We know that the speed of light is a constant, and can therefore be used to calculate many other relative values, but I'm having difficulty understanding how speed can be a constant, seeing as it's dependent on other variables.  For example, take a universe in which there is nothing other than Earth and the Sun. No other stars, galaxies, planets. In this example, when a rocket leaves Earth and heads towards the Sun, its speed is measurable, according to its varying distance from the Earth and the Sun.  Now delete the Sun from the image. The rocket hasn't changed; it's still heading away from the Earth at the same speed. But what if the Earth itself now starts moving? Now the distance is still changing, but how the individual speeds be calculated?  Now delete the Earth, and we have only a moving rocket in the entire universe. How can its speed be calculated? How do we even know it's still moving? Does the concept of 'speed' still exist?  My question is: If speed is not an entity in itself, but only dependent on other constant factors, how can the speed of anything (let alone light) be a constant? Am I completely missing something here?  Excuse the lack of scientific terms; I'm not a scientist; rather a software developer with an interest in relativity and quantum physics.  Edit: The question is not "Is it possible to have a constant of speed?", in which case it would be possible to answer with, "Yes, and the proof is that there is a constant of speed, here's how to prove it...", which is what most of the answers seem to be doing.  The question is rather "How can there be a constant of speed?" - emphasis on the 'constant' - in which case saying "Here's the proof that there is one" is not an answer. I know there is one, otherwise I wouldn't be asking the question...
103439
I've often heard that Einstein shattered the notion of absolute motion (i.e. all things move relative to one another) and that he established the speed of light as being absolute. That sounds paradoxical to me; I cannot understand how the two concepts can be reconciled.  Before going further, I'd like to say: 1) Over the years, I've seen many layman's explanations on these topics (including the nice YouTube video by Vsauce, ). I understand everything that's said (or, at least, I think I do). Just nothing I've found seems to address this apparent contradiction. 2) More recently, I've tried to find the answer on my own. That includes searching the posts on this site. Some come close (), but nothing I've been able to find seems address specifically what I'm asking.  Back to the question: Relativity shows us that there is no universal frame of reference by which to judge motion, so object A might be reckoned as moving at 10&nbsp;m/s relative to object B or as stationary relative to object C. This is fine for me. I can grasp that the universe has no intrinsic coordinate system, that we only think that way on Earth because we have the ground to move over.  Then there's the speed of light (in a vacuum). The speed of light is the ultimate "speed limit," it's often said. But if there is no universal frame of reference, how can there be any such speed? The very idea only make sense if there is a universal frame.   If one object is moving (uniformly) at 60%&nbsp;c and another object is also moving at 60%&nbsp;c, but in the exact opposite direct, then from the perspective of either one (if they could still see each other) the other would appear to violate that speed limit. All these spacetime bending consequences used to explain why nothing can move past this speed only seems to enshrine the concept that there is some ultimate speed standard. If there is only relative speed, then the concept of light having a specific speed in the vacuum should be a nonsensical one since it having speed (x m/s) would only make sense when measured against some other body.   Since I was very young, it has always sounded to me like motion is only mostly relative, that until you get close to the speed of light, the effects of an absolute frame of reference are negligible. Perhaps that there is an actual fabric of space which everything moves relative to, which is why there is something to expand between galaxies (faster than light can propagate) in the metric expansion of space. Growing up, I always thought this would just start makes sense with time. Now I'm up to a first year (college) level in physics, I even know basic calculus, yet I'm still hopelessly confused.  EDIT:  Thank you to whoever suggested this may be a duplicate of . It and others are very much related and at least partially answer my question. Unfortunately, explaining that distances become shorter and time becomes slower as a way to stop you from exceeding the speed of light does not explain how that speed is not an absolute.  By my reckoning, if all speed is relative, then no matter how fast you go light should always race away from you at the same apparent speed. I.e. there should be no speed limit. For there to be a speed which you cannot exceed or you would catch up (and make time irrelevant) requires the very concept of some external speed by which light can travel and nothing else can reach - thus my logical paradox continues unabated.
51053
Why does light have the speed it does? why is it not considerably faster or slower than it is?  I can't imagine science, being what it is, not pursuing a rational scientific explanation for the speed of light.  Just saying "it is what it is" or being satisfied saying it is 1 ($c=1$), does not sound like science.
42198
Is it possible to have an alternative theory which is consistent with experiments supporting GR, but which doesn't mandate a speed limit on causality?  In other words, I understand there is experimental evidence for gravitational/relativistic time dilation, spacetime curvature, etc. but is there any inherent reason why these effects cannot be explained without the max speed requirement?  QM clearly shows that "communication" can happen instantaneously but, supposedly, causality cannot break the speed limit.  I also know the speed of light is derived from other principles, but is there anything that says that speed has to be a max limit of any kind?  I want to emphasize that the QM "communication" doesn't imply causation or information exchange, merely the establishment of the entangled attribute.  Bell's inequality tells us that the attributes were not predetermined and were only established upon measuring one of the particles.
53302
The observed paths and speeds of objects, part of some distant galaxy, do not match up with speed vs distance curves it seems - the observed speeds are not falling off in fact they're trending as increasing or constant with distance. Wikipedia explains the phenomenon far better -   Dark matter is one explanation but it isn't without it's faults and flaws, at times raising more questions than being helpful. Particularly when trying to answer what dark matter might be composed of, and that the theory needs fine-tuning for any such model to match observations; from a lay-person's POV the idea is nice but seems to involve some handwaving regarding fine-tuning or composition (specifically what the secondary effects might be, as they may differ between candidate compositions).  With that in mind it occurred to me that galaxies are very large, and rotating. I don't have a clear picture of scale in mind when it comes to this... However it does seem like one (or both) of these two effects may be contributing:   Ehrenfest Paradox - I'm not certain it is applicable, but it is remarkable that there are features in common between a galaxy and a relativistically-rotating disk, the latter being the subject of a paradox regarding geometry. Gravitational time dilation - because of the size and mass distribution of a galaxy, to an observer outside the galaxy, the center would gain time slower than the arms / edges; effectively the edges of a galaxy would appear to move faster than they should, when using inner orbital speeds (in a higher gravitational potential) as a reference.   To help understand why I suspect these effects, it is worth noting the sheer breadth of a galaxy, that it has to be measured in kpc (kiloparsecs)... It can take many 1000's of years for light from one side of a galaxy to reach the other (enough time for cumulative time dilation to become a noteworthy factor I would think), suggesting that a galaxy's internal dynamics may be taken for granted in explaining the observed orbital speeds.  In other words it may be the case that locally (in the remote galaxy), these excessive orbital speeds may not be excessive after all.  Which, if any of these effects, are or could be contributing to the discrepancy in expected orbital speeds of objects in a remote galaxy as observed here?
19773
What's the cleanest/quickest way to go between Einstein's postulates [] of   Relativity: Physical laws are the same in all inertial reference frames. Constant speed of light:  "... light is always propagated in empty space with a definite speed $c$ which is independent of the state of motion of the emitting body."   to Minkowski's idea [] that space and time are united into a 4D spacetime with the indefinite metric  $ds^2 = \vec{dx}^2 - c^2 dt^2$.  Related to the question of what is the best derivation of the correspondence are: Is the correspondence 1:1? (Does the correspondence go both ways?) and are there any hidden/extra assumptions?    Edit  Marek's answer is really good (I suggest you read it and its references now!), but not quite what I was thinking of.   I'm looking for an answer (or a reference) that shows the correspondence using only/mainly simple algebra and geometry. An argument that a smart high school graduate would be able to understand.
68035
Assume we have a ball with diameter 1 meter and mass 1 kg rotating at 99,5% speed of light (Suppose I'm an observer placed above the ball, I see under me a disk wich external  speed is 99,5% the speed of light)  Then we accelerate such ball to 99.5% of speed of light, to make clear from wich position we look at the ball when it's moving so fast I did a picture (there's a black ring around the ball, as you se the rotational axis is vertical to our observer)    I'm interested in a full explanation of what we observe (measured rotation speed, color etc.) and why that happens, as far as I know we should not measure something moving faster than light but I'm not sure how relativity constraints would alter the "measured state" of the ball as long as we accelerate it.  What we see change while the ball accelerates?  EDIT:  A precisation, I assume the ball is spherical when I start rotating it before even moving, this is because commenters made me to note that shape may change.
39453
I don't understand how time can be relative to different observers, and I think my confusion is around how I understand what time is.  I have always been told (and thought) that time is basically a measurement we use to keep track of long it has been since an objects inception.  If that is even somewhat true, how can time be relative? If I have a rate of decay of X and you are somehow able to observe that (such as watching me age) how could I age at a different rate to 2 observers?  If time slows down the faster you go, does that mean you age slower? Or do you age at the same rate, only it seems like it takes longer? If a second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0K, how can that change at higher speeds? Assuming the temperature stays the same, shouldn't the measurement be the same?  Moving faster surely can't cause cells to decay slower, or atoms to radiate slower...can it?  Can someone explain, in the simplest of terms, how time can be relative?
26676
When a spaceship is experiencing a constant acceleration of $10m/s^2$, the astronauts will be moving at nearly the speed of light after about a year in the earth's reference frame. This means the spaceship's energy will start to diverge as a function of the speed $v$ so there will be a huge amount of energy necessary to increase the speed of the ship any further. This way, the speed of light can never be crossed.  All of this is clear to me, but all of this is also formulated in earth's reference frame. But from the astronaut's reference frame: the spaceship is simply accelerating at $10m/s^2$ and so the force on the spaceship is constant. Then why would we need huge amounts of energy to accelerate the spaceship?  For example, I read somewhere that the amount of energy that would be needed to accelerate a large spaceship to half the speed of light is more than 2000 times the current world annual energy consumption. How does this make sense in the astronaut's (non-inertial) frame?
97121
We all know that speed of gravitational waves (GW) and that of light in space are exactly the same (= $c$).  We also know that space is medium for GW.   Does that mean space is also the medium for light?  Because both of them are waves, and speed of a wave is property of the medium.   Is there any other way to justify the identical speed of the two?
59587
I have found these two formulas:  $v = at + v_0$  $x = \frac{1}{2}at^2 + v_0t + x_0$   a is the acceleration v is the velocity x is the position t is the time $v_0$ is the initial velocity $x_0$ is the initial position   The problem is that with an acceleration of $10$ m.s$^{-2}$ (for example) the object would surpass the speed of light in $3 \times 10^7$ s = $11$ months and $11$ days, which should not be possible.  Is there some other formula that gives the position of an object depending on its acceleration and on the time, but which works and does not allow the speed of the object to surpass the speed of light?
68184
I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor.  My question is, if something travels in a circle, close to the speed of light, what does the distance of the journey look like to them? They measure that the trip took them 10 minutes. And an outside observer says that the journey took 20 minutes, and the outside observer measured that they did, for example, 1000 laps of a circle circumference 1000 km.  So if the plane had a distance trip counter, what would it read? And if they were looking out of the window, would the circle still look like it had a circumference of 1000km?
2714
Some people say that mass increases with speed, some people say that the mass of an object is independent of its speed.  I understand how some (though not many) things in physics are a matter of interpretation based on one's definitions. But I can't get my head around how both can be 'true' is any sense of the word.  Either mass increases or it doesn't, right?  Can't we just measure it, and find out which 'interpretation' is right? e.g.: (in some sophisticated way) heat up some particles in a box and measure their weight?  ------------------------------  UPDATE  Right, so I've got two identical containers, each with identical amounts of water, each on identical weighing scales, and each in the same g field. If one container has hotter water, will the reading on its scale be larger than the other? If the answer is yes, and g is constant, does this mean that the m in w=mg has got bigger?
66028
This is a question that has been gnawing on me for many years now. Back a long time ago, as I recall in reference to a scene in a popular science show on TV, I was asked the following.  The claim is that when you look out into the universe, you see the universe as it appeared at some past time. (This follows from the speed of light being finite, and looking at objects by observing their emitted light or other EM radiation.) The amount of time that one looks backwards is equal to the distance to the observed object in light-distance (so looking at something ten lightyears away means you are observing it as it was ten years ago).  Matter moves at a rate of speed less than the speed of light (it has to, since matter has mass, even if miniscule at the atomic level). So $v_{mass} \lt v_{EM}$ (probably significantly less, since $v_{EM} = c$).  So let's say you're looking at an object $10^{10}$ lightyears away by observing something for which $v=c$. To the observer, that object appears as it was $10^{10}$ years ago. But the Earth is much younger than $10^{10}$ years and we established that matter moves at a slower speed than EM radiation, so wouldn't the radiation that was emitted $10^{10}$ years ago long since have passed Earth's current position?  If, say, $v_{mass} = 0.5 \times c$ (a big assumption, but bear with me for a second), it would seem that the radiation emitted $10^{10}$ years ago would have passed Earth's current position $10^{10} - (0.5 \times 10^{10}) = 5 \times 10^{9}$ years ago, around the time when the solar system was still forming. Setting $v_{mass} = 0.25 \times c$ (which seems more realistic) means the radiation would have passed "us" around $7.5 \times 10^{9}$ years ago. So how could we be observing it now?  I'm not sure I'm posing this question in the best possible way (I'll admit I do find the concept somewhat confusing), and I'm sure that there's a simple explanation for it all. Just what am I missing?  I did find  which seems peripherally related but not quite the same thing. Qmechanic brought up  but that question seems to be about whether it is so, not why it is so.
74060
I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can be empirically found, and, when plugged into the expression, yield the empirically found speed of light)  I'm really not sure how I would go about finding $v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ simply from Maxwell's equations in the following form, in SI units --  $$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon_0}$$  $$\nabla \cdot \mathbf{B} = 0$$  $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$  $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)$$  Is what I believe true? (that the speed of propagation is derivable from Maxwell's Equations)  If not, what else is needed?  If so, can you provide a clear and cogent derivation?
99658
I remember the first time I saw this formula, $F = ma$, and it seemed perfectly correct and natural to me (in the sense that it is very straight-forward and logical, not that it is easy by any means). But then, I wondered, what if an object is moving with a constant speed? Maybe a car. If it travels with constant speed and hits me, it still hurts. So it's force must not be $0$.  One more thing related to this problem. If the same car is pulling another car behind it, if the car goes with constant speed, it implies that the first car doesn't exert any force to the second car at that moment, since it is not technically pulling it anymore (espacially if we don't take into consideration the friction).  So my question would be the following: How do these two phenomenons describe the same law of motion?   PS: If gravity wasn't behaving as some kind of acceleration pulling me constantly to the Earth's core, then if I jumped upwards, would I start slowly getting away from Earth?
5561
I was told that the Galilean relative velocity rule does not apply to the speed of light. No matter how fast two objects are moving, the speed of light will remain same for both of them.   How and why is this possible?   Also, why can't anything travel faster than light?
37590
Greatings!  I'm trying to understand special relativity and have one question bugging me.  In almost every book or video about the subject there is a thought experiment with moving light clock. I hope I need not elaborate on the sutup and the outcome of the experiment.  So the question is this: When a light source on the MOVING light clock emits a photon of light the path of the photon is triangular.   How this can be?   I thought since light speed is constant in every reference frame the movment of the "emmiter" can't affect the movment of the light so light should shoot right up (from the point of stationary observer) and thus move backward and up from the point of moving observer.  So you see my logic is: light speed is invariant => you can't make it move UP &amp; FORWARD only UP. i.e. you can't change it's direction once it's emited in UP direction. Why the hell light moves sideways then?  And I'm puzzeled. There is flaw in the logic but I don't see it.  Thanks for help.