How is the universe expanding faster than the speed of light?
The resolution of this apparent problem comes down to understanding the difference between the idea of expansion, and that of motion. Read on...
The issue is solved if we understand that what we mean when we say "the universe is expanding" is the expansion of spacetime, which is distinct from the motion of the material objects that are inside the universe. Spacetime is the rather abstract construct of three spatial dimensions and time that acts as the "container" for all material in the universe; it is not a material body.
A common analogy is to picture two dots on a balloon's surface; when we inflate the balloon, the dots move apart because the surface is expanding rather than because they are traveling over it.
It is believed that the universe expanded at a rate that was many times faster than the speed of light during the inflationary phase, when it was still very, very young and smaller than your house!
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The speed of light is not the limit to the expansion of the universe; galaxies can expand faster than the speed of light due to the metric expansion of space, but individual objects within galaxies cannot expand faster than the speed of light.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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