space, and vector spaces in general can be considerably more interesting than the real Hilbert spaces considered in undergraduate linear algebra, and (as
Ziggurat pointed out) asking whether a space is orthonormal doesn't make sense even for real Hilbert spaces.
Once again your profound ignorance strikes.
It IS the other way around. The relationship between space and time defines null vectors, and photons and all other massless particles travel along them. So it's very much the case already that spacetime defines the path of photons, rather than photons defining spacetime. That is the standard view of physics, not some revolutionary insight you have come up with.
Even when you are right, you still manage to find a way to screw it all up. It's an impressive talent.
Ziggurat said that well, except xe surely meant to say "null geodesics" instead of the "null vectors" I highlighted.
I don't think you actually understand the definitions of any of the words you are using. Spacetime is not orthonormal. No vector space is orthonormal. The word doesn't apply. It is basis vectors, not the space itself, which can be orthonormal or not.
Once again,
Ziggurat is exactly right, although xe would have been even more right without appearing to limit the concept of orthonormality to basis vectors; a pair of vectors can be orthonormal even if neither vector is among the basis you have chosen to use.
Finally, I'm going to go back to a question that has already provoked some laughter, because that question illustrates some of the profound misconceptions noted above.
Ok.
So let's take an empty volume of space.
Now say five photons enter that space, and while they're there, they redshift.
Then they leave that space.
Do we have the exact same empty space we had before.
The conservation of energy says to me that space contains the energy the photons lost before they left the volume.
Is that unreasonable?
I have highlighted the key sentence. Why would the five photons redshift while in that empty volume of space?
I suspect that, in framing his question,
Mike Helland was simply assuming the crackpot idea that photons redshift of their own accord as they travel through space. That assumption is unreasonable, so any question based upon that assumption is unreasonable.
If I were being generous, however, I would consider the possibility that
Mike Helland is asking us to assume the redshift is caused by something that's compatible with relativity.
Suppose, for example, we're talking about a Minkowskian spacetime and a redshift that's compatible with special relativity. That redshift might arise in the following way:
Mike Helland has an assistant located at one boundary of the empty volume of space, and
Mike Helland speeds past that assistant, heading into the empty volume of space. Let's assume ten photons instead of five, all emitted from the same source with the same frequency and wavelength, so the assistant can look at half of them without disturbing the five photons
Mike Helland will examine. After
Mike Helland observes the frequency/wavelength of his five photons, xe turns around and returns to the assistant. Comparing the frequencies they observed,
Mike Helland notes that the photons he observed were redshifted compared to the photons observed by the assistant.
Mike Helland would undoubtedly consider that redshift as evidence for the "ideas" he's been promoting in this thread, but the assistant, being reasonable, suggests the redshift arose from the fact that
Mike Helland was travelling at a high rate of speed away from the source of the photons.
Mike Helland asserts that, on the contrary,
Mike Helland was stationary while his assistant was moving at a high rate of speed toward the source of the photons.
Special relativity tells us that both points of view are equally valid.
Mike Helland then looks at the assistant's clock and notices it is running fast (compared to his own clock). "Your measurements are no good because your clock is busted." Au contraire, says the assistant, noting that his clock is consistent with a bunch of other clocks in the area, and suggests that
Mike Helland's clock is running slow.
They agree to disagree, but
Mike Helland still wants to know the answer to his question: What happened to the energy lost by the five redshifted photons? Has that energy become part of the space through which they were travelling?
The assistant thinks the question is nonsense. They agree to settle their disagreement by taking the discussion to some obscure forum they found on the World-Wide Web.
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