Relativity and Radar Guns · 2021. 1. 17. · Relativity and Radar Guns 3 That means that whether...

Relativity and Radar Guns Edward G. Lake

Independent Researcher

January 18, 2021

[email protected]

Abstract: Radar guns use basic principles based upon Einstein’s Theory of

Special Relativity. Yet the physics of radar guns is the subject of endless debates, since

mathematicians insist on using Quantum Mechanics to explain how radar guns work,

while Special Relativity actually provides the only explanation which can be fully verified

by experiment. And radar guns can also put an end to the particles vs waves debate.

Key words: Relativity; Quantum Mechanics; light; photons; waves; radar.

When analyzing how radar guns work, the most basic question you can ask is: Do radar

guns transmit waves or photons? Mathematicians will argue that it doesn’t make any difference,

since they will use waves for their mathematical models. And their calculations work, so what

happens in reality is evidently irrelevant.

Countless references state that radar waves, radio waves, visible light waves, X-rays,

infrared light, ultraviolet and gamma rays are just different forms of electromagnetic energy,

differing primarily in their wavelengths as shown in Figure 1 below.

Figure 1

Relativity and Radar Guns

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If you try to discuss photons with mathematicians, they will always argue that light

sometimes acts like a wave and sometimes acts like a particle. A particle is an object, not a

wave. And a wave is definitely not a particle. End of discussion.

But waves are illogical! Experiments show they do not exist. How do you increase the

brightness of a light? According to wave theory, if a source is emitting visible red light, the

wavelength (or distance between wave crests) would be about 700 nanometers. The only thing

that could change is the wave height, i.e., the amplitude. In Figure 2 below, if the amount or

strength of red light was increased, the waves would get higher (the vertical distance between

crest and trough would increase), and the waves would get smaller if the light was dimmed.

Figure 2

Experiments show that that simply does not happen. Physicist Richard Feynman

described the problem this way:

I want to emphasize that light comes in this form — particles. It is very important to

know that light behaves like particles, especially for those of you who have gone to

school, where you were probably told something about light behaving like waves. I’m

telling you the way it does behave — like particles.[1]

Professor Feynman then went on to explain that you can use a photomultiplier to count

photons coming from some source. If you dim the source light, the number of photons hitting the

photomultiplier is reduced, but the intensity or energy of each individual photon remains the

same. And, of course, when you intensify the source light, the number of photons increases.

Therefore, light and all transmitted electromagnetic energy consists of photons, not waves.

Nevertheless, virtually every book or manual which describes how radar guns work will

describe them as emitting waves. The mathematics uses waves, and the Doppler Effect

originally involved sound waves, which the books and manuals will describe in excruciating

detail, even though the Doppler Effect for sound waves works very differently than the Doppler

Effect for electromagnetic radiation and photons.

It is also important to understand that, whether radar guns emit waves or photons, the

emissions are at the speed of light, in accordance with Einstein’s Second Postulate:

light is always propagated in empty space with a definite velocity c which is independent

of the state of motion of the emitting body.[2]


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That means that whether the emitter (the radar gun) is stationary or is being used in a

patrol car traveling at high speeds, the emitted photons (or waves) will always travel at the speed

of light, c, or 670,616,629 miles per hour (mph).

Additionally, all radar guns utilize the same scientific principles. That includes the

Mattel Hot Wheels Radar Gun which once had a retail price of $30[3] and was used by children to

measure the speeds of their toy cars and skateboards, Bushnell’s Velocity radar gun which can be

purchased at WalMart for about $109 to use at baseball games to measure the speed of a thrown

baseball, hand-held radar guns costing over $1,500 used by countless police departments, and

sophisticated, multi-directional dash-mounted police radar guns with prices over $3,000.

While radar guns come with many options and features for how they can be used, the

fundamental difference between the various radar guns is their emission “frequency.” When

discussing waves, the frequency is the number of waves emitted per second. When discussing

photons, the frequency is the number of times the electromagnetic fields of an individual photon

oscillate per second.

I. Radar gun frequencies.

Radar guns transmit at frequencies which were chosen because nothing else transmits

or emits at those frequencies, so the microwave emissions from a radar gun and the returned

signals won’t be confused with other emissions, and other emissions won’t interfere with the

signal processing done by a radar gun. In the United States, the most common frequency range

(particularly for hand-held police radar guns) is 33.4 to 36.0 Gigahertz (GHz), known as the “Ka

band.” “K band” radar guns which use 24.125 GHz and 24.150 GHz are also common.

Figure 3

If we pick 35 GHz as a representative frequency for this discussion, one GigaHertz is

one billion Hertz, so we are also talking about 35,000,000,000 Hertz (Hz) or 35,000,000,000


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waves per second as a transmission frequency. The basic idea behind a radar gun is that it will

transmit waves at a given frequency (35 GHz), as shown in Figure 3 above, and when those

waves hit an oncoming moving object, there will be a Doppler Effect, meaning that the waves

will be compressed and will “echo” back at a higher frequency than at which they were

originally transmitted. The difference between the transmitted frequency and the returning

frequency is called the “beat frequency.”

Figure 3 is an example from an on-line calculator[4] for the beat frequency. It shows

that if a stationary radar gun transmits 35,000,000,000 waves per second, and the oncoming

target vehicle is traveling at 70 mph, the returning waves will be received at 35,000,007,292 per

second (when rounded off to the nearest Hz). The “beat frequency” is therefore 7,292 Hz.

II. Photons vs Waves.

At this point the use of waves instead of photons becomes absurd. You just have to ask

yourself: What do the waves reflect off of? You can’t just say, “The car,” because the waves will

hit parts of the front bumper first, then the front hood (which is streamlined, so some parts are

farther back than others), then the bottom chrome around the windshield, then the top chrome

around the windshield, then the driver. Meanwhile, waves will also be bouncing off of objects

on the ground, tiny bumps in the highway, plus highway signs, trees, grass, leaves, etc.

When you are talking about 35,000,000,000 waves per second, the space between

waves is very small. Figure 3 shows 6 transmitted waves which appear to be about 10 feet apart.

In reality, the waves would be less than one centimeter apart.

And all the returning waves will be intermingled! The first object hit will return waves

before the second object, the second object before the third, etc., etc., etc. When you measure

speeds by measuring the distance between waves, you cannot have other waves between the

waves you are measuring when you have no way to tell one wave from another except by wave

frequency.

With photons, there is no such problem.

Figure 4


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A NASA web site[5] describes how single photon can measure the speed of an

oncoming vehicle. Figure 4 above is an illustration from my paper on Radar Guns and

Einstein’s Theories.[6] A single photon oscillating at 35,000,000,000 Hz is emitted, and a single

photon oscillating at 35,000,007,292 Hz is returned.

In reality, of course, billions of photons are emitted by the radar gun, and while some

are returned to the radar gun, the vast majority get bounced off in other directions, including

those bouncing off the ground, off trees, signs, rocks, etc. Figure 5 below shows only the

photons being emitted by the radar gun.

Figure 5

The key difference is that every photon that gets returned to the radar gun from the

target car oscillates at 35,000,007,292 Hz because all parts of the target car are moving at the

same speed. Almost as importantly, all photons which return from the ground, from signs, trees,

grass and building, oscillate at 35,000,000,000 Hz because those objects are all stationary. And,

in accordance with Einstein’s Second Postulate, even if the patrol car and radar gun were

moving, the photons would still return at 35,000,000,000 Hz from stationary objects.

Additionally, a radar gun emits a cone of photons that can vary in width from 9 to 35

degrees, depending upon make and model. If a radar gun has a beamwidth of 12 degrees, that

means the cone is 21 feet wide if the target is 100 feet away, 42 feet wide at 200 feet distance, 63

feet wide at 300 feet distance, and 84 feet wide at 400 feet distance.[7] If there is more than one

vehicle in the target area, the radar gun will typically just show the speed of the fastest target, but

more complex models will show multiple speeds and also the direction of movement.

How waves would work with multiple targets is never explained, since waves simply

wouldn’t work in such a situation. So, for the remainder of this paper, only radar guns emitting

photons will be discussed, since, regardless of how many manuals and texts use waves, there is

no such thing as a radar gun that emits waves.

III. How radar guns calculate speeds.

Photons, of course, do not bounce off a car as waves are imagined to do. Photons are

energy transmissions between two atoms. Atoms in the radar gun’s transmitter are infused with

energy in the form electricity from a battery, giving the atoms more energy than they can handle.

Unable to hold the extra energy, the atoms release that excess energy in the form of photons

which oscillate, per our example, at 35,000,000,000 Hz and which travel at the speed of light, c.

Those photons travel and transmit energy within the 12-degree cone to other atoms. If the atom


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is part of the oncoming target car, the photon will hit an atom in the target at c+v, where v is the

speed of the target. The atom in the car interprets the kinetic energy of its own motion toward

the radar gun as being additional energy in the photon it received. That means, if the target is

traveling at 70 mph, the atom receives the photon arriving from the gun as if that was oscillating

at 35,000,007,292 Hz instead of its actual 35,000,000,000 Hz. The atom cannot hold any extra

energy, so it emits a new photon to get rid of that excess energy.[8] The new photon it emits

oscillates at 35,000,007,292 Hz.

Some of those new photons return to the stationary radar gun. They are received and

“beat together with” examples of the photons that were originally transmitted. The beating

together produces the difference in frequencies, or the “beat frequency,” which is 7,292 Hz.

The next question is: How do you get from knowing the beat frequency is 7,292 Hz to

determining at what speed the target is traveling? Or to put it another way, how do you convert

the 7,292 Hz frequency into a speed? A clue to the answer for that may be in knowing that the

transmitted photon traveled to the target at the speed of light, 670,616,629 miles per hour, or

186,282 miles per second. And during each of those seconds, the photon oscillated 35 billion

times. Therefore, the beat frequency as a percentage of the transmission frequency should be

translatable into miles per hour as a percentage of the speed of light.

Figure 6

If the emission frequency is 35 GHz, and the target is moving at 70 mph, the beat

frequency is 7,292 Hz, which is 0.0000208333333% of the transmitted frequency. Figure 6

below shows how beat frequency percentages relate to speed of light percentages.

The percentage that 70 mph is of the speed of light is 0.0000104381545%, which is

almost exactly ½ of the beat frequency percentage. Knowing that fact, the radar gun software


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can be programmed to multiply the transmission frequency by 2 before using the corrected beat

frequency to compute the percentage in the right-most column in Figure 6.

Figure 7 below shows how knowing the transmission frequency, the speed of light, and

then developing the beat frequency enables a radar gun to compute the speed of a target.

Figure 7

The Hertz frequency used by the gun is used to obtain the “beat frequency” by simply

subtracting the Hertz frequency from the frequency returned by the target. Then the gun’s

programming computes what percentage that beat frequency is of 2 times the Hertz frequency.

When that percentage is computed, the same percentage is used against the speed of light. The

result is the speed of the target (when rounded to the nearest whole number).

When I discussed this with a radar engineer, he informed me that my description was

basically correct, but radar gun engineers develop the math one step further. They use the speed

of light to calculate a “K-factor,” which is the beat frequency representing 1 mile per hour for a

given transmission frequency. Then you just need to get the beat frequency, divide it by the K-

Factor and you get the target speed in miles per hour, as shown in Figure 8 below.

Figure 8


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IV. Moving radar guns.

Things get a bit more complicated when the radar gun is moving. When a moving

radar gun emits photons at c toward an oncoming moving target, those photons still hit the target

at c+v where v is the speed of the oncoming target. The new photons emitted by the target also

travel at c back to the radar gun. Since the radar gun is moving, it becomes a moving receiver. It

receives the returning photons at c+v. If the gun is a “stationary only” model with no capability

to decipher whether the gun is moving or not, the gun will add the speed of the target to the

speed of the gun. When I point my “stationary only” TS-3 radar gun at oncoming traffic in the

opposite lane while driving in a 40 mph zone, the gun typically shows speeds varying between

75 and 90 mph – my speed plus the speed of the fastest oncoming vehicle.

If I point my TS-3 radar gun at the back of a truck directly in front of me traveling at

my speed, the gun will show no reading. The transmitted photons hit the truck at c-v because the

truck is moving in the same direction I’m moving and away from the oncoming photons. The

return photons emitted by atoms in the truck will hit the receiver in my radar gun at c+v, because

my gun is moving toward the oncoming photons. The gun will compute c+v-v and get c, which

translates to zero speed for the target. Mathematicians might view that as a relative speed of zero

between the truck and my car, but, radar guns have no ability to measure distances. The gun,

therefore, does not “know” that the distance between my radar gun and the back of the truck

remains unchanged. As we saw in Section III, radar guns do not measure the relative speed

between objects, they measure the speed of an object relative to the speed of light.

V. A proposed radar gun experiment.

One thing is clear from the calculations described above: The speed measurements

performed by a radar gun are all relative to the speed of light. A radar gun does not measure

the speed of an object relative to a physical location. It measures the speed of a target object

relative to the speed of light. The speed of light is a “universal constant.” It is measured to be

the same everywhere. According to Encyclopedia Britannica:

With the formulation of the special theory of relativity by Albert Einstein in 1905 and its

acceptance by scientists generally, the ether hypothesis was abandoned as being

unnecessary in terms of Einstein’s assumption that the speed of light, or any

electromagnetic wave, is a universal constant.[9]

Figure 9


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In previous papers[6][10] I described how two identical radar guns would work inside a

moving truck as illustrated in Figure 9 above. Subsequent discussions of those papers made

clear that there are intense conflicts over how radar guns are believed to work.

The proposed experiment described in those previous papers involved two identical

radar guns that are pointed at one another, as show in Figure 9. “Identical” in this case means

that the two guns must emit photons that oscillate at or within 500 Hertz of the same frequency.

According to Quantum Mechanics and many mathematicians, there are no moving

objects in the experiment, therefore there is no possibility of measuring any speed. The two

guns are not moving relative to each other, nor are the interior walls of the truck. Inside the

truck, nothing is moving relative to anything else, there is no change in distances, so no speed

can be measured – even if everyone knows the truck is actually moving, and the driver is using a

cell phone to tell everyone inside the truck what his speed is. What the mathematicians fail to

understand is that a truck is NOT an inertial system, even though everything is stationary

relative to everything else. A truck is a propelled system, even when it is moving at a constant

rate. And their reasoning only works in inertial systems where no force is being used to move

the system.

When discussing Relativity, we know the truck – inside and out – is moving relative to

the inertial system that is the spinning earth. A police officer in that inertial system (standing on

the road in front of the truck) can use his radar gun to measure the speed of the truck as being 40

mph, relative to his inertial system – and relative to the speed of light in that inertial system.

In the proposed experiment, if Gun-A was the only gun being used, photons transmitted

by Gun-A would hit the front wall at c-v. Atoms in the wall would then emit new photons back

toward Gun-A. Those photons would be received by Gun-A at c+v. Gun-A would compute the

speed of the wall as c-v+v=c and show a speed of zero for the front wall. If Gun-B was the only

gun being used, it would also show no speed for the rear wall. The calculation would just be

c+v-v=c.

But what would happen if you used both guns at the same time as shown in Figure 9?

First, because all radar guns perform at least two speed measurements, both guns

would measure the speed of the far wall to be zero, just as if it was the only gun being used. But

then each gun also receives newly transmitted photons from the other gun.

The photons from Gun-B are emitted at the speed of light, c, toward Gun-A. Because

the guns are identical, and because the emitted photons from Gun-B have the same oscillation

frequency as photons emitted from Gun-A (a requirement for the experiment), the photons from

Gun-B hit the receiver in Gun-A in an unaltered form, not going through the c-v modification,

as would be the case for the photons returning from the front wall. Those photons coming from

Gun-B are compared to the photons Gun-A emits, and a speed of 40 mph is calculated and

displayed. How the speed is displayed depends upon the type of radar gun being used.


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If the guns being used in the experiment are “stationary only” guns, the 40 mph speed

will be the only speed displayed. If the guns are “moving mode” models, the 40 mph speed

should be displayed as the “target speed,” since it is the fastest speed.

Figure 10 below shows a schematic of the internal workings of a theoretical device

that should be able to measure the speed of a vehicle from inside the vehicle. It is based upon a

schematic for a “simple homodyne radar” using two antennas that I found in a book on radars.[11]

Figure 10

It is essentially two radar guns, except that the gun on the left only emits photons to the

mixer in the gun on the right, which also receives photons from the gun on the right and beats all

the photons together to produce the “beat frequency.” There is no need for a signal splitter, and

the gun on the right does nothing but transmit, it performs no signal processing at all. Both

“signal sources” produce photons that oscillate at exactly the same frequency. The gun on the

left mixes the received photons from RF Signal Source B with the generated photons from RF

Signal Source A, and sends the results to a standard High Gain Amplifier and Signal Processor

which would display the calculated speed on the outside of the box. (Due to the cosine effect, of

course, the device must be moving toward the right in order for the photons emitted by source-B

to hit Receiver-A at the most effective angle.)

In theory, the device can measure its own speed relative to the local speed of light

whenever it is located inside a non-inertial system. It can measure the speed of a moving truck

while inside the truck, and it can measure the speed of an airplane while inside the airplane,

however it would not be able to measure the speed of the International Space Station (ISS) from

inside the ISS because the ISS is an inertial system.

VI. Conclusion

The proposed experiment and the theoretical device can clarify most of Einstein’s

Theory of Special Relativity,[2] which seems to be constantly and consistently misunderstood.


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Radar guns routinely measure traffic speeds relative to the speed of light. They are

able to do so because, while light is always emitted at c, as stated in Einstein’s Second Postulate,

the light will be received by a moving observer at c+v or c-v depending upon the speed, v, and

direction of movement of the observer. College textbooks which say otherwise need to be

revised. Some examples:

“Second postulate: The speed of light is a constant and will be the same for all

observers independent of their motion relative to the light source.”[12]

“The constancy of the speed of light: The speed of light in a vacuum has the same value,

c = 2.997 924 58 x 108 m/s, in all inertial reference frames, regardless of the velocity of

the observer or the velocity of the source emitting the light.”[13]

Postulate II. The velocity of light is independent of the state of motion of the source and

the observer.[14]

Second postulate (constancy of the speed of light): Light propagates through empty space

with a definite speed c independent of the speed of the source or observer.[15]

The Speed of Light Postulate: The speed of light in vacuum has the same value c in all

directions and in all inertial reference frames.[16]

Light and all other forms of electromagnetic radiation are propagated in empty space with

a constant velocity c which is independent of the motion of the observer or the emitting

body.[17]

The principle of the constancy of the speed of light: The speed of light in free space has

the same value c in all inertial reference frames.[18]

And, once again, here is Einstein’s correct version of his Second Postulate:

light is always propagated in empty space with a definite velocity c which is independent

of the state of motion of the emitting body.[2]

If the proposed experiment works as described, then my hope is that every interested

scientist and physicist will perform the experiment. Then maybe they will agree that Relativity

describes the world around us and, in the world of physics, the speed of an object is best

measured relative to the speed of light, not relative to another object.

I. References

[1] Richard Feynman, QED: The Strange Theory of Light and Matter, Princeton University Press

(1985), Page 15


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[2] Albert Einstein, On the Electrodynamics of Moving Bodies, Annalen der Physik 17 (1905)

Translation by G. B. Jeffery and W. Perrett, The Principle of Relativity, London: Methuen and

Company, Ltd. (1923) Page 1

[3] https://www.eetimes.com/mattel-makes-a-real-radar-gun-on-the-cheap/#

[4] http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/radar.html#c4

[5] https://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/how_do_

police_radars.htm

[6] Edward G. Lake, Radar Guns and Einstein’s Theories. https://vixra.org/abs/1806.0027

[7] https://copradar.com/chapts/chapt1/ch1d1.html

[8] Bernard Schultz, Gravity from the Ground Up, Cambridge University Press, page 196 (2003)

[9] https://www.britannica.com/science/ether-theoretical-substance

[10] Edward G. Lake, Relativity vs Quantum Mechanics Experiments.

https://vixra.org/abs/2009.0124

[11] William L. Melvin & James A. Scheer, Principles of Modern Radar: Vol. III, Radar

Applications, SciTech Publishing, page 752 (2014)

[12] Michael A. Seeds, Dana Backman, Foundations of Astronomy, Enhanced, Brooks Cole;

11th edition, page 91 (2011)

[13] Raymond A. Serway & Chris Vuille, College Physics, Brooks Cole; 9th edition, Page 888

(2012)

[14] R. Shankar, Fundamentals of Physics, Mechanics, Relativity, and Thermodynamics, Yale

University Press, Page 203 (2014)

[15] Douglas C. Giancoli, Physics for Scientists and Engineers with Modern Physics, Pearson

Prentiss Hall, Fourth Edition, Page 957 (2009)

[16] Jearl Walker, Fundamentals of Physics, John Wiley & Sons, 10th Edition, Page 1117 (2014)

[17] David Cassidy, Gerald Holton, James Rutherford, Understanding Physics, Springer-Verlag,

Page 416 (2002)

[18] Kenneth Krane, Modern Physics, John Wiley & Sons, 3rd Edition, Page 31 (2012)

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