If you have an idea for a blog post or a new forum thread, then please contact us at forums@fqxi.org, with a summary of the topic and its source (e.g., an academic paper, conference talk, external blog post or news item).

Forum Home

Introduction

Terms of Use

RSS feed | RSS help

Introduction

Terms of Use

*Posts by the blogger are highlighted in orange; posts by FQXi Members are highlighted in blue.*

RSS feed | RSS help

RECENT POSTS IN THIS TOPIC

**James Putnam**: *on* 2/1/14 at 21:48pm UTC, wrote "The aficionados of infinity include Alan Guth, who argued in Puerto Rico...

**John Duffield**: *on* 1/31/14 at 17:38pm UTC, wrote Tom, I "root" for relativity. I think it's the Cinderella of contemporary...

**Ken Seto**: *on* 1/29/14 at 14:01pm UTC, wrote I invite everyone to read my paper on the origin of the universe in the...

**John Cox**: *on* 1/28/14 at 22:11pm UTC, wrote Sydney, Thanks for your views, I like to see what different perspectives...

**Sydney Grimm**: *on* 1/28/14 at 21:22pm UTC, wrote John, If I am right: first you put forwards the lack of a good...

**John Merryman**: *on* 1/28/14 at 19:49pm UTC, wrote Tom, "After that, though, some of us learned that time is illusion and...

**John Merryman**: *on* 1/28/14 at 19:46pm UTC, wrote Tom, What's this about 'quantify?' The system you insist is the word of...

**Akinbo Ojo**: *on* 1/28/14 at 18:54pm UTC, wrote Yes Tom, "If the system is closed...". That is the most difficult problem...

RECENT FORUM POSTS

**Georgina Parry**: "Hi Lorraine, yes the Daniel Amen talk is really good. Most amazing is the..."
*in* Your Invitation to FQXi's...

**John Cox**: "Tom, Okay, Minkowski sets his working limits and qualifies them such that..."
*in* Melting Spacetime

**John Merryman**: "Steve, I don't know that it has to be entirely due to usefulness. Lots of..."
*in* Why Quantum?

**John Merryman**: "Peter, Further up this thread, Aug. 25, 2014 @ 17:38 GMT, I posted a..."
*in* Why Quantum?

**Lorraine Ford**: "Georgina, The TED talk was interesting: Daniel Amen made a good case for..."
*in* Your Invitation to FQXi's...

**Akinbo Ojo**: "Vladimir, I am getting paranoid from what's in the news lately. Is World..."
*in* How Should Humanity Steer...

**Thomas Ray**: ""*You won't believe anything I say.*. I really, really wish I could,..."
*in* Melting Spacetime

**Thomas Ray**: "By the way, I think there is some significant relation between the..."
*in* Quantum theory escapes...

RECENT ARTICLES

*click titles to read articles*

**Quantifying Occam**

Is the simplest answer always the best? Connecting Medieval monks to computational complexity, using the branch of mathematics known as category theory.

**Heart of Darkness**

An intrepid physicist attempts to climb into the core of black hole.

**Why Quantum?**

Entropy could explain why nature chose to play by quantum rules.

**Reality's NeverEnding Story**

A quantum version of Darwinian natural selection could enable the universe to write itself into being.

**The Quantum Dictionary**

Mark Van Raamsdonk is re-writing how we define the shape of our universe. Can such translations help to unite quantum theory and gravity?

RECENT FORUM POSTS

RECENT ARTICLES

Is the simplest answer always the best? Connecting Medieval monks to computational complexity, using the branch of mathematics known as category theory.

An intrepid physicist attempts to climb into the core of black hole.

Entropy could explain why nature chose to play by quantum rules.

A quantum version of Darwinian natural selection could enable the universe to write itself into being.

Mark Van Raamsdonk is re-writing how we define the shape of our universe. Can such translations help to unite quantum theory and gravity?

FQXi BLOGS

August 30, 2014

CATEGORY:
Blog
[back]

TOPIC: Might the Infinity of the Universe Have a Tangible Effect on Daily Life? [refresh]

TOPIC: Might the Infinity of the Universe Have a Tangible Effect on Daily Life? [refresh]

“There is a difference between whether the universe is infinite or just really really really really really really big,” Anthony Aguirre said at the recent FQXi conference in Puerto Rico. I’m pretty sure I counted six reallys. With that remark, he encapsulated a major debate going on within physics and cosmology right now. Although the conference theme was officially the physics of information, it could just as well have been the physics of infinity, so often did that little sideways ‘8’ put in an appearance. Is the universe finite or infinite? Is nature capable of a finite or infinite number of possible states? Can spacetime be infinitely subdivided or is it made of finite-size cells? The questions seem undecidable. But maybe the finitude or infinitude makes itself felt every time you do a measurement and every time you stir cream into a coffee cup and can’t unstir it out.

The forces of finitude include Max Tegmark, who has been bad-mouthing infinity on Edge.org, in quotes to*New Scientist*, and in Chapter 11 of his new book. His complaint is what cosmologists call the measure problem: there’s no way of unambiguously counting members of an infinite set. If there’s no way to count, there’s no way to calculate probabilities and therefore no way to relate theory to experiment. The whole empirical framework of science verges on collapse. A finite universe presents no such difficulty. Even Peter Woit, who agrees with Tegmark on little else, finds common ground with him on the measure problem.

The aficionados of infinity include Alan Guth, who argued in Puerto Rico and on Edge.org that a truly infinite universe would neatly explain the arrow of time. When space has no bound, neither does entropy. It keeps on increasing forever, always pointing the way forward for time. The universe need not have begun in a contrived initial state to create the impetus toward increasing disorder.

When two opposing positions can both muster plausible arguments, what you have is less a debate and more a dilemma. If it were up to them, physicists would surely prefer finitude, yet nature seems to have made different plans. The universe is expanding at an accelerating rate and, if it keeps doing so, it is destined to spawn an infinity of baby universes. “It would be cozy if it were finite, but it doesn’t seem to be,” Aguirre told me. “Eternal inflation gives you an infinite universe, and something like eternal inflation is happening now and probably happened in the past. Nature is rubbing infinity in our face.”

Eternal inflation could cease to be eternal if the dark energy that drives it withered away on a timescale of billions of years. But if dark energy were so unstable, Aguirre has argued, we should see signs of its decay somewhere out there. All indications are that time will never end, which means that space probably doesn’t, either.

The brain-melting Boltzmann-brain paradox is one reason that infinite space and infinite time go together. If time were infinite yet space finite, the contents of the universe would cycle through their possible configurations over and over and over again. Molecules would occasionally converge to produce a conscious mind that lasted for a split second, but was under the misimpression it was the product of billions of years of cosmic evolution. Indeed, in the vastness of eternity, such flashes of deluded awareness would vastly outnumber brains that had formed the old-fashioned way, and we’d have to conclude that our observations are implanted memories, like fossils that young-Earth creationists think God planted in rock strata to fool us. It’s a paradox because an empirical science would lead us to the conclusion that empirical science is a sham.

This sort of argument is what Aguirre had in mind as a genuine distinction between a truly infinite universe and a merely ginormous one. “If it’s finite, no matter how big you make it, it still eventually runs into the paradox,” he said. Chance fluctuations that are inevitable in finite space are vanishingly unlikely in infinite space. An infinite universe is ever-changing, never doing the same thing twice, as Sean Carroll eloquently described in his prize-winning essay for the first FQXi essay contest.

The arrow-of-time argument that Guth has been developing also has the potential of distinguishing infinite from finite. The basic idea goes back to a provocative paper a decade ago by Carroll and Jennifer Chen (who has since left physics research to work on energy regulation). Whereas their scenario involved an accelerating universe, Guth gave a supersimple example involving a gas in an infinite void. At some moment you can take as*t*=0, the gas occupies some minimum volume. From then on, the gas will expand without limit. If the void is finite, the gas will eventually cycle back to its starting point. Time has a clear forward progression only if the void is truly infinite.

The overall history of Guth’s minimalist universe is fully time-symmetric, as the laws of physics demand. Prior to*t*=0, the gas was also expanding without limit, albeit backwards in time, and again time has a clear forward progression, the reverse of the arrow on the other side. Only around *t*=0 does the arrow become ambiguous. If any mortal beings are alive for the crossover, they’ll observe curious reversals of fortune such as those that Ken Wharton, who writes science fiction when not doing physics, once imagined in a poignant short story.

Guth’s scenario is classical, but similar intimations of infinity arise in quantum physics. Yasunori Nomura has argued that an infinite range of possible states (that is, an infinite Hilbert space) would make the process of quantum decoherence irreversible, explaining the arrow of time in quantum measurement.

In a funny way, then, the arrow of time we observe in daily life may reflect the infinity of space, and human mortality may hinge on the immortality of the universe. But still. Infinity? Can it be a real thing rather than simply our idealization?

Aguirre, for all his advocacy of infinity, is unconvinced by Guth’s and Carroll and Chen’s arrow-of-time arguments. “They’re brushing certain things under the rug,” he said. For instance, they take for granted that, if the maximum possible entropy is infinite, it doesn’t matter how the universe began. Any possible initial state has finite entropy, so you get the arrow of time for free. But you can’t take anything for granted when it comes to infinity. Guth and the others implicitly rule out initial states with infinite entropy. Is that really justified? Such a state is hard to imagine, but that doesn’t mean it can’t exist, Aguirre said. His musings remind me of one of the strangest concepts in mathematics: the axiom of choice. This is a rule for selecting objects from an infinite collection even when all standard rules fail. The weird thing is that, although mathematicians know that such a rule exists, they don’t know what the rule is. Worse, they know they’ll*never* know what it is. A state of infinite entropy may likewise exist even if it is impossible to specify.

Other speakers in Puerto Rico proposed ways to evade the paradoxes that imply infinity. Carroll himself argued that Boltzmann brains go away when you take care to distinguish quantum from thermal fluctuations. Andy Albrecht contended that the measure problem evaporates when you think of all probabilities as inherently quantum. Even a tossed coin, he said, ultimately lands on one side or the other because of quantum indeterminism. If so, probabilities aren’t defined in terms of repeated trials, and the inability to count elements of an infinite set is a red herring.

At this rate, physicists may not have to wonder about infinity. Their discussions may go on long enough to prove the point one way or the other.

this post has been edited by the author since its original submission

report post as inappropriate

The forces of finitude include Max Tegmark, who has been bad-mouthing infinity on Edge.org, in quotes to

The aficionados of infinity include Alan Guth, who argued in Puerto Rico and on Edge.org that a truly infinite universe would neatly explain the arrow of time. When space has no bound, neither does entropy. It keeps on increasing forever, always pointing the way forward for time. The universe need not have begun in a contrived initial state to create the impetus toward increasing disorder.

When two opposing positions can both muster plausible arguments, what you have is less a debate and more a dilemma. If it were up to them, physicists would surely prefer finitude, yet nature seems to have made different plans. The universe is expanding at an accelerating rate and, if it keeps doing so, it is destined to spawn an infinity of baby universes. “It would be cozy if it were finite, but it doesn’t seem to be,” Aguirre told me. “Eternal inflation gives you an infinite universe, and something like eternal inflation is happening now and probably happened in the past. Nature is rubbing infinity in our face.”

Eternal inflation could cease to be eternal if the dark energy that drives it withered away on a timescale of billions of years. But if dark energy were so unstable, Aguirre has argued, we should see signs of its decay somewhere out there. All indications are that time will never end, which means that space probably doesn’t, either.

The brain-melting Boltzmann-brain paradox is one reason that infinite space and infinite time go together. If time were infinite yet space finite, the contents of the universe would cycle through their possible configurations over and over and over again. Molecules would occasionally converge to produce a conscious mind that lasted for a split second, but was under the misimpression it was the product of billions of years of cosmic evolution. Indeed, in the vastness of eternity, such flashes of deluded awareness would vastly outnumber brains that had formed the old-fashioned way, and we’d have to conclude that our observations are implanted memories, like fossils that young-Earth creationists think God planted in rock strata to fool us. It’s a paradox because an empirical science would lead us to the conclusion that empirical science is a sham.

This sort of argument is what Aguirre had in mind as a genuine distinction between a truly infinite universe and a merely ginormous one. “If it’s finite, no matter how big you make it, it still eventually runs into the paradox,” he said. Chance fluctuations that are inevitable in finite space are vanishingly unlikely in infinite space. An infinite universe is ever-changing, never doing the same thing twice, as Sean Carroll eloquently described in his prize-winning essay for the first FQXi essay contest.

The arrow-of-time argument that Guth has been developing also has the potential of distinguishing infinite from finite. The basic idea goes back to a provocative paper a decade ago by Carroll and Jennifer Chen (who has since left physics research to work on energy regulation). Whereas their scenario involved an accelerating universe, Guth gave a supersimple example involving a gas in an infinite void. At some moment you can take as

The overall history of Guth’s minimalist universe is fully time-symmetric, as the laws of physics demand. Prior to

Guth’s scenario is classical, but similar intimations of infinity arise in quantum physics. Yasunori Nomura has argued that an infinite range of possible states (that is, an infinite Hilbert space) would make the process of quantum decoherence irreversible, explaining the arrow of time in quantum measurement.

In a funny way, then, the arrow of time we observe in daily life may reflect the infinity of space, and human mortality may hinge on the immortality of the universe. But still. Infinity? Can it be a real thing rather than simply our idealization?

Aguirre, for all his advocacy of infinity, is unconvinced by Guth’s and Carroll and Chen’s arrow-of-time arguments. “They’re brushing certain things under the rug,” he said. For instance, they take for granted that, if the maximum possible entropy is infinite, it doesn’t matter how the universe began. Any possible initial state has finite entropy, so you get the arrow of time for free. But you can’t take anything for granted when it comes to infinity. Guth and the others implicitly rule out initial states with infinite entropy. Is that really justified? Such a state is hard to imagine, but that doesn’t mean it can’t exist, Aguirre said. His musings remind me of one of the strangest concepts in mathematics: the axiom of choice. This is a rule for selecting objects from an infinite collection even when all standard rules fail. The weird thing is that, although mathematicians know that such a rule exists, they don’t know what the rule is. Worse, they know they’ll

Other speakers in Puerto Rico proposed ways to evade the paradoxes that imply infinity. Carroll himself argued that Boltzmann brains go away when you take care to distinguish quantum from thermal fluctuations. Andy Albrecht contended that the measure problem evaporates when you think of all probabilities as inherently quantum. Even a tossed coin, he said, ultimately lands on one side or the other because of quantum indeterminism. If so, probabilities aren’t defined in terms of repeated trials, and the inability to count elements of an infinite set is a red herring.

At this rate, physicists may not have to wonder about infinity. Their discussions may go on long enough to prove the point one way or the other.

this post has been edited by the author since its original submission

report post as inappropriate

" ... there's no way of unambiguously counting members of an infinite set."

My seven year old granddaughter told her mother recently, "Mom, if numbers just go on forever and ever, without stopping, then all numbers are small numbers."

Exactly right. Which is why Leibniz wrote that deep understanding of nature has to be based in the infinitely small. Modern day followers of Leibniz -- Hermann Weyl and Gregory Chaitin among others -- recognize this continuity of form in constructed objects, the continuum in Weyl's purely mathematical terms, the Omega number in Chaitin's mathematical-computational terms.

This is only one more reason why I simply cannot understand why Joy Christian has gotten such a harsh reception, highly undeserved and irrational IMO. His construction which depends on topological non-vanishing torsion is not only one more expression of the infinitely small, it prescribes the exact physical boundary.

" ... there's no way to calculate probabilities and therefore no way to relate theory to experiment."

There's no probability measure in Christian's framework. Like Einstein's mathematically complete theories, it makes a closed logical judgement on the correspondence between mathematical construction and physical result.

Tom

report post as inappropriate

My seven year old granddaughter told her mother recently, "Mom, if numbers just go on forever and ever, without stopping, then all numbers are small numbers."

Exactly right. Which is why Leibniz wrote that deep understanding of nature has to be based in the infinitely small. Modern day followers of Leibniz -- Hermann Weyl and Gregory Chaitin among others -- recognize this continuity of form in constructed objects, the continuum in Weyl's purely mathematical terms, the Omega number in Chaitin's mathematical-computational terms.

This is only one more reason why I simply cannot understand why Joy Christian has gotten such a harsh reception, highly undeserved and irrational IMO. His construction which depends on topological non-vanishing torsion is not only one more expression of the infinitely small, it prescribes the exact physical boundary.

" ... there's no way to calculate probabilities and therefore no way to relate theory to experiment."

There's no probability measure in Christian's framework. Like Einstein's mathematically complete theories, it makes a closed logical judgement on the correspondence between mathematical construction and physical result.

Tom

report post as inappropriate

Tom,

The question of finite or infinite universe is not a new one. Cosmologists of today would do better if they studied a bit of history of their own subject. See, for example, "From the Closed World to the Infinite Universe", by Alexandre Koyre.

The sociology of the physics community of today, on the other hand, is a largely new phenomenon. The harsh treatment of my work that you puzzle about can be traced back to the reaction of a tiny number of uninformed postdocs back in 2007 while I was based at the Perimeter Institute. That set a negative tone on my work from which it has yet to recover. The mounting evidence accumulated in its favour has mattered little. That is sociology of science for you. What is accepted and what is rejected in science depends largely on who has a louder voice and a greater political muscle.

Incidentally, Giordano Bruno, whose views on the "plurality of the worlds" are discussed in Koyre's book, did not fair well back in 1600 for his unconventional views either.

Joy

this post has been edited by the author since its original submission

report post as inappropriate

The question of finite or infinite universe is not a new one. Cosmologists of today would do better if they studied a bit of history of their own subject. See, for example, "From the Closed World to the Infinite Universe", by Alexandre Koyre.

The sociology of the physics community of today, on the other hand, is a largely new phenomenon. The harsh treatment of my work that you puzzle about can be traced back to the reaction of a tiny number of uninformed postdocs back in 2007 while I was based at the Perimeter Institute. That set a negative tone on my work from which it has yet to recover. The mounting evidence accumulated in its favour has mattered little. That is sociology of science for you. What is accepted and what is rejected in science depends largely on who has a louder voice and a greater political muscle.

Incidentally, Giordano Bruno, whose views on the "plurality of the worlds" are discussed in Koyre's book, did not fair well back in 1600 for his unconventional views either.

Joy

this post has been edited by the author since its original submission

report post as inappropriate

"What is accepted and what is rejected in science depends largely on who has a louder voice and a greater political muscle."

Peter Hayes "The Ideology of Relativity: The Case of the Clock Paradox" : Social Epistemology, Volume 23, Issue 1 January 2009, pages 57-78: "The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse."

Pentcho Valev

report post as inappropriate

Peter Hayes "The Ideology of Relativity: The Case of the Clock Paradox" : Social Epistemology, Volume 23, Issue 1 January 2009, pages 57-78: "The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse."

Pentcho Valev

report post as inappropriate

Do not conflate Joy's well constructed framework with your erroneous belief that relativity has "elementary inconsistencies." It doesn't.

Were Joy's work not fully relativistic, in fact, I wouldn't support it.

report post as inappropriate

Were Joy's work not fully relativistic, in fact, I wouldn't support it.

report post as inappropriate

I obtained, many years ago, studying the convergence of a statistical ensemble that follows the gradient back propagation, a system that have an infinite negative entropy; a system that converge to a single state, like a Dirac delta function, have an infinite negative entropy.

If the initial state of the Universe is near a Dirac delta function, then the entropy grow ever: a fluctuation of great complexity, that contain all the story of the Universe, can it possible (we see it); the initial state contain our current consciousness, so that the Boltzmann-brain and this initial fluctuation are equivalent.

report post as inappropriate

If the initial state of the Universe is near a Dirac delta function, then the entropy grow ever: a fluctuation of great complexity, that contain all the story of the Universe, can it possible (we see it); the initial state contain our current consciousness, so that the Boltzmann-brain and this initial fluctuation are equivalent.

report post as inappropriate

I think Max is onto a winner with challenging infinity. Tori aside*, I'm somewhat surprised at the non-sequitur wherein a "flat" universe is assumed to be infinite. Or a nearly-flat universe is assumed to be very large. I think it's a failure of imagination myself, because I've read a lot of the original Einstein material including his Leyden Address, and it's clear that he considered space to be a something rather than a nothing. Take a look at the stress-energy-momentum tensor and there's shear stress and pressure. One can liken space to some kind of gin-clear ghostly elastic. Waves run through it. It expands. The raisin-in-the-cake analogy is like a stress ball when you open your fist. And yet we continue to see the balloon analogy where we've dropped a dimension because we cannot conceive that space might have an edge. Like a droplet of water has an edge, wherein waves suffer total internal reflection. There is no water beyond that edge. There is no space beyond the edge of space.

Since Max's essay was an Edge essay, please can we see some discussion about the edge of the universe?

* http://arxiv.org/abs/1303.5086

report post as inappropriate

Since Max's essay was an Edge essay, please can we see some discussion about the edge of the universe?

* http://arxiv.org/abs/1303.5086

report post as inappropriate

" ... the original Einstein material including his Leyden Address, and it's clear that he considered space to be a something ..."

Space-time.

report post as inappropriate

Space-time.

report post as inappropriate

I meant space. Here's what Einstein said:

*"...This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials guv), has, I think, finally disposed of the view that space is physically empty..."*

I think it's worth explaining the distinction. We talk of curved spacetime in the context of gravitational field, but space isn't curved in the room you're in. It's inhomogeneous. Imagine you've placed an array of light-clocks in an equatorial slice through and around the Earth. When you plot all the clock rates, your plot resembles the "rubber-sheet" depiction you can see on the wiki Riemann curvature tensor article. You*measured* those clock rates, there's a curvature in your *metric*. But this "curved spacetime" isn't curved space. It's a curvature in your plot of the inhomogeneity of space. Your lower clocks don't tick slower because your plot of clock rates is curved. They tick slower because the space down here isn't the same as the space up there, because a concentration of energy tied up as the matter of the Earth "conditions" the surrounding space, the effect diminishing with distance.

report post as inappropriate

I think it's worth explaining the distinction. We talk of curved spacetime in the context of gravitational field, but space isn't curved in the room you're in. It's inhomogeneous. Imagine you've placed an array of light-clocks in an equatorial slice through and around the Earth. When you plot all the clock rates, your plot resembles the "rubber-sheet" depiction you can see on the wiki Riemann curvature tensor article. You

report post as inappropriate

John Duffield,

Can you provide us a link to the Einstein quote? You must be aware that it is claimed that Einstein is the proponent of a relational space which is nothing, in disagreement with the substantivalist view that space is something.

Akinbo

report post as inappropriate

Can you provide us a link to the Einstein quote? You must be aware that it is claimed that Einstein is the proponent of a relational space which is nothing, in disagreement with the substantivalist view that space is something.

Akinbo

report post as inappropriate

Is there at all "a tangible effect on daily life"? To me, the blogger did not give an acceptable answer.

He asked "Infinity? Can it be a real thing rather than simply our idealization?"

To me infinity is simply an ideal logical concept, the property to be endless, which was formulated by Archimedes: There is no largest natural number. Cantor's naive set theory and its replacement by ZF intended to overcome this unwelcome property. In ZF, infinity is formulated as just one axiom among seven others including AC that were fabricated in order to castrate it for the sake of an illusive paradise.

If the notion infinity has a tangible influence then in so far as it's frequent mistreatment in set theory damaged the honest strive for consistency in science.

Leibniz who also introduced a not strictly endless relative (potential) infinity which is arbitrarily large or arbitrarily small (infinitesimal) understood what Cantor called the infinitum absolutum, as a fiction with a fundamentum in re.

Hence, outside established inconsistency there are logically consistent meanings of both Archimede's potential infinity and the fictitious limit alias infinitum absolutum which I often used in EE.

This is my answer to the blogger's question whether infinity can be a real thing rather than simply our idealization: Isn't our notion of reality an idealizing tool? We may not expect an answer, neither from current nor from a fundamentally corrected mathematics. Guth's speculation on t=0 will certainly not be useful in daily life.

Eckard

has any further tangible effect on daily life.

report post as inappropriate

He asked "Infinity? Can it be a real thing rather than simply our idealization?"

To me infinity is simply an ideal logical concept, the property to be endless, which was formulated by Archimedes: There is no largest natural number. Cantor's naive set theory and its replacement by ZF intended to overcome this unwelcome property. In ZF, infinity is formulated as just one axiom among seven others including AC that were fabricated in order to castrate it for the sake of an illusive paradise.

If the notion infinity has a tangible influence then in so far as it's frequent mistreatment in set theory damaged the honest strive for consistency in science.

Leibniz who also introduced a not strictly endless relative (potential) infinity which is arbitrarily large or arbitrarily small (infinitesimal) understood what Cantor called the infinitum absolutum, as a fiction with a fundamentum in re.

Hence, outside established inconsistency there are logically consistent meanings of both Archimede's potential infinity and the fictitious limit alias infinitum absolutum which I often used in EE.

This is my answer to the blogger's question whether infinity can be a real thing rather than simply our idealization: Isn't our notion of reality an idealizing tool? We may not expect an answer, neither from current nor from a fundamentally corrected mathematics. Guth's speculation on t=0 will certainly not be useful in daily life.

Eckard

has any further tangible effect on daily life.

report post as inappropriate

Might the Infinity of the Universe Have a Tangible Effect on Daily Life?

I will answer Yes. But before some of these things can be discerned, there is a need to look at Clausius description of entropy, mathematically written as

dS = dE/T,

where S is entropy, E is energy and T is the absolute temperature, d stands for differential or change in value.

Taking all the other laws of thermodynamics as correct, what is the cosmological significance of this equation if the universe obeys it?

It is clear that the only way to obtain infinite entropy from this equation is for T to equal zero at the moment of energy change, dE. If the universe began from 'nothing' rather than a 'hot thing' what was the initial temperature at time zero? If the universe began from nothing, what was its initial entropy at time zero? Does the third law not say, when T = 0, S = 0 and vice-versa? What does energy change, dE mean? Can an isolated system change in energy without breaking a thermodynamic law? Can energy have a positive and a negative aspect so that the sum of the two in a conserved system still equals zero thereby preserving the thermodynamic law? More later...

Akinbo

report post as inappropriate

I will answer Yes. But before some of these things can be discerned, there is a need to look at Clausius description of entropy, mathematically written as

dS = dE/T,

where S is entropy, E is energy and T is the absolute temperature, d stands for differential or change in value.

Taking all the other laws of thermodynamics as correct, what is the cosmological significance of this equation if the universe obeys it?

It is clear that the only way to obtain infinite entropy from this equation is for T to equal zero at the moment of energy change, dE. If the universe began from 'nothing' rather than a 'hot thing' what was the initial temperature at time zero? If the universe began from nothing, what was its initial entropy at time zero? Does the third law not say, when T = 0, S = 0 and vice-versa? What does energy change, dE mean? Can an isolated system change in energy without breaking a thermodynamic law? Can energy have a positive and a negative aspect so that the sum of the two in a conserved system still equals zero thereby preserving the thermodynamic law? More later...

Akinbo

report post as inappropriate

Infinity negates entropy. Entropy only applies to closed sets loosing usable energy, yet in an infinite context, energy being radiated away is replaced by energy radiating in from an infinity of sources.

There is no beginning or end of the energy, because there is no way to cancel it. For all the positive and negative elements to cancel out, it would have to do so over an infinite space to stop the universe. Beginning and ending only really applies to form, which are constantly coming into being and dissolving.

report post as inappropriate

There is no beginning or end of the energy, because there is no way to cancel it. For all the positive and negative elements to cancel out, it would have to do so over an infinite space to stop the universe. Beginning and ending only really applies to form, which are constantly coming into being and dissolving.

report post as inappropriate

" ... Entropy only applies to closed sets loosing usable energy ..."

No, there are entropy formulations for open (nonequilibrium) systems, too.

report post as inappropriate

No, there are entropy formulations for open (nonequilibrium) systems, too.

report post as inappropriate

Tom,

I stand corrected.

Doesn't entropy necessarily always apply to subsets of an open system, since low entropy sets have to come from somewhere?

Which goes to the necessity of spatial and by extension, temporal infinity.

Regards,

John M

report post as inappropriate

I stand corrected.

Doesn't entropy necessarily always apply to subsets of an open system, since low entropy sets have to come from somewhere?

Which goes to the necessity of spatial and by extension, temporal infinity.

Regards,

John M

report post as inappropriate

(reposted in correct thread)

"His musings remind me of one of the strangest concepts in mathematics: the axiom of choice. This is a rule for selecting objects from an infinite collection even when all standard rules fail. The weird thing is that, although mathematicians know that such a rule exists, they don't know what the rule is. Worse, they know they'll never know what it is. A state of infinite entropy may likewise exist even if it is impossible to specify."

FWIW, in a 2006 conference paper I showed how to derive a well ordered continuum from random events, without appealing to the AC.

this post has been edited by the author since its original submission

report post as inappropriate

"His musings remind me of one of the strangest concepts in mathematics: the axiom of choice. This is a rule for selecting objects from an infinite collection even when all standard rules fail. The weird thing is that, although mathematicians know that such a rule exists, they don't know what the rule is. Worse, they know they'll never know what it is. A state of infinite entropy may likewise exist even if it is impossible to specify."

FWIW, in a 2006 conference paper I showed how to derive a well ordered continuum from random events, without appealing to the AC.

this post has been edited by the author since its original submission

report post as inappropriate

Is there at all "a tangible effect on daily life"?

Yes, of course there is. In a finite universe energy is not invariant. So there is no law of energy conservation.

report post as inappropriate

report post as inappropriate

Yes, of course there is. In a finite universe energy is not invariant. So there is no law of energy conservation.

report post as inappropriate

Sydney,

I know it's heretical to challenge the conservation laws, but seeing as how we don't really have a general definition of 'energy' which manifests itself in myriad forms, might it be an emergent phenomenon of spacetime? It is profoundly transient, and we can't truly say that the space-like dimension and the time-like dimension are themselves different things.

It is a long way from the laboratory of Lavoisier to intergalactic space. So does it matter if we see the universe as infinite or finite to accept covariance creating 'energy'? jrc

report post as inappropriate

I know it's heretical to challenge the conservation laws, but seeing as how we don't really have a general definition of 'energy' which manifests itself in myriad forms, might it be an emergent phenomenon of spacetime? It is profoundly transient, and we can't truly say that the space-like dimension and the time-like dimension are themselves different things.

It is a long way from the laboratory of Lavoisier to intergalactic space. So does it matter if we see the universe as infinite or finite to accept covariance creating 'energy'? jrc

report post as inappropriate

John,

If I am right: first you put forwards the lack of a good understanding of the nature of energy (physics). Second you put a question mark by the importance of the existence of a finite/infinite universe in relation to the conservation of energy.

Well, I cannot say there is no good understanding, because energy creates differences in the properties of the phenomena and vice...

view entire post

If I am right: first you put forwards the lack of a good understanding of the nature of energy (physics). Second you put a question mark by the importance of the existence of a finite/infinite universe in relation to the conservation of energy.

Well, I cannot say there is no good understanding, because energy creates differences in the properties of the phenomena and vice...

view entire post

report post as inappropriate

Sydney,

Thanks for your views, I like to see what different perspectives reveal.

If I understand you properly,('the total amount of energy volume must be invariant') the volume that a discrete quantity of energy would assume in reality would always be describable by a set of mathematic equations that would be the same for any quantity, in the sense that we hypothetically prescribe an idealized background independent theoretical rest mass. There-in; the energy would be distributed in a continuous range of density. jrc

report post as inappropriate

Thanks for your views, I like to see what different perspectives reveal.

If I understand you properly,('the total amount of energy volume must be invariant') the volume that a discrete quantity of energy would assume in reality would always be describable by a set of mathematic equations that would be the same for any quantity, in the sense that we hypothetically prescribe an idealized background independent theoretical rest mass. There-in; the energy would be distributed in a continuous range of density. jrc

report post as inappropriate

I invite everyone to read my paper on the origin of the universe in the following link:

http://www.modelmechanics.org/2011universe.pdf

In this paper I envisage that our universe is finite but it is contained in an infinite structured and elastic ether called the E=Matrix.

Ken Seto

report post as inappropriate

http://www.modelmechanics.org/2011universe.pdf

In this paper I envisage that our universe is finite but it is contained in an infinite structured and elastic ether called the E=Matrix.

Ken Seto

report post as inappropriate

"The aficionados of infinity include Alan Guth, who argued in Puerto Rico and on Edge.org that a truly infinite universe would neatly explain the arrow of time. When space has no bound, neither does entropy. It keeps on increasing forever, always pointing the way forward for time. The universe need not have begun in a contrived initial state to create the impetus toward increasing disorder."

I might have a comment to make with regard to the part "When space has no bound, neither does entropy. It keeps on increasing forever, always pointing the way forward for time." First I need to know if it is acceptable to say that the 'cosmological principle' includes a quasi-statically changing' temperature for the universe?

I am assuming that the type of entropy referred to is intended as thermodynamic entropy defined by Clausius. It is important to specify this because none of the other types are the same thing at all. The type of entropy was not stated. However, the thermodynamic 'arrow of time' originated with Clausius' definition of thermodynamic entropy.

James Putnam

report post as inappropriate

I might have a comment to make with regard to the part "When space has no bound, neither does entropy. It keeps on increasing forever, always pointing the way forward for time." First I need to know if it is acceptable to say that the 'cosmological principle' includes a quasi-statically changing' temperature for the universe?

I am assuming that the type of entropy referred to is intended as thermodynamic entropy defined by Clausius. It is important to specify this because none of the other types are the same thing at all. The type of entropy was not stated. However, the thermodynamic 'arrow of time' originated with Clausius' definition of thermodynamic entropy.

James Putnam

report post as inappropriate

Login or create account to post reply or comment.