Twin paradox (Pete and MacM)

[James R]

MacM:

SRT is what you are trying to test and you assume it from the start.

We're discussing your proposal here, not mine. Your proposal, as I have shown, assumes sychronisation of separated clocks, without proof.

Lets see you claim that your B clock and A clock do not have useable tick rates measured locally in SRT. You don't dare.

I have explicitly made the opposite statement on around 10 separate occasions in this thread. Selective memory again.

If local rates aply in SRT calculation they are useable in the synchronization.

I have never disputed that. But your method does not produce a valid synchronisation.

[Rambling snipped. Cut to the chase.]

1 - You stated clocks are operating correctly.

2 - You state the clocks run fast or slow compared to thier local reading?????

3 - You claim each clock still has a 1 MHz standard.

4 - You claim there is no way of knowing the standards are still the same.

5 - You claim the clocks are not synchronized.

6 - You claim they are synchronized by accident.

You have flip flopped thorughout this thread.

All of my statements were qualified. Your straw men are useless.

Here are the correct versions of the above statements:

1 - I stated clocks are operating correctly.
2 - I stated the clocks may run fast or slow compared to thier local reading, when measured in another reference frame.
3 - I claim each clock still has a 1 MHz standard, as measured locally.
4 - I claim there is no way of knowing the standards are still the same once the clocks move relative to each other.
5 - I claim the clocks are not synchronized, once they are moving.
6 - I claim they are synchronized by accident by your scheme, if they are stationary, or if absolute time exists.

You are saying just anything you can think of to claim synchronization has not occured.

Anything that is true. Yes.

Since the local standards are both still 1 MHz "A's" SBM properly calibrates "B's" monitor of "A" to tick at the same rate

No, it doesn't. As I have clearly shown.

Good then B having the same 1 MHz standard can jproperly calibrate its monitor for "A".

B doesn't have the "same" 1 MHz standard. B has a local 1 MHz standard. A also has a local 1 MHz standard. You have not shown that these standards are the same when the clocks are in motion.

You just assume it without proof.

Circular argument.

You don't seem to get it. According to Relativity the local standard of 1 MHz is still the local standard. There is no differeance to record. That is the point here. For you to be correct and claim that the 1 MHz standard is no longer 1 MHz not only violates Relativity but would in fact become apparrent upon returning the clocks for comparision. i.e. - B is now actually 500 KHz and A is 1 MHz.

We're not interested in how the standards compare at rest, but how they compare when the clocks are in motion. Remember?

Relativity routinely declares things are the same and then declares they are different.

False.

 

[Paul T]

Not due to time dilation, so due to what? Something called MacM's dilation and it's formulated exactly the same as that in SR?

It would seem it is not up to me to explain muon decay but for you to explain how it could be SRT when you can't explain its failure made obvious by synchronization of clocks.

CRAP. You claimed that muon "life elongation" is not due to time dilation. But, you have no alternative answer for it...then you are just BS farter!

I might be old but one thing that is nice is "Wisdom comes with age"

Hehehe, you called this BS of yours wisdom? But, it's at least better than what you had 50 years ago, huh. Couldn't imagine the level of your "wisdom" while you were young..... before you achieve your current "wisdom".

 

[MacM]

CRAP. You claimed that muon "life elongation" is not due to time dilation. But, you have no alternative answer for it...then you are just BS farter!



Hehehe, you called this BS of yours wisdom? But, it's at least better than what you had 50 years ago, huh. Couldn't imagine the level of your "wisdom" while you were young..... before you achieve your current "wisdom".

Since this post contains no bonafied input it is ignored.

 

[Paul T]

Since this post contains no bonafied input it is ignored.

Wrong. It indeed has bona fide input...that is you need to live much longer to achieve more wisdom.

BTW, it's bona fide, not bonafied....is it how you people spell the word(s) in Texas?

 

[MacM]

MacM:

We're discussing your proposal here, not mine. Your proposal, as I have shown, assumes sychronisation of separated clocks, without proof.

Then leave yours out of the debate. You can't attack synchronization based on assumptions of SRT. You are trying to prove SRT (Not UT) by asserting SRT as fact. You can say the two are not compatiable but you cannot declare UT invalid based on the assertion of SRT as being valid in the first instance.

I have explicitly made the opposite statement on around 10 separate occasions in this thread. Selective memory again.

This has more to do with your poorly written and thought out arguements than selective memory on my part.

I have never disputed that. But your method does not produce a valid synchronisation.

Of course it does.

All of my statements were qualified. Your straw men are useless.

Here are the correct versions of the above statements:

1 - I stated clocks are operating correctly.

Good. Lets not say again that clocks may be fast or slow or broken.

2 - I stated the clocks may run fast or slow compared to thier local reading, when measured in another reference frame.

I have not disputed that. Infact I specifically pointed out the descrepancy between B's SRT view of A and B's monitor of A matching A's local view.

3 - I claim each clock still has a 1 MHz standard, as measured locally.

Good. Then they are either matched OR as I have also allowed the arguement, they are no longer truely 1 MHz but some other number but since relative motion is "Relative" such change is mutually applied and they still synchronize.

You cannot apply t2 = t1 (1 - v^2/c^2) unless this is true. Your SRT is based on the assumption that t1 at A is still a valid number in correlation to B, otherwise your mathematics mean nothing.

4 - I claim there is no way of knowing the standards are still the same once the clocks move relative to each other.

Fine then explain your SRT results where there is no known relationship between A and B. The gamma function applies to many issues not just time dilation. Are you prepared to argue that M1 is no longer the same mass, or that L1 is no longer the same length locally when observed by an observer in relative motion?.

5 - I claim the clocks are not synchronized, once they are moving.

You can claim anything you choose, at least you seem to be doing that, but it doesn't make it so. In fact it makes it impossible for SRT to function when you destroy the very foundation of measurement.

6 - I claim they are synchronized by accident by your scheme, if they are stationary, or if absolute time exists.

Another way of putting that in real terms. They are not synchronized IF you assume SRT. But I dispute our claim in that SRT doesn't state that local rates are actually different. It states each observer considers himself at rest. Hence there is no change in local standards.

Your claim is unjustified and conflicts with Relativity. How do you propose to cause a local change where there is no relative motion. The observer is always at rest relative to himself.

His view of the other changes per SRT but that is the issue being qualified (not ignored). You don't have your feet on solid ground here.

Anything that is true. Yes.

Then eliminate your objections. None are valid or true. They are made up circular arguements and based on assumptions of SRT. This test shows that SRT cannot be physical. It does not say that it does not occur as a perception or observation.

No, it doesn't. As I have clearly shown.

You have only clearly shown that you are lost and are flopping around looking for any excuse you can to not have to acknowledge that since local rates do not change the clocks DO synchronize and shows beyond any reasonable doubt that SRT is perception and not reality.

B doesn't have the "same" 1 MHz standard. B has a local 1 MHz standard. A also has a local 1 MHz standard. You have not shown that these standards are the same when the clocks are in motion.

You have not shown they are not. I have shown they are by Relativity itself. The local rate is not subject to change due to motion of an observer. The local rate is based on the observer being at rest to himself. Further even any wrongfully claimed affect would be mutual and identical such that they remained synchronized even if not by UT to the rest of the universe.

You just assume it without proof.

False. Please show us where Relativity says a local rate changes. Don't tell me what B thinks A's local rate is that is the SRT calculation which is also run in this presentation.

You must compare A's view of A's local rate applied to B's standard (which neither have changed and both are actually still 1 MHz even though yo are arbitrarily trying to claim otherwise) and hence B's monitor of A will tick at the local rate of A in spite of SRT in B's view of A.

Circular argument.

Yours is the circular arguement. Mine is based on simple basic physical principle which are not in disagreement with SRT.

We're not interested in how the standards compare at rest, but how they compare when the clocks are in motion. Remember?

Cetainly. They are the same or still matched even if no longer 1 MHz - remember?

False.

Good. Then you do agree that Relativity holds that the two local rates are still the same.

 

[MacM]

Wrong. It indeed has bona fide input...that is you need to live much longer to achieve more wisdom.

BTW, it's bona fide, not bonafied....is it how you people spell the word(s) in Texas?

Do you really want to try and make a deal over a missed space. I can assure you (since we have done this once before) that I can follow you around sir and make numerous corrections of your spelling and in particular you use of grammar.

Go ahead dig you own grave on this one - wise guy.

As I said you have nothing to contribute.

 

[MacM]

Billy T,

Just to give you something to be thinking about regarding your muon situation.

These muons are produced coming through the atmosphere at near light speed. Substantial energetic exchanges are involved.

Upon impinging a scintillation crystal they release a photon. If they remain in the crystal they release a second photon when they convert to an electron, etc.

Just how is it that you fail to realize that the sudden release of the photon on impact with the crystal has changed the energy dynamics of the muon and affects that must have on the further decay rate into electrons etc, in the crystal?

Electrons in an atom can be prompted to release a photon by exciting it with the correct energy and it transitions to another energy state giving off a photon.

You are comparing apples and oranges to compare muons in free flight through a medium such as air and muons moving in crystal.

Also I see mass as nothing more than condensed energetic space and light for example isn't slowing down in a medium from its perspective. It is going further than we observe as distance. That is it is still traveling c in that it is traveling in compressed or condensed space. In the case of water with a 0.75 index what we see as 1 foot light sees as 16 inches. We see it as a liquid, light still sees it in terms of fields comprising distance it must traverse.

 

[Pete]

Then leave yours out of the debate. You can't attack synchronization based on assumptions of SRT. You are trying to prove SRT (Not UT) by asserting SRT as fact. You can say the two are not compatiable but you cannot declare UT invalid based on the assertion of SRT as being valid in the first instance.

And you can't declare UT valid based on the assertion of UT being valid in the first place.

Mac, you're missing the entire point of this thread. This is a theoretical discussion to examine the claims of relativity, and whether it is possible for those claims to be compatible with reality.

It is your claim that your thought experiments are sufficient to show that relativity is incompatible with reality.

The logical counter-claim to your argument is not "Relativity is true", but only "your argument does not disprove Relativity".

Do you understand?
If you were to back down from your assertions in this thread, it would not imply that you are accepting relativity as proven, it means that you are accepting that your thought experiments don't disprove it. This would give no one the right to claim that you accept relativity.

Do you see?
We're not trying to disprove relativity - we're rebutting your disproof.



If you want to disprove SR on theoretical grounds, you have to work from assumptions that your opponents accept, otherwise your arguments are empty - you'll convince noone but yourself.

If you accept that SRT produces logical conclusions based on its assumptions, then the argument is done.

If you do not, then you must show us some illogical conclusions based on the assumptions of SRT.

Can you do it?
Can you show an illogical conclusion based on the assumptions of SRT?

 

[MacM]

And you can't declare UT valid based on the assertion of UT being valid in the first place.

Mac, you're missing the entire point of this thread. This is a theoretical discussion to examine the claims of relativity, and whether it is possible for those claims to be compatible with reality.

It is your claim that your thought experiments are sufficient to show that relativity is incompatible with reality.

The logical counter-claim to your argument is not "Relativity is true", but only "your argument does not disprove Relativity".

Do you understand?
If you were to back down from your assertions in this thread, it would not imply that you are accepting relativity as proven, it means that you are accepting that your thought experiments don't disprove it. This would give no one the right to claim that you accept relativity.

Do you see?
We're not trying to disprove relativity - we're rebutting your disproof.



If you want to disprove SR on theoretical grounds, you have to work from assumptions that your opponents accept, otherwise your arguments are empty - you'll convince noone but yourself.

If you accept that SRT produces logical conclusions based on its assumptions, then the argument is done.

If you do not, then you must show us some illogical conclusions based on the assumptions of SRT.

Can you do it?
Can you show an illogical conclusion based on the assumptions of SRT?

Pete,

You do seem to have missed the issue here. I have not assumed UT. Every thing I based the synchronization on includes SRT. If you (as James R. has) want to claim the local standards of 1 MHz at A and B are not equal you violate the premis in SRT that there is no affect locally.

Further assuming that is non-descript on any true relationship, any such affect has to be mutual and equal since relative velocity is "Relative". In which case the clocks still synchronize.

No I'm afraid you have to do more than claim assumptions are UT. They aren't they are based in SRT.

 

[ryans]

Still don't understand the basics Mac? Good to see the nuts are still occupied with 100 year old solved problems, while the rest of the world has moved on.

 

[James R]

I agree totally with what Pete just said.

MacM:

You can't attack synchronization based on assumptions of SRT.

Well, you can, if the argument is UT vs. relativity. However, that is not the argument we're having here - yet. We haven't got to square 1. I have shown that your method doesn't ensure synchronisation even under UT.

You are trying to prove SRT (Not UT) by asserting SRT as fact.

I'm not trying to prove SR at all here. All I have done is shown that your proposed method is useless for disproving SR.

You can say the two are not compatiable but you cannot declare UT invalid based on the assertion of SRT as being valid in the first instance.

Correct. You're starting to get the hang of it. Now, apply the same reasoning to your universal time idea.

1 - I stated clocks are operating correctly.

Good. Lets not say again that clocks may be fast or slow or broken.

As I clearly stated, statements of this kind discussed questions of the form "What would happen if...". Such discussions can be useful to expose flaws in a scheme. Which is what I used them to do in the case of your proposal. Such a statement is called a counterfactual. I mentioned this above, but you skipped it because you didn't know what it meant. A counterfactual is a "what if...", which differs from the actual state of affairs. It is used when discussing a point.

Your SRT is based on the assumption that t1 at A is still a valid number in correlation to B, otherwise your mathematics mean nothing.

Yes. But you have assumed that t1 at A means t1 at B, without proof.

Fine then explain your SRT results where there is no known relationship between A and B. The gamma function applies to many issues not just time dilation. Are you prepared to argue that M1 is no longer the same mass, or that L1 is no longer the same length locally when observed by an observer in relative motion?

Yes. That is what SR says. But it is irrelevant for the purposes of the present discussion.

They are not synchronized IF you assume SRT.

Your method doesn't ensure synchronisation, SR or no SR, as I have shown.

But I dispute your claim in that SRT doesn't state that local rates are actually different. It states each observer considers himself at rest. Hence there is no change in local standards.

Previously agreed. There is no dispute here.

Then eliminate your objections. None are valid or true. They are made up circular arguements and based on assumptions of SRT.

No. My claim that your synchronisation method doesn't work does not rely in any way on SR being true. It is a totally independent claim, as I have explained.

Me: B doesn't have the "same" 1 MHz standard. B has a local 1 MHz standard. A also has a local 1 MHz standard. You have not shown that these standards are the same when the clocks are in motion.

You: You have not shown they are not.

You're right. I haven't.

All I have said is that your method doesn't ensure that they are. You just assume it, without proof.

I have shown they are by Relativity itself.

No you haven't.

The local rate is not subject to change due to motion of an observer. The local rate is based on the observer being at rest to himself.

Agreed, but irrelevant.

False. Please show us where Relativity says a local rate changes.

Straw man. Previously dealt with at least 11 times.

You must compare A's view of A's local rate applied to B's standard (which neither have changed and both are actually still 1 MHz even though yo are arbitrarily trying to claim otherwise) and hence B's monitor of A will tick at the local rate of A in spite of SRT in B's view of A.

No, it won't, as I have shown.

 

[MacM]

I agree totally with what Pete just said.

And we should expect anything less? That doesn't make you right I'm afraid.

Well, you can, if the argument is UT vs. relativity. However, that is not the argument we're having here - yet. We haven't got to square 1. I have shown that your method doesn't ensure synchronisation even under UT.

No you haven't. You keep trying to claim it but based on false terms.

I'm not trying to prove SR at all here. All I have done is shown that your proposed method is useless for disproving SR.

False once again. But let me clarify once again. I am only proving SRT is not reality, not that the observation doesn't occur.

Correct. You're starting to get the hang of it. Now, apply the same reasoning to your universal time idea.

This only works if the terms of synchronization were based on UT alone. It isn't it is based on terms which are consistant with SRT.

As I clearly stated, statements of this kind discussed questions of the form "What would happen if...". Such discussions can be useful to expose flaws in a scheme. Which is what I used them to do in the case of your proposal. Such a statement is called a counterfactual. I mentioned this above, but you skipped it because you didn't know what it meant.

Up yours. Your repeated feloneous personal attacks gain you nothing.[/quote]

A counterfactual is a "what if...", which differs from the actual state of affairs. It is used when discussing a point.[/qluote]

And that is infact exactly what you are attempting to do by your declaration that local rates which don't change are no longer equal (even if shifted due to relative motion).

Yes. But you have assumed that t1 at A means t1 at B, without proof.

I have SRT as a foundation. This aspect happens to agree with a UT view. You are assuming 1 MHz is not 1 MHz without proof.

Yes. That is what SR says. But it is irrelevant for the purposes of the present discussion.

You really should read more slowly and give a bit more thought to your answers. You have just flip floped again. Now you claim gamma means local values change. They do not.

Your method doesn't ensure synchronisation, SR or no SR, as I have shown.

You haven't shown. You have only claimed without a foundation to do so.

Previously agreed. There is no dispute here.

Fine then synchronization works.

No. My claim that your synchronisation method doesn't work does not rely in any way on SR being true. It is a totally independent claim, as I have explained.

You have not met your burden of proof of your claims.

You're right. I haven't.
All I have said is that your method doesn't ensure that they are. You just assume it, without proof.

Your response has deliberately ommitted the qualifier I added which states that even if there were a shift of value it is mutal because relative veloctiy IS "Relative" and they would still be synchronized.

Unless yo now want to argue that relative motion between two parties have different SRT induced affects? I don't think you dare.

No you haven't.

Show me where arelativity says otherwise. You can't just make up new rules because you need an out.

Agreed, but irrelevant.

Not irrelevant at all. Show where Relativity does anything to the equality of local standards. You can't. You are just fabricating BS for the sake of a smoke screen.

t2 = t1 (1 - V^2/c^2) rembember. That is based on t1 being a valid tick rate based on B's view. Try again. You are in left field and the ball went right.

Straw man. Previously dealt with at least 11 times.

Ditto in regard to your meaningless objections., it won't, as I have shown.

No, it won't, as I have shown.

You have shown no such thing. You have claimed it but without and substance to the claim.

 

[Persol]

Damn James ,talk about stamina. Most of us just start insulting him when he starts to act ignorant.

MacM, why the hell are you making stuff up now? You are accusing JamesR of saying the exact opposite of the theory he is defending... yet he never said it.

 

[AndersHermansson]

One second is the time interval equal to 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
Experiment has shown that if you send two airplanes from the same reference-frame in opposite directions and later let them return to that same reference-frame then they do not count equal amount of ticks.
Since time is defined this way it's one sure bet! The logical conclusion is of course that the amount of time passed for both of them is not the same.
What's so tough about this to accept?

I'm sorry but if you're gonna get any further in life i think you have to to let go of your hybris and let yourself depend on the intelligence of the scientific community for a change.

 

[Persol]

MacM is placing his bets on the H&K experiment being too inaccurate... completely ignoring that they aren't the only people who have done this.

But that's standard MacM practice.

 

[James R]

MacM:

I think we're finished here. The argument has come down to:

MacM: My method synchronises the clocks.
James R: No it doesn't. See all the posts where I explained why it doesn't work.
MacM: I'm ignoring all those posts! My method works, regardless of anything you say.
James R: No it doesn't.
MacM: Yes it does. Yes it does! I'm not listening!

We could go round and round in circles, but I have said almost all that needs to be said.

I will correct yet another misconception you have about relativity, which came up in your last post:

t2 = t1 (1 - V^2/c^2) rembember. That is based on t1 being a valid tick rate based on B's view. Try again. You are in left field and the ball went right.

1. Your equation is not a relativistic equation.
2. If tA is a time interval measured on A's local clock, and tB is the corresponding time interval measured on B's local clock, then from B's point of view the relationship between those intervals is given by:

tB = tA/sqrt(1-(v/c)²)

where v is the speed of A as seen by B.
3. The equation relates tick rates measured locally. It has nothing to do with perception or signal delay.

 

[2inquisitive]

CRAP. You claimed that muon "life elongation" is not due to time dilation. But, you have no alternative answer for it...then you are just BS farter!



Hehehe, you called this BS of yours wisdom? But, it's at least better than what you had 50 years ago, huh. Couldn't imagine the level of your "wisdom" while you were young..... before you achieve your current "wisdom".

I have an answer as to why 'fast travelling' particles have a longer lifetime
than than the same particles in their 'rest frame.' The same one I have given
before and the true answer. It has nothing to do with 'time dilation', only with
the increased energy and increased mass of the fast travelling particle. The
increase in energy and mass is not only due to increased velocity, but also
due to the absorption of energy from whatever force propelled the particle
in the first place, or is continuing to propell the particle. The more energetic
and massive a particle becomes, the longer its lifetime. Do you think an electron in a particle accelerator, for example, circles the ring at a faster and
faster velocity, thus leading to increased 'time dilation' and a longer lifetime?
SR seems to propose that is what happens. It doesn't. As the electron gains
energy, and thus mass, its frequency of rotation around the ring actually
SLOWS DOWN. Surely you physicists know this. A cut & paste:
"A serious problem with the early cyclotrons was the energy limit of about 10 MeV for the acceleration of protons. This limit depends on the slowing down of protons rotating in a constant magnetic field due to their relativistic increase of mass or equivalently total energy. The rest mass of a proton corresponds to an energy of 938 MeV and already after acceleration to a kinetic energy of 10 MeV, the rotation frequency of a proton, which is inversely proportional to its total energy (938 + 10), has decreased by one per cent. If the proton rotation frequency and the electric frequency are equal in the beginning of the acceleration cycle, there will be no phase slip and the protons will be accelerated with the same accelerating voltage at each gap. However, as the protons gain energy and slow down their rotation frequency, they will arrive later and later at each gap with respect to the maximum of the accelerating voltage of fixed frequency. After a while the phase has slipped so much that there is no longer any energy increment at gap passages.
A cyclotron is not useful for acceleration of electrons since their rotation frequency in a magnetic field slows down quite rapidly even for as low energies as a few MeV due to the small rest mass of an electron. The rest mass of an electron corresponds to a rest energy of 0.511 MeV according to the Einstein formula E = mc2. Since the frequency of rotation of an electron in a magnetic field is inversely proportional to its total energy it follows that after acceleration to a kinetic energy of 0,511 MeV, the frequency of rotation has decreased by a factor of two.
A variant of the cyclotron is the microtron in which electrons are accelerated at one gap at the periphery of the orbits. The frequency of the accelerating voltage is a multiple of the electron rotation frequency. The expanding circular orbits are tangent and touch each other at the point where the accelerating gap is situated. The energy increment per turn is designed so that the increased time for a complete revolution of an electron due to its slow-down of the frequency of rotation corresponds to one or more cycles of the electric frequency at the acceleration gap."
http://www4.tsl.uu.se/~kullander/Nobel/

That is why the Synchrocyclotron and later Synchrotron were developed, to
be able to keep the acceleration pulses in time with the SLOWING particles.
But you know what? The particles lifetimes were increased in the accelerators
even though they slowed down. They gained energy and mass.

 

[Janus58]

I have an answer as to why 'fast travelling' particles have a longer lifetime
than than the same particles in their 'rest frame.' The same one I have given
before and the true answer. It has nothing to do with 'time dilation', only with
the increased energy and increased mass of the fast travelling particle. The
increase in energy and mass is not only due to increased velocity, but also
due to the absorption of energy from whatever force propelled the particle
in the first place, or is continuing to propell the particle. The more energetic
and massive a particle becomes, the longer its lifetime. Do you think an electron in a particle accelerator, for example, circles the ring at a faster and
faster velocity, thus leading to increased 'time dilation' and a longer lifetime?
SR seems to propose that is what happens. It doesn't. As the electron gains
energy, and thus mass, its frequency of rotation around the ring actually
SLOWS DOWN. Surely you physicists know this. A cut & paste:
"A serious problem with the early cyclotrons was the energy limit of about 10 MeV for the acceleration of protons. This limit depends on the slowing down of protons rotating in a constant magnetic field due to their relativistic increase of mass or equivalently total energy. The rest mass of a proton corresponds to an energy of 938 MeV and already after acceleration to a kinetic energy of 10 MeV, the rotation frequency of a proton, which is inversely proportional to its total energy (938 + 10), has decreased by one per cent. If the proton rotation frequency and the electric frequency are equal in the beginning of the acceleration cycle, there will be no phase slip and the protons will be accelerated with the same accelerating voltage at each gap. However, as the protons gain energy and slow down their rotation frequency, they will arrive later and later at each gap with respect to the maximum of the accelerating voltage of fixed frequency. After a while the phase has slipped so much that there is no longer any energy increment at gap passages.
A cyclotron is not useful for acceleration of electrons since their rotation frequency in a magnetic field slows down quite rapidly even for as low energies as a few MeV due to the small rest mass of an electron. The rest mass of an electron corresponds to a rest energy of 0.511 MeV according to the Einstein formula E = mc2. Since the frequency of rotation of an electron in a magnetic field is inversely proportional to its total energy it follows that after acceleration to a kinetic energy of 0,511 MeV, the frequency of rotation has decreased by a factor of two.
A variant of the cyclotron is the microtron in which electrons are accelerated at one gap at the periphery of the orbits. The frequency of the accelerating voltage is a multiple of the electron rotation frequency. The expanding circular orbits are tangent and touch each other at the point where the accelerating gap is situated. The energy increment per turn is designed so that the increased time for a complete revolution of an electron due to its slow-down of the frequency of rotation corresponds to one or more cycles of the electric frequency at the acceleration gap."
http://www4.tsl.uu.se/~kullander/Nobel/

That is why the Synchrocyclotron and later Synchrotron were developed, to
be able to keep the acceleration pulses in time with the SLOWING particles.
But you know what? The particles lifetimes were increased in the accelerators
even though they slowed down. They gained energy and mass.

No, the protons do not "slow down". Their actual linear speed continues to increase. What you have to understand is how cyclotrons are designed to work. As the particle is accelerated it makes a larger and larger circuit(it spirals out from the center). As long as you can ignore relativistic effects, it turns out that the increased speed on each circuit is just enough to balance out the increased circumference traveled and it returns to the same point in the same amount of time every circuit. The charge plates that accelerate the particle are thus designed to operate timed to a fixed frequency.

Relativistic effects however decrease the acceleration of the particle, such that it does not gain enough velocity on later circuits to remain synchronized. After a certain point the phase shift becomes to great for the system to work properly. Later systems get around this by slowly decreasing the frequency to the acceleration meachanism to compensate.

 

[2inquisitive]

In the early cyclotrons, the radius of the particle being accelerated did increase as the particle moved closer to the walls of the ring. This does
not happen in synchrotrons. As the particle is accelerated, the strength of
the magnetic field that 'bends' the path of the particle is increased and the
orbital distance, and the frequency of rotation, remains the same. The linear
velocity also remains the same as particle completes one orbit around the
ring in the same amount of time, the rotational frequency, as the energy and
the mass of the particle is increased during 'acceleration.' It is my firm belief
that the lifetime of short-lived particles is increased by an increase in energy
and mass, not by 'time dilation.' I realize this viewpoint is not shared by the
majority physicists who adhere to Special Relativity's explaination, but it is
an alternative explaination. I also realize my belief carries no weigth. So be it.

 

[Quantum Quack]

It is my firm belief
that the lifetime of short-lived particles is increased by an increase in energy
and mass, not by 'time dilation.' I realize this viewpoint is not shared by the
majority physicists who adhere to Special Relativity's explaination, but it is
an alternative explaination. I also realize my belief carries no weigth. So be it.

Can you share with us why you have decided to take this position and not the SR position,? Is there a particular aspect that drives you to your position?