[hamdani yusuf (OP)]

Nothing to do with initial acceleration. I have assumed that the vehicle is moving at ground speed x, and the wind then drops from y to zero. Does the car continue to extract energy from the difference between wind speed (y = 0) and ground speed (x)?

The extractable energy is from the speed difference between wind and ground. When it's 0, the wind car can only decelerate.

[TommyJ]

Negative frequency doesn't make much sense for sinusoids, but the Fourier transform doesn't break up a signal into sinusoids, it breaks it up into complex exponentials.

Frequency is the rate at which something happens, so by defintion it must be a positive real number. both negative and imaginary numbers are very useful in the process of calculating the value of real quantities, but they have no physical reality of their own.
There is the angular frequency, which describes the angular velocity of the rotating objects (radian per seconds). Since rotation has two directions then the angular frequency may be positive or negative.
The presentation/formulation of the Fourier spectrum is simplified by using the concept of 'negative frequencies'.

[alancalverd]

Agreed, it makes the maths a lot easier, but since the FT of a delta function runs from -∞ to + ∞, you can't use it to determine the value of f for a photon of energy E = hf because the center is undefined.

[evan_au]

Negative frequency doesn't make much sense for sinusoids, but the Fourier transform doesn't break up a signal into sinusoids, it breaks it up into complex exponentials.

Euler's formula says re^i(ft) = r( cos(ft) + i sin(ft) )
- Where r is the amplitude, f is the frequency and t is time
- So a "complex exponential" can be treated as a sinusoid with an amplitude and phase.
See: https://en.wikipedia.org/wiki/Euler%27s_formula

The point is that the Fourier transform is reversible, with the inverse Fourier transform.
- The Fourier transform of a sine wave produces a positive and negative frequency
- If you throw away the negative frequency component, you have just thrown away half of the energy
- If you then apply the inverse Fourier transform to this corrupted signal, you won't get out what you put in.
See: https://en.wikipedia.org/wiki/Fourier_transform#Definition

The positive and negative frequency components become important for Amplitude-Modulated transmission (which used to be A Thing).
 - If you modulate a 1 MHz carrier with a 1kHz sinusoid, you end up with extra frequency components at 1MHz ± 1kHz.
- So the negative frequency components do appear in real applications.
- If you throw away the negative frequency component (and the 1MHz carrier), you end up with "Single Sideband" modulation. It's not very intelligible on an AM receiver...

See: https://en.wikipedia.org/wiki/Amplitude_modulation
https://en.wikipedia.org/wiki/Single-sideband_modulation

Correction: Unmixed the frequency and phase angle

[TommyJ]

- The present study proposes that the photon consists of a positive elementary charge and a negative elementary charge. The charges are loosely coupled, i.e. they do not form a fixed dipole.
It is proposed that the positive charge propagates in the radial direction and at the same time it rotates clockwise perpendicular to the radial direction. The negative charge rotates counter clockwise resulting that the two charges propagate along in the radial direction.
- Photon, which is a 'pure' energy, spin with no mass, can 'convert' itself in a particle, that has a mass. Electron or a positron can be formed (negative or positive charge). This happens all the time around us with a spontaneous emission or absorption of energy.
Changing colours in a visible spectrum. But not only the colours, but the structure of nature itself is changing. The dynamics of cell life is a fundamental of this process with the organization of positive and negative charge.

'Photon forms the momentary nature of time and evolutionary driving force of everything.'
Photon has momentum = plank constant / frequency = [kg*m/s]
No 'negative frequency' here.

[hamdani yusuf (OP)]

- The present study proposes that the photon consists of a positive elementary charge and a negative elementary charge. The charges are loosely coupled, i.e. they do not form a fixed dipole.
It is proposed that the positive charge propagates in the radial direction and at the same time it rotates clockwise perpendicular to the radial direction. The negative charge rotates counter clockwise resulting that the two charges propagate along in the radial direction.
- Photon, which is a 'pure' energy, spin with no mass, can 'convert' itself in a particle, that has a mass. Electron or a positron can be formed (negative or positive charge). This happens all the time around us with a spontaneous emission or absorption of energy.
Changing colours in a visible spectrum. But not only the colours, but the structure of nature itself is changing. The dynamics of cell life is a fundamental of this process with the organization of positive and negative charge.

'Photon forms the momentary nature of time and evolutionary driving force of everything.'
Photon has momentum = plank constant / frequency = [kg*m/s]
No 'negative frequency' here.

Is it a new theory?

[alancalverd]

 

 - If you modulate a 1 MHz carrier with a 1kHz sinusoid, you end up with extra frequency components at 1MHz ± 1kHz.
- So the negative frequency components do appear in real applications.

I'm being pernickety, but for a good reason: lots of pseudoscience lurks in the wings of this stage, ready to pounce and suck the blood out of loose physics!

999 kHz is not a negative frequency.

[alancalverd]

- Photon, which is a 'pure' energy, spin with no mass, can 'convert' itself in a particle, that has a mass. Electron or a positron can be formed (negative or positive charge). This happens all the time around us with a spontaneous emission or absorption of energy.

But what is observed is that a photon with energy greater than 1.02MeV can be converted into an e-p pair. Nothing else.
If your theory is not matched by observation, it is wrong. Or religion, politics or economics.

[hamdani yusuf (OP)]

Photon interactions are as close as you can get to delta functions.

At what frequency of photon?
What's the time resolution of the instruments used for measuring it?
Can the delta function be replaced by a very thin gaussian?

[TommyJ]

- If you modulate a 1 MHz carrier with a 1kHz sinusoid, you end up with extra frequency components at 1MHz ± 1kHz.
- So the negative frequency components do appear in real applications.

Isn't it rather frequency shift than negative frequency.

[TommyJ]

Is it a new theory?

Nothing exceptionally new in theory. Shaw case.

[hamdani yusuf (OP)]

Once again: we need two distinct mathematical models to describe the behavior of electromagnetic radiation. There is no reason why they should be interchangeable.

This reminds me of  Aristotelian physics.

Thus, in Aristotelian dynamics, there was a distinction between "natural" downward motion (for example, a rock falling to the ground when dropped) and unnatural violent motion not directed toward the center of Earth (such as that resulting from a catapult).

In contrast to earthly motions, in the supralunary regions of the heavens the natural state of motion was circular, because circles were considered to be the perfect geometric figure. Thus the planets would travel forever in circular orbits without the intervention of any force or impetus, because, well, it's the natural thing for planets to do.

https://aether.lbl.gov/www/classes/p10/aristotle-physics.html

I think that someday, someone will come up with a better idea.

[hamdani yusuf (OP)]

- If you modulate a 1 MHz carrier with a 1kHz sinusoid, you end up with extra frequency components at 1MHz ± 1kHz.
- So the negative frequency components do appear in real applications.

Isn't it rather frequency shift than negative frequency.

It's similar to negative apples or cows for farmers. If you borrow them, negative numbers will come up somewhere in the accounting records.

[alancalverd]

At what frequency of photon?
What's the time resolution of the instruments used for measuring it?
Can the delta function be replaced by a very thin gaussian?

1. E = hf

2. We usually measure wavelength for visible light to soft x-rays, and energy for higher energy photons You can be as accurate as permitted by Heisenberg, and AFAIK we have a good (quantum) explanation for any observed bandwidth.

3. Problem is that however thin you make it, a gaussian still has a curved maximum. The delta function either is or isn't - it's a mathematical concept of an infinitely differentiable function. 

There has been some work on attosecond resolution of photon-matter interactions - beyond my current pay grade but some chums at the National Physical Laboratory were investigating them back in the day. Unfortunately most undergraduate texts represent the photon as a smooth chirp, which it isn't!

[evan_au]

- If you modulate a 1 MHz carrier with a 1kHz sinusoid, you end up with extra frequency components at 1MHz ± 1kHz.
- So the negative frequency components do appear in real applications.

999 kHz is not a negative frequency.

True, but it shows the presence of negative frequencies in the Fourier transform.

What I was trying to say (but it was getting late) was the Fourier transform of a product of functions is the convolution of their Fourier transforms:
- Amplitude Modulation multiplies the Carrier wave by the Modulating wave
- This translates to a Convolution of their spectra (ie a convolution of the spectrum of 1kHz and 1 MHz):

Fourier_Transform.png (24.42 kB . 1431x84 - viewed 2436 times)

Convolution moves (if I've got my signs right):
-the normally-visible +1kHz to 999kHz
- and the normally-invisible -1kHz to 1001 kHz
- and creating new components at -999 and -1001 kHz (which are still invisible)
- If these negative frequency components did not exist, the product of 1kHz and 1 MHz would produce just one sideband and the carrier. In fact it produces two sidebands.

The reason spectrum analysers don't show you the negative frequencies is that for signals that are real in the time domain, the negative frequencies are a mirror image of the positive frequencies, and don't add any new information.

Isn't it rather frequency shift than negative frequency.

Yes, convolution can be viewed and calculated as a shift between two functions (in fact, a reversal of one, followed by every possible shift).

Convolution comes up in my work when finding the sum of two probability distributions.
See: https://en.wikipedia.org/wiki/Convolution

[hamdani yusuf (OP)]

The delta function either is or isn't - it's a mathematical concept of an infinitely differentiable function. 

Is it physically possible?

[alancalverd]

No, but it's more useful than a deity.

I guess the Big Bang was pretty close to a delta function: zillions of years later, we can still detect the low frequency components!

[hamdani yusuf (OP)]

No, but it's more useful than a deity.

I guess the Big Bang was pretty close to a delta function: zillions of years later, we can still detect the low frequency components!

What's the vertical axis? I assume the horizontal axis represents time.
Afaik, it's billions of years ago.

[hamdani yusuf (OP)]

You can be as accurate as permitted by Heisenberg, and AFAIK we have a good (quantum) explanation for any observed bandwidth.

It means that the pulse is not a truly delta function. It looks more like a thin Gaussian instead.

What's the quantum explanation for my experiments with microwave, such as longitudinal propagation in meander sheet, conjoined twin polarizers, and polarization splitter?

[Bored chemist]

What's the quantum explanation for my experiments with microwave, such as longitudinal propagation in meander sheet, conjoined twin polarizers, and polarization splitter?

Photons have a property called polarisation.