E = mc^2 is not an equation relating to gravity in the way you imply, that’d be the Einstein Field Equation [1], which still depend on G. And as far as we know, c is also a constant.
Then I’d guess a bunch of statistical constants probably show up in the humanities all the time. Is that what you are looking for, or some closed form expression with the constant?
The important facing questions are “where is my window facing” and “where is my bed facing in relation to the window and door”. Magnetism is irrelevant, as we are no migratory birds who can actually sense that field.
Although you’re practically right, we can technically actually sense magnetic fields. It’s incredibly weak and you have to drown out all other senses, but it’s possible.
Facing away from the door (I.e. having the door in the back) makes some people anxious, like people usually turn and face the door in an elevator. That’s why a hotel bed often faces the door.
The position relative to the window is a question of light.
situational awareness. humans instinctually need to feel safe. sleeping with your head right by the door gives you the least amount of reaction time/space to stave off invasion. inagine a rabbit sleeping with its nose out of a rabbit hole. in modern times with modern locks and security, its not a big consideration to be faie. but the instinct is there. people like headboards on beds for the same cavelike feelibg of protection. so yea head away from the door, bed not by the door. windows used to be avoided for being drafty or leaking light.
Think of this as this: The wavelength is the distance that light travels during one wave i.e. cycle. Light propagates with the speed of light, so the smaller the wavelength, it means the frequency must increase. If the wavelength gets two times lower, the frequency increases two times. If wavelength approaches 0, then frequency starts growing very quickly, approaching infinity.
Interesting. Sparked by your comment, I found this.
What’s the maximun frequency of light?
Approximately 2 x 10^43 Hz is the “Planck frequency” (the inverse of the Planck time). At that frequency, individual photons (or any other particle with this much energy) would be black holes (their Compton wavelength would be smaller than their Schwartzchild radius), and so until someone comes up with a theory of light which includes virtual black-holes, photons with a frequency above this cannot be considered sensible.
I think that answer is a touch misleading because it makes it sound like this is a fundamental physical limit, when really it’s just the scale where our current theories break down and give nonsense results, so we don’t really know what is going on at that scale yet.
Cold blooded means their body temperature relies on an external source. It doesn’t mean they don’t need to have warm blood. Without an external heat source they become hypothermic and will eventually die.
There are many ways to do spectroscopy because of the wide range of wavelenghts of light. I won’t go into detail, but essentially what spectroscopy does is either:
Put energy into a sample and see what is absorbed (absorbtion spectroscopy)
Put energy in a sample and see what comes out (emission spectroscopy)
The reason those two methods produce characteristic results for each element is the following: An atom is made up of a nucleus of a certain charge and electrons canceling that charge around it. Those electrons are confined to so-called orbitals due to quantum weirdness (the “quantisation” of the orbitals is literally the origin of the word quantum). Those orbitals have different energies (you can imagine that an electron being very close to the nucleus is more strongly attracted than an electron which is farther away).
Because the electrons need to always be on those orbitals with fixed energies, only certain energies of photons can interact with them (if a different energy photon wanted to interact with an electron it would need to push the electron “between” two orbitals which is forbidden by quantum mechanics)
So now only certain energies of photons (which relate directly to wavelength) are absorbed, the rest passes uninterrupted leading to bands in the spectrum where lots of photons are absorbed.
Now depending on how many electrons your atom has and how far away they are from the nucleus those absorbtion bands will vary, giving you a good idea which atom you are looking at.
Emission spectroscopy works the other way around, instead of you seeing what is absorbed, you randomly put energy (often using heat) into the atom. When the atom wants to go back to its most stable state it has to emit a photon, this photon needs to correspond to a gab between two orbitals (because else the electron either starts or ends outside of an orbital (which is forbidden))
For molecules the elecyrons of the individual atoms are mixed together into their own molecular orbitals that follow the same logic the commenter above had written with respect to energy levels and photons.
I’m specifying this because the OP was asking about individual elements within a molecule, and that’s not how that works. The electrons are shared so you don’t get the emissions from the elements composing the atoms in the molecules on their own.
Its better to not think of it as something we created in a lab. Higgs plays a part in making nature do what it does.
If you want to learn more about the Higgs Mechanism, check out this video from PBS Space Time. You might also find some good info in the comments as well.
I’ve read that all math breaks down as you approach the big bang. I’m not educated enough in math to understand how, or why, but apparently they cannot mathematically understand the origin of the universe.
But if you condense it all into something infinitely dense, then is it suddenly finite in size? Does it still have infinite size and simultaneously infinite density? Why didn’t the immense density cause it to form a black hole?
I don’t think current understanding of things is that the universe is infinite. We can estimate the size of the universe we know, because we know how fast it is spreading and for how long. Wiki says: "Some disputed estimates for the total size of the universe, if finite, reach as high as 10 10 10 122 10^{10^{10^{122}}} megaparsecs. We don’t know whether that’s all there is though. We don’t even know whether the universe has the same properties everywhere, which complicates things.
My understanding is that it has a 14 billion light-year radius from any given point. We can only see 14 billion light years away, since the universe is only 14 billion years old (actually 13.8). Light can only travel at a given speed, so we can’t see beyond the distance light has traveled during the existence of the universe. But since the universe expanded in all directions, from everywhere all at once, it’s truly infinite. If you were to teleport 14 billion light-years in any direction, you would still see 14 billion years away, since the universe expanded from that point too during the big bang. It’s mindfuck level stuff.
That understanding is intuitive but very wrong. We can see parts of the universe that are up to 46 billion light years away because of the expansion of space. The actual physical universe extends beyond that, further than we can observe.
The light didn’t travel 46 billion lightyears, but the objects whose light we are seeing are 46 billion lightyears away by the time we collect that light due to expansion. So the agreed on “radius of the observable universe” is 46.something GLY
youtu.be/XBr4GkRnY04 this old video from Veritasium explains the concept of the hubble sphere and the particle horizon, both of which are further than 13.8.Billion lightyears away
youtu.be/eVoh27gJgME this newer video from PBS Spacetime goes into much further detail about how they’re calculated
They use the Lamda-CDM model which outputs the rate of expansion of the universe at every moment in past present and future. You measure the amount of light+matter+dark matter+dark energy that your universe has, plug those values into the Friedmann equation, and it spits out the rate.
You can try out an online calculator yourself! It already has those values filled in, all you need to do is enter the z value - the “redshift” - and click generate. So for example when you hear in the news something like “astronomers took a photo of a galaxy at redshift 3”, you put in 3 for “z”, and you see that the galaxy is 21.1 Gly (billions light years) away! That’s the “comoving distance”, a convenient way to define distance on cosmic scales that is independent of expansion rate or speed of light. It’s the same definition of distance that gives you that “46 Gly” value for the size of observable universe. But the light from that galaxy only took 11.5 Gyr to reach us. The universe was 2.2 Gyr old when the light started. So the light itself only traveled 11.5 Gly distance, but that distance is 21.1 Gly long right now because it kept expanding behind the photon.
Crucially, we are able to determine the distance by redshift via the observations of objects with known distance (like standard candles) and their redshifts. The ΛCDM model only becomes necessary for extrapolating to redshifts for which we otherwise don’t know the distance, but this extrapolation cannot be made without the data of redshifts of known distances.
That’s true! There is a kind of incestuous relationship between the cosmic distance measurements and the cosmic model. Astronomers are able to measure parallax only out to 1000 parsecs, and standard candles of type Ia supernovae to a hundred megaparsecs. But the universe is much bigger than that. So as I understand it they end up climbing a kind of cosmic ladder, where they plug the measured distances up to 100 Mpc into the the ΛCDM model to calculate the best fit values for the amounts of matter/dark matter and dark energy. Then they plug in those values along with the redshift into the model to calculate the distances to ever more distant objects like quasars, the Cosmic Microwave Background, or the age of the universe itself. Then they use observations of those distant objects to plug right back into the model and refine it. So those values - 28.6% matter 71.4% dark energy, 69.6 km/s/Mpc Hubble constant, 13.7 billion years age of the universe - are not the result of any single observation, but the combination of all observations taken to date. These values have been fluctuating slightly in my lifetime as ever more detailed and innovative observations have been flowing in.
Are you an astronomer? Maybe you can help me, I’ve been thinking - how do you even measure the redshift of the CMB? Say we know that CMB is at redshift 1100z and the surface of last scattering is 45.5 GLy comoving distance away. There is no actual way to measure that distance directly, right? Plugging in the redshift into the model calculator is the only way? And how do we know it’s 1100? Is there some radioastronomy spectroscopy way to detect elemental spectral lines in the CMB, or is that too difficult?
If we match the CMB to the blackbody radiation spectrum, we can say that its temperature is 2.726K. Then if we assume the temperature of interstellar gas at the moment of recombination was 3000K, we get the 1100z figure. Is that the only way to do it? By using external knowledge of plasma physics to guess at the 3000K value?
So if you take 2 things that started say ~3 billion light years apart (which would be ~1000x a megaparsec), that means every single second the universe has existed those 2 points have gotten 70,000km further apart. And now that they’re further apart, they separate even faster the next second.
For reference:
31.5 million seconds in a year. ( 3.15 x 10^7 )
universe is 13.8 billion years old ( 1.38 x 10^10 )
So we talking about this 70,000km getting added between the 2 points ~4 x 10^17 times.
Then you gotta bring calculus into it to factor in the changing distance over time.
It … adds up. Which is why you’ll see the estimates for the observable universe’s radius being ~46.5 billion light years (93 billion light year diameter), even though the universe had only existed for ~14 billion years.
And now that they’re further apart, they separate even faster the next second.
That’s a common misconception! Barring effects of matter and dark energy, the two points do NOT separate faster as they get farther apart, the speed stays the same! The Hubble constant H0 is defined for the present. If you are talking about one second in the future, you have to use the Hubble parameter H, which is the Hubble constant scaled with time. So instead of 70 km/s/Mpc, in your one-second-in-the-future example the Hubble parameter will be 70 * age of the universe / (age of the universe + 1 second) = 69.999…9 and your two test particles will still be moving apart at 70000km/s exactly.
The inclusion of dark energy does mean that the Hubble “constant” itself is increasing with time, so the recession velocity of distant galaxies does increase with time, but that’s not what you meant. Moreover, the Hubble constant hasn’t always been increasing! It has actually been decreasing for most of the age of the universe! The trend only reversed 5 billion years ago when the effects of matter became less dominant than effects of dark energy. This is why cosmologists were worried about the idea of a Big Crunch for a while - if there had been a bit more matter, the expansion could have slowed down to zero and reversed entirely!
Oh wow thanks. You learn something new every day! I’m definitely an “armchair physicist”, and still find it hard to think about things in a nonstacically geometric way.
Sounds like the Hubble Constant ain’t so constant :)
It’s impossible to measure precisely enough to know for sure that it is completely flat, or even saddle shaped (both being infinite in size). The generally accepted understanding by cosmologists is that it is infinite. But just due to the nature of measurement and tools we can’t completely rule out a finite universe. However we do know based on the measurements that it is really really… really really really big if it’s not infinite.
Another problem lies within the mathematical framework of the Standard Model itself—the Standard Model is inconsistent with that of general relativity, to the point that one or both theories break down under certain conditions (for example within known spacetime singularities like the Big Bang and the centres of black holes beyond the event horizon).[4]
My ELI5: Both theories work great, supported by vast amounts of evidence and excellent theoretical models. It seems they are two tools with distinct purposes. One for big and heavy stuff, the other for small and energetic stuff. The problem arises when big and heavy stuff is compressed into tiny spaces. This case is relevant for both theories, but here they don’t match, and we don’t know which to apply. It’s a strong hint we lack understanding, one of the biggest unsolved problems in physics.
So math itself is probably fine, we’re just at a loss how to use it in these extreme cases.
One of the first things you learn in college-level science is accuracy and precision. A measurement can have a degree of correctness and a degree of exactness about the value. For example a sensor may get the wrong reading 3% of the time. When you have a big pile of readings, you don’t always have the time to validate them all. So, there is some uncertainty that you accept. The same sensor may only be able to give you an accurate reading down to a specific decimal point, which is expressed as precision. Anything less is given as a range in which error exists. These ideas are important, because when you do calculations based on those readings, you have to take the error with you. There may be a point where the value you reach is overshadowed by the magnitude of the error.
They weren’t all big, but anyway, they (probably) evolved like giraffes to reach for food and as protection against physical damage from predators. The climate was also different and they had plenty of food.
Anyway, evolution does not select. It’s not survival of the coolest features… it’s only reproduction of those that manage to reproduce.
Are you asking about how you reinvent the exact same meter? Well that won’t happen. Our units were arbitrary, useful, widely adopted, and then rigorously defined.
The book walks you through it all. You can don’t need to redo civilization exactly the same (the author even suggests some very important things to invent differently, especially in better orders)
That’s a fair point. Most likely if a group of people did some kind of Long Term Naked & Afraid experiment they’d just start with some length of particularly well-crafted cordage, call it a New Meter™ and go from there
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