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# Accelerating an electron to the speed of light

_AVG_
According to classical mechanics, I calculated that if an electron were to be accelerated through a potential difference of about 257 kV, it would breach the speed of light. Now, according to relativistic mechanics, this is obviously untrue. So, what are the mathematical corrections to be made whilst calculating the speed attained?

What I did was:

qV = (mv^2)/2 [Electrostatic potential energy = Kinetic energy]

How do I correct this using relativistic mechanics?
Indi
The relativistic kinetic energy is (γ - 1) × m₀ × c², where γ is the Lorentz factor.

If you use that in your equation, 257 kV will accelerate an electron to 0.747 c. (And, for reference, a potential of ten times that - 2,570 kV - will accelerate an electron to 0.986 c. A hundred times that - 25,700 kV - to 0.9998 c. And a thousand times that - 257 MV - to 0.999998 c.)
DoctorBeaver
You can't use classical mechanics where particles or high speeds are concerned.
chatrack
You should follow classical mechanics
Dennise
Anything having mass can only be accelerated arbitrarily close to light speed, but can never reach it.

Electrons have mass so one could never accelerate one to c without an infinite source of energy.
_AVG_
To re-ignite this topic, let me ask a related question to the one I initially posed:

How are photons accelerated to the speed of light? (i.e. we know that mass is converted to energy in order to create photons: but remember, it is mass at rest : I'm asking what process takes place to convert that stationary mass to a photon moving at the speed of light?)
IceCreamTruck
"An object can accelerate to many times the speed of light if you also increase the oscillation" is a claim I heard that is worth investigating on the subject because it goes against one of Einstein's proven theories. This happens all the time as things spiral into a black hole is my understanding of current popular belief.

I'll have to look up a reference for that later, but oscillation and speed of light should be some good search words to start with.
Bikerman
 IceCreamTruck wrote: "An object can accelerate to many times the speed of light if you also increase the oscillation" is a claim I heard that is worth investigating on the subject because it goes against one of Einstein's proven theories. This happens all the time as things spiral into a black hole is my understanding of current popular belief. I'll have to look up a reference for that later, but oscillation and speed of light should be some good search words to start with.

a) It isn't worth investigating because
b) It is total bollox.
IceCreamTruck
Bikerman wrote:
 IceCreamTruck wrote: "An object can accelerate to many times the speed of light if you also increase the oscillation" is a claim I heard that is worth investigating on the subject because it goes against one of Einstein's proven theories. This happens all the time as things spiral into a black hole is my understanding of current popular belief. I'll have to look up a reference for that later, but oscillation and speed of light should be some good search words to start with.

a) It isn't worth investigating because
b) It is total bollox.

Bikerman knows what he's talking about, but

a) left his statement completely closed off
b) didn't give us any tid bits to go on

dang I need to find that article
Bikerman
Well,
a) nothing massive travels at >c according to relativity. Relativity will one day be shown to be only an approximation, but I believe that this part is solid.
b) Einstein's formulation of relativity doesn't actually say that nothing can travel > c (common misconception). Some Galaxies, for example, are 'receding' from each other at multiples of c. What Relativity tells us is that no information can travel between two places at > c.
c) I think you are probably talking about phase or group velocity here.
http://en.wikipedia.org/wiki/Faster-than-light#Phase_velocities_above_c
This illustration may help you to visualise the difference

(The red dot is group velocity (gv) and the green dot is phase velocity (pv). Here gv = 1/2pv).

Alternatively, here is a case where gv and pv are in opposite directions.

source - http://en.wikipedia.org/wiki/File:Wave_group.gif
IceCreamTruck
I believe Einstein said nothing can accelerate to the speed of light without it's mass becoming infinite. I believe the talking point here is that the oscillation of the object also increases. I'm franticly searching for references... finding a ton of more good info, but most has been off topic.
IceCreamTruck
 Bikerman wrote: no information can travel between two places at > c.

Exactly... in order to even attempt to tip that scale it would take such an unbelievable amount of energy to the scale of putting a message into a black hole and then smashing that black hole into another black hole. In theory the message may have traveled to some other place faster than the speed of light but, you had no control of where that was exactly, and no one wants to read the message when it arrives!

Rest assured, Bikerman, we may have lost your package but it did arrive in one piece where ever that is!

That's actually a great idea. Black hole delivery service. I'm sure the US Government and married women would be more than happy clients of such a sure disposal... I mean delivery service.
Indi
 _AVG_ wrote: To re-ignite this topic, let me ask a related question to the one I initially posed: How are photons accelerated to the speed of light? (i.e. we know that mass is converted to energy in order to create photons: but remember, it is mass at rest : I'm asking what process takes place to convert that stationary mass to a photon moving at the speed of light?)

No one's answered this question, so i'll take a stab at it.

Photons cannot be accelerated to the speed of light, or to any other speed. They have only one possible speed: c.

In the case of a photon emission from a particle at rest, the photon doesn't start at rest "inside" the mass and then accelerate to c... it just comes into existence at c, which means it's probably not going to stay in the particle very long (hence, it's emitted).

You can think of it this way: one minute you have a mass with a mass of m and a velocity of zero... then you have conversion and you have a photon with a mass of 0 and a velocity of c. But this is a quantized, atomic change; it happens instantaneously. There is no point "in the middle" of the change where you have something with mass m/2 and velocity c/2. You are either before the change, or after the change, never "during" the change.
Bikerman
Sorry - missed this one. Indi has answered it ably.
Speaking relativistically, photons only ever travel at c, because they have zero mass. When you "create" a photon, you do so by giving it energy from some source (an oscillator, an electron in an atom changing energy levels, etc). The photon is created with both energy and with momentum, and they are equal (E=p, E^2-p^2 = 0). So there's no acceleration involved -- anything with zero mass, whether photons, or gravitons, or massless Goldstone bosons , can only travel at c in a vacuum.

(Yes, light CAN travel slower but that is due to 'banging into things' and getting partially absorbed/re-emitted - it all gets a bit complicated and whilst I'll happily continue, let's get this bit sorted first )
IceCreamTruck
This seems to be your subject, Bikerman. It's good stuff.. keep it up!
Indi
 Bikerman wrote: (Yes, light CAN travel slower but that is due to 'banging into things' and getting partially absorbed/re-emitted - it all gets a bit complicated and whilst I'll happily continue, let's get this bit sorted first )

Aaah, i gotta call you out on this one. ^_^; You know it's just going to create confusion. i would suggest saying that light can APPEAR to travel slower... not that it does.

Photons never travel at any speed other than c. They can appear to travel slower - or faster - under certain conditions. Bikerman explained one earlier: when you distort the photon wave-packet shape, you can alter the group or phase velocity way above, or below, c... but the signal velocity is always, always, always, always, always c. Another case is when photons are travelling through a material, like glass or water: although the photons all travel at c, as they move through the atomic structure of the material, they hit atoms, get absorbed, and then re-emitted a very short time later, so the overall speed of light through the material seems to be less than c... but this is only because photons are periodically "delayed" by absorption/emission events, not because the photons travel at any speed other than c.

(BTW... i glanced at your animations above... i think you got your dot colours reversed.)
kelseymh
Indi wrote:
 Bikerman wrote: (Yes, light CAN travel slower but that is due to 'banging into things' and getting partially absorbed/re-emitted - it all gets a bit complicated and whilst I'll happily continue, let's get this bit sorted first )

Aaah, i gotta call you out on this one. ^_^; You know it's just going to create confusion. i would suggest saying that light can APPEAR to travel slower... not that it does.

Hello, all! Bikerman invited me over here from another forum, so I thought I'd read the thread he mentioned to me there...

You're quite right that this discussion is going to cause confusion, but not because either Bikerman or you are incorrect. The subject itself is confusing.

 Quote: Photons never travel at any speed other than c. They can appear to travel slower - or faster - under certain conditions. [...] when photons are travelling through a material, like glass or water: although the photons all travel at c, as they move through the atomic structure of the material, they hit atoms, get absorbed, and then re-emitted a very short time later, so the overall speed of light through the material seems to be less than c...

Individual photons, moving between atoms in a transparent material, travel at c, as you say. However, the absoption/emission processes are coherent, so the pre- and post-scatting photons have a definite phase relationship. With many photons scattering, each individual event has the same phase relationship, so all the post-scatter photons are phase-shifted with respect to their parents in the same way. Whatever coherence or phase relationship the light had when it entered is preserved during propagation, so you can analyze the light within the medium as a plane wave, just as you could in the outside vacuum.

For example, you can use a laser pointer to set up a double slit experiment, or a diffraction grating, in a tank of pure water, and you'll discover that the fringes are farther apart than they would be for the identical setup in vacuum (or in air, which is close enough for this discussion). If the interference fringes are farther apart, that means the light in the water has a longer wavelength than in air.

The product of wavelength and frequency is phase velocity. Consequently, in a transparent medium, the phase velocity -- the speed of light in that medium -- really is lower than c. In fact, it is lower by exactly the factor 1/n, where n is the index of refraction.
Bikerman
Thanks Mike,
(Mike is a regular contributer to another forum I help with - the science forums.
Whenever a question arises that I do not feel able to answer, I generally ask for help from the science forums, because I know that many of the members are working scientists who have first-hand knowledge in these fields.)
_AVG_
Indi wrote:
 Bikerman wrote: (Yes, light CAN travel slower but that is due to 'banging into things' and getting partially absorbed/re-emitted - it all gets a bit complicated and whilst I'll happily continue, let's get this bit sorted first )

Aaah, i gotta call you out on this one. ^_^; You know it's just going to create confusion. i would suggest saying that light can APPEAR to travel slower... not that it does.

Photons never travel at any speed other than c. They can appear to travel slower - or faster - under certain conditions. Bikerman explained one earlier: when you distort the photon wave-packet shape, you can alter the group or phase velocity way above, or below, c... but the signal velocity is always, always, always, always, always c. Another case is when photons are travelling through a material, like glass or water: although the photons all travel at c, as they move through the atomic structure of the material, they hit atoms, get absorbed, and then re-emitted a very short time later, so the overall speed of light through the material seems to be less than c... but this is only because photons are periodically "delayed" by absorption/emission events, not because the photons travel at any speed other than c.

(BTW... i glanced at your animations above... i think you got your dot colours reversed.)

Interesting ... very well explained by both of you; however, now I'm having problems understanding the philosophical implications of "distorting" the wave such that it APPEARS to be faster than 'c' ... does this mean that all information transfer is not limited by 'c'?
Bikerman
No...if you work through the implications you will see that no information can be transmitted >c
Indi
 _AVG_ wrote: Interesting ... very well explained by both of you; however, now I'm having problems understanding the philosophical implications of "distorting" the wave such that it APPEARS to be faster than 'c' ... does this mean that all information transfer is not limited by 'c'?

No, information travel is strictly limited to c. The distortion changes the way the wave arrives, not the speed of the information it carries. First i'll give you a simple analogy to get the idea in your head, then i'll try to explain it in actual wave terms.

Suppose you were dealing with a transmission system that transmits words at a normal rate of 1 letter per 10 seconds. In that system, 3 letter words always take 30 seconds to transmit - always: SEK arrives like this: ten seconds after you send the word, the receiver gets 'S'... ten seconds later it gets 'E'... ten seconds later it gets 'K'. Now suppose you distorted the signal so that you get a burst at the beginning: five seconds after you send the word, the receiver gets 'S'... five seconds later it gets 'E'... and then twenty seconds later, it gets 'K'. Graphically, the two transmissions look like this (one space is 1 second):
 Code: 0    5   10   15   20   25   30 |....|....|....|....|....|....|           S         E         K      S    E                   K

Now here's the tricky part. Suppose you were measuring the speed of transmission by the time between the FIRST letter being sent and received. By that metric, the second transmission looks faster. But, as you can see, it's not. The information is received at exactly the same speed. You don't know what word you're going to get, until 30 seconds later... even though the second transmission measures faster than the first (because you got the first letter much sooner after it was sent in the second case).

To put it another way, if you were expecting to receive "SEK", in the second case you would "receive" it faster, because you don't need to receive the whole of "SEK" to know you're receiving "SEK" - you can say "i got 'SEK'" the moment you get that "S". But that logic is only meaningful if you already have the information about what you were going to be receiving. If you don't already have the information about what message you're getting, then even though the second transmission is distorted so that the front of it arrives faster, you still don't have the information until the same 30 seconds are past. So you see, in both cases, the ultimate speed of information in that medium is still limited to 1 letter per 10 seconds... it still takes 30 seconds to send the word... it only appears to be faster if you "cheat", by already having the information via a different medium.

That's basically how those faster-than-light light pulse experiments work. They send a light pulse from point A to B, but distort it, and at B, they count the pulse as "received" the moment they get "something" - the very front tip of the light pulse, basically - even though they can't technically know they've got the light pulse yet. But they do "know", because they were expecting it.

Now, even with this it must still sound like it's possible to send information faster than light. After all, if you're not really interested in sending a word - if you just want to send an "alert" signal - you don't care when the whole word arrives, you only care about the first letter, which arrives significantly faster than it should. (Or, you can be clever and build a transmitter with a 3 character bandwidth, and send "SSS" on one band, "EEE" on another, and "KKK" on the third, and you'd know you have "SEK" twice as fast as you should - in 5 seconds instead of 10.)

Doesn't work that way, though. To understand why, imagine just one cycle of a basic sine wave:

Now suppose you were watching a meter, like one of those paper-roll chart recorders with the moving needle that are stereotypically associated with seismographs and lie-detectors. The needle is normally at zero, then a photon of frequency f is received, and the needle goes up, then back down then back to zero (following the path of the sine wave). Now here's the riddle: how much of that signal do you have to receive to know the frequency and amplitude of that sine wave? Obviously not the whole cycle, because at around the half-way point you've got it figured out. But it does have to rise at least a little bit before you can judge the frequency and amplitude of your photon.

Let's say, for argument's sake, that you have to get to that first peak to know the frequency and amplitude of your photon. Even if you distort the signal so that the first movement of the needle from zero starts way earlier that it should for a perfect sine wave, it turns out that the time it takes to get to that first peak is unchanged. So if you're expecting a signal of frequency f and amplitude A - if you already have the information f and A - then you can count the signal as "received" once that needle begins to move. BUT, if you DON'T know what f and A are being received, you have to receive at least up to that peak before you can know that information... and that peak will always be limited to c.

To truly understand all this, you really have to do the math on waves and wave propagation, and you have to study information as a scientific concept (ie, the inverse of expectedness). But without all that, you can take this much away:
• The information of a wave signal is stored in its frequency and amplitude (eg, FM vs. AM radio transmission - which are, conveniently, transmitting information in the frequency, and the amplitude, respectively).
• You have to receive a certain portion of the signal before you can know its frequency and amplitude - you can't just get the tip of the signal and know all this.
• You can distort the shape of the signal packet such that the front end is more "pointy" or more "blunt"... but you still have to receive a certain portion of the signal to get its frequency and amplitude... so even if the tip comes earlier or later than expected, you still have to receive a certain portion of the rest of the signal to get any new information from it (assuming you don't already have that information via other means).
• In the case of a photon, that means you can distort the shape of the photon wavepacket such that the tip of the signal is way ahead of the rest of it... but you still can't get any information from that photon (that you don't already have) until you get a certain portion of that photon's wavepacket - enough to determine the frequency and amplitude.
• c limits the speed of the "meat" of a photon, so that even if you get the tip way earlier or later than expected, you still get the portion of it required to determine information at exactly the speed you expect: c.
• That's why scientists can "transmit" at faster than c - they cheat. They already have the information - they know what's going to be sent, and they're not relying on the photon transmission to get the information across. So what they do is distort the photon's shape so that the tip of the signal arrives much faster than it should... and as soon as they see the tip they say "we got the signal, and it arrived faster than c". (Technically, i know the scientists don't actually say that, but the science writers writing about them say that.) But if they didn't already know that the signal was coming, and what it's frequency and amplitude would be, they could not say they got the signal until they received enough of the signal - however distorted it may be - to determine the frequency and amplitude. If they actually had to wait to get that information... it would arrive at c.

i don't mean to sound like i'm shit-talking the scientists who got "faster-than-light" light pulse information transmission... because the scientists never said that. It was the pop writers who got it all wrong. What the scientists did does have some really neat practical value in the field of optical transmission, but it ain't faster-than-light information transmission.
Bikerman
Thanks Indi - I was preparing an answer to supplement my 'no' - but you've saved me a job
IceCreamTruck
You can't go back to the future unless the whole Delorean comes too! That and you have to hit the wire at exactly 12am, when the lightning strikes the clock tower, in order to juice the flux capacitor!

This is interesting... it's like all the runners of a race running at "c" and one of the runners leans forward right at the end to win the race. The runners all still finish the race at the speed of light, but the runner who leaned out gets to claim the "faster than speed of light" trophy... strange science. I don't think you can rightfully call that "faster than c". But, in a race, we do count the first part to cross the finish line, so from that perspective it doesn't matter how far back behind the others the runners feet are as long as his nose is over the line first.

I have this question along the same lines. If light is bent by gravity as it passes then it stands to reason in my mind that light traveling towards something with gravity would be faster than light just traveling at "c" but I know that the current idea is that gravity, even extreme gravity, cannot accelerate light. This creates in my mind the need for a force or barrier the keeps things at the speed of light once they are there otherwise forces like gravity would cause even light to accelerate if unopposed.

More study of matter transitioning to energy traveling at "c" is required. I'll be back to this conversation in roughly 10,000 years.
kelseymh
 IceCreamTruck wrote: If light is bent by gravity as it passes then it stands to reason in my mind that light traveling towards something with gravity would be faster than light just traveling at "c"

Well, light falling into a gravity well does get accelerated! Its momentum and energy are changed, just as the momentum and (kinetic) energy of anything else falling changes. The relationship between p and E is fixed (in units where c=1, for convenience): E^2 - p^2 = m^2, where "m" is a constant which is an intrinsic property of the object in question. The speed of an object is given by v=E/p (this is the factor "beta" from the relativity equations).

In the case of light, m=0, so E=p, and E/p=1 always! This is "why" light always travels at a constant speed (actually, its the other way around: a consequence of Einstein realizing that light travels at a constant speed, and working out the kinematics necessary for that to be true).

But falling into a gravity well means that E and p increase. For light, there's a relationship between energy and frequency: E = hv (h = Planck's constant, v is supposed to be the Greek "nu", the symbol for frequency). So what happens? As light falls under gravity, the "acceleration" is expressed as the frequency increasing -- hey, wait! That's just a "Doppler-like" blue shift! Light leaving a gravity well gets red-shifted, for exactly the same reason.

 Quote: More study of matter transitioning to energy traveling at "c" is required.

There's no such thing. Matter doesn't "transition to energy." You can have an interaction where a charged particle, like an electron, radiates energy in the form of photons (look up "bremsstrahlung" or "synchrotron radiation" in Wikipedia). You can also have interactions where matter and antimatter interact and annihilate, creating new energy in the form of one or more photons (or new particles).
therimalaya
As of Quantum Mechanics, Any object has two part, one its mass and another its wave. I think it is just like the body and the soul of any thing (living and non-living). As in the case of electron, it too poses its two part, one particle and the other wave nature. As the wave constituting the electron has no mass, it is just an wave, it might travel with the speed of light if enough energy is given, but it can not go alone, the mass on the other hand can not move with the same speed. That is why, i think an electron can not move in the same speed as light until some great discovery in physics can occur.
Bikerman
 therimalaya wrote: As of Quantum Mechanics, Any object has two part, one its mass and another its wave. I think it is just like the body and the soul of any thing (living and non-living). As in the case of electron, it too poses its two part, one particle and the other wave nature. As the wave constituting the electron has no mass, it is just an wave, it might travel with the speed of light if enough energy is given, but it can not go alone, the mass on the other hand can not move with the same speed. That is why, i think an electron can not move in the same speed as light until some great discovery in physics can occur.

You do know that this is nonsense don't you? How can you even think of comparing quantum events - which are well understood and modelled by quantum physics VERY accurately, to macroscopic interactions of human bodies with unproven and unobserved entities called souls? And before you start explaining a 'soul' by recourse to quantum woo-woo it would be best if you first demonstrate that the damn thing exists - and good luck with THAT one!

This sounds very much like the nonsense spouted by Deepak Choprah - quantum woo-woo as I call it. Quantum interactions and states are well modelled in the formalism. The fact that there is no analogous way of talking about them in the macro-world may mean that there is some deeper meaning we are missing, but it may simply mean that it cannot be done and the things are fundamentally not comparable.

Wave particle duality does not mean that particles have two constituents - wave and particle* - it means that in some circumstances they behave like waves and in others they behave like particles.
The reason an electron cannot achieve c is simply because it is massive (ie it has mass).

* Unless you are referring to the De Broglie/Bohm hypothesis - and that doesn't fit your description.
IceCreamTruck
Bikerman wrote:
 therimalaya wrote: As of Quantum Mechanics, Any object has two part, one its mass and another its wave. I think it is just like the body and the soul of any thing (living and non-living). As in the case of electron, it too poses its two part, one particle and the other wave nature. As the wave constituting the electron has no mass, it is just an wave, it might travel with the speed of light if enough energy is given, but it can not go alone, the mass on the other hand can not move with the same speed. That is why, i think an electron can not move in the same speed as light until some great discovery in physics can occur.

You do know that this is nonsense don't you? How can you even think of comparing quantum events - which are well understood and modelled by quantum physics VERY accurately, to macroscopic interactions of human bodies with unproven and unobserved entities called souls? And before you start explaining a 'soul' by recourse to quantum woo-woo it would be best if you first demonstrate that the damn thing exists - and good luck with THAT one!

This sounds very much like the nonsense spouted by Deepak Choprah - quantum woo-woo as I call it. Quantum interactions and states are well modelled in the formalism. The fact that there is no analogous way of talking about them in the macro-world may mean that there is some deeper meaning we are missing, but it may simply mean that it cannot be done and the things are fundamentally not comparable.

Wave particle duality does not mean that particles have two constituents - wave and particle* - it means that in some circumstances they behave like waves and in others they behave like particles.
The reason an electron cannot achieve c is simply because it is massive (ie it has mass).

* Unless you are referring to the De Broglie/Bohm hypothesis - and that doesn't fit your description.

You are really well studied on particle physics. What science non-sense will set you off is not predictable, however.

We've seen that Bikerman behaves like a chillaxed "wave" in intense physics, particle physics, or quantum mechanics conversations, but he acts more like a ballistic particle when people mix religion and science, however, his reaction cannot be predicted as observing him affects the outcome of the experiment.

You also can not know both Bikerman's speed or his position at any one point in time except if outside information is known and only general statements made, such as, Bikerman is on his bike going really fast! In this case I know he got a new bike recently and loves to ride it, and the location "on his bike" should really be considered a "fuzzy" location as his real location technically changes with each passing moment at "really fast" speeds.

It should be noted that Bikerman cannot achieve "C" on his bike because of the limitations of it's combustion engine, if the bike was moving at "c" this would require many revolving parts inside the bike to exceed that speed and it's not possible, and Bikerman himself has mass and so does the bike. Unfortunate as this may be it means, sadly, no traveling at the speed of light on a motor cycle.

We could discuss how strange things would look from your perspective if you were on a bike going the speed of light. You'd feel like you're in a tunnel, things directly to the side of you would not be visible, you wouldn't be able to see yourself if you looked down, and things behind you would appear to be getting younger if you could even notice the change. This would be cool on the highway as no one could look behind themselves and see you coming... as soon as they could see you then you would be passing them, and it would only take 16 minute round trip to the sun and back! That's a pretty fast 194 million mile round trip.
joebrown
I have a one-time need for an electron gun to measure or otherwise experimentally determine (i.e., plot), the mass vs. velocity for electrons accelerated to 0.99c, say at a potential difference of 2600 kV, or so - as near simultaneously in six directions (+/- x, y, and z). "If the relativistic kinetic energy is (γ - 1) × m₀ × c², where γ is the Lorentz factor. If you use that in your equation, 257 kV will accelerate an electron to 0.747 c. (And, for reference, a potential of ten times that - 2,570 kV - will accelerate an electron to 0.986 c.)"

Can you tell me of a university or commercial lab which can, at a minimal cost?

Thank you,

Dr. Joseph M. Brown
kelseymh
 joebrown wrote: I have a one-time need for an electron gun to measure or otherwise experimentally determine (i.e., plot), the mass vs. velocity for electrons accelerated to 0.99c, say at a potential difference of 2600 kV, or so - as near simultaneously in six directions (+/- x, y, and z). "If the relativistic kinetic energy is (γ - 1) × m₀ × c², where γ is the Lorentz factor. If you use that in your equation, 257 kV will accelerate an electron to 0.747 c. (And, for reference, a potential of ten times that - 2,570 kV - will accelerate an electron to 0.986 c.)" Can you tell me of a university or commercial lab which can, at a minimal cost? Thank you, Dr. Joseph M. Brown

Siemens, General Electric, Varian, and several other companies build turn-key electron accelerators in the several-MeV range (and higher) for industrial and medical customers. You are quite unlikely to get to "borrow" one of these machines.

I am quite curious how you intend to "measure the mass" of moving electrons. One obvious method is to use either electrostatic or magnetic fields to measure their deflection as a function of velocity. Of course, doing the computations to translate the deflection into a mass presupposes relativistic effects (Maxwell's equations are implicitly relativistic), so if you hope to find a deviation, I think you'll either be disappointed or deluded.
Bikerman
[Mod]
I want to make a pre-emptive point here.
Dr Brown - I am aware of your publication 'physics for the millions'. Whilst I have no particular problem with your request for information pertaining to electron guns, I would like to clarify that the science forums do not allow publication or advertisement of 'theory' that is not published in the peer-reviewed journals.
I am not implying that this is your intent and I am happy to treat your request at face value, but I feel that a quick intervention now might save any problems or misunderstandings later.
[/Mod]

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