The principle of relativity suggests that all inertial frames are indistinguishable. But if I consider the rest frame of a photon (i.e. an IRF traveling at speed $c$ w.r.t. me), then won't it be distinguishable from my rest frame? And both are IRFs. For example, time is not well-defined for the photon rest frame. I've heard that time stands still for a photon. Isn't that a special property of photon rest frames, and therefore something that can be used to fundamentally distinguish it from regular IRFs (like mine)?
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Quite a few of the questions given on this site mention a photon in vacuum having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at the speed of light in all frames according to special relativity.  Does a photon in vacuum have a rest frame?
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Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function spreads out, and there is a small but finite chance of finding it pretty much anywhere in the universe. Suppose it's measured one second later by a different observer more than one light second away and, although extremely unlikely, this observer discovers that electron. I.e. the electron appears to have traversed the intervening distance faster than light speed. What's going on here?  I can think of several, not necessarily contradictory, possibilities:   I'm misremembering how wave functions work, and in particular the wave function has zero (not just very small) amplitude beyond the light speed cone. Since we can't control this travel, no information is transmitted and therefore special relativity is preserved (similar to how non-local correlations from EPR type experiments don't transmit information) Although the difference between positions is greater than could have been traversed by the electron traveling at c, had we measured the momentum instead, we would have always found it to be less than $m_e c$ and it's really the instantaneous momentum that special relativity restricts; not the distance divided by time. My question is ill-posed, and somehow meaningless.   Would anyone care to explain how this issue is resolved?
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Suppose a box A is moving relative to a Box B, then by time dilation equation if I take 1 sec passed for an observer in A then for an observer in B will be little longer. Now if I suppose that the box B is moving while A is stationary under the same condition, then by the time dilation equation time passed in B must be shorter than A. How is this issue resolved? In the twin paradox problem my book says that it's due to acceleration, but in my opinion acceleration is relative (please correct me if I'm wrong), but here it is not the case.
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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?
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Can someone help me giving a qualitative answer to this problem in General Relativity:  Imagine you are on earth with two perfectly synchronized clock's. If you hold on in your hand but you throw the other one in the air and catch it after a certain time interval, would they still give the same time?  I think that the one in the air would run faster but I cannot explain why.  Thank you!
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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.
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While I was hobby-reading about quantum mechanics I came across Heisenberg's theory. But while I was trying to understand it I thought of this: if the speed of light (as well as the momentum of a photon) is well-defined, then if in an experiment the position of the photon was found, the researchers would know the exact position of the photon, but also its momentum which is constant. Is this an exception from the rule, or am I just ignorant?  PS, 12 grade physics education, please try to explain in simple words
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Two questions.  It is said that time can only go slower in gravity fields and if you move faster.  I have heard that when a gravitational wave pass earth then the space/time vibrate and time change for an instance.  But a wave is often with a top and a valley.  They have now atomic clocks that might be able to detect time variations, placed in satellites around the sun and "quantum entangled". "Using Atomic Clocks to Detect Gravitational Waves"   So what if we could compare time ticks between clocks in space at "absolute frame of reference" where time has its maximum universal speed as time in deep space between Galaxy Filaments.  Will we only detect that time ticks slower for an instance when the gravational wave pass?  1. Or will we detect that time tick slower AND faster than normal time also, as compared to zero gravity time and no movement time in "absolute frame of reference"?  2. Can time go let's say 10 times faster by theory/mathematics, by a extreme theoretical gravitational wave, than time in "absolute frame of reference time"?
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As of this writing it has been made clear to me that classical physics' Luminiferous aether was a terriblly poor discriptor of space. With the advent of Special Relativity and General Relativity, that aether ceased to be applicable. Today I began reading on the Higgs boson, and the Higgs field. How are those theories different from or similar to the seemingly irrational Luminiferous aether?  P.S. I am a first year student at Bakersfield Community College. If this question seems naive, you now have an explanation.  (EDIT) To me the similarity rests upon their fundamental influences regarding static positions in space. I currently only accept models in which static spacial positions are impossible. Contrastingly relative positions seem quite reasonable. In my humble opinion my naivatisms inhibit me from absorbing and understanding the Higgs boson. If they actually are similar, public protest would probably be more apparant. However, I have put forth my best effort to pose an direct question here.  P.S. The questions Where does space go when it falls? and What happens to time lost when matter accelerates? come much earlier in my studies, and they seem relevant.
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It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest.
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A question has recently come up that goes beyond my knowledge of special relativity.  Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant acceleration, and he has a magical engine that can maintain the thrust needed to accomplish such acceleration even as the vehicle acquires mass.  He measures his acceleration at periodic intervals and sums it up as he goes.  Observers perceive the rocket to increase in speed and gradually approach the speed of light (but never reach it). Two possibilities are being debated for what the pilot observes, and my preference is for the first:   Time dilation gives him the impression that the summation of his readings are approaching light speed at a constant rate, but there is an asymptote involved here even in the inertial frame such that he never actually perceives himself to reach, let alone exceed, $c$, because time slows down to a crawl (as seen from the reference frame) before this can happen. Although to observers he is only approaching $c$, it is possible for the summation of the measurements on his accelerometer to indicate that he has surpassed $c$ and is now traveling faster than light.  From the reference frame he is approaching $c$ and his instruments in the inertial frame tell him that he has surpassed it.   I assume (1) is true beyond a doubt?  If so, is there a straightforward explanation for this?
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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?
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Given the widespread acceptance that  “Einstein’s Relativity” reasonably proves the existence of Space-‘Time’, and thus “Time”... Can any member of the Physics StackExchange please show precisely where, in "On the Electrodynamics of Moving Bodies", (or related core Relativity) papers, “Time” is actually, in any reasonable way shown to exist, as opposed to just, or only being (unscientifically) “assumed”? (added) or, why it is legitimate for the paper to make this assumption or axiom?  Many individuals and publications refer to Relativity as our best theory of Space, and “Time”, and thus imply it is a given that time exists... because Relativity intricately employs the concept of time.   But wherever such claims are made, they are rarely accompanied by any clear justification or specific reference to a specific section of SR or GR. At best, it is claimed that SR proves “Time dilation”, and thus the existence of “time” as a genuine dimension.   Therefore  unless it can be shown that Relativity, ("On the Electrodynamics of Moving Bodies" etc), actually incorporates a reasonable proof of times existence, or cites such a proof, or even just gives a valid reason to “suspect” a thing called “time” might exist, then the “time dilation” shown may in fact prove only that moving things “are” changing “slower” (i.e just at a dilated rate), than stationary things, and not that a “temporal past”, and/or “temporal future”, or thing called “time” also exists. (As per space-“time”, block-“time”, growing block-“time” etc).  Precisely where Relativity is valid in assuming a thing called time exists, is a very important question, given the large number of theories based on the belief Relativity does proves time’s existence. And, the large number of fundamentally conflicting theories about time, problems resolving quantum and classical “time”, and even disagreement about time’s actual existence or not.   Therefore, if anyone here on the stack exchange can show just where "on the electrodynamics of moving bodies" actually, legitimately validates its use of "time", or why they accept its assumptions in the specific area of "Time",  please clarify this not just for me, but I assume many others..
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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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Is there any true  in the universe?  Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if viewed from an inertial frame. It is the definition of an inertial frame of reference. And Newton's second law states that the net external force acting on a particle equals its mass times its acceleration. Thus we need to have an inertial frame in order for Newton's 1st and 2nd laws to be applicable.  Scientists claim that Earth is an inertial frame, either the  frame or the  frame.  Why is that? Earth's different parts have different accelerations when it performs rotational motion about its axis. Now you may say that Earth's axis is inertial, but the Earth is also revolving around the Sun. Thus Earth's frame should be non-inertial.  Even supposing that earth's frame is inertial, then it means that rest of the universe is non-inertial, because only a frame that moves with constant velocity with respect to an inertial frame is also an inertial frame and according to various scientific experiments there is no other matter in this universe which satisfies that criterion. Now you may say that earth is an approximate inertial frame, but still, my question is: is there any perfect inertial frame in the universe where Newton's laws are exactly applicable?
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I understand the  as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell whether a laboratory on Earth is not actually in a rocket accelerating at 1 g".
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Describing acceleration in special relativity is in principle straightforward, and for simple cases the resulting transformations are simple. Examples include  and constant acceleration in the accelerating frame (the ). Anything more complicated is going to have to be done numerically, which is fine, but it's not immediately obvious to me how you'd go about this.  Let's call our frame $S$, and our metric is just the Minkowski metric. If we can write down an expression for the trajectory $x(t)$ in our coordinates $x$ and $t$ then everything is straightforward. But this isn't likely to be the case. It's more likely that the aceleration will be given in the accelerating object's frame $S'$ i.e. all we know is $a'(t')$.  So given that all we know is the form of $a'(t')$, how do we set about calculating the rocket's trajectory in our coordinates $S$? General principles will be fine as I'm sure I can work out the fine detail. It's just that I'm not sure where to start.  Assuming I'm not skirting too close to the homework event horizon, this might make a good blog type question. I've been thinking about writing an answer your own question post about acceleration in SR for some time.