h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Noggin. This looks very Noetherian to me! None the worse for that, I'm sure. However, I would apprecialte it if you would spell out the argument in smaller steps. I'm prepared to bet that I'm not the only one either!

toxx

me too

Having refreshed my memory on the topic of sets and the definitions of bounded/unbounded infinite/finite, can I ask a few questions?

I now understand that time maybe finite but unbounded.

Would it seem reasonable to infer that the same is true for spatial dimensions as for time, ie they are finite but unbounded?

If space can be curved, can time also be curved?

BTW thanks Member for the idiot's guide to relativity.

Hi Madent.



Member will doubtless correct me if wrong, but space too is finite but unbounded according to the standard model. Space has a radius in light years equal to the duration of time in years. This means that Member has to say that they are the same thing, since we can write an equation to relate them!

toxx

Would it be too late or too confusing to point out that the symbol used in E=mc^2 ('equals') is not the same as the symbol made up of 3 horizontal parallel lines which denotes 'is identical to', IIRC. I can't produce it here in this thread but you can see it on A1098876 near the bottom in the 'Mathematical Operators' section (try doing a 'Find in page' on the word 'identical').

So the amount of energy you could liberate from a particle is equal to its mass multiplied by the square of the speed of light, but until you perform that liberation, they are not identical... I'm stopping there because (if I haven't already) I'll only say something liable to get me shot down in flames by one of the regular posters

rt

(who swore he wouldn't get involved in this conversation)

Smaller steps, eh? That's a bit like trying to explain a circle in smaller steps, but I'll give it a go.

Disclaimer: The universe *may* not be like this. But to any extent that it's not like this it can't be understood, and nothing useful can be said about it.

"Cause and effect is (or has underlying it) an abstract conserved quantity."

Causes may only be perceived indirectly by the effects that they have and the measurement of any cause is always the measurement of the effects that it has, and the two are always, therefore, quantitatively equal. They are not identical (the cause is not identical to the effect), but they are abstractly equal. The same goes for energy transformations. Whenever energy is converted from one form to another an abstract quantity is conserved, even though the two forms are not "identical".

"If the laws of physics are invariant through rotation (ie are the same for all observers), then the existence of the universe must be underpinned by a conserved quantity. (ie energy)"

This is, as toxx spotted, Noethers Theorem (Actually NT is the mathematical proof that the above statement is the case). Can't say I understand the maths myself, and arrived at this conclusion on purely philosophical grounds, but it's nice to have one's intuitions confirmed.

"These must also apply to any interaction between an 'immaterial substance' and a material one."

If the interaction is one that preserves information (structure), and it's hard to see it as not doing so if the interaction is supposed to serve a function, then the transformations concerned are underpinned by an abstract conserved quantity. Because the quantity is abstract dividing it into a material and an immaterial part serves no purpose.

Noggin

The watch was made by a watchmaker, a peer of yours. Is it conceivable that the universe (ignoring the fact that it doesn't necessarily 'work', depending on your definition of 'work') was also made by one of your peers?
And no, I can't make a universe. But then, I can't make a rolex, either. And I don't know any single person who can.

Yo Roofie. My cyber buddy concurs that these equations simply tell us how much energy can potentially be produced by converting a certain mass. They are NOT the same thing!

Shoot people down in flames! Us?

toxx

Noggin. I'm still struggling, but maybe I can understand this bit enough to ask an intelligent question:



As my cyber-buddy points out, causes can have many effects. This also occurred to me. So if something heavy is dropped on something fragile, the latter gets smashed. One effect is that things happen that allow our perceptual organs to access the information that the 'cause' is taking place (effect #1). We are aware of the cause because of that effect. However, the smashing of the second object is also an effect (effect #2) that is unrelated to our observation of the cause.

You say that cause and effect are "abstractly equal". So effect#1 and effect#2 are both "abstractly equal" to the cause and therefore to each other! I just don't understand enough of the nature of this "abstractly equal" beast to decide whether what you say is true or whether what I say is, as I suspect, a counterexample.

toxx

<...these equations simply tell us how much energy can potentially be produced by converting a certain mass.>

There's no such thing as energy "not in a particular state". The abstract conserved quantity is what allows us to write equations in the first place.

I'm not sure what distinction you're making between effect#1 and effect#2. The smashing is not anything other than the redistribution of the cause contained in the falling heavy object.

Causes have lots of effects, yes; and indeed effects may have lots of causes. But in an ideal closed system the state of the *system* at time t is the cause of the state of the *system* at time t+1.

Noggin

Noggin. Sorry to have been imprecise. Effect#1 was supposed to be the effect of the cause on the observer - thus allowing the cause to be observed. Effect#2 was the effect on the fragile body. Same cause, two very different effects. Interestingly, we wouldn't necessarily be able to infer either effect from the other.

It helps to know that you are assuming a closed system. I wonder whether or not my observer would be included in it.

toxx

Thanks, toxx. That's much clearer.

The observer is part of the system. Effect#2 is of course part of the cause of the sequence of effects #1 too.

Noggin

Noggin. Still trying to play Stillingflete to your Locke, I fear. I had a scenario in mind whereby effect#1 is just the observation of the heavy object falling towards the fragile one. We'll cut off the sequence just before the breakage - which breakage I call effect#2.

So the observer is not directly aware of effect#2 but IS aware of its cause. Hence the cause has two effects: the awareness of it by the observer and the breakage of the object. The latter is not, however, part of the cause of effect#1.

I can't believe I've made it sound so complicated! The falling object has two effects: our awareness of it and the breakage. We are not, however, aware of the breakage as it happens. Let's suppose we blink at the crucial moment and are then aware that the object is broken. Phew!

So the two effects: that on the observer and that on the fragile object are entirely separate.

Back to the question. You said that the cause and effect are "abstractly equal":

Here we have two (probably of many) effects which are both presumably abstractly equal to the cause and therefore to each other. Can you explain what these three things have that is equal and why it matters ....... please?

A still confused - toxx

Noggin.

This is starting to sound like the old one about if a tree falls in a forest and there is nothing to hear it, does it make a sound?

Our lack of awareness of a cause/effect has bugger all to do with whether or not it exists/happens.

The separation is one of convenience for us. Both effects are part of the total system of effects produced by the total system of causes.

And it's important because it's a logical necessity for the coherence of the universe, without which we couldn't say anything.

Noggin

"Roofie"

toxx

rt

Noggin. When you put it that way it seems too true to be good! You're saying that the universe at t+1 is equal to the universe at t. Nothing has been added or taken away. I think that even this depends on quite what we're looking at. If we look at factors relevant to the 2nd law of thermodynamics, I guess we always find that the universe is 'winding down'! The energy is more uniformly distributed, entropy has increased, at t+1 as compared with the state of affairs at t.

We can talk about the conservation of energy+entropy; but that fudges an important distinction. Noether want us to also identify a symmetry, I take it. I shall have to reread your messages because maybe it's there now I think I know what I'm looking for.

toxx

Entropy is not something you can hold you cant *have* two bags then increase to having 4 bags of entropy.

I think its more accurate to say it proceeds rather than increases.

<...nothing has been added or taken away...>

It's a bit like the boundary conditions thing, toxx.

If anything appears to be being added or taken away this must either

a) Happen according to a rule (in which case it can be written into the equations)

or

b) It happens at random and there are no rules.

Entropy is not conserved; it increases.

Noggin