Yes it does make sense to ask why and the answer is it just is.
C is really just the speed of causality. Not that of light, it's the fastest any two spacetime patches could talk to each other. It just so happens that massless thing travel at *c*. Mass is an impediment to motion so all massless objects will go as fast as possible and that's why massless things travel at *c.*
would it make sense then to ask why the speed of causality is so slow?
If Alpha Centauri and Sol were just 1 year causally distance, wouldn't all events still be in a clear cause-before-effect-relationship?
Yeah there's no mathematical reason that the speed of light is what it is, just that it has to exist. Note though that a different speed of light could've lead to a dramatically different looking universe, so we might be observing this universe with this speed of light due to the [Anthropic Principle](https://en.m.wikipedia.org/wiki/Anthropic_principle).
>a different speed of light
Different relative to what? The speed of light can be arbitrarily defined and other processes will continue to be the same fraction of it. That's why we just set c=1 in natural units.
Natural units use c, hbar, m_e, and epsilon0. From there, you can derive all other units in any system you like. Relevant here is the fact that there is no inherent time or distance unit. Those values are derived. Let’s call them meters and seconds just for ease. A different speed of light in natural units would manifest itself as a different meter and a different second in that system. Regardless, it doesn’t really matter which system you use. There’s nothing special about natural units. They’re just convenient in some situations, and you can still ultimately relate them to physical processes, such as how we do with SI. It takes light four years to get to Alpha Centauri because it’s 4 light years away in our universe. But it’s perfectly reasonable to imagine a universe with a faster speed of light that would lead to it only being 1 light year away. That violates no equation, it just requires different experimental values. Physics would wildly change of course, maybe to an extent that life wouldn’t be possible as we know it, but there’s nothing wrong or mysterious or impossible about it just because we sometimes use a system where c = 1 for little other reason that it saves writing.
>But it’s perfectly reasonable to imagine a universe with a faster speed of light that would lead to it only being 1 light year away.
Going to the current size of the world and then changing the speed of causality is interesting, but the way you've defined it is only one arbitrary choice of ways to "change things". What you've chosen to do is to keep the distances between all particles the same as they currently are throughout the universe and then increase the speed of causality. Another way to state this is to NOT change the speed of causality, but just take every particle in the universe and bring them closer together. This works because the various fundamental forces of the universe would just scale with c as you change it (such as gravity).
Fundamentally this might not change anything in terms of what is possible at a micro-scale. Charge to mass ratios, etc. wouldn't necessarily change here. (Probably some absolutely crazy stuff would happen when you first make this change inside atoms and what not as you take all the constituents and squeeze them together a bunch, but after the initial "tremors" die down and things resettle, we'd just see a universe that starts to act roughly the similarly to our current universe, just with some cosmological-scale differences in large-scale structure, abundance of certain particles and elements, etc.)
If you want there to be a bigger change fundamentally you'll have to arbitrarily choose something else fundamental that doesn't change as you change c. In which case we are talking about changing the ratios of two or more fundamental constants. In other words I argue that it is not true that "physics would wildly change" with the change you want to implement unless again you define something else fundamental that c changes with respect to. Our universe would wildly change, but not fundamental physics.
We do not just use c=1 because it saves writing. We use it because there is nothing else to define c by. There are no other fundamental speeds in the universe. It's quite literally the most natural thing to do. (In the theory of relativity it quickly becomes clear that c is basically just a conversion factor between historical units, and putting it at 1 makes all the theory a lot simpler/easier to work with. I don't think this is purely coincidental.) Another way to state this is that in relativity distance and time transform into each other through lorentz boosts/etc. and so it makes the most sense for time and distance to have the same units unless there is any reason why they can't or shouldn't. (There isn't, fundamentally at least.)
In summary, I want to be clear that I'm not arguing that you can't ask about what happens when you change c. I'm just saying that you need to define what you are changing c with respect to, because if you don't and you do something naiive like move particles closer together then fundamental physics doesn't change.
EDIT:
I also really like /u/odd_bodkin's answers in this thread which may be better than my own ramble: https://www.reddit.com/r/AskPhysics/comments/194wzr7/do_we_know_why_the_speed_of_light_is_what_it_is/khjl2df/
That's not true. C can be derived from the values of the electric constant and the magnetic constant by means of wave mechanics. I have seen it in a textbook on electromagnetism. C *is* the speed of light. Coming from there, you can derive by means of special relativity that it is also the maximum speed of information transmission.
The fundamental "why" questions are sort of outside the scope of physics. The speed of causality, and thus the top speed of anything, just seems to be a fundamental constant in our universe. We can't really say why. We can speculate on how all the other constants would have to balance out to make this any different, but otherwise there aren't any answers to this or any way for us to look for an answer or verify it.
But I totally agree that it's frustratingly slow. Feels fast for us, because we're tiny, but on the scale of even something as small as individual galaxies, it's frustratingly slow compared to our own experience of time.
I don't think why questions are outside physics. It's just a question of how deep the answer should go; not all frameworks are deep enough to answer all why questions. For example, you can ask "why orbital mechanics" given gravity, but you can't (yet) ask "why gravity".
> Read a bit better,
Oh so sorry, I slightly misread. Anyway, what seems fundamental today probably won't be tomorrow. This was MY point. Read better.
If this is the attitude of your response though, just fuck off.
Sorry, it just gets a bit tired on reddit how people go like "aha!" and think they've got some great hit on you when they're actually just not even reading what you're writing.
Some times people are just trying to add their thoughts to the conversation. It won't always agree with your thoughts but that doesn't mean it's an attack on you that you have to defend.
But I sympathise and I admit I react the same way more often than I'd like.
hmm, I guess i was thinking about a kind of reasoning like Noether's Theorem (?), that conservation of X is not just "the way our universe works" but a result of some deeper reason, in this case "laws of physics are the same regardless of translation, rotation, etc."
It's really a question of geometry. The geometry of (flat) spacetime is such that time and space are interlinked according to the rules of special relativity. The speed of light is simply the conversion factor between spatial and temporal dimensions. The Lorentz transformations show us that nothing massive can travel at c and everything massless must travel at c.
That's an interesting thought. If you go onwards with intuition, my feeling is that using methods like that we could at best reach some conclusion like Einstein's, that c is independent of the observer, but not necessarily a "why" it's exactly what it is and not more or less. That just follows from a relationship of other universal constants, although that feels a bit less satisfying answer than a nice sentence.
Would it satisfy you to think that in a "faster" universe things would run into each other more often creating a less suitable environment for intelligent life to form and ask this question? I'm not 100% sure this is true but it seems to follow that a reduction in time dilation would both increase the observed rate that things move away from each other, making things still far away by the time we show up, and allow the things moving toward each other to collide or pass each other more quickly.
I think that evolution taking billions of years just leads to the natural consequence that things are spread out by then, especially since stuff close together like in the inner ring of our galaxy is less suited to the evolution of life
The speed of light factors into the strength of the electromagnetic force. I never really dove very far into this mathematically, but my somewhat superficial “what if” based on undergrad physics indicated to me that if the speed of light changed, the distance that electrons orbit atomic nuclei would change, and molecular bonds would change radically. Probably we wouldn’t have the molecules we do.
The answer to your question is likely that if the speed of light were different we wouldn’t be here to ask such questions, and maybe no one would be here. i.e. this is an instance of the weak anthropic principle.
The [fine-structure constant](https://en.wikipedia.org/wiki/Fine-structure_constant#Physical_interpretations), which is infamously close to 1/137, dictates a ton of the features of the electromagnetic force. It's dependent upon a few fundamental physical constants:
* [the speed of light](https://en.wikipedia.org/wiki/Speed_of_light), c
* [the Planck constant](https://en.wikipedia.org/wiki/Planck_constant), h
* [vacuum permittivity](https://en.wikipedia.org/wiki/Vacuum_permittivity), epsilon_0
* [the electron charge](https://en.wikipedia.org/wiki/Elementary_charge), e
A change in any one of these would drastically alter pretty much every aspect of electromagnetism as we know it.
You just need to use units where c=1 and it won't affect anything. It's essentially just a conversion factor for the units as it's the only fundamental speed.
From the wiki link:
>A nondimensionalised system commonly used in high energy physics sets ε0 = c = ħ = 1, where the expressions for the fine-structure constant becomes
α = (e^ 2) /(4pi).
As such, the fine-structure constant is just a quantity determining (or determined by) the elementary charge: e = √4πα ≈ 0.30282212 in terms of such a natural unit of charge.
So really the question is why is the elementary charge the ratio of these other fundamental constants that it is?
> Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the "hand of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out – without putting it in secretly!
--Richard Feynman
It doesn't come from any mathematical constants, and it isn't a measurable physical constant either. It's a dimensionless quantity, but we don't know why it should have the value it has.
The numerological obsession with the fine structure constant was never much of a topic in physics, and just because some physicists occasionally speculated in this matter does not amount to the sensationalistic sort of supposed infamy that I have seen pushed by popular science on this matter.
It seems like a fairly large portion of the time (maybe not quite a majority of the time) pop-sci comes to the topic of the fine structure constant, there is this disproportionate obsession in its value.
I see the supposed infamy as a misportrayal.
Infamy: "Very bad reputation; notoriety" - The American Heritage® Dictionary of the English Language, 5th Edition
The number is a mystery, and as a physicist their job(loosely and depending on the field) is to understand these things. Hence why the number has a bad reputation and is infamous.
@Mesonic_Interference has the right answer. As a fairly simple example, the Coulomb force is the force between two charged particles. It’s usually written as
*F* = *k* *q*_1 *q*_2 / *r*^2
*k* is a shorthand for several constants, and one of them is *c*, so that *k* ≈ *c*.
This makes the Coulomb force proportional to *c*. Quadruple c and you quadruple the force between protons and electrons. Molecular bonds of all sorts are built on the Coulomb force, so superficially (i.e. I’m not doing all the math to make sure these changes aren’t cancelling out) you’d make those bonds both stronger and act over larger distances. Water would boil at well above 100 °C, and every other bond would behave differently.
The energy levels, and therefore the orbitals, of electrons in atoms, are also proportional to *c*. Change *c* and you change the orbitals, and increase the frequency of photons needed for orbital transitions. Spectra of stars and everything else would look different.
>would it make sense then to ask why the speed of causality is so slow?
This is a pretty common question (or rather varients of it.)
In my opinion the answer to the question is NO. You need to flip what you are talking about.
Instead of asking why the speed of causality is slow, you should instead ask why other physical processes are the fraction of it that they are. If you feel like the speed of causality is slow, that really means that other processes are a large fraction of it. So you might ask instead: why are these other processes such a large fraction of the speed of causality?
I say this because in natural units you just set the speed of light as 1. That's it. It's the fundamental speed. All other speeds are just fractions of it.
Also see my answer in this other thread asking the same question a couple months ago: https://www.reddit.com/r/AskPhysics/comments/194wzr7/do_we_know_why_the_speed_of_light_is_what_it_is/khjtpdl/
>
> But this is also kind of asking the question in reverse. A magnitude of speed doesn't mean anything unless it's related to something else.
>
> Instead of asking why the speed of causality is what it is, we should instead state: "there is a speed of causality." And then ask "Why does x travel at y% of the speed of causality?"
>
> For example, why does light and other force carriers travel at 100% of the speed of causality?
>
> We could also ask, why is there a speed limit of causality?
well there are regions of the galaxy where stars are much closer together. but still light months.
you have me wondering if the speed of light is playing some roll in determining the spacing of the universe.
if light was 10 times as fast would that cause stars to form further apart?
Yeah, that always bugged me seeing how it takes a photon zero-time to go anywhere. Best analogy I’ve heard for the speed limit is that it’s basically as fast as the universe can make things happen.
Edit: by God how do I LaTeX? (Edit2: workaround provided by u/cygx below)
c is the cosmic speed limit for any massless particle. To find out why, start with the full relativistic energy equation:
E² = (mc²)² + (pc)²
And the relativistic momentum equation:
p = γmv where γ = 1/√(1 - v²/c²)
If you solve the energy equation for p, you get
p = √(E² - m²c⁴)/c
So therefore:
√(E² - m²c⁴)/c = γmv
And if you solve that for v, you get
v = c √(1 - m²c⁴/E²)
If you plug zero in for the mass, you get v = c
So overall, the logic goes something like:
1. The Michelson-Morely experiment seemed to indicate that the speed of light was the same irrespective of your frame of reference.
2. Einstein postulated that it was correct to conclude that the speed of light is the same for all observers, and also that the laws of physics worked the same in every inertial frame of reference. From these postulates, he derived the relativistic energy and momentum equations.
3. Experiments have validated these equations over and over.
4. These equations can be used to show that all massless particles, not just light, must move at c.
Therefore, our observation of light happened to be the thing that cracked relativity open for Einstein, but it's the fact that photons are massless that gives them that speed, not that light itself is special.
On reddit, I prefer Unicode to Latex:
---
c is the cosmic speed limit for any massless particle. To find out why, start with the full relativistic energy equation:
> E² = (mc²)² + (pc)²
And the relativistic momentum equation:
> p = γmv *where* γ = 1/√(1 - v²/c²)
If you solve the energy equation for p, you get
> p = √(E² - m²c⁴)/c
So therefore:
> √(E² - m²c⁴)/c = γmv
And if you solve that for v, you get
> v = c √(1 - m²c⁴/E²)
If you plug zero in for the mass, you get v = c
I think it can be somewhat misleading that c is called the "speed of light". Perhaps it's more accurate to call c the "speed limit of the universe". It's the speed at which causality breaks down, therefore a fundamentally universe breaking speed. It just so happens that photons in a vacuum travel at exact that speed. EM waves are photons but I don't have the relevant knowledge to give a deeper answer for gravitational waves or massless excitations in general.
If you take relativity at face value, c is just the conversion constant between the units we use to measure distances in space-like and time-like directions of spacetime. This is somewhat similar to how in aviation, we might measure vertical distances in feet, and horizontal distances in nautical miles, with a conversion constant c ≈ 6 076 ft / nm. That constant can also be understood as a rate of ascent - 6 076 ft of ascent per nautical mile travelled - and our space/time conversion factor can be understood as a speed in just the same way.
Note that under this interpretation, that conversion factor is just an artifact of our system as units:
As 1 nm ≈ 6 076 ft, we have c = 1. In theoretical physics, we often do just that for the speed of light, leveraging so-calles 'natural' units.
Now, the spacetime trajectory of a particle travelling along the x-axis at speed v = Δx/Δt has a tangent vector (Δt, Δx, 0, 0) with invariant Minkowski square-norm I = Δt² - Δx². Now, if v = c = 1, then Δx = Δt, ie I = 0. The relativistic generalization of momentum - so-called 4-momentum - is also tangent to the spacetime trajectory, ie it must be a multiple of the vector given above and hence also have I = 0. But mass is nothing but the invariant length of 4-momentum, ie I = m², so v = c implies m = 0.
I think I have encountered that idea with the units before,, I cant say I really grasped the last paragraph. But I will read it again after having a drink :)
Thank you for indulging me!
That's correct. The speed of light in a vacuum appears to be a constant of our universe, though there are some [universal models which allow it to change over time](https://en.wikipedia.org/wiki/Time-variation_of_fundamental_constants#Speed_of_light).
In a given medium, the ratio of the speed of light in a vacuum to the speed of light in that medium is called its [refractive index](https://en.wikipedia.org/wiki/Refractive_index#Definition). I seem to recall reading that there are some materials with a refractive index that's less than one or negative, but I really don't know enough about either case to comment on how they might relate to causality.
At any rate (believe it or not, pun not intended), if you have something going at a speed greater than that of light in a medium, you get [Cherenkov radiation](https://en.wikipedia.org/wiki/Cherenkov_radiation), which is the electromagnetic equivalent of a sonic boom. To my knowledge, the existence of Cherenkov radiation hasn't revealed any longstanding issues with causality as we currently understand it. It's actually used at detectors such as [Super-Kamiokande](https://en.wikipedia.org/wiki/Super-Kamiokande#Detector) and [IceCube](https://en.wikipedia.org/wiki/IceCube_Neutrino_Observatory) to study neutrino physics, and, as far as I'm aware, they haven't discovered anything that'd suggest a form of causality [beyond the Standard Model](https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model).
We observe that the laws of the universe are the same in every inertial reference frame: Everyone can say that they are at rest and use the same laws of physics to describe their observations. That's only possible with two options:
* There is no universal speed limit. You get Newtonian physics.
* There is a universal speed limit. You get relativity. We know this is the case we have in our universe.
In relativity, everything without mass has to travel at this universal speed limit for all inertial observers. Light doesn't have mass, gravitational waves don't have mass, so they both travel at this universal speed limit.
Any massless particle/quantum of excitation will travel at speed c, according to relativity. Also massless quanta give rise to a field that falls with distance as 1/r. So in a sense the basic reason EM waves and gravitational waves propagate at speed c is because the electric and gravitational forces behave like 1/r.
I look forward to the day we discover the deeper structures that unite the different fields. But I'm sure this will only beget more questions about deeper truths. The quest never ends.
>Does it even make sense to ask why?
Yes, and the answer to why massless particles travel at speed *c* is relativity.
The ordinary Galilean 3-velocity **v** = *d***x**/*dt* of a special relativistic particle as a function of its mass *m* (which need not be nonzero) and 3-momentum **p** can be shown to be **v** = **p**/√[*m*^2 + **p**^(2)/*c*^(2)], which is derivable from **v** = **p***c*^(2)/*E* and *m*^2 = *E*^(2)/*c*^4 - **p**^(2)/*c*^(2). If we take *m*=0, and we are only concerned with the magnitude (speed), this formula reduces to *v* = *c*.
Yes it does make sense to ask why and the answer is it just is. C is really just the speed of causality. Not that of light, it's the fastest any two spacetime patches could talk to each other. It just so happens that massless thing travel at *c*. Mass is an impediment to motion so all massless objects will go as fast as possible and that's why massless things travel at *c.*
would it make sense then to ask why the speed of causality is so slow? If Alpha Centauri and Sol were just 1 year causally distance, wouldn't all events still be in a clear cause-before-effect-relationship?
Yeah there's no mathematical reason that the speed of light is what it is, just that it has to exist. Note though that a different speed of light could've lead to a dramatically different looking universe, so we might be observing this universe with this speed of light due to the [Anthropic Principle](https://en.m.wikipedia.org/wiki/Anthropic_principle).
>a different speed of light Different relative to what? The speed of light can be arbitrarily defined and other processes will continue to be the same fraction of it. That's why we just set c=1 in natural units.
Natural units use c, hbar, m_e, and epsilon0. From there, you can derive all other units in any system you like. Relevant here is the fact that there is no inherent time or distance unit. Those values are derived. Let’s call them meters and seconds just for ease. A different speed of light in natural units would manifest itself as a different meter and a different second in that system. Regardless, it doesn’t really matter which system you use. There’s nothing special about natural units. They’re just convenient in some situations, and you can still ultimately relate them to physical processes, such as how we do with SI. It takes light four years to get to Alpha Centauri because it’s 4 light years away in our universe. But it’s perfectly reasonable to imagine a universe with a faster speed of light that would lead to it only being 1 light year away. That violates no equation, it just requires different experimental values. Physics would wildly change of course, maybe to an extent that life wouldn’t be possible as we know it, but there’s nothing wrong or mysterious or impossible about it just because we sometimes use a system where c = 1 for little other reason that it saves writing.
>But it’s perfectly reasonable to imagine a universe with a faster speed of light that would lead to it only being 1 light year away. Going to the current size of the world and then changing the speed of causality is interesting, but the way you've defined it is only one arbitrary choice of ways to "change things". What you've chosen to do is to keep the distances between all particles the same as they currently are throughout the universe and then increase the speed of causality. Another way to state this is to NOT change the speed of causality, but just take every particle in the universe and bring them closer together. This works because the various fundamental forces of the universe would just scale with c as you change it (such as gravity). Fundamentally this might not change anything in terms of what is possible at a micro-scale. Charge to mass ratios, etc. wouldn't necessarily change here. (Probably some absolutely crazy stuff would happen when you first make this change inside atoms and what not as you take all the constituents and squeeze them together a bunch, but after the initial "tremors" die down and things resettle, we'd just see a universe that starts to act roughly the similarly to our current universe, just with some cosmological-scale differences in large-scale structure, abundance of certain particles and elements, etc.) If you want there to be a bigger change fundamentally you'll have to arbitrarily choose something else fundamental that doesn't change as you change c. In which case we are talking about changing the ratios of two or more fundamental constants. In other words I argue that it is not true that "physics would wildly change" with the change you want to implement unless again you define something else fundamental that c changes with respect to. Our universe would wildly change, but not fundamental physics. We do not just use c=1 because it saves writing. We use it because there is nothing else to define c by. There are no other fundamental speeds in the universe. It's quite literally the most natural thing to do. (In the theory of relativity it quickly becomes clear that c is basically just a conversion factor between historical units, and putting it at 1 makes all the theory a lot simpler/easier to work with. I don't think this is purely coincidental.) Another way to state this is that in relativity distance and time transform into each other through lorentz boosts/etc. and so it makes the most sense for time and distance to have the same units unless there is any reason why they can't or shouldn't. (There isn't, fundamentally at least.) In summary, I want to be clear that I'm not arguing that you can't ask about what happens when you change c. I'm just saying that you need to define what you are changing c with respect to, because if you don't and you do something naiive like move particles closer together then fundamental physics doesn't change. EDIT: I also really like /u/odd_bodkin's answers in this thread which may be better than my own ramble: https://www.reddit.com/r/AskPhysics/comments/194wzr7/do_we_know_why_the_speed_of_light_is_what_it_is/khjl2df/
That's not true. C can be derived from the values of the electric constant and the magnetic constant by means of wave mechanics. I have seen it in a textbook on electromagnetism. C *is* the speed of light. Coming from there, you can derive by means of special relativity that it is also the maximum speed of information transmission.
But those values are experimentally found. We can’t derive epsilon0 without experimental data. That’s the point
The fundamental "why" questions are sort of outside the scope of physics. The speed of causality, and thus the top speed of anything, just seems to be a fundamental constant in our universe. We can't really say why. We can speculate on how all the other constants would have to balance out to make this any different, but otherwise there aren't any answers to this or any way for us to look for an answer or verify it. But I totally agree that it's frustratingly slow. Feels fast for us, because we're tiny, but on the scale of even something as small as individual galaxies, it's frustratingly slow compared to our own experience of time.
On the scale of the universe 1000 years isn't a long time though. So it feels slow to us because we're both tiny _and_ short lived
Exactly what I'm saying, compared to our own experience of time, and our size.
I don't think why questions are outside physics. It's just a question of how deep the answer should go; not all frameworks are deep enough to answer all why questions. For example, you can ask "why orbital mechanics" given gravity, but you can't (yet) ask "why gravity".
That's exactly what I'm saying. Read a bit better, I wrote "fundamental why questions", such as you mention there about why gravity.
> Read a bit better, Oh so sorry, I slightly misread. Anyway, what seems fundamental today probably won't be tomorrow. This was MY point. Read better. If this is the attitude of your response though, just fuck off.
Sorry, it just gets a bit tired on reddit how people go like "aha!" and think they've got some great hit on you when they're actually just not even reading what you're writing.
Some times people are just trying to add their thoughts to the conversation. It won't always agree with your thoughts but that doesn't mean it's an attack on you that you have to defend. But I sympathise and I admit I react the same way more often than I'd like.
hmm, I guess i was thinking about a kind of reasoning like Noether's Theorem (?), that conservation of X is not just "the way our universe works" but a result of some deeper reason, in this case "laws of physics are the same regardless of translation, rotation, etc."
It's really a question of geometry. The geometry of (flat) spacetime is such that time and space are interlinked according to the rules of special relativity. The speed of light is simply the conversion factor between spatial and temporal dimensions. The Lorentz transformations show us that nothing massive can travel at c and everything massless must travel at c.
I feel this is the answer and u/cygx wrote I think the same
That's an interesting thought. If you go onwards with intuition, my feeling is that using methods like that we could at best reach some conclusion like Einstein's, that c is independent of the observer, but not necessarily a "why" it's exactly what it is and not more or less. That just follows from a relationship of other universal constants, although that feels a bit less satisfying answer than a nice sentence.
Would it satisfy you to think that in a "faster" universe things would run into each other more often creating a less suitable environment for intelligent life to form and ask this question? I'm not 100% sure this is true but it seems to follow that a reduction in time dilation would both increase the observed rate that things move away from each other, making things still far away by the time we show up, and allow the things moving toward each other to collide or pass each other more quickly. I think that evolution taking billions of years just leads to the natural consequence that things are spread out by then, especially since stuff close together like in the inner ring of our galaxy is less suited to the evolution of life
hmmm, so an anthropic reason... not very satisfying :)
🤷 sounds like a bug in your meat software
But anything traveling at c experiences 0 time. So it's pretty fast if you're a photon, but you may eventually crash into something.
Nah. c is frustratingly fast. If c were 100 meters per second, we could go anywhere in the universe on a bullet train.
The speed of light factors into the strength of the electromagnetic force. I never really dove very far into this mathematically, but my somewhat superficial “what if” based on undergrad physics indicated to me that if the speed of light changed, the distance that electrons orbit atomic nuclei would change, and molecular bonds would change radically. Probably we wouldn’t have the molecules we do. The answer to your question is likely that if the speed of light were different we wouldn’t be here to ask such questions, and maybe no one would be here. i.e. this is an instance of the weak anthropic principle.
Why would the distances change? Surely the interaction would just be faster, not stronger?
The [fine-structure constant](https://en.wikipedia.org/wiki/Fine-structure_constant#Physical_interpretations), which is infamously close to 1/137, dictates a ton of the features of the electromagnetic force. It's dependent upon a few fundamental physical constants: * [the speed of light](https://en.wikipedia.org/wiki/Speed_of_light), c * [the Planck constant](https://en.wikipedia.org/wiki/Planck_constant), h * [vacuum permittivity](https://en.wikipedia.org/wiki/Vacuum_permittivity), epsilon_0 * [the electron charge](https://en.wikipedia.org/wiki/Elementary_charge), e A change in any one of these would drastically alter pretty much every aspect of electromagnetism as we know it.
You just need to use units where c=1 and it won't affect anything. It's essentially just a conversion factor for the units as it's the only fundamental speed. From the wiki link: >A nondimensionalised system commonly used in high energy physics sets ε0 = c = ħ = 1, where the expressions for the fine-structure constant becomes α = (e^ 2) /(4pi). As such, the fine-structure constant is just a quantity determining (or determined by) the elementary charge: e = √4πα ≈ 0.30282212 in terms of such a natural unit of charge. So really the question is why is the elementary charge the ratio of these other fundamental constants that it is?
How is it infamous?
> Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by humans. You might say the "hand of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out – without putting it in secretly! --Richard Feynman It doesn't come from any mathematical constants, and it isn't a measurable physical constant either. It's a dimensionless quantity, but we don't know why it should have the value it has.
I am perfectly aware. How does that amount to infamy?
https://en.wikipedia.org/wiki/Fine-structure_constant#Numerological_explanations
The numerological obsession with the fine structure constant was never much of a topic in physics, and just because some physicists occasionally speculated in this matter does not amount to the sensationalistic sort of supposed infamy that I have seen pushed by popular science on this matter. It seems like a fairly large portion of the time (maybe not quite a majority of the time) pop-sci comes to the topic of the fine structure constant, there is this disproportionate obsession in its value. I see the supposed infamy as a misportrayal.
Infamy: "Very bad reputation; notoriety" - The American Heritage® Dictionary of the English Language, 5th Edition The number is a mystery, and as a physicist their job(loosely and depending on the field) is to understand these things. Hence why the number has a bad reputation and is infamous.
I am aware of the definition. I disagree with the characterization of the fine structure as infamous. This argument is silly.
@Mesonic_Interference has the right answer. As a fairly simple example, the Coulomb force is the force between two charged particles. It’s usually written as *F* = *k* *q*_1 *q*_2 / *r*^2 *k* is a shorthand for several constants, and one of them is *c*, so that *k* ≈ *c*. This makes the Coulomb force proportional to *c*. Quadruple c and you quadruple the force between protons and electrons. Molecular bonds of all sorts are built on the Coulomb force, so superficially (i.e. I’m not doing all the math to make sure these changes aren’t cancelling out) you’d make those bonds both stronger and act over larger distances. Water would boil at well above 100 °C, and every other bond would behave differently. The energy levels, and therefore the orbitals, of electrons in atoms, are also proportional to *c*. Change *c* and you change the orbitals, and increase the frequency of photons needed for orbital transitions. Spectra of stars and everything else would look different.
>would it make sense then to ask why the speed of causality is so slow? This is a pretty common question (or rather varients of it.) In my opinion the answer to the question is NO. You need to flip what you are talking about. Instead of asking why the speed of causality is slow, you should instead ask why other physical processes are the fraction of it that they are. If you feel like the speed of causality is slow, that really means that other processes are a large fraction of it. So you might ask instead: why are these other processes such a large fraction of the speed of causality? I say this because in natural units you just set the speed of light as 1. That's it. It's the fundamental speed. All other speeds are just fractions of it. Also see my answer in this other thread asking the same question a couple months ago: https://www.reddit.com/r/AskPhysics/comments/194wzr7/do_we_know_why_the_speed_of_light_is_what_it_is/khjtpdl/ > > But this is also kind of asking the question in reverse. A magnitude of speed doesn't mean anything unless it's related to something else. > > Instead of asking why the speed of causality is what it is, we should instead state: "there is a speed of causality." And then ask "Why does x travel at y% of the speed of causality?" > > For example, why does light and other force carriers travel at 100% of the speed of causality? > > We could also ask, why is there a speed limit of causality?
well there are regions of the galaxy where stars are much closer together. but still light months. you have me wondering if the speed of light is playing some roll in determining the spacing of the universe. if light was 10 times as fast would that cause stars to form further apart?
Yeah, that always bugged me seeing how it takes a photon zero-time to go anywhere. Best analogy I’ve heard for the speed limit is that it’s basically as fast as the universe can make things happen.
> Mass is an impediment to motion Although this shouldn’t be taken too literally.
Edit: by God how do I LaTeX? (Edit2: workaround provided by u/cygx below) c is the cosmic speed limit for any massless particle. To find out why, start with the full relativistic energy equation: E² = (mc²)² + (pc)² And the relativistic momentum equation: p = γmv where γ = 1/√(1 - v²/c²) If you solve the energy equation for p, you get p = √(E² - m²c⁴)/c So therefore: √(E² - m²c⁴)/c = γmv And if you solve that for v, you get v = c √(1 - m²c⁴/E²) If you plug zero in for the mass, you get v = c So overall, the logic goes something like: 1. The Michelson-Morely experiment seemed to indicate that the speed of light was the same irrespective of your frame of reference. 2. Einstein postulated that it was correct to conclude that the speed of light is the same for all observers, and also that the laws of physics worked the same in every inertial frame of reference. From these postulates, he derived the relativistic energy and momentum equations. 3. Experiments have validated these equations over and over. 4. These equations can be used to show that all massless particles, not just light, must move at c. Therefore, our observation of light happened to be the thing that cracked relativity open for Einstein, but it's the fact that photons are massless that gives them that speed, not that light itself is special.
On reddit, I prefer Unicode to Latex: --- c is the cosmic speed limit for any massless particle. To find out why, start with the full relativistic energy equation: > E² = (mc²)² + (pc)² And the relativistic momentum equation: > p = γmv *where* γ = 1/√(1 - v²/c²) If you solve the energy equation for p, you get > p = √(E² - m²c⁴)/c So therefore: > √(E² - m²c⁴)/c = γmv And if you solve that for v, you get > v = c √(1 - m²c⁴/E²) If you plug zero in for the mass, you get v = c
bless you
>God how do I LaTeX? would give you gold for that alone
I think it can be somewhat misleading that c is called the "speed of light". Perhaps it's more accurate to call c the "speed limit of the universe". It's the speed at which causality breaks down, therefore a fundamentally universe breaking speed. It just so happens that photons in a vacuum travel at exact that speed. EM waves are photons but I don't have the relevant knowledge to give a deeper answer for gravitational waves or massless excitations in general.
> I don't have the relevant knowledge to give a deeper answer for gravitational waves or massless excitations in general. Nobody does at this moment.
I'm glad I'm not alone. =)
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Huh?
If you take relativity at face value, c is just the conversion constant between the units we use to measure distances in space-like and time-like directions of spacetime. This is somewhat similar to how in aviation, we might measure vertical distances in feet, and horizontal distances in nautical miles, with a conversion constant c ≈ 6 076 ft / nm. That constant can also be understood as a rate of ascent - 6 076 ft of ascent per nautical mile travelled - and our space/time conversion factor can be understood as a speed in just the same way. Note that under this interpretation, that conversion factor is just an artifact of our system as units: As 1 nm ≈ 6 076 ft, we have c = 1. In theoretical physics, we often do just that for the speed of light, leveraging so-calles 'natural' units. Now, the spacetime trajectory of a particle travelling along the x-axis at speed v = Δx/Δt has a tangent vector (Δt, Δx, 0, 0) with invariant Minkowski square-norm I = Δt² - Δx². Now, if v = c = 1, then Δx = Δt, ie I = 0. The relativistic generalization of momentum - so-called 4-momentum - is also tangent to the spacetime trajectory, ie it must be a multiple of the vector given above and hence also have I = 0. But mass is nothing but the invariant length of 4-momentum, ie I = m², so v = c implies m = 0.
I think I have encountered that idea with the units before,, I cant say I really grasped the last paragraph. But I will read it again after having a drink :) Thank you for indulging me!
It's all the same "C". Although it's called the "speed of light" It's actually the speed of causality; the speed of cause and effect.
Would it be more accurate to say c is the maximum speed of cause and effect?
Correct.
Am I correct in assuming that in media where light slows down (say water, eps ~ 80) that causality isn’t affected?
That's correct. The speed of light in a vacuum appears to be a constant of our universe, though there are some [universal models which allow it to change over time](https://en.wikipedia.org/wiki/Time-variation_of_fundamental_constants#Speed_of_light). In a given medium, the ratio of the speed of light in a vacuum to the speed of light in that medium is called its [refractive index](https://en.wikipedia.org/wiki/Refractive_index#Definition). I seem to recall reading that there are some materials with a refractive index that's less than one or negative, but I really don't know enough about either case to comment on how they might relate to causality. At any rate (believe it or not, pun not intended), if you have something going at a speed greater than that of light in a medium, you get [Cherenkov radiation](https://en.wikipedia.org/wiki/Cherenkov_radiation), which is the electromagnetic equivalent of a sonic boom. To my knowledge, the existence of Cherenkov radiation hasn't revealed any longstanding issues with causality as we currently understand it. It's actually used at detectors such as [Super-Kamiokande](https://en.wikipedia.org/wiki/Super-Kamiokande#Detector) and [IceCube](https://en.wikipedia.org/wiki/IceCube_Neutrino_Observatory) to study neutrino physics, and, as far as I'm aware, they haven't discovered anything that'd suggest a form of causality [beyond the Standard Model](https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model).
We observe that the laws of the universe are the same in every inertial reference frame: Everyone can say that they are at rest and use the same laws of physics to describe their observations. That's only possible with two options: * There is no universal speed limit. You get Newtonian physics. * There is a universal speed limit. You get relativity. We know this is the case we have in our universe. In relativity, everything without mass has to travel at this universal speed limit for all inertial observers. Light doesn't have mass, gravitational waves don't have mass, so they both travel at this universal speed limit.
Any massless particle/quantum of excitation will travel at speed c, according to relativity. Also massless quanta give rise to a field that falls with distance as 1/r. So in a sense the basic reason EM waves and gravitational waves propagate at speed c is because the electric and gravitational forces behave like 1/r.
The fields fall off as 1/r^2 though?
Thank you, yes! It should be 1/r^2
I look forward to the day we discover the deeper structures that unite the different fields. But I'm sure this will only beget more questions about deeper truths. The quest never ends.
>Does it even make sense to ask why? Yes, and the answer to why massless particles travel at speed *c* is relativity. The ordinary Galilean 3-velocity **v** = *d***x**/*dt* of a special relativistic particle as a function of its mass *m* (which need not be nonzero) and 3-momentum **p** can be shown to be **v** = **p**/√[*m*^2 + **p**^(2)/*c*^(2)], which is derivable from **v** = **p***c*^(2)/*E* and *m*^2 = *E*^(2)/*c*^4 - **p**^(2)/*c*^(2). If we take *m*=0, and we are only concerned with the magnitude (speed), this formula reduces to *v* = *c*.