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Every year John Brockman’s Edge web-site hosts responses to a different question. This year the question was "What scientific idea is ready for retirement?."

There was an answer from Max Tegmark that follows which I couldn't agree more with. Bill S will no doubt have a view and knows that I view infinity in physics is an absurdity but anyone else have a comment.

Perhaps finally the forces are starting to marshal to have the infinity abomination exorcised and given it's last rites smile


Quote:
Max Tegmark (Physicist, MIT; Researcher, Precision Cosmology; Scientific Director, Foundational Questions Institute)

Infinity

I was seduced by infinity at an early age. Cantor's diagonality proof that some infinities are bigger than others mesmerized me, and his infinite hierarchy of infinities blew my mind. The assumption that something truly infinite exists in nature underlies every physics course I've ever taught at MIT, and indeed all of modern physics. But it's an untested assumption, which begs the question: is it actually true?

There are in fact two separate assumptions: "infinitely big" and "infinitely small". By infinitely big, I mean the idea that space can have infinite volume, that time can continue forever, and that there can be infinitely many physical objects. By infinitely small, I mean the continuum: the idea that even a liter of space contains an infinite number of points, that space can be stretched out indefinitely without anything bad happening, and that there are quantities in nature that can vary continuously. The two are closely related because inflation, the most popular explanation of our Big Bang, can create an infinite volume by stretching continuous space indefinitely.

The theory of inflation has been spectacularly successful, and is a leading contender for a Nobel Prize. It explained how a subatomic speck of matter transformed into a massive Big Bang, creating a huge, flat and uniform universe with tiny density fluctuations that eventually grew into today's galaxies and cosmic large scale structure, all in beautiful agreement with precision measurements from experiments such as the Planck satellite. But by generically predicting that space isn't just big, but truly infinite, inflation has also brought about the so-called measure problem, which I view as the greatest crisis facing modern physics. Physics is all about predicting the future from the past, but inflation seems to sabotage this: when we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts that there will be infinitely many copies of you far away in our infinite space, obtaining each physically possible outcome, and despite years of tooth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So strictly speaking, we physicists are no longer able to predict anything at all!

This means that today's best theories similarly need a major shakeup, by retiring an incorrect assumption. Which one? Here's my prime suspect: ∞.

A rubber band can't be stretched indefinitely, because although it seems smooth and continuous, that's merely a convenient approximation: it's really made of atoms, and if you stretch it too much, it snaps. If we similarly retire the idea that space itself is an infinitely stretchy continuum, then a big snap of sorts stops inflation from producing an infinitely big space, and the measure problem goes away. Without the infinitely small, inflation can't make the infinitely big, so you get rid of both infinities in one fell swoop—together with many other problems plaguing modern physics, such as infinitely dense black hole singularities and infinities popping up when we try to quantize gravity.

In the past, many venerable mathematicians expressed skepticism towards infinity and the continuum. The legendary Carl Friedrich Gauss denied that anything infinite really existed, saying "Infinity is merely a way of speaking" and "I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics." In the past century, however, infinity has become mathematically mainstream, and most physicists and mathematicians have become so enamored with infinity that they rarely question it. Why? Basically, because infinity is an extremely convenient approximation, for which we haven't discovered convenient alternatives. Consider, for example, the air in front of you. Keeping track of the positions and speeds of octillions of atoms would be hopelessly complicated. But if you ignore the fact that air is made of atoms and instead approximate it as a continuum, a smooth substance that has a density, pressure and velocity at each point, you find that this idealized air obeys a beautifully simple equation that explains almost everything we care about: how to build airplanes, how we hear them with sound waves, how to make weather forecasts, etc. Yet despite all that convenience, air of course isn't truly continuous. I think it's the same way for space, time and all the other building blocks of our physical word.

Let's face it: despite their seductive allure, we have no direct observational evidence for either the infinitely big or the infinitely small. We speak of infinite volumes with infinitely many planets, but our observable universe contains only about 1089 objects (mostly photons). If space is a true continuum, then to describe even something as simple as the distance between two points requires an infinite amount of information, specified by a number with infinitely many decimal places. In practice, we physicists have never managed to measure anything to more than about 17 decimal places. Yet real numbers with their infinitely many decimals have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics: we describe even a single bit of quantum information (qubit) using two real numbers involving infinitely many decimals.

Not only do we lack evidence for the infinite, but we don't actually need the infinite to do physics: our best computer simulations, accurately describing everything from the formation of galaxies to to tomorrow's weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can too—in a way that's more deep and elegant than the hacks we use for our computer simulations. Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I'm betting that we also need to let go of it.


Interestingly Seth Lloyd (Professor of Quantum Mechanical Engineering, MIT; Author, Programming the Universe) is obviously working on the something with Max on this .... hmmm questions to be asked

http://www.edge.org/response-detail/25449

Last edited by Orac; 01/17/14 05:21 PM.

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Ok, I realize the idea that the universe is infinite does create some problems. But that raises the somewhat philosophical question as to what are the boundaries of the universe? If it isn't infinite there has to be some way to measure its size.

And of course then we still have the problem, if it is not infinite what is outside?

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Quote:
Bill S will no doubt have a view


No doubt! However, I might stand back and let others have a say.

Over the time I've been with SAGG I think I've said most of the things in the Tegmark quote; in layman's terms, of course. Perhaps notice will be taken in the hallowed halls of scientific academia now. After all you have to have a degree if you want to influence science. smile


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I've never had a problem with infinity myself and I don't see Tegmark's arguement to be all that strong.

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I agree the argument isn't string but his personality carries weight smile

I am surprised you don't have issues with infinity PMB have you done much with QM?

I suspect you know the background but for others who aren't I shall give the brief version.

I think the first time I ever realized there are major issues with infinity was very early when studying Schrödinger's equation. The solution has to be linear and finite to get a proper time evolution to work.

Any attempt to make the solutions non linear gives you immediate problems with superposition because if they aren't linear you can't add the superpositions in any meaningful way unless you know the equation of the non linearity and thus you just inserted "consciousness" or "god" into QM take your pick because you can't create time evolution without one of those and so now have a really bad "Wigner's friend".

Even good old wiki gives the background to the problem
(http://en.wikipedia.org/wiki/Nonlinear_Schr%C3%B6dinger_equation)

Quote:
Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state (except hypothetically, as in some early attempts, in the 1970s, to explain the quantum measurement process).


So having satisfied yourself the solution must be linear you can try infinity observers but there is an immediate problem

Now for the more advanced you can try and solve the equation for infinity. For those not capable the problem is you end up with two possibilities of the waveform at infinity the value goes to zero or at infinity the value goes to some actual value.

For any wavefunction which doesn't go to zero at infinity it is "pathological" you can not make the wavefunction evolution independant of time and you are actually back to the same problem as the non linear case. I will leave this as a statement of what ORAC says open to challenge if anyone wants a go smile

As a side note this is why any fields that are waveforms go to zero at infinity smile

So the key thing here is it tells you implicitly that at infinity the result MUST go to zero ... and ZERO means it doesn't exist or at least it's not measurable/observable or however you want to describe it.

So first under Schrödinger and that follows into QM that if there is a real infinity nothing measurable/observable or real exists there. In other words you can treat infinity in the normal mathematical way that it simply means a non existent number that represents a very large and finite number which you don't know.

Under GR/SR and even string theory things are a little easier with infinity but under strict QM infinity is something that can not be real or at the very worst it is something that is not observable.

So I guess for me it comes down to if QM correctly describes the universe it can't be infinite.

Last edited by Orac; 01/19/14 05:47 PM.

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I have no problem with the idea that the Universe (sensu Gribbin) is finite. If that is the case, I would argue that nothing infinite can exist in the Universe.

Any reference to infinity in the Universe must be either a mathematical infinity or an approximation.

This just leaves two important questions unanswered:

"Can there ever have been nothing?"

"If ever there was nothing, could there be something now?"

I would not expect the answer to either of these to admit infinity to the Universe.


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Originally Posted By: Orac
if there is a real infinity nothing measurable/observable or real exists there.


Essentially this would be an infinity of nothingness. Is that even a scientific concept?

Presumably it could not exist in the Universe. and as it would be nothing, would it be meaningful to talk about "where" it might be?


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Originally Posted By: Bill S.
Essentially this would be an infinity of nothingness. Is that even a scientific concept?

Presumably it could not exist in the Universe. and as it would be nothing, would it be meaningful to talk about "where" it might be?


Exactly correct so you invoke occam's razor and the universe is finite.


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Originally Posted By: Orac

Exactly correct so you invoke occam's razor and the universe is finite.

But Occam's razor isn't a law. It is a guideline. The fact that you see it one way, which you reach by calling on Occam's razor doesn't disprove it. Infinity may be very real, you just don't see how. But this is at the limits of our scientific knowledge and so we don't know whether there is infinity or not.

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There seems to be divided opinion among scientists as to whether or not one should try to apply Occam's razor to anything outside the Universe. Personally, I think it is justifiable, precisely because it is just a guideline. It points in a rational direction, but makes no dogmatic statement.


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BTW; the questions remain unanswered.

"Can there ever have been nothing?"

"If ever there was nothing, could there be something now?"


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Originally Posted By: Bill S.
There seems to be divided opinion among scientists as to whether or not one should try to apply Occam's razor to anything outside the Universe. Personally, I think it is justifiable, precisely because it is just a guideline. It points in a rational direction, but makes no dogmatic statement.


WOW I agree and use it often for exactly the same logic as in this case.


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Originally Posted By: Bill S.
BTW; the questions remain unanswered.

"Can there ever have been nothing?"

"If ever there was nothing, could there be something now?"


Now here is another slippery slope can I define nothing because if nothing is a hard fixed the answer is no and obviously so.

However lets take money scenario you can have nothing but you can borrow some create more pay back the original and then have money.

The real problem you are chasing I think Bill S is not nothing but can one borrow in physics and does borrowing imply that there is not nothing behind it smile

Last edited by Orac; 01/20/14 11:45 PM.

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Originally Posted By: Orac
Now here is another slippery slope can I define nothing because if nothing is a hard fixed the answer is no and obviously so.


This quickly becomes one of those circular arguments that goes nowhere. Asking to define nothing is a cop-out. You cannot define nothing, other than as a complete absence of anything, which really does nothing other than rephrase the original. All that is achieved by this is avoidance of the original question. This is clever in a “pissing contest” but gets nowhere in any real discussion.

Quote:
However lets take money scenario you can have nothing but you can borrow some create more pay back the original and then have money.


In the same way that science legitimately uses infinite to approximate a very large number, your use of “nothing” in this context is purely symbolic. In the context of whether or not there can ever have been nothing, it is yet another cop-out.

Quote:
The real problem you are chasing I think Bill S is not nothing but can one borrow in physics and does borrowing imply that there is not nothing behind it


I’m not sure that I understand this. What I think you are saying is that if you have nothing, you can borrow something, then, where there was nothing there is now something. If that’s right, I might as well drop out of this discussion, because we are talking about two different things and there seems to be no way we can align our subjects. If there is nothing, there is nothing, there is nothing to borrow and no one to do the borrowing or lending.

It has been pointed out to me that “nothing” is not a scientific concept. “Scientists do not deal with nothing”. Fair enough. It is for scientists to define the boundaries of science. All I would say is that unless scientists are willing to give some thought to the concepts of nothingness and infinity they are unlikely even to come close to considering the origin of the cosmos, there will always be infinite regression.


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Originally Posted By: Bill S
If there is nothing, there is nothing, there is nothing to borrow and no one to do the borrowing or lending


That is called "Absolute nothing" and it's not a science term smile

Absolute nothing as per your definition can't exist in science it's not possible because there is an instant falsification because you exist.

Now can I reverse the problem why do you feel the need to even consider an absolute nothing? If you really feel absolute nothing as you have defined is essential then you need to take up a religion there isn't another choice and I am serious.

I don't get why you struggle with this concept it's a black and white answer as science will never be able to have an absolute nothing start because as per your definition above it can't >>> you defined it that way <<<.

You keep asking me the same question "How do you create something from nothing" but you scarcely ever consider the reverse problem I give you "Nothing seems to be a concept, could it ever really exist".

See it is a simple two choice problem with absolute nothing

(A) Absolute nothing can not and does not exist as evidence by the fact you are here.

(B) There is some GOD, Deity or whatever who can make something from absolute nothing.


They are the only two possible start points choose (A) or (B).


Regardless of your start point there appears to be laws and logic to the universe so science will exist and we will study them to advance our civilizations. Science existence doesn't depend on the answer.

The answer to that question ultimately isn't that important we are not here to prove or disprove the existence of GOD we are concerned with science. If your question was able to be answered it would however have implications to religion.

So make a choice Bill S .... A or B .... no-one is ever going to give you any others and can't because of what absolute nothing implies.

When you have done so you will find nothing changes with anything you studied in science smile

However after answering the choice, your religious status is decided ... see the question is religious not science smile

It really is that simple with absolute nothing.

Last edited by Orac; 01/23/14 04:05 PM.

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Infinity Exist !!!


m ---------- M >>> motion

if Mass is faster than own gravitation signal ( similar like airplane can escape from own sound Mass M can escape gravitation escape from point where was in past )

What will be if ?

mass m will feel M signal
M will not feel m signal

in many tests people proved that G speed is lower than C speed

above very real model of the universe ( right now all galactics accelerate )


About mathematica and physic ?
more problematic is ZERO not infinity
we all know that Zero in real world not exist
can we eliminate ZERO from QM ?


Last edited by newton; 01/23/14 06:52 PM.
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Originally Posted By: Orac
Now can I reverse the problem why do you feel the need to even consider an absolute nothing? If you really feel absolute nothing as you have defined is essential then you need to take up a religion there isn't another choice and I am serious.

Orac, I don't really have a big problem with infinity and nothing the way Bill S. does, but this brings up a sort of a problem. Earlier you said that the universe is finite. That then raises the question of what is outside the universe. That would presumably be absolutely nothing. So there is a bit of a conflict there.

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Originally Posted By: Orac
That is called "Absolute nothing" and it's not a science term


I dislike “absolute nothing” on the basis that you cannot have degrees of nothing. Either you have something or nothing. However, if science needs degrees of nothing, so be it.

Quote:
Absolute nothing as per your definition can't exist in science it's not possible because there is an instant falsification because you exist.


Not only do I agree with this, it is what I have been saying on this forum for over three years.

Quote:
Now can I reverse the problem why do you feel the need to even consider an absolute nothing? If you really feel absolute nothing as you have defined is essential then you need to take up a religion there isn't another choice and I am serious.

Could there be a spot of fixation amnesia here Orac. Look at my “signature” smile

Of course science does not depend on the answer to this question. Science existed before the Big Bang had even been thought of as a beginning of anything, and will continue if/when something replaces the BB.

Quote:
So make a choice Bill S .... A or B .... no-one is ever going to give you any others and can't because of what absolute nothing implies.


On the contrary, as I have mentioned before, I have posting in various places on the subject of whether there can ever have been nothing; and if there was ever nothing would there be anything now. Below is just one of the many responses – backed by a PhD, and years working as a physicist:

“All these laws are assumed to be true only within our universe, since that's the only place where we can look to see if they're true. We have no idea what happens outside of our universe--if there is an outside. If our universe was created from "nothing" it's possible this law doesn't hold.

Similarly, causality can't be violated within our universe, but outside our universe it might be---in particular, the concept of causality probably wouldn't have meaning, since it describes how things interact within the space-time of our universe, which presumably doesn't extend outside of it.”


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Make something from nothing ?

above example

m--------M >>> faster than G

mass M can make work ( mass m will fill G signal from mass M but fact that mass M made work will never stop mass M )


G speed respect to what ?
Light speed respect to what ?



p1...p2....p3....p4.....M >>> G

mass M wass in past in point 1 ,2,3,4,...

below very simply and old definition






CAN WE HAVE RING RESPECT TO MANY OBSERVERS OR ONLY ONE OBSERVER
inside ring's center



Last edited by newton; 01/23/14 07:04 PM.
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Originally Posted By: Bill
Orac, I don't really have a big problem with infinity and nothing the way Bill S. does


When are you all going to realise that I am the only one who doesn't have a problem with infinity and nothing? smile

Seriously, though:

Quote:
That then raises the question of what is outside the universe. That would presumably be absolutely nothing. So there is a bit of a conflict there.


Why would you presume that?

Why might the Universe be embedded in an infinite cosmos?


There never was nothing.
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