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.
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:
For example, right now I am sitting still in my chair looking at my computer. What would be my frame of reference?
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.
On the other hand, you could use a different coordinate system defined by the table your computer is sitting on. You could say that the origin is the top front left corner of your table and +X extends to the right of the table, +Y extends to the rear of the table, and +Z extends upwards. Then you could start a stop watch on your cell phone and use the elapsed seconds as your time coordinate. Then you would probably say that the event (for the middle of your head) that describes when you read this (in [t,x,y,z] format with t in seconds and distances in feet) is something like [15,2,-1,1.5]. But note that we are not really very precise because you are using your cell phone's stop watch which probably has a resolution of a tenth of a second and light can travel a hundred million feet in that amount of time.
However, if you had some very precise electronic equipment and you wanted to set up an experiment involving light, you could actually be in a situation where details could matter. So let's say that on the left hand edge of your table, you have a very fast light strobe that can emit a very short (less than a tenth of a nanosecond) flash of light aimed at the right hand edge of your five-foot wide table where you have a mirror that reflects the light back to your strobe and right next to your strobe you have a light detector. You have wired up an electronic timer with a resolution of a thousandth of a nano second that starts when the strobe emits a flash of light and stops when the detector senses the reflected image. What do you think the timer will read when you do this experiment. Well, since the speed of light (for our purposes in this exercise) is one foot per nanosecond and the table is five feet wide and the light has to travel both directions, the timer will read 10.000 nanoseconds, correct?
But what if you wanted to measure how long it took the light to go from the left hand edge of your table to the right hand edge. Well that seems easy enough, you just put your detector on the right hand edge of your table and run a cable back to your timer to stop it when the light is detected, right? So you run your experiment and now what do you think you will get? Well if you said 5.000 nanoseconds, you'd be wrong because even if it did take 5 nanoseconds for the light to go from your strobe to the detector, it would take another 5 nanoseconds for the signal traveling in the cable to get from the detector to your timer.
So now you decide to put the timer next to the detector on the right side of the table so that you can use a very short cable to stop the timer but now you need a long cable going from the strobe to start the timer. Well you do your experiment again and what happens is that when the strobe flashes, the start signal travels down the cable right along side the flash of light so they both arrive at the other side of the table at the same time. The signal starts the timer and immediately the detector sees the flash of light and stops the timer so the reading is 0.000 nanoseconds.
So if you use your measurements to calculate the one-way speed of light, in the first case you will say that it appears the be 5 feet divided by 10 nanoseconds or 0.5 feet per nanoseconds and in the second case it appears to be 5 feet divided by 0 nanoseconds or infinite. Now these are actually the range of values that the one-way speed of light could be and there is no way to determine what it actually is.
So this is where Einstein's second postulate comes in. He simply says that whatever time it takes for the light to make the roundtrip, it takes exactly half that amount of time to make the one-way trip. Einstein says that unless you do something like this, you really have no basis for establishing the meaning of time at the right hand edge of your table just because you have a timer at the left hand edge.
So now what you can do, instead of having a stop watch to measure the time interval, you can actually use a pair of clocks with no wires in between and you synchronize them so that that when you make the one-way speed of light measurement, you will get 1 foot per nanosecond. This, of course, means that you have to go actually go through the process of synchronizing them.
One way to do this is to have a memory on each clock so that when it receives an external signal, it stores the current time. You do this at the strobe end and at the detector end. You do the experiment. Let's say the clocks have not yet been synchronized and the difference in the times on the two clocks is seven nanoseconds instead of five. Now you can set the detector clock back by two nanoseconds. The next time you do the experiment, you will get a difference in the clock readings of 5 nanoseconds. Now you can repeat the experiment with more clocks in other locations until you have a network of synchronized clocks at known locations. This, then, becomes your Frame of Reference.
goodabouthood said:
Another question I have is do different reference frames depend on both motion and position or just motion?
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:
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.
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 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.
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 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.