Time dilation flashlight problem

In summary, on page 78 of Relativity and Early Quantum Theory, there is a problem with the time dilation equation. The correct formula for the time dilation is t(1) = t/((c-v)/(c+v))^.5, where t=6 minutes. According to this equation, if an observer is on Earth and flashes their flashlight at six minute intervals, they would see the flashes arrive at the space station C at 12 minute intervals. However, the observer on the space station would see the flashes arrive at 6 minute intervals according to their own clock.
  • #36
A.T. said:
Play around with the speed slider in the animation. You will get the idea of how relative movement affects the moving clock and the length along the movement direction.

The idea is that everything advances at a constant rate in spacetime, only the direction and orientation in spacetime changes. The direction affects the rate of the moving clock, as you move more in space or more in time. The orientation affects the length in space as the projection of the object onto the spatial dimensions changes.

Thats the "mechanism".


Hmm... Will probably take some time to get hold of the spacetime thing.
Anyways, thanks :)
 
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  • #37
Hi A.T. Another lay person will bother you. I have doubt about change of dimension only in the direction of movement in velocity near the C. Let say a proton that move with 0.9C has a shape of spageti.But i think that any elementary particle is spining in itself axis allways, isn't this true? After above assertion the particle must change its dimension allways. How is it be posible do not been sociated with other physics phenomena?
 
  • #38
As another note to add to this setup. We may want to assume that Time and space are NOT flexible.

Jesse I like your phrase about Coordinate speed... I think i will use that more often. :)

I have a conumdrum for you. In all the scenarios we have mentioned we have used the terms at rest and in motion relative to X. We have also given objects certian speeds. We are in fact (at least to start a scenario) using these Coord systems of speed and time and distance.

Take for instance two objects that have an approaching coord spped of .5c. What are the observances of the other object from itself? You either cannot correctly determine this becuse you don't know if A is "moving" or B is "moving" or they both are at some combined speed. Even in relativity you cannot do the math correctly because you have no known speeds. If an object is in motion (without prior knowledge such as feeling acceleration) and is trying to find out when he will see the light directly ahead of him he will need to be able to calculate his speed as well as the speed of the light source. to do that you need to define and have a way to determine actual and complete rest. You can determine this with something similar to the apparatus i mentioned earlier. In the case of some relativity setups the math in physical space does not add up and we can see is not true by observances.

For instance you have a light source in one location and two bodies in a second location (and you are in teh stadium and can see all of it at once). That light emits a single photon... just ONE at T=0. At that point one the bodies in the second location has motion to the other body (no matter the direction no matter the speed).

According to Reletivity that photon of light will reach both bodies at the same time. We will say this time is T=100 (good for percentages)

You as the person in the stadium would have to have seen that photon of light moving at two separate speeds in two possibly different directions becaues of the movement of a completely unrelated object. This is a physical impossibility (denying the laws of physics).

You can make this even more unbelieveable using relative physics by adding more bodies at the second location then they head off all in separate directions and speeds. You will wind up with a different location (but same time) for the photon for each body. You can even claim that you are creating more energy (photons) from a single photon just because you have multiple reference points. (granted i understand that this is not true but pointing out the implications).

Now if we took the NPs into consideration with the same scenario. We can see how that one photon of light will hit only objects in its path and will hit them with a time varying based on the distance between the 3d point in space where the photon originated and where the body wound up being when the photon intercepted it. Also that photon of light would keep its path of travel in a straght line so only the bodies along that pat would percieve the photon. Makes complete sense. And everything (including the results we would see in other experiments is in harmony.
 
  • #39
Physicist1231 said:
Take for instance two objects that have an approaching coord spped of .5c.
Can you clarify what you mean by that? Do you mean for example that in my reference frame ('my reference frame' just means the inertial coordinate system where I am at rest, in case you're not clear on that) one object is moving at 0.5c in the +x direction, and the other is moving at 0.5c in the -x direction? Or do you mean that the coordinate distance between them is shrinking at a rate of 0.5 light-seconds per second in my frame, which would be true for example if one of them was moving at 0.25c in the +x direction and the other was moving at 0.25c in the -x direction?
Physicist1231 said:
What are the observances of the other object from itself?
Do you mean, what coordinate speed does one object have in the reference frame of the other object (the coordinate system where the other is at rest)? If that's what you're asking, this would be given by the velocity addition formula, which says if ship A and C are approaching each other at speeds v and u in the frame of a middle observer B, then the speed of ship A in ship C's own frame is (v+u)/(1 + v*u/c^2). So for example if I am B and ships A and C are moving at 0.5c in opposite directions in my frame, then in ship C's frame, ship A is moving at (0.5c + 0.5c)/(1 + 0.5*0.5) = 1c/1.25 = 0.8c.
Physicist1231 said:
You either cannot correctly determine this becuse you don't know if A is "moving" or B is "moving" or they both are at some combined speed.
No, that's not true, there is no need to know if either ship is "moving" in an absolute sense, or what absolute speed either has. You really must rid yourself of these absolute notions, they are totally irrelevant in relativity!
Physicist1231 said:
Even in relativity you cannot do the math correctly because you have no known speeds. If an object is in motion (without prior knowledge such as feeling acceleration) and is trying to find out when he will see the light directly ahead of him he will need to be able to calculate his speed as well as the speed of the light source. to do that you need to define and have a way to determine actual and complete rest. You can determine this with something similar to the apparatus i mentioned earlier.
No, I already explained why, even if there is such a thing as absolute velocity, because of the way each frame synchronizes their clocks, it is guaranteed that clocks on the inside of the large sphere (or at the ends of the + sign in my example) will all show the same time when the light from the center hits them, regardless of whether the sphere (or +) is at rest relative to absolute space or moving relative to absolute space. I offered to give you a numerical example if you need to see how this works, but please don't just repeating the same false claim and ignoring the response I gave you.
Physicist1231 said:
For instance you have a light source in one location and two bodies in a second location (and you are in teh stadium and can see all of it at once). That light emits a single photon... just ONE at T=0. At that point one the bodies in the second location has motion to the other body (no matter the direction no matter the speed).

According to Reletivity that photon of light will reach both bodies at the same time.
No, relativity doesn't say that. Certainly they shouldn't reach it at the same time in the stadium frame, since one of the bodies will have changed position in this frame by the time the photon reaches the body which is at rest in this frame. I suspect you're talking about what would be true in each body's own frame, but here you are again neglecting the relativity of simultaneity, which says that if the event of the photon being emitted is simultaneous with the two bodies being next to each other in one body's frame, these events are not simultaneous in the other body's frame, meaning in that body's frame the photon was actually emitted some time before or after the two bodies passed each other. Also you are neglecting length contraction, which says that the distance between the position of both bodies when they are next to each other and the position of the emitter is different in each body's frame. If you take these effects into account, you find that even if each body's clock showed the same time at the moment they passed one another, and even though the photon moves at 1c in each body's rest frame, then even if you use each body's rest frame to calculate the time on that body's clock when the photon passes it, you will still predict that clocks of the two bodies will show different times at the moment the photon passes each of them. Again, I can give a numerical example of this if you want, just ask.
Physicist1231 said:
Now if we took the NPs into consideration with the same scenario.
What are "the NPs"?
 
  • #40
mquirce said:
Hi A.T. Another lay person will bother you. I have doubt about change of dimension only in the direction of movement in velocity near the C. Let say a proton that move with 0.9C has a shape of spageti.
Spaghetti? If you assume it is a sphere at rest, it would be a pancake at 0.9c. But such assumptions about the shape of elementary particles can be misleading.

mquirce said:
But i think that any elementary particle is spining in itself axis allways, isn't this true?
I don't think so. I think you take the spin-property too literally. Your question is more about quantum mechanics.
 
  • #41
Jesse,

You need to have rigid space and time to properly calculate any movement ever. I will create a scenario and ask a few questions about the results. You solve for me using Relativity. Then I will solve using NPs.

Case in point.

Time:
T=0

Positions: Units in light seconds
A light source at 0,0,0
Body A, B and C are at coord 20ls,0,0

Velocities:
Body A remains at 20ls,0,0
Body B has a speed of .5c,0,0
Body C has a speed of 0,.5c,0

Light is emitted from the source at T=0 and at this time Body B and C start their motion.

Questions:

At what point in time does do each body percieve that light? Please have separate answers for all three and explain the math.

At what coordinates is each body when it perceives the light? Again please have separate answers and the math.
 
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  • #42
Physicist1231 said:
Jesse,

You need to have rigid space and time to properly calculate any movement ever.
No you don't, you can just calculate everything from the perspective of an inertial frame, without having to say anything about whether that frame is in absolute motion or is at absolute rest.
Physicist1231 said:
I will create a scenario and ask a few questions about the results. You solve for me using Relativity. Then I will solve using NPs.
Sure, but you didn't answer my question, what does "NPs" mean? Presumably the "N" and "P" stand for something?
Physicist1231 said:
Case in point.

Time:
T=0

Positions:
A light source at 0,0,0
Body A, B and C are at coord 20,0,0

Velocities:
Body A remains at 20,0,0
Body B has a speed of .5c,0,0
Body C has a speed of 0,.5c,0

Light is emitted from the source at T=0 and at this time Body B and C start their motion.

Questions:

At what point in time does do each body percieve that light? Please have separate answers for all three and explain the math.

At what coordinates is each body when it perceives the light? Again please have separate answers and the math.
The math is easier if we put the origin at the point where all three coincide (the Lorentz transformation assumes that the spatial origins of each frame coincide at t=0 in each frame, if you drop this assumption you need the Poincaré transformation), and hopefully you agree that where we put the origin is just a matter of convention, so let's assume that in A's rest frame, A is at x=y=z=0, and at t=0 we assume B and C are also at that position (and let's assume the clocks of all three are set to read 0 at that moment), while the light source is at x=-20, y=0, z=0, and at t=0 in this frame the source sends out a flash. And as you said before, in this frame B has a velocity of 0.5c in the x-direction, and C has a velocity of 0.5c in the y-direction. OK so far?

Let's first find the answer just using A's frame, which is pretty easy. Here a ray of light traveling along the x-axis (which will first pass A, then B) has position as a function of time given by x(t)=1c*t - 20, so it will obviously pass A 20 seconds later at t=20, while B has position as a function of time given by x(t)=0.5c*t, so the light will reach B when 1c*t - 20 = 0.5c*t, or when t=20/0.5=40. Finally, the path of the ray of light that meets C after some time t will be the hypotenuse of a right triangle whose horizontal side has length 20 and whose vertical side has length 0.5c*t, with the hypotenuse itself having length 1c*t since this ray must move at 1c as well. So we have (20)2 + (0.5c*t)2 = (1c*t)2, solving for t gives [tex]t=\sqrt{400/0.75}[/tex] = 23.094010767585. So now we know that the coordinate time of the light reaching B is t=40 and the coordinate time of the light reaching C is t=23.094010767585, but to find the actual times on the clocks of B and C we have to consider the fact that both clocks are running slow by a factor of [tex]\sqrt{1 - 0.5c^2/c^2}[/tex] = 0.866025403784439 in this frame, so when the light reaches B its clock reads 40*0.866025403784439 = 34.6410161513776, and when the light reaches C its clock reads 23.094010767585*0.866025403784439 = 20. And of course A is at rest in this frame, so when the light reaches it at t=20 it reads a time of 20 as well. So, to sum up, when we calculate everything in A's frame we find the following:

--A's clock reads 20 when the light reaches it
--B's clock reads 34.6410161513776 when the light reaches it
--C's clock reads 20 when the light reaches it

Now we can double-check that everything is consistent by analyzing things from the perspective of B's frame, and from C's frame. To save some time I'll just figure out the time on B's clock using B's frame, and the time on C's clock using C's frame, though I could also figure out the time on A and C's clock using B's frame or figure out the time on A and B's clock using C's frame if you really need to see those calculations.

Let's start with B's frame. If we denote the coordinates in B's frame using symbols x',y',z',t', then according to the Lorentz transformation the relation between these coordinates and the coordinates of A's frame (x,y,z,t) is given by:

x' = gamma*(x - vt)
y' = y
z' = z
t' = gamma*(t - vx/c^2)

where v=0.5c, and gamma = 1/sqrt(1 - v^2/c^2) = 1.15470053837925. We know that in A's frame the coordinates of the emitter sending out the flash were x=-20, y=0, z=0, t=0, so in B's frame the coordinates of the flash being sent out are:

x' = 1.15470053837925*(-20) = -23.094010767585
y' = 0
z' = 0
t' = 1.15470053837925*(-0.5*-20/c) = 11.547005383792

B is at rest at the origin in this frame, so naturally if the flash was sent out from position x'=-23.094010767585 and a ray moves towards the origin at 1c, it takes a time of 23.094010767585 for the light to reach B. But the flash wasn't sent out until a time of t'=11.547005383792 in this frame, so naturally it won't reach B until a time of t'=11.547005383792+23.094010767585=34.641016151377. And since B is at rest in this frame, its clock will also read 34.641016151377 when the light reaches it, which is the same (aside from a difference in the last decimal place due to roundoff error) as what we predicted when we calculated things in A's frame.

Now let's figure out what C's clock should read when the light hits it, using C's frame. In A's frame C is moving along the y-axis, so if C uses coordinates x'',y'',z'',t'' then according to the Lorentz transformation these coordinates are related to A's x,y,z,t coordinates by:

x'' = x
y'' = gamma*(y - vt)
z'' = z
t'' = gamma*(t - vy/c^2)

And again we have v=0.5c, and gamma = 1/sqrt(1 - v^2/c^2) = 1.15470053837925. So if we want to know the coordinates of the source sending the flash in C's frame, we take the coordinates in A's frame, x=-20, y=0, z=0, t=0, and plug them into the transformation:

x'' = -20
y'' = 0
z'' = 0
t'' = 0

Very simple in this case! And if light is sent from position x''=-20 at t''=0, while C is at rest at the origin, then obviously if the light moves at 1c in C's frame we will conclude the light hits C at t''=20, and C's clock is keeping pace with coordinate time in this frame so we conclude that C's clock reads 20 at the time the light hits it. Again, this is exactly the same as what was calculated using A's frame.
 
  • #43
Sorry for the delay guys... network difficulties at work...

Also sorry about the NP thing. That means Newtonian Physics.

I see the math you used and personally was agreeing with you up to the point where you started adjusting the times for a "slow factor" This is where you started inserting relativity. (not complaining just noting).

It is interesting that you did not calculate light approaching each object at the speed of light rather you calculated the light speed from teh point at which it was emitted. If relatively all bodies (regardless of velocity) percieve a photon of light approaching them at C then if all objects start their clocks at the same time and are in the same place (such as the beginning of this experiment) then according to that theory all three bodies would percieve the light (according to their own clock) at T=20ls. You math did not reflect that.

Both parts (relative closing speed of light and the formulas you used) are part of relativity theory but have not contradicted each other.

Regardless of that.

We were able to calculate the relative times when each body perceived the light. Let's take the experiment a bit further. Let's say that these photons were completely awesome and they stopped the body from moving upon impact. So at the time and place that they met the body stopped at that point in space (this is just for the thought exp not saying it is possible). All three bodies now form a triangle in a 2d plane.

If you as a person decided to walk (at no dramatic speed) from body A sitting at 0,0,0 (since you changed it) what coords would he reach when he hit B and C? I am not asking how far is B perceived to be from A but how far would one have to go (with their eyes closed) till they hit B from A? Then from B to C and from C to A?
 
  • #44
Physicist1231 said:
Sorry for the delay guys... network difficulties at work...

Also sorry about the NP thing. That means Newtonian Physics.

I see the math you used and personally was agreeing with you up to the point where you started adjusting the times for a "slow factor" This is where you started inserting relativity. (not complaining just noting).
That's what you asked me for, though--you said "I will create a scenario and ask a few questions about the results. You solve for me using Relativity."
Physicist1231 said:
It is interesting that you did not calculate light approaching each object at the speed of light rather you calculated the light speed from teh point at which it was emitted.
No, I first calculated when it would reach each object by assuming light moved at 1c in A's inertial rest frame, but I then showed that if you instead calculated when it would reach B using B's inertial rest frame, assuming the light moved at 1c in B's frame, you get the same answer, and likewise for when it would reach C using C's inertial rest frame. Did you miss the part where I said "Now we can double-check that everything is consistent by analyzing things from the perspective of B's frame, and from C's frame"? Everything after that line was analyzing the scenario in either B's frame or C's frame, not A's frame. And in each case I did explicitly assume that light was moving at a speed of 1c in whatever frame I was using.
Physicist1231 said:
If relatively all bodies (regardless of velocity) percieve a photon of light approaching them at C then if all objects start their clocks at the same time and are in the same place (such as the beginning of this experiment) then according to that theory all three bodies would percieve the light (according to their own clock) at T=20ls. You math did not reflect that.
My math did reflect the fact that each object measures the light approaching them at 1c in their own rest frame, you apparently didn't read the whole thing carefully enough. But this doesn't imply that each one's clock will read T=20 s, you are ignoring the relativity of simultaneity and the different definitions of "distance" in each frame, which implies (as my math showed) that in B's frame the light was not emitted at the same time that B's clock read 0, nor was it emitted at a distance of 20 ls from B in that frame.

If you are confused by the use of the full Lorentz transformation to derive the fact that in B's inertial rest frame the source emits the flash at coordinates x'=-23.094010767585 and t'=11.547005383792, I can derive this more specifically using the equations for time dilation, length contraction and the relativity of simultaneity if you want, just ask. The idea would be to imagine there is a 20 ls long rod at rest relative to A, with one end next to A and the light source sitting at the other end, and with clocks at either end that are synchronized in A's frame, and then to use length contraction to figure out the length of this rod in B's frame, and time dilation and relativity of simultaneity to figure out when the clocks on each end show various readings in B's frame (and what positions they are at in B's frame when they show those reading), including the reading of t=0 that the clock next to the light source shows when the source emits its light (it won't actually show this reading at t'=0 in terms of B's own coordinates, instead the clock at that end of the rod will show a reading of t=0 at a coordinate time of t'=11.547005383792 in B's frame as noted above).

To help understand how the Lorentz transformation relates to the fact that each frame measures the other frame's rulers as length-contracted, and measures the other frame's clocks to be slowed-down and out-of-sync, you might also want to take a look at this thread where I provided some illustrations of two ruler/clock systems moving alongside one another, as perceived in each system's rest frame.
Physicist1231 said:
We were able to calculate the relative times when each body perceived the light. Let's take the experiment a bit further. Let's say that these photons were completely awesome and they stopped the body from moving upon impact.
"Stopped" in what frame? Again there is no notion of absolute space in relativity, and even if you believe in absolute space then it makes no difference to our calculations whether you assume, for example, that A's frame is in motion relative to absolute space or at rest relative to absolute space. So if "stopped" is supposed to be an absolute statement rather than a frame-dependent one, then your question is only answerable if you pick one of the three frames (A's rest frame, B's rest frame or C's rest frame) as being at rest in absolute space, or define some other frame which is supposed to be at rest in absolute space and tell me how it is moving relative to A's frame.
 
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  • #45
JesseM said:
"Stopped" in what frame? Again there is no notion of absolute space in relativity, and even if you believe in absolute space then it makes no difference to our calculations whether you assume, for example, that A's frame is in motion relative to absolute space or at rest relative to absolute space. So if "stopped" is supposed to be an absolute statement rather than a frame-dependent one, then your question is only answerable if you pick one of the three frames (A's rest frame, B's rest frame or C's rest frame) as being at rest in absolute space, or define some other frame which is supposed to be at rest in absolute space and tell me how it is moving relative to A's frame.

So At the beginning of this we determined that all bodies were in the same location and we gave each one a relative motion away from that point (we will say A since he was "at rest"). when i say stopped i mean that there velocity went from X to 0. They ceased to increase distance away from A (whether he perceived it or not). We already determined that A was at rest so any object that is declared motionless would be relative to another motionless object. With that said. When B became "motionless" because the light hit it what was the physical distance between A and B in a straight line? If you walk along that line how far do you go till you hit B? You have no set speed just the direction. You can go as fast or slow (or any mix of the two) in a straight line from A to B. How far do you need to go to hit B from A?

Same thing from B to C and from C to A.

At the end of the day there has to be a set distance that all bodies can agree on because we did the same exact thing at the beginning of this experiment by seperating all three bodies from the light source of 20ls.

The object of these questions is not to determine where each body thinks the other is but rather where each body actually is according to the Coord system where A=0,0,0.
 
  • #46
Physicist1231 said:
So At the beginning of this we determined that all bodies were in the same location and we gave each one a relative motion away from that point (we will say A since he was "at rest").
Right, but we weren't saying A was "at rest" in any absolute sense, we were just defining the motion of B and C in terms of their coordinate speed in A's inertial rest frame. Anyway I take it you are just saying that B and C "stop" in A's rest frame? In that case, since both were moving at a speed of 0.5c, their distance from A in A's rest frame would just be found by taking the coordinate time in A's frame when the light hit them and multiplying that by 0.5c. In A's frame the light hit B at t=40 so the coordinate distance from A at that moment (and the permanent coordinate distance if B immediately comes to rest in A's frame) would be 40*0.5=20 light-seconds, and in A's frame the light hit C at t=23.094010767585, so the coordinate distance from A at that moment would be 23.094010767585*0.5=11.5470053837925 light-seconds. So after B and C stop, if you were to place rulers that reached from A to each of them which were at rest in A's frame, the one from A to B would have a length of 20 light-seconds and the one from A to C would have a length of 11.5470053837925 light-seconds.

Note though that the choice to have them "stop" in A's frame is an arbitrary one, if you had them come to rest in B or C's frame when the light hit them then the final distances would be different.
 
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  • #47
So why are we able to not need reletivistic physics here? would there not have been some Length contractionsduring the movement?

Would these measurements change if taken from B instead? or C?
 
  • #48
Physicist1231 said:
So why are we able to not need reletivistic physics here? would there not have been some Length contractionsduring the movement?
Length contraction only applies when you know a distance between two objects (or two ends of the same object) in the frame where they're at rest, and you want to know the distance between the same two objects in a frame where they're in motion. It doesn't change the fact that if an object is moving at v in some frame, then in time t it will move a distance of v*t in that frame.
Physicist1231 said:
Would these measurements change if taken from B instead? or C?
Are you asking what the distances would be in B's frame if you assume each one comes to rest relative to B's frame when the light hits them (and likewise for C), or do you still want to assume they all come to rest relative to A's frame, but now you want to know the final distances between them in the inertial frame where B was at rest prior to changing velocities and coming to rest in A's frame? Or something else?
 
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  • #49
JesseM said:
Length contraction only applies when you know a distance between two objects (or two ends of the same object) in the frame where they're at rest, and you want to know the distance between the same two objects in a frame where they're in motion. It doesn't change the fact that if an object is moving at v in some frame, then in time t it will move a distance of v*t in that frame.?

You are pointing out that you only need to use Lengh contraction when you "know" an object is in motion. What if you don't "know" it is in motion but is compared to a separate (also unknown) object. The fact that an object would actually change size/shape dependent of the "knowledge" of motion is kinda silly. It does not seem right if you can pick and chose when to use something like Lenth contraction when you "always" take into account Time contraction/expantion (Dilation).

JesseM said:
Are you asking what the distances would be in B's frame if you assume each one comes to rest relative to B's frame when the light hits them (and likewise for C), or do you still want to assume they all come to rest relative to A's frame, but now you want to know the final distances between them in the inertial frame where B was at rest prior to changing velocities and coming to rest in A's frame? Or something else?

It has already been noted and assumed that an object "at rest" compared to another object is at rest. So if C is at rest to A and B is atrest to A then C is at rest to B and B is at rest to C. At rest = 0 relative motion to all parties involved (in this instance only 4 points (if you include the light source [also "at rest"]).
 
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  • #50
In order to solve this problem (the example provided) you need to have some sort of rigid structure of space time.

For instance the assumption that the light was emitted "at the same time" as body B and C were moving is on a rigid strucure. Otherwise you can just comeback with the question "at the same time" to who's frame? That question was never brought up as it is a general assumption under NP and NOT under RP (Relativistic Physics). So at the basis of this experiment we had a rigid assumption of time THEN manipulated it with RP.

If you were to stick with RP and ask the question "at the same time relative to whos frame"? That would be difficult to define but we could say at the referece point of A. If we did that though A would not percieve the light (thus knowing when teh light was emitted) to compare it to the time B and C left A. The same holds true for the view points of B and C since they were with A at the time of interception.

If you were to put the frame at the light source then it emits the light at T=0 and it perceives B and C moving away from A at that point. But there is already a 20 second (give or take given velocities) that these objects have already traveled before the light source realized that B and C moved.

SO. If the proper RP question was asked in the beginning the math would be a little different as you would wind up with different answers depending on your perception. If you did do the math from the light source (as i originally set it up as Light source is at 0,0,0 and at rest) you would find that B would have actually traveled a lot further than the 20ls as predicted. IE, B was in motion but was not perceived to start moving according to the light source for 20s. So B was in motion for a good 20 seconds BEFORE the light was even emitted. Now the light has to traveld the first 20ls to get to where it was before. Then travel the 10ls (initial 20ls travel time at .5c) and then catch up to where the object B.

Instead we set into place a timer that was assumed to be a rigid time structure and same for all parties involved which goes against RP all together.
 
  • #51
Physicist1231 said:
You are pointing out that you only need to use Lengh contraction when you "know" an object is in motion. What if you don't "know" it is in motion but is compared to a separate (also unknown) object.
Huh? In the first sentence are you talking about absolute motion, rather than motion relative to some frame? If not I don't understand what the difference between motion relative to some frame and motion "compared to a separate object" is supposed to be. If the first sentence is talking about absolute motion, I've already told you before that no concepts in relativity have anything to do with absolute motion, so of course that applies to length contraction as well. Even if there was such a thing as absolute motion/absolute rest, it would be utterly irrelevant to relativistic length contraction: an object at rest in the absolute sense would appear shorter in the frame of an observer in absolute motion, and an object in absolute motion would appear shorter in the frame of an observer at absolute rest, all that matters is their relative velocity. (If you believe in absolute space, there would of course be an absolute truth about whose meter-stick was longer and whose was shorter, but the observer with the absolutely shorter meter-stick would still measure the other meter-stick to be shorter than his own, because he's making "simultaneous" measurements of either end with clocks that are out-of-sync in an absolute sense. The diagrams in this thread can be used to illustrate this, just imagine that one frame's perspective is the true "absolute" frame, you can see nevertheless that their measurements of one another are totally symmetrical...I can elaborate on this if you wish.)

Also, if you ever use the words "moving" to refer to absolute motion, please make this clear by specifically using a phrase involving "absolute" like "absolute motion" or "moving in an absolute sense", otherwise your posts get very confusing.
Physicist1231 said:
The fact that an object would actually change size/shape dependent of the "knowledge" of motion is kinda silly.
I don't know what you mean by "actually". In a frame where the object is moving, the coordinate distance between ends of the object at a particular moment in coordinate time is shorter than the coordinate distance between ends in the frame where the object is at rest. There is no notion of the "actual" length of any object independent of how it's described in any given coordinate system.

In relativity each frame defines length in terms of simultaneous measurements of either end of the object, but different frames define simultaneity differently, so you can partially understand the different lengths in different frames by realizing that different frames are taking different 3D "cross sections" of the same 4D world-tube. If you think of a 2D spacetime diagram where we just consider one space dimension, it's easier to visualize, see the diagram on http://www.anselm.edu/homepage/dbanach/st.htm:

st11.jpg


Here the two long slanted lines represent the worldlines of the front and back of the rod. A is an event at the back end of the rod, and B and C are two events at the front end of the rod. In the frame of the observer X whose coordinates are being represented in this diagram, A and B are simultaneous (they are at the same vertical height in the diagram, and the vertical axis represents time), so the "length" of the rod in this frame is the distance from A to B. But in the rod's rest frame, A and B are not simultaneous, rather A is simultaneous with C, so the "length" in the rest frame is the distance from A to C. You can see that the distance AB is shorter than the distance AC, so the rod is contracted in the observer's frame (there is a subtlety in that if we actually drew "ticks" of some fixed distance like 1 meter on lines of constant time in both frames, the distance between ticks wouldn't appear the same in this diagram, but still the diagram gives a qualitative sense of why the length of the rod is different in the two frames).

In ordinary 3D Euclidean geometry, we could similarly create different Cartesian coordinate systems and use them to find cross-sections of constant z-coordinate of some solid object like a cylinder (intersections of the cylinder with the xy plane of each coordinate system). If two different coordinate systems had their axes at different angles, then each one's xy plane would intersect the cylinder at different angles, and thus the concept "area of a 2D cross-section of constant z-coordinate" for the cylinder would be different in the two coordinate systems. Do you think there must be an "actual" value for "area of a 2D cross-section of constant z-coordinate" that's independent of what coordinate system we choose? Probably not. So, I don't see why you should have a problem with the analogous notion that there is no "actual" value for "distance between ends of an object at a single t-coordinate", independent of what frame's definition of simultaneity we choose.
Physicist1231 said:
It does not seem right if you can pick and chose when to use something like Lenth contraction when you "always" take into account Time contraction/expantion (Dilation).
Not sure what you mean, length contraction always applies to the coordinate distance between ends of an object moving inertially, just like time dilation always applies to the coordinate time between ticks of a clock moving inertially. If we have an object moving at velocity v in our frame, and we want to know the distance D an object travels in a time T in terms of our frame's coordinates, then no length contraction is figured into D and no time dilation is figured into T, the answer is just D=v*T. This is really true by definition, since we define velocity in a given frame by [change in position]/[change in time] in terms of the coordinates of that frame, no distances and times from other frames (or other rulers and clocks not at rest in that frame) are relevant to the definition of velocity.
JesseM said:
Are you asking what the distances would be in B's frame if you assume each one comes to rest relative to B's frame when the light hits them (and likewise for C), or do you still want to assume they all come to rest relative to A's frame, but now you want to know the final distances between them in the inertial frame where B was at rest prior to changing velocities and coming to rest in A's frame? Or something else?
Physicist1231 said:
It has already been noted and assumed that an object "at rest" compared to another object is at rest. So if C is at rest to A and B is atrest to A then C is at rest to B and B is at rest to C. At rest = 0 relative motion to all parties involved (in this instance only 4 points (if you include the light source [also "at rest']).
No, because there is an objective difference between case #1 where B and C accelerate to come to rest relative to A while A continues to move inertially, and case #2 where A and C accelerate to come to rest relative to B while B continues to move inertially, and case #3 where A and B accelerate to come to rest relative to C while C continues to move inertially. Not all types of motion are "relative" in relativity, if the relative velocity between two objects changes there is an objective truth about which one accelerated (the one that accelerated will feel G-forces which can be measured with an accelerometer), this is crucial to defining the difference between "inertial frames" (where the usual equations of SR, like the time dilation equation, are intended to apply) and "non-inertial frames" (where these equations don't apply, and light generally doesn't even have a constant coordinate speed of c). The objective difference between inertial and accelerated motion is also crucial to understanding the twin paradox, since otherwise you could say that each twin viewed themselves at rest the whole time while the other moved away and back, and then you'd (falsely) conclude that each twin should predict the other will be younger when they reunite.
 
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  • #52
If we followed NP and assumed that time and space are rigid strucures then the math is pretty easy. Since you did most of it I will not hog up the space in the forum.

with the Light source at rest at 0,0,0

the end results:

A
Location: 20,0,0
Time of impact: T=20s

B
Location: 30,0,0
Time of impact: T=40s

C
Location: 0,11.547,0
Time of impact: T=23.09401077

This still shows that since B and C were in motion they pervieved the same action at a different time and physically separate and calulateable positions that hold true even if you were to place Origin (0,0,0) in a separate location.
 
  • #53
I think we are getting confused as to wether or not there is such thing as absolute motion. Can an object be in motion if there is no other reference point other than itself. This object sees no other objects, no other mass or gravity. He is feeling no acceleration.

Personally I say yes but i have noted where you say there is not such. I wanted to get that cleared up so we are on the same page.
 
  • #54
Physicist1231 said:
In order to solve this problem (the example provided) you need to have some sort of rigid structure of space time.
By "rigid" do you just mean absolute? Each frame's coordinates can be defined in terms of readings on a rigid grid of rulers with clocks placed at each grid intersection, but I don't think that's what you mean. Again, please use the word "absolute" in your posts when you're referring to absolute notions of motion, rest, etc. so they'll be more clear.
Physicist1231 said:
For instance the assumption that the light was emitted "at the same time" as body B and C were moving is on a rigid strucure. Otherwise you can just comeback with the question "at the same time" to who's frame?
Except you didn't say originally that the light was emitted "at the same time" in an absolute sense as A,B,C being at the same position, instead you said that the light was emitted at T=0 in the same frame where A remained at position 0,0,0 while B and C moved at 0.5c:
Time:
T=0

Positions: Units in light seconds
A light source at 0,0,0
Body A, B and C are at coord 20ls,0,0

Velocities:
Body A remains at 20ls,0,0
Body B has a speed of .5c,0,0
Body C has a speed of 0,.5c,0

Light is emitted from the source at T=0 and at this time Body B and C start their motion.
This is a well-defined problem which doesn't require that we believe that the light was emitted "at the same time" in an absolute sense as the event of the positions of A,B,C coinciding. Even if you believe in absolute space and absolute simultaneity, the answer would be the same even if this frame was moving in an absolute sense and its definition of simultaneity was incorrect in an absolute sense.
Physicist1231 said:
If you were to stick with RP and ask the question "at the same time relative to whos frame"? That would be difficult to define but we could say at the referece point of A. If we did that though A would not percieve the light (thus knowing when teh light was emitted) to compare it to the time B and C left A. The same holds true for the view points of B and C since they were with A at the time of interception.
The coordinates that an event happens in a given frame are not based on when an observer in that frame perceives the event. For example, if in t=2011 I see the light from an event, and I can see that in my frame the event happened at a distance of 10 light-years in my frame, I will retroactively say this event occurred at a time coordinate of t=2001 in my frame. In most textbooks (and in Einstein's original paper) the coordinates of the frame are defined using a hypothetical grid of rulers and clocks at rest in that frame, with the clocks "synchronized" in that frame using the Einstein clock synchronization convention. Once you have such a grid, the coordinates of each event can be assigned in a local way, by looking at the marking on the ruler that was right next to the event when it happened, and looking at the reading on the clock that was attached to that marking at the moment it happened. So in the above example, even though I didn't see the event until t=2011, sitting at the x=0 light year mark on my ruler, when I look through my telescope I can see that the event happened right next to the x=10 light year mark on my ruler, and that the clock at that mark showed a reading of t=2001 at the moment the event happened next to it.
Physicist1231 said:
If you were to put the frame at the light source
A frame is not "at" a particular position, it's a coordinate grid that fills all of space. I suspect your comment here has something to do with the incorrect notion that the time an event occurs is determined by when an observer at the origin sees it, in which case it would matter where you placed the origin, but as I said above it doesn't work that way.
Physicist1231 said:
SO. If the proper RP question was asked in the beginning the math would be a little different as you would wind up with different answers depending on your perception.
My math was correct for the problem as stated, if you disagree you are misunderstanding basic aspects of relativity, please show a little intellectual humility and consider the possibility that you might actually learn something from my answers as opposed to lecturing me based on your own misconceptions about a subject you obviously haven't studied in any detail.
 
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  • #55
Physicist1231 said:
I think we are getting confused as to wether or not there is such thing as absolute motion.
My point is that absolute motion is irrelevant to relativity, even if there is some absolute truth about the matter. It is possible to have an "interpretation" of relativity which does assume an absolute truth about motion, distances and times, for historical reasons this is called a type of "Lorentz ether theory", but here the absolute truths are purely metaphysical and undetectable by any conceivable experiment, since the laws of physics still work the same way in different relativistic inertial frames.
Physicist1231 said:
Can an object be in motion if there is no other reference point other than itself.
What does "in motion" mean? Are you talking about absolute motion, or a frame-dependent idea of motion? In either case it seems to me the answer would be yes, if there is such a thing as absolute space we can imagine a single object moving relative to it, and in relativity inertial frames are just coordinate systems, you don't need for there to be any real physical object at rest in frame X in order to use the coordinates of frame X for the purposes of a calculation.
 
  • #56
JesseM said:
By "rigid" do you just mean absolute? Each frame's coordinates can be defined in terms of readings on a rigid grid of rulers with clocks placed at each grid intersection, but I don't think that's what you mean. Again, please use the word "absolute" in your posts when you're referring to absolute notions of motion, rest, etc. so they'll be more clear.

I guess we can use the term absolute in this sense. I am trying to express a non flexiblity of time and space where the distance between two coords (and the time it takes to get there at a certian velocity) is the same regardless of where the origin (0,0,0) is located. These measurements are not bent or altered by perception.

JesseM said:
Except you didn't say originally that the light was emitted "at the same time" in an absolute sense as A,B,C being at the same position, instead you said that the light was emitted at T=0 in the same frame where A remained at position 0,0,0 while B and C moved at 0.5c:.


Actually what I said was "Light is emitted from the source at T=0 and at this time Body B and C start their motion."

So I did say that they were at the same time. You either assumed that it was an absolute time (which is why I did not specify according to whom). For the correct relative math to be done you needed to know that it was the simultanious to a certian reference point. You did not take that into account. Personally I agree with the ability of having an Absolute Time and Space usage and know that these can be calcuated without being skewed by perception.

JesseM said:
This is a well-defined problem which doesn't require that we believe that the light was emitted "at the same time" in an absolute sense as the event of the positions of A,B,C coinciding. Even if you believe in absolute space and absolute simultaneity, the answer would be the same even if this frame was moving in an absolute sense and its definition of simultaneity was incorrect in an absolute sense.

You are not correct on that notion. If you have this whole setup in motion (though the measurements are not moving relative to each other, IE Light source and A remain 20ls distance apart). By simply adding a new reference point and declaring THAT point as motionless you then need to alter your formulas to account for this new speed percieved. Thus a difference in formulas all because someone else said the objects were in motion. Now if you believed in Absolute Space and Time then it would not matter the reference point. So long as you know the velocities of all parties and the distance between them you can calculate all perceptions with the same formula.

JesseM said:
A frame is not "at" a particular position, it's a coordinate grid that fills all of space. I suspect your comment here has something to do with the incorrect notion that the time an event occurs is determined by when an observer at the origin sees it, in which case it would matter where you placed the origin, but as I said above it doesn't work that way.

You are partly correct. The actual time the event occurred is NOT the time it was percieved. However, one would need to calculate the time delay it takes from the event to start to when the reference point begins to percieve. To do this you need to know the velocities and distances on a rigid and stationary coordinate system. Should you chose to calculate the end of an event (say a second wave of light sent out 6 minutes later) you can then compare the perceived start time and perceived end time to come up with how long a perciever perceived the event.

JesseM said:
My math was correct for the problem as stated, if you disagree you are misunderstanding basic aspects of relativity, please show a little intellectual humility and consider the possibility that you might actually learn something from my answers as opposed to lecturing me based on your own misconceptions about a subject you obviously haven't studied in any detail.

Not really saying that your math was off, however. It had a faulty setup (which was intentional) to see if the correct questions would be asked to get the correct relativisic answers. Given what you know about relativity your math was correct. No arguments there.
 
  • #57
Physicist1231 said:
I guess we can use the term absolute in this sense. I am trying to express a non flexiblity of time and space where the distance between two coords (and the time it takes to get there at a certian velocity) is the same regardless of where the origin (0,0,0) is located.
Well that's true if you are just talking about inertial coordinate systems which are at rest relative to each other but have the origin at different locations. On the other hand, if you're talking about different inertial coordinate systems in motion relative to each other, then of they can disagree about the distance and time between two events, although they agree on the proper time experienced by an object which travels from one event to the other (assuming the events have a time-like separation so it is possible to travel from one to the other moving slower-than-light)
Physicist1231 said:
Actually what I said was "Light is emitted from the source at T=0 and at this time Body B and C start their motion."

So I did say that they were at the same time. You either assumed that it was an absolute time (which is why I did not specify according to whom).
No, I assumed it was not absolute time, I assumed "at this time" still meant the coordinate time T=0. That's why I said the problem was solvable in relativity, because your statement of the problem only involved coordinate times and velocities.
JesseM said:
This is a well-defined problem which doesn't require that we believe that the light was emitted "at the same time" in an absolute sense as the event of the positions of A,B,C coinciding. Even if you believe in absolute space and absolute simultaneity, the answer would be the same even if this frame was moving in an absolute sense and its definition of simultaneity was incorrect in an absolute sense.
Physicist1231 said:
You are not correct on that notion.
Yes, I am, since the "answer" I was talking about was just about what coordinates would be assigned to events in A's frame, and what times various clocks would read when light hit them. I wasn't talking about answers to any questions involving the Absolute distance or Absolute time between different events.
Physicist1231 said:
If you have this whole setup in motion (though the measurements are not moving relative to each other, IE Light source and A remain 20ls distance apart). By simply adding a new reference point and declaring THAT point as motionless you then need to alter your formulas to account for this new speed percieved.
In relativity it's irrelevant whether A's frame is moving or at rest relative to some other "reference point" (even if we assume the "reference point" is at rest in an absolute sense while A is moving in an absolute sense), all that is needed to solve the problem is the coordinates of events in A's frame. As long as it's still true in A's frame that the flash is emitted at T=0 at spatial coordinates -20,0,0 and that at T=0 A,B,C are all located at spatial coordinate 0,0,0, and that A has a velocity of 0 in this frame while B has a velocity of 0.5c along the x-axis in this frame, and C has a velocity of 0.5c along the y-axis in this frame, then this is sufficient to solve the problem of how much proper time A,B,C would experience between departing from one another and receiving the light, and it would also be sufficient to figure out the coordinate position and coordinate time that each receives the light in A's frame.
Physicist1231 said:
Thus a difference in formulas all because someone else said the objects were in motion.
Are you talking about calculating things from the perspective of the rest frame of this "someone else"? In this case of course the coordinates of various events would be different in this "someone else's" frame, but the physical question of how much time would elapse on each clock between the time A,B,C departed and the time they received the light would have exactly the same answer. Also if we found the coordinates of events in this frame, and applied the Lorentz transformation to them using the relative velocity between this frame and A's frame, we would get back the coordinates of the events in A's frame. So considering the perspective of this "someone else" makes no difference to questions about what coordinates are assigned to events in A's own frame, or questions about local frame-independent facts like what a clock reads when light first reaches it.
Physicist1231 said:
Now if you believed in Absolute Space and Time then it would not matter the reference point. So long as you know the velocities of all parties and the distance between them you can calculate all perceptions with the same formula.
I don't know what you mean by "perceptions". Are you talking about local facts which are the same in each frame, like what a particular physical clock reads at the moment some light first strikes it? Or are you talking about the values of coordinate-dependent quantities like coordinate speed and coordinate time in some particular choice of frame? Or something else? If it's either of the first two, then the values of both these things can be calculated without knowing anything about Absolute Space and Time, and the answers could be calculated in some frame without it being remotely relevant whether that frame was itself moving relative to some other "reference point".
JesseM said:
A frame is not "at" a particular position, it's a coordinate grid that fills all of space. I suspect your comment here has something to do with the incorrect notion that the time an event occurs is determined by when an observer at the origin sees it, in which case it would matter where you placed the origin, but as I said above it doesn't work that way.
Physicist1231 said:
You are partly correct. The actual time the event occurred is NOT the time it was percieved.
Don't know what you mean by "actual time". I was referring to the coordinate time of that the event occurred in a particular frame, my point was that this coordinate time of the event itself is not the same as the coordinate time when some observer at rest in the frame sees the light from the event.
Physicist1231 said:
However, one would need to calculate the time delay it takes from the event to start to when the reference point begins to percieve. To do this you need to know the velocities and distances on a rigid and stationary coordinate system.
I still don't know what you mean by "rigid and stationary". Do you mean "stationary" in an absolute sense, or just stationary relative to the reference point? If you mean it in an absolute sense, please keep in mind the request I made in an earlier post:
Also, if you ever use the words "moving" to refer to absolute motion, please make this clear by specifically using a phrase involving "absolute" like "absolute motion" or "moving in an absolute sense", otherwise your posts get very confusing.
Please extend this request to any concept that you mean in an absolute sense, like "stationary", "at the same time", "time delay" etc.

Anyway, if we just want to calculate the "time delay" between the event and the observer seeing the event in the observer's own rest frame, not in any absolute sense, then the answer doesn't depend on the observer's velocity in an absolute sense. In relativity it is true in all frames that light has a coordinate velocity of c, so the coordinate time between two events (in this case, between the light being emitted and the observer receiving the light) is always equal to the coordinate distance divided by c. So, if we have a ruler at rest relative to the observer, and the observer is standing at the x=0 mark and can see through his telescope that an explosion happened right next to the x=10 light-years mark, then he knows that the time delay in his frame between the explosion itself and his seeing the light from the explosion must have been 10 years. This may not be the "time delay" in Absolute Time, but that's irrelevant if all we want to know is the time delay in the coordinates of the observer's own frame.
Physicist1231 said:
Not really saying that your math was off, however. It had a faulty setup
In what way was it "faulty"? You gave the initial coordinate times, coordinate positions and coordinate velocities in terms of the frame where A was at rest, this was sufficient to calculate the coordinate positions and times of later events in A's frame, and also sufficient to calculate the frame-independent truth about what each clock would read at the moment the light struck it. In relativity none of these answers would change if we were told A was moving relative to Absolute Space, or if we were told A was at rest in Absolute Space.
 
  • #58
JesseM,

You assumed that T=0 then according to the light source (according what my ambiguity). If that is the case how did you come to the determination that T=0 when the bodies A, B and C split up unless you were using an absolute time (or absolute distance) to go by?
 
  • #59
Physicist1231 said:
JesseM,

You assumed that T=0 then according to the light source (according what my ambiguity).
I don't understand this sentence, "according to the light source" what?
Physicist1231 said:
If that is the case how did you come to the determination that T=0 when the bodies A, B and C split up unless you were using an absolute time (or absolute distance) to go by?
You're not really making sense, if I had assumed that they all split up simultaneously with the light emission in terms of absolute time, then I would have no reason to believe they split up at T=0! After all there is no reason to believe that the definition of simultaneity in A's rest frame (the one that uses the time coordinate T) matches up with absolute simultaneity, if such a thing exists. It's only because I assumed you weren't talking about absolute simultaneity, but just meant "at the same time" in the same coordinate system that all your other statements were using, that I concluded it was a well-defined problem.

Anyway, the language of your statement did seem to suggest you meant that they split up at T=0 in A's frame:
Light is emitted from the source at T=0 and at this time Body B and C start their motion.
This would be an extremely weird sentence if right in the middle you switched from talking about coordinate time to absolute time! I assumed that since you were giving me the coordinate time of light being emitted, then when you said "at this time" you still meant a coordinate time of T=0. There was nothing to suggest that you were claiming that "Body B and C start their motion" at the same absolute time as the light being emitted, which might be at a completely different T-coordinate if this frame's definition of simultaneity doesn't match with absolute time.
 
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  • #60
JesseM said:
I don't understand this sentence, "according to the light source" what?

You're not really making sense, if I assumed it they all split up simultaneously with the light emission in terms of absolute time, then I would have no reason to believe they split up at T=0! After all there is no reason to believe that the definition of simultaneity in A's rest frame (the one that uses the time coordinate T) matches up with absolute simultaneity, if such a thing exists. It's only because I assumed you weren't talking about absolute simultaneity, but just meant "at the same time" in the same coordinate system that all your other statements were using, that I concluded it was a well-defined problem.

Anyway, the language of your statement did seem to suggest you meant that they split up at T=0 in A's frame:

This would be an extremely weird sentence if right in the middle you switched from talking about coordinate time to absolute time! I assumed that since you were giving me the coordinate time of light being emitted, then when you said "at this time" you still meant a coordinate time of T=0. There was nothing to suggest that you were claiming that "Body B and C start their motion" at the same absolute time as the light being emitted, which might be at a completely different T-coordinate if this frame's definition of simultaneity doesn't match with absolute time.

T=0 was honestly supposed to be Absolute Time but you took it as a coord time for reference A. Where according to my original setup it was T=0 and all was in relation to the light source. (hence why the light source in the original setup was 0,0,0) It does seem there was confusion as to where T=0 at.

I left this ambiguous to come to one of two conclusions about T=0.

1. T=0 in the absolute sense and for all parties

or

2. T=0 in the frame of the light source.

It was not my intent to make it T=0 (in a coord sense) for the frame A. Instead the setup was changed (by you [not making an accusation just pointing out]) to make A be at 0,0,0 and T=0 according to A.

So two things happened. First the origin (0,0,0) was changed by you, and it seems I left the interpretation for T=0 too open.

That seems to be our issue.
 
  • #61
Well, hopefully you understand that moving the spatial origin is completely irrelevant if we are trying to find the spatial distances or time intervals between events (in coordinate terms or absolute terms), so that change is totally trivial. But if T=0 was meant to be absolute time, in that case there is no way to solve your problem with the information given, because then we don't know the coordinate time interval between the light emission and the separation of A,B,C, nor do we know the absolute distance between them or the absolute velocities of A,B,C.
 
  • #62
JesseM said:
Well, hopefully you understand that moving the spatial origin is completely irrelevant if we are trying to find the spatial distances or time intervals between events (in coordinate terms or absolute terms), so that change is totally trivial. But if T=0 was meant to be absolute time, in that case there is no way to solve your problem with the information given, because then we don't know the coordinate time interval between the light emission and the separation of A,B,C, nor do we know the absolute distance between them or the absolute velocities of A,B,C.

Absolutly we could. Let's assume (just assume) that there is Absolute time and Absolute space (thus absolute velocities as well)

If the light source was at absolute rest at 0,0,0 and all three bodies are at 20ls,0,0 at the absolute T=0.

At T=0 absolute time the light is emitted and the bodies assume their respective velocities. we will find that light hits

A at T=20s and 20ls,0,0

B at T=40s and 40ls,0,0

C at T=T=23.09401077s and 20ls,11.547ls,0

This would be in the absolute time and space coords. Now still using Newtonian physics you can determine the absolute time that A perceives that B and C see the light.

According to A, B saw the light at the absolute T=60s (the time it took from the light source to hit B and back to A) at coord 20ls,0,0 (relative to A)

According to A, C saw the light at the absolute T=34.6***ls. and at the point 0,11.547ls,0 (relative to A)


B would have a different view on when in absolute time the events happened as well. So would C.

If anything using Absolute time and Spacial assumptions makes the math not only easier to comprehend but still explain why bodies in motion see things at different times and possibly different orders.
 
  • #63
Physicist1231 said:
Absolutly we could. Let's assume (just assume) that there is Absolute time and Absolute space (thus absolute velocities as well)

If the light source was at absolute rest at 0,0,0
Now you're changing the conditions! Of course if you specify that the frame in which A is at rest (the one where A's position coordinates don't change with time) is the absolute frame, then the problem is solveable. But there was nothing to indicate that in your original explanation.
Physicist1231 said:
At T=0 absolute time the light is emitted and the bodies assume their respective velocities. we will find that light hits

A at T=20s and 20ls,0,0

B at T=40s and 40ls,0,0

C at T=T=23.09401077s and 20ls,11.547ls,0

This would be in the absolute time and space coords. Now still using Newtonian physics you can determine the absolute time that A perceives that B and C see the light.

According to A, B saw the light at the absolute T=60s (the time it took from the light source to hit B and back to A) at coord 20ls,0,0 (relative to A)
Your use of the phrase "according to A" is a little confusing--normally that phrase means "the coordinate time in A's rest frame when the event happened", not the time that A saw the light from the event. But yes, A will see the light from the event of B receiving the light (perhaps B signals this by waving a flag) at T=60s.
Physicist1231 said:
B would have a different view on when in absolute time the events happened as well. So would C.
How can B have a different view on when in absolute time events happened? Absolute time is independent of the observer, by definition. Do you just mean the time that B sees the light from different events will be different? i.e. B agrees that the light reached C at an absolute time of T=23.09401077s, but the time that B sees the light from this event is different from the time that A sees the light from this event?
Physicist1231 said:
If anything using Absolute time and Spacial assumptions makes the math not only easier to comprehend but still explain why bodies in motion see things at different times and possibly different orders.
I don't think that's true, the math is exactly the same if you just assume we're calculating things in A's frame without worrying about absolute space and time. The problem with the notion of absolute space and time is that it obscures the complete physical symmetry between the way the laws of physics work in different frames, and the fact that even if absolutes space & time existed it would be totally impossible to determine which frame was the absolute one by any physical experiment.
 

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