Big Bang: Faster than the Speed of Light?

[mtasquared]

Hello everyone. Thought of this question while at work. I've read the universe appeared out of nothing and expanded very rapidly to near its final state. Would that be flinging matter faster than the speed of light?

 

[PeterDonis]

I've read the universe appeared out of nothing

It's worth noting that we don't really know whether this is true. There are various speculations that there might have been something there before the Big Bang--for example, that the Big Bang was a quantum fluctuation in some underlying field. That doesn't really affect the rest of your question, but it's always good to keep in mind the limits of what we actually know.

and expanded very rapidly to near its final state.

If by "final state" you mean the state it is in now, this isn't quite true. The inflationary epoch only got the universe to a size that is sub-microscopic on our ordinary scale of sizes. The rest of the expansion, after inflation ended, was much slower, which is why it's taken close to 14 billion years for the universe to get to its present size.

Would that be flinging matter faster than the speed of light?

No, because "speed" is not really a meaningful concept when applied to the expansion of the universe itself, as opposed to the relative motion of objects within the universe. The prohibition on matter not being able to move faster than light only applies to the relative motion of objects within the universe: a given piece of matter can't move faster than the light in its immediate vicinity. That was true even during the inflationary epoch.

 

[Mordred]

this article will expand on PeterDonis reply, its essentially a FAQ style article of observations of the hot big bang model in the current form $\Lambda$CDM.. which is essntially the hot big bang model with cold dark matter.

"What we have learned from Observational cosmology"

http://arxiv.org/pdf/1304.4446v1.pdf

As mentioned the BB model does not attempt to describe our beginnings, it merely states we had a hot dense state near its beginnings and expanded from there due to both inflation and expansion.

 

[mtasquared]

Thanks for responding Peter Donis and Mordred and the very interesting info! I have another, tangential question for you (or anyone with a minute) that probably stems from ignorance. I haven't studied relativity. Say you have three observers, with two of them traveling in exactly opposite velocities. To the third observer the maximum speed they can reach is 1/2 the speed of light in opposite directions, correct, since their total velocity must be less than the speed of light? And must it not be that the speed of one of the two observing observers is somehow dependent on the other opposing observer when viewed from the third observer as the sum of their respective speeds to the third observer must somehow always be less than the speed of light? So in our universe we see galaxies speeding away from the Earth at the near speed of light in one direction; but somehow that 'speed' is dependent on the speed of galaxies moving in the exact opposite direction?

 

[Mordred]

objects can appear to be traveling faster than the speed of light, however the objects themselves cannot travel at the speed of light. For example as a consequence of the recessive velocity * distance relation of Hubbles law

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity_recessive = H₀ × distance.

Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

Objects beyond a certain point can appear to be going faster than the speed of light, however if you were to teleport there and observe the object locally it is not. From Earth objects near the furthest observations in the universe "Appear to be traveling at 3C."

take another example observer a is traveling west at 0.9c object b is traveling east at 0.9c. their separation speed from both observers will be 1.8c however neither object is traveling at greater than c locally

 

[Nugatory]

Say you have three observers, with two of them traveling in exactly opposite velocities. To the third observer the maximum speed they can reach is 1/2 the speed of light in opposite directions, correct, since their total velocity must be less than the speed of light?

No, not correct. Observer A can be traveling to left at .99c relative to observer C, and observer B can be traveling to the right at .99c relative to observer C without any problem.

The key point here is that A's speed relative to B will not be .99c+.99c - velocities do not add linearly in relativity, so A's speed relative to B is not just the sum of A's speed relative to C plus B's speed relative to C. Instead, if A's speed relative to C is $u$ and B's speed relative to C is $v$, then A's speed relative to B will be (measuring time in seconds and distances in light-seconds so that $c$, the speed of light, is equal to one) $\frac{u+v}{1+uv}$

That's true for ordinary non-relativistic speeds as well, it's just that if $u$ and $v$ are small compared with the speed of light, this formula is indistinguishable from the $u+v$ which you are assuming.

 

[Drakkith]

Thanks for responding Peter Donis and Mordred and the very interesting info! I have another, tangential question for you (or anyone with a minute) that probably stems from ignorance. I haven't studied relativity. Say you have three observers, with two of them traveling in exactly opposite velocities. To the third observer the maximum speed they can reach is 1/2 the speed of light in opposite directions, correct, since their total velocity must be less than the speed of light?

No, from observer 3's frame of reference both ships can be traveling at any velocity less than c, whether it's 0.5c, 0.99c, or higher. For example, if both ships are traveling at 0.9c away from observer 3, then the distance between them, as viewed by observer 3, will increase at 1.8c. But that's okay, because no one is traveling at 1.8c relative to anyone else. Both ships are moving at 0.9c relative to observer 3, but they are moving at about 0.995c relative to each other due to the way velocities add in special relativity.

See here: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html

And must it not be that the speed of one of the two observing observers is somehow dependent on the other opposing observer when viewed from the third observer as the sum of their respective speeds to the third observer must somehow always be less than the speed of light? So in our universe we see galaxies speeding away from the Earth at the near speed of light in one direction; but somehow that 'speed' is dependent on the speed of galaxies moving in the exact opposite direction?

The extreme recession velocity of galaxies is due to the expansion of space, which takes place under General Relativity rules, not Special Relativity rules. In GR, objects can recede from each other at any velocity, even much greater than c, due to the way expansion works. In short, there is no acceleration that you could measure with an accelerometer and no galaxies get any closer to any other galaxies. The distances between all galaxies not bound together by gravity increases over time. This is not movement "through" space, but "with" space, to use an analogy.

 

[mtasquared]

Thank you very much, PeterDonis, Mordred, Nugatory, and Drakkith for these insights and the article links. I am motivated even more to read about this subject, as many intuitive notions on my part seem to fail. It seems to me that the 'receding into the unreachable' nature of the most distant observable things (and the space they occupy?) is a kind of mercy for the mind, if true, because it relieves us of the burden of confirming whether the universe is limitless or 'limited'. It is unobservable.

 

[PAllen]

objects can appear to be traveling faster than the speed of light, however the objects themselves cannot travel at the speed of light. For example as a consequence of the recessive velocity * distance relation of Hubbles law

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity_recessive = H₀ × distance.

Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

Objects beyond a certain point can appear to be going faster than the speed of light, however if you were to teleport there and observe the object locally it is not. From Earth objects near the furthest observations in the universe "Appear to be traveling at 3C."

take another example observer a is traveling west at 0.9c object b is traveling east at 0.9c. their separation speed from both observers will be 1.8c however neither object is traveling at greater than c locally

I have to quibble with this. A recession velocity is not an apparent velocity in any normal sense. First, note that recession velocity can approach 2c in Minkowski coordinates when you have oppositely moving objects. Further, in flat spacetime, in Milne coordinates, you can have recession velocity much larger than 2c. None of these are considered apparent velocities, because no such object is considered to move >c relative to a given object.

We observe a given Doppler from distant galaxies. Any Doppler factor, however large, corresponds to a relative velocity < c.

The greater than c recession velocity is growth of proper distance along comoving simultaneity slices by cosmic time. It is not an apparent velocity for any given observer.

 

[Mordred]

Your right, I should have been more clear on that, I didn't describe that accurately.