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August 6 - September 15, 2022
principle of equivalence. The strange consequences of special relativity are teased out of the principle of relativity, which states that it is impossible to tell whether it is me who is moving or my environment that is moving past me.
Equivalence
If you are floating out in space in a spaceship with no windows and I place a large massive planet underneath the spaceship, you will be pulled towards the floor. This is the force of gravity. But if instead I accelerate the ship upwards, you will experience exactly the same sensation of being pulled towards the floor. Einstein hypothesized that there is no way to distinguish between the two: gravity and acceleration produce the same effects.
Equivalence
The astronaut at the bottom of the spaceship is going to send a pulse of light to the astronaut at the top each time his clock ticks. The astronaut at the top can then compare the arrival of these pulses with the ticking of her clock. Without acceleration or gravity, the arrival of the pulses and the ticking of the clocks will be in synch. However, let me now accelerate the spaceship in the direction of the top of the spaceship. A pulse is emitted at the bottom of the spaceship, and, as the spaceship accelerates away, the light has further to travel each time, so that it takes longer and
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Wow what an explanation!
This is similar to the Doppler effect we experience with sound, where moving away from the source causes the frequency to decrease, resulting in a lower pitch.
Same concept
What if I reverse the experiment and get the astronaut at the top of the spaceship to send pulses down to the bottom of the spaceship? Because the astronaut at the bottom is accelerating towards the pulses, he is going to receive them at a faster rate than the pulses of light he is sending. So he will confirm that his clock is running slower than the clock at the top of the spaceship.
Reverse
According to Einstein’s principle of equivalence, whatever effect acceleration had on the clocks in the spaceship, the effect of gravity must be the same. So when I place a large planet at the foot of our Shard-sized spaceship, the impact is the same as if the spaceship was accelerating through space: clocks run slower at the foot of the Shard than they do at the top.
Well put
Ina returns younger because she has to accelerate to get to her constant speed. Similarly, when she turns around she needs to decelerate and then accelerate in the opposite direction. This causes her clock to slow down relative to that of her twin on Earth, who doesn’t accelerate. This asymmetry results in Ina heading into Magaly’s future. If I sent both twins off in spaceships in opposite directions and brought them back together then they’d be the same age – and everyone on Earth would have aged quicker.
Gravity is actually the distortion of this space-time surface. If something has mass, it curves the surface. The classic way to imagine this is to consider space-time as a two-dimensional surface, and the effect of mass as that of placing a ball on this surface. The ball pulls the surface down, creating a well. Gravity can be thought of as the way things get pulled down into this well.
Known. Gravity.
This distortion of space-time has an interesting effect on light. Light follows the shortest path between two points – the definition of a ‘straight’ line. But I am now talking about lines in space-time, where distance is measured using Minkowski’s formula that includes the coordinates of space and time. Weirdly, using Minkowski’s formula, it turns out that the distance between two points in space-time is reduced if the light takes longer to get there.
The speed at which you need to throw the ball is called its escape velocity. But imagine increasing the mass of the Earth more and more. The speed required to escape the gravitational pull also increases. But there will be a point at which the mass of the Earth is so big that the ball would need to be launched at a speed faster than the speed of light in order to escape. At this point the ball is trapped. It cannot go beyond a certain point before it is pulled back to Earth.
too big a mass to escape
But Einstein’s conception of gravity as the result of curved space-time can still result in light failing to get away. Einstein’s ideas suggest a region of space that is so curved that even light (which is massless yet still affected by the curvature of space) cannot escape. Space is curved so much that no light can find its way out but is bent back into the region of high density.
even light couldn't escape
The mass of the star needs to be sufficiently great for the mass to collapse within the region of this sphere. For example, the mass of the Earth is too small to create a black hole – it would need to be packed into a sphere with a radius of just 1 centimetre. Our Sun is also not massive enough: the radius of its event horizon would be just 3 kilometres. But if the mass of the star is 1.4 times greater than the mass of our Sun, the inward pressure of gravity will counter any outward pressure caused by the high momentum of the trapped matter and it will collapse inside its event horizon.
1.4 times
In collaboration with a young Stephen Hawking, Penrose went on to prove that the same infinite density is predicted when we rewind the universe back to the Big Bang.
blackhole and big bang
A very homespun example of a singularity can be realized by taking a coin and spinning it on a table. If there was no friction on the table or air resistance, the coin would spin forever at a constant speed. However, because in fact energy is dissipated, the coin does not spin forever. Instead, the angle of the coin to the table decreases, and, intriguingly, the speed of the rotation increases proportionally. As the angle approaches zero, the speed eventually becomes infinite. The final stages of the spinning result in the coin shuddering as it falls and there is a whirring sound whose
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example of infinity and singularity. interesting.
The spinning coin is an example of a singularity. Of course there are other effects that come into play to stop the full realization of this mathematical infinity, but it does reveal that you don’t have to disappear down a black hole for the equations of physics to produce infinities.
main
Even Newton’s equations on planetary motion can produce singularities. As I explained at the end of the First Edge, mathematician Zhihong Xia
singularity 1
revealed that four planets can be arranged in such a way to cause a fifth planet to be ejected from their midst, so that after a finite amount of time that planet hits infinite speed. The equations have nothing to say about what happens to that planet once it hits this astronomical singularity.
singularity 2.
interesting concept. the cutting point between two states is the key to a lot of issues. google.
Singularities are typically moments where infinities kick in and beyond which it is impossible to make predictions. It isn’t just in physics that these singularities can emerge. There is a famous example, published in 1960 by Heinz von Foerster, Patricia Mora and Lawrence Amiot, which predicts a serious singularity here on Earth. The rate of population growth, if it followed the pattern of behaviour observed up to 1960, indicated that the population of the planet would become infinite on 13 November 2026. A Friday, it so happens, if you’re at all superstitious.
13th November. 2026. Friday.
Population become infinite
Another example of this super-exponential growth is the rate of increase of computer power. There is a dictum called Moore’s law, which states that computers double in power every 18 months. With such an increase, computers are powerful but never hit a singularity. But others have suggested that just as the time it takes for the population to double seems to be getting shorter, the same applies to technology. The possibility of a technological singularity has given rise to something called the Singularity movement. Popularized by inventor and futurist Ray Kurzweil in his book The Singularity
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2045. singularity.
It is strange that elsewhere time seems to tick on obliviously. I guess we all have a similar fate waiting for us. When we die, time stops for us, but we know that time will continue on unawares. Just as I cannot experience my own death, I wouldn’t experience arriving at a singularity in space-time.
death
The interesting thing is that someone outside the event horizon will never know what is going on inside. From their perspective, time does appear to stop as soon as I cross the event horizon, and for them there is no telling what comes after, although there is an after for me as I carry on towards spaghettification. So asking what happens next appears to be a sensible question. It has an answer. The only trouble is that if you are outside the event horizon, you are denied access to the answer by the laws of physics.
inside and outside
Singularities in space-time are edges, points at which I hit an end and can’t go any further.
质变
An edge in space and time is difficult to understand: even though I may be prohibited from going any further, I still feel there should be something beyond that edge.
Something beyond
But provided I have complete information about all the atoms and photons involved in my bonfire, it is theoretically possible to rewind the process and recover the information contained inside the magazines. It would of course be extremely difficult in practice, but the science asserts that there is nothing about this process that is irreversible. The laws of physics work both ways. The existence of black holes offers a challenge to this idea. If I throw one magazine in one black hole and the other magazine in another black hole, it is now impossible to find out which magazine went into which
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Ultimate shredder. Interesting take
Or consider the everyday example of an egg falling from a table and smashing on the ground. The highly ordered egg becomes a scattered mass of eggshell. There are many more ways for the broken shell to be arranged than when it was in one piece around the egg. Watch a video of this scenario run forwards and backwards and it is clear which direction represents the true flow of time. Increased entropy keeps track of time’s arrow.
High entropy
The process is a bit like smashing the egg. A single photon of high frequency is absorbed by the Earth like the egg falling to the ground, and then the Earth kicks out many photons of low energy like bits of eggshell. The Earth benefits by a net decrease in its own entropy, and we witness order emerging out of chaos. But consider the whole system of the Earth and Sun, and entropy is indeed increasing just as the second law of thermodynamics demands.
Earth and sun
Heisenberg’s uncertainty principle implies that the event horizon is a little fuzzier than the mathematics of general relativity implied. As we saw in the Third Edge, the uncertainty principle means that position and momentum cannot both be known precisely. Similarly, time and energy are related in such a way that I can’t know both simultaneously. Therefore we can’t have a perfect vacuum in which everything is set to zero. If everything was zero, I’d know everything precisely.
Nah uncertainty only applies in quantum world
We get this strange effect: the particle inside gets sucked into the black hole, and since it has negative energy it reduces the mass of the black hole; while the particle with positive energy looks like something being radiated away from the black hole. The black hole is glowing – it has a temperature, just as we would expect if the black hole had positive entropy.
The striking implication of Hawking’s proposal was that it provided a mechanism for black holes to fade away, reducing in mass as time passes. As the mass decreases, the radiation increases, with the result, it’s believed, that black holes will eventually disappear with a pop. Hawking predicted the pop would be pretty grand: equivalent to the explosion of millions of H-bombs. Others believe it to be more on a par with an artillery shell going off.
End of BH
The Big Bang singularity is a state of very low entropy. As the universe evolves, entropy increases – how can we move seamlessly into the next aeon and reset the entropy? This is why Penrose was unhappy that Hawking conceded the bet about black holes. In Penrose’s view, black holes are the mechanism for resetting entropy. All the entropy entering a black hole is lost or subtracted from the whole system, so that by the end of the aeon we are at low entropy again, because all the information has been lost in the plethora of black holes that populate the universe. This sets up the conditions for
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Just for notes:
penrose. multiple aeons, crossovers and singularities.
Penrose is a great example of how the desire to know never fades. Because he wrote a book with the subtitle A Complete Guide to the Laws of the Universe, you may assume that he thinks he knows it all. But Penrose is still asking new questions.
complete guide to the laws of the universe. Penrose.
I wanted to know which problem he would like to see resolved if he could choose one. Since time is on Penrose’s mind, he chose evidence of a time before the Big Bang. ‘I’d like to see signals from the previous aeon. But we’re a long way from that.’
Signal
For religious commentators this poses an interesting challenge: what is God’s perspective? For God, did A happen before B, or vice versa? One answer is to respond as the Vatican representative had to Penrose: take God outside of time. Just as God is not located at one point in space, there is no need to locate God at one point in time.
God
If you opt for theism rather than simple deism, then God needs to have a temporal quality to intervene in the world. If God is outside, looking at the whole of space-time, the future is already there in the landscape. Interestingly, although people may argue over the order of events, they won’t argue about their order if they are causally related. This demands a God who steps in and out of time, moulding the geometry of space-time. But a God who acts in the world is a God who acts in time. So it is very difficult to square a timeless God with a God who acts in the universe.
God
The question remains: what is this thing called God that is meant to be outside of time? Can anything be outside of time? Actually, there is something that I would regard as timeless: mathematics. And as a timeless thing it is well suited to the job of sparking the creation of what we observe around us. It is the creator responsible for the equations of quantum physics that give us space-time and something from nothing. Mathematics has an attractive quality: you don’t need to ask who created the mathematics. It is something that exists outside of time and doesn’t need a moment when it was
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Interesting. Maths
quidditism: the idea that there is more to the universe than just the relationship between objects – what they are (the quid is Latin for ‘what’) provides another level of distinction.
If mathematics is eternal and outside of time, you don’t need a creator to begin things. The equations of mathematics are truly outside the universe, so they could play the role of something supernatural and godlike. It is not, however, a God that acts in the world, because this is a deistic vision. The interesting question is then: how many different ways are there to set up a universe out of a set of mathematical equations? The multiverses now arise from multi-mathematical models.
This was the aim of physicist Julian Barbour. Working without an academic position, supporting his family by translating Russian, Barbour has developed a theory of physics that removes the need for time at all. His ideas are articulated in his ground-breaking book The End of Time, published in 1999. ‘Nothing happens; there is being but no becoming. The flow of time and motion are illusions.’ A number of physicists within mainstream academia have taken his ideas very seriously.
end of time
Once the brain is removed from the skull, you first notice that there are three distinct pieces: two halves, which seem to be mirror images of each other, called the cerebrum, and then, sitting underneath, what looks like a tiny version of the brain called the cerebellum.
brain
Extraordinary footage exists of one patient who underwent such a corpus callosotomy, which shows the left side of the body physically attacking the right side. The left side of the body, which is controlled by the right hemisphere of the brain, does not have access to the language side of the brain, which is located in the left hemisphere, so was unable to articulate itself verbally. This frustration seems to have manifested itself in the attack. Eventually, the patient took drugs in order to suppress the right hemisphere and allow the articulate left hemisphere to dominate.
google
The slowest are delta waves at 1–4 hertz, which are associated with deep, unconscious, dreamless sleep. Theta waves are next at 4–8 hertz, associated with light sleep or meditation. Faster than alpha waves are the beta waves at 13–30 hertz, which the brain hits when it is wide awake. Believed to be most important for the brain’s ability to create consciousness are the fast gamma waves at 30–70 hertz, frequencies that just creep into the bottom range that my cello can play. Gamma waves are associated with the formation of ideas, language and memory processing, and with various types of
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hertz
It was as if this new mathematical object was thrust up into my conscious brain, having been honed in my subconscious, accompanied by a chemical rush to make sure I didn’t miss it. But still quite what happened so that I had that experience is a mystery.
Same as dreams to make you wake to pee
The brain is a pattern searcher and is trying to impose structure on the cacophony of information it is being bombarded with. When the information is ambiguous, as in the example of the Necker cube or the McGurk effect, the brain has to choose.
Choose
Wetness is the classic example of an emergent phenomenon: one molecule of H2O is not wet; wetness requires that you put many molecules together before it appears.
Haynes can see which button I will choose because there is a region in the brain that lights up six seconds before I press, preparing the motor activity. A different region of the brain lights up according to whether the brain is readying the left finger to press the button or the right finger. Haynes is not able to predict with 100% certainty yet, but the predictions he is making are clearly more accurate than if you were simply guessing. And Haynes believes that with more refined imaging, it may be possible to get close to 100% accuracy.
6 seconds
Tononi and colleagues have run interesting computer simulations on ‘brains’ consisting of eight neurons connected in different ways to see which network has the greatest Φ. The results indicate that you want each neuron to have a connection pattern with the rest of the network that is different from that of the other neurons. But at the same time, you want as much information to be able to be shared across the network. So if you consider any division of the network into two separate halves, you want the two halves to be able to communicate with each other. It’s an interesting balancing act
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greater connection
Tononi
That the connectivity of the brain could be the key to consciousness has led to the idea that my ‘connectome’ is part of the secret of what makes me ‘me’. The connectome is a comprehensive map of the neural connections in the brain. Just as the human genome project gave us unprecedented information about the workings of the body, mapping the human connectome may provide similar insights into the workings of the brain. Combine the wiring with the rules for how this network operates and we may have the ingredients for creating consciousness in a network. The connectome of the human brain is a
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C.elegans
If consciousness is about the connectivity of the network, what other networks might already be conscious? The total number of transistors that are connected via the Internet is of the order of 1018, while the brain has about 1011 neurons. The difference lies in the way they are connected. A neuron is typically linked to tens of thousands of other neurons, which allows for a high degree of information integration. In contrast, transistors inside a computer are not highly connected. On Tononi’s measure it is unlikely that the Internet is conscious … yet.
interesting take. maybe it is the trend and direction for how things evolve.
there is no reason for living organisms to exist yet here we are.
‘One of the unknowns is how many different sorts of brain cells are there. We’ve known for two hundred years that the body is made up of cells, but there are heart cells and skin cells and brain cells. But then we realized that there aren’t just one or two types of brain cell. There may well be a thousand. Or of the order of several thousand. In the cortex proper, we just don’t know.’
types of brain cells
Koch has a tough battle on his hands convincing others. There is a hardcore group of philosophers and thinkers who don’t believe that science can ever answer this problem. They are members of a school of thought that goes by the name of mysterianism, which asserts that there are mysteries that will always be beyond the limits of the human mind. Top of the mysterians’ hit list is the hard problem of consciousness.
mysterianism
