It appears the Universe is expanding, but what if Space is shrinking instead? Surely it would look the same? 
I was puzzling over David Hilbert's 13th problem tonight:
https://www.quantamagazine.org/mathematicians-probe-unsolved-hilbert-polynomial-problem-20210114/
I can solve a quadratic easily enough. Cubics take longer. Quartics best avoided since life is short. Quintics are generally impossible, Galois and Abel proved that.
Why should we worry about polynomials of seventh degree?
For those who don't know, David Hilbert practically designed Loudspeaker simulators:
Hilbert transform - Wikipedia
I think he was having an off night there.
I was puzzling over David Hilbert's 13th problem tonight:
https://www.quantamagazine.org/mathematicians-probe-unsolved-hilbert-polynomial-problem-20210114/
I can solve a quadratic easily enough. Cubics take longer. Quartics best avoided since life is short. Quintics are generally impossible, Galois and Abel proved that.
Why should we worry about polynomials of seventh degree?
For those who don't know, David Hilbert practically designed Loudspeaker simulators:
Hilbert transform - Wikipedia
I think he was having an off night there.
I've knocked heads (
)with a few of the professional physicists here, but what is life if we can't 'blue sky' think a bit?Suppose for a second, that time and distance were in fact one and the same thing and we used c (speed of light) as our measure since it does not change (it bends around space, but the speed is constant). This tells us how far something is away from us in kilometres (unwieldy at cosmological scales) or in time (unwieldy at very short distances) but nevertheless its time that separates everything from everything else. Stuff cannot be separated from other stuff without involving energy - the two are inextricably linked: without a change in time, no energy, without a change in energy, no time.
So, maybe the reason the universe is expanding is better understood by imagining that time itself is being created as energy changes through entropy (the amount of energy in the universe is fixed).
So when we look out and see the cosmos expanding, its doing so because time is expanding, but we see it as distance increasing.
Now, I know Galu will say time is a canvas upon which events take place and certainly at our micro level here on Earth, in the solar system etc it looks like that, but that I think is a very human view of looking at things - Its very hard to decouple ones view that time is a separate thing upon which everything happens and imagine that instead it is actually a force, or is being created by the expenditure of energy. Newton thought it was a constant reference the same everywhere in the universe, Einstein showed it was 'elastic' but maybe its even more than that.
How does EMR propagate through a vacuum? It couples into time. Maxwell thought of EMR as a force (look at his equations) and we still have no explanation as exactly how it can propagate through a vacuum. Maybe EMR energy couples through time (think about the cosmos sitting in a 'time field' created through entropy).
Just sayin'
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Where I've got to so far, is we really need to abandon the metric in favour of rotation.
Bit vague on detail except its 4 dimensional. 0, 2Pi and all that.
As tireless investigator of the Universe I think I have uncovered a mathematical scandal:
I think David Hilbert had a thing going on with Emmy Noether.
Late night discussions about "mathematical affairs". You know what I am sayin'.
Bit vague on detail except its 4 dimensional. 0, 2Pi and all that.
As tireless investigator of the Universe I think I have uncovered a mathematical scandal:
I think David Hilbert had a thing going on with Emmy Noether.
Late night discussions about "mathematical affairs". You know what I am sayin'.
Our makeup stuff interact with Higgs field in such a way that it acquire mass and let us experience the universe by moving through time at C. Photons and a few others are made of stuff that does not interact with Higgs field so they experience the universe by moving through space at C. There are also a host of other possible experiences in between.
I don't think we presently have tools developed enough to characterize time properly. Our preconceived notion of time really clouds our understanding of the matter.
I don't think we presently have tools developed enough to characterize time properly. Our preconceived notion of time really clouds our understanding of the matter.
Spacetime is four dimensional. We can think of it as consisting of the three familiar spatial dimensions x, y, z, and an added dimension, t.
Everything in the universe, including ourselves, is travelling through spacetime at a speed of c.
Because a photon travels at a speed equal to c, it uses up all of its quota of spacetime speed in moving through space and that leaves none for its passage through time. Therefore, to a photon, transit time through space is instantaneous.
A spacecraft travelling though space at a fraction of the speed of light uses up some of its quota of spacetime speed in moving through space and that leaves less for its motion through time. That is why a moving clock moves more slowly through time than a stationary one i.e. it ticks more slowly.
A clock sitting at rest uses up none of its spacetime speed in moving through space and that leaves all of its spacetime speed for whizzing along in the time direction i.e. it ticks as fast as possible.
Everything in the universe, including ourselves, is travelling through spacetime at a speed of c.
Because a photon travels at a speed equal to c, it uses up all of its quota of spacetime speed in moving through space and that leaves none for its passage through time. Therefore, to a photon, transit time through space is instantaneous.
A spacecraft travelling though space at a fraction of the speed of light uses up some of its quota of spacetime speed in moving through space and that leaves less for its motion through time. That is why a moving clock moves more slowly through time than a stationary one i.e. it ticks more slowly.
A clock sitting at rest uses up none of its spacetime speed in moving through space and that leaves all of its spacetime speed for whizzing along in the time direction i.e. it ticks as fast as possible.
Everything with no mass implies non interaction with the Higgs field and moves through space at C. So by extension, the Higgs field is somewhat tightly coupled to time but not so much to space. In other words, you absolutely need mass to acquire experience of time by trading experience of space. 
Apparently, there is no fundamental reason in particle physics that requires the photon to be massless.
In a different universe, the Higgs field may give the photon a non-zero mass.
In consequence, the c in E = mc^2 is better interpreted as the speed of massless particles rather than the speed of light.
That may be a handy bit of information for those who have always wondered why the speed of light features in the mass-energy equation!
In a different universe, the Higgs field may give the photon a non-zero mass.
In consequence, the c in E = mc^2 is better interpreted as the speed of massless particles rather than the speed of light.
That may be a handy bit of information for those who have always wondered why the speed of light features in the mass-energy equation!
How is this verified?
Then why does it take time for us to see into the past, ie: stars and galaxies?
Let me repost.
And it is the cold truth, there are more things out there to baffle us no matter how much we learn.
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