Radiation gravitates - anything that carries energy, momentum and stresses is a source of a gravitational field, i.e. a curvature in the fabric of space:

An electromagnetic field have its own gravitational field, because an electromagnetic field contains energy, momentum (Maxwell's stress-energy tensor), and so on, it is considered as a real thing capable of gravitating, as such, it will produce a gravitational field of its own. This gravitational field is in addition to that produced by the matter of the charge or magnet. Electric charges and magnets are manifestations of certain types of matter, most particularly electrons. 

Since matter carries energy (via E=mc^2), such objects will have a gravitational field and so they will curve the fabric of space. So, one way in which a charge or a magnet will curve the fabric of space is by virtue of its matter.

Please confirm the above.

#electromagneticfield #gravitationalfield 

Where is the space expanding faster than the speed of light?

The answer to the question is that, the limitation in the speed of light is applicable within a gravitationally bound system - definitely within a galaxy (up to the zero-gravity sphere around it, or within clusters or super cluster or mega clusters of galaxies respectively,

Only the space beyond that is dominated by Dark Energy that expands the space. Generally, intergalactic space expands but not within a galaxy.

However, space is not expanding faster than light everywhere; only after certain distance towards the edge of the universe space can expand faster than light, the space before that in slower than the speed of light.

When you are seeing a distant galaxy, you are actually seeing its light year travelled distance but at the time of your observation that galaxy might have changed its location to a new location known as its proper distance.

So a general understanding is that when the galaxy's proper distance is greater than the light year travelled distance then only the galaxy is considered to be receding faster than light speed, not before that.

#ExpansionOfSpace #fasterthanlight

The time of the GPS satellite's clock oscillator is affected by the wavelength enlargement, not by the time dilation:

Gravity and electromagnetism are two of the four fundamental forces, out of the four fundamental forces. There are many similarities between electromagnetic (EM) radiation and gravitational radiation - both travel at the speed of light; both carry energy away from their sources; both consist of transverse waves with two polarizations. The main difference between gravity and electromagnetism is that gravity is a force between masses whereas electromagnetism is a force between charges. 

Gravity acts on mass and also acts on all forms of energy and thus acts on all subatomic particles, including the gauge bosons that carry the forces e.g. photon. Electromagnetism acts on electric charge. The electromagnetic field carries energy, contains momentum, so it will produce a gravitational field of its own. This gravitational field, produced by charge or magnet, is in addition to gravitational field produced by the matter mass. 

The gravitational redshift or redshifting of the photon climbing farther away from a gravitational well, the bending of a photon's path by the gravity of massive objects, the drifting of a small amount of time in the atomic clock on the ground, and faster running of the GPS clocks in space are due to the effects of gravity and examples of interactions between gravitational and electromagnetic fields.

• Planck's Equation: E = hf. 

Photon energy is the energy carried by a single photon. The energy of the photon depends on its frequency. The higher the frequency, the more energy the photon has. The amount of energy is directly proportional to the photon's electromagnetic frequency (E ∝ f) and so inversely proportional to the wavelength (E ∝ 1/λ). 

In Einstein's general theory of relativity, there is an effect known as "gravitational redshift," in which photon becomes redder because of the influence of gravity; the wavelength (λ) of a photon gets longer and appears redder as the wavelength climbs farther away from a gravitational well. As it becomes red-shifted, it's wavelength becomes larger so it's energy becomes smaller (λ ∝ 1/E).

• E = hf = h(c/λ) = h(1/T).     

The number of vibrations (cycles) per second is frequency (f) and the time taken to complete one vibration (cycle) is called time period (T), wavelength (λ) is just the distance between two identical points in the adjacent cycles of a wave. Whereas, frequency (f) and wavelength (λ) are inversely proportional and so time period (T) and wavelength (λ) are directly proportional.

Electromagnetic frequency (f) ∝ 1/wavelength (1/λ), when c is constant: f = c/λ = 1/T.

• Therefore, λ ∝ T. 

The time interval for 1° of phase is inversely proportional to the frequency. If the frequency of a signal is given by f, then the time T(deg) corresponding to 1° of phase shift is T(deg) = 1/(360f)= T/360. Therefore, a 1° phase shift on a 5 MHz signal or aprox. 59.95 meter wavelength (λ) corresponds to a time shift of 555 picoseconds.

• Since,  λ ∝ 1/f ∝ T.

  1° phase shift for a 59.95 m wavelength (λ), f (5 MHz), time shifts (time delays ΔT) aprox. 555 ps.

 90° phase shift " " time shifts (time delays ΔT) aprox. 50000 ps.

360° phase shift " f (5 MHz - 1 Hz) time shifts (time delays ΔT) aprox. 200000 ps. 

A 360° phase shift means a complete cycle of the wave, so from the above calculation, we can say that a 360° phase shift or a complete cycle of a 5 MHz wave takes 200000 ps (0.0000002 s) to complete one cycle (1 Hz). 

The caesium-133 atom used in atomic clocks vibrates at frequencies 9192631770 Hz on the ground and the GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day.

(i) For 1° phase shift of a 9192631770 Hz wave time shifts (time delays ΔT) aprox. 0.0000000003021743769660185 ms on the ground i.e. time shifts in a day 0.00002610786616986399 ms on the ground.

Time shift of the caesium-133 atomic clock above the ground: 

(ii) For 360° phase shift or, 1 complete cycle (1 Hz), of a 9192631770 Hz wave; aprox. 0.00000010878277570776666 ms time is taken i.e. time shifts in a day 0.00000010878277570776666 ms.

Time shift of the caesium-133 atomic clock in the GPS satellite in space:

(iii) For 1455.50003025° phase shift (or, 4.043055639583333 cycles) of a 9192631770 Hz wave 0.0000004398148148148148 ms time is taken (or, 0.038 miliseconds time is taken per day, or, 38 microseconds  time is taken per day.)

Lesser acting gravitational force on GPS Sattelite:

Mechanical oscillators are harmonic oscillators use balance wheels or pendulums resonance, preferred at a certain rate.

Crystal oscillators use mechanical resonance of vibrating crystals of piezoelectric material and create electrical signal with a constant frequency.

However, atomic oscillators’ mechanisms are based on the interaction of electromagnetic radiation in excited states of certain atoms, used as constant frequency.

Irrespective of the type of the oscillators used in a clock for time keeping, herein specifically known as a body, are made up of either certain atomic and/or certain molecular particles.
Such a body in acceleration and in gravitational potential experiences less weight due to the experience of less gravitational force per unit mass of that body in lesser gravitational potential. Accordingly gravity exerts less force on the body and to the neighbouring particles within the continuous internal material of such a body; this causes less mechanical stress to any oscillating particles within that body causing their lesser frequency or enlarged wavelength of the oscillator. 

Therefore an accelerating body or a body in gravitational potential shall experience lesser frequency or enlarged wavelength of the oscillator.

#GPSsatellite #time #timedilation #wavelengthdilation