Question about observing the past (WMAP)

[Grumpy]

I'm seeing posts with the basic misunderstanding that the Big Bang(and the subsequent radiation)occurred in the same fashion as any other event in three dimensional spacetime. It did not. It IS three dimensional space and time. The BB was the creation and expansion of space and the beginning of time. The whole Universe is still in this expansion and we will ALWAYS be 13.7+ billion light years from some portion thereof. The radiation of the BB still occupies every cubic inch of the Universe, it has just been stretched, lowering it's energy, until the near infinite energy released has become a background equivalent to a few degrees above absolute zero. Since we will always be 13.7+ light years away from some points of that expansion, we will always see a glow from this background 13.7+ billion years ago. As more time passes we will be 14 billion years from the event, and thus see this radiation 14 billion years in the past, etc. minus the time to recombination. The range of the glow will always match the time that has passed since the beginning of time.

Grumpy

[Trippy]

The whole Universe is still in this expansion and we will ALWAYS be 13.7+ billion light years from some portion thereof.

This is another way of restating the point I have been trying to make to Cyperium.

The radiation of the BB still occupies every cubic inch of the Universe, it has just been stretched, lowering it's energy, until the near infinite energy released has become a background equivalent to a few degrees above absolute zero. Since we will always be 13.7+ light years away from some points of that expansion, we will always see a glow from this background 13.7+ billion years ago.

The CMBR we see today was (as I understand it) effectively emitted by the surface of last scattering.
The big bang occured.
A bunch of photons were emitted.
Those photons bounced around in the plasma for 360,000 years until the universe had cooled enough that the number of free electrons fell below a certain value, at which point the photons that permeated space kept going in which ever direction they happened to be going in.
This happened everywhere at more or less the same time, but from our perspective because of the relativity of simultaneity it has the apperance of having been emitted from a surface - the surface of last scattering, which is what the calculations I presented in my last post pertain to.

As more time passes we will be 14 billion years from the event, and thus see this radiation 14 billion years in the past, etc. minus the time to recombination. The range of the glow will always match the time that has passed since the beginning of time.

Grumpy

This forms the essence of another part of what I have been trying to explain to Cyperium.

[Trippy]

Ok, so the WMAP is from 380000 years after the Big Bang. That was when the radiation was released that now reaches us through cosmic radiation and which we detected using WMAP.


If we constantly measure the WMAP, year after year, wouldn't we measure from 380001 years after the Big Bang, and the next year measure from 380002 years after the Big Bang?

But that should be impossible, because then we couldn't have measured it at all 400000 years ago, still the radiation was there even then.

I guess my fundamental question is this; doesn't the detection of radiation correspond to a unique moment in time? Doesn't that moment also pass as new radiation comes in representing a moment further in time?

It just seems very weird to me that apparently a great amount of radiation comes here from that very same moment, why doesn't the radiation represent moments that passes? Or does each radiation represent a different location of that moment? But why are they so seperated in time?

To put my answer in terms of the OP.

No.
If the WMAP data is from 380,000 years after the big bang, it was effectively emitted from a surface 42million light years away.
In one year's time we will be measuring the radiation emitted 380,000 years after the big bang from a surface 42,000,001 light years away.
In two years time we will be measuring the raiation emitted 380,000 years after the big bang from a surface 42,000,002 light years away.

[Cyperium]

To put my answer in terms of the OP.

No.
If the WMAP data is from 380,000 years after the big bang, it was effectively emitted from a surface 42million light years away.
In one year's time we will be measuring the radiation emitted 380,000 years after the big bang from a surface 42,000,001 light years away.
In two years time we will be measuring the raiation emitted 380,000 years after the big bang from a surface 42,000,002 light years away.

But that's equally unsound, that would mean that 42,000,000 years ago we would measure it originating from a surface 0 light years away. And what about 60 million years ago? I would guess that expansion has to be accounted for, so that perhaps a million years equates to 1 year further or something. The answer to my question has to encorporate expansion or the question just doesn't get answered.

13 billion years ago that surface would be 0 lightyears away, then continually increasing to the distance of 42 million lightyears away today. Right?

I guess that we could also calculate the rate of expansion given these figures (I guess the CMB happened after the rapid inflation).

We are making progress though, and I'm thankful for the new perspectives your propositions give me.

[Cyperium]

And yet, it still forms part of the answer.

True. It just happened to be a part I already knew about and didn't explain the issue from the perspective I needed.

It's effectively continuous - unless you want to discuss the quantization of time and space.

I'm just saying that every one photon must have had a discrete location, at least after wavefunction collapse, or did many photons exist at the same discrete location at that point? I know about theories that space is quantizised but I don't think it will help to discuss them for the sake of the thread.

It's an inference on my part. Take a moment to think about it.
We measure the CMBR temperature distribution to be lumpy. It's not very lumpy, it's almost smooth, but it's lumpy none the less.
This means that different parts of space cooled at slightly different rates.
This in turn means that recombination occured slightly earlier in some areas, and slightly later in other areas.

Does it? I thought that the differences in uniformity had to do with quantum effects happening during the inflation period when the universe was extremely small (not 40 so million lightyears big).

Also, at a given temperature different particles don't neccessarily have the same energy. Some have more energy, others have less energy.
The combination of these facts leads me to infer that recombination occured over a finite, non zero period of time. In the areas where recombination happened slightly earlier, the photons have traveled slightly further. In the areas where it happened slightly later, they haven't traveled quite as far.

Ok, I guess that's reasonable, I don't know how long the recombination took. It would be nice to have those figures though, I don't remember seeing them while investigating.

The surface of last scattering.

Which is a surface of a time gone by, how could it capture more photons?

Understood. Meanwhile, my point was, and still is that I had assumed that you had infered from the discussion that I was still leaving expansion out of the discussion. It doesn't seem to me that there's a lot of point in discussing an expanding and curved space-time, when you still can't figure out how it can happen in a flat and static one.

But that's a important issue, it can't happen in a static one (it is still remarkably flat as far as we can see), the issues I'm having with time that goes by must be explained by a expanding universe.

According to this:

Source

At the time of recombination, the density of matter was on the order of 10^-17 to 10^-16 kg/m³ at the time of recombination.

According to the wikipedia entry on Big Bang Nucleosynthesis, by mass the universe was composed of 75% Hydrogen, 25% Helium, and trace amounts of other stuff.
This means that every cubic meter of space at the time of recombination contained an average of 860 million atoms.

According to the wikipedia entry on the Recombination epoch at the time of recombination for every atom there were approximately 10¹⁹ photons, so every cubic meter of space also contained 8.6E27 photons.

A sphere with a radius of 42 million lightyears has a surface area of 2E42 km².
Any given volume of space sees Earth as a hemisphere with a surface area of 255,036,000.
This suggests that the expected number of photons from any single cubic meter of space is 1.1E-6

Which may seem small.

But if the emitting layer is only 1m thick (it's likely to be much thicker than that, IMO), then distributed across the entire sky we would expect to see at any given time 2.2E42 photons of CMBR.

The take home message being that yes, the probability of any individual photon hitting the earth might be vanishingly small, but there were such a huge number, and they were emitted in every direction from every direction, that we expect to see (to a human brain anyway) large numbers of them.

Ok, you left out that they would have to travel at a increasingly sensitive angle as the universe expands though in order to reach us. The number may seem enormous, but so is the distance to us and the surface area of our detectors in relation to that distance is vanishingly small.

[Cyperium]

I'm seeing posts with the basic misunderstanding that the Big Bang(and the subsequent radiation)occurred in the same fashion as any other event in three dimensional spacetime. It did not. It IS three dimensional space and time. The BB was the creation and expansion of space and the beginning of time. The whole Universe is still in this expansion and we will ALWAYS be 13.7+ billion light years from some portion thereof. The radiation of the BB still occupies every cubic inch of the Universe, it has just been stretched, lowering it's energy, until the near infinite energy released has become a background equivalent to a few degrees above absolute zero. Since we will always be 13.7+ light years away from some points of that expansion, we will always see a glow from this background 13.7+ billion years ago. As more time passes we will be 14 billion years from the event, and thus see this radiation 14 billion years in the past, etc. minus the time to recombination. The range of the glow will always match the time that has passed since the beginning of time.

Grumpy

Yes, but surely the number of particles that reach us must decrease? An increasing number passes us by and are consumed by matter that it hits. It was a one-time event and as such the resources should be limited. At one time in the future all radiation should have either passed us by or gone in the wrong direction (such that it will never hit us) or it would hit something else and become part of that instead.

[Trippy]

But that's equally unsound, that would mean that 42,000,000 years ago we would measure it originating from a surface 0 light years away. And what about 60 million years ago? I would guess that expansion has to be accounted for, so that perhaps a million years equates to 1 year further or something. The answer to my question has to encorporate expansion or the question just doesn't get answered.

13 billion years ago that surface would be 0 lightyears away, then continually increasing to the distance of 42 million lightyears away today. Right?

I guess that we could also calculate the rate of expansion given these figures (I guess the CMB happened after the rapid inflation).

We are making progress though, and I'm thankful for the new perspectives your propositions give me.

More or less. It's one reason I prefer to deal with a flat and static space time. It makes the analogies easier.

It's already meaningless to talk about the 8th significant figure, when the figure quoted is only accurate to the second significant figure.
Substitute 42 million for 13.7 billion, assume flat and static minkowski space-time, move on.

[Trippy]

True. It just happened to be a part I already knew about and didn't explain the issue from the perspective I needed.

This bit feels like we're going around in circles.

I'm just saying that every one photon must have had a discrete location, at least after wavefunction collapse, or did many photons exist at the same discrete location at that point? I know about theories that space is quantizised but I don't think it will help to discuss them for the sake of the thread.

And the range of locations is continuous - hence the comment I made about discussing quantized space time.

Does it? I thought that the differences in uniformity had to do with quantum effects happening during the inflation period when the universe was extremely small (not 40 so million lightyears big).

Sort of.
Quantum variations led to variations in density. Variations in density led to variations in temperature.

Ok, I guess that's reasonable, I don't know how long the recombination took. It would be nice to have those figures though, I don't remember seeing them while investigating.

It's not likely to be something you'll ever see discussed, because comparatively speaking it's so short that it's effectively zero, and it's easier to treat as if it is, but, doing so (IMO at least) obfuscates a couple of things which are needed to understand the problem at hand.

Which is a surface of a time gone by, how could it capture more photons?

It's the inner surface of a shell, with finite non-zero thickness. As the radius of the shell increases, if its thickness is constant, then its volume increases.

Ok, for the sake of simplicity? My alarm goes off when I see things that doesn't look right, but I understood that it was probably because of simplicity, or that you made the same assumption as many others do that the size of the universe is equal to the distance that light has travelled since the beginning.

Understood. Meanwhile, my point was, and still is that I had assumed that you had infered from the discussion that I was still leaving expansion out of the discussion. It doesn't seem to me that there's a lot of point in discussing an expanding and curved space-time, when you still can't figure out how it can happen in a flat and static one.

But that's a important issue, it can't happen in a static one (it is still remarkably flat as far as we can see), the issues I'm having with time that goes by must be explained by a expanding universe.

The question you asked was why we see the CMBR as a continuous glow when recombination was a single event that occured once. Answering that question does not require consideration of am expanding universe. That question can be answered by considering nothing more than a flat and static minkowski space time.

Ok, you left out that they would have to travel at a increasingly sensitive angle as the universe expands though in order to reach us. The number may seem enormous, but so is the distance to us and the surface area of our detectors in relation to that distance is vanishingly small.

The CMBR has a z on the order of what, 10³?
The surface area of a sphere varies proportionally as r².
(10³)² is 10⁶.
Is 10^(42-6) a big number or a small number?

[Cyperium]

This bit feels like we're going around in circles.

True, let's leave it at that.

And the range of locations is continuous - hence the comment I made about discussing quantized space time.

Ok, I'm satisfied with that answer.

Sort of.
Quantum variations led to variations in density. Variations in density led to variations in temperature.

Ok, so this leads to small differences in the time of the recombination which grows very large in a larger scale.

It's not likely to be something you'll ever see discussed, because comparatively speaking it's so short that it's effectively zero, and it's easier to treat as if it is, but, doing so (IMO at least) obfuscates a couple of things which are needed to understand the problem at hand.

Ok.

It's the inner surface of a shell, with finite non-zero thickness. As the radius of the shell increases, if its thickness is constant, then its volume increases.

Ok.

The question you asked was why we see the CMBR as a continuous glow when recombination was a single event that occured once. Answering that question does not require consideration of am expanding universe. That question can be answered by considering nothing more than a flat and static minkowski space time.

I also asked how we could see that single event (although spread out both in time and space) for more years than that event was old (do you see my problem with that?), that question requires consideration of expanding universe and how it has expanded to allow light to reach us 13 billion years later.

The CMBR has a z on the order of what, 10³?
The surface area of a sphere varies proportionally as r².
(10³)² is 10⁶.
Is 10^(42-6) a big number or a small number?

I don't know, it seems small if we compare it to the distance and the available angles that each photon could travel, I guess that we could calculate what angle a photon would have to have to reach our specific location. We know that photons do reach us from the CMB, so it's just for understanding why, I'm guessing it has already been done though but it's hard to find such figures.

[Trippy]

I also asked how we could see that single event (although spread out both in time and space) for more years than that event was old (do you see my problem with that?), that question requires consideration of expanding universe and how it has expanded to allow light to reach us 13 billion years later.

Don't forget, it's not without its price - space may have expanded by a factor of 1100 in the 13.7 billion years since that photon was emitted, but that photon has performed work getting here, and its wavelength is 1100 times longer than it was when it was emitted.

I don't know, it seems small if we compare it to the distance and the available angles that each photon could travel, I guess that we could calculate what angle a photon would have to have to reach our specific location. We know that photons do reach us from the CMB, so it's just for understanding why, I'm guessing it has already been done though but it's hard to find such figures.

I don't think you're quite getting it.
That number isn't the average number of photons emitted by a given area of the surface of last scattering.
It's the average number of photons emitted in our direction by the surface of last scattering - including accounting for expansion. The total number of photons is orders of magnitude higher than that.

[Cyperium]

Don't forget, it's not without its price - space may have expanded by a factor of 1100 in the 13.7 billion years since that photon was emitted, but that photon has performed work getting here, and its wavelength is 1100 times longer than it was when it was emitted.

I can appreciate that, it has cooled down severely also.

I don't think you're quite getting it.
That number isn't the average number of photons emitted by a given area of the surface of last scattering.
It's the average number of photons emitted in our direction by the surface of last scattering - including accounting for expansion. The total number of photons is orders of magnitude higher than that.

Perhaps I'm not getting it because it's never explicitly stated. What should I know about things they never tell? It gives rise to questions, and if we don't ask them then how can we know?

[Trippy]

Perhaps I'm not getting it because it's never explicitly stated. What should I know about things they never tell? It gives rise to questions, and if we don't ask them then how can we know?

Take a moment to re-examine what I said:

This means that every cubic meter of space at the time of recombination contained an average of 860 million atoms.

According to the wikipedia entry on the Recombination epoch at the time of recombination for every atom there were approximately 1019 photons, so every cubic meter of space also contained 8.6E27 photons.

A sphere with a radius of 42 million lightyears has a surface area of 2E42 km2.
Any given volume of space sees Earth as a hemisphere with a surface area of 255,036,000.
This suggests that the expected number of photons from any single cubic meter of space is 1.1E-6

Which may seem small.

But if the emitting layer is only 1m thick (it's likely to be much thicker than that, IMO), then distributed across the entire sky we would expect to see at any given time 2.2E42 photons of CMBR.

The take home message being that yes, the probability of any individual photon hitting the earth might be vanishingly small, but there were such a huge number, and they were emitted in every direction from every direction, that we expect to see (to a human brain anyway) large numbers of them.

"This means that every cubic meter of space at the time of recombination contained an average of 860 million atoms."
This number is derived from the previously stated density, the previously stated stoichiometric ratio, and Avogadros number.

"According to the wikipedia entry on the Recombination epoch at the time of recombination for every atom there were approximately 1019 photons, so every cubic meter of space also contained 8.6E27 photons."
Derived by multiplying the just calculated 860 million by the stated ratio, to derive the total number of photons per cubic meter.

"A sphere with a radius of 42 million lightyears has a surface area of 2E42 km2.
Any given volume of space sees Earth as a hemisphere with a surface area of 255,036,000.
This suggests that the expected number of photons from any single cubic meter of space is 1.1E-6"

This is where the directionality comes into it - pay close attention to the language:
"Any given volume of space sees Earth as a hemisphere"

And the numbers:
"This suggests that the expected number of photons from any single cubic meter of space is 1.1E-6"
Note that this number is just shy of 34 orders of magnitude smaller than this one:
"so every cubic meter of space also contained 8.6E27 photons..."
Which is the same ratio of sizes between this number:
"A sphere with a radius of 42 million lightyears has a surface area of 2E42 km2"
and this number:
"Any given volume of space sees Earth as a hemisphere with a surface area of 255,036,000."
Finally, observe the language used here:
"The take home message being that yes, the probability of any individual photon hitting the earth might be vanishingly small..."

The point there was that I thought based on what I said, especially that last sentence, that anybody reading it would be able to reasonably infer that I was considering directionality, either through the language used, or be paying attention to the numbers used.

[AlexG]

This suggests that the expected number of photons from any single cubic meter of space is 1.1E-6"

Trippy, the figure I have seen from a number of sources is presently 400 million photons per cubic meter.

[Trippy]

This suggests that the expected number of photons from any single cubic meter of space is 1.1E-6

Trippy, the figure I have seen from a number of sources is presently 400 million photons per cubic meter.

That figure is the number of photons according to my approach that were emitted from the surface of last scattering towards earth, not the number of photons in every cubic meter of space today. I haven't calculated that number, and I'm fairly certain that any figure I did calculate would be an underestimate.

[Cyperium]

I think I understand how it works now, at least more or less

Thanks Trippy for your patience.