The phenomena being examined by quantum mechanics is that the motion of particles is not random at atomic levels.

Individual particles, when viewed together over a period of time, appear to be distributed in space as if they are parts of a wave pattern.

They somehow seem to “sense each other” not only when separated in space, much like a flock of birds, but also when separated in time.

Questions that spring up are:

Are these particles really discrete?

Do they really exist independent of each other in space and time?

What is the true nature of a particle?

What is the true nature of space and time?

We have created mathematical models that use the concept of probability to explain a pattern emerging from apparent randomness. But they do not really explain the underlying nature of matter, energy, space and time.

The above questions remain to be answered by science.

Einstein was unhappy with Quantum Mechanics, not because he did not understand the subject, but because he found that the subject was merely a mathematical probabilistic model, which didn’t even touch upon the real problem concerning the nature of matter, energy, space and time.

For a 220,000eV electron moving at 0.9c, the de Broglie frequency is 2^65.4. This is very close to (and slightly higher than) the frequency of gamma rays.

The gamma rays form the upper part of the wave spectrum; whereas, the electron forms the lower part of the particle spectrum.

The gamma-ray – electron seems to be the region where electromagnetic radiation is transforming into a particle. The speed is slowing down while inertia is emerging. Inertia is the essence of mass.

Here we seem to have massless photons transforming into particles with mass and charge.

There seem to be a limit to which the frequency of electromagnetic radiation may increase. Beyond that limit a transformation from wave to particle seems to set in.

That’s an assumption that may you off on a wrong path. The limit to frequency in our physical universe should be 1/t and t should be defined by the Planck time unit (5.4 x 10^-44 sec) yielding
max frequency f=1.85 x 10^43 Hz.

Since photonic EM fields are massless at least up to the gamma region (10^18 Hz), it is perhaps more probable to conjecture photons remaining massless up to 10^43 Hz than it is to assume there may be an inflection point in the mass phenomena of a photon as it approaches 10^43 Hz.

However, there are some interesting relations between E, M and space that open the doors to alternate thinking. (Not wanting to really sidetrack the flow, but it is necessary to put space into the perspective of E and M.)

Some years ago a French fellow by the name of Alcubierre came up with an idea to warp space using E and M fields:

The primary requirement of this type of space drive is an exotic substance that has a frequency “xx-sorptive” property, or a “-f” component. I’ve called this “xx-sorptive” instead of ab-sorptive, or anything else, because it is really like nothing else we have in classical or relativistic physics. However, my guess is that it may be possible using quantum physics if the “imaginary” operator can be properly utilized in a functional way.

HOWEVER, an interesting thing about the “-f” (negative frequency) factor is that it appeared in Scn 8-80 in the expression for Life which was given as

Life = (E*I / -R) * (-f)
If:
E = Energy Potential
I = Energy Flow
-R = Negative Resistance
-f = Negative Frequency

For most of us physics types, some of this is easy to understand, but negative resistance and negative frequency demand some further explanation in this equation.

Negative resistance devices generate more power OUT than power IN and are used to generate microwaves, amongst other things. So they are a real-world implementation of a wacky phenomena.

In the case of “Life” the equation shows that positively directed maximal Life will occur when the very least possible amount of “power” is generated in order to achieve a goal, (i.e. as “-R->0”, maximal life force results).

That is essentially saying “don’t use force to achieve your goals” (and that can be understood by many philosophies).

The “-f” component bothered me for many years until I recently realized that it was an expression of the being’s willingness and ability to “have” the tone levels (frequencies) of “things” in its space.

This might also be looked at as the willingness to allow other viewpoints to be, or the willingness to “assume” (take) other viewpoints (to use just a bit more of the [forbidden]-“gese”).

Another fairly recent realization was that “Energy Potential” was akin to the Postulate and “Energy Flow” was akin to Intention. If you think about this briefly you’ll see the relationship holds:

Great Idea (postulate/potential, E) but weak Intention (flow, I) yields “nothing” (no product).

Weak idea (poor postulate / potential, E) but strong intention (flow, I) yields “garbage” (undesirable product).

And, Great Idea WITH strong Intention yields “desirable product”, so this is an apparently valid relationship,

Very simply re-written,

E*I = ability to get things done well = power

What all this means is that the “Life” equation could be re-written as:

Life = (the ability to get things done well) times (the ability to assume viewpoints) divided by (the amount of expended power it took to achieve the goal)

That, in any measure, is an equation for success.

Now, as far as space travel goes, ultimately what this means is that Frank Herbert’s “navigator” is the most likely candidate for a space-warping, spacecraft driving-force.

That is, at least until some exotic material can be found to satisfy the “-f” component.

2ndxmr: “The limit to frequency in our physical universe should be 1/t and t should be defined by the Planck time unit (5.4 x 10^-44 sec) yielding max frequency f=1.85 x 10^43 Hz.”

That is not so clear when one takes relativity into account and finds that time and space are not absolute and independent of each other. The “unit of time” seems to change with frequency throughout the EM spectrum.
.

2ndxmr: “Since photonic EM fields are massless at least up to the gamma region (10^18 Hz), it is perhaps more probable to conjecture photons remaining massless up to 10^43 Hz than it is to assume there may be an inflection point in the mass phenomena of a photon as it approaches 10^43 Hz.”

Wikipedia: “Gamma rays typically have frequencies above 10 exahertz (or >10^19 Hz), and therefore have energies above 100 keV and wavelengths less than 10 picometers (10-12 meter), which is less than the diameter of an atom. ”

Since the de Broglie frequency of electron is in the vicinity of 10^19 Hz, it is more likely that gamma rays are becoming unstable at higher frequencies, and they are likely to collapse into a particle. This area needs to be investigated..

2ndxmr: “Negative resistance devices generate more power OUT than power IN and are used to generate microwaves, amongst other things. So they are a real-world implementation of a wacky phenomena.”

You seem to imply that power is being created out of nothing and that the law of energy conservation is being violated. However, this is not the case.

Per Wikipedia, “The term negative resistance refers to negative differential resistance (NDR), ∆v/∆i < 0. In general, a negative differential resistance is a two-terminal component which can amplify, converting DC power applied to its terminals to AC output power to amplify an AC signal applied to the same terminals… A device in which the "absolute resistance", the voltage divided by the current, is negative, is simply a power source, converting power from some other source to electric power out of its terminals.”
.
See https://en.wikipedia.org/wiki/Negative_resistance
.

Even if time and space are not absolute, and the relativity of space to space and time to time is difficult to grasp, it is easier to grasp the relativity of space-time to space-time.

This relativity is best represented in terms of energy, or frequency, it seems.
.

Vin:”2ndxmr: “Negative resistance devices generate more power OUT than power IN and are used to generate microwaves, amongst other things. So they are a real-world implementation of a wacky phenomena.”

Vin: You seem to imply that power is being created out of nothing and that the law of energy conservation is being violated. However, this is not the case.”

2x: Of course you are right about there being a DC source to initiate the negative resistance effect. I should have qualified the zone of action a little closer.

To that end, if you look exclusively in the “-R” zone of the action, you will see we have this apparency of power out greater than power in.

The point simply was that this is a phenomena in the “-R” region that is both visible and measurable by actual instrumentation. No such instrumentation exists to measure “-f” phenomena.

My attempt here was to juxtapose two similar wacky phenomena and show that just because we can’t measure something right now (like “-f”), the mathematics indicates there is a valid relationship going on that gives a clue towards possible action, and the validity of that math is supported by what we can measure (like “-R” phenomena).

My ultimate goal with this post was to show:

1) how the Life equation of Scn 8-80 would actually make some sense and show a correlation between the physical universe and the nature of the awareness unit that could well have been the engineer of this physical universe.

2) how the phenomena of the awareness unit (likely an E-M sort of relationship capable of both “-R” phenomena and “-f” phenomena) could alter the shape of space to create a warp drive.

3) if we are to look for exotic substances that have a “-f” property, we should also expect that these substances will have an unusual space property, possibly the ability to occupy the same space as a “Real” particle while neither particle loses its unique charge, mass and spin properties. (I infer that property from the similar property that “Life” has in sharing space.)

2ndxmr: “1) how the Life equation of Scn 8-80 would actually make some sense and show a correlation between the physical universe and the nature of the awareness unit that could well have been the engineer of this physical universe.”

Space and Time are neither absolute in themselves, nor independent of each other. Similarly, God and the Physical Universe, or awareness and motion, are neither absolute in themselves, nor independent of each other.

This ratio is not constant for particles, but we assume it to be constant for waves (EM radiation). What is the background against which we are measuring this speed?

The more massive is a particle (object) the more “static” it is assumed to be. That massiveness seems to form the background against which speed is being measured. The human-centric intuition seems to be
EXTREME MASS = LEAST SPEED APPROACHING A STATIC CONDITION

From Quora, a really good explanation of the critical mass and size of a black hole:

A black hole results when the escape velocity would be greater than the speed of light. We can affect escape velocity by adjusting mass or radius. So, a
black hole isn’t so much about having a lot of mass, it’s about having a lot of density.

The smallest blackhole would be one where the event horizon radius (Schwartzschild radius) equals the deBroglie wavelength

Schwarzschild = deBroglie

\frac { GM }{ { c }^{ 2 } } =\frac { \hbar }{ Mc }

Solve for M

M=\sqrt { \frac { \hbar c }{ G } }

where M is the mass of the blackhole, c is the speed of light, G is the gravitational constant, and hbar is the reduced Planck constant.

This seems to explain BLACK HOLES being at the center of galaxies, which seems to anchor them in space. Around the black holes are revolving objects and radiation. Radition has much faster speed than objects. Objects have variable sppeds, but radition is assumed to have hit a speed limit of c.

Similarly, a heavy nucleus is assumed to be at the center of an atom, which seems to anchor the atom in its own space. Around the nucleus are revolving electrons and maybe radiation.

There seems to be gradual transformation from wave state to a particle state as one moves toward the nucleus of an atom, or toward the black hole of a galaxy. the speed is slowing down as the mass is increasing.

That seems to follow the conservation of momentum as well as the conservation of energy, but not a conservation of speed or mass.

It seems that somehow speed is being sacrificed in order to gain mass. It could be that speed is being stored as mass.
MASS = POTENTIAL MOTION

A heavy wrecking ball striking a building has both energy and momentum, which is describable in terms of mass and velocity

A gamma wave destroying an organism also has both energy and momentum, but of a different kind, which may be better described in terms of frequency and wavelength.

At 35:50, “For now you must understand the peculiar behavior of photons. They are not particles entirely; they are not waves entirely. They are particles in the sense they have localized energy and momentum, but they don’t travel like Newtonian particles.”

From Shankar’s Notes:
“Is light a particle or wave? It is certainly particle-like in that the detector is hit by one photon at a time, each of which carries a definite momentum and energy and dumps all of it at one point. The wavelength and frequency are not evident here except in the energy and momentum they carry. If however the experiment is allowed to continue till many many photons have arrived we see an interference pattern appropriate to the λ in question.

“In other words, photons are particles, but their arrival rate at the screen or detector is controlled by a wave. The wave is not physical and is associated with each photon. It determines the odds that the photon will arrive at some point on the screen. When we send a macroscopic beam of light with zillions of photons, the interference patters seems to come on instantaneously when in fact it is built dot by dot, with the odds for each being determined by the interference pattern- the odds are high at bright regions, low at dark regions. The wave is called the wave function.”

Even though the photon is massless, its frequency seems to play the same role as mass, which is to provide inertia, or resistance to motion.

From energy relationships,
E = mc^2 = hf
Or, m = (h/c^2) f
Or, mass is proportional to frequency

The resistance to motion due to frequency seems to be very slight until inertia appears as mass in the region of gammay ray / electron.

That is why the speed of EM radiation is almost constant throughout the EM spectrum. A difference might be apparent if the speed of gamma rays could be compared to the speed of radio waves emitting at the same time from some distant celestial phenomenon.

A transition from frequency to mass property seems to occur in gamma ray / electron region. The de Broglie frequency of electron is in the same ballpark as the frequency of gamma rays.

Of course, these are conjectures. But I just have to note them down for later reference. It is simply a hunch that frequency of radiatian has something to do with inertia and momentum, which are usually associated was mass in case of particles.

Frequency also seems to impart the property of discreteness to photons.

A photon may be imagined to be a wave packet, whose extents seem to shrink as its frequncy increases. An electron could be a photon that has almost shrunk, and most of the disturbance has condensed into mass and charge.

From Shankar’s Notes:
If you look for the electron you will find all of it at one place, its charge is not smeared out in the shape of the graph [probability graph per |ψ|^{2}]… In the case of the electron, we do not know more than the probability. The theory does not tell us more than the odds. It is not as if we could predict exactly where the electron will land in the DSE if only we knew more about the initial conditions.

.

It seems that the moment the leading point of the electron touches the detector, the rest of the electron also collects at that point to be detected. The electron is a single entity, even when it is spread out like a wave.

It is like the snake going through a hole. All parts of the snake, even when apread out, come to that hole to pass through.

From Shankar’s Notes:
if you caught the electron somewhere, it is wrong to assume it was there before you found it there. To assume it was in a definite location before observation is like assuming it went via one or the other slit when you did not shine light on it to find out what it was doing, and we know that such an assumption leads to conflict with experiment: we do not predict the interference pattern with both slits open.

In other words, before the measurement of position, the electron does not have a definite position. Measurement not only tells you where it is, it endows it with a position. It is not that you did not know where it was before catching it somewhere, it did not have a location!

Where is it between measurements? It does not have a definite position. It is in the strange quantum state which can yield any answer where ψ does not vanish. Thus in the double slit example, we know when the electron is emitted (since the source recoils) and when it is detected (when the detector recoils). What happened in between? We may like to think it followed a definite path via one of the slits. This reasonable assumption is however false, it will predict I1+2 = I1 + I2.

.

Like a snake, the electron is spread out. We just don’t know where the mouth of the snake would be. Wherever the mouth is detected, the rest of the snake also goes through that location.

It is an incorrect to assume that electron is a golf ball like particle.

## Comments

Einstein was unhappy with Quantum Mechanics, not because he did not understand the subject, but because he found that the subject was merely a mathematical probabilistic model, which didn’t even touch upon the real problem concerning the nature of matter, energy, space and time.

The lecture above at 33:00 talks about Compton Scattering.

When you consider a particle, you think of energy and momentum.

When you consider a wave, you think of frequency and wavelength..

From wave to particle there seem to be a transformation of frequency to energy and of wavelength to momentum.

For a 220,000eV electron moving at 0.9c, the de Broglie frequency is 2^65.4. This is very close to (and slightly higher than) the frequency of gamma rays.

The gamma rays form the upper part of the wave spectrum; whereas, the electron forms the lower part of the particle spectrum.

The gamma-ray – electron seems to be the region where electromagnetic radiation is transforming into a particle. The speed is slowing down while inertia is emerging. Inertia is the essence of mass.

Here we seem to have massless photons transforming into particles with mass and charge.

There seem to be a limit to which the frequency of electromagnetic radiation may increase. Beyond that limit a transformation from wave to particle seems to set in.

That’s an assumption that may you off on a wrong path. The limit to frequency in our physical universe should be 1/t and t should be defined by the Planck time unit (5.4 x 10^-44 sec) yielding

max frequency f=1.85 x 10^43 Hz.

Since photonic EM fields are massless at least up to the gamma region (10^18 Hz), it is perhaps more probable to conjecture photons remaining massless up to 10^43 Hz than it is to assume there may be an inflection point in the mass phenomena of a photon as it approaches 10^43 Hz.

However, there are some interesting relations between E, M and space that open the doors to alternate thinking. (Not wanting to really sidetrack the flow, but it is necessary to put space into the perspective of E and M.)

Some years ago a French fellow by the name of Alcubierre came up with an idea to warp space using E and M fields:

The primary requirement of this type of space drive is an exotic substance that has a frequency “xx-sorptive” property, or a “-f” component. I’ve called this “xx-sorptive” instead of ab-sorptive, or anything else, because it is really like nothing else we have in classical or relativistic physics. However, my guess is that it may be possible using quantum physics if the “imaginary” operator can be properly utilized in a functional way.

HOWEVER, an interesting thing about the “-f” (negative frequency) factor is that it appeared in Scn 8-80 in the expression for Life which was given as

Life = (E*I / -R) * (-f)

If:

E = Energy Potential

I = Energy Flow

-R = Negative Resistance

-f = Negative Frequency

For most of us physics types, some of this is easy to understand, but negative resistance and negative frequency demand some further explanation in this equation.

Negative resistance devices generate more power OUT than power IN and are used to generate microwaves, amongst other things. So they are a real-world implementation of a wacky phenomena.

In the case of “Life” the equation shows that positively directed maximal Life will occur when the very least possible amount of “power” is generated in order to achieve a goal, (i.e. as “-R->0”, maximal life force results).

That is essentially saying “don’t use force to achieve your goals” (and that can be understood by many philosophies).

The “-f” component bothered me for many years until I recently realized that it was an expression of the being’s willingness and ability to “have” the tone levels (frequencies) of “things” in its space.

This might also be looked at as the willingness to allow other viewpoints to be, or the willingness to “assume” (take) other viewpoints (to use just a bit more of the [forbidden]-“gese”).

Another fairly recent realization was that “Energy Potential” was akin to the Postulate and “Energy Flow” was akin to Intention. If you think about this briefly you’ll see the relationship holds:

Great Idea (postulate/potential, E) but weak Intention (flow, I) yields “nothing” (no product).

Weak idea (poor postulate / potential, E) but strong intention (flow, I) yields “garbage” (undesirable product).

And, Great Idea WITH strong Intention yields “desirable product”, so this is an apparently valid relationship,

Very simply re-written,

E*I = ability to get things done well = power

What all this means is that the “Life” equation could be re-written as:

Life = (the ability to get things done well)

times(the ability to assume viewpoints)divided by(the amount of expended power it took to achieve the goal)That, in any measure, is an equation for success.

Now, as far as space travel goes, ultimately what this means is that Frank Herbert’s “navigator” is the most likely candidate for a space-warping, spacecraft driving-force.

That is, at least until some exotic material can be found to satisfy the “-f” component.

Happy dark-matter hunting, y’all.

It is a conjecture, actually, that I would like to explore. I have added to it here.

https://vinaire.me/2015/01/03/the-quantum-phenomenon/#comment-54385

.

2ndxmr: “The limit to frequency in our physical universe should be 1/t and t should be defined by the Planck time unit (5.4 x 10^-44 sec) yielding max frequency f=1.85 x 10^43 Hz.”That is not so clear when one takes relativity into account and finds that time and space are not absolute and independent of each other. The “unit of time” seems to change with frequency throughout the EM spectrum.

.

2ndxmr: “Since photonic EM fields are massless at least up to the gamma region (10^18 Hz), it is perhaps more probable to conjecture photons remaining massless up to 10^43 Hz than it is to assume there may be an inflection point in the mass phenomena of a photon as it approaches 10^43 Hz.”Wikipedia: “Gamma rays typically have frequencies above 10 exahertz (or >10^19 Hz), and therefore have energies above 100 keV and wavelengths less than 10 picometers (10-12 meter), which is less than the diameter of an atom. ”

Since the de Broglie frequency of electron is in the vicinity of 10^19 Hz, it is more likely that gamma rays are becoming unstable at higher frequencies, and they are likely to collapse into a particle. This area needs to be investigated..

2ndxmr: “Negative resistance devices generate more power OUT than power IN and are used to generate microwaves, amongst other things. So they are a real-world implementation of a wacky phenomena.”You seem to imply that power is being created out of nothing and that the law of energy conservation is being violated. However, this is not the case.

Per Wikipedia, “The term negative resistance refers to negative differential resistance (NDR), ∆v/∆i < 0. In general, a negative differential resistance is a two-terminal component which can amplify, converting DC power applied to its terminals to AC output power to amplify an AC signal applied to the same terminals… A device in which the "absolute resistance", the voltage divided by the current, is negative,

is simply a power source, converting power from some other source to electric power out of its terminals.”.

See https://en.wikipedia.org/wiki/Negative_resistance

.

Even if time and space are not absolute, and the relativity of space to space and time to time is difficult to grasp, it is easier to grasp the relativity of space-time to space-time.

This relativity is best represented in terms of energy, or frequency, it seems.

.

Vin:”2ndxmr: “

Negative resistance devices generate more power OUT than power IN and are used to generate microwaves, amongst other things. So they are a real-world implementation of a wacky phenomena.”Vin: You seem to imply that power is being created out of nothing and that the law of energy conservation is being violated. However, this is not the case.”

2x: Of course you are right about there being a DC source to initiate the negative resistance effect. I should have qualified the zone of action a little closer.

To that end, if you look exclusively in the “-R” zone of the action, you will see we have this apparency of power out greater than power in.

The point simply was that this is a phenomena in the “-R” region that is both visible and measurable by actual instrumentation. No such instrumentation exists to measure “-f” phenomena.

My attempt here was to juxtapose two similar wacky phenomena and show that just because we can’t measure something right now (like “-f”), the mathematics indicates there is a valid relationship going on that gives a clue towards possible action, and the validity of that math is supported by what we can measure (like “-R” phenomena).

My ultimate goal with this post was to show:

1) how the Life equation of Scn 8-80 would actually make some sense and show a correlation between the physical universe and the nature of the awareness unit that could well have been the engineer of this physical universe.

2) how the phenomena of the awareness unit (likely an E-M sort of relationship capable of both “-R” phenomena and “-f” phenomena) could alter the shape of space to create a warp drive.

3) if we are to look for exotic substances that have a “-f” property, we should also expect that these substances will have an unusual space property, possibly the ability to occupy the same space as a “Real” particle while neither particle loses its unique charge, mass and spin properties. (I infer that property from the similar property that “Life” has in sharing space.)

2ndxmr: “1) how the Life equation of Scn 8-80 would actually make some sense and show a correlation between the physical universe and the nature of the awareness unit that could well have been the engineer of this physical universe.”Space and Time are neither absolute in themselves, nor independent of each other. Similarly, God and the Physical Universe, or awareness and motion, are neither absolute in themselves, nor independent of each other.

.

The lowest frequency distubance seems to appear as space.

The mid frequency disturbance seems to appear as light (EM radiation)

The highest frequency disturbance seems to appear as mass particles.

The ratio of energy to momentum gives us speed.

This ratio is not constant for particles, but we assume it to be constant for waves (EM radiation). What is the background against which we are measuring this speed?

The more massive is a particle (object) the more “static” it is assumed to be. That massiveness seems to form the background against which speed is being measured. The human-centric intuition seems to be

EXTREME MASS = LEAST SPEED APPROACHING A STATIC CONDITION

.

From Quora, a really good explanation of the critical mass and size of a black hole:

A black hole results when the escape velocity would be greater than the speed of light. We can affect escape velocity by adjusting mass or radius. So, a

black hole isn’t so much about having a lot of mass, it’s about having a lot of density.

The smallest blackhole would be one where the event horizon radius (Schwartzschild radius) equals the deBroglie wavelength

Schwarzschild = deBroglie

\frac { GM }{ { c }^{ 2 } } =\frac { \hbar }{ Mc }

Solve for M

M=\sqrt { \frac { \hbar c }{ G } }

where M is the mass of the blackhole, c is the speed of light, G is the gravitational constant, and hbar is the reduced Planck constant.

M=\sqrt { \frac { (1.0545\times 10^{-34})(299792458) }{ 6.6738\times 10^{-11}} }

Obviously best viewed at the source instead of {copy-pasta}-unfriendly WP:

http://www.quora.com/What-is-the-minimum-amount-of-mass-needed-to-create-a-black-hole

This seems to explain BLACK HOLES being at the center of galaxies, which seems to anchor them in space. Around the black holes are revolving objects and radiation. Radition has much faster speed than objects. Objects have variable sppeds, but radition is assumed to have hit a speed limit of c.

Similarly, a heavy nucleus is assumed to be at the center of an atom, which seems to anchor the atom in its own space. Around the nucleus are revolving electrons and maybe radiation.

There seems to be gradual transformation from wave state to a particle state as one moves toward the nucleus of an atom, or toward the black hole of a galaxy. the speed is slowing down as the mass is increasing.

That seems to follow the conservation of momentum as well as the conservation of energy, but not a conservation of speed or mass.

It seems that somehow speed is being sacrificed in order to gain mass. It could be that speed is being stored as mass.

MASS = POTENTIAL MOTION

.

We associate mass with inertia.

We associate inertia with resistance to motion.

It is like motion is being condensed into mass.

MASS = CONDENSED MOTION

.

So it boils down to investigating the concept of MOTION.

Both ENERGY and MOMENTUM are aspects of MOTION.

A heavy wrecking ball striking a building has both energy and momentum, which is describable in terms of mass and velocity

A gamma wave destroying an organism also has both energy and momentum, but of a different kind, which may be better described in terms of frequency and wavelength.

At 35:50, “For now you must understand the peculiar behavior of photons. They are not particles entirely; they are not waves entirely. They are particles in the sense they have localized energy and momentum, but they don’t travel like Newtonian particles.”

From Shankar’s Notes:

“Is light a particle or wave? It is certainly particle-like in that the detector is hit by one photon at a time, each of which carries a definite momentum and energy and dumps all of it at one point. The wavelength and frequency are not evident here except in the energy and momentum they carry. If however the experiment is allowed to continue till many many photons have arrived we see an interference pattern appropriate to the λ in question.

“

In other words, photons are particles, but their arrival rate at the screen or detector is controlled by a wave.The wave is not physical and is associated with each photon. It determines the odds that the photon will arrive at some point on the screen. When we send a macroscopic beam of light with zillions of photons, the interference patters seems to come on instantaneously when in fact it is built dot by dot, with the odds for each being determined by the interference pattern- the odds are high at bright regions, low at dark regions. The wave is called the wave function.”.

Even though the photon is massless, its frequency seems to play the same role as mass, which is to provide inertia, or resistance to motion.

From energy relationships,

E = mc^2 = hf

Or, m = (h/c^2) f

Or, mass is proportional to frequency

The resistance to motion due to frequency seems to be very slight until inertia appears as mass in the region of gammay ray / electron.

That is why the speed of EM radiation is almost constant throughout the EM spectrum. A difference might be apparent if the speed of gamma rays could be compared to the speed of radio waves emitting at the same time from some distant celestial phenomenon.

A transition from frequency to mass property seems to occur in gamma ray / electron region. The de Broglie frequency of electron is in the same ballpark as the frequency of gamma rays.

Of course, these are conjectures. But I just have to note them down for later reference. It is simply a hunch that frequency of radiatian has something to do with inertia and momentum, which are usually associated was mass in case of particles..

Frequency also seems to impart the property of discreteness to photons.

A photon may be imagined to be a wave packet, whose extents seem to shrink as its frequncy increases. An electron could be a photon that has almost shrunk, and most of the disturbance has condensed into mass and charge.

From Shankar’s Notes:

If you look for the electron you will find all of it at one place, its charge is not smeared out in the shape of the graph [probability graph per |ψ|

^{2}]… In the case of the electron, we do not know more than the probability. The theory does not tell us more than the odds. It is not as if we could predict exactly where the electron will land in the DSE if only we knew more about the initial conditions..

It seems that the moment the leading point of the electron touches the detector, the rest of the electron also collects at that point to be detected. The electron is a single entity, even when it is spread out like a wave.

It is like the snake going through a hole. All parts of the snake, even when apread out, come to that hole to pass through.

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From Shankar’s Notes:

if you caught the electron somewhere, it is wrong to assume it was there before you found it there. To assume it was in a definite location before observation is like assuming it went via one or the other slit when you did not shine light on it to find out what it was doing, and we know that such an assumption leads to conflict with experiment: we do not predict the interference pattern with both slits open.

In other words,

before the measurement of position, the electron does not have a definite position.Measurement not only tells you where it is, it endows it with a position.It is not that you did not know where it was before catching it somewhere, it did not have a location!Where is it between measurements? It does not have a definite position. It is in the strange quantum state which can yield any answer where ψ does not vanish. Thus in the double slit example, we know when the electron is emitted (since the source recoils) and when it is detected (when the detector recoils). What happened in between? We may like to think it followed a definite path via one of the slits. This reasonable assumption is however false, it will predict I1+2 = I1 + I2..

Like a snake, the electron is spread out. We just don’t know where the mouth of the snake would be. Wherever the mouth is detected, the rest of the snake also goes through that location.

It is an incorrect to assume that electron is a golf ball like particle.

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