For Questions That Don't Merit Their Own Thread

[sevenperforce]

6 hours ago, p1t1o said:

"Photons themselves" is a troublesome concept when looking very closely, they aren't really little physical particles, they just behave that way under various circumstances.

Exactly. Even when you consider the behavior of a single discrete photon, its interaction with the matrix is probabilistic rather than deterministic, as if it was not a single photon at all but a collection of them.

That's the great underlying paradox of quantum mechanics: everything in the universe is quantized (meaning any substance comes in discrete, indivisible packets), and yet an individual quanta behaves as if it is a continuous wave when it interacts with other quanta.

When you sit down and do the actual math with a single photon traveling through a medium, it gets REALLY weird. Like, we-all-live-in-a-simulation weird.

Any time you have a photon (or a group of photons) hitting a medium like air or glass or water, there is a probability that it will be transmitted (absorption, phonon excitation, emission) and a probability that it will be scattered back (reflection). Suppose that for a group of photons passing from vacuum into something like glass, there is a 90% chance of transmission and a 10% chance of reflection Now, classically, we would expect that 10% of the photons are reflected, and 90% of the photons are transmitted.

But on a quantum level, those probabilities apply individually to each photon itself. According to the math, each photon is 10% reflected and 90% transmitted. 

Yet the photon is a quanta, a discrete object; it cannot be broken into smaller pieces. So each photon is either transmitted or reflected; there is no middle ground. That's the paradox.

The solution is that the interaction with the material matrix resolves the 10%-90% split. The photon is discrete, but there are actually two phonons created inside the matrix: one with 90% of the photon's energy, and one with 10% of the photon's energy. This is called a superposition of states; two different "outcomes" superimposed over each other. But this superposition of states isn't just division of energy; it's a division of probability. 90% of the time, the larger phonon "wins" and the photon is emitted out the other side for a transmission; 10% of the time, the smaller phonon "wins" and the photon is reflected.

It is this superposition -- an interaction between two phonons of different probabilities -- which causes the time-delay in the apparent velocity of the photon. This interaction also is responsible for producing refraction.

So there you have it. It's complicated as all hell, for sure.

[p1t1o]

4 minutes ago, sevenperforce said:

<snip>

My favorite example of such weirdness - https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester

A method of observing an object without interacting with it in any way whatsoever, without even bouncing a photon off it. And practically demonstrated in the real world as well!

Apparently one school of thought hypothesises that there is communication/interaction with other versions of our universe (a-la the many worlds interpretation) and extracting information from them.

[0111narwhalz]

If entropy can only increase, then that implies a "start" of the universe. But that would mean that there was no cause, or else something would have caused that cause (and so on), to start the universe itself. So that means that either everything has cause, or entropy increases; not both.

Where did I go wrong?

[Steel]

Just now, 0111narwhalz said:

If entropy can only increase, then that implies a "start" of the universe. But that would mean that there was no cause, or else something would have caused that cause (and so on), to start the universe itself. So that means that either everything has cause, or entropy increases; not both.

Where did I go wrong?

Entropy is not limited to increasing only. In fact locally you can have pretty large decreases in entropy, so long as somewhere else the entropy goes up so that universally it increases.

I got a bit lost in all your causes of causes, can you just clarify exactly what you mean by that?

[0111narwhalz]

If there is a start, then nothing could have caused that start, or it wouldn't have been the start. So a start must be uncaused.

2 minutes ago, Steel said:

Entropy is not limited to increasing only. In fact locally you can have pretty large decreases in entropy, so long as somewhere else the entropy goes up so that universally it increases.

I was under the impression that the universe could be considered a closed system.

Edited May 4, 2017 by 0111narwhalz

[Steel]

2 minutes ago, 0111narwhalz said:

If there is a start, then nothing could have caused that start, or it wouldn't have been the start. So a start must be uncaused.

Does the start need to have a cause?

2 minutes ago, 0111narwhalz said:

I was under the impression that the universe could be considered a closed system.

^^^Yeah you're right, I was misunderstanding your question^^^

[0111narwhalz]

Just now, Steel said:

Does the start need to have a cause?

If the start has no cause, then that implies other things might be causeless.

[Steel]

Just now, 0111narwhalz said:

If the start has no cause, then that implies other things might be causeless.

The thing with the beginning of the universe is that talking about a cause doesn't really make any sense, since there isn't a "before" where something could cause it. The beginning of the universe is the beginning of time and space, so how can something cause the beginning if nothing existed?

[0111narwhalz]

1 minute ago, Steel said:

The beginning of the universe is the beginning of time and space, so how can something cause the beginning if nothing existed?

But how is that different from "there was time before but nobody cares because it had no causal agency over now?"

[Steel]

1 minute ago, 0111narwhalz said:

But how is that different from "there was time before but nobody cares because it had no causal agency over now?"

I guess physically they're not that dissimilar. However, how can you have time if there is no space? What references could you possible have that differentiate one time to the next?

[0111narwhalz]

6 minutes ago, Steel said:

What references could you possible have that differentiate one time to the next?

Exactly as many as if all space were homogeneous...

...a state of maximum entropy. 

Is that how maximum entropy could equal zero entropy? 

Edited May 4, 2017 by 0111narwhalz

[Steel]

4 minutes ago, 0111narwhalz said:

Exactly as many as if all space were homogeneous...

...a state of maximum entropy. 

Is that how maximum entropy could equal zero entropy? 

Ah, but there's a fairly major difference between completely homogeneous space and no space.

[sevenperforce]

When you mix physics and philosophy, both end up muddy.

Causality in philosophy is a little different from causality in physics. Causality in physics is a physical constant, known more generally as the speed of light. Causality propagates at roughly 3e8 m/s.

If space and time are inverted, as in a black hole or at the start of the universe, causality becomes undefined. Not absent, but actually undefined.

[Green Baron]

Not sure about the inversion thing of space and time in a black hole, time ceases to exist after being prolonged almost infinitely compared to the rest of the world. I am on the no space without time side, at least not under our set of rules. No time, no change. Has change always a coordinate ? A particle moving, a wave propagating ? *shrug*

There is a limit of what we can describe with our cosmological models right now and the question of what was the universe like before the inflation thing aka "big bang" can not be answered yet. Moar theories :-)

 

Highly theoretic constructs like M-theory or string theory seem to allow almost any answer to any question, including 42 to no question :-) We grant Einstein's Old One another few decades before we call him to account :-)

Edit (i always edit): didn't i find it or has this Einstein citation not been translated into English ?

In a letter to Nils Bohr 1928 he wrote:

„Die Quantenmechanik ist sehr achtunggebietend. Aber eine innere Stimme sagt mir, daß das noch nicht der wahre Jakob ist. Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näher. Jedenfalls bin ich überzeugt, daß der nicht würfelt.“

"Quantum mechanics is very imposing. But an inner voice tells that me it is not the real McCoy yet. The theory delivers a lot, but it does not take us closer to the secrets of the Old One (der Alte). I, for one, am convinced that he does not roll dice."

Personal remark: "he" with emphasis and without a name in German can be understood as a little downgrading.

 

Edited May 6, 2017 by Green Baron

[Steel]

12 minutes ago, Green Baron said:

Highly theoretic constructs like M-theory or string theory seem to allow almost any answer to any question, including 42 to no question :-) We grant Einstein's Old One another few decades before we call him to account :-)

You say that, but actually one of the huge issues with M-theory (and why it seems to have fallen out off fashion, possibly for good) is that it produces very few verifiable predictions.

Edited May 6, 2017 by Steel

[ChrisSpace]

How do I calculate the maximum size of a sphere that can fit into a pyramid 1600m tall with a diamond-shaped base 900m long and 220m wide?

[K^2]

3 hours ago, ChrisSpace said:

How do I calculate the maximum size of a sphere that can fit into a pyramid 1600m tall with a diamond-shaped base 900m long and 220m wide?

In general, you find the size of a sphere inscribed in a convex polytope by solving a system of inequalities. But this problem is highly symmetrical, which makes things easier.

Consider such pyramid placed in a 3D Cartesian coordinate system with center of the rhombus (diamond) at the origin and apex of the pyramid on the Z axis. Maximum inscribed sphere will have its center on the Z axis as well, thanks to the symmetry, and that means we only need to consider contact with one of the 4 sides and the base. Base is easy. Sphere or radius r will have its center at (0, 0, r) so as to touch the base. Now we just need to know the distance to the side faces.

Consider face that passes through (450, 0, 0), (0, 110, 0), and (0, 0, 1600). The equation that describes this plane is given by:

110 * 1600 * x + 450 * 1600 * y + 450 * 110 * z = 450 * 110 * 1600

Consequently, distance between this plane and point (0, 0, r) is the following:

d = (1600 - r) * (450 * 110) / sqrt(110² * 1600² + 450² * 1600² + 450² * 110²)

And for an inscribed sphere, all we have to do is substitute d = r and solve for r. I'm sure you can solve a linear equation, so I'm leaving that up to you.

P.S. As one might expect from the dimensions, it's not very big.

Edited May 7, 2017 by K^2

[ChrisSpace]

On ‎7‎/‎05‎/‎2017 at 2:36 PM, K^2 said:

d = (1600 - r) * (450 * 110) / sqrt(110² * 1600² + 450² * 1600² + 450² * 110²)

And for an inscribed sphere, all we have to do is substitute d = r and solve for r. I'm sure you can solve a linear equation, so I'm leaving that up to you.

P.S. As one might expect from the dimensions, it's not very big.

The value I got was r=106.549m (3dp). Is this correct or did I mess up slightly? In any case, thanks for the visual. When I first asked the question I was a little worried someone would misinterpret what I was asking, but you got it spot-on.

[K^2]

4 hours ago, ChrisSpace said:

The value I got was r=106.549m (3dp). Is this correct or did I mess up slightly?

Slightly off. I'm getting 99.956m to the same precision. The part under sqrt comes out to a hair over 742850. So you should be getting:

r = 1600 * 450 * 110 / (742850. + 450 * 110)

And yeah, I'm extremely happy with how easy Mathematica makes it not only to solve the problems, but also generate visuals. Sure, I can set everything up by hand and then make images in CAD, but I'm entirely too lazy to bother with all that. 

[0111narwhalz]

I need a system which allows full three-axis rotation but does not suffer from gimbal lock. It needs to keep continuity with the stator (assume infinitely rotatable couplings) and exist in real space without self-intersection. It can be motor- or reaction wheel-driven.

Edited May 8, 2017 by 0111narwhalz

[Green Baron]

Fully cardanic suspension is what your looking for i think. If you could visualize your idea ? 3 drives would have to rotate with the corresponding axises, i doubt that this can be realized irl.

Real world gyros operate in 1 or 2 axis, so one needs several for 3 axis steering. Also they must be calibrated every now and then due to friction. Gimbal lock becomes a problem as soon as you have two degrees of freedom ...

Edited May 8, 2017 by Green Baron

[0111narwhalz]

To clarify: The system is to be used on a turret. It needs to be able to track targets continuously along every path. It is preferable that it is mechanically simple, but this is not a required parameter.

[K^2]

Classical solution to gimbal lock is fourth gimbal. Tracking solution for all four gimbals becomes more complex, but it's not a problem for modern computers or even MCUs.

[0111narwhalz]

1 hour ago, K^2 said:

fourth gimbal

Alright. Four gimbals it is.

But are there any clever ways? Ones which are unnecessarily complex but technically possible? Just want to explore possibilities now. I don't think there's any real way to make a quaternion exist in real space without some kind of planar bearing, but I'm almost certain there are other options.

[p1t1o]

What is wrong with a ball joint? Or I could be missing something because I have no idea what a quaternion or a cardanic suspension is...