Far from poor, when used in science journals over the whole world. Anyone who denies it is verging on flouting science altogether.

You also said, "What is a second but a man-made calculation?" and "It's true that the last few seconds of existence will seem to be longer, something like 20,000 years. This is true." These led me to believe that you felt time was changing - expanding. That is not the Mainstream view and is not what Minkowski meant.

The expansion of space-time does occur together, but it refers to the expansion of the window of time from t₀ to t_now, not to the expansion of time as we measure it.

Of course, you also said, "It's because everything is relative, but a second is still a second."

So, which is it?

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Never attribute to malice what can be adequately explained by ignorance or stupidity.
Isaac Asimov

That is something completely different Jim. I can site work by Tipler stating that the last few second of existence will seem like an eternity, because everything is relative. This has nothing to do with the original post, but instead an alternative way to look at what the poster above me was saying about time being prolonged, or extended, for whatever reason.

Now Jim, with that cleared up, do we see eye to eye, or will you continue this thread here?

Time doesn't elongate, like expanding a physical system. However, time does expand in respect that space expands.

This can be thought of simply as space expands, time engulfs it as well. this is what is meant by time expands, for it is spacetime expansion.

Try this:
http://www.astro.ucla.edu/~wright/cosmo_03.htm

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Never attribute to malice what can be adequately explained by ignorance or stupidity.
Isaac Asimov

Just for fun and perhaps some edification, let's look at a very simple FRLW style metric expansion:

ds^2 = dt^2 - a(t)*dx^2

This would be a 1T, 1D space-time using a positive time-like convention. a(t) here is a function of time, generally called the scale factor. What does this say in the most general possible case? It says, the "proper distance", which I would tend to call the metric distance because "proper" there just isn't quite proper, between space-like events (those that occur at constant coordinate time, t = somethng), varies with time according to our a(t) function.

Ie, if we have events at (x1, t) and (x2, t), the metric distance between them is going to depend on t. If a(t) is an increasing function of time, then we can say "space is expanding", as the metric distance between those events increases with time.

Now, what would be meant by "time is expanding" in the same sense? Well, it would suggest we put a b(t) on the time part of our metric:

ds^2 = b(t) *dt^2 - a(t) * dx^2

That would mean the proper time between events at constant x would depend on the time coordinate t. Now, that's just a "silly clock", indeed. That's a clock whose hands are speeding up or slowing down with time-- proper time is proper time, and that's what a proper clock measures. So all we do there is make a substitution, dT^2 = b(t)*dt^2, and replace t by T and get rid of that silly clock. Doing that would change a(t) into some a(T), of course.

So making the time part depend on time is sort of a silly operation that can be transformed away -- and there would be an equivalent thing to do on the space side, have some a(x) where the metric distance depended on the x coordinate, and that's done all the time, Schwarzschild for instance. That doesn't seem so silly, of course, and that's sort of the difference in how we think of time coordinates and spatial coordinates. (yes, space and time certainly get mixed, but there is a difference between time-like and space-like coordinates. One observer's time is some mixture of the time and space of another observer, but his time is still time-like, IOW)

So making "time depend on time" just doesn't make much sense, although it might have some mathematical utility in some situations I can imagine. But what is the difference between this and expanding space? Well, that means distance depends on time. The reverse of that would be "time depends on distance".

The former is distance goes as a(t)*dx^2 and the latter would be simply time goes as b(x)*dt^2. And that happens all that time with various metrics. In Schwarzschild, our b(x) is simply (1 - R/r). That is, the proper time between events occuring at the same coordinate spatial location depends on the spatial location. That is the analog of the "proper/metric" distance between events occuring at the same coordinate time depends on the time.

We call the latter "expanding space", but we don't call the former expanding time. But you might say "time expands with distance" if you like there, but the notion of expandING, that "ING" implies a process occuring with time, not with space.

-Richard

Jim, i do not understand the arguement of this page. We can work with models that are flat, but Einstein proved the universe was curved, and the big implication of this is that time was also a spatial coordinate. Do you understand this?

Time slows as one approaches a black hole or any gravitational source ... a clock runs slower on the top of a mountain on earth than it does at sea level.

Also speed compresses time as you near the speed of light.

If space expands ... then time has to expand or c is no longer a constant

The first two are true. The last one might or might not be, or the speed of light in the universe may change over time or with expansion, or something else. In any case, what Grant and Richard said still stands. Time is relative. I would say that time is just a measure of a comparison of motion to begin with, so with a black hole or relative speed, one can stand "outside the box" and say that time is passing differently for another. We measure time with our own clocks. But if all of the universe slowed or sped up at the same rate than there is no outside by which to compare motions in order to say that one is moving or aging faster or slower than another. The clocks still tick at the same rate that observers within the universe view them and age. It is similar to the reason that we dismissed the idea of an ether, since we couldn't observe it directly, although it couldn't be proven or disproven, but within the domain of Einstein's relativity, it wasn't necessary.

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Let's put together the pieces of The Grand Puzzle . (website)

"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."

Time is Relative, Lunchtime doubly so.

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'The eye can only see what the mind is prepared to accept'

Oh very deep. You should send that into Reader's Digest. They have a page for people like you.

( )

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Carl Matherly

Offical Battlestar Galactica Apologist

Named Time Magazine's 2006 "Person of the Year"

Drink your Beer

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'The eye can only see what the mind is prepared to accept'

Space expands and contracts but time runs faster or slower. If we choose Einstein’s c as a constant then both space and time are necessarily variables. So, if space expands, then time must also "expand" or (I think you mean to say) accelerate. When time accelerates, our clocks run faster. I don’t mean clocks in the mechanical sense but in the broader sense that everything the natural world is a form of clock. When time accelerates, atoms move faster, wavelengths grow shorter, rocks fall faster, etc.

We can’t separate space from time and what to do with time as a dimension has always been a big problem. I prefer the view that we have four dimensions of space-time called height, width, depth, and duration. Time is a part of all four and not really a dimension by itself but there are many other valid points of view including using time as a fourth dimension.

Einstein’s c is the absolute of choice in GR and SR but we can also use time as an absolute while c and space are variables or we can use space as an absolute while time and c are variables but you are right that we can’t use both c and time as absolutes in the same model.

So earlier in the history of the universe did atoms move slower, were wavelengths longer, did rocks fall slower?

That's right...and distances were shorter but light, like everything else, was slower relative to our "now" so an observer back then would still measure c as c even though his meter stick was shorter and his clock ran slower.

Then when we extrapolate back in time wouldnt we have a singularity of low energy ( around the average energy density of the current universe ) rather than a singularity of near infinite energy ( all of the energy in the universe compacted in a singularity ) ?

Light was slower in the past than it is today? How did you come to this conclusion?

Sounds like most of the people in this thread, publius and some of the referenced sources excepted, are trying to argue about consequences of a theory based on a word description of that theory rather than from the mathematical description.
This is almost invariably going to go wrong.

There's nothing wrong with describing results in words, but unless you get those results by applying the maths, there's not a high chance you'll get the description right.

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who said that ... c = c

Occam's Ghost, you are both right and wrong.

You are correct in that in terms of relativity, space and time are treated mathematically as an entity together. Despite this however, the way that space and time are treated is slightly different from one another. Check the literature.

The observed expansion of the universe is explained by General Relativity as an expansion of the metric with respect to time. A metric is simply a way of defining a coordinate system so that you can measure distances between two points.

So, your initial assumption that spacetime is expanding is borne out of a misunderstanding of relativity. It is like asking everyone here to prove that apples are oranges. With respect, it is a nonsensical proposition.

Hope this helps.