# A Singularity in Semi-Classical physics too?

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## Main Question or Discussion Point

Hello.

My question is based upon my (mis?)understanding of these two premises.

1.
General Relativity breaks down when trying to describe the extreme conditions that are inferred to have existed in the very early universe.

2.
According to this link... https://en.wikipedia.org/wiki/Semiclassical_gravity ...cosmic inflation isn't fully classical.

So, does Semiclassical gravity also break down when trying to describe such extreme conditions?

Or is that kind of extrapolation not within it's remit?

Ok, that's two questions. Any help given or guidance offered would be appreciated.

Thank you,

Cerenkov.

kimbyd
Gold Member
The energy scale of inflation is typically far below the Planck scale, so at least in the simplest arguments there's reason to hope that semiclassical gravity is sufficient. However, this is certainly one salient argument that inflation models may be inaccurate, as it is very possible that the full quantum theory of gravity differs substantially from the semiclassical approximation in the regime of inflation.

kimbyd wrote...

"The energy scale of inflation is typically far below the Planck scale, so at least in the simplest arguments there's reason to hope that semiclassical gravity is sufficient. However, this is certainly one salient argument that inflation models may be inaccurate, as it is very possible that the full quantum theory of gravity differs substantially from the semiclassical approximation in the regime of inflation."

Thank you, kimbyd.

I have another question re the comparison of classical and semiclassical physics, but I must try and word it carefully. Doing that will take a little time.

Thanks again,

Cerenkov.

mathman
Be careful in using the term "classical". Typically it refers to non
-quantum theory, so in that sense relativity is a classical theory.

mathman...

"Be careful in using the term "classical". Typically it refers to non
-quantum theory, so in that sense relativity is a classical theory."

Thanks for the cautionary note, mathman.
Yes, I'm aware that relativity is a classical theory and that quantum mechanics isn't. I'm curious about semi-classical physics and what it can and cannot do. Hence this thread and my question.

Thanks,

Cerenkov.

PeterDonis
Mentor
2019 Award
cosmic inflation isn't fully classical
Beware of using Wikipedia as a source. First, "classical", "semi-classical", and "quantum" are names for types of human theoretical models, not things in reality; if cosmic inflation actually occurred, it makes no sense to say that it "isn't fully classical", since it isn't a human model, it's something the models are trying to make predictions about.

Second, the only way I can parse the quoted claim is as the claim that a fully classical GR model can't produce cosmic inflation, which is obviously false: just put in a large positive cosmological constant or a scalar field with a large constant energy density.

Beware of using Wikipedia as a source. First, "classical", "semi-classical", and "quantum" are names for types of human theoretical models, not things in reality; if cosmic inflation actually occurred, it makes no sense to say that it "isn't fully classical", since it isn't a human model, it's something the models are trying to make predictions about.

Second, the only way I can parse the quoted claim is as the claim that a fully classical GR model can't produce cosmic inflation, which is obviously false: just put in a large positive cosmological constant or a scalar field with a large constant energy density.
Thank you Peter.

Yes, thanks for pointing out the difference between human models and reality. My understanding of which models are "classical", "semi-classical" and "quantum" leaves something to be desired. Hence this thread and my questions.

So, is there a better, more accurate source that my 'basic' eyes could look over? Which might help me gain an insight into these three categories?

Thanks,

Cerenkov.

"The energy scale of inflation is typically far below the Planck scale, so at least in the simplest arguments there's reason to hope that semiclassical gravity is sufficient. However, this is certainly one salient argument that inflation models may be inaccurate, as it is very possible that the full quantum theory of gravity differs substantially from the semiclassical approximation in the regime of inflation."

kimbyd,

Given what you've explained, I tentatively conclude that as conditions become more extreme (moving from right to left on the graphic below) so our ability to model and describe what is happening becomes more difficult. I've crudely copied an illustration in John D. Barrow's, 'The Infinite Book'... https://www.amazon.com/dp/1400032245/?tag=pfamazon01-20 ...using MS Paint, but the accompanying text is verbatim. Yes, I know this is a 'pop' science book, but that's where I'm at and we all have to start somewhere.

Is my tentative conclusion of any merit?

Thanks,

Cerenkov.

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kimbyd
Gold Member
Thanks for the cautionary note, mathman.
Yes, I'm aware that relativity is a classical theory and that quantum mechanics isn't.
Mathman's statement was a little more than this: "classical" can mean very different things in different contexts. In general it means an older theory. In some contexts, Newtonian gravity would be considered classical as opposed to General Relativity. In others, non-quantum theory is called classical. So General Relativity is in this weird middle ground where some of the time it's called classical, other times not.

Similarly, there is a notion of classical quantum mechanics using Schroedinger's equation, which which "classical" in the sense that it doesn't include special relativity and can't describe a change in the number of particles (e.g. it can't describe a positron/electron annihilating to produce a pair of photons: we need quantum field theory for that).

So it's not a bad idea to be a bit careful about what, precisely, is being described when something is called "classical", because it can mean so many different things.

In this case, the "semi-classical approximation" combines quantum field theory with non-quantum curved space-time.

kimbyd
Gold Member
"Given what you've explained, I tentatively conclude that as conditions become more extreme (moving from right to left on the graphic below) so our ability to model and describe what is happening becomes more difficult.
Yes, this is entirely accurate. One way I've described it previously is that as we look back in time, our view of what's going on gets fuzzier and fuzzier.

It's sort of like examining a crime scene: if you can observe the crime in progress, you get a lot of knowledge. If you can only see the scene a few minutes after it happened, you get more limited information. If you can only view it after days or weeks, it becomes harder still.

"Mathman's statement was a little more than this: "classical" can mean very different things in different contexts. In general it means an older theory. In some contexts, Newtonian gravity would be considered classical as opposed to General Relativity. In others, non-quantum theory is called classical. So General Relativity is in this weird middle ground where some of the time it's called classical, other times not.

Similarly, there is a notion of classical quantum mechanics using Schroedinger's equation, which which "classical" in the sense that it doesn't include special relativity and can't describe a change in the number of particles (e.g. it can't describe a positron/electron annihilating to produce a pair of photons: we need quantum field theory for that).

So it's not a bad idea to be a bit careful about what, precisely, is being described when something is called "classical", because it can mean so many different things.

In this case, the "semi-classical approximation" combines quantum field theory with non-quantum curved space-time."

Thank you for this clarification,kimbyd.
I'm reminded of the way astronomers use the term, 'metals' to describe chemical elements in a certain context, when they actually mean all elements heavier than hydrogen and helium. That would appear confusing to a layperson looking at a periodic table and seeing the categories of metals, metalloids and nonmetals. I'll take your explanation and cautionary note on board.

Thanks,

Cerenkov.

"Yes, this is entirely accurate. One way I've described it previously is that as we look back in time, our view of what's going on gets fuzzier and fuzzier.

It's sort of like examining a crime scene: if you can observe the crime in progress, you get a lot of knowledge. If you can only see the scene a few minutes after it happened, you get more limited information. If you can only view it after days or weeks, it becomes harder still."

Thanks also for this, kimbyd.

On a bit of a tangent, I wonder if you could help me a little further, when it comes to that graphic I posted? As I mentioned, I copied it from Barrow's book. It helped me see that the dip when inflation is inferred to have taken place was due to super cooling and the following peak was due to thermalization or re-heating. However, there are no scales on either of the axes in Barrow's original.

Do you happen to know where I can find a graphic of temperature versus radius in the early universe that displays some kind of scaling?

Thanks,

Cerenkov.

kimbyd
Gold Member
On a bit of a tangent, I wonder if you could help me a little further, when it comes to that graphic I posted? As I mentioned, I copied it from Barrow's book. It helped me see that the dip when inflation is inferred to have taken place was due to super cooling and the following peak was due to thermalization or re-heating. However, there are no scales on either of the axes in Barrow's original.
Axis scale would be approximate anyway, because we don't yet know what the scale of inflation actually was.

The way I interpret that graph, the high temperature prior to inflation is completely hypothetical. What happened before inflation is a complete unknown, and because the nature of inflation is to hide the nature of whatever happened before, it will always be hard to know. So it's best to completely disregard anything on that graph which happened before inflation.

For inflation itself, inflation has the impact of cooling the universe extremely rapidly. It might have started at a low temperature, or it might have started at a high temperature. But in any event, by the time inflation became close to its end, the universe can be thought of to only include the inflaton field (the field which drove inflation), plus zero-point fluctuations of that field.

That field itself had a lot of energy, though, so once inflation ended and the inflaton field decayed, that event heated the universe back up again (this is why the temperature increased).

Do you happen to know where I can find a graphic of temperature versus radius in the early universe that displays some kind of scaling?
It's not really possible to do that in anything but approximate terms, sadly, because we don't know the temperature early in inflation at all. Nor do we know precisely when the end of inflation occurred, and thus don't know how hot the universe became at that time.

The temperature of the early universe is only well-understood at about the time the light elements were produced and later. For example, here's one paper which tries to estimate the maximal temperature achieved during reheating (the end of inflation):
https://arxiv.org/abs/1212.3554

They find maximum temperatures in the range from ~100MeV (roughly $10^{12}$ Kelvin) to ~$10^{10}$GeV (roughly ($10^{23}$ Kelvin), depending upon the specific models used.

Many thanks, kimbyd.

Speculating a little, if B-mode polarization were found in the CMB or if primordial gravitational waves were found by LISA, that data might give us an insight into the pre-inflationary era? And consequently the temperatures and energies involved?

Thanks,

Cerenkov.

kimbyd
Gold Member
Many thanks, kimbyd.

Speculating a little, if B-mode polarization were found in the CMB or if primordial gravitational waves were found by LISA, that data might give us an insight into the pre-inflationary era? And consequently the temperatures and energies involved?

Thanks,

Cerenkov.
It would give us direct insight into the inflationary era itself. In particular, measuring the B-mode polarization would produce strict limits on the kinds of possible inflation models, and would also provide bounds on the energy scale of inflation. It wouldn't provide any direct insight into anything that happened before inflation.

"It would give us direct insight into the inflationary era itself. In particular, measuring the B-mode polarization would produce strict limits on the kinds of possible inflation models, and would also provide bounds on the energy scale of inflation. It wouldn't provide any direct insight into anything that happened before inflation."

Thank you, kimbyd.

I see that this would not give us any evidence-based insight into anything that happened before inflation.

However, if certain inflation models were ruled in, wouldn't we then have a much stronger basis for applying the Copernican Principle and inferring that our particular episode of inflation wasn't the very first one? That is, if something like Linde's Chaotic Eternal Inflation model were supported by the B-mode limits, then wouldn't we be obliged to infer that the inflationary process didn't begin with us? At the risk of violating the CP by assuming everything began with us?

Thanks,

Cerenkov.

kimbyd
Gold Member
"It would give us direct insight into the inflationary era itself. In particular, measuring the B-mode polarization would produce strict limits on the kinds of possible inflation models, and would also provide bounds on the energy scale of inflation. It wouldn't provide any direct insight into anything that happened before inflation."

Thank you, kimbyd.

I see that this would not give us any evidence-based insight into anything that happened before inflation.

However, if certain inflation models were ruled in, wouldn't we then have a much stronger basis for applying the Copernican Principle and inferring that our particular episode of inflation wasn't the very first one? That is, if something like Linde's Chaotic Eternal Inflation model were supported by the B-mode limits, then wouldn't we be obliged to infer that the inflationary process didn't begin with us? At the risk of violating the CP by assuming everything began with us?

Thanks,

Cerenkov.
Yes, learning more about the nature of inflation would most definitely provide insight into possible ways that inflation might have started.

One unfortunate possibility, however, is that primordial B-modes may never be detected, which would provide precious little indication as to what might have happened. Absent this signal, it will be hard to distinguish between a number of different models. Sadly, the universe does not always play nice with our attempts to understand it better.

Many thanks for you replies and explanations, Kimbyd.

Cerenkov.