Well, it seems to me that if I move faster in space I move slower in the dimension of time which is orthogonal to the dimension of space.  All speeds are then equal. Is this statement correct?
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I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward.  What troubles me here, is the fact that it is traveling through space-time at the speed of light. Why is it at the speed of light?
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?
29146
From what I've read, according to relativity, a photon does not "experience" the passage of time. (Can we say there is no past/present/future for a photon?)  Would it be better to say a photon is "fixed in spacetime"? If so, how do we explain the apparent movement of a photon? Is everything else moving relative to it in spacetime?
63366
If we call the velocity of the mass $u$, then we can say: $u \cos θ = v$ and hence $u= \frac v{\cos θ}$. But why can't we write  $v \cos θ= u$ and add the contribution from both of the strings: $u= \frac{2v}{\cos θ}$ ? Why is it only $u= \frac v{\cos θ}$? Please note that it is not a homework based  question. I just want someone to solve the doubt arising in my mind.
76733
I've always heard people saying, "Faster than light information transfer can't happen because it would violate causality!  Effects can precede their causes!"  However, I'm trying to think of a situation where this would happen.  I'm sure it has something to do with relativity or something like that.  I sort of understand that people going faster perceive time slower.  Can someone help illuminate this for me by showing a scenario where causality is clearly violated due to FTL information transfer?
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.
13627
If there are two twins. such that one of them goes on a space voyage maintaining a constant velocity, and that one never returns to earth, and the twins decide to never meet but send information about their age to each other by some light pulse or any other method.  If then one knows that he is younger, won't he know he is the one travelling thus violating the postulate of relativity that all inertial frames are equal w.r.t. all phenomena and that one can never know if he is moving with a constant velocity.
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While reading Chapter 1 of an astrodynamics textbook, I came across the statement:  $$\mathbf{v}\cdot \mathbf{{\dot{v}}}=v{\dot{v}}$$  In other words, the dot product of velocity and the time-rate-of-change of velocity is simply equal to the product of the magnitudes of the velocity and acceleration vectors.  I think I see how this works mathematically:  $$\frac{1}{2}\frac{d}{dt}\left ( \mathbf{v}\cdot \mathbf{v} \right )=\frac{1}{2}\left [\mathbf{v}\cdot \frac{d\mathbf{v}}{dt}  +\mathbf{v}\cdot \frac{d\mathbf{v}}{dt}\right]=\mathbf{v}\cdot \frac{d\mathbf{v}}{dt}=\mathbf{v}\cdot \mathbf{\dot{v}}$$  Also, since a vector is always parallel to itself,  $$\mathbf{v}\cdot \mathbf{v}=vv=v^{2}$$  So,  $$\frac{1}{2}\frac{d}{dt}\left ( \mathbf{v}\cdot \mathbf{v} \right )=\frac{1}{2}\frac{d}{dt}\left (v^{2}  \right )=\frac{1}{2}\left (2v  \right )\frac{dv}{dt}=v\frac{dv}{dt}=v\dot{v}$$  My hangup is this: are a vector and the first time derivative of that same vector always parallel (and in the same direction)?  It would seem so, since the (not shown) cosine of theta term equals 1.  Seems strange to me, because an object can be traveling in a certain direction while experiencing acceleration in another direction, such as the parabolic trajectory of a projectile near the Earth's surface (ignoring drag).  Velocity will be tangent to the arc, while the only acceleration is straight down (due to gravity) and never actually parallel to velocity, so long as there is a horizontal component to the trajectory.  Am I missing somehting very obvious here?  Thank you for your time and consideration.  Citation: See page 15 (sheet 30 of 470) section 1.4.1.2 of .     Some very helpful people left great answers, thank you. More webmining also yielded , which provided yet another good answer to the question. Seems like that one statement is responsible for a fair bit of consternation.
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In the first paragraph of Wikipedia's article on , it states one of the assumptions of special relativity is     the laws of physics are invariant (i.e., identical) in all inertial systems (non-accelerating frames of reference)   What does this mean? I have seen this phrase several times, but it seems very vague. Unlike saying the speed of light is constant, this phrase doesn't specify what laws are invariant or even what it means to be invariant/identical.   My Question   Can someone clarify the meaning  of this statement?   (I obviously know what an inertial frame is)
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Some threads here touching speed of gravity made me think about that. This lead to some questions.    The speed of gravity was not measured until today (at least there are no undebated papers to that effect). It seems common knowledge/belief among physicists that the speed of gravity is the same as the speed of light.    And this is my question: Is that speed of light = speed of gravity a result of GR or is that fed into the theory? Or is there some evidence from other sources than GR for this? Does the same speed imply some deep-lying relation between gravity and electromagnetism?
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If an observer approaches a clock at a significant fraction of the speed of light, would they see the clock's hands moving at a faster or slower than usual rate?  I figure there are two competing effects at play - time dilation and diminishing distance.
36549
Is the Lorentz transform applicable to speeds that are lower than light only?Because I'm trying to calculate length contraction of objects moving at speed $c$ (not near it) and it turns always 0. Is my calculation correct?Please help I'm just a beginner  Suppose a 5 m object is traveling at $c$,so $$        x'=x/γ$$  \begin{align} x&amp;=x'\sqrt{(1- (v^2)⁄(c^2)}\\ x&amp;=5\sqrt{1-1}\\ x&amp;=5\sqrt0\\ x&amp;=0 \end{align} Not infinite right? If so then the rule will have no length?
108971
How to prove (if it is true ... I suppose it is) that orthogonal projection from N-dimensional space onto 2-dimensional plane and rotation in this plane (I assume components of vectors out of the plane are not affected by the rotation) are commutative operations independently from dimension of N-dimensional vector space ?
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What is the chain of reasoning (beginning, of course, from observations about the universe) that leads one to predict that Minkowski space provides an accurate description of space-time in the framework of special relativity?  That is, why should flat space-time have the Minkowski metric  $$\eta = \left(\eta_{\alpha\beta}\right) = \left( \begin{matrix} 1 &amp; 0 &amp; 0 &amp; 0 \\ 0 &amp; -1 &amp; 0 &amp; 0 \\ 0 &amp; 0 &amp; -1 &amp; 0 \\ 0 &amp; 0 &amp; 0 &amp; -1 \end{matrix}\right)\,?$$
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If I'm standing at the equator, jump, and land 1 second later, the  Earth does NOT move 1000mph (or .28 miles per second) relative to me,  since my velocity while jumping is also 1000mph.   However, the Earth is moving in a circle (albeit a very large one),  while I, while jumping, am moving in a straight line.   How much do I move relative to my starting point because of this? I  realize it will be a miniscule amount, and not noticeable in practise,  but I'd be interested in the theoretical answer.
42048
I'm having a hard time understanding how changing space means changing time. In books I've read people are saying "space and time" or "" but never explain what the difference is between the two concepts or how they are related.  How are the concepts of space, time, and space-time related?
91372
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.