This article mentions that the speed of light seems fast to humans living daily lives, but is not so fast on an astronomical scale.
The best demonstration of this I've ever seen is on "If the Moon Were Only 1 Pixel - A tediously accurate map of the solar system" [1].
If you've not seen it before, I recommend opening it, using your mouse wheel to scroll from the beginning (near the Sun) to Earth. It should take about a minute, but there's some commentary on the way. Then, to save your mouse and your finger some work, try clicking the icon in the bottom right hand corner to auto-scroll the map at the speed of light.
These videos were super fun to make and kept me sane when I found myself with far too much free time and a bunch of world news to avoid. I never did the fifth (and final) walk but it's only about 100 meters long so I hope one day to do it in person (if I ever end up with that much free time again).
It’s always crazy to me how empty most of space is, and that yet despite that gravity is strong enough on large timescales to pull a lot of stuff together. Then I get concerned as to why EVERYTHING wasn’t pulled together and it’s literally just this little bit of angular momentum conserved across vast distances and added together from all these little particles that is keeping everything apart just enough for us to exist.
This is something I find incredibly counter-intuitive. At the photon’s reference frame (speed of light), time stops. In our reference frame, I’d expect some kind of “divide by zero” error in nature, resulting in the infinite speed of light. But it’s not infinite. It’s just… some constant.
It's the maximum speed through space and time. The speed of light through time is just 1s/s. Einstein says space and time are equivalent, so as your velocity through space approaches c, your velocity through time approaches zero and vice-versa.
The photon has zero velocity through time because its velocity through space is c. In its reference frame, no time passes between creation and destruction, but from all other reference frames it appears to be moving through space in discrete time but with high velocity.
This was awesome. It's strange to know that I already understood this (conceptually at least), yet seeing how slow it really is at this scale is confusing. Maybe that's not quite the right word. It makes my brain pause and go "that can't be right", but... It's right.
Brains are bad at these scales. Maybe mine is worse than average. I can't fully believe how impossibly far away so many things truly are.
I thought light in a vacuum was (outside of some corner cases) the fastest you could get in this universe? That seems pretty fast on an astronomical scale to me. I mean it’s probably just that we have extremely short lives on an astronomical scale.
The speed of light is actually the speed of causality. No matter, or more importantly information can go faster than that. This has some real consequences even on human scales.
For example, if you've ever opened an electronic device and seen squiggly traces everywhere, it's because of light speed[0]. When signals get fast enough, you have to make sure the traces have the same length to within a fraction of a millimeter. Otherwise, the signals on two traces arrive at different times and nothing works.
[0](electrons move at ~c, more or less)
There's a significant delay in satellite communications, on the order of milliseconds. It takes several seconds to reach the moon. 20 minutes to Mars, a few hours to Jupiter. Famously 8 minutes to the sun. The nearest galaxy is 1.5 million years away.
Consider how stupefyingly large our solar system is. Then consider how insanely huge the galaxy is: 90,000ly. It takes ninety thousand years for a photon to go from one edge of the galaxy to another. Then compared to the universe at large, our galaxy is essentially a single point.
Light is extremely slow and the universe is vast beyond our meat brain's ability to comprehend.
Pedantic: electrons (in a wire) move at relatively ordinary speeds. Wikipedia says this [0]:
>The drift velocity in a 2 mm diameter copper wire in 1 ampere current is approximately 8 cm per hour. AC voltages cause no net movement. The electrons oscillate back and forth in response to the alternating electric field
Think of it more like a long row of billiard balls. You hit the first one, it moves a little, then it hits the next one, that one moves a little etc. Except the "hit" is just getting closer to the next electron to make it move (like if they were magnets).
At least that's my understanding of it.
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Maybe "hit" is the correct word? Isn't it the same forces at play that stop my hand from going through the table?
You are correct, electrons (aka current) through a wire move at relatively low speeds at room temperature because of wire resistance. Changes of voltage however, like if you flip a data pin from 0V to 5V move at the speed of light.
So switching circuits need to take into account "transmission line" effects.
I don’t think you understood my point? Why did you type all of that, when it’s basically what everyone else has said. I know about max speed of information and causality and have for decades. I was talking that light in a vacuum speed is basically “fast” since nothing is fast, in both and absolute and a relative sense, at least in my take :)
I’ll steal a line from a superb YouTube physics channel (Arvin Ash): it’s not the speed of light, it’s the speed of causality. And the universe must have a finite speed of causality. Without even getting into math and physics, you can intuitively understand how infinitely fast causality would prevent time, and therefore everything else we know, from being possible.
Yes, I was often very confused as to why the speed of light shows up everywhere, until it was reframed for me in this way. The fact that light travels at the same speed regardless of your frame of reference becomes a little less mystifying.
It feels more intuitive to me when thinking about it as causality always unfolding around you at the same speed, no matter your own frame.
The constant c was not named for causality, but it is a nice coincidence.
But causalities that don't propagate at the speed of light, and are not based on light, such as ordinary objects moving around and jostling each other, do not appear the same in every reference frame.
Trick question. Am I someone on Earth? (If so, 8 minutes). Or am I in a ship that is hurtling toward the Solar System at 0.999c, roughly in line with the Sun-Earth axis? If so, although I see speed of light as c, the Sun-Earth distance is foreshortened relativistically, so it will be less than 8 minutes between me perceiving the event that the Sun disappeared and perceiving the event that the Earth lost illumination.
It's not just Arvin Ash. That's actually fairly common terminology amongst physics educators nowadays. For starters: You'll find a lot of physics YouTube channels that say "speed of causality". It has even started to make its way into the astrophysics and physics textbooks in the last couple of years.
Einstein was not talking about light in his SR and GR theories. He was talking about the "speed" of light. As simple as that is, took me a long time to get it.
Interesting thanks. I hadn’t seen it elsewhere myself but I could see how it’s taken off. OP’s article almost gets there, but never says that specifically. Rather it says “c is not a property of light, it’s a property of the universe.”
Thanks, I’ve never heard this and it’s quite profound. It’s always bothered me that there even is a top speed, and further that mass becomes infinite as it’s approached. But “speed of causality” makes these less strange.
If the universe’s causal mechanisms were infinitely fast, the entire history of the universe would play out instantly in zero time, and we’d skip straight to the heat death of the universe.
The fact that time even exists is implied by / a result of causal actions having some finite propagation time.
> causal actions having some finite propagation time.
I think I know what you're getting at, but somehow the phrasing bothers me, as if there is meta-time or as if cause and effect have time between them... for the photon at light speed, time isn't passing, it's emitted and then zero "time" later it hits something very far away.
It's more like we somehow need to think of cause and effect chains that have orderings without time.
I wonder if future generations will ever look back and casually quip something about "well they believed X existed, that was their problem, it all makes intuitive sense if you just..."
Yes, the basic idea is that photons do not 'experience' time. They 'experience' creation, all points along their path, and absorption 'simultaneously'.
However, you have to be careful with terminology. There is no inertial frame co-moving with the photon. All we can say is: as a massive particle gets faster relative to an observer's frame, the time it experiences relative to the observer's frame becomes shorter, and in the limit, as it approaches the speed of light (but never reaches c), the experienced relative time approaches zero (but never reaches 0).
This is well explained by Don Lincoln on the Fermilab YT channel:
While what you say is true, it seems to me like what you're describing isn't quite the same definition of causality being infinitely fast.
The fact that causal effects happen in the next tick means some minimal time has passed. So in your definition causality can cover the entirety of a finite universe in an incredibly short amount of time (one tick). But it seems like that's not the same as covering the entirety of a finite universe in zero time. In that case, every result would happen within the same tick as its cause.
There's more than one way to "implement a universe", but one hypothetical way to run a simulation is to alternate the simulation of forces and effects/causes.
A simulation could use particles with attributes like position, velocity, and also a "sum of forces". Then each update has the following steps:
1. Reset the sum of forces for all particles to zero.
2. For all particles, add the contribution to the forces on it from all other particles.
3. For all particles, update the next particle position based on the collected forces.
In the above, there's no intermediate state between updates, everything moves to the next position synchronously from the perspective of in-universe observers. (The external simulation can update particles one-at-a-time, but this is not an "observable" inside the simulation.)
But it is not a coincidence. Light — the EM field waves — propagates at causality speed because the EM field respects a particular property of the universe, the so-called gauge symmetry. That is intimately connected to the fact that the photobs has no mass.
Other similar particles, like the W and Z bosons, are manifestations of the weak field. Since that field breaks the symmetry, those particles have mass and move slower.
BTW, that symmetry breaking is the very same one that physicists talk about when we discuss the Higgs boson.
The question seems to me not why there is a speed of causality, but why the speed has this particular number. And it's not clear we know why that is, any more than we know why the proton mass is about 1836 times greater than the electron mass.
It's difficult to say that it has any given number, since our measurement units for both time and space are derived from it (via a short detour to the size of Terra, in the 18th century). It can have any finite number you like, just adjust the metre and second to match.
One physics convention just sets its value to 1. All of those Minkowsky diagrams that we see are measured in light seconds on the space axis, in order to make c have the value of 1 space unit per time unit; so all of the graphical sheep, spaceships, cats, people, torches and stuff that are placed upon them are very much not to scale. (-:
This convention of units is called "natural units", and it also sets a bunch of other units to be 1, depending on the flavor (planck's constant, boltzmann's constant, etc...)
Not only does this clarify the relationships, but in many ways, these "natural constants" are an artifact from our past ignorance. Boltzmann's constant, in a way, is nothing more than a "conversion factor" that we hold over from the time when we believed temperature and energy to be two separate concepts. In the same way, the speed of light is an artifact from a time when we considered time and space to be distinct concepts, measuring them in distinct units, and needing a conversion factor (in units of distance/time) to map between them.
It's as if we would all collectively agree that the "up" direction, from now on, would be measured in floops, and the slope of a hill would be measured in floops/meter.
From a philosophical point of view, it's not just saying "measure time in units such that c = 1". It's saying "let's consider time to be a distance, and measure it in the same units as we do the other ones".
No thanks. Every time I hear the argument brought up, the person putting it forward says it like it is a mic drop moment and they never discuss the counter arguments. It is effective for people who haven't heard the argument before or haven't thought it through.
Here is an example. The charge of an electron is exactly the opposite of the charge of a proton, to within measurement error (like ten digits). This is simply something which has been measured, but physics has no explanation for why they are the same. Getting to the point, what is more likely: that a God created it that way in order to achieve His goals, or that there is some reason connecting the two charges such that they must be of exactly the same magnitude but we just haven't figured it out?
I'm putting my money on the latter. If there is an all-powerful creator, there is no reason to have fine tuning at all -- He could just force the desired behavior and outcome.
If you are willing to accept multiverses then isn't this solved by the Anthropic principle where the speed of causality (or mass of the proton) is what it is, simply because it can sustain the evolution of eventual observers?
I don't think the numbers independently are valuable, but together the constants of physics are tuned to support life. To be honest, I dislike the Anthropic principle as a generalizable cop-out, but it nonetheless works.
You know how the OceanGate sub imploded so fast that their brains didn't even have time to register they were dead?
If the basic laws of the universe change, we'll be disincorporated before we have a chance to know it's happening, because it will happen at whatever the speed of light is in the new balance, and the chemical processes that make us tick will change to other chemical processes that don't actually work anymore.
In the new universe silicon based life might function. Or stars might not work anymore.
The explanation that unlocked the intuition for me was the postulate that all objects in the universe are moving at the same velocity. Some are moving faster through time and some faster through space. If you move faster in time, you move slower in space and vice versa but the vector sum of your speed through space-time is the same. Therefore a photon is moving really fast through space but does not experience any movement in time.
> Without even getting into math and physics, you can intuitively understand how infinitely fast causality would prevent time, and therefore everything else we know, from being possible.
Can you unbox this a little? I think I may just have Friday brain, but I'm having some difficulty convincing myself in the moment that infinite-speed causality development would prevent time.
A system in which information is communicated instantly will quickly reach equilibrium, after which there is nothing left for any part to communicate to another. Eg diffusion of heat eventually results in a temperature distribution in which there is no longer a flow of heat.
So this seems like a better definition until you run into a problem, which you do pretty quickly: "casuality" isn't the easiest thing to define.
The best definition I think I've seen is to view the universe as a partially ordered set of events, meaning that you can only order events (in time) if they're within each other's cones of causality. Outside of that you cannot say which happened first. That's the partially ordered part.
But even that is incomplete and arguably even self-referential. What's a "cone of causality" (without relying on causality)?
Also, there's the issue of what exactly time is and whether events are time-symmetric or not. Many physicists seem to view time as an emergent rather than fundamental property of our Universe.
That’s not intuitive to me. Any old physics engine in a video game has infinite speed of causality and all the other classical physics stuff seems to work, including time. There must be some other unmentioned property of our Universe’s physics that is important and which requires finite speed of causality.
Interestingly, infinite speed of causality in games works, but does not scale.
If you want to simulate a giant world with millions of players, you either have to slow down the frequency at which you update the world to give the computer enough time to do the computation, or you have to introduce some sort of speed of causality in the game in order to be able to distribute the computation across multiple nodes.
How does a finite speed of causality help simulation performance? You still end up computing the interaction of every event with every particle in the Universe. Despite being amortized, you still need to compute the same number of interactions per unit time.
And the other half of this is that brains are extremely complicated casual chains. Causality can traverse the diameter of the brain something like 10^8 times in the period it takes for light to be perceived.
It's kind of an anthropic principle argument.[1] If the fundamental constants had substantially different values, the resulting universe would be boring. All the mass collapsed into one black hole, or evenly distributed as fundamental particles. Or atoms don't work. Or stars don't work.
This leads to the usual problems - many-worlds theory, gods, etc. Strassler hasn't gone there, but others have.
It also kind of is not, inasmuch as it doesn't argue that there's the possibility of a universe where a "slower" speed of light (whatever that might mean) would not permit the existence of humans. It merely argues that the speeds of the human-centric world have to be small fractions of c, whatever value c is, by dint of how the macroscopic relates to the subatomic.
In natural units, in all such theoretical universes, c is 1; and all that this argument really states is that humans and similar atom-based things have to move at very small fractions of 1.
> In natural units, in all such theoretical universes, c is 1
I think this could be an instance of falling prey to the same sort of assumptions that the anthropic principle is intended to expose. For example, imagine theoretical universes where the speed of light is non-constant, or varies depending on where you are, or changes over time, etc.
I'm not sure this affects the argument. Even if c were to change, creatures made of atoms would still have to be in conditions where their velocities relative to the objects around them are low compared to c, otherwise they would disintegrate on contact. There are other assumptions about atoms that go into this of course, but the goal of the article is to explain why any creatures made of atoms would think of the speed of light as very fast compared to the interations they're accustomed to.
This is why somewhat realistic high-power fusion rockets like those portrayed in The Expanse require magnetic nozzles. The fusion plasma would never come into contact with the material the engine is made of or it would melt.
We could build a decent fusion pulse drive today if we had higher temperature more compact superconductors and super-efficient compact lasers that could fit in a spacecraft and ignite a strongly net-positive inertial confinement fusion pulse.
Our superconductors are almost good enough, but our high-power lasers are way too inefficient and bulky. We can't even make economically viable ICF on Earth with current lasers.
D + He3 and H + B are attractive precisely because the product is entirely charged particles that you can catch with such a magnetic nozzle. D + T is easier to ignite, but releases a lot of energy in neutron kinetic energy which you need to absorb in some material which lowers the temperature. D + D is the most common fuel on outer solar system and interstellar bodies but it also releases neutrons and might be most valuable in an energy system in that it products He3 and T some of which could be separated from the plasma and used to fuel reactors that are either aneutronic or low ignition energy.
Yep, there was a physicist who did the math on the Epstein Drive (unfortunate name) in The Expanse and found that it was at the edge of possibility if you use very efficient lasers, ICF, and D+He3 fuel. There is mention of helium-3 and fuel pellets in the books, so it sounds like that was the idea.
The biggest un-realism in The Expanse is the lack of huge heat-sinks, at least in the show. (They aren't mentioned in the books but I assumed they'd be there.) Without heat-sinks even if the drives were >95% efficient the ship would melt. Also in the show the thrust plumes from the engines are portrayed as looking like grill flames. In reality they'd look more like beams of light fading off into space.
the argument is that "highly efficient laser" might be an oxymoron and if you were serious about commercial fusion you might trade lasers for much more efficient particle accelerators that run at a viable shot rate. Trouble is that you need heavy ions (lead) at 8GeV and it takes multiple barrels that are a km long or so... A huge machine that might be competitive with lasers for a commercial power plant but that can't be built in a subscale prototype. It might not be compatible with the magnetic nozzle though as 8GeV is not relativistic for lead ions.
See https://cds.cern.ch/record/2743157/files/Seeman2020_Chapter_... you can get better Q for superconducting linacs and also operate them in CW mode without fear of burning them up. Off the cuff I'd speculate that superconducting magnets that can support 2x the magnetic field might support 2x the accelerating gradient but we are talking AC operation here, not DC.
That’s what I think. The efficiency of lasers is awful and they take hours to cool off after a shot whereas a commercial fusion power plant needs a shot rate between one every few seconds to several per second.
A heavy ion power plant is possible in terms of the physics but needs to be the scale of a fission power plant to work at all and is projected to cost maybe 2x what an AP1000 costs assuming everything goes well and we know things usually work worse than you expect. So nobody is interested in funding a full-scale prototype, a reasonable development plan is you build several linac barrels and a test fusion facility and expect to rebuild that and add more barrels. It probably costs about what Musk spent on Twitter in the end.
Maybe they have some sort of thermally excited laser material and use hybrid electro/thermal lasers to "heat pump" waste heat back into the laser system.
Now tell me about all the waste heat such a scheme would generate. Yes, you can generate work from a temperature difference. You cannot convert that thermal energy to work with 100% efficiency.
In Dragons’s Egg[0] by Robert L. Forward the neutron star alien race are nucleonics life forms which experience timescales a million times faster than humans.
The speed of light is not fast. It's really, really slow! That is, slow relative to the size of the universe and the timespan of the universe, relative to human scales of size and timespan.
Humans can travel around the world (our domain) in a matter of hours (on rockets, our fastest mode of travel thus far). Similarly, the fastest waves can cross the ocean in a matter of hours. Light, on the other hand, takes billions of years to cross the visible universe. It's downright glacial at those scales!
Yes, it takes forever to get anywhere at Warp 9. (-:
More seriously: Your very point is already made near to the beginning of the headlined article, in the book quote. You might want to read beyond the headline question, otherwise you're just repeating what the article already says.
I did read the article and it is not making the same point I’m making. It takes the position that humans are extremely slow, relative to the speed of light. I’m taking a different position: that humans are extremely fast, relative to the domain in which we operate (the earth, our cities, our neighbourhoods, our households).
The paragraph beginning "And yet c is also slow." in the article is pretty much what you said.
If you now want to make the point that humans are fast on human-centric scales, which you did not really make above, you enter a whole other discussion that involves biology, and humans not really being very fast at all compared to some other creatures. You have, after all, to introduce non-human entities, rockets, to show examples of humans being "fast".
And really fast rockets aren't examples of humans being fast, as they are good examples of humans becoming dead, from the accelerations involved for starters. Take a human out of a rocket system, and it can go much faster. Human-ridden rockets are in fact slow, too, even on human-centric scales, compared to the things that are extremely fast in the human-centric world. So that argument falls down.
There are even biological discussions of the same idea: why humans are slower than, say, houseflies. We're slower than c for physics reasons, and we're slower than things on our own scale for biological reasons. We actually are not extremely fast. We aren't as fast as our machines, nor even as fast as some other creatures.
If you were to travel at nearly the speed of light, you could cross the universe in a matter of minutes. Of course an external viewer on say Earth would disagree and say it took billions of years, but who’s counting?
Actually, you couldn't cross it in a matter of minutes. In fact, you would never even reach the edge of the visible universe. This is because the edge of the visible universe is expanding away from us at faster than the speed of light.
I would really like to hear from an actual physicist on this question since both of you seem correct for one of the reference frames and the only way I see to reconcile the two is with weird singularities like "the particle reaches the edge of the visible universe in infinite time according to the rest observer". (And I don't think that is right either.)
The edge of the visible universe functions for us like a cosmic event horizon. Similar to the event horizon around a black hole. A particle leaving earth at light speed can never reach or go beyond that horizon. Even in infinite time. That's assuming the universe continues to expand. If it starts to contract then, yeah, the horizon is going to crash in on us.
This is probably a huge reasoning error, but wouldn’t you “expand away” with the expanding away part of the universe at the same rate, sort of riding along with the expansion given that c is the same in the point of reference (the expanding away faster than c part)?
n.b. I obviously lack the vocubulary to communicate properly about this, help needed!
Again, this is a matter of perspective. The amazing long lived Earth observer would see the universe expand out of view, and you along with it wouldn't they?
Yes, after billions of years you would move outside of the sight horizon of the long-lived observer on earth and disappear from view. For you, the traveler, this would happen in mere minutes. But you wouldn't have crossed the universe in that time because the edge of the visible universe is constantly expanding away from us faster than we can travel to catch up with it. Even if we travel at the speed of light.
Lawrence Krauss has given a talk that mentions something similar. He says that we live in a good time because we can still see "everything" around us. At some point in the far future, any observers won't be able to determine many things about the universe because the "stuff" in it will be too far away to observe.
Even wilder to me is that one day, anyone living in the Milky Way will look up at the sky and be unable to see any other galaxies. If it weren’t for archaeological evidence they would never have any way of knowing about the existence of those other galaxies.
The size and age of the visible universe aren't that different in size though. I mean, they would have to be, the only reason they differ at all is because the universe expands.
Meanwhile we measure time in hundreds of millions of meters and space in nanoseconds. Something causes humans to be slow.
Which isn't that surprising, life is basically a diffusion process gone haywire and while we're more efficient than just a big rock being pushed by small particles we still rely on statistical physics to push molecules around and it takes a while for those statistics to average out.
So this touches on the anthropic principle, which is to say that if the Universe (and the constants within it) were other than what they were, we wouldn't be able to exist to contemplate it.
The speed of light being "slow" in cosmic terms is almost necessary for our existence in that we need a relatively long period of relative stability in order to evolve into sentient life. And that becomes a whole lot harder if, say, the Milky Way was only one light day across.
I think in the past I would’ve readily accepted this explanation but now it seems to me like a just-so story.
Bacteria can exhibit doubling times on the scale of tens of minutes. We know of trees that live for thousands of years.
On the other hand, we know of chemical reactions that can propagate significantly faster that the speed of sound (high explosives) and nuclear reactions that propagate even faster that this. At the other end of the scale, we have mildly radioactive elements with half-lives measured in billions of years.
This is all to say that everything is relative and no matter what constants you choose for the universe, they’re going to seem arbitrary.
> Light, on the other hand, takes billions of years to cross the visible universe
Right, and that's just the visible universe. The full extent of the universe is much larger -- I think that the most cautious lower bound estimate is that it's 250x larger. It could be 10^10x larger, or even infinite/unbounded. In such a vastness, the speed limits for light and baryonic matter are perplexingly slow.
It's not observable by us, so we don't know. The figure is (to simplify) a deduction from what we can see, the observable universe, and the fact that we don't see any of the consequences that there would be in the observable bit if the entire universe were smaller.
If photo started a stopwatch and proceeded to travel 100T light years, the stopwatch would still read zero. That is pretty fast imo. It all depends on perspective.
on first glance it seems like an interesting take, but then you realize (as someone else already pointed out) that the fastest thing in the universe is not fast, and therefore nothing is fast? a little more thought should make you realize this is a poorly formed take. Also, worth repeating, please read the article before posting. It may be that your insight or critique is present and discussed in the article already.
EDIT: Sorry I came back from the article to say this before reading the comments here… I should have, the top comment is already saying the exact same thing!
You can scroll through it. It's so long to go from one planet to another. So much empty space.
At some point you're tempted to click on the C button which you see on the bottom right of the page. Speed of light! Surely that will autoscroll fast! … Nope, to scale, the speed of light is waaaay slower than your scrolling was! And then you realize, at the size of the universe, how even light isn't that fast.
If I had to write a “game of life” simulation that simultaneously calculated the effects of all events at each point in a 3D matrix over time, I would:
- make the matrix as rough as possible while still enabling interesting events (ie, try and maximize the Planck length)
- make the maximum speed at which events propagate across the matrix as slow as possible to save the CPU (ie, try to minimize the speed of light)
- limit the size of the simulated universe
But our Planck length is tiny and the universe is probably humonguous unless we’re being deliberately deceived by This Simulators.
So despite the suspicions aroused by the slow speed of light, we might live in the mother / “real” universe after all.
I think you might have the same misconception about the planck length that I had:
"The Planck length does not have any precise physical significance, and it is a common misconception that it is the inherent “pixel size” or smallest possible length of the universe.[1] If a length smaller than this is used in any measurement, then it has a chance of being wrong due to quantum uncertainty.[2]"
I think that sentence as written is itself based on a misconception. The idea is not that the Planck length is physically meaningful, but rather that that quantum uncertainty is caused by the structure of the universe (discrete spacetime). In other words, that uncertainty is analogous to aliasing in a signal.
>make the maximum speed at which events propagate across the matrix as slow as possible to save the CPU
How would that save CPU time?
The Game of Life does have a maximum speed of propagation of causality, but it's not designed in, it's just a consequence of the basic rules that define the simulation.
Well, you could just slow down the execution rate of the whole simulation.
But if you limit the speed at which events propagate, my feeling is the rate of events occurring will be lower overall, since one event triggers another and each event will trigger fewer secondary events per second if it propagates less distance per second.
You could now also have islands of stability so that a cataclysm on one end of the simulation will take a long time to spread to the rest of it.
IE, Andromeda can explode and we won't even know for a long time. In that time, we will continue doing interesting / entertaining things, or continue calculating the answer to life, the universe, and everything.
But you will get fewer per step, which is my point. If you get fewer, then you'll need to run the simulation for longer, thus negating any savings.
But you're right in that you'd get different effects, because effects like gravity depend on the distance between objects, which is invariant on the speed of light, so a "human" in a universe where c is halved but everything else is the same wouldn't just be larger, but be completely different.
But if you're changing the behavior of the simulation then it's not even an optimization anymore. You just changed the simulation. It may as well be something entirely different.
It is the simplest example of what physicists call a “bound state” — the word “state” basically just meaning a thing that hangs around for a while, and the word “bound” meaning that it has components that are bound to each other, as spouses are bound in marriage. In fact, the image of a married couple, especially one with one spouse weighing a lot more than the other, is probably the one you want."
The argument given in part 2 (that the strength of nuclear forces compared to electric forces make nuclei very heavy relative to the energies that would rip their chemistry apart) does not make a lot of sense in the context of the fact that binding energy reduces the mass of bound states. For example, 56Fe is lighter than 26 protons and 30 neutrons.
The ratio of the Hydrogen atom's ground state electron binding energy to the electron's mass-energy is one half the fine structure constant squared. That implies the nuclear forces don't have much to do with it - electromagnetism is simply, and dimensionlessly (i.e. independently of any arbitrary units or scales), a weak force.
Light isn't that fast. It only goes about a foot per nanosecond. It can be fun to work out for people how many bits are in a piece of cable at any moment, and that's assuming electrical information in a cable travels as fast, which it doesn't.
A real demo is to talk via VOIP with someone on a satellite internet connection. The old, geostationary satellite kind. It takes so long for the audio to get there and back that you have to practically say "over" when you're done talking.
Some people also don't realize how linked to time C is. If you were to say not move at all. You will be moving through time at C. But if you were moving say at 50% the speed of C, you will only be moving through time at 50%. So you can never exceed natural speed + natural time.
I'm not sure he gets to the answer of the 'astonishing' bit of the speed.
Fast is relative but astonishment is a human reaction based on our brains being slow because evolution gave rise to large molecules which have to jiggle around before things work so the light is already at the moon by the time we've registered much. If instead you use a computer processor it only goes about 10 cm per clock cycle or not so fast in practical terms.
When you make a wave with a rope or on a water the speed of the wave is formed by the speed of the interaction of the molecules in it. I believe similar thing happens with the light in subatomic level. There, may be the spped of light is limited on how fast an higs boson interacts with the neighbpring higs bosons.
And it's E=mc^2 because the only 'consensus' value in the universe is c? Why is that? And so the 'mass' (whatever that is) must be moving at the speed of light for the equation to make sense, even though it's stationary?
The blogs demonstrate great factual knowledge and 'mastery', but don't really explain anything IMHO
If you break up "mv^2" into its constituent dimensions you get m(d/t)^2 = m(d^2)(t^-2). Now the so-called kinetic energy of the object only "manifests itself" whenever there is a change in velocity of the object in question. Well, the derivative of velocity is an acceleration, so the object in acceleration would be represented as mdt^-2, aka "a force". Hence the energy of the system is simply that force acting over some distance d.
As to the internal/intrinsic energy of a given object, think of it as "hidden potential energy". It is essentially the energy that was required to turn photons into the matter that you, and I, and everything else are made of! The equation itself is mc^2 simply because that is what you get when you rearrange and simplify the experimentally-verified equations which it was drawn from. Likewise, for c is nothing more than the measured value of the speed of light in vacuum for any observer. Of course the choice of units is completely arbitrary. Whether you state it in miles per hour, kilometers per second, or whatever, the ratio remains constant.
Well, depends on your viewpoint, I guess. When you really get into the details, it turns out we don't "really understand" anything.
We are just making more and more detailed observations and then creating mathematical models of these behaviors. For example, we observe that space is curved around mass. We can model that and it helps us understand what's going on, so it's useful.
We don't, however, understand what exactly is curved and what is this empty space that curves.
The mv^2 isn't a geometrical property - it's because the kinetic energy can also be thought of as the integral of an object's momentum with respect to time.
We are trying to speed everything up all the time and speed is seen as a virtue and something desirable. Could it be that we are trying subconsciously on a collective scale to get close to the natural state of the universe?
It comes from the fact that force is proportional to acceleration (F=ma). Then the factor of 1/2 comes from the formula for the area of a triangle, or equivalently, integrating a constant twice wrt time, gives term in t, then a term in t²/2.
Consider constant force acting on a mass initially at rest, for time t producing final velocity v and distance travelled x.
F = ma [Newton's 2nd Law]
v = at = (F/m)t, so mv = Ft [momentum transfer is force times time]
x = (1/2)vt [area under v-t curve: triangle formula]
E = Fx = F(1/2)vt = (1/2)v(Ft) = (1/2)mv²
I was reading this article carefully. I noticed that he uses the word "stationary" to mean both "absolutely stationary" and "relatively at rest". The reasoning in this article is based on conflating and mixing the two meanings. So for instance when he writes "photons are always in motion" [1] he assumes that there are objects that are not always in motion, that is, they are in absolute rest. But he also writes "specifically its 'rest mass' m, which is the mass as measured by an observer who is stationary relative to the object." In this quote, he defines the word "stationary" as relative rest.
This rhetorical trick is so common in physics, that's why I wanted to mention it. The trick is to define the same word twice with its opposite meanings and use the word with both meanings sometimes even in the same sentence. I wonder what is the name of this trick in logic.
It is not a fallacy. In special relativity the important concept is the frame of reference. For photons there is not no inertial frame of reference where photon will be stationary (relative or absolute means nothing actually).
The whole concept of measurement (which you will need to describe something as stationary) depends on an observer travelling at speed velocity less than speed of light. If you Try to assign a inertial frame of reference to a photon you will break laws of special relativity
- photons always travel in speed of light from perspective of any inertial observer whether it is moving or at rest (verified by experiment)
- relativity prohibited mass less particles (like photon) to be stationary.
E = mc^2 doesn't apply in photon and apply only on stationary objects. The complete equation is
E^2 = (p^2 c^2) + (m c^2)^2
Where m is the rest mass. In photon case the second terms vanishes and the energy is merely the first term.
-Time and space behave differently for photons. In relativity, time dilation and length contraction become extreme at light speed. A photon does not experience the passage of time in the way objects with mass do. Therefore, trying to define a reference frame for a photon would lead to contradictions in our understanding of spacetime.
So in general it doesn't mean much absolute vs relative on photon case.
"For photons there is [] no inertial frame of reference where photon will [appear to] be stationary (relative or absolute means nothing actually)."
I added my comments to your sentence. Obviously, if photon appears to be stationary, this means relative to something else. So relative and absolute are not meaningless.
There is no absolute reference frame that would distinguish "absolutely stationary", as you call it, from "relatively at rest". There is only relative motion. Photons are "always in motion" in that there does not and cannot exist any massive object with respect to which a photon is at rest.
I do not know where I first saw it, but I saw someone observe that the shocking thing about Einstein's theory of relativity is not that everything is relative; that was understood reasonably well for a long time before him. What is shocking is that the speed of light in a vacuum, or the speed of causality, is a constant. You can derive huge swathes of relativity from that fact alone.
As a result, of all the speeds, when discussing the speed of light (which conventionally means "in a vacuum" unless otherwise mentioned), you can in fact ignore the question of reference frame, with the exception of you don't want to use a reference frame itself moving at the speed of light. But other than that, an article exclusively confining itself to the discussion of the speed of light in fact doesn't need to worry itself about the relativity of reference frames. For that speed alone, you can't level the complaint against it that it ignores the issue of different frames, because it uniquely doesn't matter.
(Relatedly: It is frequently given as the reason you can't reach or exceed the speed of light is some stuff about masses rising. While mathematically true in its own way, I think there's a cleaner reason to explain why you can't reach or exceed it, which is that you can't even get closer to it. No matter what you do, the speed of light is c. You accelerate to a thousand miles a second in some direction, and how much closer are you to c? The answer is, none. Light continues fleeing from you, in all directions, at c. There is no "get really close to c somehow and then just push yourself over really hard" because there is no "get close to c" in the first place. No matter how hard you accelerate, in what direction, in what order, in what manner, you not only can't get "close" to c, you can't even get closer. For similar reasons, in this paragraph, I don't need to qualify in which reference frame you go a thousand miles per second different than before, because it doesn't matter for c. You can't even get slightly closer to it, let alone "exceed" it somehow. It is an absolute.)
If we're in an airplane going 250 m/s - it also takes me 2 hours to fly to NYC. The air around the plane is windy, the air inside is still.
Now we're in a spaceship headed from the earth to the moon & it's going to take us 3 seconds. We've agreed ahead of time it takes 1.5 seconds for light to go from the earth to the moon. C is the speed at which light moves, and we're taking 2x the amount of time light would. The air inside is still. But we're still going fast.
How could it be that we are not approaching the speed of light?
What do you make of time dilation at higher speeds if we aren't approaching the speed of light at all, ever?
It's the stumbling block that everyone has grasping this stuff, and it's rooted in the old faulty kind of speed calculations. Speeds don't add like you think.
There are many ways to grasp this, and one has to try several of them to find an intuitive explanation that works for onesself; but one way is to consider that you, in your spaceship (as long as you are coasting along with no rockets firing, and aren't performing orbit/deorbit burns) are, in your frame of reference, at rest. Your speed is zero. You haven't approached anything at all, and light is still whizzing away from you at c. Indeed, it's Terra and Luna that are experiencing time dilation as far as you are concerned, because they are the ones with the high speeds.
Accelerate at the beginning and end of your trip over to Luna, and of course general relativity comes into play and things get more complicated. What many gedankenexperiments get wrong is that usually there's only a short period of burning the rockets, in the real world. So for most of your trip in the rocket you aren't burning propellant and are in an inertial frame of reference. No inertial frame of reference approaches the speed of light/causality, by postulate 2 of special relativity, and one is always at speed zero in one's own inertial frame of reference.
That motion is relative was understood. That even notions like simultaneity also depend on reference frame I think was shocking. And I'm not really sure what it would mean for light to not be at rest in any reference frame but for it to not have the same speed in all reference frames. I think that would be even more shocking than light having a constant speed.
iirc Maxwell had already shown that the speed of light was constant. Einstein's quest was to explain htf that could be the case. The word Maxwell appears in the first sentence of the 1905 paper, and the first couple of pages are about what today we would call "causality".
I read the same article and I didn't find "absolutely stationary" in the article. My physics is rusty but even from my recollection of high school physics there is no such thing. It's clear that the word stationary means zero velocity, and first year high school physics taught that any measurement of velocity must be done in a reference frame. The idea that a photon is always in motion is true regardless of which reference frame you pick; it does not imply there are objects that are in absolute rest.
This article mentions that the speed of light seems fast to humans living daily lives, but is not so fast on an astronomical scale.
The best demonstration of this I've ever seen is on "If the Moon Were Only 1 Pixel - A tediously accurate map of the solar system" [1].
If you've not seen it before, I recommend opening it, using your mouse wheel to scroll from the beginning (near the Sun) to Earth. It should take about a minute, but there's some commentary on the way. Then, to save your mouse and your finger some work, try clicking the icon in the bottom right hand corner to auto-scroll the map at the speed of light.
[1] https://joshworth.com/dev/pixelspace/pixelspace_solarsystem....
On the topic of perfectly crafted depictions of scale in the Universe, I love this one: https://youtu.be/vcJHHU9upyE
Shameless plug: during lockdown I did a whole series of these, called Spacewalks: https://youtube.com/playlist?list=PLul2c76M6HJySkSXYMoLXW9VC...
These videos were super fun to make and kept me sane when I found myself with far too much free time and a bunch of world news to avoid. I never did the fifth (and final) walk but it's only about 100 meters long so I hope one day to do it in person (if I ever end up with that much free time again).
I like these kinds of visualizations for big things. Reminds me of "1 pixel wealth." https://mkorostoff.github.io/1-pixel-wealth/
It’s always crazy to me how empty most of space is, and that yet despite that gravity is strong enough on large timescales to pull a lot of stuff together. Then I get concerned as to why EVERYTHING wasn’t pulled together and it’s literally just this little bit of angular momentum conserved across vast distances and added together from all these little particles that is keeping everything apart just enough for us to exist.
Well, the other forces have something to say about it too. If you compress stuff hard enough then the other forces will violently blow it apart.
Nah gravity would win (see: black holes)
Something to do with the universe expanding faster than gravity could ever hope to pull things together right?
Also we don’t know why the universe is expanding. Not just expanding but accelerating. Why is spacetime itself stretching and what is doing it?
Yeah yeah dark matter blah blah, but it’s not a concise enough answer.
Dark matter doesn't make the universe expand. It is massive, and thus it brings things together.
Dark energy, on the other hand, is the postulated cause of the expansion of the universe.
Edit: not a Physicist!
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> but is not so fast on an astronomical scale.
This is something I find incredibly counter-intuitive. At the photon’s reference frame (speed of light), time stops. In our reference frame, I’d expect some kind of “divide by zero” error in nature, resulting in the infinite speed of light. But it’s not infinite. It’s just… some constant.
It has to do with photons not having rest mass. If something with rest mass were to go at the speed of light, then you run to the numeric problems.
It's the maximum speed through space and time. The speed of light through time is just 1s/s. Einstein says space and time are equivalent, so as your velocity through space approaches c, your velocity through time approaches zero and vice-versa.
The photon has zero velocity through time because its velocity through space is c. In its reference frame, no time passes between creation and destruction, but from all other reference frames it appears to be moving through space in discrete time but with high velocity.
This was awesome. It's strange to know that I already understood this (conceptually at least), yet seeing how slow it really is at this scale is confusing. Maybe that's not quite the right word. It makes my brain pause and go "that can't be right", but... It's right.
Brains are bad at these scales. Maybe mine is worse than average. I can't fully believe how impossibly far away so many things truly are.
I thought light in a vacuum was (outside of some corner cases) the fastest you could get in this universe? That seems pretty fast on an astronomical scale to me. I mean it’s probably just that we have extremely short lives on an astronomical scale.
The speed of light is actually the speed of causality. No matter, or more importantly information can go faster than that. This has some real consequences even on human scales.
For example, if you've ever opened an electronic device and seen squiggly traces everywhere, it's because of light speed[0]. When signals get fast enough, you have to make sure the traces have the same length to within a fraction of a millimeter. Otherwise, the signals on two traces arrive at different times and nothing works.
[0](electrons move at ~c, more or less)
There's a significant delay in satellite communications, on the order of milliseconds. It takes several seconds to reach the moon. 20 minutes to Mars, a few hours to Jupiter. Famously 8 minutes to the sun. The nearest galaxy is 1.5 million years away.
Consider how stupefyingly large our solar system is. Then consider how insanely huge the galaxy is: 90,000ly. It takes ninety thousand years for a photon to go from one edge of the galaxy to another. Then compared to the universe at large, our galaxy is essentially a single point.
Light is extremely slow and the universe is vast beyond our meat brain's ability to comprehend.
>[0](electrons move at ~c, more or less)
Pedantic: electrons (in a wire) move at relatively ordinary speeds. Wikipedia says this [0]:
>The drift velocity in a 2 mm diameter copper wire in 1 ampere current is approximately 8 cm per hour. AC voltages cause no net movement. The electrons oscillate back and forth in response to the alternating electric field
Think of it more like a long row of billiard balls. You hit the first one, it moves a little, then it hits the next one, that one moves a little etc. Except the "hit" is just getting closer to the next electron to make it move (like if they were magnets).
At least that's my understanding of it.
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Maybe "hit" is the correct word? Isn't it the same forces at play that stop my hand from going through the table?
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[0] https://en.wikipedia.org/wiki/Speed_of_electricity
You are correct, electrons (aka current) through a wire move at relatively low speeds at room temperature because of wire resistance. Changes of voltage however, like if you flip a data pin from 0V to 5V move at the speed of light.
So switching circuits need to take into account "transmission line" effects.
The this is only the drift velocity. Electrons are still orbiting the nuclei at relativistic speeds. Plenty of room at the bottom...
I don’t think you understood my point? Why did you type all of that, when it’s basically what everyone else has said. I know about max speed of information and causality and have for decades. I was talking that light in a vacuum speed is basically “fast” since nothing is fast, in both and absolute and a relative sense, at least in my take :)
I’ll steal a line from a superb YouTube physics channel (Arvin Ash): it’s not the speed of light, it’s the speed of causality. And the universe must have a finite speed of causality. Without even getting into math and physics, you can intuitively understand how infinitely fast causality would prevent time, and therefore everything else we know, from being possible.
Yes, I was often very confused as to why the speed of light shows up everywhere, until it was reframed for me in this way. The fact that light travels at the same speed regardless of your frame of reference becomes a little less mystifying.
It feels more intuitive to me when thinking about it as causality always unfolding around you at the same speed, no matter your own frame.
The constant c was not named for causality, but it is a nice coincidence.
But causalities that don't propagate at the speed of light, and are not based on light, such as ordinary objects moving around and jostling each other, do not appear the same in every reference frame.
if the sun were to disappear, how long would it take for you to notice?
Trick question. Am I someone on Earth? (If so, 8 minutes). Or am I in a ship that is hurtling toward the Solar System at 0.999c, roughly in line with the Sun-Earth axis? If so, although I see speed of light as c, the Sun-Earth distance is foreshortened relativistically, so it will be less than 8 minutes between me perceiving the event that the Sun disappeared and perceiving the event that the Earth lost illumination.
This doesn't argue their point.
If a neutron disappeared, you'd NEVER noticed that causality.
It's not just Arvin Ash. That's actually fairly common terminology amongst physics educators nowadays. For starters: You'll find a lot of physics YouTube channels that say "speed of causality". It has even started to make its way into the astrophysics and physics textbooks in the last couple of years.
Einstein was not talking about light in his SR and GR theories. He was talking about the "speed" of light. As simple as that is, took me a long time to get it.
Interesting thanks. I hadn’t seen it elsewhere myself but I could see how it’s taken off. OP’s article almost gets there, but never says that specifically. Rather it says “c is not a property of light, it’s a property of the universe.”
Landau & Lifshitz, in their (classic) book on The Classical Theory of Fields, begin with a section called "Velocity of propagation of interaction".
Thanks, I’ve never heard this and it’s quite profound. It’s always bothered me that there even is a top speed, and further that mass becomes infinite as it’s approached. But “speed of causality” makes these less strange.
Why does speed of causality make it any better? It’s still an arbitrary limit that’s even more abstract and intangible than speed.
If the universe’s causal mechanisms were infinitely fast, the entire history of the universe would play out instantly in zero time, and we’d skip straight to the heat death of the universe.
The fact that time even exists is implied by / a result of causal actions having some finite propagation time.
> causal actions having some finite propagation time.
I think I know what you're getting at, but somehow the phrasing bothers me, as if there is meta-time or as if cause and effect have time between them... for the photon at light speed, time isn't passing, it's emitted and then zero "time" later it hits something very far away.
It's more like we somehow need to think of cause and effect chains that have orderings without time.
I wonder if future generations will ever look back and casually quip something about "well they believed X existed, that was their problem, it all makes intuitive sense if you just..."
Yes, the basic idea is that photons do not 'experience' time. They 'experience' creation, all points along their path, and absorption 'simultaneously'.
However, you have to be careful with terminology. There is no inertial frame co-moving with the photon. All we can say is: as a massive particle gets faster relative to an observer's frame, the time it experiences relative to the observer's frame becomes shorter, and in the limit, as it approaches the speed of light (but never reaches c), the experienced relative time approaches zero (but never reaches 0).
This is well explained by Don Lincoln on the Fermilab YT channel:
Do photons experience time?
https://www.youtube.com/watch?v=6Zspu7ziA8Y
This is not true. You can easily measure TOF of a photon using an APD in Geiger mode or other detectors easily purchasable in 2024.
So what exactly are you talking about?
> for the photon
he’s talking about the photons frame of reference
It’s still not true.
That's really profound - thanks for sharing that insight. I've never looked at it that way before.
That doesn’t work that way.
Imagine a universe simulated in a computer with “ticks” where the entire state is updated.
It would be different to ours, but it would work just fine.
While what you say is true, it seems to me like what you're describing isn't quite the same definition of causality being infinitely fast.
The fact that causal effects happen in the next tick means some minimal time has passed. So in your definition causality can cover the entirety of a finite universe in an incredibly short amount of time (one tick). But it seems like that's not the same as covering the entirety of a finite universe in zero time. In that case, every result would happen within the same tick as its cause.
There's more than one way to "implement a universe", but one hypothetical way to run a simulation is to alternate the simulation of forces and effects/causes.
A simulation could use particles with attributes like position, velocity, and also a "sum of forces". Then each update has the following steps:
1. Reset the sum of forces for all particles to zero.
2. For all particles, add the contribution to the forces on it from all other particles.
3. For all particles, update the next particle position based on the collected forces.
In the above, there's no intermediate state between updates, everything moves to the next position synchronously from the perspective of in-universe observers. (The external simulation can update particles one-at-a-time, but this is not an "observable" inside the simulation.)
The cellular automata view of reality is entirely compatible with what I said.
Well because its decoupled from light itself or its properties.
If there’s some universal limit for causality itself, then light just happens to be the fastest thing among all the other things subject to causality.
But it is not a coincidence. Light — the EM field waves — propagates at causality speed because the EM field respects a particular property of the universe, the so-called gauge symmetry. That is intimately connected to the fact that the photobs has no mass.
Other similar particles, like the W and Z bosons, are manifestations of the weak field. Since that field breaks the symmetry, those particles have mass and move slower.
BTW, that symmetry breaking is the very same one that physicists talk about when we discuss the Higgs boson.
First person in this thread to make any sense… The level of physics knowledge has declined on this site.
The question seems to me not why there is a speed of causality, but why the speed has this particular number. And it's not clear we know why that is, any more than we know why the proton mass is about 1836 times greater than the electron mass.
It's difficult to say that it has any given number, since our measurement units for both time and space are derived from it (via a short detour to the size of Terra, in the 18th century). It can have any finite number you like, just adjust the metre and second to match.
* https://www.youtube.com/watch?v=ZbGxXyqlhbU (FloatHeadPhysics on this)
One physics convention just sets its value to 1. All of those Minkowsky diagrams that we see are measured in light seconds on the space axis, in order to make c have the value of 1 space unit per time unit; so all of the graphical sheep, spaceships, cats, people, torches and stuff that are placed upon them are very much not to scale. (-:
> One physics convention just sets its value to 1.
Interesting. So c² would also equal 1. Which (in those scaled units) implies E = m.
This not only greatly simplifies the relationship but actually makes much more sense that way.
This convention of units is called "natural units", and it also sets a bunch of other units to be 1, depending on the flavor (planck's constant, boltzmann's constant, etc...)
Not only does this clarify the relationships, but in many ways, these "natural constants" are an artifact from our past ignorance. Boltzmann's constant, in a way, is nothing more than a "conversion factor" that we hold over from the time when we believed temperature and energy to be two separate concepts. In the same way, the speed of light is an artifact from a time when we considered time and space to be distinct concepts, measuring them in distinct units, and needing a conversion factor (in units of distance/time) to map between them.
It's as if we would all collectively agree that the "up" direction, from now on, would be measured in floops, and the slope of a hill would be measured in floops/meter.
From a philosophical point of view, it's not just saying "measure time in units such that c = 1". It's saying "let's consider time to be a distance, and measure it in the same units as we do the other ones".
This is the normal implication with C constant. Nothing is different.
Search YouTube for “universe fine tuning.” Then come back here in a few years when you’ve gotten through everything. :)
No thanks. Every time I hear the argument brought up, the person putting it forward says it like it is a mic drop moment and they never discuss the counter arguments. It is effective for people who haven't heard the argument before or haven't thought it through.
Here is an example. The charge of an electron is exactly the opposite of the charge of a proton, to within measurement error (like ten digits). This is simply something which has been measured, but physics has no explanation for why they are the same. Getting to the point, what is more likely: that a God created it that way in order to achieve His goals, or that there is some reason connecting the two charges such that they must be of exactly the same magnitude but we just haven't figured it out?
I'm putting my money on the latter. If there is an all-powerful creator, there is no reason to have fine tuning at all -- He could just force the desired behavior and outcome.
Presumably charge is a property of electromagnetic field, so it's expected that they match.
Fine tuning is a pretty broad concept and is mostly orthogonal to religious beliefs.
If you are willing to accept multiverses then isn't this solved by the Anthropic principle where the speed of causality (or mass of the proton) is what it is, simply because it can sustain the evolution of eventual observers?
I don't think the numbers independently are valuable, but together the constants of physics are tuned to support life. To be honest, I dislike the Anthropic principle as a generalizable cop-out, but it nonetheless works.
If the speed of causality were to suddenly change by whatever factor, would we notice it?
You know how the OceanGate sub imploded so fast that their brains didn't even have time to register they were dead?
If the basic laws of the universe change, we'll be disincorporated before we have a chance to know it's happening, because it will happen at whatever the speed of light is in the new balance, and the chemical processes that make us tick will change to other chemical processes that don't actually work anymore.
In the new universe silicon based life might function. Or stars might not work anymore.
It appears as "c" in the important equation E = mc².
So I expect it would change a lot.
The explanation that unlocked the intuition for me was the postulate that all objects in the universe are moving at the same velocity. Some are moving faster through time and some faster through space. If you move faster in time, you move slower in space and vice versa but the vector sum of your speed through space-time is the same. Therefore a photon is moving really fast through space but does not experience any movement in time.
But how much something appears to moves in each of these dimensions depends on the observer.
Correct. The experience of time and space is dependent on the observer.
This isn’t true though…
Would love to understand more, care to elaborate?
> Without even getting into math and physics, you can intuitively understand how infinitely fast causality would prevent time, and therefore everything else we know, from being possible.
Can you unbox this a little? I think I may just have Friday brain, but I'm having some difficulty convincing myself in the moment that infinite-speed causality development would prevent time.
A system in which information is communicated instantly will quickly reach equilibrium, after which there is nothing left for any part to communicate to another. Eg diffusion of heat eventually results in a temperature distribution in which there is no longer a flow of heat.
So this seems like a better definition until you run into a problem, which you do pretty quickly: "casuality" isn't the easiest thing to define.
The best definition I think I've seen is to view the universe as a partially ordered set of events, meaning that you can only order events (in time) if they're within each other's cones of causality. Outside of that you cannot say which happened first. That's the partially ordered part.
But even that is incomplete and arguably even self-referential. What's a "cone of causality" (without relying on causality)?
Also, there's the issue of what exactly time is and whether events are time-symmetric or not. Many physicists seem to view time as an emergent rather than fundamental property of our Universe.
Causality is *bangs hammer on bell*
Time is a relationship between clocks.. beyond that, yes, it's hard to say exactly.
Time seems to be what prevents everything from happening at once.
Without time does causality exist? Does anything happen at all? What is it to 'happen' except that something was one way and now is another?
I can't even describe 'happen' without using verb tenses, which represent time.
That’s not intuitive to me. Any old physics engine in a video game has infinite speed of causality and all the other classical physics stuff seems to work, including time. There must be some other unmentioned property of our Universe’s physics that is important and which requires finite speed of causality.
Simulators do have finite time steps. Without them they'd present the end of a simulation once initiated.
Interestingly, infinite speed of causality in games works, but does not scale.
If you want to simulate a giant world with millions of players, you either have to slow down the frequency at which you update the world to give the computer enough time to do the computation, or you have to introduce some sort of speed of causality in the game in order to be able to distribute the computation across multiple nodes.
How does a finite speed of causality help simulation performance? You still end up computing the interaction of every event with every particle in the Universe. Despite being amortized, you still need to compute the same number of interactions per unit time.
And the other half of this is that brains are extremely complicated casual chains. Causality can traverse the diameter of the brain something like 10^8 times in the period it takes for light to be perceived.
Makes you wonder if neutron flux in a bomb during supercriticality becomes self aware for a short moment.
No. There being no upper bound on the speed of motion (like in Newtonian physics) is not the same as infinitely fast causality.
"Light travels at the speed of causality". Why does light have that behaviour?
Because it has no mass.
Exactly - Light cannot be subject to causality (in the philosphical sense)
Part 2: [1]
It's kind of an anthropic principle argument.[1] If the fundamental constants had substantially different values, the resulting universe would be boring. All the mass collapsed into one black hole, or evenly distributed as fundamental particles. Or atoms don't work. Or stars don't work.
This leads to the usual problems - many-worlds theory, gods, etc. Strassler hasn't gone there, but others have.
[1] https://profmattstrassler.com/2024/10/03/why-is-the-speed-of...
[2] https://en.wikipedia.org/wiki/Anthropic_principle
It also kind of is not, inasmuch as it doesn't argue that there's the possibility of a universe where a "slower" speed of light (whatever that might mean) would not permit the existence of humans. It merely argues that the speeds of the human-centric world have to be small fractions of c, whatever value c is, by dint of how the macroscopic relates to the subatomic.
In natural units, in all such theoretical universes, c is 1; and all that this argument really states is that humans and similar atom-based things have to move at very small fractions of 1.
> In natural units, in all such theoretical universes, c is 1
I think this could be an instance of falling prey to the same sort of assumptions that the anthropic principle is intended to expose. For example, imagine theoretical universes where the speed of light is non-constant, or varies depending on where you are, or changes over time, etc.
I'm not sure this affects the argument. Even if c were to change, creatures made of atoms would still have to be in conditions where their velocities relative to the objects around them are low compared to c, otherwise they would disintegrate on contact. There are other assumptions about atoms that go into this of course, but the goal of the article is to explain why any creatures made of atoms would think of the speed of light as very fast compared to the interations they're accustomed to.
I.e. it's not that light it's fast but rather it's us who are slow
Our energy scale is set by the energy scale of chemistry. When you run it is powered by chemistry. Chemical rockets are powered by chemistry.
Hypothetically you could go faster if you used fission or fusion energy but practically the chemical bonds get in the way. Even
https://en.wikipedia.org/wiki/Nuclear_thermal_rocket
is limited by the strength of chemical bonds of the reactor so it gets a factor of 2 or 3 or so on exhaust velocity compared to a chemical rocket.
This is why somewhat realistic high-power fusion rockets like those portrayed in The Expanse require magnetic nozzles. The fusion plasma would never come into contact with the material the engine is made of or it would melt.
We could build a decent fusion pulse drive today if we had higher temperature more compact superconductors and super-efficient compact lasers that could fit in a spacecraft and ignite a strongly net-positive inertial confinement fusion pulse.
Our superconductors are almost good enough, but our high-power lasers are way too inefficient and bulky. We can't even make economically viable ICF on Earth with current lasers.
D + He3 and H + B are attractive precisely because the product is entirely charged particles that you can catch with such a magnetic nozzle. D + T is easier to ignite, but releases a lot of energy in neutron kinetic energy which you need to absorb in some material which lowers the temperature. D + D is the most common fuel on outer solar system and interstellar bodies but it also releases neutrons and might be most valuable in an energy system in that it products He3 and T some of which could be separated from the plasma and used to fuel reactors that are either aneutronic or low ignition energy.
Yep, there was a physicist who did the math on the Epstein Drive (unfortunate name) in The Expanse and found that it was at the edge of possibility if you use very efficient lasers, ICF, and D+He3 fuel. There is mention of helium-3 and fuel pellets in the books, so it sounds like that was the idea.
The biggest un-realism in The Expanse is the lack of huge heat-sinks, at least in the show. (They aren't mentioned in the books but I assumed they'd be there.) Without heat-sinks even if the drives were >95% efficient the ship would melt. Also in the show the thrust plumes from the engines are portrayed as looking like grill flames. In reality they'd look more like beams of light fading off into space.
The path not taken in fusion research is
https://en.wikipedia.org/wiki/Heavy_ion_fusion
the argument is that "highly efficient laser" might be an oxymoron and if you were serious about commercial fusion you might trade lasers for much more efficient particle accelerators that run at a viable shot rate. Trouble is that you need heavy ions (lead) at 8GeV and it takes multiple barrels that are a km long or so... A huge machine that might be competitive with lasers for a commercial power plant but that can't be built in a subscale prototype. It might not be compatible with the magnetic nozzle though as 8GeV is not relativistic for lead ions.
I'd never even heard of HIF. I wonder how it could scale with today's superconductors, which are far better than what we had in the 70s.
See https://cds.cern.ch/record/2743157/files/Seeman2020_Chapter_... you can get better Q for superconducting linacs and also operate them in CW mode without fear of burning them up. Off the cuff I'd speculate that superconducting magnets that can support 2x the magnetic field might support 2x the accelerating gradient but we are talking AC operation here, not DC.
I thought laser fusion only exists for nuclear weapons research, and there isn’t any path from the current experiments to a power plant.
That’s what I think. The efficiency of lasers is awful and they take hours to cool off after a shot whereas a commercial fusion power plant needs a shot rate between one every few seconds to several per second.
A heavy ion power plant is possible in terms of the physics but needs to be the scale of a fission power plant to work at all and is projected to cost maybe 2x what an AP1000 costs assuming everything goes well and we know things usually work worse than you expect. So nobody is interested in funding a full-scale prototype, a reasonable development plan is you build several linac barrels and a test fusion facility and expect to rebuild that and add more barrels. It probably costs about what Musk spent on Twitter in the end.
That’s the funding pitch but I’ve heard the scientists claim they want to study it for possible power use.
Maybe they have some sort of thermally excited laser material and use hybrid electro/thermal lasers to "heat pump" waste heat back into the laser system.
The entropy has to go somewhere. Laser beams carry no entropy.
10.1103/PhysRevLett.109.193601
K. Sandner and H. Ritsch, Physical Review Letters (2012); Temperature Gradient Driven Lasing and Stimulated Cooling
Now tell me about all the waste heat such a scheme would generate. Yes, you can generate work from a temperature difference. You cannot convert that thermal energy to work with 100% efficiency.
In Dragons’s Egg[0] by Robert L. Forward the neutron star alien race are nucleonics life forms which experience timescales a million times faster than humans.
[0] http://mdpub.github.io/cheela
The speed of light is not fast. It's really, really slow! That is, slow relative to the size of the universe and the timespan of the universe, relative to human scales of size and timespan.
Humans can travel around the world (our domain) in a matter of hours (on rockets, our fastest mode of travel thus far). Similarly, the fastest waves can cross the ocean in a matter of hours. Light, on the other hand, takes billions of years to cross the visible universe. It's downright glacial at those scales!
Yes, it takes forever to get anywhere at Warp 9. (-:
More seriously: Your very point is already made near to the beginning of the headlined article, in the book quote. You might want to read beyond the headline question, otherwise you're just repeating what the article already says.
I did read the article and it is not making the same point I’m making. It takes the position that humans are extremely slow, relative to the speed of light. I’m taking a different position: that humans are extremely fast, relative to the domain in which we operate (the earth, our cities, our neighbourhoods, our households).
The paragraph beginning "And yet c is also slow." in the article is pretty much what you said.
If you now want to make the point that humans are fast on human-centric scales, which you did not really make above, you enter a whole other discussion that involves biology, and humans not really being very fast at all compared to some other creatures. You have, after all, to introduce non-human entities, rockets, to show examples of humans being "fast".
And really fast rockets aren't examples of humans being fast, as they are good examples of humans becoming dead, from the accelerations involved for starters. Take a human out of a rocket system, and it can go much faster. Human-ridden rockets are in fact slow, too, even on human-centric scales, compared to the things that are extremely fast in the human-centric world. So that argument falls down.
Which leads to part 2, pointed out in a top-level comment by Animats, at https://profmattstrassler.com/2024/10/03/why-is-the-speed-of... which goes on to explain that humans are by necessity slow.
There are even biological discussions of the same idea: why humans are slower than, say, houseflies. We're slower than c for physics reasons, and we're slower than things on our own scale for biological reasons. We actually are not extremely fast. We aren't as fast as our machines, nor even as fast as some other creatures.
It’s all a matter of perspective.
If you were to travel at nearly the speed of light, you could cross the universe in a matter of minutes. Of course an external viewer on say Earth would disagree and say it took billions of years, but who’s counting?
Actually, you couldn't cross it in a matter of minutes. In fact, you would never even reach the edge of the visible universe. This is because the edge of the visible universe is expanding away from us at faster than the speed of light.
I would really like to hear from an actual physicist on this question since both of you seem correct for one of the reference frames and the only way I see to reconcile the two is with weird singularities like "the particle reaches the edge of the visible universe in infinite time according to the rest observer". (And I don't think that is right either.)
The edge of the visible universe functions for us like a cosmic event horizon. Similar to the event horizon around a black hole. A particle leaving earth at light speed can never reach or go beyond that horizon. Even in infinite time. That's assuming the universe continues to expand. If it starts to contract then, yeah, the horizon is going to crash in on us.
What does this look like from the photon's frame of reference, then? Or is it nonsensical to try to describe things from a frame of reference at C?
This is probably a huge reasoning error, but wouldn’t you “expand away” with the expanding away part of the universe at the same rate, sort of riding along with the expansion given that c is the same in the point of reference (the expanding away faster than c part)?
n.b. I obviously lack the vocubulary to communicate properly about this, help needed!
Again, this is a matter of perspective. The amazing long lived Earth observer would see the universe expand out of view, and you along with it wouldn't they?
Yes, after billions of years you would move outside of the sight horizon of the long-lived observer on earth and disappear from view. For you, the traveler, this would happen in mere minutes. But you wouldn't have crossed the universe in that time because the edge of the visible universe is constantly expanding away from us faster than we can travel to catch up with it. Even if we travel at the speed of light.
I remember reading several years ago that there are celestial bodies that we will NEVER be able to see precisely because of this.
Lawrence Krauss has given a talk that mentions something similar. He says that we live in a good time because we can still see "everything" around us. At some point in the far future, any observers won't be able to determine many things about the universe because the "stuff" in it will be too far away to observe.
https://youtube.com/watch?v=7ImvlS8PLIo @ 50:57
Even wilder to me is that one day, anyone living in the Milky Way will look up at the sky and be unable to see any other galaxies. If it weren’t for archaeological evidence they would never have any way of knowing about the existence of those other galaxies.
The size and age of the visible universe aren't that different in size though. I mean, they would have to be, the only reason they differ at all is because the universe expands.
Meanwhile we measure time in hundreds of millions of meters and space in nanoseconds. Something causes humans to be slow.
Which isn't that surprising, life is basically a diffusion process gone haywire and while we're more efficient than just a big rock being pushed by small particles we still rely on statistical physics to push molecules around and it takes a while for those statistics to average out.
So this touches on the anthropic principle, which is to say that if the Universe (and the constants within it) were other than what they were, we wouldn't be able to exist to contemplate it.
The speed of light being "slow" in cosmic terms is almost necessary for our existence in that we need a relatively long period of relative stability in order to evolve into sentient life. And that becomes a whole lot harder if, say, the Milky Way was only one light day across.
I think in the past I would’ve readily accepted this explanation but now it seems to me like a just-so story.
Bacteria can exhibit doubling times on the scale of tens of minutes. We know of trees that live for thousands of years.
On the other hand, we know of chemical reactions that can propagate significantly faster that the speed of sound (high explosives) and nuclear reactions that propagate even faster that this. At the other end of the scale, we have mildly radioactive elements with half-lives measured in billions of years.
This is all to say that everything is relative and no matter what constants you choose for the universe, they’re going to seem arbitrary.
> Light, on the other hand, takes billions of years to cross the visible universe
Right, and that's just the visible universe. The full extent of the universe is much larger -- I think that the most cautious lower bound estimate is that it's 250x larger. It could be 10^10x larger, or even infinite/unbounded. In such a vastness, the speed limits for light and baryonic matter are perplexingly slow.
Are galaxies and stuff out in that 250x or is it just empty space?
It's not observable by us, so we don't know. The figure is (to simplify) a deduction from what we can see, the observable universe, and the fact that we don't see any of the consequences that there would be in the observable bit if the entire universe were smaller.
* https://doi.org/10.1111/j.1745-3933.2011.01040.x
If photo started a stopwatch and proceeded to travel 100T light years, the stopwatch would still read zero. That is pretty fast imo. It all depends on perspective.
> Light, on the other hand, takes billions of years to cross the visible universe.
Well... That's to be expected. It's right there on the definition.
I get what you are saying at, but viewed in a another way, you just said that the fastest thing in the universe is really slow.
on first glance it seems like an interesting take, but then you realize (as someone else already pointed out) that the fastest thing in the universe is not fast, and therefore nothing is fast? a little more thought should make you realize this is a poorly formed take. Also, worth repeating, please read the article before posting. It may be that your insight or critique is present and discussed in the article already.
^^ this
EDIT: Sorry I came back from the article to say this before reading the comments here… I should have, the top comment is already saying the exact same thing!
The speed of light isn't that fast. The website "the moon is one pixel" is a webpage where our solar system is represented at scale if our moon were 1px in diameter : https://joshworth.com/dev/pixelspace/pixelspace_solarsystem....
You can scroll through it. It's so long to go from one planet to another. So much empty space.
At some point you're tempted to click on the C button which you see on the bottom right of the page. Speed of light! Surely that will autoscroll fast! … Nope, to scale, the speed of light is waaaay slower than your scrolling was! And then you realize, at the size of the universe, how even light isn't that fast.
If I had to write a “game of life” simulation that simultaneously calculated the effects of all events at each point in a 3D matrix over time, I would:
- make the matrix as rough as possible while still enabling interesting events (ie, try and maximize the Planck length)
- make the maximum speed at which events propagate across the matrix as slow as possible to save the CPU (ie, try to minimize the speed of light)
- limit the size of the simulated universe
But our Planck length is tiny and the universe is probably humonguous unless we’re being deliberately deceived by This Simulators.
So despite the suspicions aroused by the slow speed of light, we might live in the mother / “real” universe after all.
I think you might have the same misconception about the planck length that I had:
"The Planck length does not have any precise physical significance, and it is a common misconception that it is the inherent “pixel size” or smallest possible length of the universe.[1] If a length smaller than this is used in any measurement, then it has a chance of being wrong due to quantum uncertainty.[2]"
https://simple.m.wikipedia.org/wiki/Planck_length#:~:text=Th....
I think that sentence as written is itself based on a misconception. The idea is not that the Planck length is physically meaningful, but rather that that quantum uncertainty is caused by the structure of the universe (discrete spacetime). In other words, that uncertainty is analogous to aliasing in a signal.
>make the maximum speed at which events propagate across the matrix as slow as possible to save the CPU
How would that save CPU time?
The Game of Life does have a maximum speed of propagation of causality, but it's not designed in, it's just a consequence of the basic rules that define the simulation.
Well, you could just slow down the execution rate of the whole simulation.
But if you limit the speed at which events propagate, my feeling is the rate of events occurring will be lower overall, since one event triggers another and each event will trigger fewer secondary events per second if it propagates less distance per second.
You could now also have islands of stability so that a cataclysm on one end of the simulation will take a long time to spread to the rest of it.
IE, Andromeda can explode and we won't even know for a long time. In that time, we will continue doing interesting / entertaining things, or continue calculating the answer to life, the universe, and everything.
If the propagation of effects is slowed down, the phenomena that you are interested in will take more simulation steps to complete.
I don’t know, I think the most interesting things are happening slowly and with high complexity in places like here on Earth.
With a slower speed of light, I think you’ll get qualitatively different events, not just fewer events.
But you will get fewer per step, which is my point. If you get fewer, then you'll need to run the simulation for longer, thus negating any savings.
But you're right in that you'd get different effects, because effects like gravity depend on the distance between objects, which is invariant on the speed of light, so a "human" in a universe where c is halved but everything else is the same wouldn't just be larger, but be completely different.
But if you're changing the behavior of the simulation then it's not even an optimization anymore. You just changed the simulation. It may as well be something entirely different.
This is a very good author. "What's a Proton, Anyway?" is also both educational and entertaining [https://profmattstrassler.com/articles-and-posts/largehadron...].
"Ok, then, what’s a hydrogen atom?
It is the simplest example of what physicists call a “bound state” — the word “state” basically just meaning a thing that hangs around for a while, and the word “bound” meaning that it has components that are bound to each other, as spouses are bound in marriage. In fact, the image of a married couple, especially one with one spouse weighing a lot more than the other, is probably the one you want."
The argument given in part 2 (that the strength of nuclear forces compared to electric forces make nuclei very heavy relative to the energies that would rip their chemistry apart) does not make a lot of sense in the context of the fact that binding energy reduces the mass of bound states. For example, 56Fe is lighter than 26 protons and 30 neutrons.
The ratio of the Hydrogen atom's ground state electron binding energy to the electron's mass-energy is one half the fine structure constant squared. That implies the nuclear forces don't have much to do with it - electromagnetism is simply, and dimensionlessly (i.e. independently of any arbitrary units or scales), a weak force.
Light isn't that fast. It only goes about a foot per nanosecond. It can be fun to work out for people how many bits are in a piece of cable at any moment, and that's assuming electrical information in a cable travels as fast, which it doesn't.
A real demo is to talk via VOIP with someone on a satellite internet connection. The old, geostationary satellite kind. It takes so long for the audio to get there and back that you have to practically say "over" when you're done talking.
There is already a Part 2 out (read it yesterday) and a Part 3 planned.
Direct link to Part 2: https://profmattstrassler.com/2024/10/03/why-is-the-speed-of...
Some people also don't realize how linked to time C is. If you were to say not move at all. You will be moving through time at C. But if you were moving say at 50% the speed of C, you will only be moving through time at 50%. So you can never exceed natural speed + natural time.
I'm not sure he gets to the answer of the 'astonishing' bit of the speed.
Fast is relative but astonishment is a human reaction based on our brains being slow because evolution gave rise to large molecules which have to jiggle around before things work so the light is already at the moon by the time we've registered much. If instead you use a computer processor it only goes about 10 cm per clock cycle or not so fast in practical terms.
"Why is the Speed of Light So Fast?"
Seems to me that we should be asking the question why is the speed of light so slow!
We're forever discussing the Higgs and how matter gets (some of) its mass but we spend precious little time discussing this relationship:
c0 = 1/(μ0 ε0)^0.5
That is why vacuum permittivity and vacuum permeability 'conspire' to slow down light to its known value.
I didn't find why.
When you make a wave with a rope or on a water the speed of the wave is formed by the speed of the interaction of the molecules in it. I believe similar thing happens with the light in subatomic level. There, may be the spped of light is limited on how fast an higs boson interacts with the neighbpring higs bosons.
But why mv^2 ?
Is the universe 2D?
And it's E=mc^2 because the only 'consensus' value in the universe is c? Why is that? And so the 'mass' (whatever that is) must be moving at the speed of light for the equation to make sense, even though it's stationary?
The blogs demonstrate great factual knowledge and 'mastery', but don't really explain anything IMHO
If you break up "mv^2" into its constituent dimensions you get m(d/t)^2 = m(d^2)(t^-2). Now the so-called kinetic energy of the object only "manifests itself" whenever there is a change in velocity of the object in question. Well, the derivative of velocity is an acceleration, so the object in acceleration would be represented as mdt^-2, aka "a force". Hence the energy of the system is simply that force acting over some distance d.
As to the internal/intrinsic energy of a given object, think of it as "hidden potential energy". It is essentially the energy that was required to turn photons into the matter that you, and I, and everything else are made of! The equation itself is mc^2 simply because that is what you get when you rearrange and simplify the experimentally-verified equations which it was drawn from. Likewise, for c is nothing more than the measured value of the speed of light in vacuum for any observer. Of course the choice of units is completely arbitrary. Whether you state it in miles per hour, kilometers per second, or whatever, the ratio remains constant.
Well, depends on your viewpoint, I guess. When you really get into the details, it turns out we don't "really understand" anything.
We are just making more and more detailed observations and then creating mathematical models of these behaviors. For example, we observe that space is curved around mass. We can model that and it helps us understand what's going on, so it's useful.
We don't, however, understand what exactly is curved and what is this empty space that curves.
The mv^2 isn't a geometrical property - it's because the kinetic energy can also be thought of as the integral of an object's momentum with respect to time.
Here's a 5 and a half hour long video of a photon travelling across the solar system.. spoiler the photon in this video doesn't move quickly
https://youtu.be/_qKOpvDa82M?si=HyO5TGSvxw0DN5yF
We are trying to speed everything up all the time and speed is seen as a virtue and something desirable. Could it be that we are trying subconsciously on a collective scale to get close to the natural state of the universe?
As fast as the GPUs running the simulation.
Why is light so slow is the question. It takes a whopping 8 minutes to get from the Sun to here.
The speed of light is in its Goldilocks zone. I wouldn’t worry about it too much.
Better to ask why light is so slow...
That was a nice read.
The content of this blog is amazing, thanks for the submission.
Regarding E=1/2mv*v, where does the 1/2 come from?
It comes from the fact that force is proportional to acceleration (F=ma). Then the factor of 1/2 comes from the formula for the area of a triangle, or equivalently, integrating a constant twice wrt time, gives term in t, then a term in t²/2.
Consider constant force acting on a mass initially at rest, for time t producing final velocity v and distance travelled x.
see also: https://tauday.com/tau-manifesto#table-quadratic_forms
I was reading this article carefully. I noticed that he uses the word "stationary" to mean both "absolutely stationary" and "relatively at rest". The reasoning in this article is based on conflating and mixing the two meanings. So for instance when he writes "photons are always in motion" [1] he assumes that there are objects that are not always in motion, that is, they are in absolute rest. But he also writes "specifically its 'rest mass' m, which is the mass as measured by an observer who is stationary relative to the object." In this quote, he defines the word "stationary" as relative rest.
This rhetorical trick is so common in physics, that's why I wanted to mention it. The trick is to define the same word twice with its opposite meanings and use the word with both meanings sometimes even in the same sentence. I wonder what is the name of this trick in logic.
[1] This quote is from a different articla: https://profmattstrassler.com/waves-in-an-impossible-sea/wav...
It is not a fallacy. In special relativity the important concept is the frame of reference. For photons there is not no inertial frame of reference where photon will be stationary (relative or absolute means nothing actually).
The whole concept of measurement (which you will need to describe something as stationary) depends on an observer travelling at speed velocity less than speed of light. If you Try to assign a inertial frame of reference to a photon you will break laws of special relativity
- photons always travel in speed of light from perspective of any inertial observer whether it is moving or at rest (verified by experiment)
- relativity prohibited mass less particles (like photon) to be stationary.
E = mc^2 doesn't apply in photon and apply only on stationary objects. The complete equation is
E^2 = (p^2 c^2) + (m c^2)^2
Where m is the rest mass. In photon case the second terms vanishes and the energy is merely the first term.
-Time and space behave differently for photons. In relativity, time dilation and length contraction become extreme at light speed. A photon does not experience the passage of time in the way objects with mass do. Therefore, trying to define a reference frame for a photon would lead to contradictions in our understanding of spacetime.
So in general it doesn't mean much absolute vs relative on photon case.
"For photons there is [] no inertial frame of reference where photon will [appear to] be stationary (relative or absolute means nothing actually)."
I added my comments to your sentence. Obviously, if photon appears to be stationary, this means relative to something else. So relative and absolute are not meaningless.
"In special relativity the important concept is the frame of reference."
I study motion not special relativity. Motion is a fundamental concept. We don't need to use Einsteinian lingo to study motion.
There is no absolute reference frame that would distinguish "absolutely stationary", as you call it, from "relatively at rest". There is only relative motion. Photons are "always in motion" in that there does not and cannot exist any massive object with respect to which a photon is at rest.
I do not know where I first saw it, but I saw someone observe that the shocking thing about Einstein's theory of relativity is not that everything is relative; that was understood reasonably well for a long time before him. What is shocking is that the speed of light in a vacuum, or the speed of causality, is a constant. You can derive huge swathes of relativity from that fact alone.
As a result, of all the speeds, when discussing the speed of light (which conventionally means "in a vacuum" unless otherwise mentioned), you can in fact ignore the question of reference frame, with the exception of you don't want to use a reference frame itself moving at the speed of light. But other than that, an article exclusively confining itself to the discussion of the speed of light in fact doesn't need to worry itself about the relativity of reference frames. For that speed alone, you can't level the complaint against it that it ignores the issue of different frames, because it uniquely doesn't matter.
(Relatedly: It is frequently given as the reason you can't reach or exceed the speed of light is some stuff about masses rising. While mathematically true in its own way, I think there's a cleaner reason to explain why you can't reach or exceed it, which is that you can't even get closer to it. No matter what you do, the speed of light is c. You accelerate to a thousand miles a second in some direction, and how much closer are you to c? The answer is, none. Light continues fleeing from you, in all directions, at c. There is no "get really close to c somehow and then just push yourself over really hard" because there is no "get close to c" in the first place. No matter how hard you accelerate, in what direction, in what order, in what manner, you not only can't get "close" to c, you can't even get closer. For similar reasons, in this paragraph, I don't need to qualify in which reference frame you go a thousand miles per second different than before, because it doesn't matter for c. You can't even get slightly closer to it, let alone "exceed" it somehow. It is an absolute.)
Please bear with me, but how is this true?
If we're in an airplane going 250 m/s - it also takes me 2 hours to fly to NYC. The air around the plane is windy, the air inside is still.
Now we're in a spaceship headed from the earth to the moon & it's going to take us 3 seconds. We've agreed ahead of time it takes 1.5 seconds for light to go from the earth to the moon. C is the speed at which light moves, and we're taking 2x the amount of time light would. The air inside is still. But we're still going fast.
How could it be that we are not approaching the speed of light?
What do you make of time dilation at higher speeds if we aren't approaching the speed of light at all, ever?
It's the stumbling block that everyone has grasping this stuff, and it's rooted in the old faulty kind of speed calculations. Speeds don't add like you think.
There are many ways to grasp this, and one has to try several of them to find an intuitive explanation that works for onesself; but one way is to consider that you, in your spaceship (as long as you are coasting along with no rockets firing, and aren't performing orbit/deorbit burns) are, in your frame of reference, at rest. Your speed is zero. You haven't approached anything at all, and light is still whizzing away from you at c. Indeed, it's Terra and Luna that are experiencing time dilation as far as you are concerned, because they are the ones with the high speeds.
* https://www.youtube.com/watch?v=Zkv8sW6y3sY (FloatHeadPhysics addressing this in another way: there are a other approaches still)
Accelerate at the beginning and end of your trip over to Luna, and of course general relativity comes into play and things get more complicated. What many gedankenexperiments get wrong is that usually there's only a short period of burning the rockets, in the real world. So for most of your trip in the rocket you aren't burning propellant and are in an inertial frame of reference. No inertial frame of reference approaches the speed of light/causality, by postulate 2 of special relativity, and one is always at speed zero in one's own inertial frame of reference.
That motion is relative was understood. That even notions like simultaneity also depend on reference frame I think was shocking. And I'm not really sure what it would mean for light to not be at rest in any reference frame but for it to not have the same speed in all reference frames. I think that would be even more shocking than light having a constant speed.
iirc Maxwell had already shown that the speed of light was constant. Einstein's quest was to explain htf that could be the case. The word Maxwell appears in the first sentence of the 1905 paper, and the first couple of pages are about what today we would call "causality".
Generally, "equivocation" is the fallacy of using the same word with different meanings in an argument.
https://en.wikipedia.org/wiki/Equivocation
I read the same article and I didn't find "absolutely stationary" in the article. My physics is rusty but even from my recollection of high school physics there is no such thing. It's clear that the word stationary means zero velocity, and first year high school physics taught that any measurement of velocity must be done in a reference frame. The idea that a photon is always in motion is true regardless of which reference frame you pick; it does not imply there are objects that are in absolute rest.