A finite universe

[Strange]

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.

 

 

Comprehensible to who, though?

 

As you say, many people cannot comprehend a finite universe. Therefore (by your logic) reality must be infinite.

But you cannot comprehend an infinite universe. Therefore (by your logic) reality must be finite.

Some people can comprehend both. Therefore (by your logic) reality must be both finite and infinite.

 

I can't understand the maths of GR. Therefore (by your logic) it must be wrong.

 

I'm sorry but being comprehensible or "making sense" is a completely useless (being polite) basis for deciding whether a theory is useful or not.

[substitutematerials]

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.

[Strange]

This is different than something which everyone agrees is fundamentally incomprehensible.

 

 

Are there any such things?

[substitutematerials]

 

 

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.

[Strange]

Single timeline time travel?

 

Are there any theories that include that?

 

 

 

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

 

Are there any scientific theories that are self contradictory?

Edited February 17, 2017 by Strange

[Delta1212]

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.

What about single timeline time travel is incomprehensible?

[substitutematerials]

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.

[Strange]

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.

 

 

1. That is paradoxical not incomprehensible.

 

2. Is that part of any scientific theory? If not, it is irrelevant.

 

So, again, are there any scientific theories that are self contradictory?

 

There are plenty of theories that are incomprehensible to those without the right background. Are there any that are incomprehensible to everyone?

[substitutematerials]

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.

[Strange]

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.

 

 

Enough with the vague assertions.

 

Please provide one or two examples of these paradoxes, and how they impact on physical theories.

[substitutematerials]

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.

[Strange]

So there are no contradictions (due to infinity or otherwise) in scientific theories. Good, glad we have cleared that up.

[Delta1212]

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.

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

[Strange]

Infinity is a limit, not a number.

 

 

And maybe the universe is unlimited.

 

 

 

There is no known instance of it in nature, so I would be surprised to have this one notable exception regarding spatial extent.

 

So all you have is an argument from incredulity.

[Outrider]

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?

[The Almighty]

2-D sphere? Explain that please

[substitutematerials]

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.

[Strange]

That's not really fair Strange. I presented paradoxes as asked,

 

 

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.

[Outrider]

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.

 

For me this too is kicking the can down the road. Whether or not we can get to the boundary much less outside of it. It still exists ergo there must be something on the other side and if it's nothing then it must be an infinity of nothing.

 

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.

But what is this boundless yet finite space contained in? Again we have kicked the can down the road.

 

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.

This is just my opinion and I can't really prove it but I am convinced there is no way around infinity.

The only other option in my mind is for time and space to have spontaneously started from a complete nothingness.

 

BTW I just gave the nothing a name so now it is something.

[MigL]

The universe, or rather space-time, does have an 'edge'.

It is 13.7 billion yrs ago that the BB created 'geometry'.

 

Everyone is fine with the notion that we can't know what happened 'before' ( can't really use that word, but have no substitute ) the BB, so why do we have to know what's on the other side of a spatial 'edge' ?

( not that I believe there could be an 'edge', since that would complicate things immeasurably, and I am a firm believer in Occam's razor )

 

And no, a finite but unbounded universe doesn't need to be contained in anything , or embedded in a higher dimension. Look up intrinsic vs. extrinsic curvature

[Strange]

The universe, or rather space-time, does have an 'edge'.

It is 13.7 billion yrs ago that the BB created 'geometry'.

 

 

This was suggested earlier (but including the singularities in black holes as well). My reply (post 18) still applies:

 

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

1. The singularity has zero size so, in a sense, this edge doesn't physically 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).

The big bang model of cosmology does not go back to a "time 0" and does not include any sort of creation event. The earliest time the model can describe is a universe in a hot, dense state.

[Delta1212]

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.

 

 

 

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.

 

 

 

 

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.

My own thoughts on the matter are as follows: Whatever you will do in the past is part of what already happened. If you travel back in time, you cannot change what happened because whatever happened already included you doing whatever it is you are going to do.

 

This feels paradoxical because we are used to thinking of the past as something known and unchanging and the future as something unknown with endless open possibilities, and time travel mixes up the two by making your future the past. The general conclusion then is that it opens the past up to endless possibilities, because we would rather assume that the past is changeable than that our future is locked into a single possible outcome, but you can just as easily draw the opposite conclusion to resolve this conflict at which point many time travel paradoxes, including the grandfather paradox, disappear.

 

The remaining paradoxes, like the Bootstrap paradox, that are still possible lend themselves to stable time loops and so aren't actually problems for single timeline time travel.

[MigL]

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.

[Strange]

Someone else used the analogy of a pole to illustrate how "before" has no meaning in this context: What is north of the North Pole?

 

It is not that the answer is "nothing" or even that there is no answer, the question itself doesn't make sense.

 

On the other hand, the north pole exists and the big bang singularity almost certainly doesn't. We just don't know why not, yet.

[substitutematerials]

 

 

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.