Relativity/Simultaneity - I understanding a few things?

[skycastlefish]

I've been learning about Special Relativity as a hobby for the past couple days and for the most part, I've been able to wrap my mind around several concepts (ah-ha moments are awesome) There are still a couple of things that just aren't making sense to me. I understand why time dilation and length contraction occur when the reference frame is moving in the same direction of travel as the light (chasing the light) but I don't understand why the speed of light measures constant if you are moving toward light that is also moving toward you? For example, a seemingly stationary spaceship is passed by a moving spaceship pointing in the same direction. When both ships appear to line up perfectly they fire a beam of light in the direction of travel. The beams of light travel at a constant speed, however, the distance between the light beams and the ships are different because one of the ships is in relative motion with the other. This is the part I DO understand and makes it makes perfect sense. If outgoing light has not reached a distance of 186,000 miles from a reference frame, then that reference frame has not experienced a second of time - time and distance adjust to meet light. Next is the part I don't understand. Imagine the same spaceship scenario as above only this time, in addition to the two light beams fired by the ships, a light beam is also fired at the space ships from directly ahead and in the line of travel. So now the moving ship is chasing a light beam and moving to meet a light beam that is also racing toward him. How can he not measure the light racing toward him as faster than the one he's chasing? If time slows down to ensure the proper distance of light is achieved, then wouldn't the light racing toward him cover so much relative distance that the time second would have to go faster to adjust? How can time slow down and speed up at the same time. If I could figure this out I think I could realize simultaneity. I know I'm missing something really obvious, so please be nice. This is my 3rd day studying physics.
Thanks,
Adam

 

[Naty1]

I don't understand why the speed of light measures constant if you are moving toward light that is also moving toward you?

no one understands that..it does NOT make intuitive sense..nor do many things in quantum mechanics, nodbody understands that either...but it turns out to be experimentally verifiable so we accept it as "fact"...

everyone measures the speed of light as "c"...like it or not it appears to be correct!

It's no crazier than space and time being variables...how can THAT be?

 

[JesseM]

Next is the part I don't understand. Imagine the same spaceship scenario as above only this time, in addition to the two light beams fired by the ships, a light beam is also fired at the space ships from directly ahead and in the line of travel. So now the moving ship is chasing a light beam and moving to meet a light beam that is also racing toward him. How can he not measure the light racing toward him as faster than the one he's chasing?

Precisely because he synchronizes his clocks differently--that's what "relativity of simultaneity" means! The Einstein clock synchronization convention is that each observer defines what it means for two clocks at different locations to be "synchronized" using the assumption that light travels at the same speed in all directions relative to themselves. One way of putting this is that each observer says two clocks at rest relative to them are "synchronized" if, when they set off a flash at the exact midpoint of the two clocks, each clock will have the same reading at the moment the light from the flash strikes that clock. But consider what that would mean if the procedure was carried out by an observer in motion relative to you--say, an observer on a ship which is moving forward at relativistic speed in your frame, who is trying to "synchronize" two clocks at either end of the ship. If he follows the Einstein synchronization convention, he will set off a flash at the midpoint of the ship, and each clock will be set to the same time, like 11 AM, at the moment the light from the flash reaches them. Since the light was set off at the midpoint of the ship, in the ship's rest frame the light naturally had the same distance to travel from the midpoint to either end, so setting the clocks to read the same time when the light reached them guaranteed that by definition the light must have traveled at the same speed in each direction (since for each of the two light beams traveling to the two clocks, speed = distance traveled/[time light reached the clock - time light was emitted from flash], and the flash happened at a single point in spacetime so naturally the time it was emitted would be the same for both beams).

But now think about how this would look in your frame where the ship is moving. If you have synchronized all your clocks in such a way as to guarantee that both beams travel at the same speed in your frame, then naturally since the back clock is moving towards the point where the flash was set off while the front clock is moving away from that point, according to your measurements the light must reach the back clock at an earlier time than it reaches the front clock (you could measure this by having a set of synchronized clocks at rest in your frame, and you could note the time on whichever one of your clocks happened to be right next to the back of the ship at the moment the light reached it, and likewise note the time on whichever one of your clocks happened to be right next to the front of the ship at the moment the light reached it). So from your point of view, the guy on the ship has set his two clocks in a way that makes them out-of-sync, by just the right amount that he gets the "illusory" result ('illusory' from your point of view) that the light beams both took the same amount of time to reach either end of his ship, when "in fact" (again from your point of view), the light traveling towards the back took less time. Of course the guy on the ship would say that it's your clocks that are out-of-sync, and your claims about the times are the "illusory" ones! And since the laws of physics work exactly the same in both your two coordinate systems (whose time coordinates are defined by clocks at rest in each frame which have been 'synchronized' in this way), there's no objective physical basis for saying one of your definitions of simultaneity and time is "right" while the other is "wrong".

For a numerical example of how it all works out, here's something I came up with on an older thread:

Say there's a ruler that's 50 light-seconds long in its own rest frame, moving at 0.6c in my frame. In this case the relativistic gamma-factor (which determines the amount of length contraction and time dilation) is 1.25, so in my frame its length is 50/1.25 = 40 light seconds long. At the front and back of the ruler are clocks which are synchronized in the ruler's rest frame; because of the relativity of simultaneity, this means that in my frame they are out-of-sync, with the front clock's time being behind the back clock's time by vx/c^2 = (0.6c)(50 light-seconds)/c^2 = 30 seconds.

Now, when the back end of the moving ruler is lined up with the 0-light-seconds mark of my own ruler (with my own ruler at rest relative to me), I set up a light flash at that position. Let's say at this moment the clock at the back of the moving ruler reads a time of 0 seconds, and since the clock at the front is always behind it by 30 seconds in my frame, then in my frame the clock at the front must read -30 seconds at that moment. 100 seconds later in my frame, the back end will have moved (100 seconds)*(0.6c) = 60 light-seconds along my ruler, and since the ruler is 40 light-seconds long in my frame, this means the front end will be lined up with the 100-light-seconds mark on my ruler. Since 100 seconds have passed, if the light beam is moving at c in my frame it must have moved 100 light-seconds in that time, so it will also be at the 100-light-seconds mark on my ruler, just having caught up with the front end of the moving ruler.

Since 100 seconds passed in my frame, this means 100/1.25 = 80 seconds have passed on the clocks at the front and back of the moving ruler. Since the clock at the back read 0 seconds when the flash was set off, it now reads 80 seconds; and since the clock at the front read -30 seconds, it now reads 50 seconds. And remember, the ruler was 50 light-seconds long in its own rest frame! So in its frame, where the clock at the front is synchronized with the clock at the back, the light flash was set off at the back when the clock there read 0 seconds, and the light beam passed the clock at the front when its time read 50 seconds, so since the ruler is 50-light-seconds long, the beam must have been moving at 50 light-seconds/50 seconds = c as well! So you can see that everything works out--if I measure distances and times with rulers and clocks at rest in my frame, I conclude the light beam moved at 1 c, and if a moving observer measures distance and times with rulers and clocks at rest in his frame, he also concludes the same light beam moved at 1 c.

 

[skycastlefish]

Thank you guys! When I get into something I really get into it. I had literally been losing sleep the last week because I couldn't understand these things. So thanks Naty1 for reminding me that its OK to sleep if I don't understand things. Thanks JesseM for helping me realize simultaneity! I think I'm putting a picture together. Simultaneity says that although two events may not appear simultaneous from one reference frame, they can be agreed upon based on the the fact that each reference frame utilizes the speed of light to set its clocks and define its measurements? So, nothing not even information can travel faster than the speed of light -- therefore an event cannot happen in a reference frame (have a cause-effect) until the light from the event has reached that reference frame ------ And since there is no absolute standard to compare motion to, we cannot conclude that one reference frame is more right than another. We can never say, with certainty, that an event was actually more simultaneous than staggered?

 

[JesseM]

Thank you guys! When I get into something I really get into it. I had literally been losing sleep the last week because I couldn't understand these things. So thanks Naty1 for reminding me that its OK to sleep if I don't understand things. Thanks JesseM for helping me realize simultaneity! I think I'm putting a picture together. Simultaneity says that although two events may not appear simultaneous from one reference frame, they can be agreed upon based on the the fact that each reference frame utilizes the speed of light to set its clocks and define its measurements? So, nothing not even information can travel faster than the speed of light -- therefore an event cannot happen in a reference frame (have a cause-effect) until the light from the event has reached that reference frame ------ And since there is no absolute standard to compare motion to, we cannot conclude that one reference frame is more right than another. We can never say, with certainty, that an event was actually more simultaneous than staggered?

You've pretty much got it, I think. The one thing I'd quibble with slightly is your comment that "an event cannot happen in a reference frame (have a cause-effect) until the light from the event has reached that reference frame". You have to distinguish the time that information about a particular event reaches a given inertial observer, and the time the event is reckoned to have happened in that observer's own inertial reference frame. If the event happens far from the observer, the observer will retroactively assign an earlier time coordinate to the event upon getting information about it, based on the time that would show on a clock at rest in that frame and right next to the event when it happened (and synchronized with the observer's own clock using Einstein's clock synchronization convention). For example, if in 2010 the observer looks through his telescope and sees an explosion 2 light-years away (as measured by a ruler at rest relative to the observer), he'll retroactively assign that event a time-coordinate of 2008. And if there had been a clock at the end of his 2-light-year-ruler, which was synchronized with his own clock, then when he saw the explosion through his telescope he'd see that the clock would indeed be showing a time of 2008 as the explosion was happening right next to it (and he'd just be seeing the light from that reading now because it took 2 years to reach him).

 

[skycastlefish]

I think I'm understanding why we can assign a time for an event based on its distance from a reference frame. We can acknowledge that an event happened at an earlier time if we know the relative distance between us and if we agree on the speed of light.

For example, if in 2010 the observer looks through his telescope and sees an explosion 2 light-years away (as measured by a ruler at rest relative to the observer), he'll retroactively assign that event a time-coordinate of 2008. And if there had been a clock at the end of his 2-light-year-ruler, which was synchronized with his own clock, then when he saw the explosion through his telescope he'd see that the clock would indeed be showing a time of 2008 as the explosion was happening right next to it (and he'd just be seeing the light from that reading now because it took 2 years to reach him).

Say there's an explosion 2 light-years away (as measured by a ruler at rest relative to the observer) that is so powerful it could destroy the Earth and our solar system. Imagine that the expanding explosion is traveling at a significant fraction of the speed of light. Anything, even the expansion of the explosion, is forbidden to travel faster than the speed of light, correct? Therefore, the explosion (cause) could not damage our reference frame (effect), nor could it be observed until it was right on top of us? Does this mean that an extreme event like an atomic explosion in space could happen 10,000,000 light years away from us (determining our fate) and not effect us at all (at all!) until 10,000,000 years after the event when the light reaches us -- followed closely by the explosion itself? In other words, If its agreed that an object is 2 light years away from our reference frame, then any physical event happening there cannot have a physical effect on our reference frame any sooner than its light could reach us, right?