Carolo Rovelli on infinity in LQC

[windy miller]

I just read Carlo Rovelli's new book about loop quantum gravity.
https://www.amazon.com/dp/0241257964/?tag=pfamazon01-20
Its a great book and i really enjoyed it. However there is a claim in that seems a little odd to me.
In LQC singularities are resolved and replaced by bounces. So the the state of infinity density, pressure, curvature etc is removed. Rovelli then claims LQC removes infinities . But I see a problem with this claim.
If singularities are replaced by bounces then the rationale for the finite age of the universe is removed and this open the door for the universe to infinitely old and so Rovellis claim seems suspect to me even assuming LQC is correct.

 

[Chalnoth]

Yes, in LQC the universe is eternal both into the past and the future. What is it about this that makes it seem suspect to you?

 

[windy miller]

Well chapter 11 is called "the End of Infinity" because LQC gets rid of singularities. But by getting rid of singularities you've now made the universe is infinite in time, so its not really the end of infinity.

 

[Chalnoth]

Well chapter 11 is called "the End of Infinity" because LQC gets rid of singularities. But by getting rid of singularities you've now made the universe is infinite in time, so its not really the end of infinity.

I don't see that that semantic quibble says anything one way or another about the viability of the theory.

 

[_PJ_]

Singularities are where current mathematical prediction breaks down. Classsically, there's no understood process which slows the collapse of degenerate neutron matter once the rresidual pressure is overcome by gravity- this leaves us with a very real hole in our understanding, a black hole in spacetime ( which forms only at critical energy density and doesn't require a singularity at all) and an incomplete mathematical appraisal/formality.

The infinity referred to in context is the problematic notion of infinite density ascribed to singular events. This is nonsensical and incompatible and typical of a flawed mathematical description of process.

The infinity of age, however does not compromise any physical process or laws and is less problematic (unless desire for a beginning or end is philosophically preferrred)

 

[Drakkith]

Well chapter 11 is called "the End of Infinity" because LQC gets rid of singularities. But by getting rid of singularities you've now made the universe is infinite in time, so its not really the end of infinity.

Imagine the function ##f(x) = \frac{1}{x}##. If you go backwards from, say, ##x=5##, everything's fine until you approach ##x=0##. Prior to this, the function behaved in a manner called "well behaved". This means that it doesn't jump around erratically or have any discontinuities or holes in it. But what happens when you try to pass ##x=0##? The value of the function shoots upwards as you approach zero. If you've taken calculus, we say that the limit as x approaches zero (from the positive side) is infinity: ##\frac{lim}{x→0^+} f(x) = \frac{1}{x} = +∞##
When the function passes over zero there is a "jump". When going from ##x=1## to ##x=-1##, a finite change in ##x## of 2, the function takes on all real numbers from 1 to positive infinity and then jumps to take on all real numbers from negative infinity to negative one. The function ceases to be smooth and continuous and we say that it exhibits a singularity at ##x=0##. We call this a "finite-time" singularity since a finite change in ##x## results in an output that tends towards infinity.

This is different than the function ##f(x)=x## (a straight line passing through the origin). This function also takes on all real numbers, but it does not do so in a finite step in ##x##. You'd have to go through every single value of ##x## to get an output of ##±∞##. This function is "well behaved" everywhere and exhibits no discontinuities or singularities.

The problem with the singularity in cosmology is that it behaves like the first function, ##\frac{1}{x}##, and goes to infinity in a finite amount of time. Changing the theory so that this doesn't happen doesn't get rid of infinity in the sense that the time variable can go to ##±∞##, but it does get rid of the "finite-time" singularity we originally had that leads to a breakdown in the predictive power of the theory.

 

[windy miller]

Thanks Darkith. if I have understood you correctly to seems then we need to make a distinction then between different types of infinity. Let's call them finite time infinities and non finite time infinities. Then would it be correct to say the physicists are ok with infinities if they don't reach infinity in a finite amount of time like the size of the universe or even its age. But object to infinities if a function becomes infinite in a finite time like the cosmological singularity.
I have notices many cosmologists say that the infinity at the singularity is some sort of major problem as physicists hate infinity. Yet some of those asme cosmologists have claimed the universe may be spatially infinite , they may be an infinite number of universes and others (the loop guys) say the universe may have existed before the big bang possibly eternally into the past. So seems to have cleared up why these are not contradictory statements. Have I understood correctly?

 

[Drakkith]

Thanks Darkith. if I have understood you correctly to seems then we need to make a distinction then between different types of infinity.

It's more that we need to understand that infinity is not the same thing as a singularity. Singularities usually result in abrupt jumps or discontinuities in the math that keep us from making good predictions around some point in a model or theory. Infinity is simply the notion that a quantity can increase (or decrease) without end.

Then would it be correct to say the physicists are ok with infinities if they don't reach infinity in a finite amount of time like the size of the universe or even its age. But object to infinities if a function becomes infinite in a finite time like the cosmological singularity.

Yes, the latter usually means that you're attempting to use a model or theory in a way in which the math fails to work properly. Sometimes you can simply shift things around or make your boundaries such that you avoid these issues. Currently, there is no known way to avoid a singularity at t=0 in the past, either because we don't know enough about physics or because it really isn't possible.

I have notices many cosmologists say that the infinity at the singularity is some sort of major problem as physicists hate infinity. Yet some of those asme cosmologists have claimed the universe may be spatially infinite , they may be an infinite number of universes and others (the loop guys) say the universe may have existed before the big bang possibly eternally into the past. So seems to have cleared up why these are not contradictory statements. Have I understood correctly?

That's right.

 

[windy miller]

I don't see that that semantic quibble says anything one way or another about the viability of the theory.

I agree that this discussion has nothing to do with the viability of the theory of LQG. But I don't think is a semantic quibble. People are interested in fundamental theories because they tell us deep truths about questions we have always wanted to know. Thats why people are interested in cosmology, its not like it has a lot of practical applications. So the issue of whether there are actual infinities in nature is a big profound questions.. It seems that Rovelli ( and its possible I'm misinterpreting him) is saying LQG removes infinities but i think from the discussion we have had here that is not quite right. It only removes certain badly behaved infinities. It doesn't remove all infinities and in fact it may imply infinite past to the universe. Maybe Rovelli being a physicists doesn't see this a problem infinity. But it is still an inanity of some type.

 

[Chalnoth]

I agree that this discussion has nothing to do with the viability of the theory of LQG. But I don't think is a semantic quibble. People are interested in fundamental theories because they tell us deep truths about questions we have always wanted to know. Thats why people are interested in cosmology, its not like it has a lot of practical applications. So the issue of whether there are actual infinities in nature is a big profound questions.. It seems that Rovelli ( and its possible I'm misinterpreting him) is saying LQG removes infinities but i think from the discussion we have had here that is not quite right. It only removes certain badly behaved infinities. It doesn't remove all infinities and in fact it may imply infinite past to the universe. Maybe Rovelli being a physicists doesn't see this a problem infinity. But it is still an inanity of some type.

I said it was a semantic quibble because a singularity and a universe that is unbounded in time are very different things. They both contain infinities in a sense, but as many others have (convincingly, I think) argued, singularities cause problems that an unbounded universe does not. The only thing they have in common is the concept of infinity, which is a very superficial statement. That's why I said it was a semantic quibble.