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Motion (and complex, multi layered, multi qualitative, 'particle decay-able' motions at that) is continuous, so every time one attempts to pint point a locality it has already moved/changed/interacted with other moving parts in other ways;
So if Earth is at the center of the universe, that might possibly explain observations without dark energy according to these mathematicians, but most scientists don't think Earth has such a special place in the universe.
In the mainstream Lambda-CDM model, two different perspectives from observers in widely separated galaxies yield very similar expansion patterns with dark energy, while in the mathematician's model two such different perspectives yield very different expansion patterns because their model has no dark energy and one observer is at the center of the universe while the other isn't. Your comment is so unclear I can't understand what it's supposed to mean, but it does seem to infer you don't understand the difference.
originally posted by: greenreflections
From being in the center of observer idea, why not7 We are at the center but not in a sense you were trying to depict it. That's what perspective means, the point of view.
originally posted by: Arbitrageur
a reply to: joelr
Even if you intended to omit dark energy from your explanation, I don't understand why you would say that "Spacetime expands slowly on a local scale". The Hubble constant infers something twice as far away is receding twice as fast (in a statistical "best fit" of data) which implies the rate of expansion is not any slower on a local scale, where local in this case would be say 30 million light years or so, near the lower end of where Hubble's law applies.
originally posted by: mbkennel
a reply to: delbertlarson
I agree that not all interactions mean a creation of particles. But I believe that in QFT the fields are more fundamental than the particles which are more ephemeral sometime things. If we think about fields first, and time evolution on fields (more like classical EM but with quantum fields) there seems to me to have less difficulty conceptually, after you swallow the Big one, that the quantum fields live in functional space and not just over x,y,z,t. So if E & B classically live in x,y,z,t; the quantum verision is a wavefunction of a function.
originally posted by: mbkennel
a reply to: delbertlarson
I agree that not all interactions mean a creation of particles. But I believe that in QFT the fields are more fundamental than the particles which are more ephemeral sometime things. If we think about fields first, and time evolution on fields (more like classical EM but with quantum fields) there seems to me to have less difficulty conceptually, after you swallow the Big one, that the quantum fields live in functional space and not just over x,y,z,t. So if E & B classically live in x,y,z,t; the quantum verision is a wavefunction of a function.
Go from point particle, to a wavefunction: QM of point particles goes from classical physics of a point in a vector space (x,y,z,t) to a function.
Next level: true quantum mechanics of electromagnetism is a function of a function, i.e. the wavefunction of the electromagnetic field. And similarly QFT of SM fields are functions of functions.
originally posted by: delbertlarson
I don't swallow the Big One either. My understanding of Hilbert Spaces is that each function within that space is an eigen function of the relevant quantum operators and that any arbitrary state can collapse to any one of those functions. Prior to a measurement a state may be in the superposition of several such functions. But each function is itself a function of x, y, z and t, and so also is the superposition.
originally posted by: joelr
originally posted by: mbkennel
a reply to: delbertlarson
I agree that not all interactions mean a creation of particles. But I believe that in QFT the fields are more fundamental than the particles which are more ephemeral sometime things. If we think about fields first, and time evolution on fields (more like classical EM but with quantum fields) there seems to me to have less difficulty conceptually, after you swallow the Big one, that the quantum fields live in functional space and not just over x,y,z,t. So if E & B classically live in x,y,z,t; the quantum verision is a wavefunction of a function.
Yes QFT starts with a classical field equation then it's quantized and you get excitations in the field which is the particle part.The purpose isn't fields themselves, it's just a better way to deal with multi-particle systems that also incorporates other important concepts like Feynman diagrams and QM.
originally posted by: mbkennel
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I would have to disagree with the "purpose". The most fundamental equations, the Ansatz which reflects one's opinion about what the facts of Nature are, starts with writing down the Lagrangian density as a function of fields.
Particles are derived from it secondarily. They're important because that's how we measure stuff in experiments, but they seem less fundamental.
Feynman diagrams come from a procedure to enumerate terms in a perturbation theory to approximate the "true" physics which comes out of the underlying field interactions. You need them to adequately compute an experimentally accessible number.
That's like solving antennae by going to a finite mode approximation (each mode would be a 'particle') and deciding to cut off counting at some level of approximation.
But the real theory is full Maxwellian EM on a continuum, and everybody agrees that the EM field is more fundamental than the modes.
No, the expansion doesn't seem slower and isn't slower locally, not in that context.
originally posted by: joelr
Because I think some people have the impression that because distant parts of the Universe can seemingly expand faster than light or even near light speed then they get an idea that you could go to that location and actually see nearby galaxies expanding near light speed. But from that point of view expansion would not be any different from our local point of view. So on a local scale expansion seems slower.
-Galaxies are moving away from us.
-Galaxies that are further away are moving faster.
originally posted by: Arbitrageur
No, the expansion doesn't seem slower and isn't slower locally, not in that context.
Local recessional velocities near the low end of Hubble's law applicability are lower, but this isn't because of slower local expansion.
Look at the balloon analogy. Attach some little pieces of paper to spots on a balloon (see video), and inflate the balloon, where the surface of the balloon is a 2D model of the 3D expansion of the universe. From the perspective of any paper dot, the closest dots aren't receding as fast as the more distant dots, but this isn't because the expansion is any slower around the observing dot; rather, the expansion is relatively uniform across the surface of the balloon.
I didn't say anything about your statement "on a local scale expansion seems slower" when you first made it, because in an informal forum like this we can be a bit sloppy with our language and it's not a big deal. But when someone questioned if this was true I had to agree that it really isn't a correct statement, and I'm kind of surprised that you haven't just admitted this was sloppy language and not correct, because I suspect you know that, though I could be wrong so if I am I'm hoping this balloon analogy will help you understand why it's wrong. This video explains observations correctly (sans dark energy as in your simplified explanation) using the balloon analogy by saying the following:
Introductory Astronomy: Balloon Analogy for Expansion
-Galaxies are moving away from us.
-Galaxies that are further away are moving faster.
That's true but it doesn't imply local expansion is slower, because in the balloon analogy they show those observations hold even when the local expansion is the same as non-local expansion, that is, the balloon is expanding at the same rate everywhere on its surface.
Now of course if you go outside the context of your original statement, to parts of the universe closer than the lower end of Hubble's law (less than about 10 megaparsecs), then gravity dominates over dark energy and at such cosmologically close distances the expansion really is slower, or even zero when you get close enough (molecules aren't expanding), but your original statement and clarification don't suggest you were referring to this type of context.
Time exists, it's one of the vectors of "position" in defining a location. There is a common mis-understanding about time that comes from some Physicists saying that the FLOW of time may be an illusion.
Flow of time may be psychological but time as an aspect of reality is 100% real. Not only can it be measured but we can predict exact changes in it's rate of change depending on it's speed and gravitational influence.