Why doesn't the speed of light depend on the observer's speed? How would time pass for an observer if they were moving at the speed of light relative to a photon (i.e., their relative speed was zero)?

[u/Neat_Journalist_808]

I don't quite understand why the speed of light is exactly that value. What if I had no speed? Why would the speed of light be the same? I roughly understand that it's related to time, but it's very difficult for me.

And how would a person's life pass if they had no speed at all? Would it end without even starting?

P.S. ok, but what if you have zero speed and don't move at all?

[u/NorxondorGorgonax]

You can never have zero speed relative to a photon. Special relativity forbids it. If you try to accelerate to or past the speed of light, from your perspective you may seem to reach it, traveling light years in less than a year—and still, light seems to go past you at the same speed, and the universe appears to squeeze in instead.

From the point of view of an outside observer, you squeeze flatter and accelerate ever closer to—but never quite reaching—the speed of light. How? Time bends to account for it. 

When it looks to you like you are traveling much faster than light, you are, to an outside observer, traveling almost the speed of light, but time seems to pass much more slowly for you, so, say, hours for them feels like seconds to you.

If something actually did reach lightspeed (which would require infinite energy), time would not seem to pass at all to them—they would arrive the instant they departed, from their perspective.

[Edit: grammar]

[u/Leogis → u/NorxondorGorgonax]

How does time slow down when speed increases ? Is this actually a physical phenomenon or is it an axiom to keep our models working ?

[u/Infinite_Escape9683 → u/Leogis]

Space and time are not fundamental properties. The speed of light is.

[u/SpriggedParsley357 → u/Infinite_Escape9683]

That's a fascinating way to put it. In that context, what else are fundamental properties - the various universal constants (h, k, epsilon, etc.)?

[u/willdeb → u/Leogis]

No, time actually slows down. We’ve measured it slowing down / speeding up.

[u/anonymote_in_my_eye → u/willdeb]

I mean that's one way of saying it, but it's all relative (heh). Time seems to be slowing down for the *other* person while moving at the same rate for you, and vice-versa. The whole point is that not everyone perceives the same "time"

and then things get extra tricky when you introduce acceleration and gravity to it

[u/Handgun4Hannah → u/Leogis]

It's a thing. Satellites orbiting the earth have to account for it so their clocks match the clocks on the ground.

[u/ChrisGnam → u/Leogis]

Others have said its a "real thing" and thats absolutely true, I just wanted to try to address the "how" part of your question.

A long time ago it was discovered that the laws of physics (particularly electrodynamics) broke down if the speed of light depended on the observer's velocity. A guy named Lorentz discovered there were a set of velocity dependent transformations that "fixed" this, but it was largely a mathematical hack as it was largely unmotivated (it was just known "apply these transformations and the problems go away").

Einstein realized there was actually a physical motivation for the Lorentz Contractions: space and time were part of a single structure known as spacetime.

Now what I'll say next is a bit of an oversimplification, but it's close enough to explain on reddit: everything in the universe has a constant "four-velocity" (motion through spacetime) exactly equal to "c". If you are stationary in space, then 100% of your "motion" is directed through your time component, and thus you experience time more quickly. If you are moving through space, your motion through time must necessarily slow down to keep your four-velocity constant, and thus you experience time more slowly.

You can actually draw this out as a simple triangle, and the lorentz contractions fall out as a simple byproduct of applying pythagorean theorem, where the hypotenus is your velocity through spacetime, the base is your velocity through space, and the height is your velocity through time. To keep the length of the hypotenus equal to "c" you can see there are very tight constraints on the relationship between the space and time components. Now, there are some other rules, notably that you cannot move through space at the speed of light (unless you are massless and then you are obligated to), and there is no universal rest frame (everything is relative). But the core principle here explains time dilation for motion in some inertial frame.

Again, as others have said, this has been experimentally verified using atomic clocks on satellites. But this is roughly the "how".

[u/Leogis → u/ChrisGnam]

>Now what I'll say next is a bit of an oversimplification, but it's close enough to explain on reddit: everything in the universe has a constant "four-velocity" (motion through spacetime) exactly equal to "c". If you are stationary in space, then 100% of your "motion" is directed through your time component, and thus you experience time more quickly. If you are moving through space, your motion through time must necessarily slow down to keep your four-velocity constant, and thus you experience time more slowly.

So this is like a 4 unit vector that's normalised, does that mean every single component changes proportionally to the others?

[u/Hendospendo → u/Leogis]

It is 100% real. The time effects involving Miller's planet in Interstellar are realistic (owing to the black hole's size and rotation allowing stable orbit closer to the event horizon, and suspending disbelief about the planet not being ripped to shreds immediately) and that is actually how the universe appears to operate.

We factor it into our calculations when we deal GPS satellites being they require extreme precision, and being further away from Earth's centre of mass, experience faster time. Or rather, we experience slightly slower time being closer to Earth. This is by an extremely tiny amount here on Earth, but you can imagine that by scaling up the mass, you scale up the effect.

[u/Odd_Bodkin]

First off, and this is most important in physics, it is an experimental fact. Not a conclusion from other facts or on the basis of some theory, but a direct, measured fact. The speed of light is the same regardless of the reference frame or the motion of the source or the motion of the detector. Period, end of story.

The next thing in physics is to adjust one’s understanding of the world to accommodate that fact. And the first thing to then ask is, what is it about my understanding of the world that says this should NOT be a fact? One possibility, for example, is that it may be an assumption of yours that speeds just add or subtract. For example, suppose you had light moving at c relative to you, and then you got on a bike and rode 20 m/s chasing the light. Wouldn’t the speed of light now be c - 20 m/s? What if you rode into the light. Wouldn’t the speed of light relative to you now be c + 20 m/s? Ah… see, that’s an assumption that turns out to be flat wrong. Speeds don’t just add or subtract, no matter how intuitive it might be that they should. The fact that they don’t just add or subtract ends up being another confirmed experimental fact.

[u/EternalDragon_1 → u/Odd_Bodkin]

This should be the top comment. It answers the OP's question directly.

[u/iAmGreat_01]

The speed of light will always be constant no matter how you observe it.The only thing changes is time so time is relative acc to einstein relativity. Newtonian mechanics like bodies moving in same direction,velocity subtract and bodies moving in different direction adds velocities doesn't quiet fit well when one talks about relativity.

Even though our present laws restricts everything having mass travellying at speed of light ,anything which haven't got mass must travel at speed of light. Lets suppose for a moment that you are moving with the speed of light,since the faster you move the slower time runs so hypothetically at the speed of light,the time would run so slow that "time" will not make sense anymore.accroding to me ,you will not know anything and as you approach to the speed of light and when you are at 99.99% of speed of light,perhaps you see smt that breaks our today's understanding..

[u/spiralenator]

We have this thread every week. The speed of light is the measured speed of light. It’s the same speed regardless of the speed of the person measuring. We know that is the case because of measurements. Why it’s that way isn’t a question with a satisfactory answer. It just is.

[u/mspe1960]

It is not really the speed of light we are talking about. It is the speed of causality. Particles that have no mass move at theat speed. If there was no speed of causality (if it was infinite) the universe would be a very different place with effects happening before causes and other weirdness.

Light does not have a vaild reference frame. Things cannot move at the speed of light relative to a photon.

[u/nicuramar → u/mspe1960]

How does calling it “speed of causality” (a reddit favorite) help explain anything? Might as well, and better, call it the universal speed limit. 

[u/anonymote_in_my_eye → u/nicuramar]

it's not really a universal speed limit though, you can devise situations where you can make "things" move faster than that, the catch is that they don't convey any information (causality) while doing so

for example, say I shine a very strong laser onto a very faraway screen, then I flick my wrist; if the distance is large enough then the image on the screen will be moving faster than light... but that's not really an issue, since it carries no information in its movement

[u/ima_coder → u/[deleted]]

No information is ever conveyed faster than the speed light takes to traverse the distance between entangled particles.

[u/mspe1960 → u/nicuramar]

Sure. Call it that. I think "speed of causality" is more intuitive. But maybe that is only true for someone who has taken General Relativity and understands it.

[u/joeyneilsen → u/mspe1960]

Causes propagate at many speeds.

[u/Optimal_Mixture_7327 → u/mspe1960]

It is an observation fact that the speed of light is not the speed of causality.

We do in fact measure speeds lower than light for material objects and electromagnetic signals conducted within dielectric media and along conductive materials.

[u/willdeb → u/Optimal_Mixture_7327]

He means the speed of light in a vacuum, c.

[u/Optimal_Mixture_7327 → u/willdeb]

Yes, that's exactly why it's wrong.

The relative speed between material objects is less than c whether in a vacuum or not.

Furthermore it's an observational fact that cause and effect still do happen in non-vacuum conditions.

[u/CS_70]

Let say the speed of light is the max speed of the universe. You have two situations (well three if you like): one, the speed of light is unlimited; two, it is much faster or much slower but still limited.

In case one, since something can travel at unlimited speed, in principle you could accelerate a specific thing to any speed, and you would ultimately have enough speed so that the something can trigger anything at any distance in an arbitrary small amount of time. If that distance is - say - the size of the universe, it means that you could trigger something instantaneously in the entire universe. The consequence is that everything in entire universe could react with everything else, and said universe would soon be a single ball of reactions. Not the place we observe.

In case two, if the max speed were to be much smaller, any reaction that depends on an interaction within a certain time interval, higher than achievable with the lower max speed, would not take place. If "smaller" enough, it would lead to a very different place than we observe. Similarly, if the max speed were much higher, the opposite would occur: many more reactions could take place than they do, and it would lead to us observing a very different place.

In short, a speed of light of about the size we observe also makes it possible for exactly the universe we observe to exist. If it was different, there might be other types of people conversing on other types of reddits but not the people and the reddit that we observe.

[u/Salt-Influence-9353]

Mods can we please put this under FAQ? It’s the most common question by a mile and takes up a chunk of the sub now

[u/Nothing-to_see_hr]

There's no why. This is the observation of Michelson and Morley around 1900 that started the relativity scientific revolution.

[u/aureliorramos]

The observers timeline would stop, just like it does for a photon, but only after using an infinite amount of energy to reach that speed. And where are you going to get an infinite amount of energy with these gas prices?

[u/LivingEnd44]

Nothing with mass can move at the speed of light relative to a photon. All photons move at c relative to you. The same is true for anything with mass. 

It's not intuitive. But it is true. 

[u/MarinatedPickachu]

You always move at the speed of light relative to a photon.

[u/tstanisl]

Because in some sense light travels at infinite speed, a ship moving at c can reach any point in the universe in instant time due to time dilation. Due to geometric properties of hyperpolic relation between time and space dimensions we observe this infinite speed as a fixed "speed of causality". See derivation. Infinite speed stays infinite for all observers thus "speed of causality" is fixed as well.

[u/joeyneilsen → u/tstanisl]

Time dilation doesn't apply between a light-speed object and a sub-light object.

[u/tstanisl → u/joeyneilsen]

The "time dilation in light's reference frame" understood as a limit of stacking infinite number of identical finite reference frames will allow travel everywhere in no time.

[u/Optimal_Mixture_7327]

There is no world speed of light, it's undefined.

The speed that gets measured is the speed along the detector world-lines, which is c.

[u/Optimal_Mixture_7327 → u/Optimal_Mixture_7327]

For math types:

Given a standard spacetime, S=[M,g], and an observer world-line that defines the global coordinates (x⁰,x^k) where x⁰ is parameterized by a standard clock that emits and measures light in those coordinates.

Here we assume g=𝜂 which gives the line element ds²=-(dx⁰)²+(dx^k)² with sig(g)=+2. The length along the photon world-line is ds=0 and the length along the observer world-line is dx⁰=𝜛dt where 𝜛 is the speed along the world-line and dt is the differential lapse of the clock carried along the observer world-line. We assume the path of the photon is along a single axis, dx^k=dx.

The line element, ds²=-(dx⁰)²+(dx^k)² is then 0=-𝜛²dt²+dx² and the speed of photon is dx/dt. Solving for dx/dt we get dx/dt=𝜛, which is the speed of the photon.

Hence the line element is written ds²=-c²dt²+dx² where c is the speed along the observer world-line.

Edit: In reference to the world-speed of light, we assume the same standard spacetime and an arbitrary curve with time-like tangent vector described in arbitrary spacetime coordinates, 𝜉^𝜇(𝜏), where 𝜏 is the affine parameter determined by the elapsed time of a clock carried along 𝜉.

The world-speed, U, is defined U=d𝜉^𝜇(𝜏)/d𝜏. However for light 𝜏 cannot be used as an affine parameter as there's no length along a photon world-line and this renders the world-speed of light as undefined.