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So the story goes like this:

A long time ago, 13.799±0.021 billion years to be exact, something happened. It was a big bang, loud explosion and universe came to existence. It grew and grew, and now we know that the observable universe is about 93 billion light years in diameter. So it means that

objects that were once close ... are now up to around 45.7 billion light years away rather than up to 13.799 billion light years away ...

Hence my question is that everything is traveling faster than the speed of light?

If it is, then what does it mean in terms of special relativity?

I did read:

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  • $\begingroup$ What I think I know is since space-time can be stretched, light just takes longer to travel between us and a galaxy far, far away. So next logical question is what does it stretch into? I'm not sure it wasn't mentioned in the textbook! $\endgroup$
    – user6760
    Commented Oct 13, 2017 at 4:40

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It was a loud explosion

First, we have to clarify what the Big Bang was. The name is a misnomer, as it was neither loud nor an explosion. All we know is that the Universe is currently expanding — that is, space is literally being created between all matter. We have plenty of answers here explaining this more intuitively, such as mine (which also answers your question about its implications on special relativity).

Anyway, if we were to look further back in time, we'd expect there to be less and less space between matter. Our equations tell us that at 13.8 billion years in the past, the amount of space in the Universe should have been zero.

This is a problem. In general relativity, you can't have a metric with zero space. Thus, we know general relativity is incomplete. It cannot explain what happened at the moment of the Big Bang.

[the] universe came to existence

No such claim is made. All we know is that something must have happened back then. Our current physical models do not accurately represent the extremely early Universe.

Hence my question is that everything is traveling faster than the speed of light?

The expansion of the Universe is not happening at the same rate as it was back then. It is slow enough that everything within our Hubble sphere is receding at a lower velocity.

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  • $\begingroup$ Time axis came into existence at the big bang too. It probably participated in the general "inflation at greater than the speed of light" as well. It's quite easy to hurt yourself thinking about the expansion of a time axis. Did a millisecond become a million years, or what? That sort of thing. Best to leave our everyday mammalian impressions of space-time behind, and just stick with the math. $\endgroup$
    – Wayfaring Stranger
    Commented Oct 12, 2017 at 21:03
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    $\begingroup$ @WayfaringStranger I made a point to be wary of saying anything was "created" at the Big Bang. That is near the point where our physical theories fail to describe the universe. We don't know what it truly was. $\endgroup$
    – Sir Cumference
    Commented Oct 12, 2017 at 21:23
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    $\begingroup$ Everything is receding at v < c within the Hubble sphere, and always has been, by definition. But there's really nothing special about the Hubble sphere, and the remaining ~97% of the observable Universe recedes at v > c. $\endgroup$
    – pela
    Commented Oct 16, 2017 at 22:04
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    $\begingroup$ Okay, I see. I still think that sentence gives the impression that "everything is not receding at $c$ because expansion is slower now than during inflation", though. But during inflation it was exactly the same as today, except that the Hubble sphere was much, much smaller. Some parts recede at v < c, some parts recede at v > c, and it has always been like that. But maybe it's just me… $\endgroup$
    – pela
    Commented Oct 17, 2017 at 10:44
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    $\begingroup$ I understand your last statement as pela did and it seems quite detrimental to your, otherwise nice, answer... $\endgroup$
    – Alchimista
    Commented Oct 20, 2017 at 12:07
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You often hear the phrase: Nothing can travel faster than the speed of light. Which is of course wrong. Public knowledge of physics is filled with somewhat true, but slightly wrong statements from physics. Something just seems to get garbled when taken from the real theories and converted into something the average bystander could understand. A more correct statement would be: Information cannot travel through spacetime faster than the speed of light.

Note the two important parts this: Information and through spacetime. This allows for plenty of cases where something can actually travel faster than light. For example, a galaxy may recede from us at speeds greater than light (and many are) because those galaxies are not travelling through spacetime. Rather spacetime itself is expanding and that can expand as fast as it pleases. Special relativity doesn't limit the expansion speed of spacetime itself, only information traveling through spacetime.

Another example is the EPR paradox by which particles may be quantum entangled and somehow "communicate" over vast distances instantly to achieve the same quantum state at the same time. Clearly if the particles are actually communicating with each other, they'd have to do so at speeds faster than the speed of light. The key in this case is that no information can be transferred between the two particles. That is, they can seemingly know about each others' state via FTL communication but this fact does not allow one to transmit information back and forth (e.g., sending ones and zeros to transmit a message). Since no information can be exchanged FTL this is not a violation of SR.

FWIW, I'm not sure if you're being facetious concerning your "loud explosion" comment, but the Big Bang most certainly wasn't an explosion.

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I do not fully understand how space and time do what they do.

But I'm sure that "universe expanding faster than speed of light" doesn't mean that locally, something (i.e. any bit of information) is moving faster than light. It means to me that particles that already are too far away to exchange any information are becoming increasingly separated by "space" at a rate that can be arbitrarily big.

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