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;
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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?
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This might have some duplicated inquiry that   had, and while I think I have some of  about it, I would like to ask the community here for more opinions.  So referring to  or , one might still beg the question: Why is the speed of light 299792458 m/s? Don't just say "because it's defined that way by definition of the metre." Before it was defined, it was measured against the then-current definition of the metre. Why is $c$ in the ballpark of $10^8$ m/s and not in the order of $10^4$ or $10^{12}$ m/s?  A similar questions can be asked of $G$ and $\hbar$ and $\epsilon_0$.  To clarify a little regarding $c$: I recognize that the reason that $c\approx10^9$ m/s is that a meter is, by no accident of history, about as big as we are and a second represents a measure of how fast we think (i.e. we don't notice the flashes of black between frames of a movie and we can get pretty bored in a minute).  So light appears pretty fast to us because it moves about $10^9$ lengths about as big as us in the time it takes to think a thought.  So the reason that $c\approx10^9$ m/s is that there are about $10^{35}$ Planck lengths across a being like us ($10^{25}$ Planck lengths across an atom $10^5$ atoms across a biological cell and $10^5$ biological cells across a being like us). Why? And there are about $10^{44}$ Planck times in the time it takes us to think something. Why?  Answer those two questions, and I think we have an answer for why $c\approx 10^9$ in anthropometric units.  The other two questions referred do not address this question.  gets closest to the issue (regarding $c$), but he does not answer it. I think in the previous EDIT and in the comments, I made it (the question) pretty clear. I was not asking so much about the exact values which can be attributed to historical accident. But there's a reason that $c \approx 10^9$ m/s, not $10^4$ or $10^{12}$.  Reworded, I suppose the question could be "Why are the anthropometric units (which are about as big as we are) as large as they are relative to their corresponding Planck units?" (which is asking a question about dimensionless values). If we answer those questions, we have an answer for not just why $c$ is what it is, but also why $\hbar$ or $G$ are what they are.
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I have seen the classical twin paradox before. It uses a twin stationary on Earth and the other traveling away and back. I have seen many contradictory solutions for it, some use general relativity, others use special relativity, either way, I am still troubled by it. They always try to break the symmetry through the traveling twin's acceleration and deceleration, but never quite succeed.  So, let's do away with the classical twin paradox and let's explain a much simpler, perfectly symmetrical version of it where both twins are moving towards each other.  So imagine we have Twin A in a spaceship, and Twin B in another, a light year apart from each other at the beginning of the experiment. They both start traveling at the same speed towards each other when the first light of one twin since the beginning of the experiment reaches the other, so they effectively start moving one year into the experiment.  If I understand relativity properly:   From Twin A's frame of reference, he's stationary and Twin B is moving at a constant speed towards him, therefore, because of time dilation, Twin B's clock is ticking slower. From Twin B's frame of reference, he's stationary and Twin A is moving at a constant speed towards him, therefore, because of time dilation, Twin A's clock is ticking slower.   Regardless of what their observations might be because of the Kepler effect and what not, time dilation dictates that a moving clock will absolutely tick slower than a stationary one. So, because Twin B is moving relative to Twin A, Twin B's clock is absolutely ticking slower than Twin A's. The same is supposed to be true the other way around. This is obviously a contradiction.
51414
Many texts about STR time dilation use as an example thought experiment with  The conclusion of this experiment is: In a frame moving relative to the clock, they will appear to be running more slowly. As I understand it, this is just a visual effect, it doesn't mean that processes in the system with clocks are affected by someone observing it from moving frame. I can't imagine any other interpretation of this, cause this would result in all sorts of paradoxes, like what if there are 3 clocks oriented: parallel, perpendicular and at 45 degree relative to direction of moving frame. If you visualise light path from moving frame perspective like it is done in wiki link above, and do analogical interpretation, this would imply that some of the 3 clocks in same frame are running slower and some are faster, depending on orientation.   According to the same wiki page this time dilations are not just visual effect and do change behavior of objects, here is a quote from 2nd paragraph:     Such time dilation has been repeatedly demonstrated, for instance by small disparities in a pair of atomic clocks after one of them is sent on a space trip, or by clocks on the Space Shuttle running slightly slower than reference clocks on Earth, or clocks on GPS and Galileo satellites running slightly faster.   So if we continue our analogy, we can take 4 pairs of atomic clocks, and send 3 of them on a space trip oriented differently, we would get different time results on them.  We can even continue this absurd, and remind "twins paradox", and conclude that the one that was perpendicular to moving frame would become older....
42673
As I understand it Newton's Laws imply that space is relative, as the laws of physics are the same in all inertial frames and as such there is no way, even in principle, to distinguish a frame that is truly at rest (absolute space). Hence the concept is physically meaningless, and the positions of (and distances between) physical objects, events, etc. are relative to the frame in which one is observing them from. Advancing on to Special Relativity, by postulating that the speed of light (in vacuum) is constant in all frames of reference, we are forced to conclude that time is relative also (as if it weren't then different observers would observe a different speed of light (in vacuum)). This leads to the result that the concepts of space and time are no longer completely separate and independent of one another and instead intertwined (as an event that occurs at rest over some time period in one frame, will occur over some spatial interval and a different time interval in another frame). Hence they should be considered as should be considered as a single entity, called spacetime.  Sorry for the waffling so far, just want to check that my understanding is correct up to this point?!  My main question is, given that space and time are (individually) relative quantities, is spacetime itself relative, or can it be considered absolute (as after all, it is the mathematical space of all possible events and exists independently of the physical events that occur within it)?
105833
I recently watched  by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assumption in his famous 1905 paper where he assumes that the speed of light is same in all directions. This made me ask this question is taking the speed of light same in all directions an axiom of some sort? As I've often read no information can be sent at more than the speed of light but here one-way taking the speed to infinite makes no difference. So are all of our physics theories based on the assumption and what would happen if light turns out to be moving at different speeds in different direction? Will that enable transfer of information faster than the speed of light and is there any way for us knowing that the transfer happens faster than the speed of light? The video takes a Earth Mars case where he says it isn't possible for us to every realize this discrepancy but is there a more general proof which says it isn't possible
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My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.  My motivation for asking this question is thinking about Special Theory of Relativity. One way of understanding why time dilation and length contraction happen is to look at it from the perspective of constancy of speed of light. Alice who is on the moving source of light and Bob, a fixed observer see the speed of light as constant. In order for Alice to see the speed of light as a constant value, time slows down and length expands (in forward direction) thus keeping the speed constant.   In the  I'm doing, the Professor tells that this constancy of speed of light could be more generally referred to as, "Principle of wave constancy". That is, the speed of any wave is a property of the medium (and thus it remains constant). So, the speed of a wave in water, for example, remains constant even if the source of the waves (say a paddle keeps moving). Frequency and wavelength may change but the speed remains constant. In a similar fashion, light is an electromagnetic wave and thus its speed is constant. And the constant speed is defined by the medium (which happens to be vaccum i.e., no medium for light).   My questions are twofold now -    Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general) Theoretically, could there be other waves that could travel through vaccum at a different speed? If yes, time dilation and length contraction will have to be different.   I'd appreciate it if the answer is kept non-technical (essential math is okay). More importantly, I request you to try and explain without using General Theory of Relativity. Because I'm thinking how the scientific understanding by 1905 had already knew that speed of light has to be constant.
50612
So, I'm traveling to another star 100 light years away in my spaceship. This ship has a solar sail pushed by a laser beamed from my home star system, so can achieve a velocity close to c. It's also got a robust parachute to slow down with.  I understand that if I measure light coming from my origin star, it will always still seem to be streaming past me at light speed (but will red shift as my speed increases). Light coming from my destination star also travels past me at light speed, and will become increasingly blue shifted as I gain speed.  I also understand that an observer checking on my speed at my origin or destination will always find it to be less than c.  However, will I perceive that in terms of the time it apparently takes me to reach my destination, my speed was greater than c? In other words, will it seem to take less than 100 years to reach the destination? 10 years on my watch, say. Or 1 year. Or a week?  Ie, as far as I'm concerned, while light keeps zipping past me at light speed, do I continue to accelerate unabated to an arbitrary apparent speed?  If not, how do I notice my continued acceleration being prevented?
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As a lowly physics undergrad who has been chewing on this 2nd postulate of special relativity for a year or more, I simply can't wrap my head around reasons why it is true or how Einstein might have been convinced enough to propose this postulate.  Consider Alfred who is riding in a car travelling at 88 m/s with his headlights on and Bernard who is on the side of the road hitch hiking. Why does the light propagating from Alfred's car move at $c$ relative to both Alfred and Bernard, and not at $c$ + 88 m/s relative to Bernard?   The nifty results of special relativity all kind of hinge on this idea, and asking my professors in class hasnt really yielded an answer much more than "because we have never observed a case otherwise".
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I don't fully understand what would happen if we could travel at the speed of light. But I saw somewhere here that it would mean events happen out of order. But why is this a problem. It is said that cause has to happen before the effect, but why does this have to be linear?   And why is it that the speed of light is the maximum? I take it that light (photons?) are massless, so why can't they travel faster?
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I just want to first say that I'm aware I am asking a question due to my own confusion and ignorance and not because of anything to do with special relativity. I hope that's alright.   What I'm confused about is whether two beams of light moving in opposite directions away from eachother, have a relative speed of $c$, or $2c$.   The thing is, we can always say it's $c$, but then when we look at the relative distance travelled for the time elapsed, the result is $2c$.   Can anyone explain what is going on?   Response to Alfred Centauri 22/08/2016   I question your reasoning for two reasons. Firstly to photons moving in opposite directions was one of Einstein's examples of the counter-intuitive implications. So what you're saying wasn't around then, and Einstein himself was misconceived. In fact you can find instances opposite direction light beam as recently as 10 years ago. Phillip Green in his popular science book uses that very example in his introduction. So the question is whether this is a formal adjustment to SR, backed by a publication and a reasonable consensus. Is it?   The second reason is to do with your reasoning. You say it is not a legitimate measurement because there is no inertial frame in which one or the other photon is at rest.  That at-rest criteria as you define the constraints, is equally applicable to two beams coming toward eachother. In fact almost every problem setup has no way to assume that one of the two frames is stationary. The way it's handled, I believe, is mathematically by the simple addition of the equal and opposite motion. This is also implicit in the Laplace transforms, I think.  The reason this can be done, I think, is because all inertial frames are assumed to be equilvant....they are part of a global reference frame.   A further matter derives from the fact the relative motion of two frames can be represented as tangential and radial components. If what you are saying is correct, then one of the two components cannot be measured in almost all cases.   I definitely want to make clear I am a novice in the theory, and you probably are not. It's possible this is all misconception, except for the historic part of my response which can easily be confirmed. Please do let me know if you can as I am trying to learn and need my mistakes corrected, especially the long running ones.
2041
I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the universal speed limit.    So, if I were to travel in a spacecraft at (practically) the speed of light, would I freeze and stop moving?  Would the universe around me freeze and stop moving?  Who would the time stop for?
93624
How do you prove that the time for two objects traveling towards each other at relativistic velocities is still d/(v1+v2).  Answer seems to have something to do with velocity addition but I'm stumped...
11392
I cannot for the life of me figure out what I am doing wrong with this problem:  If a high speed particle travels a distance of 39 Km with a half life of 1 micro sec, what must its speed be to travel said distance? I keep getting Erroneous calculations.  $$\Delta t' = \Delta t\gamma = \frac{\Delta x}{v}\gamma$$  therefore, the speed observed by the neutrino or whatever is  $$\begin{gather}\Delta t' = 1 \times 10^{-6} s = \frac{39 \times 10^3 m}{v\sqrt{1 -\frac{v^2}{c^2}}}\\  \sqrt{v^2 - \frac{v^4}{c^2}} =39\times 10^9 \frac{m}{s}\\ - c^{-2} v^4 + v^2 - (39)^2\times 10^{18} = 0\end{gather}$$  So I solve this quartic equation and I get really strange results  $$v^2 = -\frac{1}{2} \pm \frac{\sqrt{1 - 4c^{-2}\times(39)^2\times 10^{18}}}{2}$$  Which always yields imaginary values for $v$. what did I do wrong? Should my $\Delta x$ be negative? I don't see why it would matter since I can define positive in any direction.  Below the problem is stated in its entirety: "The particle is unstable. It decays into other particles with a half-life of only t = 1 microseconds. That means that, even if it were travelling at the speed of light, it would only be able to travel 300 meters  before disappearing. However," continues Professor Smith, "we find plenty of these Bluto particles at the ground level. We believe that they are created in the upper atmosphere at an altitude of H = 39 km above the ground. How in the world can they reach the ground before decaying?"  "Ah", answers Professor Jones, "have you taken into account the time dilation factor? If the Bluto particles are created with a high enough initial speed, they could reach the ground during their brief lifetime."  How fast must the particles be moving to reach the ground? Express your answer as a fraction of the speed of light. You must be correct to the sixth digit in order to be marked correct.
112034
Speed of light may be obtained by inspecting the wave equation derived from Maxwell's equations making Lorentz transformation and special relativity necessary to mediate.  My questions are:  a) Without assuming that $\mu_0$ and $\epsilon_0$ are constant, do we have any theoretical proof that speed of light is constant?  b) Do we have any experiment in high speed condition that proves the constancy of $\mu_0$ and $\epsilon_0$?  c) Do the values of the constants depend on properties of the vacuum or frame (e.g. velocity)?
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This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to $c$ and not something else, but why there is a limit at all. EDIT: Answers like &quot;if it was not..&quot; and answers explaining the consequences of having or not having a speed limit are not--in my opinion-- giving an answer to whether there is a more fundamental way to derive it from a law to explain this limit.
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Time dilation  using Schwarzschild metric for a non rotating spherical body is: $$t_0=t_f\sqrt{1-\frac{2GM}{rc^2}}$$  For such a non rotating spherical body, what would the time dilation of a clock in vacuum free-falling from infinity be?  (If the answer is non-trivial; a high level outline of the calculation would suffice / be appreciated)  Edit: I am currently working on an iOS app that is trying to model the mechanism underpinning relativity.  So, far the mechanism that I have created is shockingly simple and shockingly good at conforming to Relativity.  However, I am trying to break it.  I am trying to find any possible areas where the two may diverge.  I have noted that using my model a clock in freefall will experience no time dilation, i.e. $t_0=t_f$ and I want to make sure Relativity agrees.  I have noted the gravitational component of time dilation above.  Since my clock is moving one might also expect a kinematic time dilation.  I can calculate the velocity of my clock: $$E_k=\frac{1}{2}mv^2$$ $$E_p=\frac{-GMm}{r}$$ $$v=\sqrt{\frac{2GM}{r}}$$ Plugging this velocity into the kinematic time dilation equation: $$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$ $$\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{2GM}{rc^2}}}$$  At this point one might make the observation that the kinematic dilation is the inverse of the gravitational dilation and therefore conclude that: $$t_0=t_f$$