And I didn't mean it that way. It's always about limits of applicability too, but overthrowing SR altogether is not reasonable to even try. CMB frame is interesting, though.
This is nice. Not exactly what I thought, but there is some concentration of stars and the rear view gets empty. At least we can rule out the possibility that Earth is moving very fast relative to the stars we see?
CMB frame that was brought up sounds like preferred frame to me, at least for...
Please see the picture. Red dots are stars, lines are the path that light takes, our observer is at center. Assuming that stars are somewhat uniformly spread around us, I suppose that stationary observer (left picture) sees about as many stars in every direction, but an observer moving in...
Ok, nice. But if no single boost causes any rotation, why would two boosts in a row do that? It's like space remembers that we already had boost in one direction, and when we have another, this mysterious Thomas rotation takes place.
Maybe I'm thinking this rotation too literally. Assuming that...
It seems that combining two Lorentz boosts cause rotation:
https://en.wikipedia.org/wiki/Lorentz_transformation#Composition_of_two_boosts
Do you think this rotation is something that could be measured by gyroscope? Or is it like space rotates around the accelerating observer, and the observer...
Ok, let's try. Hopefully I understand your advice correctly. So the worldlines in #20 are the following, and we need to use t' instead of t. (It's the setup of #20 I'm considering from now on, and we can forget the original #1 setup.)
(t',x',y') = (10t,10vt,0.5)
(t',x',y') = (10t,10vt,-0.5)...
If that is not ok, I don't know what to do. Actually the two rails system of #20 (forgetting the observer, the black dot) doesn't have any length in ##x##-direction, so that dimension shouldn't have effect on relativity of simultaneity, but maybe the equations are still wrong.
I suppose that...
I suppose post #20 gives some idea of solving this question too. If runners have the same proper length, slightly uphill going runner is length contracted and much shorter than the runner that is moving horizontally.
Here is a simpler version demonstrating the same problem, or maybe there is no problem, just that the direction of length contraction is not as straightforward as someone (at least I) might expect.
The upper picture is in black rail's rest frame. Black rail's proper length is 1. The red rail is...
Here is some effort on the mathematical approach. Luckily I got some practice in this forum last autumn, here is the link if someone wants to take a look:
https://www.physicsforums.com/threads/an-apparent-paradox-with-couple-of-frames.774710/
Looking at #1 left picture, let's fix the origin at...
"I understood it until it was explained to me" :smile: Maybe I didn't explain it very well, but the key ideas I had in mind in #1 right picture
- vertical rail, as a whole, is moving to right, in the rest frame of horizontal rail
- vertical rail is strictly vertical i.e. perpendicular to...
I agree. Now the funny part is that the vertical rail must be length contracted in y-direction by factor 10, although the y-velocity is only 0.1c. If it had its proper length, even approximately, this combined with well below c speed would result that the markings in horizontal and vertical rail...
Both x- and y-velocity cannot be close to c, as you already suggested in #7, because the diagonal speed would exceed c. I don't know how to solve this thought experiment, but it's interesting.
It can be a bit misleading, but the arrows in the first picture are intended to show that the vertical rail, as a whole, is moving to right, and the vertical rail also has some velocity in y-direction.
To be more accurate, the red arrow in the first picture would be strictly horizontal, as the...
Here is a picture about the value 0.1c. I don't draw all the arrows, because it would be messy, but the motion is the same as in previous picture.
Upper picture is in crossing's (red point) rest frame. Blue point is a clock that is stationary and synchronized with the crossing, the distance...
Yes, that is the idea, but I "separated" the velocity components. So the movement is south-east, but mostly east.
I think the diagonal velocity of markings in vertical rail would be too much, if the vertical rail's y-velocity was also close to c.
The way I got 0.1c was that horizontally close...
Left picture: There are two moving rails that cross at center (red dot) which itself doesn't move. The rails speeds are close to c, so that they are length contracted by factor 10 (roughly 0.995c). There are markings in rails at interval 10 length units in rails rest frame, so the interval is...
It seems unavoidable that the particle is there all the time in some form, but I don't know if this is correct way to think about it in the end. However, it would be interesting to know if the particle in its interfered state is immune to relatively weak gravity and EM fields.
For example, if...
It would be possible to set up an experiment so that it's observer-dependent which one of the entangled particles is measured first. If the information about the spins is not contained in the particles when they are created, nor the first measured particle can tell the other what spin it should...
#30 could be my reply to your post as well. Maybe it's completely irrelevant in physics what is happening between interactions, but it's interesting to think.
Ok. Maybe it's then misleading to talk about "paths" at all. However if we let a test particle travel through a room so that it doesn't interact until the back wall, it's tempting to think that something travels through the room, and the mass, energy and momentum are conserved in some form, even...
If that is the case, shouldn't the mass of the particle be multiplied by a huge factor? If it's at multiple places at the same time. Or should we interpret that only fractions of the particle take different paths, and the combined mass of the fractions is that of the particle?
I didn't mean an experiment that forces the particle to appear at either slit, but something where we compare tiny gravitational effects at different places to get hint of the path that particle goes. This is somewhat analogous to cellular network that is able to (at least roughly) get phone...
If there was no limit for the accuracy of our equipment, we could put test masses at left and right side of the room, release an electron and see if there is any difference. I would expect that the electron creates tiny gravity field around it and interacts more with left side test mass, if it...
Ok. As there is always some gravity present in double-slit experiments on Earth, and the particles e.g. electrons (I suppose) interact with the gravity field, there must be some threshold so that tiny gravitational effects do not eliminate the interference. This threshold must be something...
If the particles used in double-slit experiment were massive enough and/or our equipment sensitive enough, could we use gravity to spy what path the particles take even before they hit the detector? Would this kind of "measurement" destroy the interference?
How about this idea? Light (as EM wave) doesn't need medium for its propagation, but it needs space. So, in a sense, empty space is the medium for its propagation.
What speed do you have relative to this "medium"? None. If you move relative to a planet, your observation about the planet chages...
The intuitive understanding is exactly what I'm looking for. I'm convinced enough that the pulse returns to the source in every frame, because otherwise there would be a contradiction, but I'm just unable to see why it would reflect into this kind of surprising direction in a frame where the...
Now I hopefully get it. You mean the light flash actual path in this frame. I tried to draw only how pulse moves "relative" to the apparatus in this frame.
I'm somewhat familiar with relativity of simultaneity and aware that if there are clocks in different parts of apparatus and the clocks are...
Thanks George for your thorough reply.
Agreed. We don't even need continuous beam, because the angle is of interest. In fact, we could use some object e.g. ball that bounces back from wall and its speed doesn't need to be "relativistic" at all. I just wanted to use light and mirror for...
It's not the same path in space, but I meant that relative to the source the light travels at certain angle to certain distance, reflects and returns in the same angle. The whole system (source and mirror) are moving.
Light beam hits the mirror perpendicularly and returns to the source (left picture).
The same system in horizontal motion (right picture) is skewed due to length contraction so that both beam and mirror are at higher angle. Because the beam returns to source in the system's rest frame, it must...
It seems clear enough that #26 is roughly correct and I don't have any particular need for exact solution (and there are even easier ways to practice world lines etc), so if there is no objection, I suppose the original problem is solved by declaring that rotation (among length contraction and...
I think I can understand the agony of OP. Or maybe we have different reasons, but I'm not comfortable with twin paradox either. Lorentz transformations, spacetime diagrams etc. do not explain why there is a difference in aging. They only describe what kind of difference or how much there is...
I'm starting to get an idea of what B's shape in A's frame might be, but only quantitatively. I'd like to do this with numbers, but that must wait, it's harder than it sounds... Anyway, here is a picture where we imagine a measuring rod (blue in the picture) moving left along the horizontal rail...
The rotation issue is very interesting. A and B could start from the same rest frame, with same orientation, and accelerate in their desired direction of motion (horizontal and 45 degrees) so that they retain their original shape in their own rest frames. To achieve that, both must accelerate so...
I would like to keep these: angle is fixed to 45 degrees in rails frame, diagonal rail goes from corner to corner in B, and B is square-shaped in its own frame. However, I don't think that B is necessarily rectangle-shaped in A's frame for example, but could be quite skewed.
If 45 degrees angle...
Here is some effort on world lines. In the rails rest frame, let's set ##x=0## and ##y=0## where rails cross and ##t=0## such moment when the center points of A and B both are on the crossing. The world lines for center points are
For A: ##(t,x,y,z)=(t,vt,0,0)##
For B: ##(t,x,y,z)=(t,vt,vt,0)##...
I guess it already: world lines. :)
About the discussion in #15 and #16, here is my understanding of the scenario. This quick picture is not accurate in all things, but it's indended to show the following:
- In rails frame (left) A and B are length contracted in direction of motion. A is...
In its own rest frame, B sees itself square-shaped and of proper size. It's just the diagonal rail that contracts in the direction of motion, as A.T. said, and I also think the angle must be 45 degrees. I checked also your advice in #4 and see what you meant. The angle would indeed be less than...
That crossed my mind too and I might well try it, just wanted to sketch this first and see what happens. I tend to dislike mathematical approach a little bit though, but nothing too serious.
The key issue seems to be the shape of B in the rest frame of A. I studied this a little and it could be...
Object A goes horizontal line and object B diagonal line in 45 degrees angle (Fig 1). A and B have the same velocity ##v## in x-direction. In y-direction, B has velocity ##v##, A has none. The magnitude of ##v## is not very important, but the total speed of B must be below ##c##.
In their own...
I did some preliminary study for the rotation, which kept bothering me, by imagining a stationary grid in the lab frame and checking how it would behave when we jump from frame to another. I didn't do the math, but the result seems to be consistent with pervect's suggestion that observers X and...
Yikes! And worse is probably coming. :)
There are few things to digest, but I think I'm getting the idea. One question that came up was that do we have to substitute world line into coordinate transfrom (like you did) or can we do other way around i.e. substitute coordinate transform into world...
In lab frame, A and B travel at 45 degrees angle with total speed that is less than ##c##. Speed components in x- and y-direction are equally large, they can be calculated if we know the total speed.
In X-frame, rockets stop in x-direction and y-component is not the same than it's in the lab...
This is much harder. I found some material on the net, but didn't understand it very well and may have applied it wrong. But let's try anyway:
X-frame spacetime point presented in terms of lab frame coordinates would be
##(t',x',y',z') = (\gamma(t-vx), \gamma(x-vt), y, 0)##
and vice versa...