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Refutation of Special Relativity for Dummies

wogoga

Critical Thinker
W
Joined
Apr 16, 2007
Messages
334
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An electron and a positron at rest can annihilate into two photons, each with a frequency corresponding to mass/energy of one electron (or positron).

In order to refute SR, we simply ask what happens in this situation:
Electron and positron annihilate while both moving at (relativistic) speed v.​
From energy conservation we conclude:

The sum of the two frequencies [1] of the emerging photon-pair is higher than the sum calculated by applying classical Doppler shift [2] to the annihilation event with rest mass, as kinetic energy of the electron-positron-pair increases the sum of the photon frequencies.​

From time dilation (or relativistic Doppler effect) we conclude:

The sum of the two frequencies [1] of the emerging photon-pair is lower than the sum calculated by applying classical Doppler shift [2] to an annihilation event with rest mass, as time dilation reduces photon frequencies.​

Using common sense, we can easily recognize that a real experiment can only confirm energy conservation (i.e. higher frequencies) and refute time dilation.

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[1] Two photons with freq1 and freq2 have the same energy as a single photon with freqsum = freq1 + freq2, i.e. total frequency is proportional to total energy.
[2] The relativistic Doppler effect is the combination of the classical Doppler effect [3] with time dilation of SR.
[3] with observer (=receiver) at rest relative to the medium, and a source moving at -c < v < c
 
wogoga said:
From energy conservation we conclude:

The sum of the two frequencies [1] of the emerging photon-pair is higher than the sum calculated by applying classical Doppler shift [2] to the annihilation event with rest mass, as kinetic energy of the electron-positron-pair increases the sum of the photon frequencies.​

From time dilation (or relativistic Doppler effect) we conclude:

The sum of the two frequencies [1] of the emerging photon-pair is lower than the sum calculated by applying classical Doppler shift [2] to an annihilation event with rest mass, as time dilation reduces photon frequencies.​
Click to expand...

"For dummies" indeed. Why would you calculating the "sum of the frequencies" and transforming it? Go ahead and transform each of the frequencies, and then sum them. (Don't forget that the two photons are moving in opposite directions.)

I recommend actually showing your transformation-formula and how you applied it. (I do not recommend skipping the math and guessing you know the answer.)
 
ben m said:
"For dummies" indeed. Why would you calculating the "sum of the frequencies" and transforming it? Go ahead and transform each of the frequencies, and then sum them. (Don't forget that the two photons are moving in opposite directions.)

I recommend actually showing your transformation-formula and how you applied it. (I do not recommend skipping the math and guessing you know the answer.)
Click to expand...
Apparently you're not dumb enough. Smoke 'em if you got 'em.
 
Because we've got no actual practical experience of smashing particles together at relativistic velocities... oh wait!
 
Refuting Einstein's theory of special relativity would involve a two-step process.
First, one must attain a thorough knowledge of the the theory, including its inherent predictions (with mathematical precision).
Second, conduct an actual experiment showing that the theory is not consistent with the outcome of that experiment (with mathematical precision).
Hint: start with step one.
 
wogoga said:
---
An electron and a positron at rest can annihilate into two photons, each with a frequency corresponding to mass/energy of one electron (or positron).

In order to refute SR, we simply ask what happens in this situation:
Electron and positron annihilate while both moving at (relativistic) speed v.​
From energy conservation we conclude:

The sum of the two frequencies [1] of the emerging photon-pair is higher than the sum calculated by applying classical Doppler shift [2] to the annihilation event with rest mass, as kinetic energy of the electron-positron-pair increases the sum of the photon frequencies.​

From time dilation (or relativistic Doppler effect) we conclude:

The sum of the two frequencies [1] of the emerging photon-pair is lower than the sum calculated by applying classical Doppler shift [2] to an annihilation event with rest mass, as time dilation reduces photon frequencies.​

Using common sense, we can easily recognize that a real experiment can only confirm energy conservation (i.e. higher frequencies) and refute time dilation.

---
[1] Two photons with freq1 and freq2 have the same energy as a single photon with freqsum = freq1 + freq2, i.e. total frequency is proportional to total energy.
[2] The relativistic Doppler effect is the combination of the classical Doppler effect [3] with time dilation of SR.
[3] with observer (=receiver) at rest relative to the medium, and a source moving at -c < v < c
Click to expand...


Okay, where's the refutation? All I see is a suggestion for an experiment that's already been performed to confirm relativity. At high enough energies, they start producing particles other than photons...
Wikipedia said:
There are also many examples of conversion of relativistic kinetic energy into rest energy. In 1974, SLAC National Accelerator Laboratory accelerated electrons and positrons up to relativistic velocities, so that their relativistic energy \gamma mc^{2} (i.e. the sum of their rest energy and kinetic energy) is significantly increased to about 1500 MeV each. When those particles collide, other particles such as the J/ψ meson of rest energy of about 3000 MeV were produced.[31] Much higher energies were employed at the Large Electron–Positron Collider in 1989, where electrons and positrons were accelerated up to 45 GeV each, in order to produce W and Z bosons of rest energies between 80 and 91 GeV. Later, the energies were considerably increased to 200 GeV to generate pairs of W bosons.[32] Such bosons were also measured using proton-antiproton annihilation.
Click to expand...
http://en.wikipedia.org/wiki/Tests_...and_momentum#Annihilation_and_pair_production
 
bruto said:
Apparently you're not dumb enough. Smoke 'em if you got 'em.
Click to expand...

When it comes to relativity (general or special), it's really easy to construct a refutation for dummies. It's a lot harder to construct a refutation for people that actually know something.
 
If "Special Relativity For Dummies" needs refutation, have at it. I'm still working my way through "Sandwiches For Dummies."
 
Well, whatever the OP was going for didn't work. When it comes to high energy physics, I am as much of a dummy as one can get. And I didn't understand a word of this.
 
If the photons are twins, does one end up younger? That's the one I want to see in a dummy version - the one where I get younger than you lot.
 
Sorry, the thread title should rather be:

Refutation of Special Relativity from Idiocy

When dealing with mass-energy equivalence and center of mass/energy considerations in another thread, I got the impression that it is possible to derive relativistic time dilation (according to the Lorentz factor). Because of an unfortunate series of events/mistakes, I came to the opposite conclusion, namely that Lorentz-factor time-dilation must be wrong.

Reasoning "mass-energy conservation"

An electron-positron pair moves at v and disintegrates into two photons, propagating along the line of v with c and -c.

The center of mass of the two emerging photons must continue to move at v. This can only happen if the relativistic mass m1 of the forward moving photon is higher than m2 of the backward moving photon:

ptot / mtot = v
(m1 c - m2 c) / (m1 + m2) = v
(m1 c - m2 c) = (m1 v + m2 v)
m1 (c-v) = m2 (c+v)
m1 = m2 (c+v)/(c-v)

In the case of photons, relativistic mass is proportional to frequency. So we conclude:

f1 = f2 (c+v)/(c-v)

The energy of the electron-positron pair was 2 y E, where E = 511 keV is the rest-energy of an electron or proton, and y the Lorentz factor of v. As f = E/h we get:

f1 + f2 = 2 y E / h

Reasoning "relativistic Doppler effect"

Now, let us apply the relativistic Doppler effect with observer velocity v to this situation: An electron-positron pair at rest gives rise to two photons moving (along the line of v) in opposite directions with each frequency f. In the rest-frame, we get:

f = E/h = 511 keV / h

For the moving observer, the relativistic Doppler effect leads to two photons of different frequency and energy:

f1 = f (c+v)0.5/(c-v)0.5 f2 = f (c-v)0.5/(c+v)0.5 E1 = h f1 = h f (c+v)0.5/(c-v)0.5 E2 = h f2 = h f (c-v)0.5/(c+v)0.5
We get:

f1 = f2 (c+v)/(c-v)

E1 + E2 = 2 h f ( (c+v)0.5/(c-v)0.5 + (c-v)0.5/(c+v)0.5 ) = 2 h f / (1-v2/c2)0.5 = 2 E y

f1 + f2 = 2 y E / h = 2 f / (1-v2/c2)0.5
Conlusion

Both reasonings lead to the same frequencies of the emerging photon pair. Therefore it is not possible to refute SR in this way.
The error in post #1

My loose concept "sum of frequencies of the emerging photon pair calculated by applying classical Doppler shift" is the main culprit. If we do the calculation (taking into account [3] of #1), we get

f1 = f / (c-v)
f2 = f / (c+v)
f1 + f2 = (c+v)+(c-v) / (c-v)(c+v) = 2 f / (1-v2/c2) = 2 f y2
Concerning "energy-conservation" we conclude:

The sum (f1+ f2 = 2 f y) of the two frequencies of the photon-pair (emerging from the moving electron-positron pair) is higher lower (by Lorentz factor y) than the sum (f1+ f2 = 2 f y2) calculated by applying classical Doppler shift to the annihilation event at rest (because despite kinetic energy of the electron-positron-pair seeming to increase the sum of the photon frequencies).​


In any case, this shows that velocity-dependent time dilation can be derived from mass-energy equivalence, conservation of momentum and conservation of mass/energy alone, without the necessity of the Lorentz transformation. So experimental proof for relativistic time dilation can only be considered evidence, but not proof for the Lorentz transformation, as time dilation follows from conservation laws simpler than the Lorentz transformation. By the way, many experimental results rather show what experimentalists think nature does than what nature actually does.

Until now I have left open the question, whether I should believe in Lorentz-factor time-dilation or not. Now I have to start to believe in it. (I'm careful and arrogant enough to only believe in what I can understand myself.)


Cheers, Wolfgang
 
Last edited:
wogoga said:
f1 = f (c+v)0.5/(c-v)0.5
f2 = f (c-v)0.5/(c+v)0.5
E1 = h f1 = h f (c+v)0.5/(c-v)0.5
E2 = h f2 = h f (c-v)0.5/(c+v)0.5
Click to expand...

This is incorrect because the speed of light is the same in all reference frames. You added the velocities linearly. However, you should have used the formula for relativistic addition of velocities.

This is a mathematical mistake on your part. It has nothing to do with any internal inconsistencies in relativity.

Let the relativistic sum of u and c be U. By the formula for relativistic sum:

U = (C+u)/(1+cu/c^2)
Therefore,
U=c.

Similarly, let the relativistic difference between u and c be U'. By the formula for relativistic subtraction of velocities:

U'=(c-u)/(1-cu/c^2)
Therefore,
U'=c.

There is no u+c or u-c anywhere in the frequencies. Both photons in the center of mass rest frame (CMRF) are moving at the same speed, c.
f = f (c)0.5/(c)0.5
E1 = h f1 = h f (c)0.5/(c)0.5=hf
E2 = h f2 = h f (c)0.5/(c)0.5=hf

Your mistake may have come from an incorrect application of
the time dilation formula. The time dilation formula has some restrictions
on it because it is only part of the Lorentz transformation. However, I'll
wait a bit to let someone else have a chance.
 
Last edited:
wogoga said:
Sorry, the thread title should rather be:

Refutation of Special Relativity from Idiocy

When dealing with mass-energy equivalence and center of mass/energy considerations in another thread, I got the impression that it is possible to derive relativistic time dilation (according to the Lorentz factor). Because of an unfortunate series of events/mistakes, I came to the opposite conclusion, namely that Lorentz-factor time-dilation must be wrong.

Reasoning "mass-energy conservation"

An electron-positron pair moves at v and disintegrates into two photons, propagating along the line of v with c and -c.

The center of mass of the two emerging photons must continue to move at v. This can only happen if the relativistic mass m1 of the forward moving photon is higher than m2 of the backward moving photon:

ptot / mtot = v
(m1 c - m2 c) / (m1 + m2) = v
(m1 c - m2 c) = (m1 v + m2 v)
m1 (c-v) = m2 (c+v)
m1 = m2 (c+v)/(c-v)

In the case of photons, relativistic mass is proportional to frequency. So we conclude:

f1 = f2 (c+v)/(c-v)

The energy of the electron-positron pair was 2 y E, where E = 511 keV is the rest-energy of an electron or proton, and y the Lorentz factor of v. As f = E/h we get:

f1 + f2 = 2 y E / h

Reasoning "relativistic Doppler effect"

Now, let us apply the relativistic Doppler effect with observer velocity v to this situation: An electron-positron pair at rest gives rise to two photons moving (along the line of v) in opposite directions with each frequency f. In the rest-frame, we get:

f = E/h = 511 keV / h

For the moving observer, the relativistic Doppler effect leads to two photons of different frequency and energy:

f1 = f (c+v)0.5/(c-v)0.5 f2 = f (c-v)0.5/(c+v)0.5 E1 = h f1 = h f (c+v)0.5/(c-v)0.5 E2 = h f2 = h f (c-v)0.5/(c+v)0.5
We get:

f1 = f2 (c+v)/(c-v)

E1 + E2 = 2 h f ( (c+v)0.5/(c-v)0.5 + (c-v)0.5/(c+v)0.5 ) = 2 h f / (1-v2/c2)0.5 = 2 E y

f1 + f2 = 2 y E / h = 2 f / (1-v2/c2)0.5
Conlusion

Both reasonings lead to the same frequencies of the emerging photon pair. Therefore it is not possible to refute SR in this way.
The error in post #1

My loose concept "sum of frequencies of the emerging photon pair calculated by applying classical Doppler shift" is the main culprit. If we do the calculation (taking into account [3] of #1), we get

f1 = f / (c-v)
f2 = f / (c+v)
f1 + f2 = (c+v)+(c-v) / (c-v)(c+v) = 2 f / (1-v2/c2) = 2 f y2
Concerning "energy-conservation" we conclude:

The sum (f1+ f2 = 2 f y) of the two frequencies of the photon-pair (emerging from the moving electron-positron pair) is higher lower (by Lorentz factor y) than the sum (f1+ f2 = 2 f y2) calculated by applying classical Doppler shift to the annihilation event at rest (because despite kinetic energy of the electron-positron-pair seeming to increase the sum of the photon frequencies).​


In any case, this shows that velocity-dependent time dilation can be derived from mass-energy equivalence, conservation of momentum and conservation of mass/energy alone, without the necessity of the Lorentz transformation. So experimental proof for relativistic time dilation can only be considered evidence, but not proof for the Lorentz transformation, as time dilation follows from conservation laws simpler than the Lorentz transformation. By the way, many experimental results rather show what experimentalists think nature does than what nature actually does.

Until now I have left open the question, whether I should believe in Lorentz-factor time-dilation or not. Now I have to start to believe in it. (I'm careful and arrogant enough to only believe in what I can understand myself.)


Cheers, Wolfgang
Click to expand...

Your title change is also an acceptable one - and it is good that you realized it - or at least appear to have, though I am not sure why you then used incorrect math to cement the point.....????
 
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