# Event horizon ad the age of our universe

## Main Question or Discussion Point

I am currently reading "Our Mathematical Universe" by Max Tegmark. From the book I learned a couple of things I find startling:

1. The event horizon, beyond which galaxies run away from us faster than light and hence cannot be seen by us, is about 14 billion light years away.

2. Our universe is about 14 billion years old, and hence at the distance of 14 billion light years, we can only "see", with microwaves, the plasma of the Big Bang.

Now, isn't it a strange coincidence that it is 14 billion years / light years in both cases? I see no reason that these figures should be the same.

Also, wouldn't one the following alternatives occur, assuming that the rate of expansion is constant (actually, we now know that it is accelerating, but let us forget that for the sake of argument):

A. The distance to the event horizon (in light years) is greater than the age of our universe (in years). In this case, we cannot see galaxies run away from us with near light speed, even in principle with infrared radiation, because not enough time has elapsed since the Big Bang for galaxies visible to us to obtain such speeds relative to us.

B. The age of our universe (in years) is greater than the distance to the event horizon (in light years). In this case, we cannot "see" the background microwave radiation caused by the Big Bang, becuse the plasma emitting the radiation is beyond the event horizon and hence cannot be seen by us, even as microwaves.

So, we cannot both detect the background radiation and "see" galaxies run away from us by near light speed.

How is this changed if we (correctly) assume that the expansion is accelerating?

Bandersnatch
Is that really correct, craigi?

Jorrie's LightCone calculator(http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html) shows the cosmic event horizon to currently be at ~16.5 Gly.

The definitions you both use seem off as well. The cosmic event horizon is the proper distance from which a signal emitted now will be able to reach us. The distance at which recession velocities begin to exceed c is the Hubble radius(currently ~14.4 Gly).

The age of the universe(elapsed time of expansion) is estimated at 13.8 Gly. The particle horizon - where the fartherst stuff we see(CMBR) is NOW, is 46.3 Gly away.

Note, none of these figures are the same. It's only if you apply some generous rounding, can you throw two of them in the same bucket of 14 billion light years.

phinds
Gold Member
2019 Award
1. The event horizon, beyond which galaxies run away from us faster than light and hence cannot be seen by us, is about 14 billion light years away.
I am sorry to hear that you have "learned" that, since it is not true. The cosmological event horizon (as opposed to the EH of a black hole) is the distance beyond which things emitting light "now" are too far away in the expanding universe for their light to ever reach us but it is NOT the point at which things start receding at c.

Galaxies at the edge of our observable universe, which we clearly CAN see, are receding from us at about 3c. Galaxies receding at just over c are somewhat closer and of course can also be seen.

Is that really correct, craigi?

Jorrie's LightCone calculator(http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html) shows the cosmic event horizon to currently be at ~16.5 Gly.

The definitions you both use seem off as well. The cosmic event horizon is the proper distance from which a signal emitted now will be able to reach us. The distance at which recession velocities begin to exceed c is the Hubble radius(currently ~14.4 Gly).

The age of the universe(elapsed time of expansion) is estimated at 13.8 Gly. The particle horizon - where the fartherst stuff we see(CMBR) is NOW, is 46.3 Gly away.

Note, none of these figures are the same. It's only if you apply some generous rounding, can you throw two of them in the same bucket of 14 billion light years.
Yeah, my post wasn't correct, so I deleted it. I followed the information in the original post, which isn't correct. Did the original poster confuse parsecs with light years?

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Well, Wikipedia gives a bunch of recent measurements of the Hubble parameter. It seems to be about 70 km/s/Mpc. The value H=70 gives the cosmic event horizon d=c/H=14.0 billion light years, very close to 13.7 billions in my opinion.

But I see no reason that those two values should be equal. Since the value of H seems to decrease for every new measurement, the cosmic event horizon seems anyway to be somewhat greater (in light years) than the age of the universe (in years).

So this means, then, that we cannot see distant galaxies run away from us approaching light speed...?

Again, I have not taken into consideration that the expansion is accelerating.

I am sorry to hear that you have "learned" that, since it is not true. The cosmological event horizon (as opposed to the EH of a black hole) is the distance beyond which things emitting light "now" are too far away in the expanding universe for their light to ever reach us but it is NOT the point at which things start receding at c.

Galaxies at the edge of our observable universe, which we clearly CAN see, are receding from us at about 3c. Galaxies receding at just over c are somewhat closer and of course can also be seen.
Yes, but that is because they have reached those high speeds long after they emitted the light (or radiation) we see (or measure) today. The speeds by which we see them run away from us are certainly less than c. The distance I meant (which is then perhaps called something else) is d=c/H, where H is Hubble's constant, and this must be the distance at which we would see galaxies run away with speeds approaching c, if the universe is sufficiently old, which it seems not to be.

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phinds
Gold Member
2019 Award
Yes, but that is because they have reached those high speeds long after they emitted the light (or radiation) we see (or measure) today. The speeds by which we see them run away from us are certainly less than c. The distance I meant (which is then perhaps called something else) is d=c/H, where H is Hubble's constant, and this must be the distance at which we would see galaxies run away with speeds approaching c, if the universe is sufficiently old, which it seems not to be.
I'm sorry, it's early for me today and I'm not following what you are saying. That's probably just me.

At any rate, just to be clear, the galaxies which are now receding from us at 3c are inside our observable universe and will ALWAYS be inside our observable universe, meaning that any light they emit "now" WILL evenutally reach us even though they are receding at > c. By the time it gets here it may be so red shifted that it will be nearly impossible to detect but it WILL get here.

I see. I belived that just because a distant object moves away from us faster than light, then it cannot be seen. But I now understand that this is wrong. If the universe would be both infintely large and infinitely old, we can in principle see all of it, no matter how fast distant objects move away from us.
That we cannot see everthing in our universe is just because the light from sufficiently distant objects has not had time enough to reach us since the universe came into existence.

Thank you!

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phyzguy