How Can the Relative Speed of Photons Exceed the Cosmic Speed Limit?

Physics news on Phys.org
The fallacy is here is the mention of a "relative speed" for photons without defining what exactly you mean by "relative speed". It depends on what you mean by that. If you mean by relative speed "the speed one object sees the other object moving at", then this is a non-question because there exist no reference frame in which a photon is at rest.

If you simply mean "how fast does the distance between the two objects shrink as measured by a 3rd, stationary observer", then the answer is the obvious 6*10^8m/s.
 
Matterwave said:
If you simply mean "how fast does the distance between the two objects shrink as measured by a 3rd, stationary observer", then the answer is the obvious 6*10^8m/s.

@Matterwave yeah it means for a 3rd, stationary observer, but the distance between two objects shouldn't shrink faster than 3*10^8m/s. The exact question is why/how here for a stationary observer, the photons are moving towards each other with a speed more than the cosmic limit?
 
Who said that the distance between two objects can't shrink faster than 3*10^8 m/s? Special Relativity certainly doesn't say that.

Special relativity says only that one object can never exceed a speed of 3*10^8m/s as viewed from another object's reference frame. It makes no claims for two objects working together.
 
Matterwave said:
Who said that the distance between two objects can't shrink faster than 3*10^8 m/s? Special Relativity certainly doesn't say that.

Special relativity says only that one object can never exceed a speed of 3*10^8m/s as viewed from another object's reference frame. It makes no claims for two objects working together.

You just tell me, isn't in this case, one photon approaching another photon(opposite one) with a speed equal to 2c? Which is more than the cosmic limit, how is this in agreement with the theory of relativity, that is what I want to know!
As far as I know speed=dx/dt, so according to this definition how is this 'shrinking of distance between the two objects' different from 'speed'? Isn't rate of shrinking of distance between two objects, what we call 'approaching speed'?
 
The "cosmic speed limit" applies to objects with mass relative to an inertial frame.

Instead of photons, imagine two massive objects approaching each other. Each object has a speed of 0.99c relative to the observer between them. This observer can calculate that the distance between the two objects, in his reference frame, is shrinking at 1.98c. This does not contradict the "cosmic speed limit", because the speed of one of the objects relative to a reference frame in which the other object is at rest is not 1.98c: it is about 0.9999c (calculated using the relativistic formula for adding velocities).
 
Michael C said:
The "cosmic speed limit" applies to objects with mass relative to an inertial frame.

Instead of photons, imagine two massive objects approaching each other. Each object has a speed of 0.99c relative to the observer between them. This observer can calculate that the distance between the two objects, in his reference frame, is shrinking at 1.98c. This does not contradict the "cosmic speed limit", because the speed of one of the objects relative to a reference frame in which the other object is at rest is not 1.98c: it is about 0.9999c .

I understand that the speed of any of the two massive objects w.r.t observer will be 0.999c but when we see from frame of reference of any of the moving objects the speed of the other object w.r.t it will be 1.98c which is more than the cosmic limit.
P.S. As far as I have understood speed is always relative(correct me if I am wrong).
 
aleemudasir said:
I understand that the speed of any of the two massive objects w.r.t observer will be 0.999c but when we see from frame of reference of any of the moving objects the speed of the other object w.r.t it will be 1.98c which is more than the cosmic limit.
Reread Michael C's post. The speed of one object with respect to the other is not 1.98c.
P.S. As far as I have understood speed is always relative(correct me if I am wrong).
The 1.98c is the closing rate as seen by the third frame. It's not the speed of anything.
 
Doc Al said:
Reread Michael C's post. The speed of one object with respect to the other is not 1.98c.

The 1.98c is the closing rate as seen by the third frame. It's not the speed of anything.
because the speed of one of the objects relative to a reference frame in which the other object is at rest is not 1.98c: it is about 0.9999c (calculated using the relativistic formula for adding velocities).
Micheal C talks about a reference frame in which the other object is at rest, but I am talking about reference frame when both the objects are moving. I am talking about the reference frame in which both the objects are moving and I am taking into account the speed of one of the object with respect to other!
 
  • #10
aleemudasir said:
Micheal C talks about a reference frame in which the other object is at rest, but I am talking about reference frame when both the objects are moving. I am talking about the reference frame in which both the objects are moving and I am taking into account the speed of one of the object with respect to other!
Realize that those two statements contradict each other. When you talk about the speed of object 2 with respect to object 1, you are talking about the speed of object 2 in a frame in which object 1 is at rest. That's what 'relative speed' means.

The problem (I suspect) is that our everyday intuitions about how speeds add, which are based on objects moving much slower than light speed, do not work when speeds are higher.

For example: If two cars move towards each other at 60 mph with respect to the earth, then their relative speed is (pretty close to) 120 mph. Not true when objects move at significantly close to light speeds.
 
  • #11
aleemudasir said:
Micheal C talks about a reference frame in which the other object is at rest, but I am talking about reference frame when both the objects are moving. I am talking about the reference frame in which both the objects are moving and I am taking into account the speed of one of the object with respect to other!

Yes, as already stated, the closing rate (being the rate of change of the distance measured between the two objects) as seen by the observer in this frame is 1.98c. That is not the same thing as the speed of one object with respect to the other one.

The fact that "closing rate" and "relative speed" are not the same is certainly a surprise when you start studying relativity, since it contradicts our everyday intuition, but it is in fact completely logical.
 
  • #13
Just now want to know one thing.Is the relative speed of one photon wrt other is greater than c or not?If not then why and how the distance is shrinking the other way?
 
  • #14
moatasim23 said:
Just now want to know one thing.Is the relative speed of one photon wrt other is greater than c or not?If not then why and how the distance is shrinking the other way?

The speed of one photon relative to another one is undefined, since a photon does not define a reference frame. You can replace the photons by objects traveling as near to the speed of light as you wish (see my example above): their relative speed will never be above c.

I must once more stress this point: "closing rate" and "relative speed" are not the same thing. A closing rate of more than c does not contradict the theory of relativity.
 
  • #15
...The speed of one photon relative to another one is undefined, since a photon does not define a reference frame.

This is accurate, but it should also be noted that if you were traveling really, really close to lightspeed, .9 or .99 or .999c, light would still go buzzing by at 'c'. Light zips by a massive observer at 'c' no matter how fast that observer is moving. Everybody sees light at speed 'c'.
 
  • #16
jtbell said:
Look up relativistic "velocity addition":

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

Velocity addition doesn't really apply here because photons don't have a rest frame. However, setting u,v=c does yield a velocity c.

moatasim23 said:
Just now want to know one thing.Is the relative speed of one photon wrt other is greater than c or not?If not then why and how the distance is shrinking the other way?

Photons don't have a rest frame, so asking about the speed of one photon relative to another doesn't have any real meaning.
 
  • #17
jtbell said:
Look up relativistic "velocity addition":

hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

Please could you tell me what would be the speed of projectile fired from #1 relative to #2. I tried to solve it using the given equations, but I think I got some error!

Detailed solution will be much welcomed and appreciated.
Thanks.
 
  • #18
aleemudasir said:
Please could you tell me what would be the speed of projectile fired from #1 relative to #2. I tried to solve it using the given equations, but I think I got some error!

Show us how you tried to do the calculation, and someone will probably be happy to point out your error.
 
  • #19
jtbell said:
Show us how you tried to do the calculation, and someone will probably be happy to point out your error.
My calculation is as following:
The speed u'(speed of projectile w.r.t to #1) in this case=0.7c, then I calculated u(speed of projectile w.r.t stationary observer) by u=0.8c+0.7c/1+0.8c*0.7c/c^2, then I calculated the relative speed of projectile w.r.t #2 by the same equation u''(#2)=u+0.9c/1+0.9c*u/c^2
 
  • #20
Doc Al said:
Realize that those two statements contradict each other. When you talk about the speed of object 2 with respect to object 1, you are talking about the speed of object 2 in a frame in which object 1 is at rest. That's what 'relative speed' means.

The problem (I suspect) is that our everyday intuitions about how speeds add, which are based on objects moving much slower than light speed, do not work when speeds are higher.

For example: If two cars move towards each other at 60 mph with respect to the earth, then their relative speed is (pretty close to) 120 mph. Not true when objects move at significantly close to light speeds.

Is absolute rest frame(as you mean here that the object 1 is at rest) possible in this universe, I think each and every object in this universe is moving with respect to one or other reference frame.

Does relative speed truly mean that other body should be at rest, I think we incorporate in this term i.e. relative velocity when both the bodies considered are moving, as far as I know when one of the bodies is at rest with respect to other then we don't use the term relative velocity.
 
  • #21
Michael C said:
The speed of one photon relative to another one is undefined, since a photon does not define a reference frame. You can replace the photons by objects traveling as near to the speed of light as you wish (see my example above): their relative speed will never be above c.

I must once more stress this point: "closing rate" and "relative speed" are not the same thing. A closing rate of more than c does not contradict the theory of relativity.

Thanks for the info, would you please give us more info on the difference on closing rate and relative speed and how they are different, or guide me to a place where I would find such info on it.
Thanks.
 
  • #22
aleemudasir said:
Is absolute rest frame(as you mean here that the object 1 is at rest) possible in this universe, I think each and every object in this universe is moving with respect to one or other reference frame.
Every object is at rest in its own rest frame. That's what 'rest frame' means. Nothing absolute about it.
Does relative speed truly mean that other body should be at rest, I think we incorporate in this term i.e. relative velocity when both the bodies considered are moving, as far as I know when one of the bodies is at rest with respect to other then we don't use the term relative velocity.
Everything is always at rest with respect to itself. So the relative velocity of something with respect to me (say) means the speed it has in a frame in which I am at rest.
 
  • #23
aleemudasir said:
My calculation is as following:
The speed u'(speed of projectile w.r.t to #1) in this case=0.7c, then I calculated u(speed of projectile w.r.t stationary observer) by u=0.8c+0.7c/1+0.8c*0.7c/c^2, then I calculated the relative speed of projectile w.r.t #2 by the same equation u''(#2)=u+0.9c/1+0.9c*u/c^2
Looks OK to me.
 
  • #24
aleemudasir said:
Thanks for the info, would you please give us more info on the difference on closing rate and relative speed and how they are different, or guide me to a place where I would find such info on it.
Thanks.

Have a look at the wikipedia article on Faster-than-light, "closing speeds"

See also the paragraph on third party observers on this page: Is Faster-Than-Light Travel or Communication Possible?.
 
  • #25
aleemudasir said:
As far as I know speed=dx/dt, so according to this definition how is this 'shrinking of distance between the two objects' different from 'speed'? Isn't rate of shrinking of distance between two objects, what we call 'approaching speed'?
The cosmic speed limit says that |\frac{dx_i}{dt}|<c where x_i is the position of some given massive object, i, in some given inertial reference frame. This does not imply that |\frac{d(x_i-x_j)}{dt}|<c. Do you see that those are entirely different quantities?
 
  • #26
DaleSpam said:
The cosmic speed limit says that |\frac{dx_i}{dt}|<c where x_i is the position of some given massive object, i, in some given inertial reference frame. This does not imply that |\frac{d(x_i-x_j)}{dt}|<c. Do you see that those are entirely different quantities?

|\frac{dx_i}{dt}| is used when reference frame is at rest, so we define change in position of object w.r.t to that reference frame by it, but we are talking about a situation in which both the objects are moving and we use one of the objects as reference frame for other, so how will you define the change in position w.r.t to reference point in this case, certainly not by "|\frac{dx_i}{dt}|", as both the objects are moving in which we use one as reference frame.
 
  • #27
aleemudasir said:
|\frac{dx_i}{dt}| is used when reference frame is at rest,

Remember that "at rest" has no meaning in an absolute sense: you can only say that something is "at rest" with respect to something else. You use the phrase "when reference frame is at rest". This phrase as it stands has no meaning.

so we define change in position of object w.r.t to that reference frame by it, but we are talking about a situation in which both the objects are moving and we use one of the objects as reference frame for other, so how will you define the change in position w.r.t to reference point in this case, certainly not by "|\frac{dx_i}{dt}|", as both the objects are moving in which we use one as reference frame.

This is unclear. You say "as both the objects are moving". Once we have used one of the objects to define a reference frame, that object is not moving in the defined reference frame.
 
  • #28
aleemudasir said:
a situation in which both the objects are moving and we use one of the objects as reference frame for other
This is a self-contradictory statement. If both objects are moving then neither is being used as a reference frame for the other.

If you want to use one object as the reference frame for the other then you must transform to a reference frame where the reference object is stationary, not moving.
 
  • #29
Michael C said:
Remember that "at rest" has no meaning in an absolute sense: you can only say that something is "at rest" with respect to something else. You use the phrase "when reference frame is at rest". This phrase as it stands has no meaning.



This is unclear. You say "as both the objects are moving". Once we have used one of the objects to define a reference frame, that object is not moving in the defined reference frame.

Either I am not able to express or you aren't getting my point! Now I will use an example to explain the situation which I am trying to define:
Suppose the distance between two missiles A and B is decreasing in space(there is nothing except these two missiles) and you are sitting in one of the missiles. Now my question is how will you define motion here, how can you say whether A is moving towards B or B is moving towards A, whether only A is moving or whether only B is moving or both are moving? And how will you define reference frame here?
 
  • #30
aleemudasir said:
Either I am not able to express or you aren't getting my point! Now I will use an example to explain the situation which I am trying to define:
Suppose the distance between two missiles A and B is decreasing in space(there is nothing except these two missiles) and you are sitting in one of the missiles. Now my question is how will you define motion here, how can you say whether A is moving towards B or B is moving towards A, whether only A is moving or whether only B is moving or both are moving? And how will you define reference frame here?

It is equally valid to say that A is moving towards B as it is to say that B is moving towards A. We cannot say in an absolute sense that one of the missiles is "moving" and the other is "at rest": we can only say that there is relative motion between the missiles.

If I am sitting on one of the missiles, then it would be simplest for me to use a reference frame in which I am at rest. Let's say I'm sitting on missile A. For me, A is at rest and B is moving. For my friend sitting on missile B, B is at rest and A is moving. We describe the situation differently, but both of us are right.

Note that I say "it would be simplest for me to use a reference frame in which I am at rest". I don't have to use this frame of reference. I could also define a frame in which both A and B are moving. The basic principle of relativity is this: all of these reference frames are equally valid. There is no single frame that tells us what is "actually" happening: any frame describes what is actually happening just as well as any other.
 
  • #31
I have a question regarding Einstien's velocity addition equation:
u'= u-v/1-uv/c^2, what if both are moving with speed of light?
 
  • #32
Michael C said:
It is equally valid to say that A is moving towards B as it is to say that B is moving towards A. We cannot say in an absolute sense that one of the missiles is "moving" and the other is "at rest": we can only say that there is relative motion between the missiles.

If I am sitting on one of the missiles, then it would be simplest for me to use a reference frame in which I am at rest. Let's say I'm sitting on missile A. For me, A is at rest and B is moving. For my friend sitting on missile B, B is at rest and A is moving. We describe the situation differently, but both of us are right.

Note that I say "it would be simplest for me to use a reference frame in which I am at rest". I don't have to use this frame of reference. I could also define a frame in which both A and B are moving. The basic principle of relativity is this: all of these reference frames are equally valid. There is no single frame that tells us what is "actually" happening: any frame describes what is actually happening just as well as any other.

OK! What if I say two persons are moving considering the same problem as above instead of two missiles in space which goes like this:
Suppose the distance between two persons A and You is decreasing in space(there is nothing except these two persons) and you are one of the persons. Now my question is how will you define motion here, how can you say whether A is moving towards You or You are moving towards A, whether only A is moving or whether only You are moving or both are moving? And how will you define reference frame here?
 
  • #33
aleemudasir said:
OK! What if I say two persons are moving considering the same problem as above instead of two missiles in space which goes like this:
Suppose the distance between two persons A and You is decreasing in space(there is nothing except these two persons) and you are one of the persons. Now my question is how will you define motion here, how can you say whether A is moving towards You or You are moving towards A, whether only A is moving or whether only You are moving or both are moving? And how will you define reference frame here?
We can do it any way we want as long as the speed at which A and You are approaching calculates out to be the same in whatever frame we choose. So let's say that A and You are approaching at 0.8c.

We could pick a frame in which A is at rest and You are approaching from the +X direction at -0.8C.

Or we could pick a frame in which You are at rest and A is approaching from the -X direction at +0.8c.

Or we could pick a frame in which A and You are both moving at the same speed toward each other, A from -X at +0.5c and You from +X at -0.5c.

Or we could pick a frame in which A is moving from -X at +0.8c and You are moving from +X at +0.97561c.

So the frame we pick determines how we assign the motion(s) of the two persons.

Please note: I am only repeating what others have said before. We can't figure out why you are struggling so hard with this.
 
Last edited:
  • #34
aleemudasir said:
OK! What if I say two persons are moving considering the same problem as above instead of two missiles in space which goes like this:
Suppose the distance between two persons A and You is decreasing in space(there is nothing except these two persons) and you are one of the persons. Now my question is how will you define motion here, how can you say whether A is moving towards You or You are moving towards A, whether only A is moving or whether only You are moving or both are moving? And how will you define reference frame here?

You've just repeated the same question. I already said this:
We cannot say in an absolute sense that one of the missiles is "moving" and the other is "at rest": we can only say that there is relative motion between the missiles.

Just replace "missile" by "person" and the same thing applies. The whole point of relativity is this: all motion is relative. You want to know how I can tell if it is A that is moving towards me or me that is moving towards A. The answer is: it depends on the chosen frame of reference. There is no absolute frame of reference that will permit me to say that A is "really" moving and B is "really" at rest.
 
  • #35
aleemudasir said:
I have a question regarding Einstien's velocity addition equation:
u'= u-v/1-uv/c^2, what if both are moving with speed of light?

Then that equation doesn't apply because you're no longer working in an inertial frame (an inertial frame can't be moving at c).
 
  • #36
Michael C said:
You've just repeated the same question. I already said this:


Just replace "missile" by "person" and the same thing applies. The whole point of relativity is this: all motion is relative. You want to know how I can tell if it is A that is moving towards me or me that is moving towards A. The answer is: it depends on the chosen frame of reference. There is no absolute frame of reference that will permit me to say that A is "really" moving and B is "really" at rest.

I repeated the question because in earlier case I had put a person in missile, and then you used that to answer me that the missile(in which the person was) is in rest w.r.t to the person, so now I just used two bodies(person A and B) to clarify what actually the question was, so as to tell you that nothing here is in rest w.r.t. anything so, how would reference frame be defined here.
Thanks.
 
  • #37
elfmotat said:
Then that equation doesn't apply because you're no longer working in an inertial frame (an inertial frame can't be moving at c).
OK what would be the case when one body is moving with 0.99999c(Body A) and other with c(Body B), and I am taking body A as reference frame?
 
  • #38
ghwellsjr said:
We can do it any way we want as long as the speed at which A and You are approaching calculates out to be the same in whatever frame we choose. So let's say that A and You are approaching at 0.8c.

We could pick a frame in which A is at rest and You are approaching from the +X direction at -0.8C.

Or we could pick a frame in which You are at rest and A is approaching from the -X direction at +0.8c.

Or we could pick a frame in which A and You are both moving at the same speed toward each other, A from -X at +0.5c and You from +X at -0.5c.

Or we could pick a frame in which A is moving from -X at +0.8c and You are moving from +X at +0.97561c.

So the frame we pick determines how we assign the motion(s) of the two persons.

Please note: I am only repeating what others have said before. We can't figure out why you are struggling so hard with this.

I just want to know few aspects of relative velocity taking relativity into account, and I think either I am not able to express my question or you aren't getting what I really want to know!
 
  • #39
aleemudasir said:
OK what would be the case when one body is moving with 0.99999c(Body A) and other with c(Body B), and I am taking body A as reference frame?
You'll find that the speed of Body B will be c as measured in any frame.
 
  • #40
aleemudasir said:
OK what would be the case when one body is moving with 0.99999c(Body A) and other with c(Body B), and I am taking body A as reference frame?

u=\frac{v+c}{1+vc/c^2}=\frac{v+c}{1+v/c}=c(\frac{v+c}{v+c})=c

So it doesn't matter what you use as v (the speed of body A), it will always come out as c. This should make sense because we expect light to have the same speed in every inertial frame.
 
  • #41
aleemudasir said:
I repeated the question because in earlier case I had put a person in missile, and then you used that to answer me that the missile(in which the person was) is in rest w.r.t to the person, so now I just used two bodies(person A and B) to clarify what actually the question was, so as to tell you that nothing here is in rest w.r.t. anything so, how would reference frame be defined here.
Thanks.

You can still define a reference frame to be at rest with respect to A, or one that is at rest with respect to B. You can also define a reference frame to be moving at a velocity x with respect to A, or one that moves at velocity y with respect to A, or one that moves at velocity z with respect to B...

In short, you can define an infinity of reference frames for any situation. Each one is as valid as the next one.
 
  • #42
aleemudasir said:
ghwellsjr said:
We can do it any way we want as long as the speed at which A and You are approaching calculates out to be the same in whatever frame we choose. So let's say that A and You are approaching at 0.8c.

We could pick a frame in which A is at rest and You are approaching from the +X direction at -0.8C.

Or we could pick a frame in which You are at rest and A is approaching from the -X direction at +0.8c.

Or we could pick a frame in which A and You are both moving at the same speed toward each other, A from -X at +0.5c and You from +X at -0.5c.

Or we could pick a frame in which A is moving from -X at +0.8c and You are moving from +X at +0.97561c.

So the frame we pick determines how we assign the motion(s) of the two persons.

Please note: I am only repeating what others have said before. We can't figure out why you are struggling so hard with this.
I just want to know few aspects of relative velocity taking relativity into account, and I think either I am not able to express my question or you aren't getting what I really want to know!
This thread started off with a question about two photons approaching each other. Unfortunately, that question has several different unrelated issues with regard to it and they have all been covered in different posts. If the question had been regarding two bodies (or persons or missiles or whatever as long as they are traveling less than the speed of light), then the answers could have been focused on that one issue. Unfortunately, you continue to bring in one body traveling at the speed of light and it diverts the answers off in another direction again. So please don't bring up a body traveling at the speed of light, OK, it will just bring about more confusion. A body can go at any speed approaching the speed of light such as 0.999999999c but not 1.0000000000c.

Now in my previous answer, I picked a relative speed of 0.8c to use in my examples. Note that I said we could use a reference frame in which both persons are approaching at 0.5c. If you simply added these two speeds together, you would get exactly 1.0c. Do you understand that in this reference frame, even though the closing speed is 1.0c, there is nothing traveling at 1.0c and the two bodies don't have a relative speed of 1.0c? If you use the velocity addition formula, you will see that their relative speed is 0.8c. Do you understand all this?

Whether or not this is what you want to know, do you understand what I have explained? If it isn't what you want to know, tell me what about my explanation is not related to what you want to know.
 
  • #43
This comes back every now and then; isn't it a FAQ?
aleemudasir said:
I understand that the speed of any of the two massive objects w.r.t observer will be 0.999c but when we see from frame of reference of any of the moving objects the speed of the other object w.r.t it will be 1.98c which is more than the cosmic limit.
P.S. As far as I have understood speed is always relative(correct me if I am wrong).
The limit for that kind of relative speed is simply the sum of each: thus c+c=2c. And why this is so, has been elaborately explained already; that can't be the problem. The only problem is to correct the misunderstanding - and that can be a big problem, if the misunderstanding has been ingrained.

Apparently you think that a light ray can only move with a velocity of c relative to another object or light ray. So, here's another reply -by a certain A. Einstein- in one of the papers in which also your "cosmic limit" is explained:

"the ray moves relatively to the [moving] initial point of k, when measured in the stationary system, with the velocity c-v".
- http://www.fourmilab.ch/etexts/einstein/specrel/www/

Note that c-v>c for the case that the two move in opposite directions.
moatasim23 said:
Just now want to know one thing.Is the relative speed of one photon wrt other is greater than c or not?If not then why and how the distance is shrinking the other way?
That question is also answered in that same section; as long as you use a single reference system you must subtract the two velocities from each other, taking in account the angles. Thus for perpendicular motion one has (a few lines above the earlier quote):

"applied to the [moving] axes of Y and Z—it being borne in mind that light is always propagated along these axes, when viewed from the stationary system, with the velocity √(c2-v2)"

That's standard Pythagoras. :smile:
 
Last edited:
  • #44
elfmotat said:
u=\frac{v+c}{1+vc/c^2}=\frac{v+c}{1+v/c}=c(\frac{v+c}{v+c})=c

So it doesn't matter what you use as v (the speed of body A), it will always come out as c. This should make sense because we expect light to have the same speed in every inertial frame.
Thanks, but!
If both the bodies are moving in the same direction in the +ve x-direction the value of relative velocity comes up:
u=\frac{v-c}{1-vc/c^2}=\frac{v-c}{1-v/c}=c(\frac{v-c}{c-v})=-c

What does -c mean here?
 
  • #45
ghwellsjr said:
This thread started off with a question about two photons approaching each other. Unfortunately, that question has several different unrelated issues with regard to it and they have all been covered in different posts. If the question had been regarding two bodies (or persons or missiles or whatever as long as they are traveling less than the speed of light), then the answers could have been focused on that one issue. Unfortunately, you continue to bring in one body traveling at the speed of light and it diverts the answers off in another direction again. So please don't bring up a body traveling at the speed of light, OK, it will just bring about more confusion. A body can go at any speed approaching the speed of light such as 0.999999999c but not 1.0000000000c.

Now in my previous answer, I picked a relative speed of 0.8c to use in my examples. Note that I said we could use a reference frame in which both persons are approaching at 0.5c. If you simply added these two speeds together, you would get exactly 1.0c. Do you understand that in this reference frame, even though the closing speed is 1.0c, there is nothing traveling at 1.0c and the two bodies don't have a relative speed of 1.0c? If you use the velocity addition formula, you will see that their relative speed is 0.8c. Do you understand all this?

Whether or not this is what you want to know, do you understand what I have explained? If it isn't what you want to know, tell me what about my explanation is not related to what you want to know.
I understood the difference between closing speed and relative speed, and how the relative speed comes up 0.8c!
 
  • #46
aleemudasir said:
Thanks, but!
If both the bodies are moving in the same direction in the +ve x-direction the value of relative velocity comes up:
u=\frac{v-c}{1-vc/c^2}=\frac{v-c}{1-v/c}=c(\frac{v-c}{c-v})=-c

What does -c mean here?
It just means you messed up with a sign.

You'll have less chance of messing up signs when you use this version of the addition of velocity formula:
V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}

Here V_{a/c} means the velocity of A with respect to C. So call the first body C and the second body A. And the third frame B.

So Va/b = c;
Vc/b = v, so Vb/c = -v;

What you want is u = Va/c.

Do all that and you'll get u = +c.
 
  • #47
aleemudasir said:
Thanks, but!
If both the bodies are moving in the same direction in the +ve x-direction the value of relative velocity comes up:
u=\frac{v-c}{1-vc/c^2}=\frac{v-c}{1-v/c}=c(\frac{v-c}{c-v})=-c

What does -c mean here?
You need to substitue v with -c instead of putting the minus sign in front of the c. Then you will get:

u=\frac{-c+c}{1-cc/c^2}=\frac{-c+c}{1-1}=\frac{0}{0}=?

which is indeterminate meaning you need some other way to calculate the answer.

However if you start with the orginal equation:

u=\frac{v+u'}{1+vu'/c^2}

and set u' equal to -v (since the formula assumes opposite directions and you want the same direction), then:

u=\frac{v-v}{1-vv/c^2}=\frac{0}{1-v^2/c^2}=0

unless v=c but u approaches zero in the limit as v approaches c.
 
  • #48
aleemudasir said:
ghwellsjr said:
This thread started off with a question about two photons approaching each other. Unfortunately, that question has several different unrelated issues with regard to it and they have all been covered in different posts. If the question had been regarding two bodies (or persons or missiles or whatever as long as they are traveling less than the speed of light), then the answers could have been focused on that one issue. Unfortunately, you continue to bring in one body traveling at the speed of light and it diverts the answers off in another direction again. So please don't bring up a body traveling at the speed of light, OK, it will just bring about more confusion. A body can go at any speed approaching the speed of light such as 0.999999999c but not 1.0000000000c.

Now in my previous answer, I picked a relative speed of 0.8c to use in my examples. Note that I said we could use a reference frame in which both persons are approaching at 0.5c. If you simply added these two speeds together, you would get exactly 1.0c. Do you understand that in this reference frame, even though the closing speed is 1.0c, there is nothing traveling at 1.0c and the two bodies don't have a relative speed of 1.0c? If you use the velocity addition formula, you will see that their relative speed is 0.8c. Do you understand all this?

Whether or not this is what you want to know, do you understand what I have explained? If it isn't what you want to know, tell me what about my explanation is not related to what you want to know.
I understood the difference between closing speed and relative speed, and how the relative speed comes up 0.8c!
So are we done?
 
  • #49
Doc Al said:
It just means you messed up with a sign.

You'll have less chance of messing up signs when you use this version of the addition of velocity formula:
V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}

Here V_{a/c} means the velocity of A with respect to C. So call the first body C and the second body A. And the third frame B.

So Va/b = c;
Vc/b = v, so Vb/c = -v;

What you want is u = Va/c.

Do all that and you'll get u = +c.

Sorry for that question, I realized just a few moments after posting the question that I have done a mistake while solving the equation!
Anyways thanks!
 
Last edited:
  • #50
ghwellsjr said:
So are we done?

Yes to some extent, now I understood the dilemma of this relative velocity taking relativity into account. I have some last questions regarding relativity, do we know the reason why a particle moving @c can't be taken as reference frame and why does the behavior/properties and laws change so abruptly when we move from speed c-1m/s to c?

Thanks to all for you kind help and precious time.
With regards
Mudasir
 

Similar threads

B Meaningfulness of the speed of light
Replies
25
Views
2K
B Can an Object Exceed the Speed of Light?
Replies
12
Views
2K
I Can there be a maximum curvature of spacetime?
Replies
9
Views
1K
I Conventionality of the One-Way Speed of Light
Replies
5
Views
309
I The speed of one photon through a transparent medium
2
Replies
74
Views
4K
B Can Motion Exceed the Speed of Light in General Relativity?
Replies
20
Views
1K
Math Game: True or False - Correct/Incorrect?
Replies
3
Views
2K
B Light Speed in Vacuum: Does It Reach Cosmic Limit?
Replies
12
Views
3K
B Speed of Light & Space: Exceeding the "Universal Speed Limit
Replies
3
Views
1K
A Electrodynamics of moving bodies - §2: On the relativity of... (again)
Replies
35
Views
4K

Hot Threads

Recent Insights

Back
Top