- #36
CClyde
- 35
- 2
All coordinates move relative to an appropriately chosen frame of reference.PeterDonis said:This makes no sense. Coordinates don't "move".
My point is none of the coordinates of light emissions are appropriate.
All coordinates move relative to an appropriately chosen frame of reference.PeterDonis said:This makes no sense. Coordinates don't "move".
No, they don't. This is nonsense. Objects move.CClyde said:All coordinates move relative to an appropriately chosen frame of reference.
What coordinates? Your own? What are you talking about?CClyde said:My point is none of the coordinates of light emissions are appropriate.
I think you are trying to say that a thing having "constant spatial coordinates" in one frame is moving in another.CClyde said:All coordinates move relative to an appropriately chosen frame of reference.
Appropriate for what?CClyde said:My point is none of the coordinates of light emissions are appropriate.
I can: With math!CClyde said:I cannot think of a more clear way to state this.
1. In an inertial frame and using units where ##c=1##, the equation for a light wave emitted at ##\mathrm{R}=(t_0,x_0,y_0,z_0)## is given by ##(t-t_0)^2=(x-x_0)^2+(y-y_0)^2+(z-z_0)^2## for ##t\ge t_0##. For any given ##t## this is the equation of a sphere centered at ##(x_0,y_0,z_0)## with radius ##t-t_0##.CClyde said:1. The spatial coordinates of a light emission (t0, x0, y0, z0) remain at the center of the sphere that is the propagating wavefront.
2. The invariance of ##c## means that the equation is also ##(t’-t’_0)^2=(x’-x’_0)^2+(y’-y’_0)^2+(z’-z’_0)^2## in any other (primed) inertial frame.CClyde said:2. The constancy of c holds the wavefront symmetrical for all observers.
This one I don’t know what you are trying to say. Please try to express it clearly using math as demonstrated for 1. and 2.CClyde said:3. All such light emission coordinates are, by the definition of lights independence of the motion of the source incapable of motion relative to each other.
If you are moving toward an object and the object disappears, are you still moving, or did the coordinates of its position only exist because the object existed?PeterDonis said:No, they don't. This is nonsense. Objects move.
The continuing spatial co-incidence of the object (flashbulb) and the center of the resultant spherical (to all observers) light pulse is true only in the rest frame of the flashbulb. These positions coincide for all observers only at t=0 when the flashbulb fires.CClyde said:If you are moving toward an object and the object disappears, are you still moving, or did the coordinates of its position only exist because the object existed?
The principle of relativity says motion is not a property of some “thing”, it is a measure made by an observer. A thing you measure at rest is in motion relative to a frame not at rest with you. This reciprocal symmetry of kinematics allows any inertial frame to be at rest, or in uniform motion by simply defining it relative to the appropriate frame.Ibix said:I think you are trying to say that a thing having "constant spatial coordinates" in one frame is moving in another.
You should stop saying this because it is wrong. We are here to try to understand what you are saying (which currently is unclear) so that we can help you see where your reasoning fails. But to be clear your reasoning must fail somewhere because your conclusion here is false. Do not repeat this conclusionCClyde said:So I said, none of the coordinates of light emissions are appropriate.
What is the frame of a light emission?CClyde said:The frame of a light emission
Yes, I agree but I am not concerned with the whereabouts of the flashbulb after emission. I am concerned with the center of the spherical light pulse which remains at the center of the sphere it defines relative to the center of all other such centers, none which can move relative to each other without violating the constancy of the speed of lighthutchphd said:The continuing spatial co-incidence of the object (flashbulb) and the center of the resultant spherical (to all observers) light pulse is true only in the rest frame of the flashbulb. These positions coincide for all observers only at t=0 when the flashbulb fires.
For all other times everthing depends upon reference frame motion (as described by Lorentz transformations)
Nobody understands what this means. What is "a coordinate of light emission" The center of the light sphere is not a good marker.CClyde said:So I said, none of the coordinates of light emissions are appropriate.
So, where do you go from here? I would claim you are new to the concept of having the same events described in two different reference frames and, in particular, cannot reconcile the invariance of ##c## with your mental picture of the motion of light. What do you do next? Accept you are wrong? Persist in your error? The choice is yours. No one can force you to understand SR.CClyde said:Yes, I agree but I am not concerned with the whereabouts of the flashbulb after emission. I am concerned with the center of the spherical light pulse which remains at the center of the sphere it defines relative to the center of all other such centers, none which can move relative to each other without violating the constancy of the speed of light
Please explain how two light spheres from two emission events (0,0,0,0) and (0,1, 1, 1) move away from each other such that at a time > 0 the centers of these spheres, are no longer at (0,0,0,0) and (0,1, 1, 1).hutchphd said:For each observers in uniform relative motion we can choose coordinate systems such that the emission event occurs at (t,x,y,z)=(0,0,0,0). The rest is as given by Lorentz transformation and does not comport with the picture in the head of the OP. Physics is hard.
My goal is to find out if I have misconceptions, or if I have discovered an internal inconsistency in the principle of relativity.Vanadium 50 said:@CClyde I reread this thread and confess I am confused as to your goial.
Is is:
1. To clear up your misconceptions?
2. To convince us that re;ativity is internally inconsistent and you are the first person in more tnan a century who notic4d?
Relativity is self-consistent. If any chain of reasoning leads you to believe otherwise then that chain of reasoning is incorrect.CClyde said:My goal is to find out if I have misconceptions, or if I have discovered an internal inconsistency in the principle of relativity.
What do you mean by this?CClyde said:Please explain how two light spheres from two emission events (0,0,0,0) and (0,1, 1, 1) move away from each other such that at a time > 0 the centers of these spheres, are no longer at (0,0,0,0) and (0,1, 1, 1).
There is such a reference. If you are moving inertially (you determine this by the absence of proper acceleration - an accelerometer you are holding reads zero) you can choose your position in three-dimensional space to be at rest with coordinates (0,0,0) and your position in four-dimensional spacetime to have coordinates (t,0,0,0) where t is your wristwatch time. Once you’ve done that, you can determine the coordinates of any other point in space, and it is a simple calculation to convert these values to other coordinate systems.CClyde said:If there were some reference, some coordinate you could actually prove cannot move, not just state it as you are, but prove the existence of, and by law that such coordinates cannot move, well, then you could measure your position over time relative to such coordinates
There is no such distinction. When we say “THIS is moving and THAT is not” we are actually saying “We have chosen to use a coordinate system in which THIS is moving and THAT is not”. Thus we are free to consider either to be at rest, just by choosing our coordinates.and know if it is you or the object that is moving.
Here’s a rule of thumb: If you do not do the math, you have not found an inconsistency. Words are not precise enough to perform physics with.CClyde said:My goal is to find out if I have misconceptions, or if I have discovered an internal inconsistency in the principle of relativity.
Ahhhh…. That would be #2 of this thread.CClyde said:Please explain how two light spheres from two emission events (0,0,0,0) and (0,1, 1, 1) move away from each other such that at a time > 0 the centers of these spheres, are no longer at (0,0,0,0) and (0,1, 1, 1).
Let's see, whether we can make the entire trouble concrete. Since it's only about kinematics, let's just consider a massless scalar field. Wo so we can simply look at the spherically symmetric solution of the wave equation,PeroK said:So, where do you go from here? I would claim you are new to the concept of having the same events described in two different reference frames and, in particular, cannot reconcile the invariance of ##c## with your mental picture of the motion of light. What do you do next? Accept you are wrong? Persist in your error? The choice is yours. No one can force you to understand SR.
Although there is nothing wrong here, there are easier ways of approaching the math and OP may want to start with those.vanhees71 said:Let's see, whether we can make the entire trouble concrete….
If there are two emission events, different observers will not agree as to either their distance apart or their simultaneity. You cannot intuit the details (nor can I)CClyde said:Please explain how two light spheres from two emission events (0,0,0,0) and (0,1, 1, 1) move away from each other such that at a time > 0 the centers of these spheres, are no longer at (0,0,0,0) and (0,1, 1, 1).
I suspect calculations are anathema to the OP.Nugatory said:Ahhhh…. That would be #2 of this thread.
But it would be a good exercise to actually calculate the position of the spreading flash of light twice, using the two coordinates systems in which each of two observers moving relative to one another are at rest.
If you have a more simple model for a "light source", let's see it. Perhaps it's my limited imagination that I couldn't find a simpler one ;-)).Nugatory said:Although there is nothing wrong here, there are easier ways of approaching the math and OP may want to start with those.
Then, s/he has no chance to ever talk about physics in such a way that s/he can understand it.PeroK said:I suspect calculations are anathema to the OP.
So, instead of talking about light spheres, for a moment let's talk about light cones. In this case in some given (unprimed) inertial frame with coordinates ##(t,x,y,z)## we have two light cones: $$\mathrm{A}=(t,x,y,z) : \ t^2=x^2+y^2+z^2$$$$\mathrm{B}=(t,x,y,z) : \ t^2= (x-1)^2+(y-1)^2+(z-1)^2$$ So here we have two light cones, each of which is a full 4D object. These 4D objects represent right circular cones with the axis along the ##t## direction and with the apex at ##(0,0,0,0)## and ##(0,1,1,1)## respectively.CClyde said:Please explain how two light spheres from two emission events (0,0,0,0) and (0,1, 1, 1) move away from each other such that at a time > 0 the centers of these spheres, are no longer at (0,0,0,0) and (0,1, 1, 1).