When a light bulb is turned on, it emits photons at the speed of light in all directions. This means that photons traveling in opposite directions are going twice the speed of light relative to each other. How is this possible?
Relativity limits the speed of an individual object to the speed of light. It doesn't place the same limit on the difference in velocity between two external objects (in this case, photons).Tojen said:When a light bulb is turned on, it emits photons at the speed of light in all directions. This means that photons traveling in opposite directions are going twice the speed of light relative to each other. How is this possible?
In every inertial reference frame, each photon's velocity is exactly c. Photons do not have their own rest frame (any attempt to create one would violate the postulate that the laws of physics should work the same way in all inertial reference frames), so asking what the velocity of the photons is "relative to each other" is not physically meaningful--asking what B's velocity is relative to A is just another way of asking what the velocity of B is in A's rest frame. You can ask how fast the distance between them is increasing in a particular inertial reference frame, and the answer will indeed be that it's increasing at 2c, but the light-speed limit only applies to things like particles and information, it doesn't apply to concepts like "the distance between two objects".Tojen said:When a light bulb is turned on, it emits photons at the speed of light in all directions. This means that photons traveling in opposite directions are going twice the speed of light relative to each other. How is this possible?
Sure, I just mean that the limit is on how fast we measure an object to move. That is, it says those individual photons can't move faster than the speed of light. It doesn't say, however, that the distance between the photons can't change at a rate faster than the speed of light.ArielGenesis said:SpaceTiger, can you explin that in a more simpler way , as i have the same way of thinking as Tojen.
As SpaceTiger said, addition of velocities doesn't work the same way in relativity as it does in Newtonian physics--see Relativistic Velocities for details. If the galaxy is moving to the right at velocity u in Dick's frame, and Jane is moving to the right at velocity v in the galaxy's frame, then Jane's velocity in Dick's frame is not u+v but (u+v)/(1 + uv/c^2). So in your example Dick would measure Jane to be moving to the right at (7/4)*c/(1 + 49/64) = (112/113)*c.Tojen said:Thanks for the replies. Maybe I'm wrong in using Relativity and photons. I'm trying to imagine a situation where an object is travelling faster than the speed of light compared to another object, and what that would look like. How about this? Dick is travelling past a galaxy at 7c/8. Jane goes whizzing past in the opposite direction at the same speed. Comparatively, each is going faster than c. How does that look to each of them?
To make this explicit here, we're dealing with two different kinds of velocities. The equations of relativity always deal with the velocity of an object as measured by a specific observer, or more precisely, in a specific inertial reference frame.SpaceTiger said:[...] Now, from our point of view, opposing particles are moving apart from one another at about twice the speed of light, and that's perfectly alright, because neither one of them is individually moving faster than c.
The real tricky part comes when you ask how things appear from the point of view of one of the particles.
Congratulations Mr. TOJEN, U have done it. Now , Forget light,Tojen said:
Just going to take a guess.Tojen said:How about this? Dick is travelling past a galaxy at 7c/8. Jane goes whizzing past in the opposite direction at the same speed. Comparatively, each is going faster than c. How does that look to each of them?
Thanks, new image. That was the best explanation, and not just because it was the only one. Even with my limited understanding of relativity I understood it.Just going to take a guess.
I would think when you 2 are coming at each other you would see her as ultra violet light because of the blue shift. Then when you pass her she would shift to the red shift. But you would still be able to see her because neither of you are going faster then the speed of light, the light coming back off her is still going at the speed of light, but would be change in wavelength.
The light catching up with you and leaving her is at the same speed. This is because time is moving slower for both of you, and light remains constant.
That's why I came here to ask a question, because I don't know ALL of relativity.This all comes of talking about relativity without using ALL of it:
I'm sure your intellectual superiority is exceeded only by your humility.Congratulations Mr. TOJEN, U have done it. Now , Forget light,
If two objects are going in the opposite directions from earth at 99% C. Then just knowing this we understand that from earth the two objects are going at 198% C to each other.
Actually, I don't think New Image's argument is correct, because when physicists talk about the position and time coordinates of events in a given reference frame ('speed' is just change in position-coordinate divided by change in time-coordinate), they're not talking about what they actually see using light signals, they're talking about when and where the event happened if they compensate for the finite speed of light. For example, if in the year 2005 I observe a nova that's 100 light-years away according to my measurements, then I retroactively say this event happened in 1905 in my coordinate system, even though in 1905 I wasn't actually aware of the nova since its light had yet to reach me. Likewise, if in 2005 I see a spaceship 10 light years away, and in 2010 I see that the ship is 9 light years away, that does not mean the ship is moving at 1/5 light speed in my frame...instead, I will reason that the ship must have been 10 light years away in 1995 (2005 - 10), and that it was 9 light years away in 2001 (2010 - 9), so its speed must actually be 1/6 light speed, although it appeared to be travelling faster because the light was blueshifted. So you can see that blueshift and redshift are factored out when physicists talk about the speed of different objects in a given frame.Tojen said:Thanks, new image. That was the best explanation, and not just because it was the only one. Even with my limited understanding of relativity I understood it.
I am sorry if I offended U sir, I appologide for it.HallsofIvy said:No, we don't! We know that the correct formula, for relativistic speeds is NOT
Oh, wait, you were being sarcastic- never mind.
Only with the term. I don't have a head for math so even the simple eqauation you and others have offered I have a hard time with. But I do understand that the fixed speed of light creates interesting scenarios in time and space. I think I wasn't considering frames of reference originally.Are you familiar with the Lorentz transformation?
The fact that they don't see the velocity as 0.75+0.75 doesn't really have to do with the fact that the light takes longer to reach them. Suppose instead of measuring the other's distance at a particular time using light signals, they each were sitting on enormous rulers which were at rest relative to themselves, and mounted on these rulers were a series of clocks which were all synchronized in their own reference frame. Each time person #2 passes a mark on person #1's ruler, a camera goes off and takes a picture, showing both his position on that ruler (the mark he is next to) and the time on the clock that's mounted to the ruler at that position. These pictures are all collected by a mailman walking along the ruler and finally delivered to the guy sitting on that ruler, with the mailman travelling much slower than light. So he won't know the other guy was at a particular position until long after he would have found out if he had been using light signals. Still, in retrospect he can calculate the other guy's speed using these pictures--if he has a picture showing the other guy crossing the 1-light-year mark on the ruler with the clock at that mark reading 2005 and then another picture showing him crossing the 2-light-year mark with the clock at that mark reading 2010, he can conclude that the guy was traveling at 1/5 the speed of light.Tojen said:Just to see if I've got it right...If two people take off in opposite directions from Earth, both at 75% c, that's what I, from my spot on Earth, would see. I look one way and see someone leaving at 75% c, and I can turn around and see the other leaving at 75% c. But to the travellers, the situation is different. The increasing distance between them means the light from each traveller is taking longer and longer to reach the other, which would slow down the apparent time and thus slow down the apparent speed of the other. The faster they are going, the more the apparent time and speed slows.
Yes, this part is right (although to use the proper terminology, what you call the 'relative speed of two objects' should really be called the 'closing velocity' between them, to avoid confusion).Tojen said:Or, in short, the relative speed of two objects can be greater than c--from an independent frame of reference. From the frame of reference of each object, though, that is impossible.
Actually, it is completely logical and quite easy to derive from the empirical evidence that the speed of light in vacuum is invariant with respect to inertial reference frames. While you may disagree with said evidence, it doesn't make sense to then say that any logical derivatives are illogical.RoboSapien said:Although I agree that if speed is measured form one object to another then it will be for sure what U r saying, but I have decided never to understand why it is so as it sounds completely illogical.
According to whose measurements? I assume you mean that measured from a frame in which A, B, and D are at rest the distances A-B & B-D are two light-hours. Of course, other frames (moving with respect to A, B, D) will measure different distances.RoboSapien said:There 3 points A, B and D equidistant from each other, the length of each is TWO LIGHT HOUR.
If they are moving with respect to each other, each rocket will measure the other's clock as running slow.From point A, Rocket A1 is traveling towards point C ie. center of line BD; At speed such that clocks in A1 have slowed down to half the rate of clocks in Rocket C1 at point C.
What makes you say that?Form inside A1 with a powerful telescope it can be seen so. The funny this is everything that is seen happening in Rocket C1 at point C is seen at twice the speed of normal motion.
Again, the time for light to travel from D to C as measured from a frame in which A, B, C, and D are at rest will be 1 hour. Other frames will measure different times (and distances).A LASER beam is fired from point D to B. When the Laser Beam passes through point C it destrorys an apple kept there. Scientist at C1 Note down the time it took the laser to reach there as 1 hour.
According to the moving rocket A1, the distance between D and C is only 1/2 of a light-hour; so, according to the moving rocket A1, the time it takes for the light to travel from D to C is only 1/2 hour.Scientist at A1 observer this and note down the time it took the laser to reach the apple as half hour, all the things at point C were fast forwarded at twice the speed in A1 as rate of time in A1 had halfed compared to that at C1.
Nope. All frames agree that light travels at the same speed with respect to the observer.Hence thoes in A1 have concluded that their observations showed that light was traveling twice its speed.
I should have put BOLD font for the words "Think Again".Doc Al said:...
According to the moving rocket A1, the distance between D and C is only 1/2 of a light-hour; so, according to the moving rocket A1, the time it takes for the light to travel from D to C is only 1/2 hour. ...
How about adding this to your list: Learn relativity!RoboSapien said:I should have put BOLD font for the words "Think Again".
It's a problem for you, since you don't seem to understand how length and time are frame dependent.The 1/2 light hour that we get as a result is a problem because when physically measured the distance between D and C the light must be at twice its speed to cover it in half hour.
You've gotten precise, unambiguous answers. You just don't like them! (Thinking harder won't help if your thinking is based on incorrect physics.)I am expecting no answer to the above comments or some vague statements as usual with vague refrences instead of thinking harder about the thought experiment.
There is nothing hard about it to think. Its impossible that atoms and distance between them are gona vary just because some alien is zooming around earth at near light speeds.Doc Al said:...
It's a problem for you, since you don't seem to understand how length and time are frame dependent...
They don't vary in the rest frame of the atoms, they only vary in the frame of an observer moving at different velocities relative to them. Why should this be any more troubling than the idea that an object's velocity varies depending on what reference frame you're using? (This is just as true of Newtonian mechanics as relativity, of course.) Would you say "its impossible that the velocity of atoms are gonna vary just because some alien is zooming around earth at near light speeds"?RoboSapien said:There is nothing hard about it to think. Its impossible that atoms and distance between them are gona vary just because some alien is zooming around earth at near light speeds.