Ask a physicist anything. (7)

[Chalnoth]

Thanks again. Is there such a thing as low and high entrophy behavior. For example I might draw an intricate pattern on a piece of paper, or just crumple it up and throw it in the bin. Would these count as examples of low and high entropy activities respectively?

Entropy is a state, not a behavior. Different behaviors can, however, have different effects on entropy. But it's often not so easy to see what those effects on entropy are. Any action, of course, increases total entropy. But some actions also reduce the entropy of an isolated system while they're at it. For instance, I can set a house on fire and increase total entropy (destroying the house), or I can heat a house with a fire in the fireplace to increase total entropy while decreasing the entropy of the house (because you are increasing the difference in temperature between the inside and the outside).

 

[GrowingSmaller]

Ty. Now, if I understand according to Einstein there is no absolute motion, onluy relative motion. So why persist with the idea that the Earth orbits the Sun, rather then the other way round? If motion is relative, aren't both interpretations equally valid?

 

[Chalnoth]

Ty. Now, if I understand according to Einstein there is no absolute motion, onluy relative motion. So why persist with the idea that the Earth orbits the Sun, rather then the other way round? If motion is relative, aren't both interpretations equally valid?

In a sense. However, the center of mass of the Solar System is very nearly the center of the Sun. This makes the Sun a natural symmetry point of our Solar System, which in turn makes the equations work out vastly more simply if we take the Sun as the center.

You could always take the Earth as being stationary at the center of your coordinate system when calculating, say, the movement of Jupiter, but that makes the calculations horrifically complicated, and counterintuitive as well. The behavior of the Solar System is just so much easier to understand if you use coordinates where the Sun is in the center.

 

[GrowingSmaller]

Also I remember that we can have a '2 dimensional' equaiton y=x, which would be a 45 degree line.

What would a similar 5 dimensional equation look like i.e y = ...... or whatever?

 

[GrowingSmaller]

@#523 I have heard that one before thanks. So really it seems to be a matter of simplicity and conveniance rather than an absolute insistence.

 

[Chalnoth]

Also I remember that we can have a '2 dimensional' equaiton y=x, which would be a 45 degree line.

What would a similar 5 dimensional equation look like i.e y = ...... or whatever?

Well, in five dimensions, we'd have five variables. So let's choose x,y,z,r,s. To fix a line, we have to write four equations. For example:

y = x
z = x
r = x
s = x

Of course, there are many possible ways to write the four equations, but in the end you do need four separate equations to define the line in five dimensions.

 

[Chalnoth]

@#523 I have heard that one before thanks. So really it seems to be a matter of simplicity and conveniance rather than an absolute insistence.

Well, yes and no.

The issue comes down to what you mean by the word "center". There is no such thing as an absolute center, period. So if we are to use the word at all, we have to mean something else than an "absolute" center. If instead we think of what we mean, well, it differs slightly in different contexts. But usually it's a point of symmetry of some sort or other: it's a location where the stuff on one side is more or less the same as the stuff on the other. And if you're asking about the Solar System, there is indeed a unique point of symmetry: the center of the Sun. So the only way the word "center" means anything at all for the Solar System is if it's the center of the Sun (or very close to it....the center of mass isn't exactly the center of the Sun, but it's close).

 

[GrowingSmaller]

Ty I never got the point about symmetry the first time.

 

[GrowingSmaller]

Ok is there anything in math (maybe applied in developmental biology who knows) where we have axes x, y and z that are not at right angles, but maybe at 30[sup]o[/sup] rather than 90[sup]o[/sup] to one another, i.e. not orthoganal / perpendicular, or perhaps with curved or even branching axes rather than linear/straight ones? Or would the math be "redundant" in a sense as it would be just subset of ordinary graphs?

 

[Chalnoth]

Ok is there anything in math (maybe applied in developmental biology who knows) where we have axes x, y and z that are not at right angles, but maybe at 30[sup]o[/sup] rather than 90[sup]o[/sup] to one another, i.e. not orthoganal / perpendicular, or perhaps with curved or even branching axes rather than linear/straight ones? Or would the math be "redundant" in a sense as it would be just subset of ordinary graphs?

Oh, yes. But it makes the math quite complicated.

 

[RickG]

Ok is there anything in math (maybe applied in developmental biology who knows) where we have axes x, y and z that are not at right angles, but maybe at 30[sup]o[/sup] rather than 90[sup]o[/sup] to one another, i.e. not orthoganal / perpendicular, or perhaps with curved or even branching axes rather than linear/straight ones? Or would the math be "redundant" in a sense as it would be just subset of ordinary graphs?

The different crystal systems come to mind.

 

[Chalnoth]

The different crystal systems come to mind.

Ah, yes, that's very true. Describing crystals is one of those areas where non-orthogonal axes can be extremely useful, because the system itself has particular directions which are just not orthogonal to one another.

 

[acropolis]

Ok is there anything in math (maybe applied in developmental biology who knows) where we have axes x, y and z that are not at right angles, but maybe at 30[sup]o[/sup] rather than 90[sup]o[/sup] to one another, i.e. not orthoganal / perpendicular, or perhaps with curved or even branching axes rather than linear/straight ones? Or would the math be "redundant" in a sense as it would be just subset of ordinary graphs?

Yes, sometimes it is useful to use non-orthogonal coordinates. Sometimes it is useful to use arbitrary coordinate systems, such as defining one coordinate to be along the curve of a parabola or something. Lagrangian mechanics involves the use of arbitrary coordinate systems, for example. It is always true, however, that a certain number of coordinates is needed to define spaces of specific dimensionality. You'll only get a line out of a single coordinate, even if that line curves about, and only a surface with two coords etc.

edit: Somewhat related, dimensions are a matter of mathematical and descriptive utility more than anything. Say you have a particle which translates, rotates, and vibrates. It may be useful in this case to use seven coordinates to describe that particle, but that does not mean the particle is a 7-dimensional particles. Pop-sci authors declaring that we live in an 11-dimensional world make a mistake similar to that.

 

[GrowingSmaller]

Can there only ever be one temporal dimension, even in theory? Can there be other dimensions that space and time, for example do number lines like the imaginaries count as dimensions?

 

[GrowingSmaller]

As I type this, the electrons (according to Copenhagen interpretation at least) in my hand, body, keyboard etc are in a superposition of states described by a wave function that streatches out across the entire universe. Is that right?

 

[Chalnoth]

Can there only ever be one temporal dimension, even in theory? Can there be other dimensions that space and time, for example do number lines like the imaginaries count as dimensions?

Well, having more than one time dimension leads to theories which just don't seem to be sensible. Basically, more than one time dimension leads to closed time-like curves, which leads to really strange behavior (as in, the ability to go back and kill your grandfather, for example). While I don't think there's anything we know of yet that makes them fundamentally impossible, our inability to make sense of such theories tends to make us suspect that they aren't possible.

 

[Chalnoth]

As I type this, the electrons (according to Copenhagen interpretation at least) in my hand, body, keyboard etc are in a superposition of states described by a wave function that streatches out across the entire universe. Is that right?

Well, that wavefunction is effectively zero outside your body. So, not in any sense that matters.

 

[acropolis]

Can there only ever be one temporal dimension, even in theory? Can there be other dimensions that space and time, for example do number lines like the imaginaries count as dimensions?

The tricky part is defining what those extra temporal dimensions would describe exactly. Saying you can go sideways in time is like saying you have a square circle: there is no reality described that that phrase, so far as we can tell. You can certainly construct a theory that does describe and incorporate that extra time dimension, but it will be of limited value and will be unlikely to have any extra explanatory power.

As I type this, the electrons (according to Copenhagen interpretation at least) in my hand, body, keyboard etc are in a superposition of states described by a wave function that streatches out across the entire universe. Is that right?

The probability function that is used to describe the location of an electron is defined for all space, so there is a small chance that at a time in the future the electron could appear some large distance away, at least the math implies this. However, the odds are so small as to be negligible. It's like if you flipped a coin a billion times there is still a small chance they will all land on heads, but the odds are very, very small.

This is neither here nor there, but I'm a condensed matter physicist (at least I will be in a year when I finish my dissertation), so while I use quantum mechanics as a tool to describe and predict the behavior of small-scale systems I don't work with the fundamental interpretations of it. I do work with physicists who do work in fundamental quantum theory and try to pick their brains as often as possible. According to them quantum theory is still quite contentious, and even those apparently monolithic interpretations such as the Copenhagen interpretation are not nearly as certain as they appear. There is still a collection of theories in play that theorists continue to battle each other to prove or disprove, so whenever someone says "This is how it is" with quantum always take it with a grain of salt.

 

[Zippy the Wonderslug]

What is the highest charge (amps/voltage) that a single capacitor can carry, and what might be the possible outcome of bombing a city with a thousand of these?

Cheers.

Still waiting for an answer on this.

*taps fingers*

 

[pgp_protector]

Still waiting for an answer on this.

*taps fingers*

High voltage capacitor bank vs watermelon - YouTube