The first part is a fairly qualitative description of special relativity and most readers who don't already know this can get something out of it. The second part is a short mathematical analysis of a thought experiment which results in deriving the basic equation of special relativity. It will be tricky for people with insufficient math/physics backgrounds to understand, and won't be that useful for people who already know/understand special relativity fairly well. It will target a somewhat small part of the TL community.
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.
The main postulate of special relativity is that the speed of light is constant in all inertial reference frames. In vacuum, the speed of light is about 3x10^8 m/s. If you were to shoot a photon of light forwards, and run after it at 2.9x10^8 m/s, would the light appear to be getting ahead of you at a rate of 0.1x10^8 m/s?
You, pictured on top, chasing a photon of light; what would an observer (bottom) see?
The answer is no (by the way you can't actually run that fast). This completely violates the basics of mechanics prior to Einstein. Most students learn in basic physics classes that you calculate relative velocity by adding the velocities of two moving objects in a given direction. You cannot do this with light because most cases would violate the postulate that the speed of light is constant in all reference frames.
So what is actually happening if you shoot a photon of light forwards at 3E8 m/s and then run after it at 2.9E8 m/s? From your perspective (reference frame) the light is traveling away from you at a speed of 3E8 m/s. This might not seem like that big of a deal to you, but consider what another, stationary person (observer) would see if they were watching the event from the sidelines. Wouldn't they see you running forwards at 2.9E8 m/s, and the light traveling forward at 5.9E8 m/s? How can light be traveling so fast from the perspective of a stationary observer?
While you are running you are not "allowed" to see light traveling slower than 3E8 m/s, and the stationary observer is not "allowed" to see light traveling faster than 3E8 m/s. Either we are missing something or you and the stationary observer must exist in different universes (which isn't the case). In order for the universe to make sense there must be something else going on besides what was already identified. The only way this can all make sense, Einstein and others discovered, is if the rate of passage of time is different for you than it is for the stationary observer.
The stationary observer isn't doing anything so let's say the passage of time for him is 'normal.' You are moving (ridiculously and unreasonable) fast, and so apparently the rate of passage of time for you will be different than it is for the stationary observer. Most people know that according to relativity time 'slows down' as you travel faster and faster. Is that consistent with the situation in the picture above?
If the rate of passage of time slows down for you, the moving person, then that will give light a 'chance' to get ahead of you. When you are slow everything around you seems fast (many of us have learned that lesson on iccup or battle.net). Since your rate of passage of time is slowing due to your fast movement, light seems like it's moving a lot faster than the 0.1E8 m/s you expected. In fact, it is moving away from you at 3E8 m/s. But the stationary observer's rate of passage of time is normal so light continues to travel from his perspective at 3E8 m/s as he expected. Therefore, in both your reference frame and the reference frame of the observer light is traveling at the correct speed, c, 3E8 m/s.
You might need to reread the past few paragraphs a couple of times to get it if you haven't learned this before; it is quite confusing. I am now going to set up a thought experiment to mathematically calculate the rate at which time slows down as you move with a speed v.
Derivation of Gamma
Common way of demonstrating special relativity
A car is driving to the right with a speed v, as shown in the picture. Mounted to it is a laser pointer (orange) shooting light up towards the ceiling. The ceiling is a mirror and reflects light back down towards the ground. A detector on the car determines how much time it took the light to return to the car after being emitted by the laser. There are two reference frames to discuss:
You riding in the car analogously to you running in the previous example. Let's call this reference frame #1. Let's call the time it takes light to travel up to the ceiling and back t for this reference frame.
A stationary observer standing on the ground or somewhere else. Let's call this reference frame #2. Let's call the time it takes light to travel up towards the ceiling and back t' in this reference frame.
Let's make sure we understand what is happening. If you are riding in a car and throw a ball straight up, it should fall straight down and back into your hand, from your perspective. However, from the perspective of a stationary observer on the ground you threw the ball diagonally: up and forwards. Something similar happens with the light. From your point of view (RF#1) the light goes straight up towards the ceiling, and then comes back down to you. The ceiling appears to be moving to the left from your perspective but there is no horizontal component to the light's velocity.
The stationary observer (RF#2) sees the light moving diagonally up and to the right. The horizontal component of the light's speed is v and the vertical component is less than c. The light takes a diagonal path until it strikes the mirror, then reflects. The angle of incidence equals the angle of reflection and the light continues down and to the right with the same pitch.
You might already see a weird inconsistency occurring (just like we did for the first example in this thread). In RF#1 the light travels up a distance D/2 and then down a distance D/2 for a total distance of D. In RF#2 the light travels up a distance D/2, down a distance D/2, but also horizontally to the right the same distance as the car traveled in that time (remember, the light was traveling diagonally in this reference frame). Apparently, from the stationary observer's perspective light traveled further in one trip than it did from your perspective. This means light must have been traveling faster in RF#2 than it did in RF#1. However, according to the main postulate of Special relativity this absolutely cannot be the case (think of our first example). The only way the light could have traveled further in RF#2 despite having the same speed in both reference frames is if time passed more slowly in one reference frame than the other.
The Math
In RF#1 the time it took light to complete one trip, t, is pretty easy to calculate based on the relationship t=d/v. t=D/c. Remember this as we will use it later.
In RF#2 we need to use the Pythagorean Theorem in order to analyze the path of the light. Even though the light traveled in two paths, one before striking the mirror and another after reflecting off the mirror, let's simplify this a bit by saying the light traveled upward a distance D and rightward a distance v * t'. According to the Pythagorean Theorem:
(c * t')^2 = D^2 + (v * t')^2
The first term is the hypotenuse, the second is the vertical component of the right triangle, and the third term is the horizontal component. You need to understand how this equation was put together or you cannot continue. It is not obvious how to use the equation labeled in red above and this one to find a useful relation between t and t' so I will step you through. First, divide both sides of the equation by c^2:
t'^2 = (D/c)^2 + (v/c)^2 * t'^2
Place the rightmost term on to the left side (this is grouping) and then factor out the t'^2 to get:
t'^2 (1 - [v/c]^2) = (D/c)^2
See the red note above; t=D/c so t^2=(D/c)^2. Substitute this into the above equation to get:
t'^2 (1 - [v/c]^2) = t^2
Finally solve for t' and get:
t' = t / sqrt(1 - v^2/c^2) This is the Main Result
This is commonly written as:
t' = t * Gamma
And Gamma is commonly written as:
Gamma = 1 / sqrt (1 - Beta^2)
Where Beta can be written as:
Beta = v/c
This may seem overwhelming but if you follow along and work this all out on paper it should become fairly obvious.
Analysis of the Result
You can determine how much time will dilate (slow down) for the person in the moving car by using this equation. For example, if the car was moving at half the speed of light (ridiculous in practice but good for a mathematical example) then you would find:
t' = t * Gamma = t / sqrt (1 - (.5c)^2/c^2) = 1.1547 t
The difference in the rate of passage of time between the moving person and stationary observer is substantial (more than 15%). At everyday speeds like 30 meters per second or 60 miles per hour relativistic effects are negligible. If you don't believe me calculate t' for the case where v = 0.0000001c.
If I have anything mixed/backwards in my explanations or reference frames then please let me know. If this all makes sense to you and you want to know more about it, then your next step would be to see how time dilation can cause a few interesting things:
Length Contraction
Simultaneity (things can actually happen in a different order depending on reference frame)
Relative Velocities according to special relativity (this came up in Card's Ender series)
The list could go on and on but I did not intend to make an exhaustive guide. I hope many of you enjoyed reading this.
edit: another thing to note: Einstein did not get his Nobel Prize in Physics for Relativity. He got it for his study of the Photoelectric Effect which demonstrated that light has a particle nature as well as a wave nature.
edit 2: Einstein was famous for saying (paraphrasing from memory) that the rate of passage of time is elastic: it goes quickly when talking with an attractive girl but quite slowly when sitting on a hot stove.
This app helps you determine how much the motion of every every day life affects you. Unless you are an astronaut moving through space very quickly for a long period of time the effects won't really be noticeable though.
Wow. He found a way to extend his life by about 2 seconds. That's more than the astronauts who have spent months traveling at speeds more than 20 times the speed that he was traveling!
If i recall correctly an airplane traveling 10 times faster barely made a difference in time (in an experiment), although it did make a small difference. Now I don't remember exactly how big of a difference it was but it was very small, maybe 1e-10 seconds
Here's a video, didn't see all of it though.
But as you can read in the description a satelittes move 0.01s per year and they move way faster than a car.
So when "time slows down" for the running guy in the first segment, both he and the stationary observer see light going at its 3E8 speed. But how fast does the runner appear to the stationary observer?
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Quite obviously just false as I see it.
What confuses me about this subject / way of testing it as a whole though is that this movement is only relative to our planet - not space. Imagine the Earth is right this second traveling (around the sun) through space to the direction you would call "west". Then imagine you started driving east. Wouldn't you then essentially slow down your own speed i space? I have no idea how this works, but that would seem logical to me. At least if our speed can at all be considered independent from that of the Earth's.
Also I love how it's a Special theory. It would be far less interesting if it was Einstein's Just Another Relativity Theory. That guy knew how to sell his theories.
Thanks for writing this up; I was always interested in physics and special relativity/general relativity, its nice that you found a way to clearly and concisely explain this topic.
The next thing I wish I could understand is how gravity is explained or related to the bending of space-time . I wish I took physics instead of engineering
Isn't this video fake because wouldn't the stopwatch he took with him in the car be ahead of the stopwatch left at home?
edit: lol, nevermind. The stopwatch he took with him in the car should be behind the stopwatch at his house. but no where near 2 seconds behind from just a car ride lol.
only read beginning but wouldn't that little proton of light travel at the speed of light? Too fast for any human "observing" without the tools of science. Therefore wouldn't the answer to the proposed "what would the observer see" "nothing" cause you can't detect a single glimpse of light or prolly anything moving that fast. Iunno how fast moving numbers with the letter E added on to them are, but I assume its damn fast.
read more, thanks for the links. even though i dont try to think about the math, i like the concepts they use the math to support and just take their word for it.
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Quite obviously just false as I see it.
What confuses me about this subject / way of testing it as a whole though is that this movement is only relative to our planet - not space. Imagine the Earth is right this second traveling (around the sun) through space to the direction you would call "west". Then imagine you started driving east. Wouldn't you then essentially slow down your own speed i space? I have no idea how this works, but that would seem logical to me. At least if our speed can at all be considered independent from that of the Earth's.
Please correct me.
The only thing that matters is the frames you choose and their relative speed. If you choose the Earth and the car and measure the car relatively towards the movement of the Earth (ie. Earth is stationary in this reference frame), the speed of the Earth is 0, because you used a reference frame that is moving along with the Earth (in which Earth has 0 speed), so the speed of Earth (towards the third reference frame - "universe") doesn't have any say in the measurement - only the relative speed of the car and the Earth play a role.
^^ To conclude, only the relative speed between two reference frames is important.
Also, note how this is very convenient. Xou have no way to know the real speed of Earth, as it "orbits" around the center of our galaxy, and the galaxy orbits around the cluster of galaxies etc. and it's hard to find the "center" of the space...
But as only the RELATIVE speed of the two reference frames is important, we don't need to know it's speed.
On April 25 2011 01:31 PaPoolee wrote: Wow that stop watch video can't be real! how did he do it?.
I assume he just paused one of the timers for two seconds off-camera.
Yea or something similar.
On April 25 2011 01:42 Bippzy wrote: What happens if you're going at the speed of light? In theory.
Also, happy birthday!
You can't travel at the speed of light according to Einstein. Just like how
t' = t * Gamma = t / sqrt (1 - (.5c)^2/c^2)
you can say
E = mc^2 / sqrt(1 - (.5c)^2/c^2)
thus when your speed is c your energy (E) is infinite. You would need an infinite amount of energy to accelerate an object with a nonzero mass to the speed of light.
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Yes.
On April 25 2011 01:45 Antifate wrote: This was fun to read, but I have a question.
So when "time slows down" for the running guy in the first segment, both he and the stationary observer see light going at its 3E8 speed. But how fast does the runner appear to the stationary observer?
Edit: Lol, it's 2.9E8 m/s isn't it? Kind of dumb.
Good question. You will need to read about relative velocity like I mentioned... time dilation causes the answer to be different than you expected.
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Quite obviously just false as I see it.
What confuses me about this subject / way of testing it as a whole though is that this movement is only relative to our planet - not space. Imagine the Earth is right this second traveling (around the sun) through space to the direction you would call "west". Then imagine you started driving east. Wouldn't you then essentially slow down your own speed i space? I have no idea how this works, but that would seem logical to me. At least if our speed can at all be considered independent from that of the Earth's.
Please correct me.
There is no universal reference frame that we know of. Everything about relativity is relative (surprise surprise). It's common to use the sun or the Earth as a 'fixed' reference point.
On April 25 2011 02:05 HwangjaeTerran wrote: That's one ugly car.
Also I love how it's a Special theory. It would be far less interesting if it was Einstein's Just Another Relativity Theory. That guy knew how to sell his theories.
Yeah but I hope you see there is also a good 'scientific' reason for why he chose that name :p
On April 25 2011 02:15 radscorpion9 wrote: Thanks for writing this up; I was always interested in physics and special relativity/general relativity, its nice that you found a way to clearly and concisely explain this topic.
The next thing I wish I could understand is how gravity is explained or related to the bending of space-time . I wish I took physics instead of engineering
We could discuss general relativity a bit more qualitatively I guess, but I cannot help you with the math behind it :p
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Quite obviously just false as I see it.
What confuses me about this subject / way of testing it as a whole though is that this movement is only relative to our planet - not space. Imagine the Earth is right this second traveling (around the sun) through space to the direction you would call "west". Then imagine you started driving east. Wouldn't you then essentially slow down your own speed i space? I have no idea how this works, but that would seem logical to me. At least if our speed can at all be considered independent from that of the Earth's.
Please correct me.
The only thing that matters is the frames you choose and their relative speed. If you choose the Earth and the car and measure the car relatively towards the movement of the Earth (ie. Earth is stationary in this reference frame), the speed of the Earth is 0, because you used a reference frame that is moving along with the Earth (in which Earth has 0 speed), so the speed of Earth (towards the third reference frame - "universe") doesn't have any say in the measurement - only the relative speed of the car and the Earth play a role.
^^ To conclude, only the relative speed between two reference frames is important.
Also, note how this is very convenient. Xou have no way to know the real speed of Earth, as it "orbits" around the center of our galaxy, and the galaxy orbits around the cluster of galaxies etc. and it's hard to find the "center" of the space...
But as only the RELATIVE speed of the two reference frames is important, we don't need to know it's speed.
I was basically going to say this, but also keep in mind that you require an inertial frame of reference for special relativity, meaning your frame of reference can't be accelerating.
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Quite obviously just false as I see it.
What confuses me about this subject / way of testing it as a whole though is that this movement is only relative to our planet - not space. Imagine the Earth is right this second traveling (around the sun) through space to the direction you would call "west". Then imagine you started driving east. Wouldn't you then essentially slow down your own speed i space? I have no idea how this works, but that would seem logical to me. At least if our speed can at all be considered independent from that of the Earth's.
Please correct me.
Keep in mind that not only are we (the earth) in constant motion around the sun, but the sun is orbiting the center of the milky way galaxy, which is itself hurtling through the local group at a great speed relative to its gravitational center, which is also moving with some speed relative to some other celestial object. The bigger things get the less sense it makes to measure things like "speed" on that scale. It becomes a meaningless question to ask "how fast is our galaxy/star/planetary system traveling through space?" since there are an infinite number of equally valid answers given the vague context.
On April 25 2011 02:25 MiniRoman wrote: only read beginning but wouldn't that little proton of light travel at the speed of light? Too fast for any human "observing" without the tools of science. Therefore wouldn't the answer to the proposed "what would the observer see" "nothing" cause you can't detect a single glimpse of light or prolly anything moving that fast. Iunno how fast moving numbers with the letter E added on to them are, but I assume its damn fast.
read more, thanks for the links. even though i dont try to think about the math, i like the concepts they use the math to support and just take their word for it.
First of all it's technically a 'photon' of light. A proton is a particle and thus has mass and cannot travel at the speed of light :p
As someone else pointed out E means "x10^" so c = 3E8 m/s = 300000000 = very fast
On April 25 2011 02:50 divinesage wrote: You forgot to add that it would then be impossible to achieve the speed of light. Happy Birthday!
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?
Happy birthday! And awesome post, love the random spread of interesting scientific knowledge. I'm a Physics undergrad (about to finish jr. year) and we just did a pretty hefty chapter on Special Relativity in my Theoretical Mechanics class. It's really interesting stuff, and the math behind it (with four-vectors and transforms and such) is interesting as well. I also had a 1 credit online course that one of the professors at my University (and my research advisor for this summer) hosted for fun about a lot of unique and profound things in Physics, paradoxes and the lot. Lot of stuff on Relativity, tons of fun thought experiments. (link to all the lectures if anyone is interested)
On April 25 2011 01:42 Bippzy wrote: What happens if you're going at the speed of light? In theory.
Also, happy birthday!
While micro above just showed that it is indeed impossible to do so, imagining this has always been one of my more interesting thought experiments / curiosities. If time dilation and length contraction actually worked as described AT the speed of light (which we can not know), lots of interesting things would happen. The way I always enjoy imagining it is, picture you're just stand still in space, on a space station or something. There's a platform coming up behind you that will whiz by you at the speed of light exactly, which you can step on. What would happen if you did? Length contraction and the aberration of light says all the light in the Universe would be focused to a single infinitely small point directly ahead of you. You would see nothing all around you. In addition, time would dilate "infinitely", so when you stepped on for a fraction of a second and decided to step off again, you could be anywhere, or the universe might not even exist (assuming you didn't run into anything!). Other interesting things like the Doppler effect as well... very fun stuff!
On April 25 2011 02:57 Nuttyguy wrote: 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?
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.
As someone else pointed out E means "x10^" so c = 3E8 m/s = 300000000 = very fast
And for people who don't have a concept of how fast a meter per second is, you can get a rough conversion to miles per hour by just multiplying by 2. So 300,000,000 m/s is about 6 hundred million miles per hour!
On April 10 2011 00:18 micronesia wrote: A car is driving to the right with a speed v, as shown in the picture. Mounted to it is a laser pointer (orange) shooting light up towards the ceiling. The ceiling is a mirror and reflects light back down towards the ground. A detector on the car determines how much time it took the light to return to the car after being emitted by the laser. There are two reference frames to discuss:
I already know all about special relativity, and I know that this setup gives the correct math. But this example always really bugged me. The problem is that it depends on a specific kind of clock. I don't think you can generalize from "this specific kind of clock that relies on laser beams slows down" to "time slows down". There are better ways to derive the lorentz equation for time dilation.
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?
You can mathematically calculate the speed of light in a vacuum by the permittivity and permeability of electric and magnetic fields (they are universal constants). One way to find these constants is to take special relativity cases which involve charges and/or currents in inertial reference frames.
I must say Micronesia, awesome post! I am glad to see some other people on TL who are scientifically minded. I think it would be cool to then express special relativity to the TL community with space-time diagrams. People seem to have a grasp of time dilation and length contraction, so maybe we can move into geometry
On April 25 2011 01:42 Bippzy wrote: What happens if you're going at the speed of light? In theory.
Also, happy birthday!
all i know is that it would burn like hell
It is harder to increase speed as you are going faster. That is, the amount of energy that is needed to speed up from 1 m/s to 2 m/s is not as much as moving from 9 m/s to 10 m/s. This is true in both classical mechanics and relativistic mechanics. Theoretically, it would take an infinite amount of energy to accelerate any massive object to the speed of light, thus the only way an object can travel at the speed of light is if it has no mass (i.e. photons of light and other force carriers such as gravitons gauge bosons).
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).
It's actually very straight forward when you sit down and read through it slow and do the math stuff yourself. gj explaining this to a retard such as myself. Gonna have to fire up khanacademy after tsl3.
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).
I'm not incredibly knowledgeable on the subject, but isn't whether photons have mass or not still an experimental question? Also, this would only mean that c is a constant for maximum possible speed, rather than the speed of a photon per se, right?
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.
Is this simply false because he's not going nearly as fast (or for as long) as he needs to be going for any actual time dilation to occur?
Quite obviously just false as I see it.
What confuses me about this subject / way of testing it as a whole though is that this movement is only relative to our planet - not space. Imagine the Earth is right this second traveling (around the sun) through space to the direction you would call "west". Then imagine you started driving east. Wouldn't you then essentially slow down your own speed i space? I have no idea how this works, but that would seem logical to me. At least if our speed can at all be considered independent from that of the Earth's.
Please correct me.
There is no universal reference frame that we know of. Everything about relativity is relative (surprise surprise). It's common to use the sun or the Earth as a 'fixed' reference point.
Actually, I would argue against that point. General relativity covers space-time, and although I advise to avoid general relativity in a forum thread, this part is relative (no pun intended, damn it Einstein!)
Space-time, is almost by definition the universal frame of reference. Space-time is the plane upon which we move, and consists of all 4 dimensions. (Don't start string/M theory with me, I just wont listen to a theory that has no chance of ever being proven, you can keep your 10/24 dimensions!). Although often portrayed as a taught sheet of rubber (or the like) that still misses time, which I'm afraid, you're just not going to get your head round. But, the effect of this is that it is an absolute frame of reference, and was constructed to be so. Space time was made using the same postulates that Einstein used for his theories of relativity. Essentially, the outcome is that everyone and everything travels through space-time at the same rate.
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.
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.
If there wasn't this absolute frame of reference, then the twin paradox would be all together more confusing. If one twin is off in a spaceship travelling at near the speed of light, relative to them it will seem like their sibling is travelling at near the speed of light (or at least earth is). So they would both observe the other one travelling slower through time, so it would cancel out yes? No. Because the twin in the spaceship has travelled further through space (ie, is the green arrow to the earthbound twins red arrow)
I'm very tired at the moment so may have not been very clear, or in fact may have been wrong, so please do point out anything I've missed/you don't understand.
P.S. With my last point, I am infact missing out parts. It is also due to the acceleration of the space ship twin, and how they decelerate through gravitational fields. But the explanation I gave suits. And it avoids nasty explanations .
P.P.S. Also, when I say everything has to go through space-time at the same rate, that is also a lie. In fact everyone must observe everything else going through space-time at the same rate. Individual paths may differ. But they are *almost* the same thing. It only makes small changes in this area.
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"? :/
On April 25 2011 01:18 micronesia wrote: Can you tell what is wrong with this video? XD
To lose 2s in 24 minutes you'd need a gamma = 1442/1440, so a speed of .002772c, 831600m/s, 3million miles per hour. Luckily if your car can go that fast they usually don't pull you over for filming yourself while driving.
Ok, so he has a really fast car. The problem is that he accelerates massively (~120g) during the trip and so this should be treated as a general relativity problem, not special.
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).
I'm not incredibly knowledgeable on the subject, but isn't whether photons have mass or not still an experimental question? Also, this would only mean that c is a constant for maximum possible speed, rather than the speed of a photon per se, right?
Its one of those things which agrees so overwhelmingly with all theories and tests, that it is nigh on impossible for it not to be true.
But if through some bizarre circumstance it turns out photons have a minuscule amount of mass, then yes. c would cease to be the speed of light, and return to being a cosmological speed limit (of sorts).
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"? :/
Its still interesting that it's slowed down in a medium. I seem to remember that you could slow down light to 24 miles an hour in sodium crystals. But, yes. All things assume travelling in a vacuum, unless stated otherwise. Which I guess should have been stated earlier
Relativity is interesting, but there are many factors and variables in theory that are not true or doesn't reflect the way things behave in the normal universe and is also incomplete.
As for the first one, light doesn't behave like that and doesn't apply in real world, only in theory. We shouldn't even use light as an example of relativity to sight, because we are dependent on light as sight. Or light = sight
You can't see the photon of light you are chasing. It's like taking a picture in completely dark vacuum space with a flash of light and running after it. You will never see the light again if you don't have enough speed to get in sync with it in the same direction. Theoretically, if you travel faster than that flash of light, you can't even see as well since it's too slow to hit your eyes. In order for you to see the same light source twice, you would have to see it first, move faster than it in the same direction, then stop and wait for it to hit you again, or move in the speed to stay in sync with it for it to hit your eyes constantly.
For the stationary person, all he will see is a flash at most of both the photon and the person chasing it, depending on whether his brain can comprehend the little amount of time to see it.
So the question is, what are we using to see sight, if light or something to the speed of light is used as a reference in relativity?
On April 25 2011 04:14 Pleiades wrote: Relativity is interesting, but there are many factors and variables in theory that are not true or doesn't reflect the way things behave in the normal universe and is also incomplete.
As for the first one, light doesn't behave like that and doesn't apply in real world, only in theory. We shouldn't even use light as an example of relativity to sight, because we are dependent on light as sight. Or light = sight
You can't see the photon of light you are chasing. It's like taking a picture in completely dark space with a flash of light and running after it. You will never see the light again if you don't have enough speed to get in sync with it in the same direction. Theoretically, if you travel faster than that flash of light, you can't even see as well since it's too slow to hit your eyes. In order for you to see the same light source twice, you would have to see it first, move faster than it in the same direction, then stop and wait for it to hit you again, or move in the speed to stay in sync with it for it to hit your eyes constantly.
For the stationary person, all he will see is a flash at most of both the photon and the person chasing it, depending on whether his brain can comprehend the little amount of time to see it.
So the question is, what are we using to see sight, if light or something to the speed of light is used as a reference in relativity?
I'll get back to the second one later.
Ahh, you're ruining all the fun of though experiments. One of the major advantages of thought experiments is that the don't have to feel the restrictions that real experiments do. It is true that you cannot effectively chase a photon, because you cannot observe it. But you can certainly use the situation in a thought experiment. In fact I defy you to try to imagine the real life circumstance. I doubt that anyone could realistically imagine some of the situations that come up when you talk about these topics.
for some reason, I was usually fine doing simple time dilation / length contraction, but could never get the hang of Lorentz transforms (at least the way I was taught). Maybe I'd be better at them now that I know linear algebra... lol.
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).
I'm not incredibly knowledgeable on the subject, but isn't whether photons have mass or not still an experimental question? Also, this would only mean that c is a constant for maximum possible speed, rather than the speed of a photon per se, right?
Its one of those things which agrees so overwhelmingly with all theories and tests, that it is nigh on impossible for it not to be true.
But if through some bizarre circumstance it turns out photons have a minuscule amount of mass, then yes. c would cease to be the speed of light, and return to being a cosmological speed limit (of sorts).
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"? :/
Its still interesting that it's slowed down in a medium. I seem to remember that you could slow down light to 24 miles an hour in sodium crystals. But, yes. All things assume travelling in a vacuum, unless stated otherwise. Which I guess should have been stated earlier
I'm pretty sure that the speed of the photon doesn't slow down, but it only appears to. This is because of the mass about of molecules in a medium, meaning that the photons will hit those molecules. They, in turn, produce another photon after the collision, and it continues on. So the speed of the photon doesn't really change but it looks like it because of the multiple collisions.
On April 25 2011 04:14 Pleiades wrote: Relativity is interesting, but there are many factors and variables in theory that are not true or doesn't reflect the way things behave in the normal universe and is also incomplete.
As for the first one, light doesn't behave like that and doesn't apply in real world, only in theory. We shouldn't even use light as an example of relativity to sight, because we are dependent on light as sight. Or light = sight
You can't see the photon of light you are chasing. It's like taking a picture in completely dark space with a flash of light and running after it. You will never see the light again if you don't have enough speed to get in sync with it in the same direction. Theoretically, if you travel faster than that flash of light, you can't even see as well since it's too slow to hit your eyes. In order for you to see the same light source twice, you would have to see it first, move faster than it in the same direction, then stop and wait for it to hit you again, or move in the speed to stay in sync with it for it to hit your eyes constantly.
For the stationary person, all he will see is a flash at most of both the photon and the person chasing it, depending on whether his brain can comprehend the little amount of time to see it.
So the question is, what are we using to see sight, if light or something to the speed of light is used as a reference in relativity?
I'll get back to the second one later.
Ahh, you're ruining all the fun of though experiments. One of the major advantages of thought experiments is that the don't have to feel the restrictions that real experiments do. It is true that you cannot effectively chase a photon, because you cannot observe it. But you can certainly use the situation in a thought experiment. In fact I defy you to try to imagine the real life circumstance. I doubt that anyone could realistically imagine some of the situations that come up when you talk about these topics.
Oh I have some ideas... like jet planes and Mach numbers or lightning and thunder. Just that I haven't had the time to do a scenario yet
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.
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.
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).
I'm not incredibly knowledgeable on the subject, but isn't whether photons have mass or not still an experimental question? Also, this would only mean that c is a constant for maximum possible speed, rather than the speed of a photon per se, right?
Its one of those things which agrees so overwhelmingly with all theories and tests, that it is nigh on impossible for it not to be true.
But if through some bizarre circumstance it turns out photons have a minuscule amount of mass, then yes. c would cease to be the speed of light, and return to being a cosmological speed limit (of sorts).
On April 25 2011 04:07 Dagobert wrote:
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"? :/
Its still interesting that it's slowed down in a medium. I seem to remember that you could slow down light to 24 miles an hour in sodium crystals. But, yes. All things assume travelling in a vacuum, unless stated otherwise. Which I guess should have been stated earlier
I'm pretty sure that the speed of the photon doesn't slow down, but it only appears to. This is because of the mass about of molecules in a medium, meaning that the photons will hit those molecules. They, in turn, produce another photon after the collision, and it continues on. So the speed of the photon doesn't really change but it looks like it because of the multiple collisions.
On April 25 2011 04:46 rubio91 wrote: I'm pretty sure that the light produces in the nucleus of the stars takes years to get on the surface, this is pretty much impressing isn't it?
These two points are very related. The reason photons produced in the centre of stars takes years to leave is because of the collisions. They collide, interact and then produce another photon. With the "random walk" statistical proof, its for every N "steps" a photon takes (at least, its a photon in this example) it travels sq.rt(N) in a straight line. So it takes so long, because it has to go through so much.Though I find it interesting that even though its random, it has a direction. I can't remember the reason exactly.
And the light is slowed down, at least I'm pretty certain. Though the collision/interaction is the reason it takes time to leave stars, it genuinely slows in medium. (Please do correct me if I'm wrong). I always thought of it as the material being more dense, so there is (relatively) more distance to go through. Speed=dist/time and all.
So the speed of the photon doesn't really change but it looks like it because of the multiple collisions.
Somewhat, the speed of light in a material is an average. The speed of light in a vacuum is a consequence of the permittivity and permeability of free space. In a material those values can change and so the speed of light will be lower even without collisions.
Photons travel at the speed of light, regardless of what that value is, because they are particles of light.
I've always been familiar with the concept (and it made sense), but, having never taken physics, I never knew the specifics.
What this suggests to me is that the idea of practical deep space travel is impossible, at least in the sense of simple travel between point A and point B. The speeds necessary to travel such a distance in a practical amount of time would mean that you are "accelerating" through hundreds of years, for a one way trip. If you were to return to your destination, everyone you knew and loved would be long gone.
This brings me to the idea that the only practical way to be able to travel to and from the deeper parts of the universe would require a sort of "fold" space itself (thus shortening the distance required to travel) and I don't even know if/how that would be possible.
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?
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.
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.
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.
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 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"? :/
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.
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 ...
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
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?
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.
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.
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.
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.
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.
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.
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?
Can I be the first to say that it would be really REALLY cool to have LaTeX integrated into the forums so we didnt have to look at crappy text formula's?
On April 25 2011 13:47 Dave[9] wrote: Can I be the first to say that it would be really REALLY cool to have LaTeX integrated into the forums so we didnt have to look at crappy text formula's?
That would be oh so very awesome. We could have some nice nerdly mathspeak conversations.
On a side note, I completely endorse this thread. Relativity is a very interesting subject to get into, and its applications are very fun. Good on you micronesia!
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"
On April 25 2011 12:37 GGTeMpLaR wrote: 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?
Time is stopped entirely for a photon (or anything) travelling at the speed of light. Just put v=c in the equations time dilation (gamma) = 1/(sqrt.(1-v^2/c^2). If v = c, then it becomes 1/0 which is infinite, so time is slowed by an infinite amount, and thus is "stopped". Though that is only for the photon itself, it doesnt age at all. It doesnt mean that it travels though time infinitely fast.
And yes, time does slow if you're in a car going 60mph. But it is so tiny (as in, infinitesimal) that it makes no difference. I seem to remember Stephen Hawking saying that you could technically make yourself live a little further into the future by staying on a plane for many years, but your life would be cut even shorter by having to survive on air line food!
Happy birthday, and lovely post. Took a few upper division Philosophy courses on Space, Time, and Quantum Mechanics in college, and this was always a pretty fun topic to discuss.
On April 25 2011 13:47 Dave[9] wrote: Can I be the first to say that it would be really REALLY cool to have LaTeX integrated into the forums so we didnt have to look at crappy text formula's?
Oh man, that would be so ridiculous. It'd be kind of silly though considering what this forum is actually supposed to be for. Not a lot of need for LaTeX when discussing Starcraft and progaming.
On April 25 2011 12:37 GGTeMpLaR wrote: 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?
You're still thinking within the box, you have to expand your mind.
Light is not affected by 'time'. 'Time' is not constant. The one and only thing that is constant for everyone in any inertial frame of reference is the speed of light. Time is different for different people in different inertial reference frames. You have to understand this, it is at the core of special relativity. ie. The whole premise of your post is invalid.
tl;dr no
One more thing:
TIME DOES NOT SLOW DOWN FOR YOU EVER Even if you're going at super fast speeds, time will seem exactly the same in your eyes. It will be everyone else speeding up, not you slowing down.
On April 25 2011 12:37 GGTeMpLaR wrote: 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?
You're still thinking within the box, you have to expand your mind.
Light is not affected by 'time'. 'Time' is not constant. The one and only thing that is constant for everyone in any inertial frame of reference is the speed of light. Time is different for different people in different inertial reference frames. You have to understand this, it is at the core of special relativity. ie. The whole premise of your post is invalid.
tl;dr no
One more thing:
TIME DOES NOT SLOW DOWN FOR YOU EVER Even if you're going at super fast speeds, time will seem exactly the same in your eyes. It will be everyone else speeding up, not you slowing down.
Actually, time will appear to move slowly for the stationary reference frame while you are moving near the speed of light. Conversely, the stationary reference frame will see time moving for you slowly. At first glance, this is very counter-intuitive but if you switch reference frames, so the one speeding along is the stationary reference frame and the one at the origin is the speeding reference frame then you should be seeing the same thing (time moving slowly).
EPT
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. I wish I took physics instead of engineering
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