twice the speed of light

[altergnostic]

Well, let's carry on. We have found that:

 

- each photon travels at c away from the origin

- an observer at that origin would calculate the relative velocity of the photons with respect to one another as 2c using the addition of velocities equation

 

Technically speaking, this observer can only measure the speed of each photon by a roundtrip measurement.

That each photon can't possibly make such a measurement is clear as well, I hope.

 

Maybe one last thing to address that may be of interest to the OP is if this number has any physical meaning, i.e. if it is a true value or a sort of pseudo velocity, since the number 2c seems to contradict Einstein's light postulate. Logically, if I measure some rigid body travelling at 0.1c in the +x direction, relative to me, and a light beam travelling at 1c in the -x direction, relative to me, there is no reason I can't conclude that the speed of this light relative to the rigid body is 1.1c. But I am not allowed to state that this speed is measured to be the same in the rigid body's frame, if such body is measuring the speed of the photon relative to himself. This applies when we are dealing with ordinary speeds as well.

 

If two rigid bodies can be said to move at v>c relative to one another, we could conclude that the same can be said for two photons. But how do we arrive at v>c?

Let's play with that and see if we can unveil the physical meaning of the number 2c.

 

Suppose:

Two rigid bodies, A and B, emited from an origin O.

B moves in the +x direction while A moves in the -x direction.

The distance AO = BO = L.

A and B have synchronized clocks.

Each rigid body emits a photon towards the other at every tick of it's own clock.

Both rigid bodies move at the same speed relative to O.

 

Say we want to know the speed of each body relative to O without bringing light into play, as to avoid relativistic effects. We can do this with a round trip measurement of the rigid body, just like we do with light. So assume we have a rigid wall W placed +2 lightseconds away from O, send A towards it at t=0s, wait for it to bounce off the wall and return and read the time on our clock. If t=4s, vOWO=c. We know we can't determine a frame for something moving at c, so let's use t=5s. So vOWO=0.8c. Since W is stationary relative to O, with no outside influences, we can assume vOW=vWO=vL=0.8c and call it vA.

 

Notice that L=2ls is a given distance, just like in any speed of light measurement, where we are given the length of the arms (the distance between mirrors). We must ask how is this distance arrived at. In our everyday experiments, we simply measure it directly with a ruler or something like that, because we can't use the speed of light to determine the distance used to determine the speed of light (that would be two unknowns). By the same token, we can imagine a 2ls long ruler placed between O and W. This is not a distance measured from O or from W, it is a distance measured locally along the line AW. Each distance marked on any ruler is placed right on top of whatever is being measured, it is not measured from an observer at O or any other distant observer, it is a local measurement, equivalent to a measurement made by an observer sitting right next to that coordinate. In this sense, a ruler is equivalent to an array of observers between A and W. Hence, we can directly use L ignoring length contraction effects altogether, just like we do when we measure the speed of light. This is allowed because we are not using light to measure this length: any distance along AW can be directly observed simply looking at the number on the ruler. This number is brought by light emitted from each coordinate, and admittedly, light takes different times to cross different distances, so let's bring that into play:

 

For the rigid body A moving at v=0.8c relative to the ruler (also relative to O), we calculate:

 

x1=0ls

t1=0s

x2=L=2ls (A reaches W)

t2=(L/v)+(L/c)=2.5s+2s=4.5s

 

This reads: when A sees itself right on the wall, at the 2ls mark, his own clock reads 2.5s, but light emitted from O at that moment would take another 2s to reach W, hitting it at t=4.5s (2s after A has bounced off of W). By that logic, the light from O that is seen at W, by A, when it reaches W, is light emitted 2s earlier, so the observer sees the origin 2ls away as it was 2s in the past. This is very straightforward and is the same logic that we are used to when looking at distant stars to see how the universe looked like in the past.

So far so good, but what about B? We know how A observes O, but where does A observe B when A is at W? Well, it can't be seen at -L, or 4ls away, because light from -W takes 4s to reach W, so when B reaches -W (when B's clock reads 2.5s itself), light takes another 4s to reach W. If A is at W when t=2.5s, it will see the opposite wall -W as it was 4s in the past. So where does A see B? It must be the only point along O-W that satisfies

 

tB+tW=2.5s

 

Where tB is the time it takes B to reach the point where light emited from it takes tW seconds to reach W

 

I will not calculate it here since this is already longer than I expected, but B must be seen somewhere near the midpoint between 0ls and -0.5ls from the origin O. So, as A moves toward W, it sees B move away at no more than the speed of light. This should apply for any conceivable body or frame.

 

The body A could only calculate 2c if he knows somehow that when he is at W, B is at -W (and he can't know it, by the way, only assume it - he can't receive data from 4ls away in 0s, thatwould imply instantaneous communication). Hence, no body is seen to move faster than c. The same should apply for the return trip and for any speed, including c, provided there could be such a frame of reference.

But there's a catch: if both bodies collide back at the origin, each travelling at 0.8c relative to O, will the impact force be equivalent to 1.6c or 1c? And what about two photons? Will they collide at c or 2c?

 

I'm tired. Any thoughts?

[swansont]

!

Moderator Note

OT gravity discussion has been split http://www.scienceforums.net/topic/71788-speed-of-gravity/

[Cassandre]

 

You're using a confusing definition of "relative velocity." What you're describing is separation velocity. "Relative velocity" is traditionally defined as the the speed of one object from the rest frame of another.

Hi isn't it the other way round? Do you know an old physics text that uses separation velocity? I had learned it many years ago as timo understood it in post #3, and "separation velocity" is a term that I had not heard of until well after my studies. In contrast, Einstein used one century ago "relative motion" in the sense of leveni and timo here.

[elfmotat]

Hi isn't it the other way round? Do you know an old physics text that uses separation velocity? I had learned it many years ago as timo understood it in post #3, and "separation velocity" is a term that I had not heard of until well after my studies. In contrast, Einstein used one century ago "relative motion" in the sense of leveni and timo here.

 

Separation velocity is the rate at which the distance between two objects increases in an arbitrary frame. Separation velocities adds linearly, like velocities did in Galilean relativity. For example, if a red ball is moving in the +x direction with speed v_red, and a blue ball is moving in the -x direction with speed v_blue, then the separation velocity between the red and blue balls is just v_red+v_blue. Since nothing can travel faster than c, separation velocity cannot possibly be equivalent to relative velocity because all we would need to do to have objects moving at >c is let the velocities of the balls be some significant fraction of c.

 

The relative velocity between the balls (i.e. the speed of one ball as measured by the other) is found via Einstein velocity addition, and never exceeds c.

[SamBridge]

photon A<----[light source]---->photon B

 

Two photons are ejected from a light source at the same time, in opposite linear directions, in a vacuum. They are named photon A and photon B. The light source is stationary and Photon A travels at c in a westerly direction and photon B travels at c in an easterly direction.

 

Question A:

Immediately after being emitted from the light source, is photon A travelling at two times c relative to photon B?

 

In regards to question A: If the light source is stationary, then relative to the light source then the answer should be yes(Photon A is travelling at 2 times c relative to photon B from the light sources point of view).

 

Question B:

But from the point of view of photon B, would photon A be travelling at two times c?

 

In regards to question B: Is this question possible? That is, can photons ever be at rest relative to something else. Do they have rest mass?

Photons always travel at "c", it's called the lorentz transformation. The distance between objects is relative, as an object accelerates near the speed of light, it's relative measurement between increments of distancem easurement from the frame of reference of a near c object of distance becomes smaller. I still haven't quite figured out how to change it, but essentially time and distance change as something changes its position more and more at the rate of light.

http://en.wikipedia.org/wiki/Lorentz_transformation

It also has to do with time slowing down as something approaches the speed of light.

But as for the frame's of reference actually being photons, there is no frame of reference of a photon.

Edited January 13, 2013 by SamBridge

[Cassandre]

 

Separation velocity is the rate at which the distance between two objects increases in an arbitrary frame. Separation velocities adds linearly, like velocities did in Galilean relativity. For example, if a red ball is moving in the +x direction with speed v_red, and a blue ball is moving in the -x direction with speed v_blue, then the separation velocity between the red and blue balls is just v_red+v_blue. Since nothing can travel faster than c, separation velocity cannot possibly be equivalent to relative velocity because all we would need to do to have objects moving at >c is let the velocities of the balls be some significant fraction of c.

 

The relative velocity between the balls (i.e. the speed of one ball as measured by the other) is found via Einstein velocity addition, and never exceeds c.

Elfmotat, I learned that "relative velocity" means the difference in velocities (compare Einstein's 1905 paper*, third section: the ray moves relatively [..] with the velocity c-v). I asked if you know an old physics text that uses "separation velocity". From your answer I get that just like me you don't know one; and with the above definition there is little need for such. Thus, once more, it appears that the definition of "relative velocity" that you use is the more recent one. And that definition lacks distinction between "relative veloctiy" and "velocity" as also your comment illustrates.

 

Leveni, do you like me to elaborate or does this go too far off-topic?

 

*http://www.fourmilab.ch/etexts/einstein/specrel/www/

Edited January 13, 2013 by Cassandre

[elfmotat]

Elfmotat, I learned that "relative velocity" means the difference in velocities (compare Einstein's 1905 paper*, third section: the ray moves relatively [..] with the velocity c-v). I asked if you know an old physics text that uses "separation velocity". From your answer I get that just like me you don't know one; and with the above definition there is little need for such. Thus, once more, it appears that the definition of "relative velocity" that you use is the more recent one. And that definition lacks distinction between "relative veloctiy" and "velocity" as also your comment illustrates

I think you may be a little confused. I certainly don't know of any texts that take a difference in velocity to be the definition of "relative velocity." Einstein's certainly didn't, despite that quote you misunderstood. The Wikipedia page on relative velocity uses the same definition as me: http://en.wikipedia.org/wiki/Relative_velocity . Edited January 17, 2013 by elfmotat

[Cassandre]

I think you may be a little confused. I certainly don't know of any texts that take a difference in velocity to be the definition of "relative velocity." Einstein's certainly didn't, despite that quote you misunderstood. The Wikipedia page on relative velocity uses the same definition as me: http://en.wikipedia.org/wiki/Relative_velocity .

 

I certainly understood the text that I quoted, and Wikipedia isn't a scientific reference.

However see an older version of the same page:

http://en.wikipedia.org/w/index.php?title=Relative_velocity&oldid=360389838

As well as the current page on "Velocity":

http://en.wikipedia.org/wiki/Velocity#Relative_velocity

 

By chance (and contrary to that article's current claims!), the first reference in that "Relative velocity" article is such a text that you don't know. I can send you a copy of the definition in it if you like, and you can also find it in many libraries.

 

I will not comment more on different definitions in this thread except if the OP asks for it.

 

 

Thanks elfmotat and altergnostic. My intuition tells me altergnostic is correct but elfmotat has proven, mathematically, the difference in speed between the two photons is c. I guess the next step would be to calculate 'time dilation' and 'length contraction' between the two photons. Would this be right?

 

 

Hi leveni,

 

That can't work as was briefly mentioned [edit, also somewhat discussed].

Was the explanation sufficiently clear or do you need more clarification?

Edited January 17, 2013 by Cassandre

[manderson]

photon A<----[light source]---->photon B

 

Two photons are ejected from a light source at the same time, in opposite linear directions, in a vacuum. They are named photon A and photon B. The light source is stationary and Photon A travels at c in a westerly direction and photon B travels at c in an easterly direction.

 

Question A:

Immediately after being emitted from the light source, is photon A travelling at two times c relative to photon B?

 

In regards to question A: If the light source is stationary, then relative to the light source then the answer should be yes(Photon A is travelling at 2 times c relative to photon B from the light sources point of view).

 

Question B:

But from the point of view of photon B, would photon A be travelling at two times c?

 

In regards to question B: Is this question possible? That is, can photons ever be at rest relative to something else. Do they have rest mass?

A: yes

B: yes.

 

if both photons travel in same direction then there is ZERO relative motion (ie at rest). if in opposite directions, then the relative speed doubles, notwithstanding speed relative to inertial reference does not change. what you are addressing is space warp and wormholes. the answer is only NO if you stay on the surface of the universe, but interdimensionally it makes sense.

[Cassandre]

A: yes

B: yes.

 

if both photons travel in same direction then there is ZERO relative motion (ie at rest). if in opposite directions, then the relative speed doubles, notwithstanding speed relative to inertial reference does not change. what you are addressing is space warp and wormholes. the answer is only NO if you stay on the surface of the universe, but interdimensionally it makes sense.

Sorry but no, photons can't be "at rest": see replies #3 and #7.

And this has nothing to do with "space warp" or wormholes.

Edited January 18, 2013 by Cassandre