# How long was the first second?

I'm currently reading "Many Worlds in One: The Search for Other Universes" by Alexander Vilenkin to entertain my curiosity in cosmology and metaphysics while applying to medical school. Anyhow, the current chapter is discussing George Gamow and his thoughts on the nature of the universe at the exact moment of and immediately following the Big Bang. One sentence struck me as curious when it said "the most eventful part of the fireball history, marked by a rapid succession of exotic particle populations, occurred during the first second of its existence." How is this second measured? Is it a second as we would perceive it here on Earth, or would this first second last on the order of an infinite number of years relative to Earth seconds due to the rate at which space was expanding during the first second (measured in "Big Bang seconds")?

PeterDonis
Mentor
2019 Award
How is this second measured?

Like this:

http://physics.nist.gov/cuu/Units/second.html

would this first second last on the order of an infinite number of years relative to Earth seconds due to the rate at which space was expanding during the first second (measured in "Big Bang seconds")?

No. The second (at least as it's currently defined, as above) is an unchanging unit of time; it's the same everywhere and at all times.

Like this:

http://physics.nist.gov/cuu/Units/second.html

No. The second (at least as it's currently defined, as above) is an unchanging unit of time; it's the same everywhere and at all times.
Okay, so when the book says "the first second of the universe," it does indeed mean the same 1/3600 of an hour we experience on Earth? If so, then what are the implications of the rapid rate of expansion in terms of general relativity? Would the annihilation of elementary particles take place at a slower rate than they would in a less rapidly expanding universe (e.g. today)?

Staff Emeritus
2019 Award
You seem not to like the statement "The second is an unchanging unit of time; it's the same everywhere and at all times." Why not?

PeterDonis
Mentor
2019 Award
so when the book says "the first second of the universe," it does indeed mean the same 1/3600 of an hour we experience on Earth?

To the extent there is a meaningful comparison between the Earth now and the early universe, yes.

what are the implications of the rapid rate of expansion in terms of general relativity?

In terms of "rate of time flow", none.

Would the annihilation of elementary particles take place at a slower rate than they would in a less rapidly expanding universe (e.g. today)?

No.

You seem not to like the statement "The second is an unchanging unit of time; it's the same everywhere and at all times." Why not?

To the extent there is a meaningful comparison between the Earth now and the early universe, yes.

In terms of "rate of time flow", none.

No.

Why do I dislike the statement "the second is an unchanging unit of time; it's the same everywhere and at all times?" Thus far, everyone who has taught me anything about relativity has stated "as you approach the speed of light, time slows down." Of course, you are helping me understand that the second is a constant unit of measure, but it is understandably difficult to come to terms with a new piece of information that conflicts with a strongly held previous belief. When I asked about the "implications of the rapid rate of expansion in terms of general relativity," my intent was to expand the discussion beyond the "rate of time flow," seeing as I was already informed that the answer would be "none."

My expertise is in chemical engineering and human biology. Lacking formal training in physics beyond the introductory college level, I came here to learn more about the book I'm reading and explore certain topics in greater detail. Quite frankly, both of your reluctance to elaborate upon what is likely a very common misunderstanding is frustrating. It's disappointing to have such a negative first impression of this community. I'm sorry if I've misinterpreted either of your intentions.

PeterDonis
Mentor
2019 Award
Thus far, everyone who has taught me anything about relativity has stated "as you approach the speed of light, time slows down."

Unfortunately, that is a misleading way of putting it, because, as you are now finding out, it leads you to a false inference.

Have you looked at any textbooks on relativity?

When I asked about the "implications of the rapid rate of expansion in terms of general relativity," my intent was to expand the discussion beyond the "rate of time flow,"

In what way would you like to expand the discussion?

What I'm getting at here is that you are asking very general questions, so all you're getting are very general answers. If you could narrow things down to a more specific scenario, we could try to give more specific information.

The first thing I would say is that the book you are reading is about a very advanced topic, one which you can't really get a better understanding of without having a firm foundation in simpler topics. It is as if you were trying to understand an advanced topic in chemical engineering without having a firm understanding of the periodic table of the elements.

both of your reluctance to elaborate upon what is likely a very common misunderstanding is frustrating.

It's fairly common for people to misinterpret pop science presentations of relativity, yes. But everyone's misinterpretation is different. Without more specific information from you, such as picking a specific scenario and asking how it would be modeled in relativity, we can't know what particular misinterpretation you are making, out of the wide variety of possible misinterpretations.

For example, you said you want to expand the discussion around the rapid rate of expansion of the early universe. What effects do you think such a rapid rate of expansion would have? Or, to take a step back even further, what do you think "rapid rate of expansion" means?

Chalnoth
Why do I dislike the statement "the second is an unchanging unit of time; it's the same everywhere and at all times?" Thus far, everyone who has taught me anything about relativity has stated "as you approach the speed of light, time slows down."
Right. This kind of description of relativity is quite confusing.

What relativity actually says is that different observers will observe one another's clocks running at different rates, depending upon those observers' relative motions or positions in a gravitational field. Each observer, however, always sees their own clock running at the same rate, no matter what.

phinds
Gold Member
2019 Award
Thus far, everyone who has taught me anything about relativity has stated "as you approach the speed of light, time slows down."
You, right now as you read this, are traveling at about .999999c from the reference frame of a particle in the CERN accelerator. Did your time slow down any?

If 'a second' (locally) was a variable then you would need another dimension of time in order to describe it's value at some given moment.
Seconds per second?
Occams razor prefers time to be one dimensional.

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Chalnoth
If 'a second' (locally) was a variable then you would need another dimension of time in order to describe it's value at some given moment.
Seconds per second?
Occams razor prefers time to be one dimensional.
There are also theoretical problems with multiple time dimensions, namely that they result in causal paradoxes.

Garth
Gold Member
If 'a second' (locally) was a variable then you would need another dimension of time in order to describe it's value at some given moment.
Seconds per second?
Occams razor prefers time to be one dimensional.

Following on from Chalmoth's comment, we can also add that as a logical tautology time can only pass at "one second per second" for any particular observer.

Relativity deals with the measurement of time in one observer's frame of reference as measured by another observer in a different frame of reference, and if the observers are moving relative to one another then that is when the first observer's clock appears to slow down as observed by the second observer, and vice versa.

That first observer however will need some kind of clock to measure that second, otherwise how would they know when that second has 'passed'? If it is physical time we are talking about, as we are, then we need some kind of physical clock to measure it by.

Many years ago I was in a postgraduate lecture on cosmology that was discussing events in the first microseconds of the universe's history, after which one of the professors in the audience asked, "What do you mean by the first second?" i.e. How do you measure it, and with what type of clock? So the OP question is a quite profound one.

If we indeed define a second by "The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." then in order to demonstrate that that second is an unchanging unit of time we have to have an unchanging caesium atom, which might be difficult to prove in the first second when there were no caesium atoms around!

As the radiation corresponding to the transition between the two levels, n and n', of the caesium 133 atom is dependent on
$\nu = \frac{2\pi^2mZ^2e^4}{h^3}\vert\frac{1}{n^2}-\frac{1}{n'^2}\vert$ , in order for a second to be an "unchanging unit of time" we have to demonstrate that m or e does not change over those cosmological time scales.

In GR they do not, but in alternative cosmologies such as conformal gravity theories, varying fine structure constant theories, or a mass field theory such as that of Hoyle (see for example http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...196..661H&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf [Broken],) they do vary.

If the physical process that calibrates the clock is allowed to vary then that would affect the response to the question, "How long was the first second?"

It would depend on which clock you measure it by.

Garth

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xAxis