The big bang

Passionflower

If you read what I wrote before:

"So what is time? Well for any timelike observer time is the metric distance between two events on his worldline."

You have the answer as to what time is for an observer. Time is observer dependent in GR.

Again, time is the metric distance between two events on a worldline.

Now if you use for instance a Fermi normal coordinate chart in curved spacetime or simply a rest frame in Cartesian coordinates in flat space you can use time (which is then proper time) on one axis so it looks like it is a separate dimension. But just by using such a charts does not make it a dimension.

There is a distinction between the manifold and a choordinate chart and it is a mistake to assume that any of the dimensions of the manifold is time.

Chalnoth

I don't see how this distinction is any different from any of the other dimensions. After all, which dimension on a manifold is "forward/backward"?

Passionflower

What do you mean by "any of the other dimensions"? The manifold is 4-dimensional, but no singe dimension is a spatial or temporal. Only a coordinate chart maps (a region of) this manifold, with or without off-diagonal components, onto 4 dimensions of which one is temporal and three are spatial.

finiter

Dimensions are strictly mathematical. It may or may not represent the physical reality. The real world is just three dimensional. However, to analyze it, we can use one-dimensional or four-dimensional frames.

An expanding system requires a four dimensional frame. As time moves forward, the three space dimensions increase. The spherical surface of the expanding system, or the Gauzian surface described by the three space dimensions, encloses the spacetime. The spacetime can be regarded as the volume at a given time; it is the product of a volume factor and a time factor, ie, it is four dimensional. When the system contracts, the time factor decreases. Mathematically it is time moving back. But in real terms, the direction of time does not change, but the directions of the space dimensions are reversed.

Chalnoth

Right. But your point about time being the metric distance between two space-time points for an observer is important, because the choice of dimensions is not completely arbitrary: the motion of an observer picks out a specific set of them. This indicates, for instance, that while no particular direction on the manifold can be identified uniquely as time, one cannot pick any direction as being time: there are some directions on the manifold which no observer can traverse (because it would mean moving faster than the speed of light).

Chalnoth

While true, the empirical evidence for four dimensional space-time is exceedingly robust.

That would merely indicate that you chose a poor proxy for "increasing time", as increasing time should always be identified with increasing entropy.

AC130Nav

[QUOTE=Chalnoth;2839984]While true, the empirical evidence for four dimensional space-time is exceedingly robust.[QUOTE]

Is it really evidence for FOUR-dimensional space-time? I think quantum mechanics indicates time must have at least two dimensions. After it's absolute nonsense that the observer determines and outcome.

The original evidence for the Big Bang was a uniform background radiation and seeming uniform expansion in all directions. The first was seen as making the formation of galaxies impossible and quickly non-uniformity was found. The second is based on the part of the universe we can observe. Is the world really flat?

Chalnoth

Yes.

Huh? No, not at all. All of quantum mechanics is based around a single dimension of time. And when people try to add a second dimension of time, they end up with closed timelike loops, which many people consider to be contradictory.

Yes, but that doesn't require more than one dimension of time. Everett explained how this works back in the 50's.

Er, it wasn't that quickly. The non-uniformity of the CMB wasn't observed until the early 90's (with the COBE satellite), about 40 years after it was first observed. That isn't very fast in my book. But it was pretty obvious that such non-uniformity had to exist, it was just too small to detect until that time.

finiter

I agree. In the case of universe that is the accepted opinion. But in the case of a theoretical system, is it not possible that entropy decreases with time? Here, I am tempted to question the concept of entropy itself. Is it not logical to take that the entropy of a contracting star decreases, while the entropy of the universe increases? Both are related and there would be symmetry. Matter contracts while universe expands and vice-versa, and expansion would thus be self limited. Of course, this would go against the existing concepts.

Chalnoth

The direction in which time increases is defined as the direction where entropy increases, so the answer is no. This is, by the way, the only way in which you have an arrow of time at all: if the entropy is constant (which would mean the system is at equilibrium), then there is no way to distinguish the past from the future, and there is no arrow of time.

Obviously one has to be careful when describing what one means by "entropy increasing". In general the direction of increasing time is the direction of increasing entropy only for a closed system. If it's an open system, we can still make the same identification, but it requires we take into account anything flowing into/out of the system, so the full statement becomes more complicated.

In general we actually have a rather poor understanding of exactly how entropy relates to gravitational systems, so we don't actually know how to write down the entropy of a contracting star. But we can write down the entropy of a diffuse gas, and we can write down the entropy of a black hole. The entropy of the black hole (which can be seen as a far extreme of the contraction of th star) vastly exceeds the entropy of the diffuse gas from which it came. From arguments like this we understand that the universe becoming more clumpy with time is a manifestation of increasing entropy. In fact, it is this fact, the clumpiness increasing with time, and not the expansion, that is the primary increase in entropy since the end of inflation.

If it were to be the case that our universe were to recollapse (which today seems manifestly unlikely), then we would still expect our universe to become more and more clumpy as it did so.

finiter

Is it not that the entropy of a black hole thus obtained is more speculative than factual?

Chalnoth

No. Basically, a black hole is a much simpler system than, say, a star, and the entropy can be derived through a variety of independent methods, all arriving at the same result: the entropy of a black hole is proportional to the area of its horizon.

Ultimately, understanding the entropy of most systems where gravity is a significant factor (e.g. stars, galaxies) is likely to require knowledge of quantum gravity. But a black hole is just one of those special cases that is mathematically simple enough that we can be quite sure about its entropy already.

finiter

Then, what about the black holes themselves? Are these not just a theortical stuff, that too more mathematical than physical?

One should be sceptical about mathematical models. Mathematics is a tool, in fact, an excellent tool, for analyzing. But of late, it has changed its role, it appears, and has become a shaping tool.

Coming back to black holes, does the scientific community accommodate the Doubting Toms even now, or do the Doubting Toms outnumber the others?

Chalnoth

There are different degrees of skepticism where black holes are concerned. Most today are largely convinced that they are the objects at the centers of galaxies, and also make up one member of certain binary systems. We have some observational tests in the works using extremely large baseline interferometry to actually observe the shape of the event horizon, so in any case we'll be quite sure whether or not these objects are black holes in a few years' time.

The scientific community doesn't kick anybody out. It's just that nobody listens to "Doubting Toms" that don't bring evidence to the table, or worse refuse to pay attention to the evidence we already have. This is the way it works in science: slowly more and more people become convinced of an idea as more and more evidence mounts in support of it. There typically remain some holdouts who continue to seek alternative explanations, and often even if we don't agree with them, the rest of the scientific community recognizes that they provide essential value to the scientific enterprise as a whole because there is always the possibility that we are wrong.

But at the moment my impression of people who do research in the area of black holes has been that the number of people who seriously doubt that black holes are real (or at least are not a very good approximation to reality) is vanishingly small.

AC130Nav

I would expect most who spend time and money looking for black holes to believe in them. But how many have the earlier Hawking belief they are forever (might even be little universes), or adopt the Hawking revision which allows them to dissipate? Hopefully, there are yet other positions.

Obviously, something happens when too much mass gets in one place, ergo some kind of black hole. But math belongs in the experiment phase of the scientific method, not in theory.

Chalnoth

Well, no, this is a false characterization, because we're talking about people who are studying the most compact objects. Whether or not they are black holes is a crucial question that must be answered when studying these objects.

There is no question that black holes evaporate. If they don't evaporate, they're not black holes. It's intimately connected with the entropy calculation I mentioned above.

There have not yet been any compelling alternatives to black holes presented.

I hope you realize that this has been tested? That people haven't merely taken this on faith?

DaveC426913

I don't know what you mean by 'tested'. We can't test the physics of BHs, but our mathematical models of them do explain what we see via (albeit rather remote) observation.