Light clock: floor, ceiling, light signal Case 1: when light colck is in rest, light signal propagates straight up. The time the light signal needs to pass the distance floor-ceiling-floor is t Case 2: when light colck is moving, light signal propagates obliquely, one says. The time the light signal needs to pass the distance floor-ceiling-floor is t' = tγ, where γ is the Lorentz factor.  I consider that case 2 and the following calculations are incorrect.   A light signal moves at a constant speed c and with the same  direction regardless of how the light source moves.  What causes the light signal goes obliquely in case 2?
38022
If I am standing on a platform moving along the X-axis and I throw a basketball vertically upward along the z-axis, the ball also travels along the x-axis. Does the same apply to a photon? According to a special relativity postulate  speed of light is not affected by the velocity of the inertial frame or the velocity of the emitter. If this postulate is true, shouldn't a photon fired vertically as above should travel only along the z-axis but not along the x-axis?
15651
The speed of light is the same in all inertial frames.  Does it change from a non-inertial frame to another? Can it be zero?  If it is not constant in non-inertial frames, is it still bounded from above?
14381
Let's say we have $2$ particles facing each other and each traveling (almost) at speed of light.    Let's say I'm sitting on #$1$ particle so in my point of view #$2$ particle's speed is (almost) $c+c=2c$, double light speed? Please say why I am incorrect :)    EDIT: About sitting me is just example, so in point of view of #1 particle, the second one moves at (almost) $c+c=2c$ speed?
8016
I have very little background in physics, so I apologize if this question is painfully naive.  Consider the following thought experiment: an observer is in a closed room whose walls, floor, and ceiling are made entirely of mirrors, with a single light source in the middle of the room. When the light is on, the observer can see many copies of his reflection all over the place.  Suddenly, the light source turns itself off. Intuitively, I would expect the observer to "instantly" see darkness. However, I can't figure out why that is the case under the "particle" interpretation of light. There are obviously lots of photons already in the room from before. Furthermore, we know that they don't get "consumed" when they hit a wall, because otherwise the observer wouldn't see so many reflections of himself. Basically, when the light goes off, what happens to the photons already in the room?  I suspect the answer goes something like this: the photons in the room lose a little bit of energy every time they bounce off a mirror, but it's so minuscule that we can still see more reflections than our eye can resolve anyway. When the light goes off, however, it takes them a very small fraction of a second to bounce around the room enough times to diffuse completely, which our eye cannot detect.  Is that about right? If we had a theoretical "perfect reflector", would the light remain trapped in the room forever? If we had instruments that could measure such things very finely, would it take (slightly) longer for the light to go out in a room made of mirrors as opposed to a room made of, say, black cloth?
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I understand that nothing can move faster than light due to time dilation. I want to build upon my understanding of Einstein's theory of Special Relativity, so I came up with this hypothetical problem for myself:  If both particles are moving at 0.9c towards each other (according to an observer on Earth), what speed does each particle have relative to the other?  I'm stumped since I am only familiar with Newtonian classical mechanics to solve this (which would be wrong). I am aware of Lorentz' factor $\gamma =\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ and the time dilation equation $t_m = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}}$, but I'm not sure how to apply it in this instance. I'm just looking for a gentle push in the right direction. Edit: My prior research:  This article, ,  talks about the effect of a baseball thrown at 0.9c would have as it traveled towards a batter. This is not what I'm looking for since it doesn't explain the math behind finding the collision speed between two high velocity entities.  This question on Yahoo, , asks a similar question to mine, but no math is involved to demonstrate the calculations behind the reasoning.  This question on Physics.SE, , does not answer my question either. I have not been able to find a similar Physics.SE question which can provide me to clues to my own hypothetical question.  I have also Googled the following phrases:    i. &quot;collision faster than the speed of light&quot; ii. &quot;collision of high speed particles&quot; iii. &quot;lorentz transformation in a collision&quot; iv. &quot;collision analysis at light speed&quot;
106628
I've been trying to learn about the speed of light and time dilation, but I'm at an impasse.  The presented facts say that if I travel around the solar system at 50% the speed of light and then come back to earth I will have experienced less local passage of time than them. I will effectively have traveled to their future. I've also read that gravity causes time dilation too.  I understand that space-time is a sort of unified thing and that affecting space affects time. It makes sense then that gravitational forces bending space will also bend time. But velocity? I can't wrap my head around it and I can't find a good explanation for it.  People cite orbiting craft and planes as proof of time dilation, since their clocks will go slower than those in the surface (and vice-versa). This certainly explains gravitational time-dilation, but not necessarily velocity. Can't the change in local time passage be caused solely by the gravitational bending of space-time?   Trying to find an answer, I came to a very recurring and frustrating example in texts that seek to explain time dilation. A man on a moving train throws a ball forward. Since he's moving with the train and the train is his point of reference, the ball to him only moves at the speed he threw it. But to a woman on the station the ball is moving at the speed of the train plus the speed it was thrown with. To some authors, this seems to open the mind to time-dilation understanding. To me it only explains the relative nature of motion. It says nothing of time.  Another example I've found: if person A speeds away from person B very quickly, A's clock will seem to advance slower from B's point of view. How is this time dilation, though? The difference can be explained by the longer time it takes light to get to B, can't it?  I realize I can't be right against the fine physicists out there, so I was hoping someone here could enlighten me. Where does the notion that velocity causes time-dilation come from?
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.
23783
This is my first time posting here, I am a school student who is just curious. So today I was wondering about how light works and how it travels, and this thought came to my mind:  Light is made of photons traveling in transversal waves, doesn't this mean that photons are moving in longer distances than light itself because photons don't move in a straight line, while taking the same time that light does to reach the same position, so does this mean that the speed of photons is actually greater than the speed of light?
42056
On a systems level, I understand that as electrons are pushed into a wire, there is a net field and a net electron velocity.  And I've read that the net electron drift is slow.  But electricity travels through the wire, essentially at c, and I want to understand that mechanism.  My apologies if my question is poorly stated, I know bare bones undergraduate quantum theory circa 1990s but it doesn't explain the motion of electricity in detail.  Here's my conception, I'm hoping someone will fill in the holes, ha ha.  An electron moves into the wire.  It's got a kinetic energy.  After travelling a short distance, it spontaneously emits a photon, which hits another electron in a valence shell.  That electron then presumably does the same.  If this conception is simply wrong, please enlighten me.  The questions that arise:   Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way? If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be?  I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible? Why should a photon emitted by an electron be in the direction of travel?  Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction?  If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling. What is the mechanism by which electrons propagating increase the temperature of the material?  Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way?  Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon.  By how much is this slower than light, and what is the speed of each interaction?
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?
83328
From this ,     Let’s say Alice is holding a light clock, and Bob is watching her run by, while holding it, with speed V.  Alice is standing still (according to Alice), and the time,$ \tau$, between ticks is easy to figure out: it’s just $\tau = \frac{d}{C}$.  From Bob’s perspective the photon in the clock doesn’t just travel up and down, it must also travel sideways, to keep up with Alice. The additional sideways motion means that the photon has to cover a greater distance, and since it travels at a fixed speed (EEP y’all!) it must take more time   My question is, why does photon need to travel sideways to hit the Alice light clock?
24386
This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows.    Rest frames are easy to understand. They are just for clarification. Lets move on to the moving frames. The velocity of the box is $0.1\ c$. Now a photon is emitted (I am not taking a light ray to avoid complication in discussion). After emission the box also moves a certain distance ahead. So the photon takes more than one second to reach the wall. But even the source moves that much distance ahead. When the light is reflected back, the source and the wall again move forward as the box is moving. But after reflection the wall has no role to play. We are concerned about the source. The source moves a certain distance ahead and therefore light takes less than one second to reach back. But the difference of the first case and the second case is not the same. To explain, I will give some equations.  Moving frame 1:  Velocity of the box: $0.1\ c = 30,000km/s$  Time taken by light to reach the wall $=\frac{330,000\ \text{km}}{300,000\ \text{kms}^{-1}}= 1.1s$  Distance moved ahead by the box from original position: $30,000\ \text{km}$  Moving frame 2:  distance moved ahead by the box from original position  $&gt;30,000\ \text{km}$ as the box also moves ahead after reflection.  let $d$ be the distance moved ahead by the box after reflection.  Time taken by light to reach the source: $\frac{270,000\ \text{km}\ -\ d}{300,000\ \text{kms}^{-1}} &lt;0.9s$  Therefore we see that this could possibly determine the absolute motion.  So in total we see that the light will take lesser time to reach the source. Please correct me if I am wrong and give your opinion why is it so.  EDIT 2 for clarification  The box is the compartment in space in which you are moving and I am calculating the time the light takes to reach back the source. I am not even adding velocities. Please correct me and tell me where did I add velocities. For clarification just let me give a simple example. Suppose person A is standing still and B is running towards a light source. Obviously he will see the light before person A even though the speed would be the same. So, what I am doing over here is not increasing the speed of light, but instead decreasing the distance to be covered by it.
49243
I am reading a new popular science book where a thought experiment proposed by Albert Einstein is explained.  It is a thought experiment with a light clock. The light clock is emitting light straight into a mirror, the mirror reflects the light and when the light makes the round trip clock-mirror-clock this registers the passage of a certain amount of time, e.g. 1 millionth of a second.  In the first part of the experiment the clock is standing in a train which is not moving so the clock and the mirror are still. As seen in the first picture (below).    In the second part of the thought experiment the train is moving and the book suggests that the light travels a longer distance because the train is moving and therefore it kind of travels on a diagonal as presented in the second picture (below).    Now I disagree with this suggestion. I see no reason for the light to change trajectory or travel a longer distance. I argue that even when the train is moving the first picture still holds true.   There is also one more thing that it seems to me is wrong with that picture. There is no mirror against the clock at t0, no clock against the mirror at t1 and again no mirror against the clock at t2. This placement of the clock and mirror in time is crucial because it results in the longer diagonal path of the light but the clock and the mirror are moving at the same time! So the only illustration that makes sense is one where the clock is always against the mirror.  In the experiment it is said that light travels a longer trajectory with reference to an observer outside of the train standing still beside the railway.  I think that the train travels with reference to the still observer but the light travels with reference to the train. So I argue that regardless of whether the train is moving or not the light travels the same distance for the same time.  After all when it comes to measuring distances the reference is central.  More food for thought: It could just as well be a ping pong (table tennis) ball clock. If you are playing table tennis on a train the ball travels directly along the length of the table while the train is moving, would you suggest that the ball is traveling on a diagonal trajectory? I think not.  Please share all your arguments.
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.
95275
This is a summary from Physics World of the paper: L J Wang et al. 2000 Nature 406 277-- "Wang and colleagues begin by using a third continuous-wave laser to confirm that there are two peaks in the gain spectrum and that the refractive index does indeed change rapidly with wavelength in between. Next they send a 3.7-microsecond long laser pulse into the caesium cell, which is 6 centimetres long, and show that, at the correct wavelength, it emerges from the cell 62 nanoseconds sooner than would be expected if it had travelled at the speed of light. 62 nanoseconds might not sound like much, but since it should only take 0.2 nanoseconds for the pulse to pass through the cell, this means that the pulse has been travelling at 310 times the speed of light. Moreover, unlike previous superluminal experiments, the input and output pulse shapes are essentially the same."   I realise that the velocity of light in a medium is comprised of the phase velocity, the group velocity, and the front velocity. While the group velocity can exceed the value of c in a vacuum, the front velocity is not supposed to. The way this sounds, the front velocity is exceeding c in a vacuum by 310 times.    blue dot=phase velocity, green=group, red=front (wiki)  The wavepacket seems to exit the cell well before it enters, but the negative refractive index "forward shifts" the leading edge of the pulse. It is argued that although this is superluminal, information cannot be transmitted faster than c.  introduced a jump discontinuity into the waveform.Its max speed was c Here is a popular account from  . What if you used one photon? What if the photon itself were the information and not a carrier?
2102
So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to lowering its energy.  My question is, where does the energy of the light go? Energy must go somewhere!   Does the energy the light had before go into the mechanism that's expanding the space? I'm imagining that light is being stretched out when its being red-shifted. So would this mean that the energy is still there and that it is just spread out over more space?
29313
I have just started special theory of relativity. The limiting speed known as speed of light fascinated me most. I asked my teacher:      Consider two massless objects moving in the same direction at the speed of light. What would be their relative velocity w.r.t each other?   My teacher tells me that their relative velocity would be zero. But then the speed of light is universal constant regardless of the motion of its frame of reference, so shouldn't their relative velocity be $c$? What is their relative velocity and how? Do objects moving at the speed of light obey law of addition of velocities?