# Light in opposite directions

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?

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SpaceTiger
Staff Emeritus
Gold Member
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?
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).

SpaceTiger, can you explin that in a more simpler way , as i have the same way of thinking as Tojen.

JesseM
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".

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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?

SpaceTiger
Staff Emeritus
Gold Member
ArielGenesis said:
SpaceTiger, can you explin that in a more simpler way , as i have the same way of thinking as Tojen.
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.

To illustrate what relativity is really limiting, let's look at a different case. Let's say, instead of photons, we have particles being emitted from the light bulb. Although they aren't aloud to move at the speed of light, they can move very close to it, so close that we'll just say that they're moving at c (the speed of light). 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. Since, from our point of view, it seems that they're moving apart at nearly 2c, you would think that each particle would "see" the other moving away at this same velocity. Not so. In fact, relativity says that there is no point of view from which you can see something moving faster than c, so something has to be different from the point of view of these moving particles. In turns out that they both experience "time dilation", meaning their clocks run slower than ours, so they don't measure the other particle to be moving away from them at faster than the speed of light.

It's a vast subject and I recommend much more research if you really want to get the hang of it. It's cool stuff, though, so it would be a good use of your time.

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JesseM
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?
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.

I certainly won't argue with Einstein. Thanks for clearing it up for me.

HallsofIvy
Homework Helper
This all comes of talking about relativity without using ALL of it: In classical mechanics, If object A is moving away from us with speed u and object B is moving away from us, in exactly the opposite direction, then the "speed of B relative to A" is u+ v (and so, if u= v= c, we get 2c).

But in relativity, precisely because we have the "upper limit" of c on speeds, the formula is $$\frac{u+v}{1+ \frac{uv}{c^2}}$$. What do you get when you take u= v= c there?

jtbell
Mentor
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.
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.

The velocity in the first part of SpaceTiger's example is a different kind of velocity. We didn't measure that velocity "directly"; we inferred it from the difference in the velocities of the two objects, as measured by us. People often call this a "separation velocity" or "closing velocity" depending on whether which direction the objects are moving.

Classically, the separation or closing velocity of two objects as measured by a third observer equals the velocity of either object as measured by the other one (ignoring signs). In relativity this is not true. To get the velocity of either object as measured by the other one, from the velocities of the two objects as measured by the third observer, you have to use the relativistic velocity-addition formula.

There's nothing fundamentally wrong with the separation velocity. Sometimes it's a perfectly sensible quantity to use. It's just not the kind of velocity that the relativistic transformation equations apply to.

Light speed barrier theory broken by TOJEN

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?
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.

HallsofIvy
Homework Helper
No, we don't! We know that the correct formula, for relativistic speeds is NOT
"u+ v" but $$\frac{u+v}{1+\frac{uv}{c^2}}$$. In particular, if u= v= 0.99 c, that gives, as the speed of one relative to the other $$\frac{0.99c+ 0.99c}{1+ 0.99^2}$$= 0.99995c.

Oh, wait, you were being sarcastic- never mind.

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?
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.

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New Image wrote:
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.
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.

HallsofIvy wrote:
This all comes of talking about relativity without using ALL of it:
That's why I came here to ask a question, because I don't know ALL of relativity.

RoboSapien wrote:
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.

JesseM
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.
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.

Are you familiar with the Lorentz transformation? This is the rule that shows what coordinates different observers will assign the same events, the velocity-addition rule (u+v)/(1+uv/c^2) can be derived directly from 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.
I am sorry if I offended U sir, I appologide for it.

All I meant to say was that when two object are simultaneous going away in opposite direction from earth its logical for a non physicts person like me to think that they have exceeded the speed of light to eachother because I am using earth as a refrence point to addup their speeds.

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.

JesseM wrote:

Are you familiar with the Lorentz transformation?
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.

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.

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.

I hope that's it cause if it isn't, I'm giving up.

JesseM
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.
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.

So, the fact that velocities don't add in relativity the same way they do in classical physics is a consequence of three factors:

1. Each guy sees the other guy's ruler shrunk in his own frame--they don't agree about distances.

2. Each guy sees the other guy's clocks slowed down relative to his own--they don't agree about time intervals.

3. Each guy sees the other guy's clocks as all being out-of-sync--they don't agree about simultaneity.

Since "velocity" is really distance covered in a particular time interval, these facts give you a basic idea of why velocities might not add the same way in relativity as they do in classical physics (where none of these disagreements will be present).

If it helps, I drew up some diagrams showing two rulers moving alongside each other, illustrating how in each ruler's frame it's the other one that's shrunk, and that has its clocks slowed down and out-of-sync--see this thread.
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.
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).

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.
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.

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Here is what Einstine fell short at imagining

It is said that speed light of light remains constant for all object no matter at what speed they are traveling. Thoes who believe this must think again.

There 3 points A, B and D equidistant from each other, the length of each is TWO LIGHT HOUR. 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.

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.

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.

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.

Hence thoes in A1 have concluded that their observations showed that light was traveling twice its speed.

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Doc Al
Mentor
RoboSapien said:
There 3 points A, B and D equidistant from each other, the length of each is TWO LIGHT HOUR.
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.

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.
If they are moving with respect to each other, each rocket will measure the other's clock as running slow.

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.
What makes you say that?

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.
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).

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.
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.

Hence thoes in A1 have concluded that their observations showed that light was traveling twice its speed.
Nope. All frames agree that light travels at the same speed with respect to the observer.

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. ...
I should have put BOLD font for the words "Think Again".

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.

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.

Doc Al
Mentor
RoboSapien said:
I should have put BOLD font for the words "Think Again".

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.
It's a problem for you, since you don't seem to understand how length and time are frame dependent.

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.
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.)

Doc Al said:
...
It's a problem for you, since you don't seem to understand how length and time are frame dependent...
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.

JesseM