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goodabouthood
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Reference frames change according to motion?
Also what does it mean by -.5c?
I am referring to the diagram I posted above.
Also what does it mean by -.5c?
I am referring to the diagram I posted above.
goodabouthood said:Reference frames change according to motion?
Also what does it mean by -.5c?
I am referring to the diagram I posted above.
ghwellsjr said:No, it's not relative. As I said in post #47:
As far as the gravitational contribution to time dilation goes, yes. During the long orbital times of the two planets, there would be other variations in the observed differences in the clocks but these would average out so that every time the two planets are in the same relative position in the solar system, there will be a steadily increasing time on the Earth clock compared to the Jupiter clock.
You get to define a reference frame any way you want (as long as you follow Einstein's convention).goodabouthood said:Well, what exactly defines a reference frame?
There are an infinite number of reference frames possible but until we express a definition for one, it doesn't exist. It only exists in our minds not out there is space.goodabouthood said:Are there infinite number of reference frames?
Part of the answer comes from our choice, the other part of the answer comes from the way nature works.goodabouthood said:Why do different reference frames have different coordinates?
Yes.goodabouthood said:Also, are these infinite set of clocks in each reference frame always synchronous?
OK, that might help you understand what we're talking about.goodabouthood said:Can you give me an example of the coordinates of the reference frame of the train and the coordinates of the reference frame of the ground?
I'm also going to assume that the platform is 1000 feet long.goodabouthood said:So for simplicity's sake, let's say that the speed of light is 1 foot per nanosecond and let's say the train is traveling at 0.6c and it is 1000 feet long.
The Lorentz Transform converts the coordinates of any event in one Frame of Reference to the correct coordinates of another Frame of Reference moving with respect to the first Frame of Reference. A value of -.5c simply means the second FoR is moving at .5c along in the -X direction instead of the +X direction.goodabouthood said:Reference frames change according to motion?
Also what does it mean by -.5c?
I am referring to the diagram I posted above.
If you mean the values of the coordinates are different and if the reference frames are in relative motion, then almost always the values of the coordinates will be different, so in general, yes. But it's always the same event, no matter what FoR we use to describe it.goodabouthood said:Is it correct to say this?
The space and time of an event is different for all reference frames.
If the time coordinates for the two events in a given FoR are equal, then the events are simultaneous. Even if the train stopped somewhere before it got to the platform or somewhere after and so the observer on the train doesn't see the lightning flashes coincidently like the observer at the midpoint of the platform who does see the flashes coincidently, they are still simultaneous because simultaneity has nothing to do with what anybody actually sees. So they both agree and so do all of us watching this scenario that the lightning flashes are simultaneous in the given FoR.goodabouthood said:Now what about this?
If the train happened to be still and the observer on the ground happened to be still. They both were just at their places with a velocity = 0. Would they both agree that the lightning bolts were simultaneous since they are both at rest?
Everybody and everything is in all Frames of Reference. If they are both at rest in one ground Frame of Reference, then they are both at rest in all ground Frames of Reference.goodabouthood said:Would they be in the same frame of reference?
ghwellsjr said:This thread is about the meaning of simultaneity. The purpose of the train example is to show that in one Frame of Reference (where the ground is at rest), the two lightning bolt events that occur at different locations nevertheless occur at the same time, not because nature demands it, but because the clocks that are located at those two events have been previously synchronized and the problem is stated such that they are simultaneous. That's one point to focus on.
ghwellsjr said:The second point to focus on is that the events defined according to one FoR need to be at different locations, otherwise two events at the same location and the same time are not two events but one event (they have the same four coordinates).
ghwellsjr said:The third point to focus on is that in many other FoR's (not all, just some), those same two events, when transformed into a set of new coordinates will have a totally different set of four coordinates and the time components may be different in which case they are not simultaneous in that FoR.
ghwellsjr said:But the gal on the train and the guy on the platform are both living in the same world. There's only one world.
ghwellsjr said:The issue is how we describe the 3 spatial coordinates and the 1 time coordinate that define an event--what numbers do we (and they) use? The gal on the train can use a Frame of Reference where the ground is stationary (of which there are an infinite such FoR's) and in which the two events will be simultaneous and the guy on the platform can use a FoR in which the train is stationary (of which there are an infinite such FoR's) and in which the two events will not be simultaneous. But whichever FoR is used, it includes everyone and every thing.
ghwellsjr said:People, other observers and objects don't own their own FoR to the exclusion of the other observers and objects. And it's the FoR that determines if two events are simultaneous not any observers or objects no matter what their states of motion are.
So it's really wrong when discussing the meaning of simultaneity in Special Relativity to link it to particular observers or especially to say that one person lives in a different 3-D world than another one and that's what determines the simultaneity of events, it should only be linked to particular FoR's.
goodabouthood said:How about this?
My friend and I are sitting still on the ground and we see a moving train come by at uniform motion. A flash of lightning hits each end of the train. Now me and my friend will still have different frames of reference even though we are both not moving. Right?
I know we would have different spatial differences but would we still agree on the simultaneity of the lightning because we are both still relative to the ground?
What I mean to say is would our time differences change as well even though we are both still?
A Frame of Reference is nothing more than a coordinate system with time included but with the remote clocks synchronize according to Einstein's convention.goodabouthood said:I appreciate the answers you are giving me. I am still taking some time to digest what you have said.
I think I am having trouble seeing what a frame of reference really is.
Well how about that? I'm sitting still in my chair looking at my computer, too. Since we are both sitting still at different places on the surface of the Earth (I presume you're on the Earth and not up in the space station) we can define a common rest frame that includes both of us. There's already a coordinate system for the surface of the Earth that we could use that includes lattitude and longitude and latitude. I can look on my GPS receiver and see what my spatial coordinates are and you could do the same thing. We also have standard time here on the Earth (GMT) and we could use that for our time coordinate. My GPS receiver will tell me the local time but it is easy enough to calculate GMT. Since GPS has already done the work of synchronizing time for both of us, we don't have to worry about that. Note that if we define or common Frame of Reference this way, it will be very difficult to use the Lorentz Transform because we need both the time and the spatial coordinates to have a common origin. But my point is to show you the arbitrariness of establishing a Frame of Reference and to show that it doesn't have to be linked to either one of us.goodabouthood said:For example, right now I am sitting still in my chair looking at my computer. What would be my frame of reference?
Yes, but not just motion and postition but also directional orientation, although if two reference frames differ by only position or directional orientation (but not motion) then any events that are simultaneous in one will also be simultaneous in the others.goodabouthood said:Another question I have is do different reference frames depend on both motion and position or just motion?
But like I said earlier, your friend sitting next to you is in whatever frame of reference you define and you are in what ever frame of reference he cares to define but you are both at rest in the frames you each define, then you both are at rest in both frames.goodabouthood said:I imagine position changes the frame of reference as well. If my friend was sitting still next to me we would still have different frames of reference even though we are both stationary.
And relative to your floor, the Sun is moving. All states of motion are relative to something, whether that something be another object, a defined Reference Frame, or even a previous state of an object that has accelerated.goodabouthood said:I also know that there really is nothing that is still. It's all relative. Relative to my floor I am still but relative to the Sun I am moving.
goodabouthood said:I know some of these questions might be a bit obvious to some but I just need to ask them and hope they might help others as well.
Thanks.
You don't have to have different Frames of Reference. You can both be at rest in a single frame of reference and differ by your location coordinates which never change. Let's say that you are sitting near where one flash of lightning strikes the front of the train (with an X coordinate of 500 feet) and your friend is sitting near the rear of the train (with an X coordinate of -500 feet) where the second flash of lightning strikes. Now you will each see the lightning that struck near you first and then later see the other one. So you will see the flashes in a different order. But this has no bearing on whether the two flashes were simultaneous in your chosen common Frame of Reference. What matters is what the pre-synchronized clocks read at the locations of the lightning strikes. If they read the same time, then the strikes were simultaneous, otherwise they were not simultaneous.goodabouthood said:How about this?
My friend and I are sitting still on the ground and we see a moving train come by at uniform motion. A flash of lightning hits each end of the train. Now me and my friend will still have different frames of reference even though we are both not moving. Right?
If you had a common rest reference frame, then if your friend synchronized all the clocks to the one closest to him, then the one closest to you will also be synchronized to all the other clocks which include his.goodabouthood said:I know we would have different spatial differences but would we still agree on the simultaneity of the lightning because we are both still relative to the ground?
What I mean to say is would our time differences change as well even though we are both still?
It's motion of Frames of Reference that matter, not of any people who may or may not be at rest or in motion in any particular frame. Remember, everyone and everything is in every Frame of Reference. Events are defined by Frames of Reference not by people observing things differently.goodabouthood said:The graphs are helping.
I am taking it that motion is what will really make people disagree on events and not spatial differences.
Only in a Frame of Reference in which they are at rest. In other frames, the same events could happen at different times.goodabouthood said:For instance if the two people sitting still always stay still they will always agree on the simultaneity of events. Am I correct in saying this?
You have to quit thinking in terms of the events being seen by people remotedly located from the events. It has nothing to do with how people see things, it has only to do with the times on the synchronized clocks colocated with the events.goodabouthood said:Also considering time slows down as you speed up wouldn't the event at E3 be seen after for a moving observer than for the two people staying still?
Here are a few sketches to help with graphically visualizing motion in 4-dimensional space. Before (earlier post) we had the red guy sitting still with the black guy. Now, we put the red guy in motion. He is moving along the black guy's X1 axis. In the upper left corner sketch you can see that the farther red advances in time along the red time axis--the farther red advances along the black X1 axis. He advances to a point, XA, by the time black's clock is time, t. The speed calculation is shown below the sketch.goodabouthood said:The graphs are helping.
I am taking it that motion is what will really make people disagree on events and not spatial differences.
For instance if the two people sitting still always stay still they will always agree on the simultaneity of events. Am I correct in saying this?
Also considering time slows down as you speed up wouldn't the event at E3 be seen after for a moving observer than for the two people staying still?
goodabouthood said:I am taking it that motion is what will really make people disagree on events and not spatial differences.
goodabouthood said:Thanks.
But why do the red coordinates shift in the particular way they do?
goodabouthood said:Also what is the purpose of the photon?
goodabouthood said:Also do you mean that time at tB is one second for red?
goodabouthood said:Is it possible you could draw out the time and space numbers for both sets of coordinates? Thanks.
BruceW said:These graphs show us how the position and time of some event are interchangeable depending on the reference frame used.
In the original (green) reference frame, an event might be given as [itex](x,t)[/itex] and in the new (red) reference frame, the same event might be denoted by [itex](x',t')[/itex]. So what we're saying is that the spatial coordinate and the time for an event are not absolute. Each can change depending on the speed of the reference frame used.
But one thing that is absolute is the quantity [itex]x^2 - c^2t^2[/itex]. In other words, [itex]x^2 - c^2t^2 = x'^2 - c^2t'^2[/itex]. (This is true because we are not changing the origin of the reference frame). The shape that the red graph takes is such that this quantity is the same when calculated by either graph.
goodabouthood said:I am pretty much saying I would like to see a visual reference of both the train and observers coordinates.
goodabouthood said:Thanks.
I am still wondering why the other coordinate system takes on the position it does. I see as the coordinate system approaches the speed of light it closes in on each other I just don't understand why.
goodabouthood said:It also would help to see the numbers for both coordinate systems.
goodabouthood said:I really appreciate the diagrams you are making. I can now see that the act of when the lighting hits and when the observer sees it are two different events in the frame of reference. Am I correct in saying that?
goodabouthood said:Also in regards to the last diagram you posted, is there anyway you could show me an example with actual numbers filled in for the variables in the equations? I think that would help me a lot.
goodabouthood said:I really appreciate the diagrams you are making. I can now see that the act of when the lighting hits and when the observer sees it are two different events in the frame of reference. Am I correct in saying that?
...
I am trying to visualize in my head what each frame of reference would look like for the train example.
BruceW said:Yes! The lightning hitting ground and observer seeing the light from that strike are two different events.
For the train example, the only difference between the frames of reference is the relative speed of the two frames of reference. So the origin and coordinate axes are the same in both cases, but the frames have a relative motion. One frame measures the two lightning strikes to have happened at the same time in different places, so the other frame must measure the strikes to have happened at different times.
This may seem weird because the origin and axes of the two reference frames are identical, but in special relativity, the relative speed of the reference frames also decides where/when events happen.
goodabouthood said:I can now see that the act of when the lighting hits and when the observer sees it are two different events in the frame of reference. Am I correct in saying that?
The velocity of an object through spacetime is called its four-velocity. The equivalent magnitude of this vector is equal to the speed of light for all objects with mass.goodabouthood said:What is meant when you say everyone travels at the speed of light on the time dimension?
If the train is going at .5c, then the time difference between the events according to the train's FoR is:goodabouthood said:Let say the observer on the platform sees them simultaneously at t=0. Now let say that the train passing is going at .5c. Would that mean the lightning bolt will hit a half second latter in the train's frame of reference?
From the platform's FoR, for the beams of light from each strike to reach the train at the same time, one strike would have to happen earlier, so its light could 'catch up' with the train. So if the events were simultaneous for the train's FoR, they can't be simultaneous for the platform's FoR and vice versa.goodabouthood said:The thing that is bothering me in my head is that I imagine the train situation and I imagine the observer on the platform and the observer in the train passing each other when the bolts hit simultaneously for the observer on the platform. What I don't understand is why they can't hit simultaneously for the train FoR. I know it's because the train of reference is in motion I just don't understand why it happens.
goodabouthood said:It would be nice to see what the equations you posted in your last diagram look like with actual numbers.