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Special Relativity and momentum

SDG

Graduate Poster
S
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It is easy to show that two inertial observers in relative motion do not agree on the conservation of linear momentum when they observe emission of one photon.
The thought experiment:

L8MFbHo.png


An LED flashlight in an intergalactic space emits one photon (wave packet) with the momentum P.
The recoil generated velocity vrecoil represents the conservation of the linear momentum.
The figure represents the LED flashlight rest frame and the recoil direction is through the flashlight center of mass G.
The end result is linear motion of the LED flashlight in the vrecoil direction.

Any comments so far?
Do we have an agreement this is the case?
 
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SDG said:
It is easy to show that two inertial observers in relative motion do not agree on the conservation of linear momentum when they observe emission of one photon.
The thought experiment:

[qimg]https://i.imgur.com/L8MFbHo.png[/qimg]

An LED flashlight in an intergalactic space emits one photon (wave packet) with the momentum P.
The recoil generated velocity vrecoil represents the conservation of the linear momentum.
The figure represents the LED flashlight rest frame and the recoil direction is through the flashlight center of mass G.
The end result is linear motion of the LED flashlight in the vrecoil direction.

Any comments so far?
Do we have an agreement this is the case?
Click to expand...


Why is Vrecoil orthogonal to P?
 
SDG said:
It is easy to show that two inertial observers in relative motion do not agree on the conservation of linear momentum when they observe emission of one photon.
The thought experiment:

[qimg]https://i.imgur.com/L8MFbHo.png[/qimg]

An LED flashlight in an intergalactic space emits one photon (wave packet) with the momentum P.
The recoil generated velocity vrecoil represents the conservation of the linear momentum.
The figure represents the LED flashlight rest frame and the recoil direction is through the flashlight center of mass G.
The end result is linear motion of the LED flashlight in the vrecoil direction.

Any comments so far?
Do we have an agreement this is the case?
Click to expand...

Flashlight.jpg

If the photon is emitted in the direction of the small arrow above P, why would vrecoil be in the same direction. Shouldn't it it be in the other direction - to the left as we look at the diagram?

What does the double-ended thick back arrow represent?
 
Last edited by a moderator:
I believe that the thick black arrows are supposed to be the opposite direction momentum vectors and that the other arrows are only the vector notation for the names of the vectors. If the arrow above Vrecoil had been only one character wide and above only the V, maybe it would have looked less confusing.
 
OK - so SR is wrong and you are the only person in a hundred years to have spotted this, even though you have never ever conducted one single piece of actual research.

And what is your next step?
 
smartcooky said:
If the photon is emitted in the direction of the small arrow above P, why would vrecoil be in the same direction. Shouldn't it it be in the other direction - to the left as we look at the diagram?

What does the double-ended thick back arrow represent?
Click to expand...

The position where the recoil happens is very very important.
It will become more obvious in the following analysis.

Now what is important is to agree the recoil happens at the point where the emission happens and the fact the recoil goes through the center of mass and the recoil generates linear momentum on the LED flashlight.

Do we have an agreement?
 
Shepherd said:
I believe that the thick black arrows are supposed to be the opposite direction momentum vectors and that the other arrows are only the vector notation for the names of the vectors. If the arrow above Vrecoil had been only one character wide and above only the V, maybe it would have looked less confusing.
Click to expand...

Correct.
 
Darat said:
OK - so SR is wrong and you are the only person in a hundred years to have spotted this, even though you have never ever conducted one single piece of actual research.

And what is your next step?
Click to expand...

I did my own research. I've been at it for a long time.
We will make more analysis here, and you will make your own conclusion and research if anybody else came with the same type of thought experiment.
 
smartcooky said:
...
What does the double-ended thick back arrow represent?
Click to expand...

The momentum is mass m of the flashlight multiplied by v... mv.

The vrecoil is the velocity vector generated by the recoil.
 
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SDG said:
I did my own research. I've been at it for a long time.
We will make more analysis here, and you will make your own conclusion and research if anybody else came with the same type of thought experiment.
Click to expand...

As I said never done any actual research. SR isn't accepted because of thought experiments it is accepted because of real world experiments and observations.

And again - so you show us that only you have spotted the error in SR that has eluded millions of people over decades, and then?
 
SDG said:
The position where the recoil happens is very very important.
It will become more obvious in the following analysis.

Now what is important is to agree the recoil happens at the point where the emission happens and the fact the recoil goes through the center of mass and the recoil generates linear momentum on the LED flashlight.

Do we have an agreement?
Click to expand...

Ok. I think I understand your notation now.


Great. So far so good, except that in the above there's a little bit of unusal phrasing that makes me suspicious of what comes next.

"The recoil goes through the center of mass" as something that is very important is somethig that seems like it might be about to mix up something that happens at very different scales, but whatever. So far so good, but reserving the right to advise and extend my remarks at a later time.

Lead on.
 
What is m here? Rest mass (invariant mass)? Or `relativistic mass', which seems not to be used much (at least not without a specific label) since it leads to confusion, such as forgetting that it's frame dependent. In SR the formula for momentum uses the latter, or, as normally written, invariant mass times gamma times velocity. See e.g., wikipedia .

What you appear to mean (m_0 v) is not a conserved quantity in SR.
 
boy this forum moves slow...after the first post I was anxiously awaiting some amazing new insight and here I am, still left hanging! :rolleyes:
 
SDG said:
It is easy to show that two inertial observers in relative motion do not agree on the conservation of linear momentum when they observe emission of one photon.
Click to expand...

This is absolutely wrong. But it’s not a terribly common wrong, so I can’t predict what mistakes you have made before you reveal them.

The figure represents the LED flashlight rest frame and the recoil direction is through the flashlight center of mass G.
Click to expand...

Is your point here solely that you want a situation where the recoil applies no torque to the flashlight? If so, this is a slightly awkward way of phrasing it, but it’s a reasonable constraint to apply for the sake of simplicity.

Assuming that is what you mean, press on so I can find your mistakes.
 
Meridian said:
What is m here? Rest mass (invariant mass)? Or `relativistic mass', which seems not to be used much (at least not without a specific label) since it leads to confusion, such as forgetting that it's frame dependent. In SR the formula for momentum uses the latter, or, as normally written, invariant mass times gamma times velocity. See e.g., wikipedia .

What you appear to mean (m_0 v) is not a conserved quantity in SR.
Click to expand...

Egads, NO! Do not use relativistic mass. It has overstayed its welcome. There is a reason modern relativity texts tend not to use it anymore. Make the nonlinearities explicit, don’t hide them. There is never a situation where you need relativistic mass rather than rest mass, and it is more likely to confuse than to illuminate.
 
Darat said:
SR isn't accepted because of thought experiments it is accepted because of real world experiments and observations.
Click to expand...

That’s true, BUT…

Thought experiments alone were enough to get every physicist who was paying attention to sit up and take note. Even without doing a single experiment, SR made Maxwell’s equations invariant. And that alone is enough to indicate that it was a theory worth taking a very long look at. So we shouldn’t undersell the usefulness of thought experiments.

That being said, you’ve still got to do them right, and SR skeptics never seem to be able to.
 
I hope that the OP takes into account that two relatively-moving observers will not agree on the value of P (the momentum of the photon). Because Doppler shift.
 
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