Where the rules change, is it sudden?

[narrator]

I've been thinking about some of the topics where the rules change.

For example,
- before Plank time
- in the core of black holes
- at the quantum level
- others

Do these events/regions/horizons suddenly experience a change in the rules or is it a more gradual change?

If some of them have a gradient change, can (or do) the new rules be inferred to some extent by observing the gradient?

 

[Drakkith]

The rules change at varying degrees of "speed" depending on each specific instance. Most of the time the way things behave in the unknown area can be guessed at to limited success, but there further away from known laws the less that can be inferred.

 

[Nabeshin]

In general, the change is slow. If you imagine trying to taylor approximate sin(x) to first order, you know you just get x. Now this is a good approximation near zero, but as you continue it gets worse and worse. This is rather analogous to how the transition is expected to occurr -- our current theories will just be worse and worse of an approximation.

The exception is some events which are macroscopic but completely non-classic. For example, if we were trying to use Newtonian fluid mechanics to describe Helium, we would be doing OK until suddenly we encounter the superfluidity, at which point Newtonian mechanics is completely wrong.

If some of them have a gradient change, can (or do) the new rules be inferred to some extent by observing the gradient?

Essentially, this is just getting new data and modeling the new data.

 

[Chalnoth]

I've been thinking about some of the topics where the rules change.

Well, our understanding is that the rules don't change, but rather that the rules we know today are only approximations to reality, and as we move to more and more exotic circumstances further from the experiments that we used to lay down the current rules, the less likely we are to get the answer right. But whatever "true" rules exist must describe the universe at all scales.

Just to give a couple of simple examples, quantum field theory, which is the combination of quantum mechanics and special relativity, reduces to classical quantum mechanics in the limit of slow motion. So QFT describes everything classical quantum mechanics does plus a little bit more. Similarly, classical quantum mechanics reduces to Newtonian physics for objects that aren't very tiny or very cold: if we really wanted to, in principle we could use classical quantum mechanics to calculate the trajectories of baseballs.

So it isn't that the rules change in any sense, but rather that the older rules aren't as accurate as the newer ones. We still use the older rules often not because they are more correct in any sense, but instead because they are still good approximations in many instances and the calculations are one heck of a lot easier to do.

 

[narrator]

Thanks guys for the explanations. Makes a lot of sense.

So it isn't that the rules change in any sense, but rather that the older rules aren't as accurate as the newer ones. We still use the older rules often not because they are more correct in any sense, but instead because they are still good approximations in many instances and the calculations are one heck of a lot easier to do.

Would that also be true of the areas where we don't yet know the rules? (e.g. deep inside a black hole or before plank time)

 

[Chalnoth]

Would that also be true of the areas where we don't yet know the rules? (e.g. deep inside a black hole or before plank time)

We expect so, yes. One way of thinking of it is that this really isn't anything special. Imagine, if you will, that you can describe the world as obeying two different sets of physical laws. One set is applicable in certain scenarios, the other is applicable in other scenarios. Just given this fact, I can trivially write down a "higher" law which is little more than including the other two and explaining when they apply.

From this, the assumed sensibility of the natural world requires there to be one overarching set of laws which govern everything.

But this isn't really that contrary to what you asked about: whether different natural laws apply in different scenarios. I mean, having an overall law that breaks down in this way would look that way, wouldn't it? Well, here we have to make use of some theoretical bias that has worked well in the past: the search for mathematical simplicity. When writing down a theory mathematically, finding a way of writing our equations in as simple a manner as possible has, time and again, proven to give tremendous insights into the nature of reality.

Perhaps the most striking example of this is General Relativity, which was driven not by experiment, but instead by asking the question of what special relativity would look like in the presence of accelerations, and supposing that gravity acts like an acceleration. This theory, based upon pretty much purely theoretical arguments, has remained our best theory of gravity for nearly a hundred years now. Similar achievements have been made in other areas such as quantum field theory and electromagnetism by fitting apparently disparate laws into one larger structure.

So we expect, then, that this is likely to continue: that the overall laws of physics, whatever they turn out to be, are very likely to be very simple while at the same time describing a wide variety of outcomes, from the interiors of black holes to biology to the early universe to the vast reaches between the stars.

 

[narrator]

Thanks Chalnoth.. that clarifies things nicely.

I guess this leads to the "theory of everything".

Aren't there those who disagree with the possibility? Didn't Hawking once believe then change his mind?

 

[mjacobsca]

I think most scientists believe a TOE exists. They just don't agree on what it looks like.

 

[Drakkith]

I like your explanation Chalnoth, if I could paraphrase it: The way the Universe works doesn't change, only our understanding of it does.

 

[twofish-quant]

I've been thinking about some of the topics where the rules change.

For example,
- before Plank time
- in the core of black holes
- at the quantum level
- others

Do these events/regions/horizons suddenly experience a change in the rules or is it a more gradual change?

Depends. There is an entire field of physics dealing with the physics of "phase changes." A good example of a phase change is when ice freezes or melts. You have a block of ice at -1 celsius, and everything is fine, and then you move the temperature up by two degrees and suddenly you have a pool of water.

There is a branch of physics and mathematics dealing with these sorts of sudden changes, and a lot of the work that has been put into understanding how and why water freezes turns out to be very useful in the early universe. Also to give an example of how this can be useful outside of cosmology, there are people that have been working on using the concept of phase change to explain economic crashes.

If some of them have a gradient change, can (or do) the new rules be inferred to some extent by observing the gradient?

Sometimes :-) :-)

 

[Lost in Space]

Don't some phase transitions have a critical point in which one state becomes another? Does this mean that the transition is instantaneous and could this be said to be independent of time as there is no interval between the states?

 

[Chalnoth]

Don't some phase transitions have a critical point in which one state becomes another? Does this mean that the transition is instantaneous and could this be said to be independent of time as there is no interval between the states?

It's fast, but not instantaneous. The point I was making is that the same underlying rules describe the system both before and after the phase change, but obviously the configuration is different so the behavior is different.

 

[Lost in Space]

It's fast, but not instantaneous. The point I was making is that the same underlying rules describe the system both before and after the phase change, but obviously the configuration is different so the behavior is different.

Yes but how fast is fast? Is it greater or less than Planck time?

 

[Chalnoth]

Yes but how fast is fast? Is it greater or less than Planck time?

How fast is going to depend upon which sort of phase change you're talking about. But the speed is going to depend upon a lot of factors.

To get an idea of how phase changes happen, imagine boiling water. The whole pan of water never boils at the same time. Instead, small bubbles form and grow. If you have a pan of rapidly boiling water, you can see this effect very easily, where a bubble that starts small at the edge of the pan (usually the bubbles will form on scratches on the pan), and then grows rapidly before reaching the surface. So you can't talk so much about the amount of time it takes for that bubble to appear. Instead you talk about how rapidly the bubble expands, which is going to depend upon a number of factors.

With a phase change that changes the effective physical laws that govern our universe, you're going to get a somewhat similar situation where a small bubble forms then expands into the surrounding space. This expansion cannot proceed at faster than the speed of light, and will likely proceed more slowly by some amount. Exactly how close to the speed of light it expands will depend upon the specific nature of the phase change.

 

[Lost in Space]

How fast is going to depend upon which sort of phase change you're talking about. But the speed is going to depend upon a lot of factors.

To get an idea of how phase changes happen, imagine boiling water. The whole pan of water never boils at the same time. Instead, small bubbles form and grow. If you have a pan of rapidly boiling water, you can see this effect very easily, where a bubble that starts small at the edge of the pan (usually the bubbles will form on scratches on the pan), and then grows rapidly before reaching the surface. So you can't talk so much about the amount of time it takes for that bubble to appear. Instead you talk about how rapidly the bubble expands, which is going to depend upon a number of factors.

With a phase change that changes the effective physical laws that govern our universe, you're going to get a somewhat similar situation where a small bubble forms then expands into the surrounding space. This expansion cannot proceed at faster than the speed of light, and will likely proceed more slowly by some amount. Exactly how close to the speed of light it expands will depend upon the specific nature of the phase change.

Yes, I can appreciate that any phase changes within the continuum would be limited to less than or equal to the speed of light, but if the Big Bang was the result of a phase change do you think it would it still be less than or equal to c, or possibly even greater?

 

[Chalnoth]

Yes, I can appreciate that any phase changes within the continuum would be limited to less than or equal to the speed of light, but if the Big Bang was the result of a phase change do you think it would it still be less than or equal to c, or possibly even greater?

Yes, it had to be slower than the speed of light. This is one of the reasons why inflation was proposed: it allows a phase change that propagates at slower than the speed of light to fill all of the observable universe.

 

[DavidMcC]

Yes, it had to be slower than the speed of light. This is one of the reasons why inflation was proposed: it allows a phase change that propagates at slower than the speed of light to fill all of the observable universe.

That isn't consistent with the hugely FTL expansion of the universe as a whole during inflation, Chalnoth.

 

[narrator]

That isn't consistent with the hugely FTL expansion of the universe as a whole during inflation, Chalnoth.

Brian Greene's The Hidden Reality explains nicely just how it is consistent. It's a good read.

 

[Chalnoth]

Well, turns out I was talking to a string theorist about this a few days ago, and it looks like the domain walls do tend to expand rather more rapidly than I had thought. At least in the context of string theory, when you have a tunneling event to a lower-energy vacuum, the expansion rate starts slow but rapidly approaches the speed of light, so that by the time the domain has reached about one meter, it is close enough to the speed of light that the difference is irrelevant.

This means that the maximal warning you get is on the order of one nanosecond, so yeah, we can't say that these things don't happen observationally.

 

[DavidMcC]

Brian Greene's The Hidden Reality explains nicely just how it is consistent. It's a good read.

A good read doesn't necessarily mean good science, narrator.

 

[narrator]

A good read doesn't necessarily mean good science, narrator.

It is both a good read and a clear explanation of the "science" as it currently stands (including appendixes with the more technical detail).

Don't toss out the baby with the bathwater - look it up and judge for yourself! It's downloadable for free in PDF format.