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I have read answers to several similar questions but I still don't get it. Earlier explanations seem to say that laws of quantum physics and general relative are different. Let me get this straight. As I understand things, planck length divided by planck time is the speed of light. Is that just a coincidence? If not, the speed of light, C, must be a constant ratio of Planck length/time. Correct? If only space expands, that would increase Planck length, which would change the ratio and thus the speed of light. Therefore, I am lead to believe that Planck length and Planck time must expand proportionally or the speed of light would not be constant. Where have I gone wrong? Please tell me why only space expands rather than spacetime.

Please don't overwhelm me, a novice, with complex equations that I can't handle yet. Many thanks.

Qmechanic
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Baird1939
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    time is expanding at a rate of 1 second per second – Señor O Dec 26 '18 at 21:01
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    @SeñorO Using your logic, space is expanding at a rate of 1 meter per meter. – safesphere Dec 27 '18 at 01:00
  • Planck units are only relevant for quantum gravity. We don't have a theory of quantum gravity. –  Dec 27 '18 at 01:32
  • Instead of clarifying the question, the Planck units only create more confusion. Your question is perfectly meaningful at the macroscopic level. For example, does an increase of the scale factor in the Friedman metric imply a change in the speed of light over time? This paper has some relevant discussion, if you can get through the terminology: https://academic.oup.com/mnras/article/421/4/3356/1094860 – safesphere Dec 27 '18 at 03:47
  • As John Rennie said in answer to the question you found yesterday, "[...] when we're describing the universe we start with the assumption that time isn't expanding or contracting. That is, we choose our coordinate system to make the time dimension non-changing". General relativity lets us to do that, it's very liberal in allowing us to use whatever coordinate system is convenient for a particular problem – PM 2Ring Dec 27 '18 at 04:02
  • @safesphere no because an "expansion rate" requires units with time in the denominator. You could conceive of a 3-D space that's expanding at a rate that's a specific volume/time. The space could get to a maximum volume before contracting. You can't say the same for time, since the 'time axis' of the 4-d spacetime is always increasing, and the rate at which it increases depends on our definition of units. – Señor O Jan 06 '19 at 17:55
  • @SeñorO Right, the local speed of light is always one light-second per second no matter what. However, a remote speed of light can be different. Here "remote" usually means "at a distance", but my comment above refers to the speed of light in a distant past. If light-second was different due to the space expansion, second also had to be different to keep the ratio as unity. – safesphere Jan 06 '19 at 19:02

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Planck's time results from a dimensional analysis involving the gravitational constant $G$, the speed of light $c$ and the reduced Planck constant $\hbar$, the result is

$$ t_p = \sqrt{\frac{\hbar G}{c^5}} $$

This is a constant of nature independent of expansion, that is $t_p$ had the same value 1Gyr ago, and 13 Gyr ago. Now you define Plank's length as

$$ \ell_p = c t_p $$

Again, this is a definition. If the universe expands, the ratio remains constant because $c$ remains constant

caverac
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Is it spacetime or space that is expanding?

Its both. But its better said that it is spacetime that is expanding and hence space is expanding too, since - obviously - space s a part of spacetime. The metric, the way we measure space and time remains the same (otherwise we would see no difference).

Dark energy is responsible for the expansion. It's essentially the energy carried by empty spacetime itself. It's the physical notion that corresponds to the cosmological constant term in Einsteins equation. Another way of thinking about it is that its a new force that only kicks in at the cosmological scale - we could call it the cosmological force to go along with the four forces - strong, weak, electromagnetic and gravitational.

Mozibur Ullah
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    This is wrong. Spacetime is not expanding, and dark energy is not responsible for cosmological expansion. –  Dec 28 '18 at 01:18
  • @Ben Crowell: Not according to Susskinds book on black holes. Do you have a reference for your statement? I appreciate that there are more than one point of view in cosmology, and perhaps Susskinds view is not mainstream. – Mozibur Ullah Dec 28 '18 at 13:53
  • I see that there are two or more opinions. Perhaps, I should keep monitoring the answers until I see some kind of resolution. But is it possible that space and spacetime are expanding in parallel? What would that mean anyway? Thanks for all your efforts. – Baird1939 Dec 29 '18 at 00:33