substitutematerials

2 hours ago, Strange said:

As far as we know, the entire universe is full of matter just like the observable universe.

I assume it could also be uniformly filled but not repeating like your (d). 

 

So if it is infinite and uniformly filled, but not repeating (c), there is definitely a moon with invisible unicorns right?

To push this question back towards cosmology, can we ask what would fill a infinite universe? 

The possibilities I can think of are:

a.) we live within a finite section of an infinite volume which contains matter, which is surrounded by infinite emptiness.

b.) We live within one of a finite number of such finite sections in an infinite volume.

c.) the universe is homogenous and isotropic on an infinite scale, and all configurations of matter exist in it, including a bizarro Earth where invisible unicorns live on the moon

d.) the universe is homogenous and isotropic on an infinite scale, filled with an infinitely repeating pattern of precisely the same configurations of matter we observe in our observable universe

Is this list of possibilities exhaustive?

Alright, I'll take it. And your point that scientific theories are rarely abandoned completely is valid.

Note that examples like phlogiston where a theory is shown to be completely wrong, and is abandoned, are incredibly rare. I can only think of one other (the steady state universe).

 

It is far more common for a theory to be replaced by a more accurate one, but to continue to be used in some cases. The obvious example is Newtonian gravity, which was shown to be "wrong" by Einstein, but is still the standard theory of gravity used in most cases.

I can think of a host of abandoned theories that are prescientific or were only ever quasi-scientific, but it depends in part on where you draw the line for Science right? We've tossed out the four humors in medicine, geocentrism in astronomy, the four elements and alchemy in chemistry, phrenology in biology, homeopathy in medicine... But like you said, most of these were probably abandoned more due to contradictory evidence than internal contradiction.

Can we close by returning to this narrower question: In the case of a finite universe (bounded or unbounded), could we define the aggregate rate of spatial expansion by

[math]d*H_o[/math]

Imagine that we obtain a really fantastic measurement of curvature, and the universe is curved right at the threshold of what we can't observe right now- so implying a diameter of 14 trillion light years or 4292419 megaparsecs as per the article mentioned. Why couldn't I multiply that diameter by the present rate of spatial expansion, 72 km/s/megaparsecs, and state that the diameter of the universe is increasing by 309,054,168 km/s?

This rate might have no use whatsoever, but wouldn't it be logically implied, when we assume a scaling factor and finite diameter?

I can virtually guarantee you that there is a scientific theory, accepted presently, that will be shown to self-contradictory at some future point. If I knew which theory this was, I would not be lurking in science forums. Furthermore, mathematics and logic are the foundations of the physical sciences, so the things you can say about them necessarily also apply to science, although not necessarily the other way around. My example of Euclidean mathematics discovering internal contradictions most definitely has relevance to scientific models. A historical example from the physical sciences of self-contradiction could be Phlogiston theory, which ended up suggesting that phlogiston had both positive and negative mass- an internal contradiction that helped undo the theory.

 

 

But none of them relate to science. Not one.

 

Is there a scientific theory that is self-contradictory or paradoxical?

 

To save you wasting any more of our time, the answer is: no.

Why you gotta be like this Strange? If your time is being wasted, you are wasting it, not me. Your diligence in responding to these forums is appreciated, but you are not required to.

And on these points you are wrong. Thompson's lamp relates to the fact that there is a maximum speed that operations can occur in reality, as dictated by special relativity. And the painter's paradox illustrates that real objects made of matter are discrete and quantized. And come on dude, the quantization of light to resolve the ultraviolet catastrophe doesn't relate to science?

Your assurance that all scientific theories are obviously self-consistent is contradicted by Godel's second incompleteness theorem at least, isn't it?

Yes I saw the earlier comments Strange, and I agree with your analysis of BH singularities. If they actually exist, they are at best, a local edge.

The BB event ( notice I don't use singularity ) is different, as it is not localized but encompasses the whole universe, i.e. its global. It is an edge in time, before ( I hate using that word in this context )which there is no universe, as there is no geometry.

You cannot get around it, it is a hard edge.

I agree MigL, A beginning to time would be an edge. And the combination of the big bang and the second law of thermodynamics sure make it look like time has a beginning.

Hi substitutematerials

I think you meant inconceivable as in you find the concept of infinity inconceivable. I think you comprehend the concept just fine but you refuse to accept it. And that's OK as I don't think we have a lot of evidence either way.

 

I do think however that we have to accept at least one of two hard to accept concepts.

1) Something is infinitely old.

2) Something came from nothing.

Both are very hard for me to accept but I have to accept that at least one and possibly both are true.

 

One question for you.

If the universe is finite what lies on the other side?

Thanks Outrider,

The jury is definitely out on this very old question, I'm just sharing the things that have shaped my intuition.

I think your 2 additional concepts are equally vexing- something from nothing, or why did the universe start, might be truly unanswerable.

As for what lies on the other side of the universe, there are several ways of looking at this:

Firstly, there can be a boundary condition from any observer's perspective, which is easy to achieve in an expanding universe. No observer can get any closer to the receding edge by real travel, so there is no way to interact with such an edge. Like the event horizon of a black hole from the inside, a causal boundary.

The more popular solution which we've been discussing here is boundlessness, where travel in any direction will eventually return the observer to the place they started, like traveling on the surface of the Earth.

And my least favorite option which just kicks the can down the road, the boundary of our universe is other multiverses or a parent universe.

 

 

And maybe the universe is unlimited.

 

 

So all you have is an argument from incredulity.

That's not really fair Strange. I presented paradoxes as asked, as well as an important example of infinity disappearing from science history. Of course I'm not going to prove here that the universe is finite, I'm just telling you what informs my intuition. It is most definitely possible that the universe is unlimited, I'm just leaning in the other direction.

There are plenty of ways to resolve the grandfather paradox. Most notably, if everything that has happened is what happened. If your trip back in time is already part of history, then you clearly didn't kill your grandfather because you exist in order to go back in time and make the attempt.

 

See: the Novikov self-consistency principle

I read about this self-consistency principle a bit- it's interesting, although I'm not sure I understand the mechanism through which it is proposed to operate. I would say that our world is pretty fantastically chaotic, and that the idea of a whole live human being going back in time and not generating any paradox-inducing situation at all is a challenge. The grandfather paradox usually talks about killing your grandfather, but heck, all you'd have to do is add a one second delay to the day he and grandma conceived your parent, and you'd probably still prevent your existence because a different sperm would make it over the finish line. And culture is just as stochastic. The past is so elaborately determined that there would not be a lot of room to move around if something was preventing any paradoxical situation from occurring.

Sure thing.

Thomson's lamp:

A lamp is turned on or off when half the time left until midnight has elapsed. If the lamp can be toggled instantaneously, the switch will be toggled infinitely many times as midnight approaches, since we can always divide the remaining time in half. What state does the lamp end up in at midnight?

For the abstract instaneous lamp, there is no answer. Real lamps, however, have a minimum amount of time to flip the switch, which would render the answer simple.

Painter's paradox:

Take a mathematical object like Gabriel's horn, the rotation of y= 1/x around the x axis cut off at x=1. Calculus shows us that such an object encloses a finite volume but has an infinite surface area (isn't calculus neat). Can you paint the inside of Gabriel's horn with a finite amount of paint? On the one hand, obviously no, since the surface area is infinite. But if you completely fill the finite horn with paint, won't you also paint the entire surface?

Again the resolution is that paint is a real physical thing that is not infinitely sub-dividable, it's made of molecules with a size, and at some point the horn will be too thin for them to pass and part of the surface will remain unpainted. In truth anything real thing that horn could be made of would have the same restriction. Gabriel's horn is an abstraction.

The most important scientific removal of infinity that I know is the Ultraviolet Catastrophe. Unless we quantize the emission of light into photons, blackbody objects should emit an infinite amount of energy, which obviously they do not.

Infinity is a limit, not a number. There is no known instance of it in nature, so I would be surprised to have this one notable exception regarding spatial extent.

Previous scientific systems such as pythagorean mathematics were undone by self-contradiction- the premise that "all phenomena in the universe can be reduced to whole numbers and their ratios" was shown to lead to paradoxes.

We're also not being rigorous about what incomprehensible means in this thread and we should keep that word out of the conversation. Let's stick to discussing the self-contradictory or paradoxical, that's what I'm trying to talk about. And there is a pretty big list of paradoxes associated with the idea of infinity, suggesting it is not a physical concept but purely abstraction.

What about single timeline time travel is incomprehensible?

It leads to unresolvable paradoxes like the grandfather paradox. These paradoxes suggest that single timeline time travel isn't possible, because it leads to situations that don't make sense, i.e. are not comprehensible.

 

 

Are there any such things?

Single timeline time travel?

The most fundamental requirement of a scientific theory is that it be logically self-consistent, right? Internal paradox renders an idea fundamentally incomprehensible.

Ha yes! Comprehensible by who, that's the rub.

I also don't understand the maths of GR, but I trust that others out there do. This is different than something which everyone agrees is fundamentally incomprehensible.

We don't know that.

You're right, we don't know that reality itself isn't infinitely subdividable. But everything we do know about it points to quantization, that's particle physics. We know that if a spectrum of blackbody radiation were infinitely sub-dividable, it would contain infinite energy as per the ultraviolet catastrophe. Zeno's paradox also argues against infinite subdivision.

Reality isn't determined by whether we can comprehend it or not.

I think you are allowing a broad fallacy of 20th century science in your second point. I think it stymies critical thinking and the pursuit of new models if we accept an incomprehensible reality. "Making sense" is an important part of our tool box. If a scientific model isn't comprehensible, I assume it is provisional, no matter how well it generates results. "Shut up and calculate", as quantum physicists sometimes say, is a bad attitude.

Many laypeople have trouble imagining a finite universe; I'm a layperson who struggles more with an infinite one. It seems to me that infinity is purely a useful mathematical abstraction. Just as reality is not infinitely subdividable, i.e. it is quantized, I can't imagine it being infinite in extent. Especially if we adhere to the Copernican principle and assume we are in a representative section of the universe, an infinite universe seems absurd to comprehend. We couldn't do calculus without the abstraction of infinite subdivision, but there is math that requires the square root of -1 as well. These abstractions are useful but non-real.

 

 

I guess you can think of it like that. Two things though:

 

1. They have zero size so, in a sense, this edge doesn't exist.

 

2. There is no reason to think that singularities have any physical meaning (existence); they are the result of trying to use a theory where it no longer applies (like a "divide by zero" error).

Those are both good points Strange, especially the uncertainty about the physical existence of singularities.

Flat things can still be finite, though. For example, a 2-torus can be made flat (though not in 3-dimensional space).

Ah this is good guys thanks. I had thought that perfect flatness necessitated an infinite space, without realizing the the cylinder and 2 torus are geometries that are flat and finite.

Imagine that we obtain a really fantastic measurement of curvature, and it is curved right at the threshold of what we can't observe right now- so implying a diameter of 14 trillion light years or 4292419 megaparsecs as per the article mentioned. Why couldn't I multiply that diameter by the present rate of spatial expansion, 72 km/s/megaparsecs, and state that the diameter of the universe is increasing by 309,054,168 km/s?

I have to let some crankiness rip here though: the precise observations of apparent flatness make FLRW space look endangered to me. Sure, flatness is a possibility in FLRW space, but we have no explanation for how mass-energy should be so precisely balanced to achieve this. Include the acceleration of expansion, and you've got a universe made of 95% undetectable mystery sauce balanced on the head of a pin.

I'm also curious what you think of my suggestion in post #9, that a singularity is a spatial edge, akin to a needle punching a hole in a sheet.

 

 

As the universe is many times larger than the observable universe then it would never be possible to make any such measurement (the nearest you can do is measure things like the (local) curvature.

 

The rate of spatial expansion (which we can measure) has nothing to do with whether the universe is finite or infinite, bounded or unbounded.

I disagree Strange. The Earth is also larger than my tape measure, but Eratostene could measure its curvature and then infer the Earth's circumference. We should be able to calculate a circumference of a finite and unbounded universe if we know it's global curvature, provided it is not perfectly flat or open. Furthermore, this curvature should be becoming flatter over time, as the universe becomes larger.

Also back to my original conjecture: in both a bounded or unbounded finite universe, we have to be able to take a measurement of the total extent-like a simple radius or a higher dimensional circumference. And that measurement should be increasing in an expanding universe, and therefore an aggregate speed of spatial expansion should be definable in the case of a finite universe.

Since we are safely ensconced in the speculations forum, anybody got non-standard cosmologies that feature an edge?

Could you argue that any singularity is an edge? It seems to me that a horizon where both space and time end alleviates the problem of describing what lies beyond, since it is not possible to travel beyond it.

We are talking about 2 potential finite scenarios- finite and bounded versus finite and unbounded (Earth surface analogy) right? As I understand it, both are possible.

But both cases should be measurable though, or they don't qualify as finite. Distance to edge, or distance back to where you started from.

If space is finite, you can define a distance from yourself to the edge of the universe. If space is finite but expanding, this distance will grow larger over time.

Spatial expansion is a scaling factor, not a speed. But if space is finite, a speed can be defined at which the edge is receding.

Are these correct assumptions for a finite universe?

Here's an expansion of the shadow on the moon premise: Two moon bases are separated by a large distance. They both have laser death rays pointed at each other, but they also have force-fields they can turn on to protect against the death ray. There is no way to be warned that the other side has turned on their death ray, in order to turn on the force field in time, since the death ray will travel between them at the speed of light- as fast as any warning signal could. However, if the death ray is connected to a light sensitive switch, it could be triggered if it is shadowed by our hand puppet back on Earth. The nimble-handed puppeteer back on Earth could swoop the shadow first over one moon base and then to the other one, faster than light and so before the death ray has arrived, activating the force field through a similar switch. This situation is a ruse though- really the information originated at Earth and traveled to the 2 locations at luminal speeds.

Sounds right?

The pointing a hosepipe at the moon is analogous to the observation, made many years ago, that the writing speed of the beam of an oscilloscope can exceed the speed of light.

 

None of the electrons is faster than c, but the point where they hit the screen can do so.

So what? It's not a real thing?

Oh that's neat, never thought about that. In that instance though again, no information is passing from the first point on the screen to the second; the information originated at the cathode and traveled at the speed of the electrons. Just like with the 2 moon bases falling in the shadow cast by a hand puppet, no information about the state of one is conveyed to the other as the shadow or the beam passes between them.

Ok, so this entirely classical and the shadow therefore propagates down the cone of the spotlight with a delay due to light travel time. Thanks that was my question.

It seems pretty well agreed upon that shadows can 'travel' faster than speed of light, because a shadow is not a thing, and carries no information- it is simply the absence of light. One could pass a shadow puppet across the surface of the moon at faster than light speed by moving the puppet across the beam of a spotlight on Earth quickly enough. Like the rim of a bicycle wheel traveling faster than the hub, the angle subtended by the shadow is preserved.

My question is, does this require a quantum mechanical explanation? It seems to me that it does: the hand puppet isn't objectively blocking the waveform of the photons moving towards the moon, only affecting the probability that they will arrive at a particular spot. So as we see the shadow disappear in a spot, it is really illuminated by photons that were already there. Otherwise it seems to me that the progress of the shadow's path across the surface will be limited by the time it takes the photons to reach the moon. I.e. the shadow should move with a delay. Make sense?

The hazy glimpse I am getting of this theory reminds me an idea Peter Huber put forth, that day/night thermal cycling was the initial power source for biological self-replication, akin to the the thermal cycling of PCR machines. In PCR a hot stage unzips DNA into 2 halves, and a cold stage allows the 2 halves to reconstitute 2 new full strands in the presence of the right chemical building blocks. Repeat, and you can endlessly multiply the DNA. This is a metabolic theory more than an evolutionary one though I think.

Some of the OPs other details, about when lunar days and solar days aligned, sound pretty numerological to me at first blush.

 

How will a brain form out of empty space? Just like magic it appears?

 

I believe the OP is referring to the Boltzmann Brain hypothesis. Sean Carroll describes it well here, although he takes a while to get to the point. The basic gist of it is this: Why did our universe begin with such low entropy? A tempting answer is that our universe is only a tiny patch of a much larger multliverse which is at maximum entropy, and all the order we see is the result of a highly improbable random fluctuation. However if we accept this idea, we must acknowledge that in this larger arena, it is much more likely for a entirely formed and functional brain to pop into existence than for our entire ordered universe to come about, since the single brain doesn't require nearly as low an entropy fluctuation. So the vast majority of consciousnesses are likely to be not the product of natural selection in ordered environments, but disembodied brain that pop into existence only long enough to contemplate their existence and then vanish.

This idea is hilarious and alarming and seems to disprove something, although I'm not sure what exactly.