|
On April 25 2011 05:19 QuAnTuM314 wrote:Show nested quote +On April 25 2011 05:06 garbanzo wrote:On April 25 2011 04:06 QuAnTuM314 wrote:Here is a time-space graph depicting movement through space-time. Dont ask me why they do a time-space graph instead of a space-time graph, I never understood. + Show Spoiler +![[image loading]](http://imgur.com/L2zTn.png) Please forgive my poor paint skills. The red arrow depicts every day objects, that move at non-relativistic speeds. Because everything moves through space-time at the same rate, and they aren't moving through space very quickly, the majority of their movement is through time. And this is the time you measure on your watch whilst going about your life. The green arrow shows what would happen as we accelerate. Because the object is moving (much) faster through space, and has to move the identical amount through space-time, it moves less along the time axis. I.e. It experiences less time (relative to space-time) than the red arrow. The yellow arrow is for photons, and anything travelling at the speed of light. Here, all of its movement through space-time is going through space (you can prove this by putting in v=c in the equation for gamma/time dilation). Therefore, it experiences no time at all. I'm not entirely sure what exactly you're trying to say in your post. I think you're saying that there is an absolute frame and I'm pretty sure that's not true. It sounds like you're describing the concept of an aether. But like I said, I don't really get what you're saying so I will just comment on what I quoted above. I'm not really sure if there's a "real" reason why spacetime diagrams always have time on the vertical axis. It really does just make sense that way, especially in general relativity. Horizontal cones are just awkward to look at. Your diagram is also not correct. Something traveling at the speed of light is not the same as something traveling at infinite speed (your yellow line). Light still takes a certain amount of time (relative to a stationary observer) to travel a certain distance. For instance, light takes about 8 mins to get from the sun to earth. The green arrow is what is actually traveling at the speed of light. The usual point of that diagram is that if you are an observer at (0,0) then you can't affect anything outside of the light cone (the lines x=t and x=-t (c=1)). Likewise anything outside your light cone won't affect you until their light cone cross your light cone. No. As I said at the end of my post, space-time *isnt* an absolute frame of reference, but the difference in these cases is not really worth noting (though in other circumstances, it would definitely have to be explored further). I am also most definitely not describing an aether either. And with my diagram? It isn't wrong, the time on the graph is time relative to space time, not time as we perceive it. In effect, it is the individual time for whatever is on the graph. If something is going at the speed of light, (eg, light), it will experience no time. This is what the graph is saying, and it doesnt because of poor wording on my part. If what you said is true (relative to my graph) then that would mean that the light would experience time, so therefore would not travel at the speed of light (gamma would have to be > 0, which would mean that the speed would be > c). The graph you're thinking of is in reference to hyperbolic functions. Which although (in this case) have the same axis labels, they are subtlety different. Here they are not for an object, but for the properties of time and space themselves. I believe the misunderstanding has been from my poor wording/expression. I'll return to this thread when I'm less tired.
Okay, I think I just don't understand what you're saying, so I'll leave it alone and just say that special relativity is awesome, but tricky. I generally don't deal with it too much outside of class and when in class I mostly use it as a mathematical concept (with physical implications) but not to try to think too hard on it. Unless, of course, thinking about the consequences is the exercise.
|
|
|
On April 25 2011 04:07 Dagobert wrote:Show nested quote +On April 25 2011 03:58 Luddite wrote:On April 25 2011 03:35 Dagobert wrote:On April 25 2011 03:00 Duka08 wrote:
Photons, the way we treat them as particles, have NO mass. Ever. They carry momentum and energy, but they have no mass. And they ALWAYS travel at the speed of light. Nope, they can be slowed down (Akopian et al., 2011). only when traveling through a medium, not in a vacuum. Irrespective of whether that's the case - what part of "only when travelling in a vacuum" amounts to, and I quote, "ALWAYS"? :/ + Show Spoiler +
No I did not misspeak. They will always travel the speed of light, but that is not to say that the speed of light is always ~3e8 m/s. In any medium, the speed of light may be different (lower) than that in a vacuum, for reasons previously discussed above. However, this "new" speed is still THE speed of light IN that medium, and thusly photons will always travel the speed of light, WHATEVER it may be in that medium (the fastest being in a vacuum, our "typical" c=3e8m/s).
|
Heh. I'll come back tomorrow and word my point correctly. Rereading my posts is a bit embarrassing. They hardly make any sense. I'll try again tomorrow.
|
Thank you for this. It's very concise and extremely easy to understand.
|
well the video isn't a real fake (he didn't create that differnce on purpose)
the difference was probably caused because the guy did not started both watches at the same time.
In order to synchronize those watches he would have to use a mechanic using lightspeed to reduce the difference to a minimum ...
In addition this is not possible since otherwise the police would have caught him with 10% of c (c=3*10^8m/s) and he would have to pay a heavy fine ...
|
United States24734 Posts
On April 25 2011 06:07 sceroh wrote:
well the video isn't a real fake (he didn't create that differnce on purpose)
the difference was probably caused because the guy did not started both watches at the same time.
In order to synchronize those watches he would have to use a mechanic using lightspeed to reduce the difference to a minimum ...
In addition this is not possible since otherwise the police would have caught him with 10% of c (c=3*10^8m/s) and he would have to pay a heavy fine ...
Haha that reminds me of a poster I saw where a guy was trying to explain to the police officer that the traffic light wasn't red to him when he went through because of a doppler shift so the police officer said "then you were speeding" and ticketed him anyway XD
|
damnn its phys 2A all over again
|
On April 25 2011 02:57 Nuttyguy wrote:Show nested quote +On April 25 2011 02:36 MiniRoman wrote:On April 25 2011 02:29 Nuttyguy wrote:
E is x10^y
so E8
x10^8
its like on the calculator (EXE) or whatever brand you have
so "damn fast" was right? Yes light can travel 7.4 times around the earth in 1 second to put things into context. How would they measure the speed of light? And mass increase with speeds near speed of light, so a light photon's mass would increase. Does the photon slow down with the maximum speed being speed of light? EDIT unless you treat it as a wave because of its wave-particle duality?
Holy god damn, thats fast, thanks for putting it into context. My brain when it thinks of how fast its been told light is, recalls something like "takes like from the sun like 4-7 days to reach earth" so if anything that just tells me how far away the sun is (that time was a guestimation at what i remember - i know i know nothing about science or math beyond basic water makes plants grow). I watched a show called "The Universe" and it was about (obviously) space and stuff, but, one episode was titled: "Time Travel" and they mentioned what this thread is about. In it they said "time travel" was possible but only to jump into the future and that is because the faster you move the slower you move in time - so if we sent an astronaught at the speed of light to another planet an 8 year journey at the speed of light would have sent him 500 years into our future.
My question is: how far along are science and engineering to actually doing some "cool shit" with the knowledge you guys acquire? Or is it mostly an intellectual exercize cause we want to know 'the truth' of stuff?
Great math takes passion and I respect the passion of all men (save addicts) so what motivates you badass math/science minds into turning into even badder-assed math/science minds?
|
|
|
United States24734 Posts
On April 25 2011 07:23 MiniRoman wrote:Show nested quote +On April 25 2011 02:57 Nuttyguy wrote:On April 25 2011 02:36 MiniRoman wrote:On April 25 2011 02:29 Nuttyguy wrote:
E is x10^y
so E8
x10^8
its like on the calculator (EXE) or whatever brand you have
so "damn fast" was right? Yes light can travel 7.4 times around the earth in 1 second to put things into context. How would they measure the speed of light? And mass increase with speeds near speed of light, so a light photon's mass would increase. Does the photon slow down with the maximum speed being speed of light? EDIT unless you treat it as a wave because of its wave-particle duality? Holy god damn, thats fast, thanks for putting it into context. My brain when it thinks of how fast its been told light is, recalls something like "takes like from the sun like 4-7 days to reach earth" so if anything that just tells me how far away the sun is (that time was a guestimation at what i remember - i know i know nothing about science or math beyond basic water makes plants grow). I watched a show called "The Universe" and it was about (obviously) space and stuff, but, one episode was titled: "Time Travel" and they mentioned what this thread is about. In it they said "time travel" was possible but only to jump into the future and that is because the faster you move the slower you move in time - so if we sent an astronaught at the speed of light to another planet an 8 year journey at the speed of light would have sent him 500 years into our future. My question is: how far along are science and engineering to actually doing some "cool shit" with the knowledge you guys acquire? Or is it mostly an intellectual exercize cause we want to know 'the truth' of stuff? Great math takes passion and I respect the passion of all men (save addicts) so what motivates you badass math/science minds into turning into even badder-assed math/science minds?
I don't think I can answer all of your questions but it takes light about 8 minutes to reach Earth from the surface of the sun. We are in no way close to being able to use special relativity to send people to the distant future lol.
|
Got quite a few answers to my initial question. Just wanna say thanks for that!
I also forgot to say happy birthday, micronesia! So there! 
|
United States102 Posts
On April 25 2011 05:17 illumiel wrote:
You have to appreciate time dilation of the Relativity theory. What it actually means is that time is closely related to motion. Time is caused by motion in respect to something (Our cluster of galaxies/galaxy/cluster of stars/star/planet is constantly moving).
The real question is - motion with respect to what? And what will happen if you sufficiently slow down?
I think you are getting a few of the concepts mixed up. Time is relative. Motion is also relative. If you are driving in a car at a constant speed on a smooth road you cannot tell you are moving, but in respect to an observer, you obviously appear to be moving. If I observe you driving at 60 mph as I drive behind you at 55 mph, I will observe you traveling at 5 mph away from me. However, a man on the street will observe me traveling at 55 mph away from him, and you as traveling 60 mph away from him. Like motion, time is relative to the frame from which it is being observed.
If you look at a clock on your wrist it will always appear to move at the same speed, no matter what speed you are traveling at. However, if someone moving at a different speed than you looks at the clock on a wrist, it will appear to move at a time relative to their own frame of reference. The theory of relativity says that time is not a constant as it was believed to be in Newtonian times.
If you where to be standing outside the universe, and had "no motion", then the clock on your wrist would still appear to move at the same rate to you as it did when you where standing on earth. However, if you where looking at a clock on earth it would appear to move slower than the clock on your wrist, because the earth is moving in respect to you. Time is relative to where you are observing it from.
It also happens that time is also effected by things such as gravity, so it's important to break yourself of the concept that time is a constant by which everything else can be measured.
|
If you thought Lorentz transforms were tough, wait till you study general relativity and have to calculate Christoffel symbols.
|
On April 10 2011 00:18 micronesia wrote:
What is meant by Special Relativity and General Relativity?
General Relativity is simply an analysis of the idea that physical laws are the same regardless of the reference frame of the observer (accelerating or inertial). Gravity causes accelerations. The math involved in calculating the influences in different non-inertial reference frames due to gravity is very difficult and I have not studied it... I will not talk about it here. Special relativity is the "special" case where gravity is negligibly weak and all reference frames are inertial (not accelerating). Special relativity is just a subset of General relativity but is much easier to study.
This is not entirely accurate, actually. It is a common misconception that special relativity doesn't handle accelerating reference frames, when in fact it does so perfectly fine. Simply take the equations involving velocity (dx/dt) and take the time derivative to make it (d^2 x/dt^2). And there you go, you have equations for acceleration!
|
Simply take the equations involving velocity (dx/dt) and take the time derivative to make it (d^2 x/dt^2).
LOL
Special relativity challenges the very meaning of time. Wrapping your head around what a time derivative means in that context is non-trivial, let alone acceleration when time is a function of velocity.
|
I have seen some people who are confused about space-time diagrams so I will attempt to explain them.
![[image loading]](http://i.imgur.com/oRuRu.jpg)
This first picture shows the general structure of a space-time diagram. The y-axis is units of light-time and the x-axis is position. This graph represents two separate reference frames, the xy axis is the reference frame of the stationary observer and the blue-red lines are the reference frame of the moving reference frame. The dashed line is a beam of light.
The second picture is showing how to view a space-time diagram relative to moving in time. You can think of each horizontal line as a snapshot in time.
Now that you are familiarized with space-time graphs I can tell you about the interesting part. These types of graphs follow hyperbolic geometry, which is what allows the moving reference frame to still have its axis at right angles even though they look <90 in the stationary reference frame.
Now I want to draw your attention to the red and blue lines. These represent a moving reference frame. As it increases in speed, these two lines converge on the light-beam line but never quite touch it. You can think of this by drawing a hyperbola on either the x or y axis that has an asymptote on the light-beam line.
![[image loading]](http://i.imgur.com/6s0xm.jpg)
This picture shows my crude attempt at drawing a hyperbola. The important things to note is I d1 and d2 which is the distance from the origin to the parabola in each reference frame. Now this may seem odd by just looking at it but d1 and d2 are both the same distance due to the hyperbolic geometry of the graph. This is a very nice way to visualize the relativistic effects on length and time.
![[image loading]](http://i.imgur.com/jR7sN.jpg)
Anyway, I am going to let this stew for a little while. If you have specific questions feel free to PM me. You can use space-time diagrams to show acceleration using a hyperbolic trajectory for constant acceleration.
|
quick question:
does time slow down for the light traveling at the speed of light? the speed of light changes in certain mediums so does time speed up for light when it travels through those mediums (such as diamond with a high index of refraction) and then slow back down as it exits the medium back into air?
if so, what is the rate at which it slows down compared to the rate at which time slows down for you "running at 2.9*10^8" so that it still appears to be going 3E8 to both you at 2.9E8 and the stationary observer. (in other words how much does time slow down per unit of velocity, or does it only slow down for acceleration? and does it speed up or slow down if you deccelerate?)
also, technically speaking, does time slow down if I'm accelerating in a car from 0 to 60 mph (only the amount which time slows would be negligible/unnoticed since the acceleration is negligible)? or is it only a phenomena at high speeds?
|
|
|
the reasone the video is wrong is because in order to slow time u need to be going near the speed of light
|
|
|
|
|
|
EPT![[image loading]](http://i116.photobucket.com/albums/o4/GinRyuChan/brain.png)
