Here's one simple thing about relativity and speed of light I can't wrap my head around for the life of me.
In classical physics, forces that act in the same direction, add up. If you forcefully throw an object out of the back of a moving car, its speed at the moment you throw it would be the speed of the car + the speed of the throw. Simple and intuitive enough.
But when you involve near-light speeds... So, if you're moving at 90% of the speed of light, and you have a lightbulb in your vehicle, what would be the speed of the photons coming out of it? Logically, it would be 190% of the speed of light. But apparently that's not how it works. So how the hell does it work then?!
Classical physics is based on observations that humans can make with very low technology: polished metals and glasses, relative velocities up to a few thousand meters per second, timekeeping accurate to milliseconds in one location. Those observations lead to approximations which "feel" correct because humans spend most of their lives in those circumstances.
But at the edges of those circumstances, we see discrepancies not predicted by classical physics. That lets us know that classical physics is an approximation. The truth is that even in your car + thrown object example, the velocities do not actually add linearly -- it's just that the difference between the linear approximation and the reality is tiny.
One analogy that might be helpful: consider every object in the universe to be moving at c, but for most objects that you encounter, the vast majority of that motion is forward in time rather than space. As you add energy to the object, it transfers that velocity from time-motion to space-motion. Because c is so large compared to our usual experience, we have to look really hard to discover the change in time-motion... but it's real. GPS uses satellites that are in a sufficiently different frame from the surface of the Earth, and requires sufficient time precision, that relativistic time difference calculations are required.
Reading this entire thread (I didn't expect this many replies this detailed!), I think it finally clicked with me after all these years.
So, for me, in a vehicle moving at 90% of the speed of light, the time itself slows down such that I observe the photons coming out of my lightbulb still at the speed of light, right? Basically, it would adjust the t in v=s/t because the speed and the distance are to remain constant. And because me and my spaceship or whatever have mass, there will always be a bit of difference between my speed and the speed of light to accommodate this adjustment. That's just so weirdly backwards to think about.
Now, I wonder about redshift and universe expansion deduced from it. Wavelength is a frequency, right? And frequency, by definition, is how many times something (wave period) happens per unit of time. So maybe the universe isn't expanding after all, maybe it's just that time runs faster in the parts of the universe where this light comes from, and the photons just keep oscillating with the frequency that was "correct" in whichever reference frame they were emitted? Besides, the idea that universe expands seems silly tbh. There must be a more sensible explanation. Maybe time slows down over time (?!) and it just ran faster when the universe was younger?
If "time slows down over time" then we would still observe the light at its original frequency - why would the energies of the states of hydrogen atoms in distant stars change over time, but the energies of the photons emitted long ago not change?
How does this hypothesis account for the CMB?
Wikipedia has a nice summary of alternative cosmological theories (and why they are often dismissed by experts):
> Logically, it would be 190% of the speed of light.
The important point here is that this is is not "logically" but "intuitively", and it turns out our intuition is simply wrong. Historically, this was in fact the motivation for special relativity: we noticed that the speed of light does not obey Newton's relativity principle: if you fire two beams of light, one from the ground and one from a moving train, they will both arrive at a detector at the exact same time.
Having observed this concerning fact about the world, we now had to come up with a theory that explained it. The one we landed on was that speed is a number that goes not from 0 to infinity, but from 0 to c. This then must mean that accelerating an object from 0 to 1/3c is easier (requires less force) than accelerating that same object from 1/3c to 2/3*c, and that this difficulty increases the closer you get to c. The final theory in fact predicts that an object with mass can't even reach c, it's speed can only grow infinitely close to c. However, massless particles (such as the photon) do move with speed exactly c.
Note that we have since repeated this experiment with other particles of non-0 mass and confirmed that photons themselves are not special, c is indeed a limit. For example, electrons have some mass and don't move with speed c, and an electron fired from a moving train will arrive faster than an electron fired from the platform, but the speed of the speedier electron will NOT be V_e + V_train as Newton would predict, it will be (V_e + V_train)/sqrt(1-(V_e+V_train)^2/c^2) if I remember the Lorrentz transform correctly.
The other answers here attempt to "reason" it from the currently accepted formulas, but it's not how the humanity learned that there's no "190% of the speed of light."
The author of the article we all comment here wrote a book which, if I remember, covers that story in more detail (I linked to it in another post and I highly recommend it to anybody who wants to learn a bit more than when reading an article here or there or read some comments).
Just to give you some hints, the real story is not "reasoning" something but the experiments -- the experiments practically produced the results that, when analyzed, are still the best explainable by accepting that the speed of light doesn't change. See:
Michelson is such a genius, that even the most currently advanced experiments today use the same ideas that he used then -- LIGO is also an interferometer:
Learning from these experiments, even before Einstein, some important formulas we know today as related to special relativity were already developed by others:
In my mind, it simply can't go faster because you get fastest speed already, with light.
Just consider that you have this object, light, that will always travel at the fastest speed possible. You can approach that speed. But throwing light in front of you can not increase light's speed.
I'm not sure how right this is but I was told it's to do with time dilation. If you're moving close to the speed of light, stuff that isn't is experiencing way more time than you. As light isn't affected by time dilation it's still traveling at the same speed but now has much longer to do so. So from your perspective the speed of light seems to be 190% not because it's traveling faster than C but because it's traveling more C seconds per your second when your time is dilated.
Edit: on further reading perhaps I haven't even addressed your question...
If I had to hazard a guess I would say it's to do with light having no mass. Once it's emitted it's no longer in your frame of reference so your supposed speed is irrelevant to it.
I like to think that the universe is discrete, composed of "slots", like a big multidimensional array. If you imagine that the discrete universe has some kind of transition, where the properties of a given slot can be transferred to a neighbor slot, then the speed of light is the upper limit on the rate of change. Why does this upper limit exists? We don't know, maybe we live in a simulation, maybe the universe would no be stable enough without this limit.
Maybe thinking about lightspeed as the upper speed limit helps? You could also think about the clock experiment by Hafele and Keating where two synchronised clocks where flown all over the globe and after a while they disagreed with each other.
Or the popsci answer: Things that move fast get more massiv and time gets slower for them, at the speed of light time stops. Without time no speed.
Part of your next conceptual step is realizing that the speed of the photons will measure the same to anyone, 100% of light speed.
In the vehicle, you'll measure the photons moving at 100% c.
Someone outside the vehicle as it speeds by will see the photons moving at 100% c - as you approach and as you move away. Other parts of spacetime change to accommodate this, effectively.
A hand-wavy explanation would be that photons are both particles and waves, so different rules apply.
When you create waves on a water surface with your hands, the speed in which they propagate along the surface is the same regardless of whether you just tap the water straight down, or make a sweep with your hand.
(in case you didn't know - we're talking mainly about special relativity here, which applies in situations where things are not accelerating; general relativity is a broader theorem that also accounts for acceleration and gravity, and is much more involved)
In our daily life we have a handy stationary frame of reference - the Earth; it's therefore intuitive and normal for us to think about speed in an absolute sense. In reality though, speed can only ever be measured relative to some other point, so if you're an astronaut freely floating in space, you can't make any definitive statement about your absolute speed because there is no such thing.
Another thing that we are used to experiencing is a uniform flow of time - you and I can both synchronize our watches and believe that we're reading the same time even if we're on opposite sides of the globe. This is in fact only true in a very limited set of circumstances, and generally speaking not the case. Just as there is no such thing as absolute speed (or more properly, velocity), there is also no such thing as absolute time.
Special relativity stipulates that light always travels at c in every reference frame; this is not a discovery of relativity but a prerequisite of it, and a key insight that allowed Einstein and friends to explain things that had previously been inexplicable. The explanation for this, as others have commented, comes from general relativity, and is due to the interconnection between space and time - space-time - such that every non-accelerating thing is moving at the speed of light through time (whatever that means). The speed of light is therefore not so much the speed of photons, as it is that photons move at the speed of time. Something like that I think - this is beyond the scope of my brain to explain!
So why aren't your photons moving at "190% the speed of light"? In our normal life, we think of time as fixed, and velocity as variable; in reality, the speed of light is fixed, and time is the variable. What changes for a 'stationary' observer is not the speed of the incoming photons, but some time-related factor - their frequency. This is (a simplified explanation) of redshift, that led Hubble to theorise that the Universe is expanding. Everything is moving away from us emitting light, and since the velocity of light is fixed, it's the colour that appears to change.
A note about the notion of velocities adding up - in fact they don't ever, exactly. That they appear to is an approximation due to the enormous velocities needed before you would notice any difference. This is another consequence of relativity. Likewise synchronizing clocks - we can get so close that we couldn't measure any difference, but it would be insanely impractical to set and keep totally synchronous time.
(source: physics-related undergrad some years ago - I stand to be corrected on any of the above :-)
In classical physics, forces that act in the same direction, add up. If you forcefully throw an object out of the back of a moving car, its speed at the moment you throw it would be the speed of the car + the speed of the throw. Simple and intuitive enough.
But when you involve near-light speeds... So, if you're moving at 90% of the speed of light, and you have a lightbulb in your vehicle, what would be the speed of the photons coming out of it? Logically, it would be 190% of the speed of light. But apparently that's not how it works. So how the hell does it work then?!