# Relative Speed of Photon!

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Matterwave
Gold Member
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.

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?

Matterwave
Gold Member
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.

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).

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).

Doc Al
Mentor
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.

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!

Doc Al
Mentor
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.

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.

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?

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 travelling 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.

...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'.

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.

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.

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.

jtbell
Mentor
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.

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

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.

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 travelling 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.

Doc Al
Mentor
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.

Doc Al
Mentor
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.

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"

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?