Time...? Sound waves, and light waves...?

Neogaia777 said:

How strong does a gravitational field need to be to affect time...?

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Any gravitational field slows time. The stronger the field, the more it slows time relative to something in weaker gravity or no gravity at all.

And we're sure that is correct, etc...?

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Yes, it's been tested.

Neogaia777 said:

But when it is returned back to the unaccellerated one, we're sure that time has gone more slowly for the accellerated one, etc...?

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Yes.
Twin Paradox.

Neogaia777 said:

Did those clocks actually loose time...?

What about when the clocks were re-united at the same speed, or place in time, or space-time, etc...?

God Bless!

Click to expand...

Read about it yourself:-
https://www.scientificamerican.com/article/wayward-satellites-test-einsteins-theory-of-general-
Yes they did.
relativity/#:~:text=Einstein's%20theory%20predicts%20time%20will,is%20known%20as%20gravitational%20redshift.

Neogaia777 said:

I have another question, if you'll bear with me for a minute, and I don't want to start another thread on it, but, are we really sure, or has it been able to be proven or tested fully, that an object or piece or matter or material, at the speed of light, truly has "infinite mass"...?

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That's not the right way to think about it. Only massless objects can (and must) travel at the speed of light. No object with rest mass can accelerate to the speed of light.

But it is true that the faster you go, the more energy of motion you have, and the more energy you have, the more it takes to accelerate you. In theory, you can get arbitrarily close to the speed of light, but no amount of energy will actually get you there - and since energy gravitates, and mass is (crudely) a form of energy, the implication is that you would have to gain infinite mass - which, of course, is impossible.

Can infinite mass really be shown or proven beyond any doubts at all, etc...?

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Not to my knowledge. No single object can have infinite mass, but if the universe is infinite (and homogenous on cosmological scales), which many cosmologists think may be the case, it would, by implication, contain infinite mass.

Neogaia777 said:

I have another question, if you'll bear with me for a minute, and I don't want to start another thread on it, but, are we really sure, or has it been able to be proven or tested fully, that an object or piece or matter or material, at the speed of light, truly has "infinite mass"...?

Cause I have some trouble with terms like that sometimes, etc...? "Infinite", etc...?

What if it just has a lot of mass, or drag, etc, and the amount of drag/mass is just maybe still finite, etc...?

Like with Einsteins famous or infamous equation on the amount of energy contained within an amount of mass, maybe also being the amount of drag at light speed, is that time the speed of light squared or something maybe...?

Can infinite mass really be shown or proven beyond any doubts at all, etc...?

Much thanks,

God Bless!

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To refer to "infinite" mass, one needs to have an understanding of relativistic mass.

Relativistic mass is observer dependant.
The rest mass in this case is constant; its relativistic mass will depend on the velocity of the observer.
Two observers at different velocities will measure a different relativistic mass.
Furthermore relativistic mass is independent of time dilation.
This is explained by considering the momentum of the object in its rest frame
p = mv = m(dx/dτ) where τ is the proper time.
In the observer’s frame dτ = dt√(1-(v/c)² and momentum p' in this frame becomes;
p' = mdx/( dt√(1-(v/c)²)) = m(1/√(1-(v/c)²))dx/dt = mγ(dx/dt)
Hence the Lorentz factor γ = 1/√(1-(v/c)² for time dilation applies to the velocity dx/dt not the mass.
In other words a particle accelerated to near the speed of light doesn't gain relativistic mass but relativistic momentum.

Relativistic mass is an archaic definition, the modern day definition is to consider momentum not mass and apply the Lorentz transformation to the momentum.

Neogaia777 said:

I guess my main question at this point is, does time actually actually slow for a thing that is moving faster away from or to or towards something else, etc...? or is it just because of their respective places in space-time, etc...?

Take the clocks again, we know that time "seems to slow down" for a clock moving faster away from another clock, etc, but what about if they are re-united, etc...?

Does that show, or still show, that time actually slowed down for that clock, etc...?

Has that kind of experiment ever been done or tested, etc...?

I'd just like to know if time itself actually did or actually does slow down or not, etc...?

Don't really care if I am right or wrong at this point or not, etc...

Does how fast you are going or moving actually slow down time, etc...?

Or is it just the signals or waves or images...? or just because of your being in two different places in space-time, etc...?

God Bless!

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The correction of atomic clocks on Earth for both special and general relativity effects so they remain synchronized with GPS satellite clocks is good example that time dilation is very much a real effect.
The atomic clocks on GPS satellites are designed to operate at 10.23 Mhz.
Since the clocks tick faster in orbit, the clocks are adjusted on Earth to a slightly lower frequency of 10.22999999543 Mhz to compensate for this.

It’s an interesting exercise to show how Relativity is used to come up with this adjusted clock speed.

The two relevant equations are:
Δt = dτ[1-G/c²(M/r₂-M/r₁)] which is time dilation due to gravity.
Δt= dτ /√(1-v²/c²) which is time dilation due to velocity.

Δt is the coordinate time interval for the satellite clock in orbit and dτ is the proper time interval of the satellite clock on Earth.

For the latter equation since satellite velocities are very small compared to the speed of light c, v²/c²<< 1 and √(1-v²/c²) ≈ 1- v²/2c² as a binomial approximation.
Therefore Δt= dτ/(1- v²/2c²)

In both equations there is a time drift term.
Δt = dτ[1-G/c²(M/r₂-M/r₁)], has the time drift term G/c²(M/r2-M/r1).

When satellite clock is on Earth r₁ = r₂ and G/c²(M/r₂-M/r₁)=0 hence Δt = dτ since there is no time drift between satellite clocks on the surface.

For Δt= dτ/(1- v²/2c²) the time drift term is v²/2c².

A stationary satellite clock on the Earth’s surface has the conditions v=0 and v²/2c²=0 hence Δt = dτ as there is no time drift between stationary satellite clocks on the surface.

The time drift values are the errors tₑ that need to be corrected.
The gravitational time dilation error is t₁ₑ = G/c²(M/r₂-M/r₁).
The Earth’s mass is 5.972 x 10²⁴ and radius 6370 km.
A GPS satellite orbit is typically at the specified altitude of 20200 km or radius of 26570 km.

t₁ₑ = [(6.674 x 10⁻²⁰)/(299670)²][(5.972 x 10²⁴/26570)-(5.972 x 10²⁴/6370)]
=-5.296 x 10⁻¹⁰ s/s
=-5.296 x 10⁻¹⁰ x 1000000 x 24 x 60 x 60 μs/day
=-45.8 μs/day

The Special Relativity time dilation error is t₂ₑ = v²/2c².
The orbital velocity v as a function of radius r is given by the equation v ≈√GM/r.

For a satellite with a 26570 km orbital radius:

v = √[(6.674 x 10⁻²⁰)(5.972 x 10²⁴)/26570]
= 3.87 km/s

t₂ₑ = v²/2c²
= (3.87)²/(1.796 x 10¹¹)
= 8.337 x 10⁻¹¹ s/s
= 8.337 X 10⁻¹¹ x 1000000 x 24 x 60 x 60 μs/day
= 7.2 μs/day

The total error tₑ = t₁ₑ + t₂ₑ = -45.8 + 7.2 = -38.6 μs/day or -4.462 X 10⁻¹⁰ s/s

The adjustment of the satellite clock before launching requires the frequency to be offset by a certain amount according to the equation:

tₑ= ΔF/Fₑ, ΔF=F₀-Fₑ where F₀ and Fₑ are the frequencies of the clock in orbit and on Earth respectively.

F₀ = tₑFₑ+Fₑ
=(-4.462 x 10⁻¹⁰)10.23 + 10.23
= 10.22999999543 Mhz

Neogaia777 said:

Man I wish I knew more math, but I am working on it currently right now...?

Mathematics has become of far much more greater interest to me of late, and I am working on it right now...

Maybe I'l be able to come back on here in few years and discuss some of the math with you guys maybe...?

Thanks guys, thanks a bunch...

God Bless!

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The first equation Δt = dτ[1-G/c²(M/r₂-M/r₁)] which is time dilation due to gravity has an interesting history.
It was derived from a solution to Einstein's field equations which describes non rotating black holes.
It shows how a mathematical solution to the esoteric subject of black holes has been put to use in calculating the required correction for a satellite's atomic clock.

To go into a little bit more detail how a mathematical solution for a black hole is used to correct satellite clocks the story goes back to 1959.

An explanation of a metric can be found in this post.
The Schwarzschild metric for a non rotating black hole is found to be;

ds² = c²(1- 2GM/c²r) dt² - dr²/(1- 2GM/ c²r) - r²(dθ² +sinθdφ²)

The metric is also a good approximation for any slow rotating body such as the Earth or Sun.

In 1959 two smart dudes Pound and Rebka who went on to win the Nobel Prize in physics proposed an experiment for two stationary clocks in a gravitational field.
For a stationary clock dr = dθ = dφ = 0 and the Schwarzschild metric reduces to:

ds² = c²(1- 2GM/c²r) dt²

If the clock is an atom or molecule which emits or absorbs radiation at a given frequency f which is unaffected by gravitational forces ds = cdτ or dτ = ds/c.
Substituting this into the reduced Schwarzschild equation gives;

dτ = √(1- 2GM/c²r)dt

For two stationary clocks in a gravitational field, the ratio of the clock time intervals between a given pair of events is defined as;

dτ₁/dτ₂ = √[(1- 2GM/c²r₁)/(1- 2GM/c²r₂)] measured by observers at radii r₁ and r₂.
If 2MG << c²r then √(1- 2GM/c²r) ≈ 1-GM/ c²r using the binomial theorem approximation and then dividing the equation gives;

dτ₂ = dτ₁[1-G/c²(M/r₂-M/r₁)]

Note how this equation looks very similar to the equation for the time dilation of a satellite clock due to gravity.

Δt = dτ[1-G/c²(M/r₂-M/r₁)]

In the experiment since both clocks, one of which emits radiation, the other absorbs radiation, are stationary the coordinate time Δt is the same as the proper time dτ.

Since the proper time is simply the inverse of the frequency f, the equation;

dτ₂ = dτ₁[1-G/c²(M/r₂-M/r₁)]

can be rewritten as

fₑ = fₐ[1-G/c²(M/r₂-M/r₁)]

where fₑ is the emitted frequency and fₐ is the absorbed frequency.

What Pound and Rebka wanted to show the frequency of the clocks changed according to where the clocks were located in the gravitational field.
They set up an experiment where they placed radioactive ⁵⁷Fe which emits gamma rays inside a loudspeaker cone at the top of the university building and ⁵⁷Fe in the basement which was the absorber.
The vertical distance between the absorber and emitter was 22.6 meters.
⁵⁷Fe should emit and absorb gamma ray photons at the same frequency; since emitter and absorber were at different levels in the gravitational field this did not occur since photons reaching the absorber were gravitationally blueshifted.
By adjusting the vibrations of the loudspeaker for the emitter they induced a Doppler shift which cancelled out the gravitational blueshift so that absorption did occur.

Mathematically the condition is.

fₑ/fₐ = [1-G/c²(M/r₂-M/r₁)] = √[(c-v)/(c+v)]

The last term is the formula for Doppler blueshift and v is the approach velocity of emitter inside the vibrating loudspeaker which is relative to the absorber when ⁵⁷Fe emits and absorbs photons at the same frequency.
By Einstein’s equivalence principle, absorption occurred when the upward acceleration of the loudspeaker was equal to –g, the acceleration due to gravity but in the opposite direction.
If the distance between the emitter and detector is d and the time of flight of a photon travelling from the emitter to absorber is d/c, then approach velocity v of the emitter is v = gd/c.

fₐ/fₑ = √[(c+v)/(c-v)] = √[(c+gd/c)/(c-gd/c)] ≈ 1 + gd/c².
fₐ/fₑ = 1 + gd/c²
Δf/fₑ= gd/c²

The theoretical or predicted fractional change in shift is;
Δf/fₑ = (9.8 x 22.6)/(3 x 10⁸)² ≈ 2.5 x 10⁻¹⁵ which was about 5% out from the experimentally determined value.

Neogaia777 said:

Did those clocks actually loose time...?

What about when the clocks were re-united at the same speed, or place in time, or space-time, etc...?

God Bless!

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You are correct. At speeds near light speed, time dilates, length contracts, mass bulges.

lordjeff said:

You are correct. At speeds near light speed, time dilates, length contracts, mass bulges.

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Strictly speaking, they occur at any speed, but are only significant at very high relative speeds.