Math is Beautiful, math is the absolute truth and that makes it beautiful. Mathematicians even go so far as calling it an art form.
mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show - Bertrand Russel
One of the most amazing equations, in my opinion, is the Lorentz factor,
Virtually all of the mathematics behind Einsteins theory or special relativity can be reduced back to this one, simple equation. basically, these few lines describe exactly what happens when you travel close to the speed of light, and the fact that it is as simple and short as it is, is beautiful.
A Gravity well or gravitational well is defined as “a conceptual model of the gravitational field surrounding a body in space.”
The more massive the body, the deeper and more extensive the gravity well associated with it. The Sun is very massive, relative to other bodies in the Solar System, so its gravity well appears “deep” and far-reaching.
(picture a very heavy object sinking deep into a bed mattress; the more mass the object has the deeper it sinks in and creates a deeper sinkhole; a deeper sink hole will pull in any nearby objects towards the centre object with greater influence. Objects of mass bend the fabric of spacetime this way also as the theory of general relativity explains)
Regular, otherwise known as Newtonian physics only applies on the average, everyday, scale. That is, objects larger than an atom at low energy, where energy in this context refers to velocity and (sometimes) temperature.
Once you step it up, increasing to high energy levels, (when velocity approaches c, the speed of light) newtonian physics no longer works due do what we call relativity, and observations or calculations need to take into account this effect usually using some form of the Lorentz factor,
gamma = [ 1 - (v^2)/(c^2) ]^(-1/2)
On the other hand, if you keep to a low energy system but bring the scale down to sub-atomic particles, such as electrons, things change yet again, but this time in an entirely new way. This is where Wave-Particle dualtity theory comes into play, the theory that waves (namely electromagnetic, i.e. light) are particles, and particles are wave packets. not only do you need to account for this, but you also need to take into account Heisenbergs uncertainty principle; It is impossible to know both the exact velocity and exact position of a sub atomic particle, the more certain you make one the less certain the other becomes.
Finally we come to Quantum Field Theory, which i honestly do not know anything about, at least i won’t until third year physics when i start taking courses on it.
I was just wondering how many hours of existence 36-year-old John has left, and it got me thinking. youve-got-your-love-online, who lives in a very different time zone from me, reminded me that it’s John’s birthday, and I was like, “wait, no, it’s tomorrow” because here it’s still Saturday. But John’s actual age has nothing to do with what time zone any of us live in now, including John. Your age doesn’t change as you change time zones, it’s completely dependent on what time it was (and where you lived) when you were born. Unless of course you’re travelling over time zones at light speed.
Great visualization of gravity. I’m sure most of you have seen something like this before, it’s fairly common, but stick with it. At first the lecturer just covers the basics, but then he goes into more complex orbital systems.
Our brains have a hard time putting the immense scale of Time (as in “all of it”, which is why it’s capitalized) into perspective. We’re just not built for that kind of thing. While we’re at it, scales of size throw us for a loop too.
That scale of that time, be it seconds, years or atomic oscillations of cesium atoms, is just the construction of humans, signposts along the way so that we can mark how different now-now is from then.
But wait, is now inherently different from then? Yes. That’s where time comes from in the first place. Time only moves in one direction. There’s a reason that the universe can not be reversed, a rule that makes today different from yesterday.
The arrow of time points forward. As long as the universe is getting messier, time will continue to tick on. Entropy, man. All the things are in a more disordered place than they just were, just then.
Life itself depends on the fact that the universe is not in thermal equilibrium. There are simply many more ways that matter can be disordered than it can be organized neatly, and our biochemical reactions take advantage of that. Be thankful for entropy.
Like Brian Cox says, there are more sand dunes than sand castles. I mean, probability says sometimes you’ll get a sand castle spontaneously forming on the beach, but you’ll get a gazillion random piles of sand in the meantime. So entropy marches on, and the universe gets disordered, and new nows become different from just thens.
Then why isn’t our world just some strange exception among the mess?
If ordered piles of molecules named Joe are just some rare, low-probability fluctuation in a universe that would much rather be in all kinds of disordered non-Joe-ness, then why does so much of the universe seem to look organized? I mean, there’s you, and there’s the rest of Earth, and the rest of everything. Why isn’t this the only planet, star, galaxy, etc?
Well, maybe we’re only a chicken that’s come out of a larger egg. Maybe we’re not a closed system. Maybe, there’s more beyond this universe?
If any of this time business turns out to be too stressful, there’s a way out. But there’s a catch, it involves moving close to the speed of light. And if you dilate yourself out of this time scale, you’ll leave all of us behind, and we don’t want to see you go. Unless you take us with you. It’s that pesky twin paradox:
Born March 14, 1879, in Ulm, Germany, Albert Einstein (1879−1955) seems not to have anticipated how famous his theories and ideas would make him. And as you see from the quotation in the image above, Einstein professed to be mystified by the adulation and attention that rained down on him as his last name became, even during his lifetime, a byword for “genius.”
The truth is, however, that his life and work continue to intrigue. After all, as the Museum’s Einstein exhibition (on display in 2002−2003) points out, “Albert Einstein reinterpreted the inner workings of nature, the very essence of light, time, energy, and gravity. His insights fundamentally changed the way we look at the universe—and made him the most famous scientist of the 20th century.”
The Law of Initeria can be said to be “A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line” This law talks not only about the body that is in the reference state but as well as other objects that are ‘removed sufficiently far from other bodies’. This can be viewed as the Earth with stars that appear to be fixed since they are sufficiently far away. Over the time of a day the stars can trace out a circle around the Earth, a circle as we all know is not at rest or a linear trajectory. This breaks the law of initera in this reference frame.
Scientists studying cosmic microwave background (the faint afterglow of the Big Bang) have detected a signal generated a trillionth of a trillionth of a trillionth of a second after the Big Bang began. They’ve found gravitational waves — ripples in the fabric of space-time. Physicists are especially excited (and they’re trying their best to get their non-physicist friends excited too) because studying these waves could help bridge the divide between our understanding of gravity and quantum mechanics. You can hear more about it here.
Image credit: This is the telescope they used to detect the gravitational waves. It’s called the South Pole Telescope, and it was photographed by Eli Duke.