You always hear this phrase if you watch something about astrophysics ‘Nothing can move faster than light’. But speed is only relative. How can this be true if speed can only be experienced/measured relative to something else?
In: Physics
Hey mate, I defend for my Ph.D. in physics in a month. This explanation is not ELI5 but, unfortunately, it doesn’t seem like the more elementary explanations are really that, explanations. Rather… just kind of rehashing different ways of saying “yup that’s just how it is.” So a little more detail may be needed.
The paradox seems to arise because of how you’re used to looking at relative velocities. If you’re driving in a car, someone looks like they’re going backwards to you at the same speed that you’re going forward to them. And if you introduce a third object, moving at half your speed in the same direction, then you see it as moving backwards at half of your speed while the ground observer sees it as moving forward at half your speed.
This type of shifting between different points of view (reference frames), where you can just add or subtract velocity differences, is what’s called a [Galilean Transformation](https://en.wikipedia.org/wiki/Galilean_transformation) and does a good job at describing different the points of view as we humans perceive them. To us also, the differences in velocity between us and other things we see from day to day is extremely small compared to the speed of light. So the difference in the effects between light appearing to move a bit slower or faster in different frames (what a Galilean transformation prescribes) versus light actually always being the same speed, are extremely small.
But it just so happens that some people [1](https://en.wikipedia.org/wiki/James_Clerk_Maxwell) [2](https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) from ~1850-1900ish figured out that light should actually appear to always be moving at *exactly* the speed of light in any frame, not just approximately. This obviously contradicts the Galilean transformation since the simple addition of velocities between frames isn’t satisfied anymore.
The ability to mathematically shift between different points of view without changing the underlying reality is called symmetry. Its the same idea that if you rotate a ball it looks the same all around. Galilean transformation is a form of symmetry. It was found that there’s another form of symmetry for changing frames of reference called a [Lorentz transformation](https://en.wikipedia.org/wiki/Lorentz_transformation). The Lorentz transformation functions very similarly to the Galilean transformation when things are moving slowly relative to each other when compared to the speed of light. But it also doesn’t break down when account for light having to always be the same speed in every reference frame.
Since the Lorentz transformation accurately describes reality, its differences with the Galilean transformation have implications on the way that we have to frame our physical interpretation of the world. Among other things, it implies that the coordinates of length can expand and contract as seen in different reference frames, and that the concept of time, which was formerly thought to be a distinct entity, must be treated similarly to position. In other words, time is, in some ways, a ‘fourth spatial dimension’, and just like space under the Lorentz transformation, it can “shrink” and “expand” and observers may “rotate” towards and away from the “time” axis, just like you can turn left and right when you walk. Consequently, the paradox of the speed of light seeming to be the same to all observers is accommodated by the notions of space and time changing for observers to preserve the speed of light from every point of view.
I must be 4. I’ve read most of the comments and still can’t understand what people are saying.
The explanation that worked best for me: the speed of light is not so much the speed of *light*, but of *causality*: nothing can cause an effect on something else faster than that speed. Since light is not limited by anything (at least in a vacuum), light travels at max speed of causality, ergo, the speed of light is the fastest that anything can go.
Wow, OP. You’ve asked the very same question that Einstein asked himself to come up with one of the most revolutionary ideas in physics!
You are correct that speed is relative. If I’m walking up an escalator at 2 m/s and the escalator is moving at 5m/s then my speed relative to a person standing still at the bottom of the escalator is 7 m/s, but to someone else on the escalator who is standing still and waiting patiently for the escalator to transport them to the next floor my speed is 2 m/s.
But light travels at the same speed from all perspectives. Say a spaceship is traveling at 90% the speed of light. If I shine a torch from the back of the spaceship to the front and someone on the ground can see through the spaceship’s window, then the light from the torch will appear to move at the speed of light to both of us. But the escalator example would suggest that to the person on the ground, it should be traveling at 90% of the speed of light + the speed of light i.e. at 190% of the speed of light. So how can it appear to move at the speed of light to both of us? Well, if the person on the ground is looking through the window and everything in the ship (including not only the beam of light from the torch, but the people inside the ship) is moving in slow motion, then the beam of light can appear to move at the speed of light.
Mind blowing, eh? To solve the paradox, time must be relative! Time inside the ship appears to be slowed down to the person on the ground, and conversely everyone outside the ship looks like they’re running around like ants to the people inside. Actually, there’s a bit more to it than that, since distances are affected too. But thinking about it like this is a good starting point.
It is hard to ELI5, but here goes:
You are standing beside a train, you shine your flashlight at someone else standing beside their train, they shine their flashlight when they see yours. You measure the time for the round trip, you get the speed of light.
You both get on your trains, heading toward each other. You shine your flashies, you measure the round trip.. wow, same speed of light.
You both go real fast, say leaving the station at half light speed each toward each other. You shine your flashies, you measure the round trip.. same speed of light.
Now, the reason for this complicated, but essentially your point of view, your perspective, is where all the distances and times are measured from. And those numbers don’t work by adding up, when they get closer to the speed of light, the figuring starts to distort.
For example if you hop on a spaceship and head toward a distant planet and start accelerating. The rest of the universe, including the distance to that planet, will seem to get shorter (not just because you are moving that way). Essentially you turn everything into pancakes. But, people on that other planet see that happening to you.
The takeaway, is that is actually how movement works, our ability to add and subtract distances and speeds is actually the weird little simplified version of reality that we get to live in.
This is long, but it breaks down the problem/answer in details.
The rule concerning the speed of light, more specifically, would be that nothing can travel faster than the speed of light *relative to you.*
Now, you as an observer to something else, would be what is referred to as a ‘reference frame’. Think of yourself as the big clock in town square that everyone else uses to synchronise their own wristwatches. You’re the baseline, the standard, the metric against which other things are measured, because as far as you’re concerned, you’re the centre of the universe. You and your outwards perception of the world is simply **zero.**
All speed is relative. If I’m standing still and a car whizzes by at 100mph, then I see it moving at 100mph. But if I’m in a car next to it that’s doing 95mph, then I only see that car inch forward at 5mph. Any speed you experience is the relative difference between you and all other moving things. Are you moving forward at 95mph, or is the Earth is turning backwards at 95mph? There is literally no actual empirical way to answer that question, because physically there is no difference.
Meaning, if I travel forward at 10mph and something else travels towards me at 10mph, it feels the same as if I’m staying still and it moves towards me at 20mph, right? Correct. Two cars moving towards each other at the same speed would takes the same amount of time to collide as one car staying still and the other car moving at twice the speed. The relative motion between the two is identical.
So, if I’m moving towards a photon at 1mph, and that photon is moving towards me at the speed of light, then the relative speed between us is the speed of light +1mph, right?
Nope. It’s just the speed of light. If one of the two objects is moving at the speed of light, the speed between you and it is only *ever* the speed of light. It doesn’t matter how fast you’re moving. 0mph, a million mph, it simply makes no difference.
This phenomenon sounds like a space-breaking paradox. If it works at 100mph, why not an arbitrarily high speed? What happens, where’s the shift? Despite the oddness of it, this behaviour is an absolute proven fact, as sure as gravity pulls you down and the sky is blue. Even if you move towards something travelling at the speed of light and that something moves towards *you* at the speed of light, the relative speed between you is… still just 1x the speed of light.
This trippy phenomenon is called *frame invariance,* and is the founding principle on which Einstein based his theory of relatively, which describes how time is relative and is not static between two different frames of reference. Frame invariance says everything I’ve described in a single sentence: *”The speed of light is invariant* [does not change] *between inertial* [no acceleration; constant speed between the two] *frames of reference”.*
So, the two assertions you’ve made – that speed can only ever be relative and that nothing can move faster than light – are both true, both at the same time. If you’re moving towards something at the SoL and it moves towards you at the SoL, the speed between you is still just the SoL. It would take the same amount of time for that photon to hit you as if you just stood still and waited for it to arrive. If you were travelling alongside a photon at the SoL and you were just ever so below the SoL, it would still move away from *you* at the SoL. It would move away from a stationary observer at the SoL, even though you’re moving relative to them, and so on. It makes no sense, but our monkey brains simply are not equipped to conceptualise how seemingly broken physics starts to become when you approach speeds this high.
We used to measure how far one traveled across the seas in ‘leagues’ and how deep the water was in ‘fathoms.’ (short side note: 20000 Leagues Under the Sea does not mean 20000 Leagues below the surface of water, but rather travelling such a distance while submerged. It is approximately circumnavigating the Earth in a sub, essentially) We had one unit of length for horizontal distance, but another unit of length for vertical distance. But of course they’re really the same thing, just different units, so we know we can convert one of them into the other. There are about 3038.6 fathoms in one league.
Let’s imagine another scenario where we used km for measuring distances north/south, and miles for measuring east/west. Again, same ‘thing’ being measured, just in different directions. I face north and now in front of me is km, and to my right is miles. But if I turn some amount, now in front of me is some weird mix of km and miles and so too to my right. The units mix up a little together according to some trigonometry rules.
This, at its heart, is what we mean when we talk about space-time. Meters and seconds *measure the exact same thing.* Just as meters and inches do, meters and seconds do as well. There’s a conversion factor to tell you how many meters are in a second 299,792,458 is equivalent to 1 second, there’s about 1.08 Trillion meters in an hour. That’s what that number really means. We’ll get to why it *happens* to be the speed of light in a bit.
When I lay out my grid of meters and seconds, in all my “space” dimensions using meters, and my “time” dimensions using clocks, everything looks fine. A meter is a meter, a second is a second. You stand beside me and you lay out your grid, and you agree with my grid.
However if you are moving relative to me, your motion acts like a ‘rotation’. You still see a second as a second, a meter as a meter. I still see them as the same, but when we look at each others’ grids, we each see the other person is mixing in a little of the ‘time’ dimension with the space ones and a little of the ‘space’ ones in with time. We each appear a bit shorter or ‘flatter’ along the direction of motion, and we each see the others’ clock as running a little bit slower.
As we go faster and faster that disagreement about rulers and clocks becomes more pronounced and leads to other interesting effects, namely ways we have to change how we calculate certain things physically because what we thought to be a good description of things was only valid at low speeds.
Here’s what ties it all together. We are, all of us, moving through space-time at 1 second per second. That may seem like a tautology or something simple, but think about what it _really_ means if space and time are the same thing. If I am going 1 second per second always, and I want to start going 30 meters per second, I’m going to have to take those 30 meters out of that 1 second per second. I’m going to have to take some of my travelling toward the future in time and turn it into ‘moving’ through space. The best I could ever possibly hope to do is to convert *all* of my 1 second per second into 299792458 meters/second. At which point I’ve stopped ‘going into the future’ and am entirely moving through space.
There’s a bit of a catch here though. Having mass means (for reasons) the closest I can ever do is get *arbitrarily close* to 299792458, but I can never *quite* get there. If I had precisely no mass, I could do nothing *but* travel at that speed. Light has no mass. So light *always* travels at the 299792458 m/s. So far we only know of two other things we think to be massless. Gravity (if it is particles, then gravitons) is massless, and the particles of the strong force, gluons, are massless. Gluons don’t travel very far at all, so we don’t often think about this, but gravity, changes in gravity, travels at 299792458 m/s. (Gravitational waves for example).
For more from back when I was really active about this stuff:
[https://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/](https://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/)
[https://www.reddit.com/r/askscience/comments/fqxbh/does_a_mass_particle_traveling_close_enough_to/](https://www.reddit.com/r/askscience/comments/fqxbh/does_a_mass_particle_traveling_close_enough_to/)
[https://www.reddit.com/r/askscience/comments/pu1uj/are_time_dimensions_the_same_relatively_as_space/c3sfmbc/?context=3](https://www.reddit.com/r/askscience/comments/pu1uj/are_time_dimensions_the_same_relatively_as_space/c3sfmbc/?context=3)
[https://www.reddit.com/r/askscience/comments/gegwv/why_is_the_speed_of_light_299792458ms_would_the/c1mzszd/](https://www.reddit.com/r/askscience/comments/gegwv/why_is_the_speed_of_light_299792458ms_would_the/c1mzszd/)
You can even think about it this way:
The “speed of light” is really just “THE speed.”
It’s the default speed of everything. It’s just that matter gets in the way and makes things slower. But when all those limitations like matter or external forces or whatever are eliminated, the speed of light (also just called “c” in equations) is the speed it would go.
You can view it as “the speed of light is the speed limit of the universe”. Nothing (so far) can go faster than that. Because of mass, or lack thereof for the case of photons, as zazieely said. No matter what you try to do to them, they always go as fast as they can.
Imagine a motorbike speeding down the highway. Its speed is relative to the rotation of the Earth, or someone standing still.
Now, the motorbike turns on its headlights. The light beaming out from it moves at the speed of light instantly regardless of how fast the bike is moving. The bike’s speed is not added to the speed at which that light travels. The speed of light is not relative, that’s why it’s special.
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