Difficult Concepts (for me)

[notFritzArgelander]

I also find this thread very interesting.
I think, to science there is no unobservable universe - because we can't observe it.
Science is models. "The real truth" is more or less religion.
Also, I've got this funny idea that if you travel in speed of light, you wouldn't notice. Everything would look normal to you. Just the time and spatial dilatations make everything look normal to you.

I may be totally wrong, though.

The consequences of the unobservable portions of the universe, have observable consequences, though. For instance we can never observe (because of Dark Energy and the accelerating expansion of the universe) all of the universe even if we wait for an infinite time. Nevertheless the observations we can make are consistent with the universe being flat, homogenous and isotropic. Noether's Theorem guarantees that an infinite, homogenous, isotropic universe (no need for flatness, yet) has momentum and angular momentum conservation. So every experiment that we do (and there are a lot of them) where momentum and angular momentum are conserved is in accord with there being parts of the universe that we can never see. Flatness guarantees zero average energy density and so infinite extent and energy conservation.

Science constructs models that explain the observations. It is rather rigorous in that a compelling contradiction to a theory chucks the theory out and demands a replacement. That, I think, is as close to "the real truth" as one can get. I don't think that "The Real Truth" is knowable. Others might differ. But I think Platonism (knowing The Real Truth) has been dead since the 14th century. YMMV.

As you approach light speed the appearances of objects become increasingly distorted. MIT had a neat game to play online that illustrated the distortion of optics caused by relativistic motion. I've tried to find it again but failed. Instead this 6 minute YouTube clip shows the same effects.



There are several different ways in which relativity distorts appearances and the video starts out simple and then adds each effect in turn.

But in the "vehicle" you are not moving relative to, everything looks normal?
And is indirectly observable unobservable...?

The vehicle I’m sitting in looks normal.
Unobservable means no signal in this context.

[notFritzArgelander]

PS On the optical effects of Special Relativity, the Doppler Effect is somewhat familiar as is the "aberration" effect (the distortion that comes from moving through the rain of photons). The "aberration" is somewhat analogous to when running through vertically falling raindrops your front gets wetter than your back.

Less familiar is what the computer generated narrator refers to as the Terrell rotation effect. It's been known for over 60 years but there is a short summary and a neat graphic here: https://en.wikipedia.org/wiki/Terrell_rotation

Edit: There is also a good wikipedia entry on aberration: https://en.wikipedia.org/wiki/Aberration_(astronomy)

The aberration was new to me, but your comparison to moving in a rain made it very understandable.
Sorry for the late response, but my first work day after summer vacation just ended.

Thanks. No pressure.

[chasmanian]

"As you approach light speed the appearances of objects become increasingly distorted. MIT had a neat game to play online that illustrated the distortion of optics caused by relativistic motion."

is this it nFA?

http://gamelab.mit.edu/games/a-slower-speed-of-light/

[chasmanian]

It’s true that the multiverse folks speak of bubbles but I’m understanding chasmanian’s bubbles as different. Different bubble for each observer, no multiverses implied, unless I’m mistaken. Multiverses toss out Noether’s Theorem and are repugnant.

nFA, just chiming in to say that you are understanding me in toto. thank you.

[notFritzArgelander]

"As you approach light speed the appearances of objects become increasingly distorted. MIT had a neat game to play online that illustrated the distortion of optics caused by relativistic motion."

is this it nFA?

http://gamelab.mit.edu/games/a-slower-speed-of-light/

Yes! That's exactly what I was looking for. Thanks.

[chasmanian]

you are very welcome!!

[notFritzArgelander]

thank you Mark.

thank you so much again nFA.
I remember reading that a reason why its called dark, is because of how little we know about
dark energy. we're in the dark about it. and dark matter too.

nFA,
I was just wondering:
what would have Aristotle have thought about all of this that we talked about in this thread?
how about Newton?
and Einstein? how much of this did Einstein know?
some, all?
would would Hawking have thought?
would he have agreed?
how about Leonard Susskind, or Kip Thorne?

You know I was going to take this very seriously and answer something based on how different philosophies in the foundations of mathematics treat infinities...... The folks above had VERY different ideas about infinity. But then when you mentioned....

or Alyssa Milano, or Scarjo?
hahahaha

I decided to watch a movie or two... Perhaps another time...

Well, I was recently reminded by PM that I had not returned to address this more seriously, i.e. omitting Alyssa M and Scarjo. So I went to find my notes and/or a popular book I liked on the topic. Alas both notes and book have vanished, presumably yet another casualty of my relocation.

The popular book I had in mind ( pun intended here) was https://en.wikipedia.org/wiki/Infinity_and_the_Mind which I thought had a good treatment except for a few cases where some biases showed. Nothing wrong with that, we all have them. It was a sufficiently fun read that I've ordered the Kindle version due to downsizing. So as a stopgap measure until I recover my thoughts, I think that the most important distinctions to be made here are between potential versus actual ideas of infinities and how this applies to numbers, times, and spaces. So here's a start.

https://en.wikipedia.org/wiki/Actual_infinity

Aristotle is the key troublemaker: https://en.wikipedia.org/wiki/Actual_infinity#Aristotle and the author of the potential-actual distinction https://en.wikipedia.org/wiki/Actual_in ... istinction

My position is opposed to consensus mathematical practice which has swelled Georg Cantor's Platonist interpretation of infinity whole. People always like to flatter themselves that they have a direct line to the deity. So this section is closest to my views.

https://en.wikipedia.org/wiki/Actual_in ... ist_school

[chasmanian]

thank you nFA.

I read all of your wiki links.

I am very grateful to you for taking the time and energy to post about this.

it is fascinating. partly so, because though I read as carefully as I could,
I don't know that I understood much about it at all.
I am just that dense.
thank you again.

Charlie

[notFritzArgelander]

Well, I wouldn't worry about "density".

If you like now that I've required a digital copy of the book I can post more or answer Qs as desired.

[Baurice]

I think one of the big conceptual barriers we need to break down is that Euclidean geometry applies to the universe. It may well do, IMO it doesn't but it is not necessarily so. I have often seen the distance between galaxies is like a balloon with dots representing galaxies being inflated. Every galaxy is moving away from each other. So it is possible that we are on the surface of an expanding sphere? No but we can be on a 3-dimensional surface of a 4-dimensional object or the n-dimensional surface of an n+1-dimesional object. This, IMO, tallies with observations that suggest that the CMB is coming at us from all directions, as if it was travelling around a sphere. It also suggests that the universe is bounded and not infinite, at last in spatial dimensions. It also does not require the universe to have an edge or centre.

However, the universe can be infinite in the time dimension. This assumes that all possible pasts, presents and futures exist but that at least some possible universes do not have an end. In a mooted "goldilocks" scenario, the expansion of the universe slows down but never quite reaches zero. Many astrophysicists (at least at one time) thought that was a likely scenario to several decimal places.

Getting even more complicated, we may even ask ourselves what we mean by "universe".

[notFritzArgelander]

@Baurice thanks for your response. I agree that on a fundamental level (here meaning the equations of GR and solving them) that Euclidean geometry is not a good starting point. However the CMB shows that the universe is (within observational error for the peace of mind of @WilliamPaolini just this once, in the future it is always implied) flat and Euclidean! The fluctuations in the CMB reveal whether the universe is positively closed and finite, flat and infinite, or negatively curved and infinite. The texture of the fluctuations differs among the three possible alternatives for curvature.

Looking at the measurement errors, there's even a slight bias, if anything, toward negatively curved and infinite. There is only a 1 in 3 chance that it is positively curved and finite.

BTW when I say universe, I usually refer only to the observable bit. Sometimes I also refer to the bit beyond the event horizon of observability that we infer as a result of the cosmological principle of homogeneity and isotropy. I try to be careful that it's at least clear from context.

Also BTW I think that the multiverses of string theorists are a failure of imagination or perhaps work.

[chasmanian]

thank you for your kindness nFA.
and your patience.

and thank you for all your excellent thoughts and writing.

is it not logical to think that both space and time are infinite?

if you are of a mind, and have time, would you explain simply the difference between actual and potential infinity?

and why do you take the position you take?

[notFritzArgelander]

thank you for your kindness nFA.
and your patience.

and thank you for all your excellent thoughts and writing.

is it not logical to think that both space and time are infinite?

if you are of a mind, and have time, would you explain simply the difference between actual and potential infinity?

and why do you take the position you take?

It logical to make any assumptions about space and time that you want to make, there is no harm in metaphysical speculation. When such ideas are testable, it is then scientific to test those assumptions against empirical data.

It's late, and I'm tired. So I'll address the rest briefly with the promise that if there are more questions I can deal with them later.

An actual infinity exists independently of the mind. Recall that most working mathematicians adhere to Platonic Realism: https://en.wikipedia.org/wiki/Platonic_realism

Platonic realism is the philosophical position that universals or abstract objects exist objectively and outside of human minds. It is named after the Greek philosopher Plato who applied realism to such universals, which he considered ideal forms.

This "actual Infinity" is thought of as completely independent of the mind. However there is also a Zero, a One, a Two, etc. all existing apart from any mind that thinks them. There is a problem though.... Where do such universal ideas exist? When one writes the simple formula "1+1=2" do the first and second "1" refer to the same Universal Idea of One? That One is no available for computation so then there is a whole hierarchy 1s or ones that are contingent upon the existence (somewhere?) of the Universal Idea of One.

Plato thought that the Universal Ideas such as Actual Infinity, Zero, One, Two,... existed outside space and time. So then what is the relationship to the marks I make on a paper doing a calculation? Some theologians adopted Plato's ideas modifying them by putting their existence in the Mind a Supreme Deity. Cantor's approach to set theory was motivated in part by his religious feelings.

I believe that Platonic Realism was refuted in the 14th century by William Ockham. In particular his Razor was directed against the Universal Ideas that exist "somewhere else".

https://en.wikipedia.org/wiki/Nominalism

I accept as Wm Ockham would, a potential infinity while rejecting Actual Infinity. I accept zero, one, two, etc. as concepts that exist only in the human mind that thinks them. The electron does not need an on board computer to obey the Schroedinger equation. Planets do not need Newton's laws in a database to orbit the Sun. All these mathematical objects exist in our minds only so that we can construct the Schroedinger equation and Newtonian metaphors for the data we observe.

A potential infinity refers to something that has no end. Take 0, add 1. Take 1 add 1, get 2. One never ends. That is a potential infinity.

That's all we need. We don't need Pi in the sky by and by.

I also have religious reasons why I feel Platonic realism is not a good move for any faith. I know it's attractive to many theologians, but it is best not to discuss those problems here as details would violate TOS.

[Baurice]

@Baurice thanks for your response. I agree that on a fundamental level (here meaning the equations of GR and solving them) that Euclidean geometry is not a good starting point. However the CMB shows that the universe is (within observational error for the peace of mind of @WilliamPaolini just this once, in the future it is always implied) flat and Euclidean! The fluctuations in the CMB reveal whether the universe is positively closed and finite, flat and infinite, or negatively curved and infinite. The texture of the fluctuations differs among the three possible alternatives for curvature.

Looking at the measurement errors, there's even a slight bias, if anything, toward negatively curved and infinite. There is only a 1 in 3 chance that it is positively curved and finite.

BTW when I say universe, I usually refer only to the observable bit. Sometimes I also refer to the bit beyond the event horizon of observability that we infer as a result of the cosmological principle of homogeneity and isotropy. I try to be careful that it's at least clear from context.

Also BTW I think that the multiverses of string theorists are a failure of imagination or perhaps work.

Thanks. I am inclined to think of a multiverse but do not believe the more imaginative idea of "many interacting worlds". I consider it likely that all possible universes past, present and future exist but it is not possible to travel between them. Many folks (usually not scientists) speculate about travelling through black holes into other universes but I always point out that they would not survive the journey.

Many theorists have pointed out that the conditions inside a black hole are similar to the early universe.

[chasmanian]

nFA,

thank you very much for your excellent fascinating explanation.

I agree with you.

"All these mathematical objects exist in our minds only so that we can construct the Schroedinger equation and Newtonian metaphors for the data we observe."

this makes sense to me.
I think Math is man made.
and exists in our minds.

thank you again for your superb reply.

and I am astonished at how little I know and how much there is to learn about Philosophy.
and how some of it (to me), seems like its written in an extremely difficult foreign language.

really, you are brilliant beyond description nFA.

Charlie

[notFritzArgelander]

You're welcome. But..... Aw, shucks. I don't think I'm brilliant. I do think I've been a very careful schoolboy for a half dozen decades.

[WilliamPaolini]

However the CMB shows that the universe is (within observational error for the peace of mind of @WilliamPaolini just this once, in the future it is always implied) flat and Euclidean! The fluctuations in the CMB reveal whether the universe is positively closed and finite, flat and infinite, or negatively curved and infinite.

*Phew*. Thank you! That sets my mind so at ease, the hubris of belief that "within observational error" estimates have never been found to be wrong And that flatness means must be infinite -- even though the likes of Joseph Silk, ESA, NASA would of course entirely disagree with you venturing off beyond the realm of observation At any rate, no need for you to worry about my peace of mind...it is quite at peace in the camp of reality instead of cosmological meanderings. But I must admit that the meanderings are always entertaining, even more so when re-read in the future

[notFritzArgelander]

However the CMB shows that the universe is (within observational error for the peace of mind of @WilliamPaolini just this once, in the future it is always implied) flat and Euclidean! The fluctuations in the CMB reveal whether the universe is positively closed and finite, flat and infinite, or negatively curved and infinite.

*Phew*. Thank you! That sets my mind so at ease, the hubris of belief that "within observational error" estimates have never been found to be wrong

A bit of straw man sophistry, mayhap?

I never said never, BTW, just hardly ever!

And that flatness means must be infinite -- even though the likes of Joseph Silk, ESA, NASA would of course entirely disagree with you venturing off beyond the realm of observation

Well I rather doubt that is true. I think Silk and I would agree. Since flatness implies infinite is given by simply solving the GR field equations for the FLRW metric as usual I'm quite certain Silk would have to agree with that it, since it only relies on GR being valid throughout. Anyway some grand old guys go off the deep end. I hope that isn't the case with Joe. Certainly Alfven went a bit dotty.

Anyway, Emmy Noether strikes again.

Specious appeal to a misunderstanding or misreporting of one's reading of an alleged authority is another sophistry, of course.

At any rate, no need for you to worry about my peace of mind...it is quite at peace in the camp of reality instead of cosmological meanderings. But I must admit that the meanderings are always entertaining, even more so when re-read in the future

You completely misunderstand the scientific process. Of course there will be revisions in the future. I do not share your superior and snarky attitude to well motivated revisions. That is irrelevant to discussions of what passes observational muster now. You always promise Pi in the sky by and by, if you offered it a la mode (i.e. respecting data and well supported theory) you might attain something interesting to say on these things. Your eyepiece reviews are nice an valuable. Your attempts to wrap scientific cow pies in puff pastry are somewhat less toothsome.

[chasmanian]

"It logical to make any assumptions about space and time that you want to make, there is no harm in metaphysical speculation. When such ideas are testable, it is then scientific to test those assumptions against empirical data."

nFA, I thought about this some more just now.

what you wrote is brilliant and very helpful.
and really amazing to think about.

the assumption that time is infinite is not testable.

the assumption that space is infinite, also not testable.

pre Big Bang (and perhaps even Big Bang) conditions and events, also not testable.

thank you again.
Charlie

[notFritzArgelander]

"It logical to make any assumptions about space and time that you want to make, there is no harm in metaphysical speculation. When such ideas are testable, it is then scientific to test those assumptions against empirical data."

nFA, I thought about this some more just now.

what you wrote is brilliant and very helpful.
and really amazing to think about.

the assumption that time is infinite is not testable.

the assumption that space is infinite, also not testable.

pre Big Bang (and perhaps even Big Bang) conditions and events, also not testable.

thank you again.
Charlie

What is testable is GR. Without a quantum gravity we have a well tested theory that is only testable back to a Planck time after a Big Bang or Big Crunch. Whether space NOW 13+ billion years after is infinite is testable assuming GR and the CMB observations. Given those assumptions and observations the odds are 2:1 that space is infinite. By reducing observational error one can get more definite about the test result.