If there’s one thing I’ve learned from watching How the Universe Works to go to sleep every night, it’s that space can expand faster than the speed of light.
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How do you calculate that? This includes overcoming the original lose of close to $800m?
Feynman, because he’d fight dirty.
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The present value of an annuity that pays out $1.6b over 30 years is less than $800m so you aren’t actually losing anything.
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Ok I guess I was failing to account for the fact that they pay out the annuity based on its future value.
Ok two questions:
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Do quarks have any empty space in them as far as we currently understand?
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If you removed all the empty space in the observable universe - including the empty space inside atoms, and the empty space inside protons/neutrons/electrons, and any empty space inside quarks that we know of - how big would the universe be?
The Lorentz factor was developed to resolve an issue in electrodynamics. Maxwell’s equations should hold true in all reference frames. You can derive the speed of light in a vacuum from Maxwell’s equations. But that means in a reference frame moving with respect to that light, Maxwell’s equations still have to work, which means that light still has to be moving at c, but how can it when you are moving with respect to it? The Lorentz factor was a mathematical fudge to allow light to move at c in all reference frames. No one had any motivation for why it existed other than that it made the numbers work. The theory of relativity’s magic is that if you assume the Lorentz factor, not just for light, but for distances and times, a whole host of other verifiable physical phenomena also follow.
This isn’t uncommon in physics. Planck resolved the ultraviolet catastrophe with what was basically curve-fitting, and it wasn’t until the concept of photons that the reason for the math became clear. In quantum mechanics we use a procedure called renormalization, in which a bunch of infinite quantities are divided by the same infinite quantity to make them all finite and preserve their proportions. It works, but it still makes you feel a bit itchy.
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It’s just observable and we have to accept that? Physicists don’t focus on “why” quite as much as you’d think. The first priority is to find a concept that fits the observations, then see if that concept leads to predicted behaviors that we can also observe, then worry about why it works that way.
Edit: Also what econophile said.
Sure. You’re not going to like my answers to questions like that. When students ask me about the multi-world interpretation of quantum mechanics, I always say, “Until you can suggest a way for more than one of those worlds to influence or communicate with each other, I don’t care.” I’m hardcore experimentalist/instrumentalist.
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I get that until you can observe something else, the rest is just philosophy.
But isn’t that kind of what string theory is - an attempt at connecting behaviors seen in our world using other dimensions that we can’t see? Is it true that so far no one has come up with any experiment to test string theory?
Yeah I have a BS in physics. If I ever went further with it I was definitely going to be on the experimental side. I like things I can touch.
My favorite experiment was where we put a small dumbell hanging from a string next to two big balls. Then we shine a laser on a mirror attached to the string and measure the gravitational effect of the big balls on the dumbell - as it twists the string ever so slightly. That was awesome.
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Can you just explain why that slit experiment works the way it does? I still don’t get it.
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On a similar vein, I seem to remember Lisa Randall suggesting that the proof for string theory was “the numbers seem to work,” despite how far-fetched to a layperson the theory seems.
Of course, I’m not a physicist and I couldn’t get more than half-way through her book. 
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We don’t know what’s going on inside a quark. We can only get a general sense of their size from their scattering cross section (like determining the shape of a bicycle from the angles at which bullets bounce off of it.)
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Atomic radii are on the order of 10^-10 meters. Nuclear radii are on the order of 10^-15. So pull out all the empty space, and you’d shrink things at least on the order of 10^5 = 100,000 times.
A good test example is a neutron star, which has been compressed to the point where only nuclear repulsion is preventing complete collapse to a black hole. Our Sun’s radius is about 70,000,000 m. A small neutron star (1.4 solar masses) would have a radius of about 20 km = 20,000 meters. That’s a ratio of only 3500 (but to be fair, the Sun was already pretty densely packed).
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So if the universe was just a ball of quarks - it would still be 465,080 light years across.
And all that from a single point of energy smaller than an atom.
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Don’t get me started on string theory. It comes from a good place - setting a minimum length scale over which physical interactions can occur, in order to eliminate the need for the renormalization technique I mentioed above. But sometimes I feel like its developers (and I’ve known a couple as my friends’ PhD advisors) are oddly proud of its improvability. In a room with no objective truth, the person who argues best wins.
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To properly explain the double slit experiment, I need you to accept one thing from quantum mechanics: we can describe particles/waves with a wavefunction, and the probability of the particle being in any one spot is equal to the wavefunction at that spot SQUARED. The square is key.
When you fire a particle (photon, electron, cat, whatever) at the slits, it can go through either one, Its quantum state is therefore (top + bottom), with a normalization factor out front. The probability of it then hitting a particular point on the screen is then:
(top + bottom)^2 = top^2 + bottom^2 + topbottom + bottomtop
(Note that those last two terms aren’t necessarily equal. If you don’t like linear algebra, don’t do QM).
It is those last two cross terms that create the interference pattern. If you observe which slit the particle passes through, you “collapse” the wavefunction to either just top or just bottom, and so the probability will go as just top^2 ot just bottom^2, and you only get two peaks at the screen.
That’s why the double slit experiment works even if you only send through one particle at a time. The particle is interfering with itself.
(And as somebody said earlier, “observation” is poorly defined and how/why wavefunctions collapse isn’t either. That’s the hairy edge of the unknown.)
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What is the exact mechanism of observation in the double slit experiment?
There are many possible ways to do it. Feynman suggests putting a thin piece of scintillator crystal in front of one of the slits (this only works with particles, not photons), so that you get a light pulse if the particle passes through there. The fun thing about that setup is if you make your sensor inefficient (either make ot too thin, or not cover the whole slit, or use a poor light detector), you will get a mixture of interference and non-interference patterns. Other setups work by directing particular polarization or spin states to a specific slit.