Big Bang: Discovering the Reasons Behind Its Occurrence

[Passionflower]

To address a common misunderstanding: time is not an actual dimension on the manifold.

The confusion arises because often a coordinate chart is used where an observer's x₀ (or sometimes denoted as t) is identical to his proper time. For instance a rest frame in Minkowski spacetime using Cartesian coordinates or Fermi normal coordinates in curved spacetimes.

Curved spacetime is a four dimensional manifold but no single dimension is explicitly time.

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

In GR worldlines can simply end (at a singularity), by time symmetry (and GR is time symmetric) that implies that worldlines can simply begin as well. Hence according to GR it is possible that for a given observer time can have a begin and an end.

 

[Chalnoth]

To address a common misunderstanding: time is not an actual dimension on the manifold.

The confusion arises because often a coordinate chart is used where an observer's x₀ (or sometimes denoted as t) is identical to his proper time. For instance a rest frame in Minkowski spacetime using Cartesian coordinates or Fermi normal coordinates in curved spacetimes.

Curved spacetime is a four dimensional manifold but no single dimension is explicitly time.

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

In GR worldlines can simply end (at a singularity), by time symmetry (and GR is time symmetric) that implies that worldlines can simply begin as well. Hence according to GR it is possible that for a given observer time can have a begin and an end.

Well, obviously there's ambiguity as to which sort of direction on the manifold we can identify with time. There is no definitive direction that is associated with time, and different observers will see time as being different directions on the manifold. But then, this is the same with all other directions as well, so time isn't exactly special in regard to this ambiguity.

 

[FizixFreak]

Well, obviously there's ambiguity as to which sort of direction on the manifold we can identify with time. There is no definitive direction that is associated with time, and different observers will see time as being different directions on the manifold. But then, this is the same with all other directions as well, so time isn't exactly special in regard to this ambiguity.

so may i say that time is a direction but the answer of WHICH DIRECTION changes with observer?
or may be that time exists within the three dimensions of space occupying some part of all three dimensions?

 

[Chalnoth]

so may i say that time is a direction but the answer of WHICH DIRECTION changes with observer?
or may be that time exists within the three dimensions of space occupying some part of all three dimensions?

No, time is definitely separate from the three dimensions of space. Which direction in space-time you see as time depends upon things like your velocity and acceleration.

Mathematically, time is exactly the same as the other dimensions, except that the sign of a metric component associated with time is opposite from the spatial dimensions. For example, if the spatial dimensions have positive metric components, then time has a negative metric component. With this convention, if you find the metric distance between two different times for a particular observer, you get a negative number (a timelike distance...this is the actual time that the observer sees on their clock). If you find the metric distance between two simultaneous events, by contrast, you get a positive number (a spacelike distance: this is the distance you would measure between these events in a reference frame where they occur simultaneously).

Finally, if you find the metric distance between two points in the travel of a light ray (for example, from when a light ray is emitted to when it is absorbed), you always get zero. So light rays themselves act as a boundary between timelike distances and spacelike distances.

 

[Passionflower]

so may i say that time is a direction but the answer of WHICH DIRECTION changes with observer?
or may be that time exists within the three dimensions of space occupying some part of all three dimensions?

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.

Mathematically, time is exactly the same as the other dimensions, except that the sign of a metric component associated with time is opposite from the spatial dimensions. For example, if the spatial dimensions have positive metric components, then time has a negative metric component.

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]

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.

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]

I don't see how this distinction is any different from any of the other dimensions.

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]

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.

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]

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.

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

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.

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

 

[AC130Nav]

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

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]

Is it really evidence for FOUR-dimensional space-time?

Yes.

I think quantum mechanics indicates time must have at least two dimensions.

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.

After it's absolute nonsense that the observer determines and outcome.

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

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?

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]

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

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]

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?

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.

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.

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]

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.

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

 

[Chalnoth]

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

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]

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.

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]

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

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.

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

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]

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.

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]

I would expect most who spend time and money looking for black holes to believe in them.

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.

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?

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.

Hopefully, there are yet other positions.

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

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.

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

 

[DaveC426913]

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

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.

 

[Chalnoth]

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.

Well, theories are only really tested in science through the collection of a variety of independent sources of evidence. When the evidence from many directions all agrees with a given theory, and no compelling alternatives are presented, most scientists become convinced that the theory is at least approximately true. From what I gather from those who study this sort of thing, black holes passed that point some time ago.

Now, we may speculate wildly as to whether or not the objects we currently call black holes may be something that we haven't thought of yet. And they may be. But there isn't really a good way to actually go out and investigate the vague notion of, "something we haven't thought of yet," so it only makes sense to provisionally accept the theory we have until such time as evidence is presented that contradicts this.

Edit: And I'd like to point out that I purposely don't often express this level of skepticism, because it turns out that once a majority of scientists become reasonably convinced something is true within their own field of study, that is almost never overturned. In fact, I can't think of a single situation where this has occurred since the onset of modern science (say, about 150 years ago for physics, give or take). The possibility always remains, of course, but it's just unlikely.

 

[AWA]

I'd like to point out that I purposely don't often express this level of skepticism, because it turns out that once a majority of scientists become reasonably convinced something is true within their own field of study, that is almost never overturned. In fact, I can't think of a single situation where this has occurred since the onset of modern science (say, about 150 years ago for physics, give or take). The possibility always remains, of course, but it's just unlikely.

How about the aether, energetic versus atomic theory of matter (Boltzmann suicide included), blackbody radiation continuous emission, static universe... just to name a few that come to mind.
You haven't given your assertion much thought, have you?

 

[Chalnoth]

How about the aether, energetic versus atomic theory of matter (Boltzmann suicide included), blackbody radiation continuous emission, static universe... just to name a few that come to mind.
You haven't given your assertion much thought, have you?

Demonstrate that a majority of scientists were convinced of any of these things at one time.

Yes, there have been many ideas in science that turned out to be false. But it seems to me that the majority of them never passed the level of, "Well, maybe this explains things, let's test it!" Many others stem from pre-science concepts, and weren't overturned until we developed the ability to actually investigate them (thus they couldn't be rightly considered conclusions of science, and instead just suppositions).

 

[AWA]

Demonstrate that a majority of scientists were convinced of any of these things at one time.

Demonstrate? As if this was some math theorem? Go to a public library and read some History of Physics book. It is public knowledge available to anyone with a little interest in learning about past mistakes. That a majority of the academy favors one theory guarantees nothing about the validity of the theory.

Yes, there have been many ideas in science that turned out to be false. But it seems to me that the majority of them never passed the level of, "Well, maybe this explains things, let's test it!" Many others stem from pre-science concepts, and weren't overturned until we developed the ability to actually investigate them (thus they couldn't be rightly considered conclusions of science, and instead just suppositions).

You are describing models such as L-CDM in this paragraph "they are at the level of, "Well, maybe this explains things, let's test it!", or "waiting until we developed the ability to actually investigate them ,thus they can't be rightly considered conclusions of science, and instead just suppositions"(Dark matter, Dark energy...). Exactly like the examples I showed, and exactly like them they are supported by the majority of scientists. Certainly we have better technology now but our current technology is in its infancy to deal with such entities as black holes, dark matter and dark energy too so they can'be rightly considered conclusion of science, just suppositions.
Only time will tell which way they are considered in the future. Let's not be so naive as to believe everything is settled.

 

[Chalnoth]

Everything is certainly not settled. Dark energy I would also place in the same category of these things that later turned out to be false. But not dark matter or black holes. There's a lot we don't know about dark matter in particular, and a fair amount we don't know about black holes, but there really isn't much of a question any longer that both of these things exist (at least as a very good approximation to the real objects).

Perhaps more importantly, dark matter and black holes are supported by a wide body of mutually-corroborating evidence. This is something that none of your examples had.

With the aether, for instance, this was merely assumed to exist based on existing theory, and it quickly became apparent that its properties were becoming more more magical all the time. When it was finally looked for, though, the search came up empty, and so it was (correctly) dropped.

With the continuous black body spectrum, it was immediately obvious that something had to be wrong with that idea, as it predicted infinite emission of energy (I would also note that this one also turns out to be approximately correct, as it is accurate for low frequencies/long wavelengths compared to the temperature).

Given that observational cosmology began with Edwin Hubble, in essence, I don't see how a static universe could ever have been considered a majority view.

 

[AWA]

Everything is certainly not settled. Dark energy I would also place in the same category of these things that later turned out to be false. But not dark matter or black holes. There's a lot we don't know about dark matter in particular, and a fair amount we don't know about black holes, but there really isn't much of a question any longer that both of these things exist (at least as a very good approximation to the real objects).

There is not any question they exist as theoretical entities, not as physical entities. They could exist as physical objects, we don't know yet, believing on it is just a matter of personal election. Many physicists even those actively publishing papers on this subjects consider them theoretical constructs as long as no direct physical evidence for them is available and just think of it as the most plausible explanation so far.

Perhaps more importantly, dark matter and black holes are supported by a wide body of mutually-corroborating evidence.

They are suported by theoretical models, and are not contradicted by observation (basically they can't be with current technology, so as long as this state of things doesn't change, they are actually unfalsiable and therefore not real science for the moment, they might be in the near future)

With the aether, for instance, this was merely assumed to exist based on existing theory, and it quickly became apparent that its properties were becoming more more magical all the time. When it was finally looked for, though, the search came up empty, and so it was (correctly) dropped.

You are describing again something very similar to things like strings, WIMPS,etc, let's give it some time and they may or may not be dropped.

With the continuous black body spectrum, it was immediately obvious that something had to be wrong with that idea, as it predicted infinite emission of energy (I would also note that this one also turns out to be approximately correct, as it is accurate for low frequencies/long wavelengths compared to the temperature).

Well, "inmediately" took at least 30-40 years. Certainly little in geological terms but not so little in the history of modern science.

Given that observational cosmology began with Edwin Hubble, in essence, I don't see how a static universe could ever have been considered a majority view.

You lack in imagination and notions of science history, a static universe was not a majority view, it was the only view since the first concepts of a universe outside the Earth was formed by ancient astronomers to 1922 when a universe of changing radius was theoretically hypothesized by Friedmann, and certainly it was stil the majority view until a few years after the 1929 Hubble observation of the redshift-distance law. When Einstein in 1917 proposed the first modern model of universe he reccurred to the static universe even if his equations allowed other solutions because that was the standard view at the time, this can be read in most books on the matter.

 

[Chalnoth]

They are suported by theoretical models, and are not contradicted by observation

This is a statement that is true about any theoretical model ever produced that has yet to be falsified. The point remains that a wide body of observations have consistently followed the expected results based upon these theoretical models. This is what science is, this is how it works, this is how we can be reasonably confident that they are at least approximately correct.

And yes, we are talking about real objects here. There is some possibility that what we know of as a black hole is in reality some other compact object. But there is no question that these compact objects we think are black holes exist. With dark matter there is very little known about its specific nature, but there is no serious question that there is some form of non-luminous matter out there, and none of the standard model particles fit. With dark energy we are less sure, but that's largely because it's an observationally difficult problem.

It is true that there are dissenters for both dark matter and black holes, but they are a strong minority. Most in the requisite subfields of cosmology/astrophysics are quite convinced that dark matter and black holes are real (caveat: I'm sure this is true about dark matter, but black holes are a bit outside my field, so I am less sure they're this confident...I think it's true, but it's a more vague impression on my part, sadly).

(basically they can't be with current technology, so as long as this state of things doesn't change, they are actually unfalsiable and therefore not real science for the moment, they might be in the near future)

This isn't correct. There are a number of observations that could, in principle, have falsified black holes and dark matter. They haven't. Now, we may not have the ideal observations that some people might prefer, but this is often not an option in science. We work with the evidence we have, not the evidence we wished we had. Yes, it would be nice to get a picture of a black hole's event horizon (this may happen relatively soon, actually, which would be rather exciting). Yes, it would be nice to detect and measure the properties of whatever particle it is makes up dark matter. But it is foolish to think that without a specific sort of observation that we might like to have that we can't be reasonably confident as to whether or not the model is at least approximately accurate.

Well, "inmediately" took at least 30-40 years. Certainly little in geological terms but not so little in the history of modern science.

Huh? I'm pretty sure the ultraviolet catastrophe was known about from the start, even though they didn't know the solution at the time.

You lack in imagination and notions of science history, a static universe was not a majority view, it was the only view since the first concepts of a universe outside the Earth was formed by ancient astronomers to 1922 when a universe of changing radius was theoretically hypothesized by Friedmann, and certainly it was stil the majority view until a few years after the 1929 Hubble observation of the redshift-distance law. When Einstein in 1917 proposed the first modern model of universe he reccurred to the static universe even if his equations allowed other solutions because that was the standard view at the time, this can be read in most books on the matter.

And this would impact upon my point how? Obviously before Hubble, there was no observational cosmology, so there could be no science-based conclusion on whether or not the universe was static. This seems to me a case of science overcoming the presumptions that came before, not a case of science giving the wrong answer.

 

[AWA]

Look, you made a silly statement (or bad informed)in post 52, and I pointed it out, you might as well admit it, if you don't I couldn't care less, to go on would be a waste of time since it all should be clear for anyone with a minimum discernment.

 

[Chalnoth]

Look, you made a silly statement (or bad informed)in post 52, and I pointed it out, you might as well admit it, if you don't I couldn't care less, to go on would be a waste of time since it all should be clear for anyone with a minimum discernment.

I don't think it was a silly statement at all. It may have been a bit short and poorly-explained, but I don't think it was silly.

Every field of science has had a period of "growing pains" where people were just settling into the field and learning how things work. Lots of bad ideas abounded and it took time to expunge them with experimental data. But once that initial period of "growing pains" passed, as happened with cosmology some time ago, I'm not aware of a single instance of an evidence-supported theory being widely-held as true that was overturned.

There are some important qualifiers there, of course, and you may argue that those qualifiers are invalid/inconsistent, but I have seen you present nothing that makes that case.